Intrinsic Structures and Properties of Energetic Materials 981992698X, 9789819926985

Table of contents :
Preface
Introduction
Contents
About the Authors
1 Overview
1.1 Energetic Materials
1.2 Intrinsic Structures of Energetic Materials
1.3 Benefits of the Introduction of Intrinsic Structures
1.4 Intention and Organization of This Book
References
2 Category of Energetic Crystals
2.1 Introduction
2.2 Criterion for Categorizing Energetic Crystals
2.2.1 Primary Constituent Part
2.2.2 Type of Energetic Crystals
2.3 Category of Energetic Crystals
2.3.1 Energetic Molecular Crystal
2.3.2 Energetic Ionic Crystal
2.3.3 Energetic Atomic Crystal
2.3.4 Energetic Metallic Crystal
2.3.5 Energetic Mixed-Type Crystal
2.4 Understanding of Energetic Crystals
2.4.1 Interactions Between PCPs in Crystals and Their Stability
2.4.2 Energy Content
2.5 Conclusions and Outlooks
References
3 Application of Molecular Simulation Methods in Treating Intrinsic Structures of Energetic Materials
3.1 Introduction
3.1.1 Weight of Simulation in Energetic Material Researches
3.1.2 Importance of Molecular Simulation
3.2 Quantum Chemical Methods for Treating Energetic Molecules
3.2.1 Quantum Chemical Methods
3.2.2 Description for Geometric Structure
3.2.3 Description for Electronic Structure
3.2.4 Description for Energetics
3.2.5 Description for Reactivity
3.3 Dispersion-Corrected DFT Methods and Their Application
3.3.1 Reliability to Density Prediction
3.3.2 Reliability to Geometric Prediction
3.3.3 Reliability to Lattice Energy Prediction
3.3.4 Comparison of Computation Efficiency
3.4 Molecular FF Methods and Their Application
3.4.1 Classic FFs and Their Application
3.4.2 Consistent FFs and Their Application
3.4.3 Reactive Forcefield and Its Application
3.5 Hirshfeld Surface Analysis Method
3.5.1 Principle
3.5.2 Description for Intermolecular Interaction
3.5.3 Description for a Same Molecule in Various Crystal Environments
3.5.4 Description for a Same Ion in Various Crystal Environments
3.5.5 Predictions for Shear Sliding Characteristic and Impact Sensitivity
3.5.6 Summary of Advantages and Disadvantages
3.6 Codes and Database Applied for Energetic Molecules and Crystals
3.6.1 Gaussian
3.6.2 Multiwfn
3.6.3 VASP
3.6.4 Materials Studio
3.6.5 DFTB+
3.6.6 CP2K
3.6.7 LAMMPS
3.6.8 COSMOlogic
3.6.9 CrystalExplorer
3.6.10 CSD
3.7 Conclusion and Outlooks
References
4 Energetic Molecules and Energetic Single-Component Molecular Crystals
4.1 Introduction
4.2 Traditional Energetic Molecular Crystals
4.2.1 Energetic Nitro Compounds
4.2.2 Energetic Conjugated N-heterocyclic Compounds
4.2.3 Energetic Organic Azides
4.2.4 Energetic Compounds with Different Heat Resistance
4.2.5 Energetic Compounds with Different Impact Sensitivity
4.3 Energetic Halogen Compounds
4.3.1 Energetic Fluorine Compounds
4.3.2 Energetic compounds with Chlorine, Bromine, or Iodine
4.4 Entropy Explosives: Energetic Peroxides
4.4.1 Energetic Peroxides
4.4.2 Introduction of Entropic Explosion
4.5 Full Nitrogen Molecules
4.6 Conclusions and Outlooks
References
5 Polymorphism and Polymorphic Transition in Energetic Molecular Crystals
5.1 Introduction
5.2 Polymorphism and Polymorphic Transition
5.2.1 Polymorphism
5.2.2 Polymorphic Transition
5.3 Factors Influencing the Polymorphic Transition
5.3.1 Crystal Quality
5.3.2 Additive
5.4 Polymorph-Reduced Differences in Structure and Energetics
5.4.1 Molecular Structure
5.4.2 Molecular Packing
5.4.3 Morphology
5.4.4 Energetics
5.4.5 Detonation Property
5.5 Polymorph-Dependent Mechanism of Thermal Decomposition
5.5.1 Mechanism of Thermal Decomposition of CL-20 Polymorphs
5.5.2 Mechanism of Thermal Decomposition of HMX Polymorphs
5.6 Polymorph Transition-Induced Low Impact Sensitivity of FOX-7
5.6.1 Stacking Structures of FOX-7 Polymorphs
5.6.2 Sliding Characteristics of FOX-7 Polymorphs
5.6.3 Correlation Between the Low Impact Sensitivity of FOX-7 and Its Heat-Induced Polymorphic Transition
5.7 Strategies for Controlling Polymorphic Transition
5.7.1 Recrystallization
5.7.2 Coating Crystal
5.7.3 Adding Additive
5.8 Conclusions and Outlooks
References
6 Energetic Ionic Crystals
6.1 Introduction
6.2 Composition and Category
6.2.1 Composition of Energetic Ionic Crystals
6.2.2 Category of Energetic Ionic Crystals
6.3 Volumetric and Electric Variabilities of Constituent Ions
6.3.1 Volumetric Variability
6.3.2 Electric Variability
6.4 Packing Structure and Intermolecular HB
6.4.1 Packing Structure
6.4.2 Intermolecular HB
6.4.3 Consequence of Strengthened HB
6.5 Energetic Inorganic Ionic Crystals
6.6 Energetic Organic Ionic Crystals
6.6.1 Ionic Crystals Containing Tetrazole Derivative
6.6.2 Ionic Crystals Containing Triazole Derivative
6.6.3 Other Energetic Organic Ionic Crystals
6.7 Conclusions and Outlook
References
7 Energetic Cocrystals
7.1 Introduction
7.2 Redefinition and Intension of the Term Cocrystal
7.2.1 Insufficiency of the Existent Definitions and Classifications
7.2.2 History of Cocrystal and Its Relatives
7.2.3 Redefinition of Cocrystal with a Broader Intension
7.3 Component, Intermolecular Interaction, and Packing Structure of Energetic Cocrystal
7.3.1 CL-20-Based Cocrystals
7.3.2 HMX-Based Cocrystals
7.3.3 EDNA, BTATz, DNPP, aTRz, BTNMBT, and BTO-Based Cocrystals
7.3.4 TNT, DNBT, DNAN, and HNS-Based Energetic Cocrystals
7.3.5 BTF-Based Energetic Cocrystals
7.3.6 TXTNB-Based Cocrystals
7.3.7 Heterocycle Molecules-Based Cocrystals
7.4 Thermodynamics for the Formation of Energetic Cocrystal
7.4.1 Calculation Methods
7.4.2 Thermodynamic Parameters
7.5 Property and Performance of Energetic Cocrystal
7.5.1 Density, and Detonation Velocity and Pressure
7.5.2 Thermal Stability and Impact Sensitivity
7.5.3 Reactivity: A Case of CL-20/HMX
7.6 Conclusions and Outlooks
References
8 Energetic Atomic Crystals, Energetic Metallic Crystals, and Energetic Mixed-Type Crystals
8.1 Introduction
8.2 Energetic Atomic Crystals
8.2.1 Polymeric Nitrogen
8.2.2 Polymeric CO and CO2
8.3 Energetic Metallic Crystals
8.3.1 Metallic Hydrogen
8.3.2 Metallic Nitrogen
8.4 Energetic Mixed-Type Crystals
8.4.1 Energetic Perovskites
8.4.2 N5−-based Mixed-Type Crystals
8.4.3 Other Mixed-Type Cocrystals
8.5 Conclusion and Outlooks
References
9 Hydrogen Bonding, Hydrogen Transfer, and Halogen Bonding
9.1 Introduction
9.2 Hydrogen Bonding
9.2.1 Hydrogen Bonding in Energetic Homogeneous Molecular Crystals
9.2.2 Hydrogen Bonding in Energetic Cocrystals
9.2.3 Hydrogen Bonding in Energetic Ionic Compounds
9.3 Effects of Hydrogen Bonding in Energetic Compounds
9.3.1 On Crystal Packing
9.3.2 On Impact Sensitivity
9.4 Hydrogen Transfer
9.4.1 Intramolecular H-transfer
9.4.2 Hydrogen Transfer in Crystal
9.5 Effect of H-transfer
9.5.1 On Thermal Stability
9.5.2 On Impact Sensitivity
9.6 Halogen Bonding in Energetic Compounds
9.7 Conclusions and Outlooks
References
10 π-Stacking in Energetic Crystals
10.1 Introduction
10.2 π-π Stacking
10.2.1 Energetic Planar π-Bonded Molecules
10.2.2 HB-Aided π-π Stacking
10.2.3 Non-HB-Aided π-π Stacking
10.2.4 Heat/pressure Induced Variation of π-π Stacking
10.3 n-π Stacking
10.3.1 Intension of n-π Stacking
10.3.2 n-π Stacking Structures
10.3.3 Nature of n-π Stacking: Electrostatic Interaction
10.4 Comparison Among n-π Stacking, π-π Stacking, and Intermolecular HB
10.5 Molecular Structure-Stacking Mode Relationship: A Case of D2h and D3h Molecules
10.5.1 Data Collection and Verification of Molecular Stacking Pattern
10.5.2 Molecular Structures and Stacking Patterns
10.5.3 Intralayered Intermolecular Interactions
10.5.4 Characteristics of D2h and D3h Molecules Stacked in the Planar-Layer Mode
10.6 Conclusions and Outlooks
References
11 Crystal Engineering for Creating Low Sensitivity and High Energy Materials
11.1 Introduction
11.2 Energy-Safety Contradiction of Energetic Materials
11.3 Crystal Packing-Impact Sensitivity Relationship of Energetic Materials
11.4 Strategy to Achieve High Packing Density
11.4.1 Crystal Structural Data Collection
11.4.2 dm-PC Contradiction of High Density Energetic Compounds
11.4.3 Influences of Molecular Composition and Intermolecular Interaction on Density
11.4.4 Strategy for Increasing dc
11.5 Strategy for Creating LSHEMs
11.5.1 Strategy for Creating Traditional Low Sensitivity Energetic Materials
11.5.2 Strategy for Creating Low Sensitive or Desensitized Energetic Cocrystals
11.5.3 Strategy for Creating Low Sensitive or Desensitized Energetic Ionic Compounds
11.6 Conclusions and Outlook
References
Appendix A Symbols and Meaning
Appendix B Abbreviations of Molecules
Appendix C Crystal Codes and Full Names

Citation preview

Chaoyang Zhang Jing Huang Rupeng Bu

Intrinsic Structures and Properties of Energetic Materials

Intrinsic Structures and Properties of Energetic Materials

Chaoyang Zhang · Jing Huang · Rupeng Bu

Intrinsic Structures and Properties of Energetic Materials

Chaoyang Zhang Institute of Chemical Materials China Academy of Engineering Physics Mianyang, Sichuan, China

Jing Huang Institute of Chemical Materials China Academy of Engineering Physics Mianyang, Sichuan, China

Rupeng Bu Institute of Biopharmaceutical Research Liaocheng University Liaocheng, Shandong, China

ISBN 978-981-99-2698-5 ISBN 978-981-99-2699-2 (eBook) https://doi.org/10.1007/978-981-99-2699-2 Jointly published with Science Press The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: Science Press. © Science Press 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

Energetic materials are a class of substances that can transiently release a large amount of gases and heat by self-redox after stimulated sufficiently and usually refer to explosives, propellants, and pyrotechnics. As a special group of materials, energetic materials play an irreplaceable role in promoting the progress of science, technology, and society. Nowadays, many new kinds of energetic materials like energetic extended solids, energetic ionic salts, energetic metal organic frames, energetic cocrystals, and energetic perovskites have been created. It is somewhat dazzling, and an issue of how we can understand these new types of energetic materials, as well as old ones, is raised. By defining a concept of intrinsic structures of energetic materials, which refers to the crystal packing structure and its substructure, the microscopic structures of energetic materials can be well clarified in combination with experimental measurement and molecular simulation and related to many macroscopic properties. This book presents our understanding about it. A simply and new way to readily understand energetic materials is expected to be paved, based on this book. On the time of the publication of this book, I would like to greatly thank Dr. Fangbao Jiao (焦方宝) for writing the draft of Chap. 8, and graduate students Chunjie Zuo (左春洁) and Kairui Xue (薛凯瑞) for proofreading, graduate students Shijie Li (李仕洁), Shitai Guo (郭世泰), Haitong Liu (刘海涛), Peng Chen (陈鹏), Guangrui Liu (刘广瑞), Kai Zhong (钟凯), and Wen Qian (钱文) for data collection! I also appreciate Profs. Hui Huang (黄辉), Xiaolin Wang (汪小琳), Yu Liu (刘渝), and Hongzhen Li (李洪珍) for their cooperation and supports! Besides, I am grateful to Ms. Fuzhi Li (李涪汁) from Scientific Press for her considerate and meticulous work on this book! The financial support of Challenge Project (TZ-2018004) and National Natural Science Foundation of China (NSFC, 21673210, 21875227, and 22173086) is greatly appreciated! Finally, I should thank my families for their understandings and supports! Mianyang, China Mianyang, China Liaocheng, China

Chaoyang Zhang Jing Huang Rupeng Bu

v

Introduction

Intrinsic Structures and Properties of Energetic Materials consists of 11 chapters. Chapter 1 “Overview” briefs energetic materials, the definition and intension of the intrinsic structures of energetic materials, and intention of the book. Chapter 2 “Category of Energetic Crystals” describes the criterion for categorization, category of energetic crystals, and the understanding of the category. Chapter 3 “Application of Molecular Simulation Methods in Treating Intrinsic Structures of Energetic Materials” briefs the quantum chemical methods for dealing energetic molecules, DFT dispersion correction methods, molecular force field methods, Hirshfeld surface analysis methods, and some related codes and databases. Chapter 4 “Energetic Molecules and Energetic Single-Component Molecular Crystals” deals with traditional energetic molecular crystals, energetic halogen compounds, energetic peroxides, and full nitrogen molecules. Chapter 5 “Polymorphism and Polymorphic Transition in Energetic Molecular Crystals” covers the polymorphism, determining factors of polymorphic transition, polymorph-induced differences of structure and property, and polymorphic control. Chapter 6 “Energetic Ionic Crystals” describes the component and category of energetic ionic crystals, variability of ionic volume and electricity, packing structures and intermolecular hydrogen bonding, and some main inorganic and organic crystals. Chapter 7 “Energetic Cocrystals” introduces the definition and intension, composition, intermolecular interaction and packing pattern, formation thermodynamics, and property and performance of energetic cocrystals. Chapter 8 is titled “Energetic Atomic Crystals, Energetic Metallic Crystals, and Energetic Mixed-Type Crystals”. Chapter 9 “Hydrogen Bonding, Hydrogen Transfer, and Halogen Bonding” describes the hydrogen bonding, hydrogen transfer, and halogen bonding of energetic compounds, and their influences on structures, properties, and performances. Chapter 10 “π-Stacking in Energetic Crystals” introduces the π-π stacking, n-π stacking, and molecular structure-stacking mode relationship of energetic crystals. Chapter 11 “Crystal Engineering for Creating Low Sensitivity and High Energy Materials” briefs the energy-safety contradiction of energetic materials, crystal packing mode-impact sensitivity relationship, strategy for constructing

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Introduction

high pacing density energetic compounds, and strategy for creating low sensitivity and high energy materials. This book can be a reference for scientific researches and students in the fields of energetic materials, molecular materials, and computational materials.

Contents

1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Energetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Intrinsic Structures of Energetic Materials . . . . . . . . . . . . . . . . . . . 1.3 Benefits of the Introduction of Intrinsic Structures . . . . . . . . . . . . . 1.4 Intention and Organization of This Book . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 5 11 13 13

2

Category of Energetic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Criterion for Categorizing Energetic Crystals . . . . . . . . . . . . . . . . . 2.2.1 Primary Constituent Part . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Type of Energetic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Category of Energetic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Energetic Molecular Crystal . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Energetic Ionic Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Energetic Atomic Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Energetic Metallic Crystal . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Energetic Mixed-Type Crystal . . . . . . . . . . . . . . . . . . . . . . 2.4 Understanding of Energetic Crystals . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Interactions Between PCPs in Crystals and Their Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Energy Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15 15 16 16 19 20 20 25 29 30 31 31

3

Application of Molecular Simulation Methods in Treating Intrinsic Structures of Energetic Materials . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Weight of Simulation in Energetic Material Researches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Importance of Molecular Simulation . . . . . . . . . . . . . . . . .

33 35 35 36 41 41 42 43

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3.2

Quantum Chemical Methods for Treating Energetic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Quantum Chemical Methods . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Description for Geometric Structure . . . . . . . . . . . . . . . . . 3.2.3 Description for Electronic Structure . . . . . . . . . . . . . . . . . 3.2.4 Description for Energetics . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Description for Reactivity . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Dispersion-Corrected DFT Methods and Their Application . . . . . 3.3.1 Reliability to Density Prediction . . . . . . . . . . . . . . . . . . . . 3.3.2 Reliability to Geometric Prediction . . . . . . . . . . . . . . . . . . 3.3.3 Reliability to Lattice Energy Prediction . . . . . . . . . . . . . . 3.3.4 Comparison of Computation Efficiency . . . . . . . . . . . . . . 3.4 Molecular FF Methods and Their Application . . . . . . . . . . . . . . . . 3.4.1 Classic FFs and Their Application . . . . . . . . . . . . . . . . . . . 3.4.2 Consistent FFs and Their Application . . . . . . . . . . . . . . . . 3.4.3 Reactive Forcefield and Its Application . . . . . . . . . . . . . . 3.5 Hirshfeld Surface Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Description for Intermolecular Interaction . . . . . . . . . . . . 3.5.3 Description for a Same Molecule in Various Crystal Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 Description for a Same Ion in Various Crystal Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Predictions for Shear Sliding Characteristic and Impact Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.6 Summary of Advantages and Disadvantages . . . . . . . . . . 3.6 Codes and Database Applied for Energetic Molecules and Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Gaussian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Multiwfn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 VASP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Materials Studio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.5 DFTB+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.6 CP2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.7 LAMMPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.8 COSMOlogic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.9 CrystalExplorer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.10 CSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Conclusion and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

46 46 49 50 52 54 54 55 59 60 62 64 65 70 70 72 72 74 80 82 82 84 86 86 87 87 88 92 93 93 94 95 95 96 96

Energetic Molecules and Energetic Single-Component Molecular Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.2 Traditional Energetic Molecular Crystals . . . . . . . . . . . . . . . . . . . . 116

Contents

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4.2.1 4.2.2 4.2.3 4.2.4

Energetic Nitro Compounds . . . . . . . . . . . . . . . . . . . . . . . . Energetic Conjugated N-heterocyclic Compounds . . . . . Energetic Organic Azides . . . . . . . . . . . . . . . . . . . . . . . . . . Energetic Compounds with Different Heat Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Energetic Compounds with Different Impact Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Energetic Halogen Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Energetic Fluorine Compounds . . . . . . . . . . . . . . . . . . . . . 4.3.2 Energetic compounds with Chlorine, Bromine, or Iodine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Entropy Explosives: Energetic Peroxides . . . . . . . . . . . . . . . . . . . . 4.4.1 Energetic Peroxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Introduction of Entropic Explosion . . . . . . . . . . . . . . . . . . 4.5 Full Nitrogen Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Polymorphism and Polymorphic Transition in Energetic Molecular Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Polymorphism and Polymorphic Transition . . . . . . . . . . . . . . . . . . 5.2.1 Polymorphism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Polymorphic Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Factors Influencing the Polymorphic Transition . . . . . . . . . . . . . . . 5.3.1 Crystal Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Additive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Polymorph-Reduced Differences in Structure and Energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Molecular Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Molecular Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.5 Detonation Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Polymorph-Dependent Mechanism of Thermal Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Mechanism of Thermal Decomposition of CL-20 Polymorphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Mechanism of Thermal Decomposition of HMX Polymorphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Polymorph Transition-Induced Low Impact Sensitivity of FOX-7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.1 Stacking Structures of FOX-7 Polymorphs . . . . . . . . . . . 5.6.2 Sliding Characteristics of FOX-7 Polymorphs . . . . . . . . .

116 121 130 131 133 135 135 137 138 138 139 139 146 146 157 157 158 158 158 162 163 163 165 165 168 172 173 175 177 178 182 186 186 187

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5.6.3

Correlation Between the Low Impact Sensitivity of FOX-7 and Its Heat-Induced Polymorphic Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Strategies for Controlling Polymorphic Transition . . . . . . . . . . . . . 5.7.1 Recrystallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.2 Coating Crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.3 Adding Additive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

192 193 194 194 194 195 195

6

Energetic Ionic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Composition and Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Composition of Energetic Ionic Crystals . . . . . . . . . . . . . 6.2.2 Category of Energetic Ionic Crystals . . . . . . . . . . . . . . . . . 6.3 Volumetric and Electric Variabilities of Constituent Ions . . . . . . . 6.3.1 Volumetric Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Electric Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Packing Structure and Intermolecular HB . . . . . . . . . . . . . . . . . . . . 6.4.1 Packing Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Intermolecular HB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Consequence of Strengthened HB . . . . . . . . . . . . . . . . . . . 6.5 Energetic Inorganic Ionic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Energetic Organic Ionic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Ionic Crystals Containing Tetrazole Derivative . . . . . . . . 6.6.2 Ionic Crystals Containing Triazole Derivative . . . . . . . . . 6.6.3 Other Energetic Organic Ionic Crystals . . . . . . . . . . . . . . 6.7 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

203 203 203 203 205 206 206 208 210 210 211 217 217 222 222 223 226 230 231

7

Energetic Cocrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Redefinition and Intension of the Term Cocrystal . . . . . . . . . . . . . 7.2.1 Insufficiency of the Existent Definitions and Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 History of Cocrystal and Its Relatives . . . . . . . . . . . . . . . . 7.2.3 Redefinition of Cocrystal with a Broader Intension . . . . 7.3 Component, Intermolecular Interaction, and Packing Structure of Energetic Cocrystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 CL-20-Based Cocrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 HMX-Based Cocrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 EDNA, BTATz, DNPP, aTRz, BTNMBT, and BTO-Based Cocrystals . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4 TNT, DNBT, DNAN, and HNS-Based Energetic Cocrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.5 BTF-Based Energetic Cocrystals . . . . . . . . . . . . . . . . . . . .

235 235 237 238 242 242 244 245 257 257 260 260

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7.3.6 TXTNB-Based Cocrystals . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.7 Heterocycle Molecules-Based Cocrystals . . . . . . . . . . . . . 7.4 Thermodynamics for the Formation of Energetic Cocrystal . . . . . 7.4.1 Calculation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Thermodynamic Parameters . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Property and Performance of Energetic Cocrystal . . . . . . . . . . . . . 7.5.1 Density, and Detonation Velocity and Pressure . . . . . . . . 7.5.2 Thermal Stability and Impact Sensitivity . . . . . . . . . . . . . 7.5.3 Reactivity: A Case of CL-20/HMX . . . . . . . . . . . . . . . . . . 7.6 Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

262 262 263 264 266 270 270 271 272 279 281

Energetic Atomic Crystals, Energetic Metallic Crystals, and Energetic Mixed-Type Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Energetic Atomic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Polymeric Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Polymeric CO and CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Energetic Metallic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Metallic Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Metallic Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Energetic Mixed-Type Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Energetic Perovskites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 N5 − -based Mixed-Type Crystals . . . . . . . . . . . . . . . . . . . . 8.4.3 Other Mixed-Type Cocrystals . . . . . . . . . . . . . . . . . . . . . . . 8.5 Conclusion and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

291 291 291 291 297 300 300 303 304 304 305 307 312 313

Hydrogen Bonding, Hydrogen Transfer, and Halogen Bonding . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Hydrogen Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Hydrogen Bonding in Energetic Homogeneous Molecular Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.2 Hydrogen Bonding in Energetic Cocrystals . . . . . . . . . . . 9.2.3 Hydrogen Bonding in Energetic Ionic Compounds . . . . . 9.3 Effects of Hydrogen Bonding in Energetic Compounds . . . . . . . . 9.3.1 On Crystal Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 On Impact Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Hydrogen Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Intramolecular H-transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Hydrogen Transfer in Crystal . . . . . . . . . . . . . . . . . . . . . . . 9.5 Effect of H-transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 On Thermal Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2 On Impact Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Halogen Bonding in Energetic Compounds . . . . . . . . . . . . . . . . . .

317 317 318 319 322 328 329 329 331 331 333 339 348 348 361 365

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9.7 Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 10 π-Stacking in Energetic Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 π-π Stacking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Energetic Planar π-Bonded Molecules . . . . . . . . . . . . . . . 10.2.2 HB-Aided π-π Stacking . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.3 Non-HB-Aided π-π Stacking . . . . . . . . . . . . . . . . . . . . . . . 10.2.4 Heat/pressure Induced Variation of π-π Stacking . . . . . . 10.3 n-π Stacking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Intension of n-π Stacking . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2 n-π Stacking Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 Nature of n-π Stacking: Electrostatic Interaction . . . . . . 10.4 Comparison Among n-π Stacking, π-π Stacking, and Intermolecular HB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Molecular Structure-Stacking Mode Relationship: A Case of D2h and D3h Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Data Collection and Verification of Molecular Stacking Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.2 Molecular Structures and Stacking Patterns . . . . . . . . . . . 10.5.3 Intralayered Intermolecular Interactions . . . . . . . . . . . . . . 10.5.4 Characteristics of D2h and D3h Molecules Stacked in the Planar-Layer Mode . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Conclusions and Outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Crystal Engineering for Creating Low Sensitivity and High Energy Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Energy-Safety Contradiction of Energetic Materials . . . . . . . . . . . 11.3 Crystal Packing-Impact Sensitivity Relationship of Energetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Strategy to Achieve High Packing Density . . . . . . . . . . . . . . . . . . . 11.4.1 Crystal Structural Data Collection . . . . . . . . . . . . . . . . . . . 11.4.2 d m -PC Contradiction of High Density Energetic Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.3 Influences of Molecular Composition and Intermolecular Interaction on Density . . . . . . . . . . . . 11.4.4 Strategy for Increasing d c . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5 Strategy for Creating LSHEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.1 Strategy for Creating Traditional Low Sensitivity Energetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

379 379 380 380 382 385 387 388 388 389 390 393 396 398 398 400 405 408 408 415 415 416 417 421 423 424 427 431 434 434

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11.5.2 Strategy for Creating Low Sensitive or Desensitized Energetic Cocrystals . . . . . . . . . . . . . . . . 11.5.3 Strategy for Creating Low Sensitive or Desensitized Energetic Ionic Compounds . . . . . . . . . . 11.6 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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437 440 441 442

Appendix A: Symbols and Meaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 Appendix B: Abbreviations of Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Appendix C: Crystal Codes and Full Names . . . . . . . . . . . . . . . . . . . . . . . . . 457

About the Authors

Chaoyang Zhang is a professor and a Ph.D. supervisor of Institute of Chemical Materials, China Academy of Engineering Physics (CAEP). He got his doctor’s degree of physical chemistry from Fudan University. Now, he is the member of Combustion Chemistry Division of Chinese Chemical Society (CCS), the member of Materials and Devices under Extremes Division of Chinese Materials Research Society (CMRS), and the member of Scholar Committee of State Laboratory of Explosives and Combustion. And currently he is the part-time professor of Beijing Computation Science Research Centre, University of Science and Technology of China, Chongqing University, and Southwest University of Science and Technology. He has published about 200 scholar papers. He was awarded Yu-Min Mathematical Prize and Deng-Jiaxian Youth Science and Technology Prize for his scientific research on energetic materials. Now, his interest is in energetic materials design and physical chemistry of energetic materials. e-mail: [email protected]

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About the Authors

Jing Huang is a research associate of Institute of Chemical Materials, China Academy of Engineering Physics (CAEP). She got her doctor’s degree of theoretical and computational chemistry from Nanjing University in 2021. Her research interests are on the machine learning for energetic materials, construction of high-accuracy potential energy surfaces, and molecular spectroscopy. Now she has publications more than 10, including seven papers as the first author. She is also supported by the National Natural Science Foundation for Young Scholars of China (2022). e-mail: [email protected]

Rupeng Bu is a research associate of Institute of Biopharmaceutical Research Liaocheng University. He got his doctor’s degree of Materials Science and Engineering from CAEP in 2022, supervised by Prof. Chaoyang Zhang. His major interest is crystal engineering of energetic materials. Up to the present, he has published ten papers and been awarded twice Scientific Innovation Prize of CAEP. e-mail: [email protected]

Chapter 1

Overview

This chapter briefly introduces energetic materials, the intrinsic structures thereof, the benefits of the introduction of the concept of intrinsic structures, and the intention of this book. Energetic materials are a special group of energy materials applied for both civilian and military purposes, due to their high efficiency of gas and heat release. The intrinsic structure of an energetic material refers to crystal packing and the substructure of the crystal packing, such as the molecule, atom, and ion. Correspondingly, the interactions in an intrinsic structure may be intermolecular interaction, electrostatic interaction/ionic bonding, or covalent bonding, but what concerned in this book are only the intermolecular interactions in energetic molecular crystals and energetic ionic crystals. In general, compared with an extrinsic structure, an intrinsic structure can maintain in larger ranges of variations of external fields like pressure and temperature, i.e., it is the invariability of the intrinsic structure. Meanwhile, the intrinsic structure and the interactions therein originally determine macroscopic properties and performances, as a starting point for exploring and understanding energetic materials.

1.1 Energetic Materials Energetic materials are a class of energy materials that can transiently release a large number of gases and heat by self-redox after stimulated, and usually refer to explosives, propellants, and pyrotechnics, which can be compounds or mixtures [1–3]. In fact, energetic materials serve as a group of functional materials, i.e., energy materials, and thereby categorizing them into three subgroups of explosives, propellants, and pyrotechnics is usually implemented in terms of application purposes. Owing to the capability of doing working of the released gas and heat, energetic materials are extensively applied in many fields from life beautification to defense armament, such as the civilian purposes of firework, air bag, mining, building, oil industry, metallurgy, machining, etc., and the military purposes of propellant, explosive, pyrotechnics, etc.; © Science Press 2023 C. Zhang et al., Intrinsic Structures and Properties of Energetic Materials, https://doi.org/10.1007/978-981-99-2699-2_1

1

2

1 Overview

besides, energetic materials have been used in some smart micro-explosion devices with damage or self-damage capability. Wholly, the progress of energetic materials has promoted that of human society. The history of energetic materials can be traced back to B.C. 220 in old China, as the black powder is the earliest ancestor. In 1885, picric acid was synthesized as the ancestor of modern high explosives. Afterwards, some famous energetic compounds, such as TNT, PETN, TATB, RDX, HMX, CL-20 [4], FOX-7 [5], LLM-105 [6], and NTO [7] (Fig. 1.1) appeared continuously and were put into assessment and use. Nowadays, in combination with various theories and simulation-aided material design technologies, many new kinds of energetic materials like energetic extended solids [8], energetic ionic salts [9], energetic metallic organic frames (MOF) [10], energetic cocrystals [11], and energetic perovskites [12] have been created. Although most of these novel energetic materials have not been applied yet, or even have no practical application value, more selections and thinks for potential applications are presented. More importantly, it makes energetic materials research more scientific and rational, with an increasingly lessened empirical sense. That is, the history of energetic materials exhibits an evident evolution from passive finding to proactive creation. On the other hand, the energetic materials are wholly evolved slowly, with respect to the energy level. For example, TNT was found in 1880 which is still in use today, while CL-20 was synthesized in 1987 and becomes the currently most powerful energetic compound, but the energy level is promoted by only 40% over a century. In contrast, electronic materials and devices are evolved fast. For example, the development speed of integrated circuit follows Moore’s Law, which deems that the processor performance can double every two years. To meet one of the elementary characteristics of energetic materials, i.e., the decomposition products should contain gas, it is necessary to include some light elements like C, H, N, and O. Certainly, some other elements exist sometimes for special purposes, for example, active metallic particles are usually added to energetic formulations to increase heat release. In this book, energetic materials generally refer to CHNO compounds unless otherwise specified. As to the structures of energetic

TNT

TATB

RDX

LLM-105

CL-20

NTO

HMX

DAAF

PETN

FOX-7

HNS

Fig. 1.1 Molecular structures of some representative traditional energetic compounds. The grey, green, red, and blue represent C, H, O, and N atoms, respectively

1.1 Energetic Materials

3

materials, we show them in Fig. 1.2 with a typical applied PBX as an example. The structure of a PBX is hierarchical, and covers micro-, meso-, and macro-scales. In a PBX, molecules, crystal, and composite particles are involved [13]. The properties of an energetic material usually refer to energy, safety, mechanical property, compatibility and environmental adaptability, as well as machining and storage properties. In the entire lifetime of an energetic material, it undergoes molecular design & synthesis, crystallization, coating and powder modeling, compression, machining, and final application, i.e., decay to combustion, deflagration, or detonation. All these structures and properties, and their evolution against the environmental change are of great concern in the research and development of energetic materials. In principle, energetic materials are thermodynamically metastable relative to the final stable products of decomposition like N2 , H2 O, CO2 , and CO, as well as C-rich clusters [14], and thus generally preserve high risks and sometimes cause irretrievable disasters. The decomposition of energetic materials proceeds very fast, usually < 0.01 s. This fast decomposition leads to a difficulty in revealing the detailed energy release mechanism. Besides, the research and development of an energetic material is generally expensive in manpower, materials resource, time and finance, because it undergoes a long-time, complex and strict flow of molecular design and synthesis, crystallization, powder-molding, compression, machining to a certain size and shape, to satisfy application requirements. In this flow, the energetic materials should be forced to pass some strict examinations and evaluations on stability, safety,

Kinetics

Responses to stimuli

Decomposition

Molecular design & synthesis

Oxygen Balance Intermolecular interaction

Equation of state Thermodynamics Packing

Energy/power Mechanics

Shock

Molecule Responses to stimuli

Lattice structure Other physics

Microscale

Crystal defects Interfaces in crystal Crystal habit

Coating & Powder modeling

Crystal particle

PBX particle

Interfaces in PBX

Mesoscale

Machining Application

Macroscale Main property

PBX block Main structure

Main processing

Lifetime

Fig. 1.2 Main structures, properties, and processing in the lifetime of energetic materials, exemplified by a PBX

4

1 Overview

mechanics, environmental adaptability, compatibility, etc. (Fig. 1.3); and any failure will make it inapplicable and abandoned. In fact, the most widely applied energetic compounds are generally those that were synthesized a long time ago, even nearly 150 years before, instead of those in recent decades as illustrated in Fig. 1.4. This case is much different from other materials like electric semi-conductor materials, whose computational ability or storing capacity can increase by an order of magnitude in a short period. It is full of risk, and highly time- and money-consuming to create a new energetic material and put it into use. With respect to the intension of energetic material, three elements can be summarized: self-redox reaction, fast release of gas and heat, and a certain stability. The

Energetic materials

Fig. 1.3 Main properties and performances of energetic materials

Typical Energetic Compounds TNT

TATB

RDX

HMX

Year of synthesis

1880

1888

1889

1943

CL-20 1987

Application time

WWs I and II

WW II to now

WW II to now

WW II to now

In assessment

TNT equivalent

1.00

1.10

1.17

1.31

1.40

Fig. 1.4 Year of synthesis, application time, and energy characteristic for some typical energetic compounds

1.2 Intrinsic Structures of Energetic Materials

5

reaction occurs with a sufficient external stimulation while without the participation of external substances. • Regarding composition, an energetic material can be a compound or a mixture. Generally, CHNO atoms are contained in a traditional energetic molecule. Some other elements like Al and B can be added up to energetic formulations for a special purpose. For a conventional CHNO energetic molecule, it can be readily partitioned into oxidizing and reducing moieties, while it is difficult to do so in new-concept energetic materials like metallic hydrogen and polymeric nitrogen. • Thermodynamically, an energetic material is a metastable substance; in other words, it is located on a local minimum of the potential energy surface. Relative to the stable products, the energetic material is thermodynamically unstable. • Electronically, the energy release of energetic materials is resulted from the interatomic rearrangement of valence electrons, i.e., such energy release is that of chemical energy stored. Thereby, the energy release of energetic materials is generally limited at a level of several kJ/g. Obviously, there is a limit of the energy release of energetic materials, even though it has not been presented by strict deduction. • Kinetically, the decomposition of energetic materials proceeds very fast, and can be finished within 0.01 s. In principle, the kinetic stability of energetic materials is governed by the energy barrier of decay. • Combining thermodynamics with kinetics together, it is understandable that the energetic materials are a group of high-power energy release materials, instead of high energy density materials, because they do not outperform traditional fuels like coal and oil in energy density.

1.2 Intrinsic Structures of Energetic Materials The intrinsic structure of an energetic material refers to the crystal packing of the energetic component and the substructure of crystal packing. This definition can be exemplified by the structures of various TATB-based PBXs, as illustrated in Fig. 1.5. Regarding the energetic components of various TATB-based PBXs, they are all TATB; and the crystal packing and molecule of TATB are the intrinsic structures. These two levels of structures will almost keep invariable when temperature and pressure change in rather large ranges. As such, these PBXs belong to TATB; otherwise, they would belong to others. It is the invariability for only intrinsic structures. In comparison, the extrinsic structure of an energetic materials refers to the structure beyond the intrinsic structure or on higher levels, for example, crystal morphology, crystal size and distribution, crystal surface, interface between energetic crystal and polymer binder, various defects in crystal or on crystal surface, etc. As demonstrated in the figure, the crystalline grain, the modeling powder, and the PBX block all belong to extrinsic structure. An evident characteristic of these extrinsic structures is the variability, depending on the practical formulations. In fact, for two TATB-based PBXs, we can hardly guarantee they have exactly the same extrinsic structures, even

6

1 Overview

Extrinsic structure

Crystalline grain

Modeling powder

B/O

PBX block

A

C

Crystal packing

Molecule

Intrinsic structure Fig. 1.5 Intrinsic structures and extrinsic structures of energetic materials, exemplified by TATBbased PBXs

though they possess the same intrinsic structures. Vividly speaking, the intrinsic structure is the true appearance of the various complex formulations unveiled, as the same parts therein. The properties and performances of energetic materials are governed by both the intrinsic and extrinsic structures, and it is just the variability of the extrinsic structures that leads to that of the properties and performances. Meanwhile, it becomes unclear with respect to the influence of extrinsic structures on the properties and performances, or the mechanism responsible for them, because we can hardly completely clarify the details of the extrinsic structures. This can also be exemplified the various morphologies of LLM-105 in Fig. 1.6. Even though these crystalline particles are morphologically different from one another, their intrinsic structures are the same, i.e., the same molecular structure and crystal packing of LLM-105. Experimentally, these differently-shaped particles exhibit different safety and mechanical properties [14]. It shows that the extrinsic structure may play a significant role in determining the properties and performances of energetic materials. The impact sensitivity values (H 50 ) of any traditional energetic compound shown in Fig. 1.7 can vary in a large range. The ratio of the maximal H 50 to the minimal one (R) of a same compound can reach 3.3. In principle, the intrinsic structures of molecule and crystal packing appear naturally and keep invariable when a new compound is synthesized successfully and suffers from certainly wide ranges of external fields; while the extrinsic structure can possess significant variability and lead to significant differences of properties and performances for the same compound. It provides a chance to optimize the properties of energetic materials by adjusting extrinsic structures. In fact, a material with only the intrinsic structure can appear ideally, while that with both the intrinsic and extrinsic structures are the real. Thus, for one thing,

1.2 Intrinsic Structures of Energetic Materials

7

Fig. 1.6 Extrinsic structures of energetic materials exemplified by various morphologies of LLM105

R=

MAX MIN

(a) PETN

(b) RDX

(c) TNT

(d) TATB

H50=13 cm H50=14.5 cm H50=15 cm H50=16 cm H50=23 cm H50=25 cm

H50=15 cm H50=19 cm H50=20 cm H50=24 cm H50=25 cm H50=27 cm H50=28 cm H50=31 cm

H50=59 cm H50=65 cm H50=80 cm H50=98 cm H50=100 cm H50=112 cm H50=158.5 cm H50=160 cm H50=200 cm

H50>200 cm H50=320 cm H50>320 cm H50=337 cm H50=490 cm

1.92

2.07

3.33

2.45

Fig. 1.7 Variability of the experimentally measured impact sensitivity (H 50 ) of four energetic compounds

the intrinsic structure generally starts a study of the component-structure-property relationship of energetic materials, setting a basis for further studies with extrinsic structures considered; for another thing, considering the extrinsic structures is also necessary in the research and development of new energetic materials, despite the difficulty increased, as they necessarily exist in practice. Regarding energetic materials, although it is full of risk and restriction to explore both intrinsic and extrinsic structures, the basic knowledge about them and their influences on properties and performance needs to be further enriched. Otherwise, how can we understand a result that is significantly related with both the intrinsic and extrinsic structures? As mentioned above, many new kinds of energetic compounds have come into being like energetic extended solid, energetic ionic salt, energetic MOF, and energetic cocrystal. These energetic compounds are much structurally different from the conventional ones, which are composed of neutral molecules of the same kind.

8

1 Overview

Figure 1.8 demonstrates some kinds of energetic compounds reported. For conventional energetic compounds, they are the most popular in application and generally consist of neutral molecules with C, H, N, and O atoms. Typically, the intermolecular interactions support the crystal packing of this kind of energetic compounds. Because of the highest population of the conventional energetic compounds, they will be discussed and described mostly in this book. Energetic ionic salts have been synthesized for a long time, and are thriving nowadays, due to the successful creation in a large quantity. Literally, the ionic bonding consolidates the crystal packing of energetic ionic salts. Still, intermolecular interactions also play an important role in arranging ions. As to energetic MOFs, their intrinsic structures generally exhibit more complexity compared with the conventional energetic compounds. The substructures of an energetic MOF can be atoms or ions, so the interactions therein can be covalent bonding or ionic bonding. Of course, the mix-typed energetic MOFs were also prepared, with both molecule and ion as substructures. The intrinsic structures of energetic molecular cocrystals are intrinsically the same as those of conventional energetic compounds, only with a difference in the quantity of molecular kinds. Energetic extended solids are generally stabilized under high pressures. Polymeric nitrogen is a typical energetic extended solid and thought to possess a huge energy density. The intrinsic structures of the polymeric nitrogen are the covalently bonded crystal and the N atoms. The huge energy content of the polymeric nitrogen is based on a significant energy difference between one triple bond and three single bonds linking two N atoms. It should be noted that Fig. 1.8 does not list all types of energetic crystals and the related substructures. It will be discussed in the following chapters. Substructure Interactions among the substructures Crystal type

One kind of molecule Intermolecular interactions Molecular crystal

Atom/ion Covalent/ionic bond Atomic/ionic crystal

Ion Ionic bond Ionic crystal

Intrinsic structure

Atom Covalent bond Atomic crystal

Two or more kinds of molecules Intermolecular interactions Molecular crystal

Fig. 1.8 Intrinsic structures and interactions stabilizing crystal packing of some representative energetic compounds

1.2 Intrinsic Structures of Energetic Materials

9

Energetic crystal is the core of energetic materials and mediates between a molecule and an applied mixed form like PBX shown in Fig. 1.2. As demonstrated in Fig. 1.9, the basic characteristics that are employed to describe an energetic crystal usually refer to composition, purity, density, packing structure, shape, particle size and distribution, and defect. With respect to an energetic crystal, it contains some issues like polymorph prediction, morphology prediction, crystal design, crystallization kinetics, structure–property relationship, and origin of macroscopic properties. Meanwhile, by means of analysis on the structure and composition of energetic crystal, we can deduce its macroscopic properties, such as energy, stability, safety, mechanical property, and so forth. In fact, numerous insights into the origins of properties and performance of energetic materials are derived from the crystals. For example, an energetic crystal model is usually employed to assess mechanical property, mechanical sensitivity and thermal stability by simulations. Relative to molecules, crystals are much closer to practice. Thus, studying an energetic crystal is more practically meaningful. Certainly, issues in a crystal are more complex than those of an isolated molecule, as a consequence caused by intermolecular interactions. The packing structures of some energetic compounds with the most stable polymorphs under common conditions are shown in Fig. 1.10. Because the outer moieties of these energetic molecules are composed of H and O, intermolecular hydrogen bonds usually exist in crystal packing. Due to different molecular shapes

Energetic Crystal

Fig. 1.9 Energetic crystal, as a core of energetic materials

10

1 Overview

and intermolecular HB, these crystals exhibit various molecular stacking modes. For example, the face-to-face π-π stacking (planar layered stacking) is found in TATB and DAAF, while FOX-7, LLM-105, and NTO appear in the wavelike π-π stacking (wavelike layered stacking). For the same energetic molecules, they can be stacked in different forms as polymorph. Polymorph is universal in the common energetic crystals due to a certain flexibility of energetic molecules. Usually, the polymorphic transition of energetic materials is heat- or pressure-induced, and causes different consequences of variation of properties and performances. For example, the heatinduced polymorphic transition from the ε- to γ -forms of CL-20 leads to density reduction and impact sensitivity enhancement; while, that of the α- → β- → γ forms of FOX-7 makes the interlayered sliding increasingly ready, contributing to its low impact sensitivity [15]. C B

B

O/C

A

o-TNT A/O

O/C

A

A

O/B

α-RDX

TATB O/A

C

B

B

B

O/C

A

B

β-HMX

PETN-I

B

C

A

α-FOX-7

O/C

HNS

B B

A

O/A

A/O

C A

DAAF

O/C

LLM-105

C

B

O/C

NTO

ε-CL-20

Fig. 1.10 Packing structures of some traditional energetic compounds with the most stable polymorph under common conditions

1.3 Benefits of the Introduction of Intrinsic Structures

11

1.3 Benefits of the Introduction of Intrinsic Structures As defined and discussed above, the intrinsic structure possesses high invariability, while the extrinsic structure is usually variable in practice. Thus, some benefits can be obtained by the introduction of intrinsic structure in studying energetic materials. This can be exemplified by an intrinsic sensitivity research based on the intrinsic structure. The intrinsic sensitivity is defined as the degree of the response of an ideal structural model of an energetic compound to a kind of external stimulation like heating and shock. The first benefit is to give full play to the advantages of computational simulation and presenting a new way to resolve the complex issues of sensitivity. For a given energetic compound, according to the definition of intrinsic sensitivity, the situation “samples in similar but not identical states + similar but not identical testing conditions → different sensitivity measurement values” can be changed to “same intrinsic structure + same simulation loading conditions → single intrinsic sensitivity value”. This is actually a transition from the “complex reality” to a “simple ideal”, including three parts shown in Fig. 1.11: from various actual states (such as the differences of various defects and morphologies of energetic crystals) to a perfect crystal packing structure, from inconsistent testing conditions (for example, it is difficult to ensure the complete consistency of different test device, test temperature and humidity) to completely consistent loading conditions, and from different measured results of sensitivity to a single sensitivity value. It is also an important link to solve the practical complex sensitivity problem through simplified simulations. The second is that it is helpful to improve the sensitivity prediction accuracy of energetic materials and promote energetic materials design into the era of big data.

Now

Similar states of various samples Intrinsic structure +Extrinsic structure

+

Actual sample

Different values of sensitivity

Identical loading conditions

Single value of sensitivity

Change

Similar measuring conditions

Future

Identical state

Intrinsic structure Ideal model

+

Fig. 1.11 Illustration of expected simplification of sensitivity researches by defining the intrinsic structure and intrinsic sensitivity

12

1 Overview

As shown in Fig. 1.7, the uncertainty of sensitivity measurement is just one of the fundamental reasons for its poor predictability. Referring to the intrinsic sensitivity prediction based on the intrinsic structure, this problem will be solved, once the transformation in Fig. 1.11 is realized. With the deepening of the understanding of sensitivity mechanism and the increasing of intrinsic structure and intrinsic sensitivity data, the suitability of sensitivity prediction model with intrinsic sensitivity as the independent variable will be broadened and its accuracy will be improved. In addition, as many specific sensitivity tests standardized in experiments, the simulation calculations of intrinsic sensitivity can also be standardized, with specified modeling, simulation and analysis methods. Thereby, the produced sensitivity data is more standardized and easier to be incorporated into the big data of energetic materials, setting a basis for the intelligent design of energetic materials in the future. Finally, it is advantageous to deepen the understanding of sensitivity mechanism and promote the development of energetic materials. Sensitivity reflects the response of an energetic material to external stimulus. It involves a series of complex processes from external stimulus loading to final ignition, which is related to many factors, such as the multi-level structures of an energetic material, stimulation modes and test conditions. These factors also largely lead to the uncertainty of sensitivity and restrict the understanding of sensitivity mechanism. Based on the determined intrinsic structure, simulated loading conditions and analysis methods, and intrinsic sensitivity, it is easier to establish clear composition-structure-sensitivity relationships. It is beneficial to deepen the scientific insights into the sensitivity mechanism, richen the theoretical basis of energetic materials, and promote their development. Besides the aforementioned issue of sensitivity, the introduction of the intrinsic structure is also beneficial to promote the application of crystal engineering in energetic materials. Crystal engineering is the understandings of the relationship between molecular and crystal structures and the applications of such understandings to tailor materials with desired properties and performances [16, 17]. Accordingly, the crystal engineering of energetic materials is to understand the intrinsic molecular-crystal structure relationship, to construct new energetic crystals with desired properties and performances. Crystal engineering has grown and developed for over half a century [18–20], while it is still a new thing for the crystal engineering of energetic materials in recent years. Although the finding of energetic materials applied is full of occasionality and experience, we strongly believe that the crystal engineering will be a main stream to produce desired energetic materials rationally. In fact, it becomes thriving after the appearance of energetic cocrystals, so that people can manufacture new energetic materials based on existing molecules, instead of organic syntheses [21]. Besides, the crystal engineering can make a large quantity of deserted and forgotten molecules alive. Furthermore, the crystal engineering presents a bright perspective for creating low sensitivity and high energy materials (LSHEM) and alleviating the usual energy-safety contradiction [22–26].

References

13

1.4 Intention and Organization of This Book This book will focus upon the intrinsic structures of all kinds of energetic compounds, including packing structures of energetic molecular crystals, energetic ionic crystals, energetic atomic crystals, energetic metallic crystals and energetic mixed-type crystals, substructures of crystal packing, and interactions among the substructures, with theoretical and simulation methods applied to deal with briefed. Meanwhile, the polymorphism as a level of intrinsic structures will be briefly discussed. In the final of this book, we will introduce the crystal engineering of energetic materials based on the relationships between intrinsic structures and properties. Furthermore, this book features understanding the properties and performances of energetic materials by maintaining a concept that structure determines property. It will help to promote the rationality in creating new energetic materials, rather than increase the experience of energetic materials alone. Thereby, a simply and new way to readily understand energetic materials is expected to be paved, based on this book.

References 1. Dong, H., & Zhou, F. (1994). Properties of high energetic explosives and relatives. Science Press. 2. Teipei, U. (2005). Energetic materials. Wiley-VCH Verlag GmbH & Co. 3. Klapötke, T. M. (2007). New nitrogen-rich high explosives. In T. M. Klapötke (Ed.), High energy density materials. Structure and bonding (Vol. 125). Springer. 4. Nielsen, A. T., Chafin, A. P., Christian, S. L., Moore, D. W., Nadler, M. P., Nissan, R. A., Vanderah, D. J., Gilardi, R. C., George, F., & Flippen-Anderson, J. L. (1998). Synthesis of polyazapolycyclic caged polynitramines. Tetrahedron, 54, 11793–11812. 5. Bolotina, N., Kirschbaum, K., & Pinkerton, A. A. (2005). Energetic materials: α-NTO crystallizes as a four-component triclinic twin. Acta Crystallographica, B61, 577–584. 6. Latypov, N. V., Bergman, J., Langlet, A., Wellmar, U., & Bemm, U. (1998). Synthesis and reactions of 1,1-diamino-2,2-dinitroethylene. Tetrahedron, 54, 11525–11536. 7. Pagoria, P. F., Mitchell, A. R., Schmidt, R. D., Simpson, R. L., Garcia, F., Forbes, J., Cutting, J., Lee, R., Swansiger, R., & Hoffmann, D. M. (1998). Synthesis, scale-up and experimental testing of llm-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide). In Proceedings of the Insensitive Munitions and Energetic Materials Technology Symposium, Meeting No. 956, San Diego, CA. 8. Eremets, M. I., Gavriliuk, A. G., Trojan, I. A., Dzivenko, D. A., & Boehler, R. (2004). Singlebonded cubic form of nitrogen. Nature Materials, 3, 558–563. 9. Gao, H., & Shreeve, J. M. (2011). Azole-based energetic salts. Chemical Reviews, 111, 7377– 7436. 10. Li, S., Wang, Y., Qi, C., Zhao, X., Zhang, J., Zhang, S., & Pang, S. (2013). 3D Energetic metalorganic frameworks: Synthesis and properties of high energy materials. Angewandte Chemie International Edition, 52, 14031–14035. 11. Landenberger, K. B., Bolton, O., & Matzger, A. J. (2015). Energetic-energetic cocrystals of diacetone diperoxide (DADP): Dramatic and divergent sensitivity modifications via cocrystallization. Journal of the American Chemical Society, 137, 5074–5079. 12. Chen, S., Yang, Z., Wang, B., Shang, Y., Sun, L., He, C., Zhou, H., Zhang, W., & Chen, X. (2018). molecular perovskite high-energetic materials. Science China Materials, 61, 1123– 1128.

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13. Li, G., & Zhang, C. (2020). Review of the molecular and crystal correlations on sensitivities of energetic materials. Journal of Hazardous Materials, 398, 122910. 14. Zhou, X., Zhang, Q., Xu, R., Chen, D., Hao, S., Nie, F., & Li, H. (2018). A novel spherulitic self-assembly strategy for organic explosives: Modifying the hydrogen bonds by polymeric additives in emulsion crystallization. Crystal Growth & Design, 18, 2417–2423. 15. Bu, R., Xie, W., & Zhang, C. (2019). Heat-induced polymorphic transformation facilitating the low impact sensitivity of 2,2-dinitroethylene-1,1-diamine (FOX-7). Journal of Physical Chemistry C, 123, 16014–16022. 16. Desiraju, G. R. (1989). Crystal engineering. The design of organic solids. Elsevier. 17. Desiraju, G. R. (2013). Crystal engineering: From molecule to crystal. Journal of the American Chemical Society, 135, 9952–9967. and references therein. 18. Schmidt, G. M. J. (1976). In D. Ginsburg (Ed.), In solid state photochemistry. Verlag Chemie. 19. Addadi, L., & Lahav, M. (1978) Photopolymerization of chiral crystals. 1. The planning and execution of a topochemical solid-state asymmetric synthesis with quantitative asymmetric induction. Journal of the American Chemical Society, 100, 2838–2844. 20. Thomas, J. M. (1981). Diffusionless reactions and crystal engineering. Nature, 289, 633–634. 21. Bolton, O., & Matzger, A. J. (2011). Improved stability and smart-material functionality realized in an energetic cocrystal. Angewandte Chemie International Edition, 50, 8960–8963. 22. Jiao, F., Xiong, Y., Li, H., & Zhang, C. (2018). Alleviating the energy & safety contradiction to construct new low sensitivity and highly energetic materials through crystal engineering. CrystEngComm, 20, 1757–1768. 23. Zhang, C. (2018). On the energy & safety contradiction of energetic materials and the strategy for developing low-sensitive high-energetic materials. Chinese Journal of Energetic Materials, 26, 2–10. 24. Zhang, C. (2018). Origins of the energy and safety of energetic materials and of the energy & safety contradiction. Propellants, Explosives, Pyrotechnics, 43, 855–856. 25. Zhang, C., Wang, X., & Huang, H. (2008). π-stacked interactions in explosive crystals: Buffers against external mechanical stimuli. Journal of the American Chemical Society, 130, 8359– 8365. 26. Zhang, C., Jiao, F., & Li, H. (2018). Crystal engineering for creating low sensitivity and highly energetic materials. Crystal Growth & Design, 18, 5713–5726.

Chapter 2

Category of Energetic Crystals

2.1 Introduction The categorization of energetic crystals is beneficial to understand the intrinsic structure of energetic materials; in turn, the intrinsic structure is the basis for categorizing energetic crystals. This chapter introduces the category of energetic crystals. In general, energetic crystals are composed of C, H, N, and O atoms, and belong to molecular crystals. Nowadays, with multiple theories and molecular simulationaided material design technologies, many new kinds of energetic materials like energetic extended solids (e.g., polymer nitrogen, CO and CO2 ) [1], energetic ionic compounds that are generally organic [2], energetic MOFs [3], energetic cocrystals (in particular, the energetic-energetic cocrystals) [4], and energetic perovskites [5] are continuously being created. Moreover, the metallic hydrogen, predicted to have a super high capability of explosion, was synthesized using high-pressure techniques [6]. Overall, these energetic crystals can be molecular, ionic, metallic or atomic crystals, as well as mixed-type crystals containing both molecules and ions simultaneously. It seems that all the crystal types have been covered in energetic materials. The classification of energetic crystals depends on the characteristics of the primary constituent parts and the interactions among them. These primary structures are also the substructures of crystal packing, as well as the intrinsic structures of energetic materials. Thus, correctly categorizing energetic crystals is helpful to understand the structures and properties of energetic materials and use them rationally. In fact, classifying energetic crystals is also a basis for molecularly simulating them in a right way. For example, choosing a right theoretical method is very important for us to simulate the crystal packing structure and properties of an energetic compound. In the simulation of neutral compounds containing C, H, N, and O atoms, which have sufficient experimental and simulated parameters for validation, most simulation methods are viable, such as the density functional theory (DFT) [7–9],

© Science Press 2023 C. Zhang et al., Intrinsic Structures and Properties of Energetic Materials, https://doi.org/10.1007/978-981-99-2699-2_2

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16

2 Category of Energetic Crystals

self-consistent-charge density-functional tight-binding (SCC-DFTB) [10–12], semiempirical ab initio [13], and forcefield (FF) methods [14]. As to ionic compounds with C, H, N, and O atoms, only the DFT method is the most reliable, while it is not necessarily the case. It is still challenging to verify the reliability of general DFT methods for energetic metallic crystals like metallic hydrogen and metallic nitrogen, only relatively stable at extremely high pressures and with poor experimental data. After introduction, the remaining of this chapter is organized as follows. The criterion for categorizing energetic crystals will be described in Sect. 2.2; based on it, all the five types of energetic crystals will be introduced, including energetic molecular crystals, energetic ionic crystals, energetic atomic crystals, energetic metallic crystals, and energetic mixed-type crystals, as in Sect. 2.3; and finally, the understandings of the intrinsic structure–property relationships will be presented in Sect. 2.4.

2.2 Criterion for Categorizing Energetic Crystals 2.2.1 Primary Constituent Part In general, solids can be classified into crystals, liquid crystals, and amorphous solids, based on the degree of order of the component particles arranged in space. Liquid crystals and amorphous solids are absent from their intrinsic structures at the level of crystal packing, i.e., their intrinsic structures could be a molecule, atom or ion only. As for crystals, it is necessary to clarify the concept of the components in crystals if a further classification is realized based on it. In fact, the description of the component can be readily found in many textbooks, where the component could be an atom, molecule, or ion. This is consistent with the definition of crystal by the American Heritage Dictionary, a homogenous solid formed by a repeating, three-dimensional pattern of atoms, ions, or molecules and having fixed distances between constituent parts. There is someone who also agree with it [15]. Nevertheless, it is somehow rough and primary to say that the component only refers to atom, ion, or molecule in our opinion, which is further used to classify the crystals. Therefore, we proposed that the PCP should be considered for categorizing crystals. Follows are the explanations. Zhang et al. recently stressed that, at the crystal level, atoms, ions, molecules, or even electrons (together with cations) should be specified as PCPs, as they are the closest substructures to crystal [16]. Figure 2.1 demonstrates five crystal types standardized in textbooks, which possess different PCP types. For atomic crystal (e.g., diamond), molecular crystal (e.g., ice), ionic crystal (e.g., NaCl) and metallic crystal (e.g., metallic Na), their PCPs are different from one another, i.e., atoms (C), molecules (H2 O), cations/anions (Na+ and Cl− ), and metallic ions/free electrons (Na+ and electron), respectively. Note that the type of a crystal is differentiated by the PCP type, instead of the PCP itself. For example, the PCP types of ice and TNT are both the molecule, thus they both belong to molecular crystal.

2.2 Criterion for Categorizing Energetic Crystals

17

Fig. 2.1 Crystal classification based on PCPs and the nature of their interactions. From outer to inner: crystal type, type of interactions among PCPs and PCP type. In the figure, FE represents free electron

Besides, different from the aforementioned four types of crystals, there are at least two types of PCPs in mixed crystal. For instance, a case of a compound with water of crystallization shows that ions and molecules can coexist in a same lattice, as two types of PCPs. Because the term mixed crystal has been widely accepted to denote solid solution, Zhang et al. had to use another one of mixed-type crystal to differentiate it. Hopefully, Zhang et al. proposed that the term of mixed crystal should possess the intension of the existing term mixed-type crystal, as solid solution (AuCu and AuCu3 [17]) can cover one of the five crystal types shown in Fig. 2.1 (metallic crystal), and the former term should be replaced by the latter [16]. Recently, the successful synthesis of cyclo-N5 − causes a fast increase of various pentazole compounds and development of pentazole chemistry. Here, (N5 )6 (H3 O)3 (NH4 )4 Cl (1) [18], [Mg(H2 O)6 (N5 )2 ]·4H2 O (2) [19], and [Mn(H2 O)4 (N5 )2 ]·4H2 O (3) [19] are employed to show what is the PCP further. As illustrated in Fig. 2.2, the closest substructures of 1 are N5 − , H3 O+ , NH4 + , and Cl− , while those of 2 and 3 are Mg(H2 O)6 2+ , N5 − , and H2 O, and Mn(H2 O)4 (N5 )2 and H2 O, respectively. These closest substructures are the PCPs of the three crystals. Someone will find that the coordinated H2 O in 2, and the coordinated H2 O and N5 − in 3 are the closest substructures of the Mg(H2 O)6 2+ and Mn(H2 O)4 (N5 )2 , instead of the crystals; thus, they are not the PCPs. Interestingly, N5 − appears in all the three crystals, but it acts as a PCP in 1 and 2. Similarly, only the water of crystallization in 2 and 3 acts as PCP, while coordinated water is not the PCP. It shows the first importance of identifying the closest substructures to crystal, followed by the PCP type and its determination of crystal type. Furthermore, alum is also taken to identify the PCP type, owing to its high complexity of component. As illustrated in Fig. 2.3, four PCPs, Al(H2 O)6 3+ , K+ ,

18

2 Category of Energetic Crystals

B

C

A

O C A O

B

(N5)6(H3O)3(NH4)4Cl, 1

[Mg(H2O)6(N5)2]·4H2O , 2

Cl Mg Mn N O H

[Mn(H2O)4(N5)2]·4H2O , 3

Fig. 2.2 Three crystals containing N5 − synthesized recently. In each plot, the left and right denote the surroundings of a cyclo-N5 − ion and crystal packing structure, respectively. In 1 and 2, the cyclo-N5 − ions interact with surrounding ions/molecules through HB, while the covalent bond, as well as intermolecular HB, are formed with the cyclo-N5 − ion in 3. Reprinted with permission from Ref. [16]. Copyright 2019 American Chemical Society

SO4 2− , and water of crystallization exist in the alum crystal. It should be noted that the coordination cation Al(H2 O)6 3+ is one of the PCPs of alum, while the constituent Al3+ and coordinated H2 O are not. Among the four PCPs, three (Al(H2 O)6 3+ , K+ , and SO4 2− ) are of ions, and one (water of crystallization) of molecule, belonging to two types. Thus, alum should belong to mixed-type crystal. This can be also identified by the two interaction types among the PCPs, i.e., the intermolecular interactions around all the four PCPs and the interionic interactions around Al(H2 O)6 3+ and SO4 2− . From above examples and discussions, we can know that the PCP is not completely identical to the component of a crystal, and the key is to ascertain the closest substructure to a crystal as its PCP.

2.2 Criterion for Categorizing Energetic Crystals

K+

19

H2O

Unit cell

Al(H2O)63+

SO42-

Fig. 2.3 Crystal structure of alum (center), and interactions enclosing PCPs of K+ , water of crystallization, SO4 2− and Al(H2 O)6 3+ (surrounding). O, H, S, Al, and K atoms are represented in red, green, yellow, purple, and scarlet, respectively. Reprinted with permission from Ref. [16]. Copyright 2019 American Chemical Society

2.2.2 Type of Energetic Crystals The PCP type and interaction type among PCPs of a crystal reflect the physical nature of its structure, and they are also the criterion for categorizing crystal classifications, as demonstrated in Fig. 2.1. In fact, the nature of PCP interactions can be readily confirmed once the PCPs are ascertained. Thereby, the existing and predicted energetic crystals can be classified into five types as follows. Atomic crystals are a group of crystals with all the atoms held in lattice by covalent bonds, thus, they are also termed as covalent crystals. Because of the high strength of covalent bonds, an atomic crystal generally exhibits a higher stability, compared with other types of crystals. However, it is not always the case. For example, the polymeric nitrogen, with the N atom as its PCP, is thus an atomic crystal. However, it can only be held at high pressures thanks to the rather weak N–N single bond, resulting in a low stability [1]. Molecular crystals are a class of crystals with discrete molecules consolidated by weak intermolecular interactions. Obviously, this weak intermolecular interaction is the root for the high brittleness of traditional energetic crystals, which generally consist of small organic molecules with C, H, N, and O atoms. Thus, it is necessary to add binders into the recipe of energetic materials, in order to remedy their high brittleness and make them machinable.

20

2 Category of Energetic Crystals

An ionic crystal is a crystal consisting of ions held by electrostatic attractions. At present, energetic ionic compounds are thriving and mostly composed of organic ions. Because the polarity strength of these organic ions is generally between neutral molecules and inorganic ions, the strength of the PCP interactions in energetic ionic crystals mediates those of molecular crystals and inorganic salts. A metallic crystal consists of metallic ions and free electrons, whose interactions are metallic bonding, with the outer electrons of metallic atoms shared by the crystals. To date, energetic metallic crystals have not been completely experimentally confirmed yet. Although it is reported that metallic hydrogen was synthesized under extremely high pressures, its experimental stacking structure is still absent, with some predictions reported only [6]. Finally, a crystal consolidated by at least two types of interactions among PCPs is a mixed-type crystal. As pointed out above, both the intermolecular and interionic interactions appear in 2 in Fig. 2.2 and alum in Fig. 2.3, thus they both belong to molecularly and ionically mixed-type crystal. 3 in Fig. 2.2 belongs to molecular crystal. That 3 was roughly seen as salt in the original literature [19] turned to be somehow questionable. All the five types of energetic crystals will be detailed in next section and following chapters. with various examples. Furthermore, the types of both PCPs and PCP interactions are also the basis for defining and discerning cocrystal types, as discussed in Chap. 7.

2.3 Category of Energetic Crystals The categorization of energetic crystals is implemented in terms of the aforementioned PCP type, instead of the quantity of PCPs. That is, an energetic crystal containing two or more PCPs of the same type also belongs to the crystal type classified by the PCP type. For instance, the CL-20/TNT cocrystal contains two components, i.e., CL-20 and TNT, which are both molecules, thus, it belongs to molecular crystal too. More insights of the structures and properties of all types of energetic crystals will be detailed in the following chapters.

2.3.1 Energetic Molecular Crystal An energetic molecular compound, picric acid, started the era of modern energetic materials, which featured artificial synthesis. The single-component energetic molecular crystals, such as the widely-used TNT, RDX, and HMX, possess the largest quantity and have received the widest interests and applications. The single-component energetic molecular crystals are seen as the common or traditional ones. Up to the present, the traditional energetic molecular crystals is still the main body in practical

2.3 Category of Energetic Crystals

21

use, even though both kinds and quantities of new energetic compounds and composites increase rapidly. In practice, it is so hard for these new energetic compounds and composites to pass the strict and comprehensive examinations about energy, safety, mechanics, environmental adaptability, compatibility, and so on. According to above criterion, in the case of a single-component energetic molecular crystal, the PCP is identical to the component, molecule. Due to the low molecular polarity, thus the lack of strong HBD or HBA, these molecular crystals generally have weak intermolecular interactions [20, 21]. Nitro compounds are the most abundant in traditional energetic materials, especially in energetic molecular crystals. Some of these compounds have been already in practical applications, such as TNT, RDX, and HMX. As shown in Fig. 2.4 [22], NO2 group can be covalently bonded with C, N, or O atoms. The corresponding compounds, with C–NO2 , N–NO2 , or O–NO2 bond, exhibit a decrease of molecular stability, as their bond strengths reduce as well. For example, energetic compounds with low sensitivity or high heat resistance, such as TNB, TNA, DATB, TNT, and TATB [23–27], often possess high molecular stability, thanks to the big conjugated structures formed by combining NO2 and benzene ring together. In contrast, geminaldinitro and nitroform compounds like TNAB, NF, TETB, and ONDO [28–31] possess worse molecular stability, because of the reduced electrons that are shared with the increased NO2 . This difference in molecular stability can lead to a difference in sensitivity, and determines their usage. For instance, the more stable compounds can be used as secondary explosives, whereas the less stable ones can be employed as primary explosives. Surely, the energetic molecules containing N–NO2 or O–NO2 usually possess less stability compared with the aforementioned highly heat-resistant molecules [32–37]. In addition to nitro group, azide (–N3 ) and peroxide (–O–O–) groups are sometimes contained in energetic molecular crystals as explosive or oxidization groups, illustrated respectively in Figs. 2.5 and 2.6. In contrast to nitro compounds, the molecular stability of azide and peroxide ones is generally weakened, because of the easier dissociation of azide and peroxide groups. For example, the bond dissociation energies (BDEs) of CH3 –N3 and CH3 O–OCH3 are respectively 174 and 163 kJ/mol, much less than that of CH3 –NO2 , 260 kJ/mol [38]. Therefore, azides are generally applied as primary explosive in industry, while peroxides are rarely thanks to their low safety and low power. Owing to the low polarity, intermolecular interactions in organic azides are generally weak, giving rise to low PC. In Fig. 2.5, there are some azides featuring high molecular planarity and face-to-face π-stacking with a singleatom thickness, such as TAHA, NADAT, and ANTHA [39–41]. The face-to-face π-stacking is prone to low impact sensitivity, which is helpful to remedy the shortcomings of low molecular stability. In this case, it is also verified that we can improve molecular stacking mode to release the so-called energy-safety contradiction. The explosive peroxides DADP and TATP (Fig. 2.6) possess a rather high accessibility and low power [42, 43], becoming the main explosives adopted by terrorists. This is a main reason for restricting the use of acetone, which generally serves as the precursor of peroxides.

22

2 Category of Energetic Crystals

Fig. 2.4 Crystal packing and molecular structures of some typical NO2 compounds. In general, they are divided into four groups in terms of the functional groups Ar–NO2 , C–NO2 , N–NO2 , and O–NO2 , which have largely different molecular stability, and further different sensitivity. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

Energetic N-heterocyclic compounds are another important family in the entire energetic molecular crystals, such as the most famous RDX, HMX, and CL-20. Energetic N-heterocyclic compounds are also abundant in energetic materials, similar to the aforementioned NO2 compounds, thanks to the high structural multiformity of Nheterocycle. For this group of compounds, only some of them feature non-planar Nheterocyclic structures, such as the applied nitroamino compounds of CL-20, HMX, RDX, and TNAZ. Most of the N-heterocycles possess planar conjugated structures, with thus a higher molecular stability, such as azines, azoles, furazans, and their fused and bridged derivatives. Similar to TATB, the planar molecular structures of

2.3 Category of Energetic Crystals

23

B C

B

C

O

A

AAF

O

A

O

NGA

B

A

ANTHA

A

O

DATZ

B

O/C

B

C

A

O/C B

C

A

ANB

NADAT

B

C

C O

O/B

A

A

O

B

A C

TAHA

ANP

DAG

Fig. 2.5 Crystal packing and molecular structures of some organic azide compounds. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

B

B

O/C

A

O/A

C

DADP

TATP

Fig. 2.6 Crystal packing and molecular structures of two typical peroxides. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

ANTA, 2-nitriminoimidazolidine, and LLM-116 [44, 45] root for their π-stacking (Fig. 2.7) and further possible low impact sensitivity. Furthermore, the neutral precursors of most energetic ions are also N-heterocyclic compounds. Thereby, Nheterocyclic structures significantly richen the energetic compounds, which can be neutral molecules and ions. The most popular of energetic compounds in use are of traditional singlecomponent molecular crystals. Particularly, the compounds containing NO2 are the main stream of applicable energetic compounds. Furthermore, only this kind of compounds have undergone sufficient examinations and strict evaluations on properties and performances. All these build a basis for systemizing energetic compounds as science. Regarding the energetic molecular crystals composed of C, H, O, and N atoms, it is impossible to significantly elevate the energy content in principle. Largely, it is the consequence of the essentiality of the aforementioned energy-safety contradiction at the molecular level [46]. That is, at the molecular level, the more chemical

24

2 Category of Energetic Crystals B

B B

A

C/O O/C

A

1,4-Dinitro-1,4-diazacyclohexane B

TNAZ O/A

O/A

C

1,4-Dinitroglycoluril

C

O/A

ANTA B

B

C

C

2-Nitraminoimidazolidine

A O

LLM-116

Fig. 2.7 Crystal packing and molecular structures of some N-heterocyclic compounds. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

energy stored in an energetic molecule should be at cost of the more weakening of the chemical bonds involved, or the less molecular stability. It seems to be impossible to create new energetic compounds with significantly increased energy and high stability under common conditions. It seems that full nitrogen compounds can help us beat the odds. Plenty of energy will be released as N–N or N=N transforms into N≡N bonds, because the N–N and N=N bonds respectively have much less than 1/3 and 2/3 of the bond dissociation energy of a N≡N bond. For example, a N4 molecule, with a T d symmetry and containing six single N–N bonds, will release a huge quantity of heat, with an environmentally friendly product N2 . Thereby, it has attracted much attention for Nrich compounds, especially all N compounds, as illustrated in Fig. 2.8. Unfortunately, except for the nitrogen molecule, we have not experimentally synthesized other all N molecular crystals. Recently, the dc of caged N4 , N6 , N8 , N10 , and N12 were predicted with Lennard-Jones potentials fitted by QC calculations, as 1.81, 2.08, 2.47, 2.46, and 2.57 g/cm3 , respectively, without packing structure reported [47]. The chained N6 and N8 were reported with predicted packing structures, as well as dc of 1.95 and 1.561 g/ cm3 , respectively [48, 49]. Theoretically, it is difficult to predict the packing densities of these full nitrogen molecules, as most existing density functional approaches are bad at dealing with the intermolecular repulsions among the lone pairs of electrons, which are generally located on N atoms. Intermolecular interactions in these crystals feature weaker vdW forces, as a consequence of the intermolecular repulsions among the lone pairs, compared with traditional energetic crystals. Although the all-nitrogen molecules are of a new group compared to the aforementioned traditional energetic molecules, they can hardly be free of the intrinsic energy-safety contradiction at the molecular level. After all, the working ability of these compounds still depends on the release of chemical energy in principle. As a matter of fact, these molecules have not been successfully synthesized yet due to the contradiction. Energetic eutectic may also provide insight into how to alleviate the essential energy-safety contradiction at the molecular level. Energetic cocrystal is not a new thing, as the energetic solvates reported a long time ago are actually the energetic cocrystals according to our redefinition of cocrystal [16]. Nevertheless, it is thriving

2.3 Category of Energetic Crystals

25

1.81

2.08

2.47

2.46

2.57

N4 (Td)

N6 (D3h)

N8 (Oh)

N10 (D5h)

N12 (D6h)

C

B

C

O/A O/B

N6

A

N8

Fig. 2.8 Theoretically predicted molecular structures and crystal packing of some full nitrogen compounds. The values on the top of the molecular structures are the predicted densities in g/cm3 . Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

nowadays, with a large quantity of energetic cocrystals coming into being, such as the CL-20-based (Fig. 2.9) [50–53] and TNT-based (Fig. 2.10) [54–56] molecular cocrystals. Because of the similar components, the intermolecular interactions in molecular cocrystals are similar to those in single-component molecular crystals [57]. That is, there is no significant enhancement of intermolecular interactions after cocrystallization; thus, the entropy increase is thought to drive the energetic molecular cocrystals [58]. This can be also ascribed to the same PCP and PCP interaction types in the two groups of energetic molecular crystals. Nowadays, the energetic-energetic cocrystals (both components are energetic) are a mainstream of energetic cocrystal, to avoid much energy dilution.

2.3.2 Energetic Ionic Crystal The energetic ionic crystals exist as another crystal form of energetic compounds. Reasonably, the decomposition of constituent ions should feature heat release. These ions are various and can be inorganic, organic, or metallic. Figure 2.11 shows the crystal packing of some common energetic inorganic ionic crystals [59–61]. As a consequence of decomposition, it may be different in the energy release manner for different ionic crystals. This can be exemplified by NaN3 , Pb(N3 )2 , and AP shown in Fig. 2.11. For AP, the released heat comes from the reactions between anions and cations. Because of a very high valence of the Cl atom (+7), AP is usually used as an oxidizer certainly in numerous formulations. As to Pb(N3 )2 and NaN3 , it is mainly resulted from the decomposition of N3 − . It has been ascertained that the decomposition of metallic azides into metal elements and N2 is usually implemented through the reactions between the neighboring N3 − in crystal. Because the reduction

26

2 Category of Energetic Crystals

B A

C

O/B

O/A

C

CL-20/NAQ

CL-20/NMP·H 2O

B

A

B

O/C O/A

C

CL-20/HMX

CL-20/H2O2

Fig. 2.9 Packing structures (surrounding) and molecular structures (center) involved in some CL20-based molecular cocrystals. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

O/C

B A

C

A

O/B

TNT/1-BN

TNT/Nap A A

C

O/B

TNT/BTF

O/C

B

TNT/TTNB

Fig. 2.10 Packing structures (surrounding) and molecular structures (center) involved in some TNT-based molecular cocrystals. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

of a metal from N3 − is naturally endothermic, and double and triple bonds exist in N3 − already, it is expected that the heat release from metallic azide decay is generally limited. In contrast to common energetic molecular crystals, the polarity of PCPs in energetic ionic crystals is significantly enhanced, owning to the strong ion-counterion interactions in energetic inorganic ionic crystals. It should be noted that numerous energetic ionic crystals do not belong to the typical inorganic ionic compound like NaCl, in which one electron of each Na atom is transferred to a corresponding Cl

2.3 Category of Energetic Crystals

27

B

A

O/C

AP

B

C

O/A

Pb(N3)2

B

A

O/C

NaN3

Fig. 2.11 Packing structures of some common energetic inorganic ionic crystals. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

atom, and every Na atom is completely charged with one positive charge (+1 e). In comparison, the ionization is discounted in an energetic ion, especially in an energetic organic ion. For example, in an energetic ionic crystal TKX-50, there is in fact less one electron positively charged on one NH3 OH+ . Thus, the PCP interactions among energetic ionic crystals are mainly attributed to electrostatic interactions, but these interactions are not as strong as those in typical ionic compounds like NaCl. In general, energetic ionic compounds have some advantages over molecular compounds. For example, a series of ionic compounds with a same anion or a same cation will be created once it is successfully synthesized. The combination of a same ion with various counterions can significantly decrease cost and facilitate to find new scientific rules and regularities. Besides, ionization can be beneficial to increase molecular stability. In particular, this is remarkable for N-rich compounds. In general, the low molecular stability of many N-rich compounds is rooted from the acidic H atom, which tends to leave, and a couple of anion and cation is formed if conditions allowed. After ionization (deprotonation), the molecular stability increases. Thus, lots of energetic ionic compounds can be seen as the hydrogen transfer products of energetic molecular cocrystals. In recent 10 years, energetic ionic compounds increase rapidly, with some highperformance ones found. In contrast to the common energetic inorganic ionic compounds, the organic ions that can have negative and positive signs are introduced into the new kind of energetic ionic compounds. As illustrated in Fig. 2.12, all the anions in the NH3 OH+ -based compounds are organic and energetic [62–66], while both anions and cations of the energetic ionic compounds in Fig. 2.13 are organic [62, 67–71]. In Fig. 2.13, guanidinium (G+ ) and its counterions respectively serve as the reducer and oxidant source for the energy release of these ionic compounds once stimulated. The quantity of energetic ionic compounds significantly increase by means of the introduction of organic ions. While, some issues are meanwhile raised, such as reaction complexity, low compatibility, low heat-resistance, as challenges in practical use. Besides, more and more N5 − -based energetic ionic compounds (Fig. 2.14) [72] were created after the successful synthesis of cyclo-N5 − . It is understandable that the considerable stability of these energetic ionic compounds results from that the anionization of cyclo-N5 enhances its stability and the ionic bonds strengthen the entire crystal [73]. It should be stressed that the considerably high stability still implies

28

2 Category of Energetic Crystals B

O/A

C

HA-AFTA

B

O

A

C

B O/C

A

HA-DBO

HA-DNBTO

A

C/O

O

B

C A

B C

HA-BT2O

B/O

HA-BTO

A

HA-DNABF

Fig. 2.12 Packing structures of some energetic ionic crystals containing NH3 OH+ . Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

A O/C B

C/O

B

G-BT2O

C/O

A

A

G-NTX

G-C7H4NO5

A/B C

B

B

C/O A

O

G-BTO

G-CO3 O

C/A

B

G-DNBTO

Fig. 2.13 Crystal packing of some energetic organic crystals containing G+ . Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

2.3 Category of Energetic Crystals

29

C

C

B

O/A

B

(NH3OH)+N5C O

A

O/C

O/B

C

B/O

A

[C(NH2)3]+N5-

(NH4)+N5C

B

A

A

(N2H5)+N5-

[AgN5]n

O/B

A

[N(CH3)4]+N5-

Fig. 2.14 Crystal packing and interionic interactions of some energetic inorganic crystals containing N5 − . Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

a limit for the energy content. As a matter of fact, these N5 − -based energetic ionic compounds can hardly outperform the traditional energetic molecular compounds in energy release [74].

2.3.3 Energetic Atomic Crystal Wholly, energetic atomic crystals are still limited in quantity. Most of them are theoretical predictions, while much less are observed experimentally. Polymeric nitrogen (poly-N, Fig. 2.15), CO, and CO2 possess the largest population among these energetic atomic crystals. Different from the polymerization of unsaturated C–C bonds that is exothermic, the formation of poly-N, –CO and –CO2 stores chemical energy. This class of energetic crystals are yielded under high pressures. For instance, by a laser-heated diamond anvil, the cubic gauche structure of poly-N (cg-N) was successfully synthesized from N2 at > 2000 K and > 110 GPa [1]. And cg-N will diminish if unpressed. Because the neighboring N atoms in cg-N are all linked by single bonds, it belongs to atomic crystal. Interestingly, the poly-N structures can be also exhibited in other kinds of crystals [75–81], also shown in Fig. 2.15. While, it should be noted that some compounds like MgN4 , BeN4 and K2 N16 , and ReN8 · xN2 fall into the types of ionic crystal and molecular crystal, respectively, despite poly-N contained. That is, the PCPs of MgN4 , BeN4 , and K2 N16 are cations and anions (polymeric anions); while those of ReN8 · xN2 are two kinds of molecules, polymeric ReN8 and N2 . It shows that the polymeric structure is necessary but not certainly adequate to an energetic atomic crystal. In addition, it is reported that poly-CO can exist stably after unloading pressures. However, the energy content of poly-CO was predicted at the level of common energetic compounds with C, H, N, and O atoms.

30

2 Category of Energetic Crystals B

B

B

A O

A

C

C

O

O

A

cg-N

C

t-N

B

FeN4

B C

O O

C

A

C

A

MgN4

O

AlN5 B

C

A

C

B

BeN4 B

B

A

O

O

K2N16

A

FeN6

O

A C

ReN8·xN 2

Fig. 2.15 The crystal packing and poly-N structures therein for some experimentally observed or theoretically predicted compounds. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

2.3.4 Energetic Metallic Crystal Recently, it was reported that a molecular to metallic transition of the hydrogen occurs at an extremely high pressure of 495 GPa. This transition was ascertained by the measurements of reflectivity (0.91) and the plasma frequency (32.5 ± 2.1 eV at 5.5 K or an electron carrier density of 7.7 ± 1.1 × 1023 particles/cm3 [6]), which agree with earlier theoretical prediction (Fig. 2.16) [82]. Still, there is no diffraction result or packing parameter reported in this work. In addition, another transition from molecular to metallic for fluid nitrogen was found to occur at > 125 GPa and 2500 K [83]. Obviously, it was shown that the metallic nitrogen under the condition is not a solid, and does not belong to a crystal, i.e., metallic fluid. Compared with molecular hydrogen or nitrogen, valence electrons of an atom are no longer constrained around the atomic nucleuses anymore, and cruise in the entire condensed matter. Reasonably, these energetic metallic crystals or metallic fluid will yield a huge amount of energy when decompressed. Obviously, the metallic condensed matter may change to molecular condensed matter first and then molecular gas.

2.4 Understanding of Energetic Crystals Fig. 2.16 Structures of the ground-state phases of metallic hydrogen. Unit cell of I41 /amd (c/a > 1) (a). 2 × 2 × 1 supercell of R-3m. Fictitious bonds have been drawn for clarity (b). Reprinted with permission from Ref. [82]. Copyright 2011 American Physical Society

(a)

31

(b)

2.3.5 Energetic Mixed-Type Crystal Mixed-type crystal is in fact mixed-type cocrystal, with two or more types of PCPs and PCP interactions involved. This kind of crystals are now booming, as the extension of some new structures that are originally non-energetic. For instance, energetic MOF structures [3, 84, 85] shown in Fig. 2.17 appear in the torrent of MOF researches. As in other MOF structures, the anions (or the negatively charged moieties) on the frames are still strongly linked by central metallic cations through coordination bonding in energetic MOF structures, with a difference that the anions are energetic. It should be noted that, in some energetic MOFs, only the skeletons are periodic, and solvents or other fillers in the channels are usually amorphous. Similarly, energetic perovskites [5, 86] extend the perovskite structures (Fig. 2.18). Wholly, this kind of crystals appears rarely. The nature of heat release of energetic MOF and energetic perovskites could be identical to energetic ionic compounds mostly, i.e., the reaction between anions and cations. The successful synthesis free cyclo-N5 − promotes the evolution of this group of crystals, as two PCPs or more coexist in each of them [87–90]. Figure 2.19 shows that HB, coordination bonding and/or π-π stacking hold cyclo-N5 − in lattice [73].

2.4 Understanding of Energetic Crystals The main aim of categorizing energetic crystals is to understand and apply them. As pointed out above, the PCP and PCP interaction types involved in an energetic crystal type is the basis for verifying which crystal type it belongs to. By categorizing energetic crystals into five types, we can understand them as follows.

32

2 Category of Energetic Crystals

A B

[Cu(atrz)3(NO3)2]n

B

C/O

[Cu(en)2(trans-AT)0.5](trans-AT)0.5

B/ O

A/O

C

A

C

[Ag(ATZ)]n

[Ni(en)2(trans-AT)](trans-AT)(trans-H2en)·2H 2O

Fig. 2.17 Packing structures and coordinated structures of some mixed-type cocrystals with MOF structures. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

B

B

O

O

A

A

C

C

(H2dabco)[Na(ClO4)3

A B2-

(H2dabco)[K(ClO4)3

X-

B

B

O

A

C

O A

C

(H2dabco)[Rb(ClO4)3

(H2M4)[NH4(ClO4)3]

Fig. 2.18 Packing structures and constituent parts of some energetic perovskites. dabco: 1,4diazabicyclo[2.2.2]octane; H2 M4 : 1-methyl-1,4-diazabicyclo-[2.2.2]octane-1,4-diium. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

2.4 Understanding of Energetic Crystals

33

B A C C

O

O/A O/C

A

[Na8(N5)8(H2O)3]n

(N5)6(H3O)3(NH4)4Cl

B

A

A

A

B

Mn(H2O)4(N5)2]·4H2O

O/C

C

O/B

[CuN8]n

O/C

[Na(H2O)(N5)]·2H 2O

A

O/C

B

B

[Ag(NH3)2][Ag3(N5)4]

O/C

A

B

Co(H 2 O) 4(N 5)2]·4H2O

O/C

B

Mg(H2O)6(N5)2]·4H 2O

A

O/C

A

B

B

Fe(H2O)4(N5)2]·4H2O

Zn(H2O)4(N5 )2]·4H2O

Fig. 2.19 Packing structures and PCPs of some mixed-type cocrystals containing N5 − . Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

2.4.1 Interactions Between PCPs in Crystals and Their Stability For energetic molecular crystals, their PCPs are molecules. These molecules can be homogeneous or heterogeneous in a crystal, corresponding to a singlecomponent crystal or a molecular cocrystal, respectively. In this case, the PCP interactions include vdW interactions and electrostatic interactions. Note, heterogeneous molecules belong to the same type of PCP, molecule. The intermolecular interactions therein are generally rather weak, because of the weak molecular polarity and the absence of strong HBA or HBD [20, 21, 57]. In general, the heat release of an energetic molecular crystal is at the level of several kJ/g to guarantee a certain molecular stability, due to the contradiction between energy stored chemically and bond strength, i.e., the more energy stored should be at the cost of the more bond weakened. According to theoretical predictions, all nitrogen molecular crystals may possess higher energy contents, compared with a common CHON molecular crystal; however, this class of more energetic molecules has not come into being, because the higher energy content suggests the lower molecular stability. It is just confirmed that they cannot be free of the contradiction either. The interionic interactions in energetic ionic crystals increase significantly with larger lattice energy, in contrast to a common energetic molecular crystal. Obviously, the significantly increased lattice energy will lower the energetic content. Because the HBs in energetic ionic crystals are generally ionic, they are stronger than those

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2 Category of Energetic Crystals

in molecular crystals. Meanwhile, it was found that hydrogen transfer can take place reversibly when heating and cooling, as a reason for low impact sensitivity of some energetic ionic compounds like TKX-50 [91]. On the other hand, a ready hydrogen transfer may cause low thermal stability of energetic ionic compounds, as well as bad compatibility, restricting their use in practice. Thus, there are some challenges for applying energetic ionic compounds, even though their predicted detonation properties are usually attractive. Another kind of energetic ionic compounds, such as K2 N12 (Fig. 2.15), may possess high energy contents, but they can hardly be applied owing to a strict requirement of high pressures for stabilizing it. For energetic molecular crystals and energetic ionic crystals, it has been believed that it is feasible to improve their molecular stacking style to alleviate the energysafety contradiction of energetic compounds through crystal engineering, in which constructing the planar layer (face-to-face) π-stacking is thought to be one the most important strategies for developing high-energy and low-impact sensitivity materials [92]. A typical case is TATB, which possesses an intramolecular HB-aided planar molecular structure, and a molecular stacking mode of planar layer. This high molecular stability and ready shear sliding characteristic contribute to its low impact sensitivity, even insensitivity. In addition, stronger intermolecular HBs in low impact sensitive compounds require more energy to dissociate them when stimulated, in contrast to impact sensitive ones. This also roots for the low impact sensitivity, because covalent bonds in an energetic molecule is much stronger than intermolecular HB and molecular dissociation begins with the cleavage of the latter. Combining all these together, three points are summarized to be beneficial to the low impact sensitivity of energetic crystals: high molecular stability (planar conjugated molecular structure), strong intermolecular interaction (strong intermolecular HB) and planar layer π-π stacking. Meanwhile, the molecular composition and topology should be accounted for increase stacking density and energy [93]. It is a basis for designing new low impact sensitive and highly energetic molecular and ionic compounds to weaken the contradiction between energy and safety. Atomic energetic crystals mostly exist at high pressures, such as poly-N simple substances and metallic hybrid poly-N compounds. It is deemed that a larger amount heat can be yielded by decomposing this kind of crystals, compared with common energetic molecular and ionic crystals. While, the strict high pressure is required to stabilize them and makes them far from practical use. With respect to another group of atomic energetic crystals that can be stabilized under ambient conditions, poly-CO and poly-CO2 compounds, they are less energetic, and even exhibit less than a common energetic molecular crystal. Combining the higher manufacturing cost relative to common syntheses of tradition energetic materials, it is too hard to put them into use. Regarding energetic metallic crystals like the aforementioned metallic hydrogen and metallic nitrogen (of course, they may exist as fluid), it also needs extremely high pressures to stabilize them, for example, 495 GPa is required for stabilizing metallic hydrogen. As a matter of fact, there is a tendency for any substance to be metallized when increasing pressure. This very strict condition can hardly make them applicable under common condition. Presumably, the use of energetic metallic crystals as an

2.5 Conclusions and Outlooks

35

energetic material may proceed along a transition way from a metallic crystal to a molecular crystal and then to gas. Thereby, the energetic atomic and metallic crystals are still far from practical use and largely feature a conceptual sense. However, these two kinds of matters indeed raise some interesting hot issues of both condensed physics and energetics. Finally, as to energetic mixed-type crystals, such as energetic MOFs and perovskites, they possess not only special structures, but also a characteristic of energetic materials. Because of the frequent existence of metallic ions, it suggests the lessened product gas, and further the lowered detonation velocity and pressure, in contrast to common energetic molecular crystals. Thus, we cannot expect that the energy content level of these crystals is much enhanced compared with traditional energy materials.

2.4.2 Energy Content Thereby, we can roughly compare the energy level of all five types of energetic crystals in Fig. 2.20. It shows that, molecular crystal and ionic crystal, as well as mixed-type crystal generally possess the lowest level; while atomic crystal and metallic crystal stand higher levels. However, the higher energy requires the stricter stabilization condition. It makes these high-energy materials far from use.

2.5 Conclusions and Outlooks In summary, although energetic crystals are increasingly thriving and appearing in various styles, they can be scientifically and readily categorized in terms of the types of PCP and PCP interaction involved, i.e., all the five crystal types is found to appear in experimental determination and theoretical prediction. As to the energy content, metallic crystal ranks the first, followed by atomic crystal, and molecular crystal, ionic crystal, and mixed-type crystal. Generally, the high-energy crystal should be stabilized at high pressure, and vice versa. Through the crystal classification, we can readily predict and understand the formation and energy release mechanisms of various and dazzling energetic crystals. Also, a perspective about fabricating new energetic materials for special purposes in terms of crystal category will be realized in future, since the crystal type can roughly determine energy storage and release mechanism.

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Full-N EAC

Metal hybrid EAC

Poly-CO/CO2

Mixed-type crystal

Poly-N contained EISs

Common EISs

Full-N EMC

Molecular cocrystal

Common EMC

Energy content

Molecular crystal

Metallic H

Atomic crystal Mixed-type crystal Ionic crystal

Metallic N

Metallic crystal

Energetic crystal type Fig. 2.20 Rough comparison in energy content of various energetic crystals. EMC, EIS, and EAC represent energetic molecular crystal, energetic ionic compound, and energetic atomic crystal, respectively. Reprinted with permission from Ref. [22]. Copyright 2021 American Chemical Society

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Chapter 3

Application of Molecular Simulation Methods in Treating Intrinsic Structures of Energetic Materials

3.1 Introduction This chapter introduces the application of molecular simulation and corresponding theoretical methods in dealing with the intrinsic structures of energetic materials, instead of the principles of these methods which can be referred from numerous textbooks or tool books. Molecular simulation is naturally feasible to deal with the intrinsic structures of energetic materials. It should be attributed to that the intrinsic structures, such as the molecular and crystal (molecular stacking), are on the microscale, to which molecular simulation is apt. Because it is compulsory for a strict requirement on overall performances of an energetic material, to guarantee its application, we should understand, consider, and treat energetic materials more comprehensively and scientifically so as to promote their evolution and applications. For example, we can ascertain the application field for a given energetic material by understanding the rule of energy release; in turn, for a given application requirement, we can also select a special energetic formulation. Moreover, safety is another important performance of energetic materials, and is usually evaluated and determined by experimental measurements, which are called sensitivity measurements. So far, it is still inadequate to understand the underlying mechanism of sensitivity, due to the great challenge therein. Still, if we have achieved enough exact QSPR, designing and creating new energetic materials will become more efficient. In other words, it requires much deeper and broader insights into the mechanisms of energetic materials, such as synthesis reactions, intermolecular interactions, mechanics, decomposition, and energy release, and so forth, to set a basis for accelerating their progress. Unfortunately, most of these mechanisms can hardly be revealed by common experiments.

© Science Press 2023 C. Zhang et al., Intrinsic Structures and Properties of Energetic Materials, https://doi.org/10.1007/978-981-99-2699-2_3

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3.1.1 Weight of Simulation in Energetic Material Researches It has been ascertained in the past dozens of years that molecular simulation has accelerated the progress of energetic materials, as it could remedy many experimental disadvantages or inadequateness to present deep insights into many complex mechanisms at the molecular level. Molecular simulation was established in the early twentieth century and became increasingly developed later. In general, it refers to the use of quantum chemistry (QC), molecular mechanics (MM), molecular dynamics (MD), and molecular Monte Carlo (MC) methods to reveal underlying physical mechanisms of structures, properties, performances, and processes of materials. Based on existing principles of physics and chemistry, a model that is usually a mathematic one is constructed to ideally describe a molecular system or a chemical reaction. Subsequently, molecular simulation is implemented on the model by computer and code, to present related physical and chemical information. Molecular simulation is a powerful tool to explore material structures, properties, and performances on the microscale, as it plays important roles in confirming structures, predicting properties and performances, verifying and explaining experimental results, and establishing QSPRs and theories, etc. As in other fields, energetic materials also benefit from the molecular simulations. For example, a forehand prediction for the structures and properties of a potential energetic material is now very common in organic synthesis of energetic compounds, and such prediction has already proceeded for a long time actually. Some famous energetic compounds like FOX-7, LLM-105, NTO, CL-20, and ONC were all predicted successfully before experimentally synthesized. In the earlier time, molecular predictions based on semi-empirical QC methods were mostly performed to confirm the geometry structures, vibrational frequencies, and molecular orbitals. With the establishment and development of DFT, more and more energetic molecules were treated based on this highly efficient method. With the enhancement of computer capability, some expensive ab initio methods were also applied to predict the structures and properties of energetic molecules more accurately, such as coupled-cluster single-double (CCSD), Gaussian (Gn ), and complete active space self-consistent field (CASSCF). Meanwhile, MM and MD methods were established as well, and made great progress in energetic materials. Nowadays, it tends to establish a specific molecular forcefield (FF) with high accuracy for a given target energetic molecule. This highly accurate molecular FF combined with MC methods is the base for exactly predicting the crystal packing structure. Furthermore, MD methods based on DFT or a reactive molecular FF like ReaxFF were extensively employed to simulate the performances of energetic materials against external thermo-mechanical stimuli. Besides, dissipate particle dynamics (DPD) methods were used to predict phase state structure and property of energetic fluids at the mesoscale. Because the parameterization of DPD is mostly based on molecular simulations, DPD belongs to molecular simulation too. We retrieved the published papers about energetic materials, including computational energetic materials, molecular simulations on them and others, to know their

3.1 Introduction

43

2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001

EMs Computational EMs Molecular simulations of EMs

Year

2000 1999 1998 0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Paper number

Fig. 3.1 Comparison in published paper number from 1998 to 2018 of energetic materials, computational energetic materials and molecular simulations of energetic materials

development tendencies in the past 21 years (1998–2018). The reason why we choose 1998 as the beginning year is that is the time when the Nobel Prize in chemistry was awarded to John, A. Pople, and Walter Kohn, for their great contributions to molecular simulation. As demonstrated in Fig. 3.1, the quantity of papers related to energetic materials increased quickly since 2011. And total publications increased by about six times in the past 21 years. Moreover, among all papers about energetic materials, we find that the publications about computations and molecular simulations account for more than 1/2 and more than 1/4 of the total, respectively. Figure 3.2 indicates that weight of the molecular simulation papers maintains > 28% after 2007, showing that molecular simulation is a main means to study energetic materials.

3.1.2 Importance of Molecular Simulation Importance of molecular simulation can be embodied by Fig. 3.3. Combining theories, simulation methods, modeling mainly based on experimentally determined

44

3 Application of Molecular Simulation Methods in Treating Intrinsic … 32 30

Weight, %

28 26 24 22 20

19 9 19 8 9 20 9 0 20 0 0 20 1 02 20 0 20 3 0 20 4 05 20 0 20 6 0 20 7 0 20 8 09 20 1 20 0 11 20 1 20 2 1 20 3 1 20 4 1 20 5 1 20 6 17 20 18

18

Year Fig. 3.2 Evolution of the weight that the publications about molecular simulation account for among all energetic materials papers

structures, codes and computers, we can be able to produce the results of structure, property and performance, processing, and QSPR for energetic materials, which either have been experimentally observed or not. (a) Structural confirmation. By means of molecular simulation, we can confirm molecular geometric structure, electric structure, crystal packing structure, crystal defect, crystal shape, surface, and interfacial structures. Also, the structural evolution against external stimuli can also be ascertained. These structures can be either static or dynamic. Besides, experimental infrared, Raman, and nuclear magnetic resonance spectra can be assigned with the aid of molecular simulations. Thus, molecular simulation is regarded as the eyes of structural confirmation. (b) Property and performance prediction. As aforementioned, a strict requirement on overall properties and performances for an energetic material guarantees its practical application. The properties and performances include molecular stability, intermolecular interaction, density, thermodynamics, kinetics of synthesis, crystallization and decomposition, thermal property, mechanic property, thermo-mechanic response, other responses in some special physical fields like electricity and radiation, and so forth. Accurate predictions for these properties and performances will promote the creation and application of energetic materials. (c) Processing control. Molecular simulation is also a tool to help processing control. Different from the early research manner of trials and errors, current

3.1 Introduction Molecular design & synthesis

Molecule

Lattice

45 Simulation & Theoretical methods Quantum chemistry Molecular mechanics Molecular dynamics Dissipate particle dynamics Statistic mechanics Statistic method Multiscale shock technique Detonation theory ……

Crystal particle

+CODES PBX particle

Structures Geometric structure Electronic structure Packing structure Crystal defects

Molecular stability Thermodynamics Kinetics

Crystal habit

Density

Surface

Thermal property

Interface …

Detonation

Processes Molecular design Crystal design Interface design Synthesis design Crystallization control …

QSPR PBX block

Properties & Performances

Sensitivity Packing density …

Intermolecular interactions Polymorphic transition Mechanics Binding strength Mechanical response Thermo-mechanical coupling response Response to electric field or radiation …

Fig. 3.3 Scheme of the molecular simulation on energetic materials

researches feature forehand prediction and evaluation. Besides aforementioned structural ascertainment, it is also benefit for process control of energetic materials. Some special cases are the process control of organic synthesis (selections on reactant, solvent, temperature, agitation, etc.), crystallization (selections on solvent, ratio of solvate to solvent, agitation, container size, temperature, modifier, adding rate, etc.) and formulation (selections on additives, temperature, mechanic force, etc.), as well as molecular, crystal, and composite designs. The forehand molecular simulation, in combination with other numerical simulations, can largely save time, materials, and money, and help to effectively obtain high-quality products. (d) QSPR and theory establishment. The final importance of molecular simulation here is due to its aid to establish QSPRs and theories. A distinctive characteristic of molecular simulation is the idealization of the model involved. We can conveniently study an effect of a single factor by molecular simulation. However, we can hardly change one factor while fix the others in experiments. Consequently, many QSPRs and some theories related to some important properties and performance like energy and sensitivity can be constructed based on molecular simulation. These QSPRs and theories can guide the energetic material design and deepen the understandings of energetic materials. In a word, the increasing attention is paid to energetic materials due their importance for civilian and military purposes, in which the molecular simulation possesses a high weight of 28% from the viewpoint of publication amount. This high weight is attributed to the great progress of the molecular simulation itself and the broadening of molecular simulation applications to energetic materials. Besides, molecular

46

3 Application of Molecular Simulation Methods in Treating Intrinsic …

simulation is now facing a great opportunity with the coming of the new era of big data, which will promote its application in energetic materials. After introduction, the remaining of this chapter is organized as follows. In Sect. 3.2, the applications of QC methods on energetic molecules are briefed. The applications of the molecular simulation methods dealing with energetic crystals are introduced from Sects. 3.3 to 3.5, including dispersion-corrected DFT, molecular FF and Hirshfeld surface analysis. Also, the codes applied to energetic molecules and crystals are briefed in Sect. 3.6 finally.

3.2 Quantum Chemical Methods for Treating Energetic Molecules As an important division of molecular simulation methods, QC generally presents high reliability for a larger range of predictions [1]. Earlier, the use of QC methods in energetic materials covers many aspects, such as the understandings and predictions of molecular structure, crystal structure, intermolecular interaction, thermodynamic property, mechanisms of decomposition, sensitivity and compatibility, and performance under extremely high temperature and pressure. Also, they were employed for calculating or predicting key parameters of energetic materials, such as HOF, vd , Pd , and impact sensitivity [2]. In general, sensitivity of energetic materials is primarily and strongly governed by their reactivity against external stimuli. Energetic molecules, as the basic bricks of energetic materials, can be dealt by QC methods readily. For example, a most general issue is molecular reactivity, or molecular stability, which can be thermodynamic or kinetic. The thermodynamic stability of an energetic molecule refers to the energy change after it changes to products. If the energy decreases more, it means the higher thermodynamic instability. The kinetic stability can be reflected by the energy barrier height from reactant to product. The higher barrier, the higher kinetic stability. This section focuses upon the applications of some QC methods that have been extensively applied in energetic molecules.

3.2.1 Quantum Chemical Methods Energetic molecules generally consist of C, H, O, and N atoms, as well as halogen atoms sometimes. Figure 3.4 illustrates some objects treated by QC at molecular scale, such as isolated neutral molecule, ion, dimer, and polymer. Therein, it covers Hartree Fock (HF), semi-empirical, DFT, and high-level ab initio methods. In principle, it requires a good trade-off between accuracy and cost to treat differentlysized energetic molecules well. By means of QC calculations, many properties can be predicted for energetic molecules, including electron density, molecular orbital (MO), electrostatic potential (ESP), heat of formation (HOF), and bond dissociation

3.2 Quantum Chemical Methods for Treating Energetic Molecules

47

energy (BDE). Thereby, some macroscopic performances like detonation performances and sensitivity can be further deduced or predicted, as shown in Fig. 3.5. The molecular design of energetic materials just usually proceeds along this way. For example, EM-Studio 1.0 [3], as the first high-throughput computing interactive application system for energetic materials, makes all the related procedures in a flow and accelerates the computation and analysis efficiency significantly. The principle of QC can be referred elsewhere, and the core is to solve the Schrödinger equation [4]. As exhibited in Fig. 3.6a, with respect to energetic molecules, the applied QC methods can be divided into four categories, including HF, semi-empirical, DFT, and high-level ab initio methods. First of all, HF features a mean-field technique for searching the dominant Slater determinant in the system wave function, by means of the optimization of the spatial form of the spin orbitals [6]. The related properties cannot be well predicted based on HF method since it does not account for the electron correlation effect. Thus, it is seldom adopted to calculate energy barrier or bond dissociation energy, in particular for conjugated systems or lone pairs containing systems. Semi-empirical QC methods refer to intermediate neglect of differential overlap (INDO), complete neglect of differential overlap (CNDO), modified neglect of differential overlap (MNDO), AM1, PM

Energetic molecules Traditional energetic molecules

TNT

TATB

Full-nitrogen molecules

Cations/anions

Dimers

LLM-105 N4(Td)

AFTA

BT2O

TNB-TNB

N6(D3h)

DNABF

DNBTO

DATB-DATB

N8(Oh)

DBO

NO3-

TATB-TATB

N10(D5h)

BTO

ClO4-

TNA-TNA

CL-20

RDX

PETN

FOX-7

Tetryl

TNA

HMX

Fig. 3.4 Various types of objects in the energetic molecule calculations. The gray, green, red, and blue balls represent the C, H, O, and N atoms, respectively

48

3 Application of Molecular Simulation Methods in Treating Intrinsic …

Fig. 3.5 Properties and performances derived from QC calculations. The inner and outer circles represent the calculated microscopic indexes from molecular structure, and the properties of molecules that can be deduced from microscopic indexes in conjunction with relevant theories, respectively

Fig. 3.6 QC methods and some trade-offs thereof. a QC methods for treating energetic molecules. b The dependence of system size, computational cost and computational accuracy of QC methods. Reprinted with permission from Ref. [5]. Copyright 2021 Elsevier

3.2 Quantum Chemical Methods for Treating Energetic Molecules

49

serials, etc. [7–13]. This group of methods generally deals with larger systems more quickly, compared with HF, DFT, and high-accuracy ab initio methods, because the integrals in solving Schrödinger equation are greatly reduced by approximations. PM3 and AM1 perform similarly and is usually apt to geometric prediction, while inapt to energy calculation. In contrast to previous version, PM6 and PM7 have been greatly improved, thus regarded as a standard of general semi-empirical methods [12, 13]. High-accuracy ab initio methods refer to MPn , Gn , CI, CC, CBS, and CASSCF [14–17], with consideration of electron correlation. They are extensively adopted to predict molecular geometry, energy, vibration, etc., for the purposes of both theory and experiment. Many researches showed that G4 provides both accurate and economical prediction for thermodynamics results [18, 19], while CBSQB3 is much fitter to predict E a [20]. As a highly efficient and reliable QC method, DFT is indispensable in the modeling of materials, physics and chemistry. As the core of DFT, the Hohenberg-Kohn theorem suggests that all properties in ground state of a molecule are determined by the electron density [21]. DFT is the most popular and successful QC method, since it balances well the conflict between accuracy and computational consumption. Nowadays, B3LYP, as the most popular functional, is prone to be replaced by new ones, like the M06 families with better overall performance [22]. In general, the higher accuracy goes along with more time consumed, so the methods with higher accuracy are fit to smaller systems [23]. Figure 3.6b shows that the accuracy generally increases from semi-empirical to HF, DFT, and highlevel ab initio methods, while with time cost significantly increased and applicable system size reduced. Largely, the semi-empirical methods are usually apt to energetic oligomers; HF is suitable for analyzing MOs, such as their composition and energy levels, but its use is increasingly lessened; the high-level ab initio methods are apt to the energy calculations of small systems; while DFT methods are applied the most extensively, even for a system with > 1000 atoms.

3.2.2 Description for Geometric Structure In this section, we exemplify the application of QC methods for treating energetic molecules, covering many issues, such as geometric structure, thermodynamics, electronic structure, and reactivity (Fig. 3.7). Usually, an energetic molecule construction is required to be optimized to be a local or global energy minimum conformation, for discussing following properties, but the subsequent accurate predictions are implemented from the global energy minimum, instead of a local one. Molecular geometry is often described by the bond lengths, bond angles, and dihedral angles. It is feasible to obtain the energy minima by scanning the related bond lengths, dihedral angles, and the total energy. For common CHNO energetic molecules, DFT method at a usual level of B3LYP/6-311G** can present satisfactory geometric structures [24]. Molecular geometry can reflect molecular stability, i.e., the more deviation from the normal

50

3 Application of Molecular Simulation Methods in Treating Intrinsic …

Fig. 3.7 Application of the QC methods for treating energetic molecules

structure usually suggests the less stability. Of course, a comprehensive combination of geometry, electron, and energy will provide more reliable confirmation.

3.2.3 Description for Electronic Structure In contrast to the aforementioned geometric optimization, more values can be embodied when QC methods applied to explore electronic structures, including electron density, charge, ESP, HOMO and LUMO, bond order, excited state, etc., as shown in Fig. 3.8. Electron density is a measurable variable, presenting lots of electronic information [25]. Bader’s theory of Atoms in Molecules (AIM) [26] provides a straightforward tool with wave function to understand the nature of chemical bond and reactivity. In general, the higher electron density suggests the more electrons located, and further the stronger bonding and the higher molecular stability. Thus, a high electron density of the trigger bond of an energetic molecule suggests higher molecular stability and further the lower impact sensitivity of the compound, since molecular stability is a main indicator of impact sensitivity [27]. B3LYP/6-31G** is a common level of electron density calculations, due to its economic advantage over MP2 and CCSD(T) [28, 29]. For example, on this level, Rice et al. predicted the dc of 180 energetic compounds composed of C, H, N, and O atoms, based on a method of volume enclosed by a specified isosurface with an electronic density of 0.001 a.u., in good agreement with experimental results [30].

3.2 Quantum Chemical Methods for Treating Energetic Molecules

51

Electronic Structure

Fig. 3.8 Electronic structures and properties of energetic molecules

ESP can also reflect electronic structure, as it provides information about charge density distribution and further molecular reactivity. Therefore, it is a common tool for understanding intermolecular interaction and corresponding impact sensitivity [31, 32]. In principle, the more negative ESP suggests the larger electron density, the stronger bonding, the higher molecular stability, and lower sensitivity. This roots for the ESP-impact sensitivity relationship proposed by Murray et al. [33]. The ESPs of six energetic nitrobenzene molecules (Fig. 3.9) indicate that the positive ESP is mostly positioned on the center and partly at the edge of any molecule, corresponding to areas of benzene ring, and H, NH2 , and CH3 , respectively, while all the negative ones appear at the molecular edge of the area of NO2 . Klapötke et al. proposed that the alternate arrangement of positive and negative ESPs facilitates the enhancement of molecular stability [34]. Besides, the charge distribution is also indicative of chemical reactivity and electrostatic interactions, as ESP. For example, the charge of specified atoms or groups contained in trigger bonds, such as nitro group charge (Q NO2 ) and azide group charge (Q N3 ), has been adopted to assess molecular stability and further impact sensitivity of the related compounds [35, 36]. Among MOs, the frontier ones, including HOMO and LUMO, represent the capabilities of denoting and accepting electrons. Their difference (△E LUMO-HOMO ), energy gap, is an important parameter indicative of the chemical reactivity and kinetic

52

3 Application of Molecular Simulation Methods in Treating Intrinsic …

Fig. 3.9 ESPs of the six nitrobenzene molecules at a density of 0.001 a.u. The orange and blue values indicate the maximum and minimum ESP points on each surface, respectively. Reprinted with permission from Ref. [5]. Copyright 2021 Elsevier

stability against photic stimulation. For example, RDX and HMX possess high photic insensitivity, due to the large energy gaps of 5.634 and 5.304 eV, respectively [37, 38]. Furthermore, the high temperature, as a consequence of the decomposition of energetic materials, can cause reactions with electronic excited states, which may influence the total decomposition reaction in turn. Recently, the optically excited dissociation processes of TATB, RDX, and NM molecules were studied using timedependent DFT combined with MD simulations [39]. Therein, it was found that the elevation of initial temperature broadens the energy gap. As time proceeds, the LUMO energy continues decreasing, while HOMO energy rising, accompanied by oscillations of various frequencies. Although the high temperature can cause the electronic excitation, the heat-induced ignition of energetic materials is extensively accepted.

3.2.4 Description for Energetics HOF is a fundamental index of the energetics for energetic molecules. Thus, it is of great interest in exactly predicting it. Up to the present, there are three schemes for HOF calculation: atomization, atomic equivalent, and isodesmic reaction (Fig. 3.10a). HOF is predicted in the atomization scheme by means of an atomization reaction, with the known HOFs of isolated atoms. The atomic equivalent scheme differs from the atomization scheme with the concept of equivalent only. The prediction accuracy of these two schemes significantly depends on the levels of QC methods

3.2 Quantum Chemical Methods for Treating Energetic Molecules

53

used. In comparison, the isodesmic reaction scheme generally presents more accurate prediction of HOF, with a small dependence on the QC methods. Thus, this scheme is especially suitable for big molecules. In this scheme, molecular skeleton, small substitutes, and quantities of chemical bonds and electron pairs should be maintained in the designed isodesmic reaction, i.e., the electronic circumstance of any atom stays invariable. Thereby, the HOF of a target energetic molecule is calculated based on Hess law [40], and the accurate predicted and referred HOFs of all the molecules involved in the reaction. Figure 3.10b exhibits the highest accuracy of PM3 in calculating the HOFs of methane and its nitro derivatives, followed by AM1 and MNDO [41]. Thus, PM3 is fit to larger systems when any DFT method is infeasible. Figure 3.10c ascertains the highest reliability of MP2/6-311G**, B3LYP/6-311G**, and B3P86/6-311G** to the HOF predictions of 1,2,4,5-tetrazine compounds, whereas HF method does not perform well in this case [42]. Checking the root mean square deviation (RMSD) and mean absolute deviation (MAD) of HOFs calculated by various DFT methods at the same basis set of 6-311+G**, and comparing with the benchmark G4 calculated results, Gu et al. confirmed the highest accuracy of the hybrid meta-generalized

Fig. 3.10 HOF prediction by various QC methods. The methods for calculating HOF (a). HOFs of methane and its nitro derivatives calculated using semiempirical QC methods and compared with experimental (b). Reprinted with permission from Ref. [41]. Copyright 2007 American Chemical Society. Calculation of HOFs of 1,2,4,5-tetrazine derivatives by different QC methods (c). RMSD and MAD of calculated HOFs at various levels (d). MUE, MSE, and MAD for individual compound methods, and combinations thereof, upon comparison with the ATcT (e). Reprinted with permission from Ref. [46]. Copyright 2015 American Chemical Society

54

3 Application of Molecular Simulation Methods in Treating Intrinsic …

gradient approximation (meta-GGA), as demonstrated in Fig. 3.10d [43]. Besides, Fig. 3.10e shows the prediction accuracy of some composite methods and their combinations in calculating the HOFs of 38 molecules, which decreases as G4 , G3 , W1BD, CBS-APNO, and CBS-QB3, based on the mean unsigned errors (MUE) and mean signed errors (MSE) analyses in comparison to the references in Active Thermochemical Tables (ATcT) [44–46]. Additionally, it is a trend for molecular design of energetic materials to extend single molecule to two or multiple ones to describe molecular stacking, since the latter presents a much closer prediction to the practice. Therein, the accurate calculation of intermolecular interaction is the core, as it governs the crystal packing. As the simplest case, dimerization energy of two molecules is adopted to understand molecular stacking and construct molecular FF [47]. Furthermore, vibration is another characteristic of energetics, and QC calculations are generally used to assign infrared and Raman spectra.

3.2.5 Description for Reactivity Acceptable sensitivity is indispensable to guarantee the safety during the lifetime of energetic materials. BDE is an elementary indicator of molecular stability, i.e., the smaller BDE, the weaker the trigger bond, the lower molecular stability, and the higher reactivity [48]. The NO2 partition is usually seen to trigger the decomposition of energetic nitro molecules. Thus, the related BDE is adopted to primarily assess molecular stability and further sensitivity. For a group of molecules with R–N3 /NH2 / NO2 bonds (R = methyl, phenyl, and trinitromethyl), it showed the highest accuracy of the M06 functionals with the basis set 6-31+G*, followed by MPWB1K, BB1K, B3P86, and other functionals [49], compared with experimental determination [50]. Energy barrier is a kinetic indicator of reactivity. For example, the hydrogen-transfer was revealed in a series of heated energetic molecules, and the reversible hydrogen transfer was found to be partly responsible for the low sensitivity of some energetic compounds [51]. Also, revealing synthesis mechanism is of benefit to design more effective techniques for creating new energetic molecules. Recently, pentazole ring (cyclo-N5 ) received increasing attention for its interesting structure and potential as energetic materials [52, 53].

3.3 Dispersion-Corrected DFT Methods and Their Application In this section, we focus upon the reliability of various dispersion-corrected DFT methods to the predictions of density, lattice parameter, and LE, as well as computation consumption. In general, three categories are included in dispersion correction

3.3 Dispersion-Corrected DFT Methods and Their Application

55

methods, including nonlocal density-based dispersion corrections (I), semi-classical treatments of the dispersion interaction (II), and effective one-electron potentials and further aspects (III) [54]. For category I, the medium- and long-range interactions are described by a traditional exchange-correlation functional with nonlocal correlation energy added, such as various vdW density functionals (vdW-DFs) [55–60]. In fact, it is a non-empirical approach, based on that dispersion energy is determined by electron density only. The functional of revPBE is adopted in original vdW-DF, while PW86 in vdW-DF2. Later, people proposed other optimized methods, such as optB86b-vdW, optB88-vdW, and optBPE-vdW [56–58, 60]. As to category II, interatomic interaction potentials are directly added to the traditional DFT. DFT-D [61–63], DFT-TS [64], and some of their extensions belong to this category. The widely applied DFT-D2 only accounts for two-body dispersion energy by adding a purely empirical correction [61]. In comparison, the three-body dispersion energy is included in DFT-D3 [62], which can be further distinguished as DFT-D3(0) [62] and DFT-D3(BJ) [63]. DFT-TS is an electron density-dependent and atom pairwise method, with dispersion energy description similar to DFT-D2 [64–70]. With respect to Category III [71–74], the methods thereof usually behave badly, and their application is restricted. Recently, Liu et al. calculated the lattice parameters and LE for 54 energetic crystals, including ε-CL-20 and 53 energetic cocrystals (ECCs), to verify the accuracy and efficiency of the above methods [75]. These ECCs are categorized into three groups, in terms of the component and intermolecular interaction characteristics. The first 18 ECCs are based on CL-20 (labeled as C-ECCs), in which the common weak interactions are dominant, without π-π stacking and strong HB therein. π-π stacking and rather strong HB govern the intermolecular interactions in the second group of 21 TNT-based ECCs, as labeled by T-ECCs, and the third groups of 15 ECCs (labeled as H-ECCs), respectively, as listed in Table 3.1. It should be noted that this verification on these ECCs should also be feasible to single-component crystals, due to their similar components and intermolecular interactions. There were totally 14 methods adopted for the verification of computational accuracy and efficiency on the 54 energetic crystals, including the original PBE, vdWDF, vdW-DF2, optPBE-vdW, optB88-vdW, optB86b-vdW, D2, D3(0), D3(BJ), TS, TS(HI), TS(SCS) (self-consistent screening), MBD (many-body dispersion), and dDsC (density-dependent energy correction) combined with GGA-PBE each [75, 76]. In calculations, some parameters of the default sets were adopted, with ENCUT = 800 eV, EDIFF = 1 × 10−4 , and KSPACING = 0.5 [75]. Meanwhile, relative deviation (RD), RMSD, relative average deviation (RAD), and maximal relative deviation (RDmax ) are employed to evaluate the accuracy.

3.3.1 Reliability to Density Prediction Figure 3.11 exhibits a largely underestimated density of any ECC by the pure PBE, since it does not account for dispersion correction, as found in previous work [77, 78].

56

3 Application of Molecular Simulation Methods in Treating Intrinsic …

Table 3.1 Molecular ratio (MR), formula, space group (SG), measurement temperature (T), number of atoms in unit cell (Natom ) and labels of 53 interested ECCs and ε-CL-20 [75] Crystal

MR

Formula

SG

T, K

Natom

Label

ε-CL-20

\

C24 H24 N48 O48

P21/N

293

144

C-1

CL-20/1,4-DNI

1:1

C36 H32 N64 O64

P212121

296

196

C-2

CL-20/2,4-MDNI

1:1

C40 H40 N64 O64

P21/N

130

208

C-3

CL-20/4,5-MDNI

1:1

C80 H80 N128 O128

PBCA

130

416

C-4

CL-20/4,5-MDNI

1:3

C72 H72 N96 O96

P-1

130

336

C-5

CL-20/AZ1

1:1

C24 H14 N38 O30

P21

100

106

C-6

CL-20/AZ2

1:1

C24 H16 N40 O30

P21

150

110

C-7

CL-20/BTF

1:1

C48 H24 N72 O72

P212121

293

216

C-8

CL-20/DNB

1:1

C96 H80 N112 O128

PBCA

293

416

C-9

CL-20/DNG

1:1

C22 H36 N32 O32

P21

200

122

C-10

CL-20/DNDAP

2:1

C60 H80 N112 O112

P21/C

296

364

C-11

CL-20/DNT

1:2

C40 H36 N32 O40

P-1

296

148

C-12

CL-20/HMX

2:1

C32 H40 N64 O64

P21/C

95

200

C-13

CL-20/MAM

1:2

C80 H144 N128 O128

PBCN

200

480

C-14

CL-20/MDNT

1:1

C36 H36 N68 O64

P212121

95

204

C-15

CL-20/MNO

2:1

C32 H36 N56 O60

P21

150

184

C-16

CL-20/MTNP

1:1

C20 H18 N34 O36

P21

293

108

C-17

CL-20/TNT

1:1

C104 H88 N120 O144

PBCA

95

456

C-18

TNT/1-BN

1:1

C34 H24 N6 O12 Br2

P-1

95

78

T-1

TNT/9-BN

1:1

C42 H28 N6 O12 Br2

P-1

95

90

T-2

TNT/AA-1

1:1

C28 H24 N8 O16

P-1

95

76

T-3

TNT/AA-2

1:2

C84 H76 N20 O40

P-1

95

220

T-4

TNT/ABA-1

1:1

C56 H48 N16 O22

P21

95

152

T-5

TNT/ABA-2

1:2

C84 H76 N20 O40

P21/C

95

220

T-6

TNT/Ant

1:1

C84 H60 N12 O24

P21/C

95

180

T-7

TNT/BTF

1:1

C52 H20 N36 O48

P-1

145

156

T-8

TNT/DBZ

1:1

C152 H104 N24 O48 S8

P21/N

95

336

T-9

TNT/DMB

1:1

C60 H60 N12 O32

P21/N

95

164

T-10

TNT/DMDBT

1:1

C42 H34 N6 O12 S2

P-1

95

96

T-11

TNT/Nap

1:1

C34 H26 N6 O12

P-1

95

78

T-12

TNT/NN

1:1

C34 H24 N8 O16

P-1

296

82

T-13

TNT/PA

1:1

C76 H56 N16 O24 S4

P212121

95

176

T-14

TNT/PDA

1:1

C52 H52 N20 O24

PNA21

95

148

T-15

TNT/Per

1:1

C108 H68 N12 O24

P212121

95

212

T-16

TNT/Phe

1:1

C84 H60 N12 O24

P212121

95

180

T-17 (continued)

3.3 Dispersion-Corrected DFT Methods and Their Application

57

Table 3.1 (continued) Crystal

MR

Formula

SG

T, K

Natom

Label

TNT/Pyr

1:1

C92 H60 N12 O24

P-1

293

188

T-18

TNT/T2

1:1

C26 H18 N6 O12 S4

P-1

TNT/TNB

1:1

C52 H32 N24 O48

P21/C

TNT/TT

1:1

C26 H18 N6 O12 S8

P-1

95

66

T-19

293

156

T-20

95

70

T-21

aTRz/DNBT

1:1

C16 H12 N32 O8

P21/C

153

68

H-1

aTRz/DNM

1:2

C20 H16 N32 O16

P21/C

153

84

H-2

aTRz/DNP

1:1

C28 H24 N48 O16

P21/N

153

116

H-3

BTATz/2-pyridone

1:4

C24 H24 N18 O4

P-1

85

70

H-4

BTATz/DMF

1:2

C20 H36 N32 O4

P-1

85

92

H-5

BTATz/pyrazine

1:1

C8 H8 N16

P-1

85

32

H-6

BTATz/pyridine

1:4

C47.20 H47.20 N33.20

P21/C

85

132

H-7

BTNMBT/MATZ

1:1

C32 H28 N56.48 O24.96

P21/C

298

176

H-8

BTNMBT/TZ

1:2

C40 H32 N72 O48

P1

298

192

H-9

EDNA/A3

1:1

C96 H112 N48 O32

C2/C

120

288

H-10

EDNA/A4

1:1

C28 H36 N12 O8

P-1

120

84

H-11

EDNA/A5

1:1

C14 H16 N6 O4

P-1

120

40

H-12

EDNA/A7

1:1

C12 H14 N8 O4

P-1

120

38

H-13

EDNA/A8

1:1

C6 H10 N6 O6

P-1

120

28

H-14

EDNA/A12

1:2

C96 H96 N40 O16

C2/C

120

248

H-15

Following the original PBE, vdW-DF underestimates density too, as proven previously [57]. In comparison, dDsC, optB88-vdW, and optB86b-vdW present overestimated density more or less. In general, D2 presents relatively small RDs for C-ECCs, but rather large ones for both T-ECCs and H-ECCs; and D3(0), D3(BJ), TS, TS(HI), optBPE-vdW, and vdW-DF2 behave better among the all 14 methods [75]. These methods were further assessed by RAD, RMSD, and RDmax . Regarding the first group of energetic crystals, as exhibited in Fig. 3.12a, the smallest RAD (0.9%) is provided by optPBE-vdW, showing the highest accuracy, followed by vdW-DF2 (1.06%), D2 (1.18%), D3(0) (1.44%), TS (1.58%), and D3(BJ) (1.61%). In fact, the three most accurate methods behave similarly, with the largest difference in RAD of 0.28% only. A recent verification showed the more appropriateness of optPBE-vdW and vdW-DF2 to new and disordered systems [57, 58, 79, 80]. While, D3(0) and optPBE-vdW differ in the RAD of 0.54%, about twice of 0.28%, so the preferred method for C-ECCs is not D3(0). Moreover, the high accuracy of the six methods is also verified by their RMSDs, which are all smaller than 0.04 g/cm3 . Furthermore, the RDmax ranges from 2.5% to 4.0% (Fig. 3.13a), where C-4, C-12, C-13, and C-18 are in the forefront. It can be understandable for their large RDmax , because the dispersion energy is corrected in terms of the structures at ambient conditions, while their crystallographic information is collected below the room temperature. In general,

58

3 Application of Molecular Simulation Methods in Treating Intrinsic … PBE dDsC

D3(0) optPBE

D2 vdW-DF

TS optB86b

D3(BJ) optB88

TS(HI) vdW-DF2

8

RD, %

4 0 -4 -8 -12 -16 C-1

C-2

C-3

C-4

C-5

C-6

C-7

C-8

C-9 C-10 C-11 C-12 C-13 C-14 C-15 C-16 C-17 C-18

8

RD, %

4 0 -4 -8 -12 -16 T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 T-11 T-12 T-13 T-14 T-15 T-16 T-17 T-18 T-19 T-20 T-21 8

RD, %

4 0 -4 -8 -12 -16 H-1

H-2

H-3

H-4

H-5

H-6

H-7

H-8

H-9

H-10

H-11

H-12

H-13

H-14

H-15

Fig. 3.11 RDs of densities derived from various dispersion-corrected methods. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

optPBE-vdW behaves the best for common weak interactions consolidated systems like C-ECCs, followed by vdW-DF2 and D2. Regarding T-ECCs, Fig. 3.12b shows the smallest RAD (0.85%) comes from optPBE-vdW, showing the highest accuracy. In fact, D3(0) (0.86%), D3(BJ) (1.01%), and TS (1.10%), as well as TS(HI) (1.41%) and vdW-DF2 (1.67%), are feasible to T-ECCs too. This can be ascertained again by the RMSD in Fig. 3.12b. Previously, the excellent viability of D3 to describe the noncovalent interactions in aromatic systems was confirmed [81]. The largest RDmax shown in Fig. 3.13b is of T-18, followed by T-8 and T-20. In fact, the largest RDmax of T-18 is derived from many methods, possibly due to a complex conjugated structure of pyrene. Therefore, optPBE-vdW presents the highest accuracy for TECCs, which are consolidated by π-π stacking, followed by D3(0), D3(BJ), and TS. As to H-ECCs, D3(BJ), D3(0)), and TS act as the three most accurate methods, with

3.3 Dispersion-Corrected DFT Methods and Their Application RAD RMSD

7

(a) C-ECCs

0.10 0.08

4

0.06

3 0.04 0.02

0

5

0.08

4

0.06

3

D2 3(0) D

0.02

1

0.00

E F2 tPB -D op vdW

0

0.00

E (0) J) tPB D3 D3(B op

TS (BJ) (HI) DsC 86b tB88 -DF d ptB op dW TS D3 v o

7

TS (HI) -DF2 86b TS dW optB v

D2 tB88 DsC -DF d dW op v

7

(c) H-ECCs

0.10 0.08

4

0.06

3 0.04 2

RAD RMSD

(d) All ECCs

0.10

5

0.08

4

0.06

3 0.04

RMSD, g/cm3

5

6

RAD, %

RAD RMSD

RMSD, g/cm3

RAD, %

0.10

2

1

2 0.02

1 0 (B D3

(b) T-ECCs

0.04

2

6

RAD RMSD

RMSD, g/cm3

5

6

RMSD, g/cm3

RAD, %

6

RAD, %

7

59

0.00 J) 3(0) D

TS (HI) tPBE -DF2 TS op dW v

D2 86b tB88 DsC -DF d dW tB op v op

0.02

1 0 (0) BE BJ) D3 optP D3(

0.00 TS -DF2 (HI) TS W vd

D2 86b DsC tB88 -DF d op dW tB v op

Fig. 3.12 RAD and RMSD of density of various dispersion-corrected methods. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

RD < 1% and RMSD < 0.03 g/cm3 (Fig. 3.12c). The high viability of D3(BJ) was also verified to 42 small intermolecular HB dimers [82]. Because A8, a coformer of H-14, features an O-based HB acceptor, the strong HB is formed via the acidic protons [83]. This strong HB of H-14 much differs from those in other ECCs, and leads to the largest RDmax , derived from most methods (Fig. 3.13c). From above discussion, we can know that the feasibility of some methods is sensitive to the intermolecular interaction type. For example, with respect to D2, it presents a RAD of 1.18% for C-ECCs, while > 3% for the H-ECCs and T-ECCs. In general, D3(0) behaves the best, followed by optPBE-vdW (1.02%), D3(BJ) (1.09%), TS (1.18%), vdW-DF2 (1.58%), and TS(HI) (1.67%) (Fig. 3.12d), as verified previously [54, 76, 79, 84].

3.3.2 Reliability to Geometric Prediction Furthermore, the calculated unit cell parameters are also employed to assess the feasibility of these methods. First of all, there is generally a slight difference observed in axial angles, while a large one in axial length. Next, it is ready to make sure the similar accuracy of any method by analyzing both the density and axial length, with only a few exceptions. Despite a slightly different deviation of the three axes possibly caused by the same method, a negligible impact on the description of accuracy is

60

3 Application of Molecular Simulation Methods in Treating Intrinsic … 6

(a) C-ECCs

(b) T-ECCs

5 T-18 T-18

RDmax, %

4 C-12

3

C-4

C-13

C-18

C-18

3.09

2.97

TS

D3(BJ)

T-20

3.33

2.73

2.6

optPBE

vdW-DF2

1

6

T-20

4.01

2

0

T-8

T-18

C-13

2.85

D2

D3(0)

(c) H-ECCs

3.22

3.04

optPBE

D3(0)

4.31 3.25

D3(BJ)

TS

TS(HI)

2.95

vdW-DF2

(d) All-ECCs

5 T-18

H-14

T-18

RDmax, %

4 H-9

T-18

H-14

H-14

T-20

3 2 1 0

H-14

H-14 H-14

2.01

1.89

D3(BJ)

D3(0)

4.07

4.01 3.21

3.04

3.22

optPBE

D3(0)

optPBE

4.31

3.89

4.07

vdW-DF2

TS(HI)

2.23

TS

TS(HI)

D3(BJ)

TS

Fig. 3.13 RDmax of various dispersion correction methods. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

produced with respect to the entire cell [85]. As illustrated in Fig. 3.14, the above best methods for the density prediction also present the best prediction of lattice parameters, with RAD < 1% and RMSD < 0.16 Å, apart from the large deviations of a of T-ECCs by D3(BJ), suggesting that it is feasible to assess the prediction accuracy of lattice structures through that of density. Nevertheless, it should be noted that the axial lengths of some ECCs, such as C-4, C-8, C-13, T-14, T-18, T-21, H-2, H-7, and H-9, are overestimated or underestimated, with RD < 2%, possibly due to the crystallographic determination below the room temperature. In terms of the deviations shown in Fig. 3.14, optPBE-vdW and D3(BJ) behave the best for C-ECCs and T-ECCs, and H-ECCs, respectively. Regardless of the type of ECCs, D3(0) is the most suitable to describe lattice parameters, followed by optPBE-vdW, D3(BJ), and TS.

3.3.3 Reliability to Lattice Energy Prediction LE of a crystal represents the strength of intermolecular interactions therein, and it was also adopted to evaluate the viability [75]. To date, there is no report about the LE of ECCs, thus the accurate predictions of LE are of great interest. However, it should still be faced up to a difficulty in achieving highly accurate LE and dc by the same method, and the balanced dispersion correction methods are generally sought for

3.3 Dispersion-Corrected DFT Methods and Their Application a 1.2

b

61

c

(a) C-ECCs

(c) H-ECCs

(b) T-ECCs

1.0

0.6 0.38

0.54

0.47

0.3

0.4

0.36

0.47

0.46

0.7 0.69 0.52

0.39

0.65

0.69 0.49

0.47

0.44

0.38

0.43

0.41

0.32

0.54

0.47

0.2

0.38

0.4

0.95

1.07

0.6 0.74 0.59 0.41

RAD, %

0.8

0.0 (e) T-ECCs

(d) C-ECCs

(f) H-ECCs

vdW-DF2

D3(0)

D3(BJ)

D3(0)

D3(BJ)

0.072

0.077

0.064

0.067

0.061

0.041

0.062

optPBE

0.055

TS

0.051

0.146 0.119 0.142

0.115 0.089 0.117

0.115

0.076

0.055

0.081

0.049

optPBE

0.12 0.105 0.122

D2

0.111 0.122 0.104

0.00

0.09

0.04

0.142

0.08

0.102

0.12

0.047

RMSD, Å

0.16

TS

Fig. 3.14 RADs and RMSDs of calculated axial lengths a, b, and c, for the three groups of ECCs. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

[86]. Based on aforementioned best methods for describing lattice parameters and density, Liu et al. employed 21 molecular crystals with experimental sublimation enthalpies as a benchmark set, and calculated their LE to identify the viability of the methods that are the most suitable for the above geometry optimization to the LE prediction [75, 77]. The predicted LE is sensitive to the methods applied and shows large RADs > 10% from experimental measurements [75], as exhibited previously [77, 87], showing again the disagreement of accuracy between structure and energy predictions by the same method [86–88]. By comparison, Liu et al. ascertained that PBE-D3(BJ) and PBE-D3(0), and vdW-DF2 and PBE-D2 are the most suitable to predict LE for T- and H-ECCs, and C-ECCs, respectively [75]. Table 3.2 shows the increased LE of C-2 to C-18 compared to ε-CL-20, ascribed to the addition of coformer molecules in asymmetric unit. That is, the most significantly increased LE is exhibited in C-5 (573.7 kJ/mol), C-12 (424.9 kJ/mol), and C-14 (373.3 kJ/mol), which possess three, two, and two coformer molecules per asymmetric unit, respectively. In the same way, the lager LE of T-4 and T-6 compared with other T-ECCs can be understandable. In general, the larger LE appears in HECCs, due to the stronger intermolecular interaction of HB. Furthermore, CED is adopted to assess the strength of intermolecular interactions to avoid an issue of different molecular quantity in asymmetric unit, which means no benchmark for the comparison of interaction strength. The CEDs of C-ECCs, T-ECCs, and H-ECCs in Table 3.3 are fallen in the ranges of 0.80–1.10, 0.66–1.12, and 0.92–1.72 kJ/cm3 , respectively, showing a reduction in the strength of molecular interactions from HB

62

3 Application of Molecular Simulation Methods in Treating Intrinsic …

Table 3.2 LE (in kJ/mol) of C-ECCs calculated by vdW-DF2, and of T- and H-ECCs by PBED3(BJ) [75] ECC

LE

ECC

LE

ECC

LE

ECC

LE

ECC

LE

ECC

LE

C-1

195.9

C-10

318.1

T-1

193.3

T-10

185.5

T-19

189.1

H-7

519.1

C-2

301.4

C-11

257.9

T-2

215.5

T-11

218.2

T-20

193.2

H-8

373.5

C-3

328.3

C-12

424.9

T-3

219.8

T-12

186.1

T-21

225.9

H-9

371.0

C-4

300.1

C-13

284.3

T-4

333.9

T-13

195.8

H-1

316.6

H-10

259.5

C-5

573.7

C-14

373.3

T-5

232.8

T-14

230.6

H-2

390.7

H-11

274.2

C-6

327.7

C-15

311.3

T-6

368.7

T-15

207.8

H-3

245.9

H-12

287.3

C-7

332.2

C-16

242.1

T-7

209.4

T-16

237.9

H-4

666.2

H-13

266.4

C-8

290.3

C-17

337.7

T-8

179.1

T-17

203.8

H-5

376.8

H-14

249.2

C-9

299.4

C-18

318.4

T-9

206.3

T-18

215.1

H-6

328.1

H-15

373.7

Note LE is denoted in terms of molecular number in asymmetric unit

Table 3.3 CED (in kJ/cm3 ) of C-ECCs calculated by vdW-DF2, and of T- and H-ECCs by PBED3(BJ) [75] Name

CED

Name

CED

Name

CED

Name

CED

Name

CED

Name

CED

C-1

0.91

C-10

0.89

T-1

0.77

T-10

0.76

T-19

0.86

H-7

1.33

C-2

0.98

C-11

0.94

T-2

0.75

T-11

0.75

T-20

0.73

H-8

0.92

C-3

1.01

C-12

0.96

T-3

0.96

T-12

0.78

T-21

0.90

H-9

1.08

C-4

0.92

C-13

0.96

T-4

1.04

T-13

0.78

H-1

1.34

H-10

1.26

C-5

1.10

C-14

1.05

T-5

1.01

T-14

0.86

H-2

1.39

H-11

1.15

C-6

0.98

C-15

0.97

T-6

1.12

T-15

0.99

H-3

1.27

H-12

1.27

C-7

0.95

C-16

0.86

T-7

0.79

T-16

0.77

H-4

1.62

H-13

1.21

C-8

0.80

C-17

1.01

T-8

0.66

T-17

0.75

H-5

1.42

H-14

1.56

C-9

0.94

C-18

0.91

T-9

0.78

T-18

0.75

H-6

1.72

H-15

1.04

to π-π stacking and common weak intermolecular interaction. In contrast to the ε-CL-20 (C1), as the polymorph with the largest CED [89], the CED of the CL-20based ECCs is not necessarily elevated, such as C-8, C-10, and C-16. It suggests that the enhancement of intermolecular interactions is not necessary for cocrystallization. Certainly, in some cases, the enhancement will drive the cocrystallization by forming intermolecular HB with H free molecules like BTF [90].

3.3.4 Comparison of Computation Efficiency Liu et al. also checked the computation efficiency of above best methods from geometric optimization by comparing time consumption, as illustrated in Figs. 3.15, 3.16 and 3.17 [75]. First of all, the larger system usually consumes the more computer

3.3 Dispersion-Corrected DFT Methods and Their Application

63

time. It should be noted that the heavier element of S-contained in T-14 causes its more time consumption, compared with those each with a similar total number of C, H, O, and N atoms. Secondly, D3(BJ) and D3(0) often need the least time, with a small difference between themselves. The exceptional cases are of C-4, C-18, T8, and T-14, for which the fastest methods are D2, vdW-DF2, TS, and vdW-DF2, respectively. In comparison, the longest computer time is needed for TS(HI) in most cases, which serves the improvement of TS and requires more computer time to implement iterative Hirshfeld partition to enhance accuracy [66]. In addition, the optPBE-vdW and vdW-DF2 calculations require longer time than D3(BJ) and D3(0) calculations. Additionally, Liu et al. comprehensively evaluated the accuracy and efficiency of two high-accuracy methods, TS(SCS) and MBD, and did not recommend them in treating ECCs, owing to much more time consumed while without advantage of accuracy [67, 68, 91]. D3(0)

D3(BJ)

TS

TS(HI)

optPBE

vdW-DF2

D2

Elapsed Time, h

36

27

18

9

Elapsed Time, h

0 36

C-2(196)

C-3(208)

C-4(416)

C-5(336)

C-6(106)

C-7(110)

C-8(216)

C-9(416)

C-10(122)

C-11(364)

C-12(148)

C-13(200)

C-14(480)

C-15(204)

C-16(184)

C-17(108)

C-18(456)

27

18

9

0 36

Elapsed Time, h

C-1(144)

27

18

9

0

Fig. 3.15 Elapsed time of various dispersion-corrected methods for C-ECCs. The number in parentheses is the atom quantity of in a unit cell. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

64

3 Application of Molecular Simulation Methods in Treating Intrinsic … D3(0)

D3(BJ)

TS

TS(HI)

optPBE

vdW-DF2

Elapsed time, h

12 9 6 3

Elapsed time, h

0 12

T-2(90)

T-3(76)

T-4(220)

T-5(152)

T-6(220)

T-7(180)

T-8(156)

T-9(336)

T-10(164)

T-11(96)

T-12(78)

T-13(82)

T-14(176)

T-15(148)

T-16(212)

T-17(180)

T-18(188)

T-19(66)

T-20(156)

T-21(70)

9 6 3 0 12

Elapsed time, h

T-1(78)

9 6 3 0

Fig. 3.16 Elapsed time of various dispersion-corrected methods for T-ECCs. The number in parentheses is the atom quantity of in a unit cell. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

3.4 Molecular FF Methods and Their Application Nowadays, most of the extensively used energetic crystals are organic molecular crystal, such as PETN, TNT, TATB, HMX, and RDX. For these crystals, it is of great scientific and practical significance to study their thermal property, mechanical property, and chemical reactivity. With the development of theory, computer technology, and algorithm, theoretical methods play an increasingly important roles in exploring energetic crystals. Based on theoretical methods, molecular simulation can be capable of describing the intermolecular interactions and pave a way to predict structure and property, and construct QSPR as well [92, 93]. As an important part of molecular simulation, MD uses the second Newton’s law to describe the movement of particles in a given system [94]. For a molecular material, it is popular to construct or select a fitful molecular FF for the MD simulation, which may be a classic, consistent, or reactive one. Figure 3.18 shows some FFs applied for energetic crystals and applications thereof.

3.4 Molecular FF Methods and Their Application D3(0)

D3(BJ)

TS

TS(HI)

65

optPBE

Elapsed time, h

12

9

6

3

Elapsed time, h

0 12

H-2(84)

H-3(116)

H-4(70)

H-5(92)

H-6(32)

H-7(132)

H-8(176)

H-9(192)

H-10(288)

H-11(84)

H-12(40)

H-13(38)

H-14(28)

H-15(248)

9

6

3

0 12

Elapsed time, h

H-1(68)

9

6

3

0

Fig. 3.17 Elapsed time of various dispersion-corrected methods for H-ECCs. The number in parentheses is the atom quantity of in a unit cell. Reprinted with permission from Ref. [75]. Copyright 2022 American Chemical Society

3.4.1 Classic FFs and Their Application Classic molecular FFs were refitted to precisely study the structures and properties of energetic molecular crystals, and related evolution is listed in Fig. 3.19. In 1990s, Sorescu et al. developed the SRT (Sorescu-Rice-Thompson) FF with a pair potential refitted for predicting lattice parameters and some mechanical moduli of aliphatic energetic compounds, such as RDX, HMX, CL-20, PETN, and FOX-7 [96–102]. In addition, Smith-Bharadwaj (SB) potential, as another kind of multi-particle one, was established to study the responses of HMX, CL-20, and RDX to shock and compression [103–107]. More classic FFs were developed in first ten year of the twentieth century. By coupling the advantages of AMBER and SRT, the SRT-AMBER FF was refitted to treat the issues of molecular flexibility, such as lattice parameter, melting point, and mechanics of RDX [108, 109]. Another multi-particle potential for RDX was also developed by Boyd et al. to predict vibration spectra, thermodynamics, and thermal behaviors [110]. Meanwhile, a multi-particle FF (GRBF) was constructed by Gee et al. to predict the cell parameter, density, thermal expansion and pressure–volume isotherm of TATB [111]. And its vibration spectrum, elastic stiffness coefficient and isotropic modulus, and further the thermal conductivity were investigated by another potential [112, 113]. In 2010s, the molecular FFs increased too. For example, some special FFs were developed to study the structures and properties of

66

3 Application of Molecular Simulation Methods in Treating Intrinsic …

Molecular FFs

Fig. 3.18 Representative molecular FFs applied for energetic crystals and the main applications

FOX-7 [114], TNT and DNT [115], RDX [116], TATB [117, 118], and CL-20 [119, 120]. The energy expression of a classic FF generally consists of terms of covalent, vdW, and electrostatic interaction. Various FFs differ in functional forms (Table 3.4). For example, SRT is feasible to aliphatic energetic compounds, with a pairwise Buckingham 6-exp form and a Coulomb potential, denoting repulsion and dispersion, and electrostatic interaction, respectively [96]. SAPT possesses a similar energy expression to SRT [114]. For the multi-particle potentials, the energy terms of SB

1990s

First 10 years of 2000s

2010s

2020s

SRT (RDX HMX CL-20

SRT-AMBER (RDX TNAZ)

NETMFF (RDX)

OPLS-AA

PETN FOX-7)

Boyd (RDX)

SAPT (FOX-7)

(CL-20)

SB (RDX HMX CL-20)

GRBF (TATB)

Neyertz (TNT DNT)

Bedrov (TATB)

Dreiding (TATB)

Fig. 3.19 Development of classic FFs refitted for energetic crystals. The energetic compounds in brackets represent the application objects of related FFs. Reprinted with permission from Ref. [95]. Copyright 2022 MDPI

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include bond, angle and dihedral as covalent terms, and non-bonding Buckingham and Coulomb interactions [103]. The forms of SRT and AMBER are combined in SRT-AMBER, with non-bonding term replaced by the Buckingham (6-exp) potential and Coulomb potential in SRT [108]. With respect to NETMFF, more covalent terms are contained therein [116]. For the aromatic nitro compounds, such as TATB, TNT, and DNT, GRBF, Bedrov’s and Neyertz’s FFs are viable. GRBF contains covalent terms, and non-bonding Coulomb term and a L-J 12-6 term [111]. It should be noted that the Neyertz’s potential contains the terms of angle-bending and torsional motion around the dihedral angles; thereby, sp2 ring and NO2 structures are described by harmonic functions [115]. In general, the application of the refitted FFs for energetic molecular compounds can be summarized as follows. (a) Cell parameters prediction. The refitted FFs can predict cell parameters well. For instance, the cell parameters of RDX were separately predicted with SRT, SRT-AMBER, Boyd’s FF, SB, and NETMFF potentials [96, 103, 108, 110, 116]. As a result, NETMFF presents the closest result to the experiment [121], while SRT and SRT-AMBER do not work well, ascribed to the absence of covalent terms, which are crucial to describe cell parameters accurately. GRBF, Bedrov’s, and Dreiding FFs present good predictions of the cell parameters of TATB [110, 111, 118], while Neyertz’s FF [115] and SB [103], and OPLS-AA FFs [120] work well for TNT and DNT, and CL-20, respectively. (b) Polymorphic description. For example, the density and mechanic moduli of both monoclinic and orthorhombic TNT were predicted by Neyertz’s FF, consistent with experimental measurements [115]. (c) Vibration spectrum assignment. For example, the vibration spectra of TATB were studied by a modified Bedrov’s potential, with a gap between the prediction with the original version and experimental observation overcome, as the vibration modes were assigned well by calculation [113]. Similarly, the vibration spectra of RDX were also assigned well by the Boyd’s potential calculation [110], with vibrations of 200–700 cm−1 described as “doorway modes” for the energy transition from lattice phonons to molecular vibrations, in which the bond rupture is involved [122, 123]. (d) Thermal property prediction. The refitted SRT FF for FOX-7 was used to predict the coefficients of linear and volume thermal expansion (CTE), showing a rather high anisotropy because of the wavelike molecular stacking pattern, consistent with experimental determinations [102]. This high anisotropy was also confirmed the MD simulation with the fitted SAPT potential [104]. In contrast, SRT described the thermal expansion of FOX-7 better than SAPT [114], as done for other energetic crystals [124], because of the same vdW term of SRT as SAPT and a more complex Coulomb term. It also shows the significance of the electrostatic interaction therein. Moreover, these FFs were refitted to study the thermal behavior of RDX [114], with better results from SRT and Boyd’s FF calculations confirmed [96, 103, 110, 116]. Besides, the GRBF FF [111] presented the CTE of TATB, close to the experimental determination

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3 Application of Molecular Simulation Methods in Treating Intrinsic …

Table 3.4 Summary of the energy expressions and application scopes for the classic FFs [95] FFs

Covalent term

vdW interaction term

Electrostatic interaction term

Applications

SRT [96]

\

Buckingham 6-exp form

Coulomb function

RDX, HMX, CL-20, PETN, and FOX-7 (lattice parameter, density, mechanics)

SAPT [114]

\

Buckingham 6-exp form

Simplified Coulomb function

FOX-7 (thermal property, pressure response, isotherm)

SB [113]

Bonds term, angles term, Buckingham torsions term, dihedrals form term

Coulomb function

RDX, HMX, CL-20 (shock compression, shear band, elastic constant and modulus)

SRT-AMBER [108]

Bonds term, angle bending term, dihedral torsion term

Buckingham 6-exp form

Coulomb function

RDX (lattice parameter, density, melting point, mechanics)

Boyd’s [110]

Bond stretching described by Morse function, angle bending described by harmonic function

Buckingham LJ 12-6 form

Coulomb function

RDX (lattice parameter, density, thermodynamics, vibration spectra, thermal expansion, mechanics)

NETMFF [116]

Bonds term, angles term, Damped dihedral (torsion angle) Buckingham term, out-of-plane form bending angle term, cross-coupling terms of bond–bond, bond–angle couplings

Coulomb function

RDX (lattice parameter, density, thermal expansion)

GRBF [111]

Harmonic bond stretch term, bond–angle bend term, dihedral angle torsion term

LJ 12-6 form

Coulomb function

TATB (lattice parameter, density, thermal expansion, isotherm)

Bedrov’s [112]

Harmonic functions of covalent bonds, three-center bends, and improper dihedrals

Buckingham 6-exp form

Coulomb function

TATB (lattice parameter, thermal expansion, mechanics, vibration spectra, thermal conductivity) (continued)

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Table 3.4 (continued) FFs

Covalent term

vdW interaction term

Electrostatic interaction term

Applications

Neyertz’s [115] Angle-bending LJ 12-6 form deformations described by harmonic function, torsional motions around the dihedral angles, sp2 ring and NO2 structures kept planar described by harmonic function

Coulomb function

TNT, DNT (lattice parameter, density, tensile, bulk and shear modulus)

Dreiding [117]

Bond stretching LJ 12-6 form interaction term, angle bending interaction term, dihedral angle interaction term, inversion interaction term

Coulomb function

TATB (geometry, crystal packing, thermal expansion)

OPLS-AA [119]

Bonds term, angles term, LJ 12-6 form dihedral term

Coulomb function

CL-20 (lattice parameter, density, polymorph prediction)

[125]. The anisotropic thermal behavior of TATB was also reproduced successfully by Dreiding [117, 118]. And its thermal conductivity was calculated by using non-equilibrium MD simulations with Bedrov’s potential [112]. Therein, it was ascertained that the high anisotropy of the thermal flux and temperature gradient cause the high thermal conductivity [113]. (e) Mechanical property prediction. Accurate mechanical property prediction is one of the aims of FF refit. For example, the refitted SRT pair potential was used to predict mechanics of RDX, such as bulk modulus and volume compressibility, matching well with experimental measurements [96]. The SB potential was used to predict the elastic constants and bulk modulus for CL-20, HMX, and RDX [103]. This was also done for TNT and DNT by Neyertz’s potential [115]. (f) Detailing shock response. The response of an energetic material against shock reflects its ability to evolve and ignite under the shock. Through MD simulations with the SB potential, Cawkwell et al. observed the shock-induced shear bands in RDX, as well as the temperature difference between crystalline and sheared regions [104]. Moreover, the shock compression induced evolution of stress and temperature evolution was revealed [105].

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3.4.2 Consistent FFs and Their Application Compared with the universal FFs [126–132], consistent FFs each possesses more complicated energy terms. The consistent FFs are more accurate as they are parameterized from a large number of experimental and/or calculated data. The classic CFF series [133–137], and commonly used PCFF [138–140] and COMPASS [141–144] belong to this type of FF. In contrast, PCFF and COMPASS outperform CFF, with some same functional forms shared, and they differ mainly in the range of functional groups parameterized and the combination rules for non-bonding terms. Based on the CFF series and PCFF, COMPASS was developed to improve the accuracy with the addition of much more cross items in energy expressions. The consistent FFs are applied directly without any refitting. Herein, we exemplify their applications as follows. (a) Morphologic prediction. Crystal morphology serves as an important factor influencing the properties of energetic crystals. Thus, accurate morphologic prediction of energetic crystals is of great interest. Theoretical models, such as AE (attachment energy) [145, 146] and BFDH (Bravais-Friedel-DonnayHarker) models [147–150], were used to perform morphologic prediction for various energetic compounds under conditions of solvent, temperature, pressure, additive, etc. [151–154]. For example, COMPASS was used to predict the morphologies of β-HMX, RDX, and ε-CL-20 in various solvents, revealing the mechanism of the more or less influence of solvents on the morphologies [155, 156]. The similar work was done for DNP [157] and MTNP/CL-20 cocrystal [158] grown from different solvents. (b) Polymorphic prediction. For example, COMPASS was adopted to predict the polymorphs of CL-20 [159] and a series of compounds of polynitrohexaazaadmantanes [160], covering various space groups and in agreement with experimental observations. (c) Property prediction. In the past, COMPASS was widely applied to predict properties of energetic crystals. Through COMPASS-MD simulations, it was confirmed that the molecular conformer of β-CL-20 was the most energetically preferred, and the β-CL-20 crystal can be easily converted into the ε-form [161]. It was also adopted to calculate LE for co-crystals [162] and interactive energies [151–154]. Also, it was applied to predict the thermal expansion properties [118, 163–165] and mechanical properties [166–172] for some explosive compounds.

3.4.3 Reactive Forcefield and Its Application Reactivity is a key property for energetic materials, and largely roots for sensitivity. Theoretical methods, such as reactive FFs-based MD [173–176], AIMD [177–183], and DFTB-MD [184–190] were utilized to reveal the mechanisms of heat, shock, and electronic field induced reactions. Among them, ReaxFF-based MD is the most efficient. Reactive FFs started from REBO FF [173], and became popular after ReaxFF

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developed with many combined parameters [174–176]. In addition, the dispersion was accounted in a new version as ReaxFF-lg [191]. This corrected FF can give lattice parameter much closer to experimental observation. The ReaxFF-based MD simulations can detail chemical reactions of energetic compounds induced by various stimuli. (a) Vibration spectrum assignment. For example, ReaxFF-MD simulations were performed with an additional oscillating electric field on RDX and TATP to achieve the Terahertz absorption and 2D spectroscopy, with a result comparable to experiment [192]. (b) Revealing induced chemistry shock. ReaxFF has been widely applied to reveal shock induced chemistry for a large variety of energetic crystals [173, 193– 196]. A compress-shear reactive dynamics (CS-RD) procedure was developed to investigate the anisotropy of shock sensitivity. Therein, the shock sensitivity was evaluated by the reaction kinetics, and it was found that the anisotropic sensitivity is caused by the difference in internal molecular steric hindrance against shear sliding [197–202]. In particular, the shock induced reaction of TATB features a shallower shear sliding barrier and longer delay time to release heat, compared to other explosive compounds, in agreement with its insensitivity [203]. Moreover, Strachan et al. detailed the chemistry of shocked RDX, such as the unimolecular decomposition mechanism, shock velocity as a function of time evolution of gas products [193]. The gaseous products observed in simulation is close to the measurement by mass spectra. Besides, combined with the multiscale shock technique (MSST), ReaxFF-MD simulations were carried out to explore the origins of the twin and dislocation-induced enhancement of shock sensitivity of RDX and HMX, respectively [194, 204, 205], as well as those of the coupling effects of shock, heat, and defect on the RDX decay [206], and the molecular disorder induced shock sensitivity enhancement [207]. (c) Revealing heat-induced chemistry. Another important use is to reveal thermal decomposition mechanism [208–212]. For example, it was confirmed that the enhancement of self-heating ability is a consequence of the increased internal energy of the molecules around the defects, compared to those in perfect crystal [208]. Similarly, it was found that the heat-induced clustering of TATB roots for its lower sensitivity, compared with relatively sensitive β-HMX and sensitive PETN [209, 210]. Moreover, the mechanism of the mediated thermal stability of the cocrystal CL-20/HMX in contrast to the pure HMX and CL-20 [211], as well as the influence of volume filling degree of RDX on the thermal decomposition [212], was understood by the MD simulations. Still, the feasibility of ReaxFF-MD simulations to some energetic systems has not been identified sufficiently, such as heterocycle compounds and energetic ionic compounds, despite the aforementioned wide use in common energetic compounds. Nowadays, the more accurate reactive FFs have been sought for various molecular crystals [213], by continuous improvement through more accurate QC calculations [214, 215] and even machine learning molding [216–218], such as a neural network reactive FF (NNRF) [219].

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3.5 Hirshfeld Surface Analysis Method After the first introduction by Zhang et al. [220], the Hirshfeld surface method [221– 224] has been widely applied in energetic crystals. As a straightforward tool, the Hirshfeld surface method can rapidly present the visualization of intermolecular interactions. Thereby, many interaction types can be readily distinguished, such as HB, close and distant vdW contacts, as well as π-π stacking [225]. In addition, because the method can also discern the molecular stacking pattern, it can predict shear sliding characteristic and further impact sensitivity, which significantly depends on the shear sliding characteristic.

3.5.1 Principle The basic principle of the Hirshfeld surface method can be consulted elsewhere [221–226]. By calculating intermolecular interatomic close contacts, the interaction information around of a molecule can be reflected by its Hirshfeld surface. To map Hirshfeld surfaces, five functions were defined, including (1) di and (2) de representing the distance from the surface to the nearest atom interior and exterior to the surface, respectively; (3) dnorm ; (4) shape index; and (5) curvedness. In practice, the function of dnorm is used the most popularly, with relative size of the atoms considered and the close contacts between large atoms stressed effectively [225], i.e., dnorm combines de and di together for assigned atoms in close contact with the surface. By means of the vdW radius, Eq. 3.1 normalizes each contact distance, and therein rivdW and revdW denote the vdW radii of the atoms closest to the points inside and outside the surface, respectively. In general, the functions of shape index and curvedness are rarely applied. dnorm =

de − revdW di − rivdW + vdW revdW ri

(3.1)

TATB is a very insensitive energetic compound with a distinguished planar layer π-π stacked crystal structure [228] and distinguished Hirshfeld surfaces from other compounds. Herein, it is adopted to exemplify the principle of the method. Figure 3.20 exhibits the six Hirshfeld surfaces of the TATB molecule in crystal mapped with the aforementioned five functions. The color on the surface represents the difference of the five surfaces from a blank background (denoted as None). With respect to the two surfaces separately mapped with the functions of curvedness and shape index, the color is recognized to represent curvature. That is, red and blue denote the complementary recess and protrusion, respectively. All the three surfaces mapped with di , de , and dnorm functions are defined by the intermolecular interatomic distances. Regarding dnorm , the smaller di + de suggests the shorter contact distance, and further the stronger the interactions. Mapping the points on a Hirshfeld surface to a 2D di

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73

and de coordinated system, we can achieve a 2D fingerprint plot, setting a basis for straightforwardly discerning the type and strength of intermolecular interactions. It should be noted that, for a given molecule in a crystal, both Hirshfeld surface and 2D fingerprint are unique [224], rooting for the discernment of a specific molecule in a specific crystal. By means of Hirshfeld surfaces and 2D fingerprint plots, the type and weight of the related close contact can be readily clarified. For example, in Fig. 3.21, the remarkable red dots sided on the Hirshfeld surface block of TATB denote the strong intermolecular HB thereon, while the planar layer π-π stacking is denoted by the blue flat area. It can quantitatively present the weight of the close contacts, while, at most, with a semi-quantitative meaning. After all, the method features straightforward and rough. The red dots sided on the surface mainly belong to the H· · · O close contact. This is also illustrated in another way, as two sharp spikes generally extending to the coordinate origin of the 2D fingerprint plot. The top and bottom ones represent

di

None

di

de

dnorm

de

Curvedness

Shape index Fig. 3.20 Hirshfeld surfaces of TATB mapped with various functions. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

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3 Application of Molecular Simulation Methods in Treating Intrinsic …

HBD and HBA, respectively. According to a statistic result, the close contact of O· · · O generally rank the second in all intermolecular interatomic close contacts of energetic crystals [229]. In the fingerprint plot, a bright yellow feather represents the close contact of O· · · O and the π-π stacking of TATB [230]. In the TATB crystal, because the C atoms of a TATB molecule are far from the atoms of a neighboring molecule, and they can hardly appear in the high weight contacts. Therefore, all the close contacts related to the C atoms, such as C· · · O, C· · · C, C· · · H, and C· · · N, are long distant and belong to the planar layer π-π stacking, denoted by the blue areas on the surface. Summing up, π-π stacking features a pair of wings in the 2D fingerprint plot. The dense contact points, as denoted by red dots sided on the surface of TATB, suggest the orientationality of intermolecular interactions, i.e., stronger ones along the molecular plane, while weaker ones perpendicular to it [231]. Thus, a procedure can be summarized to predict stacking pattern, and further mechanic property and sensitivity, based on Hirshfeld surface analysis method. As showing in Fig. 3.22, by running the code of CrystalExplorer with the input of crystallographic information file (CIF) of an energetic crystal, we can get the Hirshfeld surface and 2D fingerprint plots. Next, the Hirshfeld surface is analyzed, with respect to the shape, and the distributions of red dots and blue areas thereon (Fig. 3.21). Meanwhile, the 2D fingerprint plot (Fig. 3.21) is analyzed too. Thereby, the strength and orientation of intermolecular interactions involved in the energy crystal is approximately ascertained, with impact sensitivity predicted roughly.

3.5.2 Description for Intermolecular Interaction In general, HB, π-π stacking, and XB [232], as the main types of intermolecular interactions, are the keys to discuss packing structure and properties of an energetic compound. In fact, the Hirshfeld surface method is sufficient to describe them in a straightforward way. (a) π-stacking. π-stacking always appears in the systems that contain π-bonded molecules or ions, as one of the most common intermolecular interactions. There are two forms of π-stacking: π-π stacking and n-π stacking (lone pair-π stacking). A π-conjugation structure facilitates high molecular stability, while it may not sufficiently suggest a LSHEM. For example, TATB is a typical representative of insensitive compounds, with all molecules π-π stacked in infinite planar layers, with dense intramolecular and intermolecular HBs therein [233]. While, another planar π-bonded molecule, BTF, is not stacked as TATB and appears very sensitive to impact, because it is in absence of HB and stacked in a mixed mode [234]. Figure 3.23 exhibits the molecular and stacking structures of six π-conjugated energetic compounds, including ICM-101 [235], NTO [236], DAAF [237], DAAzF [238], TNA [239], and TNB [240]. These molecules are the derivatives of azole, furazan, and benzene. Different from benzene ring, the azole and furazan rings are

Fig. 3.21 dnorm surfaces and related 2D fingerprint plots showing specified intermolecular interatomic close contacts. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

3.5 Hirshfeld Surface Analysis Method 75

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3 Application of Molecular Simulation Methods in Treating Intrinsic … Crystal information (CIF) CrystalExplorer

2D fingerprint plot

Hirshfeld surface Shape of the surface and distributions of red dots and blue areas

Distribution and shape of colorful plots

Orientation and strength of close contacts

Intermolecular interaction

Strength of close contacts

IFS, sliding characteristic, and impact sensitivity

Molecular stacking mode

Fig. 3.22 Procedure for producing Hirshfeld surfaces and 2D fingerprint plots and applying the information to understand and predict the structure and property of energetic crystals. IFS is the abbreviation of intermolecular friction symbol. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

composed of C, O, and N atoms, and thus their π-π stacking close contacts are governed by N· · · O and C· · · N ones, as well as N· · · N one sometimes, in combination with substituent groups of NO2 , NH2 , and acyl O. As for the two nitrobenzene compounds, they are mainly C· · · O and N· · · O. Each of the surfaces is exhibited in a block shape while with different flatness. The evident intermolecular HBs are identified by the intense red dots concentrated on the block sides, as well as by the two spikes on the 2D fingerprint plot. That is, all the π-π stacking is supported by the intermolecular HBs. The bright part of wing-shaped area (di > 1.4 Å and de < 2.0 Å) in each 2D fingerprint plot represents the dense intermolecular interatomic contacts of C· · · O, C· · · N, C· · · C, N· · · O, and C· · · N. Besides, these compounds differ to a certain extent in the shape and distribution of close contacts, implying a certain difference in stacking pattern. More attention has been paid to the planar layered π-π stacking, as it is prone to ready shear sliding and low impact sensitivity [233]. Here, a dependence of Hirshfeld surface characteristics on the interlayered distance is discussed by adopting four planar layer-stacked molecular crystals of RAVSOW [241], CYURAC03 [242], FITXIP [243], and TATNBZ (TATB) [228]. Interlayered distance dominates the sliding barrier [244]. Figure 3.24 exhibits that the shorter distances of RAVSOW (2.723 Å, Fig. 3.24a) and CYURAC03 (2.906 Å, Fig. 3.24b) cause more irregular Hirshfeld surfaces and distributions of red dots and blue areas thereon, compared

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Fig. 3.23 Molecular structures and stacking structures of six representative compounds. In particular, the description of π-π stacking is implemented by the Hirshfeld surfaces and the 2D fingerprint plots, including some special close contacts and wing-shaped plots. In the pie charts, the size of the sector area represents the weights of the close contacts. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

with FITXIP (3.129 Å, Fig. 3.24c) and TATB (3.193 Å, Fig. 3.24d). This can be readily understandable, because the surface shape and distributions of red dots and blue areas in principle depend on the interlayered distance. Taking RAVSOW as an example, its Hirshfeld surface is far from a block shape, and the red dots disperse thereon, denoting a close interlayered N· · · O contact, instead of an intralayered one. Thus, there are strong interlayered intermolecular interactions instead of intralayered ones. It also suggests that it is not necessary for a planar layer π-π stacking to produce Hirshfeld surface block as of TATB. Thus, we can conclude that a planar layer π-π stacking with much interval should feature a regular block shape of the Hirshfeld surface, and regular distributions of red dots and blue areas thereon. Such characteristics of the Hirshfeld surface also imply ready shear sliding and further low impact sensitivity. It stems for the impact sensitivity prediction based on the Hirshfeld surface method. In principle, n-π stacking features the T-shape and an essential type of weak electrostatic attraction. Figure 3.25 exhibits four n-π stacked energetic compounds, including TFTNB [245], NADF [246], FDNM2-BOD [247], and BTF [248]. Correspondingly, the n-π stacking is described by the intermolecular interatomic

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3 Application of Molecular Simulation Methods in Treating Intrinsic …

2.723 Å

2.906 Å

(a) RAVSOW

3.193 Å

3.129 Å

(b) CYURAC03

(c) FITXIP

(d) TATNBZ

Fig. 3.24 Plot showing a dependence of the shape of Hirshfeld surface and the distributions of red dots and blue areas on the interlayered distance for a planar layer π-π stacking. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

close contacts of O· · · C from NO2 · · · benzene ring (TFTNB), NO2 · · · furazan ring (NADF), NO2 · · · adiazole ring (FDNM2-BOD), and N=O· · · benzene ring (BTF). (b) HB. Intermolecular HB is common in energetic crystals, and can be clearly described by the Hirshfeld method. Briefly, if the spike at the bottom left in a

2.4 2.2 2.0 1.8 1.6 1.4

O …C

1.2 1.0

C…O

0.8 0.6

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

C···O O···O

others

F···O

TFTNB C···O O···O

N···O

N···N

C···O

NADF

BTF

O···O

N···O

FDNM2-BOD 2.4

2.4

2.2

F···O

2.0 1.8

1.4

O···O

O…C

1.2 1.0

2.2 2.0 1.8

1.6

C…O

1.6

C···O

1.4 1.2

0.8

1.0

0.6

0.8

N···O

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

O…C C…O

0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

2.4 2.2 2.0

O …C

1.8 1.6

C…O

1.4 1.2 1.0 0.8 0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Fig. 3.25 Molecular and packing structures of four n-π stacked energetic compounds, with the n-π stacking described by Hirshfeld surfaces and the related 2D fingerprint plots. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

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79

fingerprint plot is closer to the coordinate origin and possesses a higher brightness, it will suggest a stronger HB [249, 250]. Reminding this, we can readily make sure the stronger intermolecular HBs in NQ [251], FOX-7 [252], and LLM-105 [253], while the weaker ones in RDX [121], as illustrated in Fig. 3.26. The relatively strong HBs in NQ, FOX-7, and LLM-105 stem from the conjugated molecular structure and strong HBD, while neither strong HBD nor HBA results in the weak HB of RDX. All these was clarified in a recent review of HB in energetic compounds by Bu et al. [254]. (c) XB. For a special purpose, the introduction of halogen to energetic materials is to remove chemical and biochemical agents. As exhibited in Fig. 3.27, the XB in energetic crystals, such as TITNB, TBTNB, TCTNB, and DCTNB [255, 256], can be described by means of the Hirshfeld surfaces and 2D fingerprint plots. The Hirshfeld surfaces of TBTNB and TITNB each appears to be a planar block, and the red dots are concentrated on its sides, implying that they are planar layer stacked, with strong intralayered intermolecular interactions of X· · · O. Previously, it was confirmed that the contact distance of X· · · O are shorter than the sum of the vdW radius of X and O atoms, showing a strong intermolecular interaction thereof [255]. This XB supported planar layer stacking is somewhat

2.4

2.4

2.2 2.0 1.8

2.2 2.0

H…N

1.6 1.4

N…H

H…O

1.2

N···H

1.8 1.6 1.4 1.2

O…H

1.0

H···O

H···O

0.6

NQ LLM-105

2.4

0.6

HB

RDX

2.4

2.0 1.8

1.8

1.6

1.6

1.0

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

2.2

2.0

1.2

0.8

FOX-7

2.2

1.4

N…H O…H

1.0

0.8

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

H…N H…O

N···O

H…O

1.2

0.8

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

O…H

1.0

H···O

0.6

H…O

1.4

O…H

H···O

0.8 0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Fig. 3.26 Molecular and packing structures of four intermolecular energetic compounds containing HB, with HB described by the Hirshfeld surfaces and the related 2D fingerprint plots. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

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3 Application of Molecular Simulation Methods in Treating Intrinsic …

2.4 2.2 2.0

2.4

O…I

2.2 2.0

O···O

1.8 1.6 1.4

O···O

1.8 1.6

1.2

I···O

1.0 0.8

Cl···O

1.0 0.8 0.6

0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

XB

TITNB TBTNB

2.4 2.2

O…Br

TCTNB DCTNB C···O

2.0

O···O

1.8 1.6 1.4 1.2

Cl…O

1.4

I-O

1.2

O…Cl Cl…Cl

Br…Br

Br…O

0.8 0.6

H···O

2.4 2.2

O…Cl

2.0 1.8 1.6 1.4

Cl…O

1.2

Br···O

1.0

O···O

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Cl···O

1.0 0.8 0.6

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Fig. 3.27 Molecular and packing structures of some typical energetic crystals containing XB, with XB denoted by the Hirshfeld surfaces and related 2D fingerprint plots. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

like that by HB. In comparison, TCTNB and DCTNB do not feature a high regularity of the surfaces, suggesting some additional close contacts therein. Although TCTNB is also planar layer stacked, the interlayered sliding is unallowed, due to the short contacts of O· · · O, as in HNB [257]. It partly roots for the high impact sensitivity of TCTNB and HNB.

3.5.3 Description for a Same Molecule in Various Crystal Environments Because of a large variety of polymorphs [258, 259] and cocrystals [260, 261], CL-20 is preferred to exemplify the same molecule crystallized in various environments. In fact, the same molecule in different crystal environments undergoes different intermolecular interactions, leading to the differences in density, reactivity, detonation property, and safety [89, 189, 261, 262]. The difference in intermolecular interaction can be straightforwardly described by the Hirshfeld surface method [263]. As shown in Fig. 3.28, seven crystals are adopted to exemplify the CL-20 molecule encompassed in eight different crystal environments, including four polymorphs (β-, E-, γ -,

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and ζ-forms) [258, 264] and three cocrystals (CL-20/TNT [265], CL-20/HMX [266], and CL-20/BTF [267]). In CL-20/HMX, CL-20 appear to two conformers, i.e., the β- and γ -forms. The Hirshfeld surfaces and 2D fingerprint plots of CL-20 appear unique in the eight crystal environments. Still, the difference among them is small, reflecting the close crystal environments. In fact, the H· · · O, O· · · O, and N· · · O generally dominate the close contacts of these seven crystals, ascribed to that C–H and NO2 groups act as the external moieties of the molecules involved [268]. Thus, the driving force of formation of these energetic cocrystals was ascribed by entropic increase [269]. Such small difference also partly roots for the moderated density, impact sensitivity, and detonation property, compared with the pure components [270].

Fig. 3.28 Hirshfeld surfaces and 2D fingerprint plots of CL-20 molecules consolidated in various crystals, and the related populations of various close contacts, with molecular and stacking structures presented. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

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3.5.4 Description for a Same Ion in Various Crystal Environments Energetic ionic crystals are consolidated more strongly by significantly stronger electrostatic attractions among anions and cations, in contrast to energetic molecular crystals [271]. Because ionization can facilitate the enhancement of both molecular stability and intermolecular interaction, it has been regarded as a strategy for creating LSHEMs [272]. NH3 OH+ -based energetic ionic compounds have received wide attention and reached the largest population, as NH3 OH+ is beneficial to reach the highest densities compared with other cations [273]. The largest amount of NH3 OH+ based energetic ionic compounds naturally makes them as example to show how to describe the same ion in various crystal environments by the Hirshfeld surface method. Figure 3.29 exhibits six energetic ionic compounds containing NH3 OH+ [274–279]. Similar to the case of the CL-20 molecules embedded in eight different crystal environments, NH3 OH+ in any of the crystal environments exhibits unique a Hirshfeld surface or a 2D fingerprint plot. In Fig. 3.29a, it shows there are two spikes at the bottom left for almost all the fingerprint plots, except for NH3 OH+ (HA)DNBTO. The upper spike of the two are all long and sharp, representing NH3 OH+ acts as a strong HBD. However, the other spike appears much differently, i.e., it is long for HA-BT2 O, moderate for HA-DNABF, HA-AFTA, and HA-BTO, short for HA-DBO, or missing in HA-DNBTO, suggesting that NH3 OH+ should always be a HBD, but not necessarily a HBA. Moreover, Fig. 3.29b exhibits the high populations of HB in NH3 OH+ -based compounds, largely implying the strong HB therein [280].

3.5.5 Predictions for Shear Sliding Characteristic and Impact Sensitivity (a) Construction of intermolecular friction symbol (IFS). In order to simply describe the orientation and strength of intermolecular interactions in crystal, and possible characteristic of shear sliding, Zhang et al. proposed IFS. Thereby, impact sensitivity can be further simply predicted [220]. Figure 3.30 briefs the procedures for producing and ordering IFS based on the analysis of the Hirshfeld surface, and the related detail can be referred from Ref. [220]. According to the orientation and strength of intermolecular interaction, the close contacts can be discerned as a dispersed and weak one, and a concentrated and strong one. A molecule in a lattice is assumed to interact with its neighbors by means of contacts a, b, c, d, e, and n, or interatomic connections. These contacts can be pairwise independent in different planes, as type I, and partly coplanar as three or more of them are in a same plane, as type II. In the case of type I, five planes (from p1 to pn ) are determined by these close contacts, and a sectional view of these planes is achieved and regarded as the IFS, as shown in Fig. 3.30a (i–iii). An

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(a) Molecular and stacking structures, Hirshfeld surfaces, and 2D fingerprint plots 2.4

2.4

2.2

1.6

2.0

1.6 1.4

2.0

1.8

2.2

1.8

2.2

2.0

2.4

H…N

1.4 1.2

H…O

O…H

1.8

H…N

1.6

H…H

H…O

1.4

0.8

1.0

0.6

0.8

O…O H…O

1.0

1.0

1.2

H…N

1.2

O…H

0.8 0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

HA-AFTA HA-DBO HA-BT2O

HA-DNBTO HA-BTO

HA-DNABF

2.4 2.2

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2.0 1.8

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H…N

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O …H

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O…H

1.0 0.8 0.6

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H…N H…O

1.2

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

0.8 0.6 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

(b) Populations of various close contacts H···O

H···N

H···H

others

HA-DBO HA-BT2O HA-DNABF HA-BTO HA-DNBTO HA-AFTA 0%

20%

40%

60%

80%

100%

Fig. 3.29 Hirshfeld surfaces and 2D fingerprint plots of NH3 OH+ (HA) consolidated in various crystals and the related populations of various close contacts, with geometric and stacking structures presented. Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

IFS is composed of a circle and one or more double-arrows, indicating a section and one or more oriented planes, corresponding to a molecule and its close contacts with neighbors, respectively. Additionally, the thickness of doublearrow denotes the strength of close contacts. For type II, as indicated Fig. 3.30a (iv–vi), it can be first ascertained a plane to include as many close contacts as possible. For instance, a, b, c, and e are contained in p1 . Thereby, other planes can be determined pairwise. An IFS is gotten by cross-cutting these planes through a plane vertical to a, supposing that a is strongest contact. Thereby, IFS can be ordered to reflect the difference of intermolecular friction (Fig. 3.30b): it enhances from left to right. It should be noted that IFS can only roughly reflects the orientation and strength of intermolecular interactions [220]. (b) Prediction of impact sensitivity. As pointed out above, the shapes and distributions of red dots and blue area derived from the Hirshfeld surface method can

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(a) Procedure for plotting IFS

(b) Ordering of IFS by typical energetic molecules

TATB

DAAzF

FOX-7

LLM-105

Fig. 3.30 Schematic procedure for plotting and ordering intermolecular friction symbol (IFS). Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

straightforwardly reflect characteristics of molecular stacking, shear sliding, and further impact sensitivity. That is, flat block and large distribution of blue area thereon suggest low impact sensitivity [230]. Among the four stacking modes (Fig. 3.31a), the planar layer (face-to-face) mode is prone to ready shear sliding, thanks to the shallowest sliding energy barrier, facilitating low impact sensitivity. Typically, as shown in Fig. 3.31b, on the block-shaped and highly flat Hirshfeld surface of TATB, there are dense red dots on the side and blue area covering the rest, just corresponding to its high insensitivity. Such case does not happen for PETN and HNB, corresponding to their high impact sensitivity.

3.5.6 Summary of Advantages and Disadvantages After the first introduction the Hirshfeld surface method to the field of energetic materials [80], it was extensively applied to describe the intermolecular interactions in energetic crystals [281–290]. Recently, Li et al. summarized the advantages and disadvantages of using it to understand energetic crystals [227]. The advantages are straightforward descriptions of intermolecular interactions and molecular stacking mode, rough predictions of shear sliding characteristic and impact sensitivity, and possible benefit for encoding intermolecular interaction information. And the disadvantages are the roughness or inaccurateness. Thus, it will be more beneficial if the Hirshfeld surface method serves as a primary tool and another more accurate method is adopted subsequently to achieve accurate description, explanation or prediction.

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(a) Dependence of sliding potentials on stacking modes wavelike

TATB, DAAF DAAzF

NTO, FOX-7 LLM-105

Potential

face-to-face

crossing NQ, TNA

β α

β α

mixing

β

TNB

α β

β α

(b) Correlation between impact sensitivity and Hirshfeld surface

• • • •

Hirshfeld surfaces: less and less block-shaped Red dots on the surfaces: more and more spatially dispersed Crystal packing: less and less face-to-face π-π stacking EMs: more and more impact sensitive

Fig. 3.31 Relationships between molecular stacking mode and Hirshfeld surface, and impact sensitivity. The relationship between stacking modes and the potential increasement along sliding distance d. α (black curves) and β (red curves) denote the cases when shear sliding occurs along front/back and right/left, respectively (a). Hirshfeld surfaces can straightforwardly correlate with stacking mode and impact sensitivity through surface shape and red dots distribution thereon. The values in brackets are H 50 in m, a threshold height of a drop hammer weighing 2.5 kg and causing 50% detonation of a sample (b). Reprinted with permission from Ref. [227]. Copyright 2021 American Chemical Society

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3.6 Codes and Database Applied for Energetic Molecules and Crystals 3.6.1 Gaussian

Gaussian is the most commonly used QC software package and has a long history of development, by Carnegie Mellon University and Gaussian, Inc. The main contributor Prof. J. A. Pople won the Nobel Prize in Chemistry in 1998 for designing Gaussian. Gaussian programs began from 1970 (G70) [291], and went through a series of published multiple versions [292–303]. Now the newest version is G16 [304]. GaussView [305] is a visualization tool used along with Gaussian software, which can not only initiate and control Gaussian jobs, but also view calculation results and display predicted properties in graphical forms. The computation in Gaussian is based on QC theories, as well as MM. The principles of these theories can be referred elsewhere. In Gaussian calculations, various DFT methods and high-level ab initio methods can be applied. For energetic molecules, Gaussian can generally do anything introduced in Sect. 3.2, such as: (1) Geometric structure optimization. The geometric structure of energetic molecules can be optimized using Gaussian. (2) Electronic structure calculations. The electronic structure, such as electron density, electrostatic potential, charge, bond order, HOMO/LUMO, and excited state, can be derived from Gaussian calculations. Firstly, the electron density of energetic molecules can be calculated using Gaussian combined with AIM theory [26]. In general, the higher electron density suggests the more electrons located, the stronger bonding, and the higher molecular stability. The electron density is also used to determine the molecular shape and volume. Secondly, ESP is a common index showing electronic structure, and can readily be achieved by calculation with Gaussian. Additionally, atomic charges and MO can also easily be obtained as well. (3) Energy and vibration spectrum calculations. Thermodynamic properties, interaction energy, and vibration spectrum for an energetic molecule can be obtained by running QC calculations using Gaussian. (4) Reactivity calculations. Properties related with chemical reactions like BDE, energy barrier, reaction path, excited states, and solvent effect on reaction, can also be predicted using Gaussian for energetic molecules.

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3.6.2 Multiwfn

Multiwfn was developed by Lu et al. [306], as an extremely powerful wave function analysis program supported on Windows, Linux, and MacOS. It supports almost all the important wave function analysis methods and is also free (Multiwfn official website http://sobereva.com/multiwfn), open-source, highly efficient, user-friendly, and flexible. There are many functions for Multiwfn. It can show molecular structures and various orbitals, output all supported real space functions, and decompose many calculated results to orbital contributions. Also, it can deal with other issues, such as topology of any real space function, wave function; orbital composition, bond order/strength, density-of-states, spectrum, molecular surface, electronic structure, electron excitation analyses, etc. Multiwfn has been widely used in treating energetic molecules. For example, Ping Yin et al. employed isochemical shielding surfaces to evaluate spatial magnetic property of a new fused N-heterocyclic framework, dipyrazolo-1,3,5-triazinane [307]. Mayer, Wiberg and Laplacian bond orders of the N–N bonds in RDX and HMX were analyzed with it [308]. Besides, it was employed to calculate Vm , ESP, and the balance of charges [309].

3.6.3 VASP

Vienna Ab-initio Simulation Package (VASP) is a package based on a program written initially by Mike Payne at MIT [310]. It has been officially presented by the group of Hafner, university of Vienna, and generally used in electronic structure calculations, quantum mechanics, and MD simulations. It is one of the most popular commercial software in material simulation. VASP is a DFT calculation program based on the pseudopotential plane wave basis set. It can study a variety of systems,

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such as metals and their oxides, semiconductors, crystals, doping systems, nanomaterials, molecules, clusters, surface systems, and interface systems, etc. It can predict the equilibrium structure, and electronic, energetics and reactivity. In comparison, VASP possesses a high efficiency, as it can implement large-scale and high-efficiency parallel computations with small memory. The principle of VASP is to obtain the energy and electronic state by approximately solving the Schrödinger equation in DFT framework. The VASP can optimize the geometry of various systems, such as atoms, molecules, surfaces, and clusters under the periodic boundary condition, to obtain their stable configurations with various structural parameters, such as lattice constants, atomic positions, and bond lengths and angles between atoms. By solving the Kohn-Sham equation, VASP can obtain the wave function and equation of state for the system. Meanwhile, the conjugate gradient methods or the steepest descent method combined with the Damped algorithm can be adopted to calculate the force of each atom in the system along various directions. It can also describe the electronic structures and properties, including wave function, energy level distribution at each k-point, density of state of each atom in each orbital, band structure, electron localization function, charge density, and spin density, etc. Besides, by adding linear response in ion position and electrostatic field, it can be used to calculate elastic constant matrix, Born effective charge tensor, real and imaginary parts of dielectric function, and total magnetic moment of the system and to calculate interatomic force constant, elastic constant, and phonon of Gamma point based on supercell approximation. VASP has been extensively applied to predict and understand the structures and properties of energetic crystals.

3.6.4 Materials Studio

Materials studio is a full-scale material simulation platform developed by Accelrys Company [311]. It has excellent operation interface, which can quickly realize model building, parameter setting, and visual analysis of results. It also integrates a variety of simulation methods and integrates up to 23 functional modules, which can realize

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full-scale scientific research from electronic structure analysis to macro performance prediction. The follow briefs some modules applied for energetic materials already. • Materials visualizer. Materials visualizer is a graphical interface of Materials Studio and the core of the whole platform. It can be used to build and adjust various three-dimensional visible structural models, including crystals, small molecules, polymers, nanomaterials, clusters, surface interfaces, various defect structures, and electrode models. Also, it provides a window interface for module parameter setting and result analysis, the management interface of structure file, parameter file and result file, and a monitoring interface for the calculation process. The simulation results can be analyzed in various ways, which can be combined with the structural model to display the data in 2D and 3D, and can give data charts, animation demonstrations or vector diagrams for specific results. Besides, it supports the input and output of various structures, graphics and text file formats, and the sharing of structural data among different functional modules, and provides Perl language environment and script writing. • Simulation module. There are separate products integrated into Materials Studio to create a comprehensive range of materials modeling tools, including quantum mechanics, classical molecular mechanics, dynamics, mesoscopic dynamics, and Monte Carlo. The specific module functions are shown in Table 3.5. As to the application of the above modules to energetic materials, we brief some of them as below. (1) CASTEP. CASTEP is an advanced quantum mechanics program based on DFT developed by Cambridge Condensed Matter Theory Research Group [312]. It uses plane wave function to describe valence electrons and pseudopotential to replace inner electrons, so it is also called plane wave pseudopotential method. It is suitable for solving various problems in the fields of solid physics, material science, chemistry, and chemical engineering. The main functions of CASTEP include structural optimization, transition state search, electronic structure analysis, dielectric, mechanical, thermodynamic, optical performance calculation, and dynamic calculation. Zhu et al. used CASTEP program to study the structural parameters, Raman/IR spectra, vibration and thermodynamic properties of α-RDX and γ -RDX [313]. In addition, AIMD simulation was carried out by CASTEP to study the initial decomposition mechanism and subsequent decomposition of TATB crystal under initial decomposition temperature and different pressure [314]. (2) DMol3 . DMol3 is an advanced DFT-based program released by Prof. Bernard Delley. It uses the method of linear combination of atomic orbits to describe the electronic state of the system, so it is also known as a method of linear combination of atomic orbitals. The most important feature of DMOL3 , different from other methods, is the use of numerical functions to describe atomic orbitals. This method takes the calculation accuracy and efficiency into account, making DMol3 more efficient and practical. DMol3 can simulate the electronic structure and energetics of organic and inorganic molecules, molecular crystals, covalent

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Table 3.5 Materials modeling tools embedded in Materials Studio Methods

Principle

Modules

Quantum mechanical method

Quantum mechanics

CASTEP (plane wave pseudopotential method) DMol3 (a method of a linear combination of atomic orbitals) QMERA (quantum mechanics/ molecular mechanics hybrid method) ONETEP (linear scaling method)

Semiempirical quantum mechanics

DFTB+ (tight binding approximation) VAMP (a method of a linear combination of atomic orbitals)

Classical simulation method

Molecular mechanics, dynamics

COMPASS II (high precision force field) Forcite plus (including various general force fields) GULP (containing various special force fields for inorganic systems)

Monte Carlo

Amorphous cell (amorphous model construction) Adsorption locator (adsorption site, adsorption conformation) Blends (compatibility of mixed system) Conformers (polymer conformation) Sorption (adsorption site and adsorption isotherm)

Mesoscopic simulation

Quantitative structure performance relationship

Synthia (prediction of polymer properties by group contribution method)

Mesoscale simulation

Mesocite (dissipative particle dynamics, coarsening MD) MesoDyn (mean field density functional method) MesoProp (finite element analysis of fixed mesh based on displacement method) (continued)

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Table 3.5 (continued) Methods

Principle

Modules

Crystal, crystallization and instrumental analysis methods

Crystal structure analysis

Polymorph predictor (finding the stable accumulation of molecules based on force field) Analysis kit of X-ray, neutron and electron diffraction patterns

QSAR method

(3)

(4)

(5)

(6)

Grain morphology prediction

Morphology (it contains a variety of general force fields to predict the grain morphology)

QSAR

Quantitative structure activity relationship analysis

solids, metal solids, and infinite surfaces. It enables us to predict structure, reaction energy and barrier, thermodynamic properties, optical and vibrational spectra, etc. For example, the structure and vibrational properties of TATB molecule and crystal were studied by DMol3 program [315]. COMPASS II. COMPASS is a powerful force field based on quantum mechanics and capable of atomic scale simulation of condensed system. The investigation on the effectiveness of its parameters not only includes the quantum mechanical calculation results and experimental results for single molecule (gaseous state), but also fully considers its condensed state properties. Therefore, COMPASS can accurately predict the structure, conformation, vibration, and thermophysical properties for various single molecules and their condensed states in a large temperature and pressure range. COMPASS II also adds support for ionic liquids to enhance the calculation accuracy of polymer and heterocyclic systems. Classical simulations of models using COMPASS are possible with Forcite, Polymorph, Morphology, Sorption, Adsorption Locator, and a number of other modules. Forcite Plus. Forcite is a collection of MM tools for studying a large variety of systems. The key approximation is that PES, on which the atomic nuclei move, is represented by a classical FF. FFs are developed by parameterizing data from experiments and high-level QC calculations. Forcite is apt to the geometric optimize of a system before a MD simulation or a QC calculation. Forcite Plus is an enhanced version of Forcite. In the field of energetic materials, analysis tool of Forcite Plus is mainly used to analyze the kinetic results from CASTEP and DMol3 . Amorphous Cell. Amorphous Cell is a tool for building amorphous model by Monte Carlo method. It can be used to build an amorphous model according to the set composition and molar ratio. The gap of the existing structure can also be filled with specified molecules and atoms according to the set proportion. Sorption. Sorption is a program based on grand canonical Monte Carlo (GCMC) method to predict the adsorption of single or mixed components in microporous and mesoporous materials. Sorption can directly give the adsorption isotherm

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(load curve), Henry constant, and other properties, simulate the adsorption under fixed pressure and fixed load, confirm the most stable adsorption site, and characterize more relevant adsorption conditions. (7) Morphology. Morphology is a tool to predict the grain morphology of materials by their crystal packing structure. It provides three different criteria of surface spacing, surface adhesion energy, and surface free energy to help judge the possible grain morphology of specific crystal structure materials. It can also be combined with classical simulation methods to consider environmental factors. It is helpful for the study of crystal morphology in the presence of specific additives, solvents and impurities. In application, Hou combines calculations with experiments [316]. Therein, the attachment energy model of Morphology module was used to calculate the five main growth planes of the β-HMX crystal with COMPASS FF.

3.6.5 DFTB+

DFTB+ is the implementation of the DFTB method, with many extensions contained. It offers efficient methods for performing quantum mechanical simulations. By various methods approximating DFT, it can carry out simulations of larger systems and longer timescales with reasonable accuracy, compared with ab initio methods. DFTB+ can simulate thousands of atomic systems, which provides a new simulation method to solve the related problems of various complex systems and processes in the fields of electronics, catalysis, chemical industry and so on. The research objects involved in DFTB+ include various non-periodic and periodic systems such as organic molecules, clusters, insulators, semiconductors, metals, and even biological macromolecules. DFTB+ is a free software developed by several contributors around the world, and it could be download at https://dftbplus.org [317, 318]. DFTB+ can be used for geometric optimization, dispersion correction, phonon transport calculation, etc., as well as the mechanic exploration of chemical reaction against heat and shock for energetic crystals [186, 189].

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3.6.6 CP2K

CP2K is a QC and solid-state physics software package, and apt to in atomistic simulations, since it presents a general framework for various simulation methods. In particular, it does excellently in massively parallel and linear scaling electronic structure methods, as well as state-of-the-art AIMD simulations. By means of the improvements of algorithms and high-performance computers, it appears excellently in electronic structure calculations. CP2K is an open software package and can be freely downloaded at https://www.cp2k.org [319]. There are many theories supporting CP2K, including DFTB, MP2, semi-empirical methods, classical force fields, etc. Specially, CP2K adopts a plane wave (PW) auxiliary basis set as in a Gaussian orbital scheme, making CP2K distinctive from most other electronic structure programs. CP2K provides state-of-the-art methods for efficient and accurate atomistic simulations, and it can do simulations of MD, metadynamics, Monte Carlo, Ehrenfest dynamics, vibrational analysis, core level spectroscopy, energy minimization, and transition state optimization. For example, Xue et al. used CP2K to calculate the decomposition of CL-20 under shock and revealed the early decay mechanism of CL-20 [184].

3.6.7 LAMMPS

LAMMPS stands for Large-scale Atomic/Molecular Massively Parallel Simulator, which was developed originally at Sandia National Laboratories in the mid1990s. It is a classical MD simulation code that can simulate atomic, polymeric, biological, metallic, granular, and coarse-grained systems using a variety of FFs. On the computational scale of LAMMPS, it can cover 2D and 3D systems with only a few particles up to millions or billions. In addition, LAMMPS has good flexibility. As some new modified and extended capabilities, new force fields, atom types, boundary conditions, and diagnostics are contained in it. Finally, LAMMPS is

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a freely-available open-source code, which can be downloaded at https://www.lam mps.org for academic purposes [320, 321]. Newton’s equations of motion are integrated by LAMMPS to collect interacting particles. A single particle can be an atom, molecule or electron, a coarse-grained cluster of atoms, or a mesoscopic or macroscopic clump of materials. The interaction models included in LAMMPS are mostly short-range in nature, with some long-range models included as well. LAMMPS adopts neighbor lists to keep track of nearby particles to enhance computational efficiency. On parallel machines, LAMMPS uses spatial-decomposition techniques to partition the simulation domain into small 3D sub-domains, one of which is assigned to each processor. Processors communicate and store “ghost” atom information for atoms that border their sub-domain. Furthermore, LAMMPS also formulated the various molecular dynamics algorithms to enable parallelism across CPUs (via MPI). LAMMPS can be used to implement non-equilibrium MD (NEMD), coarsegrained MD (CGMD), and reactive MD (RMD) simulations on energetic materials, such as flow and arrest in stressed granular materials [322], shock loading of inhomogeneous PBX [323], crack of Al nanoparticles [324], and Nanoindentation of RDX crystal [325].

3.6.8 COSMOlogic COSMOlogic is a set of software, bridging QC and fluid thermodynamics. It is suitable for any mixture system, and applied for predicting thermodynamic properties thereof. COSMO (Conductor-like Screening Model) is a statistical thermodynamics theory based on the polarization charge density, which overcomes many of limitations and theoretical shortcomings of dielectric continuum models. Because COSMOlogic can deal with mixtures at variable temperatures, it has been widely applied in the fields of chemical engineering, physical chemistry and medicinal chemistry. In COSMOlogic, COSMO-RS may currently be considered the most accurate model for predicting solvation energies. The function of COSMOlogic covers activity coefficient, vapour liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), solid–liquid equilibrium (SLE), azeotrope, miscibility gap, distillation separability, solubility of gas, liquid and solid, vapour pressure and heat of vaporization, Henry constants and solute partition coefficient in two arbitrary solvent, mixed heat (excess enthalpy and free enthalpy of mixtures), reaction thermodynamics of the solution, chemical potentials and chemical potential gradient, and density and viscosity of pure compounds. Regarding the application to energetic materials, the COSMO-RS method was used to screen energetic-energetic cocrystals by the variations of enthalpy (△H) and Gibbs free energy (△G).

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3.6.9 CrystalExplorer

CrystalExplorer is a native cross-platform program supported by Windows, Linux, and MacOS, with a primary function of visualization. CrystalExplorer is a code for investigating intermolecular interactions and molecular packing, based on the decorated Hirshfeld surface and its corresponding 2D fingerprint. It is freely available at https://crystalexplorer.net. See the basic principle and the wide application to energetic crystals of the code in Sect. 3.5.

3.6.10 CSD

The Cambridge Crystallographic Data Centre (CCDC) is located at the University of Cambridge, UK. It grew out from the activities of the crystallography group led by Dr. Olga Kennard OBE FRS. From 1965, the group began to collect the published bibliographic, chemical, and crystal structure data for all small molecules studied by X-ray or neutron diffraction. Subsequently, the collection was encoded in an electronic form and became known as the Cambridge Structural Database (CSD). CSD is a rich database of crystal structures of small and organometallic molecules, and is compiled and published by CCDC, as one of the earliest numerical scientific databases to begin operations anywhere in the world. The CSD only collects and provides crystal structure data for all crystal structures with C–H bonds, including organic compounds, metal–organic compounds, and coordination compounds. It currently contains nearly a million entries. The database has been in operation for over 50 years and remains the primary means of sharing structural chemical data and knowledge across disciplines. In addition to publicly supporting structures for scientific articles, it includes many structures published directly as CSD communications. ConQuest is the basic software for searching and extracting structural information from CSD. The software provides a full range of text and numerical queries in CSD, as well as more advanced search functions: chemical substructure search,

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geometric structure search, intermolecular search, and the search for intramolecular interactions. Each piece of information in the database includes: (1) 3D structural data: atomic coordinates, unit cell parameters, space group, structural precision index, temperature and pressure conditions, details of distribution; (2) 2D structure diagram: properties and associations of atom and bonds; (3) chemical formula and compound name, amino acid sequence of polypeptide compound; (4) complete documents, some of which are directly connected to the electronic documents; (5) cross-reference to stereoisomers and details on reinterpretation and confirmation; and (6) other published information about the molecule: source of the compound, crystallization conditions, experiments to determine the configuration of the pair, polymorphism, and biological activity. User can perform the analysis according to the name, molecular formula, element, space group, unit cell, Z value, original literature, author, experimental conditions, and other items of the compound.

3.7 Conclusion and Outlooks In summary, we summarize the general methods for dealing with the intrinsic structures of energetic materials, molecule and crystal, and introduce some molecular simulation codes and a database applied for energetic materials. As to the QC methods for describing energetic molecules, appropriate methods should be carefully chosen for a given purpose, with a trade-off faced up to usually and necessarily. Regarding the dispersion corretion methods for descripting energetic molecular crystals, D3(0) and D3(BJ) were verified to be most effective. Additionally, we brief the commonly used FFs for treating energetic molecular crystals and their prediction applications. Furthermore, the advantages and disadvantages of Hirshfeld surface method are summarized, and the right use of it is expected. Obviously, these methods, as well as the codes and database, are indispensable to reveal and understand the intrinsic structures of energetic materials. Meanwhile, machine leaning (ML) combined with DFT calculations and ML-aided FF construction are verified to be more efficient in treating the intrinsic structure, and it could serve as a main trend for molecular prediction.

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Chapter 4

Energetic Molecules and Energetic Single-Component Molecular Crystals

4.1 Introduction This chapter introduces the intrinsic structures of energetic single-component molecular crystals, including molecule structure and crystal packing. Most of the applied energetic compounds, such as picric acid, TNT, PETN, TATB, RDX, and HMX, belong to molecular crystals. Almost all of them contain NO2 . More recently, a large quantity of N-heterocyclic compounds was successfully synthesized and richened the family members of energetic compounds. Of course, most of these N-heterocyclic compounds also contain NO2 . Since these newly synthesized compounds consist of C, H, N, and O atoms, as the old ones of picric acid and TNT, they are usually regarded as the traditional energetic compounds as well. For energetic all-N systems, some of them are molecular crystals and most energetic all-N molecules only remain in theoretical research stage. There are some energetic all-N ions like N3 − , N5 + , and N5 − has been successfully synthesized, but they do not belong to simple all-N substances, since they have to exist with their counter ions in compounds to form energetic ionic crystals. The polymeric nitrogen, as another kind of all-N systems, actually belongs to the atomic crystal and can be seen as an extremely huge molecule. Thus, it is a long way to go to obtain this group of molecular crystals. It should be stressed that a large variety of energetic cocrystals belong to molecular crystal too, while with a difference of two or more components in comparison to single-component molecular crystals. The energetic cocrystals will separately be introduced in Chap. 7, due to a large population. Because the energetic molecular crystals are composed of molecules, the interactions therein belong to the rather weak intermolecular interactions, including vdW interaction and electrostatic force, compared with the strong covalent bonding that holds atomic crystals. Chemically, these weak interactions are generally divided into HB, halogen bonding (XB), and π-stacking, depending on the chemical environments of the interactions. In a word, energetic molecular crystals possess the largest population among applied energetic compounds, and remain as the focus of the applicable energetic compounds research and development.

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4.2 Traditional Energetic Molecular Crystals There is no clear definition of the traditional energetic compound up to the present. In general, it is thought to be a kind of energetic compound that is neutral and consist of C, H, N, and O atoms, with a common structure like organic molecule. Whereas, the new type of energetic compounds may be attributed to that their components contain other elements besides C, H, N, and O, or they do not belong to molecular crystal. In this section, we discuss the intrinsic structures of traditional energetic compounds, including energetic nitro compounds, energetic conjugated N-heterocyclic compounds and energetic organic azides. In fact, such classification is not scientifically strict, as their intensions partly overlap one another. For example, the N-heterocyclic compounds and organic azides can also contain NO2 and thereby be classified as nitro compounds too. Besides, these compounds are discussed based on their thermal stability and impact sensitivity in the latter of this section.

4.2.1 Energetic Nitro Compounds Traditionally, energetic nitro compounds are divided into three groups of C–NO2 , N– NO2 and O–NO2 compounds based on the functional groups involving NO2 . Thereby, some representatives of energetic nitro compounds are introduced as follows. Nitrobenzene compounds have a pivotal position in energetic materials. In fact, from the ancestors of modern explosives to the energetic compounds used currently, nitrobenzene compounds play an important part all along. Figure 4.1 shows the intrinsic structures, including molecule and crystal packing, of some representatives of this kind of compounds [1–8]. Picric acid is thought to be the ancestor of modern explosives, while TATB and TNT were also synthesized early in the nineteen century (Fig. 1.4). There are high electron-donating and conjugation abilities on the benzene ring, from where sufficient electrons can be transferred to the NO2 group, enhancing the stability of C–NO2 compounds. Therein, the C–NO2 bond can be also denoted as Ar–NO2 bond, where Ar represents aromatic ring. HNB has the highest power among all the nitrobenzene compounds. The molecular stability for HNB is also rather high because its DSC decomposition temperature peak exceeds 473 K, even though the donated electrons of the benzene ring of HNB are partitioned by six NO2 groups. However, the application for HNB is still restricted, owning to its ready hydrolysis and thus poor environmental adaptability. TATB is highly thermostable, and also very insensitive to other stimuli, such as shock, impact, friction, and electronic spark. It is actually the exclusive insensitive high explosive accepted by the Department of Energy, United States, becoming the most representative of insensitive energetic compounds. At the molecular level, all the non-hydrogen atoms of TATB are located in a same plane and conjugated with each other, where strong intramolecular HBs are formed. And on the aspect of the crystal packing, the molecules are stacked in parallel, called as the face-to-face π-π stacking

4.2 Traditional Energetic Molecular Crystals

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Fig. 4.1 Molecule and crystal packing structures of some nitrobenzene compounds

or planar layered stacking. Such stacking is the most prone to ready shear sliding and contributes to low impact sensitivity or even impact insensitivity [9–15]. Moreover, the dense intermolecular HBs leads to a dense arrangement of TATB molecules in the crystal. Thus, both the packing coefficient and crystal density of TATB are higher than those of its analogs, such as DATB, TNA, and TNB. It partly makes TATB the most powerful, since the detonation properties have positive correlations with the crystal density. That is to say, compared with the three analogs, TATB is not only the least sensitive, but also the most powerful. It is a typical case of the energy-safety contradiction alleviated [11]. In addition, as the earlier event of the heat-induced reactions of TATB, intramolecular hydrogen transfer can proceed more readily, compared with the NO2 partition from the benzene ring. Therein, the hydrogen transfer can be reversible, where a part of external stimulation energy can temporarily be stored therein as the chemical energy, which can be released once the external stimulation unloaded. This reversible hydrogen transfer can buffer against impact chemically and also be beneficial to low sensitivity [16]. To summarize, TATB is more insensitive to many kinds of stimuli compared with most of traditional energetic compounds. Indeed, TATB is a very interesting energetic compounds and have been employed as the most popular representative of insensitive compounds. Nitrobenzene compounds are good representatives for exploring the compositionstructure–property relationships of energetic compounds. Among the eight nitrobenzene compounds shown in Fig. 4.1, HNB possesses the highest packing density and the highest energy content, since it does not contain the hydrogen atom that is disadvantageous to increase density. HNB also possesses an excellent oxygen balance (OB) of zero (supposing the balance product of C is CO2 ). Thanks to the repulsion effect of adjacent NO2 groups, all the six NO2 groups of HNB are deviated from the plane of the benzene ring, and make the HNB molecule like a scroll wheel. In comparison, other nitrobenzene molecules like TATB, DATB, TNA, and TNB are all

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planar, because there is no such adjacent NO2 groups on the ring and no intramolecular repulsion effect in any of them. Therefore, all of them are more stable than HNB at the molecular level. To further explore the sliding property, a sliding barrier calculation of TATB and HNB was carried out, resulting in a difference of 125 against 1380 kJ/mol [17]. This significant difference in sliding barrier leads to significantly different consequences. For TATB, the barrier is much lower than its dissociation energy of the weakest bond (BDE), 320 kJ/mol, suggesting allowed sliding and no damage of molecular integrity, whereas HNB is restricted to slide because the predicted sliding barrier is significantly above its BDE (230 kJ/mol). Besides the six discussed species in Fig. 4.1, there are many other nitrobenzene compounds, and their sensitivity is generally moderate between those of HNB and TATB. The large population of the nitrobenzene analogues and their sufficient experimentally measured structures and properties build a strong basis for exploring the relationships between the intrinsic structures and properties of energetic materials, further speeding up the design of new energetic molecules. Another kind of C–NO2 compounds is the nitro compounds derived from chain hydrocarbons [18–23]. Nitromethane (CH3 NO2 ) is one of them and is also the simplest prototype of energetic compounds. Hence, many theoretical and experimental studies have been conducted on this compound, presenting a reference for studying the properties and mechanism of more complex ones. Among the nitro compounds derived from chain hydrocarbons, nitroform is applied as oxidizers or primary explosive, due to its highly positive OB and high impact sensitivity. Nevertheless, a compound of this type, FOX-7 (Fig. 4.2a), possesses low impact sensitivity instead. The reason is that the NO2 groups in FOX-7 are linked with an electronic donor (the vinyl), which helps to enhance the molecular stability. Such case is more similar with that in nitrobenzene compound, instead of in hydrocarbon chains. In fact, FOX-7 was created recently, as a rare low impact sensitive and high energy compound. Besides the high molecular stability, the low impact sensitivity is also related to heat or pressure induced polymorphic transition, which helps with readier shear sliding [9, 24]. Nitroamines illustrated in Fig. 4.3 are a group of important energetic compounds too [25–30]. For example, HMX and RDX are the two most extensively applied nitroamine compounds from World War Two, while CL-20 is the most powerful explosive commercialized already so far. For these three nitroamines, the N–NO2 bond thereof is rather weak and its cleavage can proceed readily. Thus, they are usually less stable than the nitrobenzene compounds like TATB and DATB. In addition, HMX, RDX, and CL-20 are nonplanar N-heterocyclic compounds, much different from the conjugated N-heterocyclic compounds with planar molecular structure. Interestingly, NQ is a planar molecule with all non-hydrogen atoms conjugated in the entire molecule, and it is impact insensitive as TATB. But the mechanism of its insensitivity remains still largely unknown. After all, the moderate thermal stability and crossing π-stacking can hardly root for its so low sensitivity. The third group of nitro compounds are nitric esters. The common funtional group of these compounds is O–NO2 , as illustrated in Fig. 4.4 [31–34]. Because of the high

4.2 Traditional Energetic Molecular Crystals

119

B

B

O/A

A/O

B

C

C O/A

α-FOX-7

C

NF

C

A

C

B/O

A

TNP

B/O

TETB C

A/O

B

HNE

TNAB

Fig. 4.2 Molecule and crystal packing structures of some nitro-derivatives of chain hydrocarbons

C

A C C

O O/B

O/B

A

B

A

ε-CL-20

β-HMX

NQ

B C

B

C C/O

A/O

A

α-RDX

CE

B

O/A

ONDO

Fig. 4.3 Molecule and crystal packing structures of some nitroamine compounds

eletronegativity or high ability to accept electrons for both O atom and NO2 group, the bonding of the two to form O–NO2 bond will make it intrinsicly weak. This low stability is one of the reasons why the nitric esters are often used as primary explosive, just like PETN. Meanwhile, the funtional group O–NO2 is beneficial to increase positive OB. The nitric esters, such as NG, are applied as oxidizers in many propellant and pyrotechnics formulations. On many aspects of compositions and properties, nitric esters are much close to nitroforms. For common C–NO2 , N–NO2 , and O–NO2 compounds, their molecular stability generally reduces sequentially while sensitivity increases. At the molecular level, molecular stability acts as a determinative factor of the sensitivity, that is to say, the chemical reactivity determines the sensitivity. A large amount of sensitivity correlations has been summarized recently based on molecular stability [35], and therein the trigger mechanism is widely accepted for understanding the sensitivity. Because of the ready accessibility of molecular electronic structure-stability relationship, QC calculations that are apt to present detailed electronic structure information play a great role in understanding the sensitivity and build a basis for establishing molecular structure-sensitivity relationships of the aforementioned different nitro compounds.

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

A B

C/O O/C

A

B

NG

ETN C A

O/B

C

A

B/O

DINA

PETN

Fig. 4.4 Molecule and crystal packing structures of some nitric esters

In general, the molecular electronic structure refers to electron density, charge, ESP, bond order (BO), electronegativity, and molecular orbital composition. These indices are related with one another in principle, i.e., the indices of electronic structure can be deduced from electron density. The higher electron density of the trigger bond suggests the higher strength of the bond, thus higher molecular stability and further lower sensitivity [36–40]. The electron densities on C–NO2 , N–NO2 , and O–NO2 bonds reduce in order generally, suggesting the increasingly worsening of these bonds. Moreover, the charges of atom or group involved in trigger bonds can serve as an indicator to grade sensitivity. Taking the trigger bond R–NO2 as an example, the groups charge of NO2 (Q NO2 ) is adopted to relate with the impact sensitivity, i.e., the more negative Q NO2 suggests the lower impact sensitivity [41–47]. In fact, the negative Q NO2 of the C–NO2 , N–NO2 , and O–NO2 compounds generally reduces sequentially, even changes from negative to positive, also implying the worsening of molecular stability. Owens, Politzer, and Rice et al. constructed many models for ESP-sensitivity relationship [48–56]. Applying the ESP method should proceed at a premise of that energetic molecules are grouped based on bond type, such as the C–NO2 , N–NO2 and O–NO2 bonds. Besides, the electronegativity represents the ability of a molecule to attract electrons, and can also adopted as an indicator of molecular stability; thereby, it was also used to correlate with sensitivity [57]. In principle, the electronegativity of the functional groups of C–NO2 , N–NO2 , and O–NO2 increases in sequence, suggesting the increasement of their impact sensitivity. Largely, whether an energetic material can be readily ignited or not depends on the reactivity of energetic molecules, rooting for the reactivity-sensitivity correlations. Reaction activation energy (E a ), BDE, and the rate constant of molecular decomposition (k) are often employed to understand and predict sensitivity. Among them, BDE is the simplest and the most extensively used indicator of reactivity in energetic

4.2 Traditional Energetic Molecular Crystals

121

chemistry. Considering energetic compounds are usually with NO2 , their BDE refers generally to the energy required to partition NO2 . The BDE of C–NO2 , N–NO2 , and O–NO2 bonds generally decreases in turn, also showing the decreasing of molecular stability and the increasing of sensitivity. In practice, BDE and E a were related to the electrostatic sensitivity [58, 59]. In addition, compared with the aforementioned electronic structure-based methods, it costs much more to obtain BDE or E a . Thus, a fast E a prediction was implemented to save time [60–62]. In summary, owing to the decreasing in the bond strength of C–NO2 , N–NO2 , and O–NO2 , the corresponding compounds exhibit the decreasing of molecular stability and the increasing of sensitivity. Based on this, NO2 compounds can be designed in terms of different requirements of sensitivity.

4.2.2 Energetic Conjugated N-heterocyclic Compounds This section introduces the molecular structures and crystal packing of some energetic N-heterocyclic conjugated compounds. Since N atom is isoelectronic with CH group, it can be used to replace CH group, which can significantly increase the molecular density and OB and is also beneficial to the detonation property promotion. Thus, this displacement is popular in designing new energetic molecules. (a) Furazan and furoxan compounds. Figure 4.5 exhibits the intrinsic structures of some furazan and furoxan compounds [63–68]. Zelinsky Institute of Organic Chemistry of Russia may create the most furazan and furoxan compounds in the past as far as we know. A large quantity of compounds has been achieved by directly linking or bridging the furazan and furoxan rings. It is a way to design the furazan and furoxan molecules. For example, Zhang designed a series of furazan and furoxan molecules and predicted their main properties as energetic compound (Figs. 4.6, 4.7 and 4.8) [69]. Based on the calculated results, Zhang concluded that they are commonly high for dc , Q d , vd and Pd , specific impulse, and sensitivities of furazans and furoxans [69]. Therefore, they should be the important objects in designing and synthesizing high energetic compound. Besides, the author found that it was not necessary to promote detonation properties by increasing molecular size. Both furazan and furoxan groups are generally more energetic than the NO2 group. The furazan ring is more energetic than its isomers which are all with a fivemembered ring. However, most furazan and furoxan compounds are highly sensitive to impact and shock, and can hardly be put into practical use. Interestingly, this high sensitivity facilitates some of them to be applied as primary explosive. For example, BTF is a famous and typical one. For many furazan and furoxan compounds, there is no intermolecular HB because of the absence of hydrogen, leading to rather weak intermolecular interactions therein. This is the origin for that some of them possess low melting points and can be used as fused cat explosives. In addition, some furazan and furoxan compounds were reported to be greatly energetic. For

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

A B

O

O

B

B C/A

A

C/O

C

ANF O

A

DAAzF C

BTF A

O

C

B O

C

B B

A

ANBDF

DAAF

DNBF

Fig. 4.5 Molecule and crystal packing structures of some furazan and furoxan compounds

Fig. 4.6 Molecular structures of some nitro mono-furazans and nitro mono-furoxans. Reprinted with permission from Ref. [69]. Copyright 2005 Elsevier

example, 3,4-dinitrofuroxans has a predicted denotation velocity >10,000 m/s, but this compound is very sensitive unfortunately, making it useless so far, the same as the aforementioned HNB [5]. It seems that the energy-safety contradiction of energetic materials [11, 12] goes usually. Low stabilities of furazan and furoxan compounds make them almost inapplicable as secondary explosives. It can significantly enhance molecular stability to introduce the NH2 group to furazan rings, considering its high electron-denoting ability. This can be exemplified by two furazan compounds, DAAF and DAAzF. The high molecular stability and close face-to-face π-π stacking that favor low sensitivity, make these two energetic compounds very impact insensitive, even close to TATB. Nevertheless, the densities of DAAF and DAAzF, 1.747 and 1.728 g/cm3 , are both relatively low so that disadvantageous to denotation properties [64, 67]. In addition, DAAzF was experimentally determined to be sensitive to the short pulse. All these suggest that DAAzF is a potential booster explosive with a high safety, because of its fast response to short pulse and insensitivity to the thermal and mechanical stimuli. (b) Azole compounds. Azole compounds are also widely distributed in energetic compounds. They have been successfully synthesized for the compounds with

4.2 Traditional Energetic Molecular Crystals

123

Fig. 4.7 Molecular structures of some chained poly-furazan (furoxan) compounds. Reprinted with permission from Ref. [69]. Copyright 2005 Elsevier

Fig. 4.8 Molecular structures of some cyclic poly-furazan (furoxan) compounds. Reprinted with permission from Ref. [69]. Copyright 2005 Elsevier

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

B B

B C

A O

O/A

A

C/O

C

NTO

LLM-116

ANTA

B

C

C

B A

O/A

C

A

O

4,5-Dinitroimidazole

2,4-Dinitroimidazole

B/O

4-Nitroimidazole

Fig. 4.9 Molecule and crystal packing structures of some azole compounds

one to five N atoms in the azole ring. Specifically, pentazole ring, as an isolated full nitrogen fragment stabilized under common conditions, has been waited for a very long time [70–72]. Increasing the nitrogen content in the azole ring is beneficial to increase the heat of formation, while disadvantageous to the enhancement of molecular stability. The molecular structures and crystal packing of some representatives of simple azole compounds are shown in Fig. 4.9 [73–78]. These compounds exhibit high molecular planarity, implying good molecular stability. While, these compounds can exhibit a certain acidity when the H atom is linked with N atom in the ring. The acidity reduces the molecular stability and restricts the application of related compounds. For example, NTO has a certain acidity, which facilitates its salinization with some strong bases, and the NTO-based salts can be used as primary explosive. Meanwhile, the acidity decreases the compatibility with some substances and restricts its application. Azole is a source of a large part of energetic salts. Recently, Gao et al. reviewed azole-based energetic ionic compounds, with the azole ring structures shown in Fig. 4.10 except pentazole ring, when the isolated pentazole ring ion did not come into being [79]. The neutral pentazole is actually so unstable that can hardly exist under common conditions. It was found that the vd of many azole-based energetic salts were predicted to be larger than 8500 m/s while their E dr were measured to be larger than 7 J, i.e., they possess comprehensive properties superior to those of RDX, which serves as a benchmark of traditional energetic compounds. This indicates a possibility to design and discover well-defined neutral molecules and their cations or anions, to promote the performance of energetic ionic compounds, even to replace traditional energetic compounds [79]. However, for these neutral azole compounds, especially neutral nitrogen-rich azole compounds, they are usually with low thermal stabilities and high impact sensitivities. In addition, their packing densities are not so high as expected thanks to the low packing coefficients, leading to relatively low detonation performance. Thus, the energetic azole compounds in application are significantly less than nitrobenzene compounds and nitroamine compounds.

4.2 Traditional Energetic Molecular Crystals

125

Fig. 4.10 Structural formulae of unsubstituted neutral azoles

(c) Azine compounds. Azine compounds are also an important group of energetic compounds with high heat of formation. Very recently, the most energetic azine compound TTTO was successfully synthesized [80]. TTTO exists as a solvate with benzene and can be hydrolyzed readily. Among the six representatives of azine compounds shown in Fig. 4.11 [81–86], LLM-105 has been applied in some explosive formulae, since it is more powerful than RDX while with much less heat, impact and shock sensitive than RDX. Thus, LLM-105 is thought to be a rare and promising low sensitivity and highly energetic molecule. The excellent performance is attributed to its high molecular stability and wavelike molecular stacking, prone to low mechanical sensitivity [13–15]. For the four azine compounds with N3 groups, they are usually mechanically sensitive. It was reported that they are potentials as gas producer or primary explosive. However, they are still left aside due to the extremely high sensitivity. Besides, similar to the aforementioned azole compounds, the increasing of N atom in the azine ring will increase energy content, as well as sensitivity. (d) Compounds with N-oxidation. In addition to the aforementioned conjugated N-heterocyclic compounds, it is a crucial strategy to enhance density and energy of energetic compounds by N-oxidization, as well as their safety possibly. According to the IUPAC criterion, the N–O bond is denoted by N+ –O− , because it is in fact a coordinate double bond. For example, the conversion from tertiary amines into N-oxides has served as an important strategy for creating high energy density compounds [87]. By means of the N-oxidization, the OB will be improved and the packing density will be enhanced. Thus, it will be beneficial

A

C

C

O

B

C

A/O

LLM-105

B

O/B

A

TAT

TAHA

A

B B

O/C B

A

C/O

DAmT

O

C/A

NADAT

Fig. 4.11 Molecule and crystal packing structures of some azine compounds

TAAT

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

Fig. 4.12 Molecular structures of some N-rich heteroaromatic N-oxides

to enhance energy release and detonation properties. For instance, by means of N-oxidization, TKX-50, as a newly synthesized energetic ionic compound (Fig. 4.12), outperforms several common energetic compounds in several properties [88]. In contrast to dihydroxylammonium-5,5' -bistetrazole, as the O-free analogue of TKX-50, the OB is elevated and the density increases from 1.742 to 1.877 g/cm3 . Thereby, it becomes understandable that the calculated vd elevates from 8854 to 9698 m/s [88, 89]. So does LLM-105. It outperforms its O-free analog, ANPZ, in both dc and detonation properties. Another new Nrich compound 6-amino-tetrazolo[1,5-β]-1,2,4,5-tetrazine-7-N-oxide follows this rule and also exhibits a dc elevation relative to its O-free analog [90]. Besides aforementioned density and energy, the introduction of N-oxidization may also affect safety [91]. The N+ –O− bond has been ascertained to exhibit a stabilization effect sometimes. For example, compared with ANPZ, the N+ –O− bond formation can lower the impact sensitivity of LLM-105 (Fig. 4.12) by enhancing the molecular stability, as well as the intra- and intermolecular HB [81]. Such introduction of O atoms to be adjacent to NH2 could be a strategy to design low sensitive and highly energetic molecules. In addition, the derivatives of TDO shown in Fig. 4.12 exhibit considerable stability, whereas the corresponding O-free molecule, 1,2,3,4-tetrazine, has not been synthesized due to a serious issue of low molecular stability [92– 94]. Meanwhile, TTTO (Fig. 4.12), a compound containing the N+ –O− bond with relatively higher decomposition temperature (456~459 K), suggests its considerable stability too [80]. This enhancement of molecular stability stems from the removal of lone-pair repulsion and promotion of σ-π orbital separation by the N+ –O− bond [95]. The understandings of the N-oxidation effect on molecular stability contains can be summarized as the following 4 points: (1) The N+ –O− bond formation increases molecular stability, because it facilitates the removal of lone-pair electron repulsion and the promotion of σ–π orbital separation [95, 96]. Moreover, introducing O to be adjacent to HB donors could facilitate to form intramolecular HB and increase molecular stability too. (2) The nitrogen catenation weakens the thermodynamic stability of N-oxidized azines, as recent QC calculations confirmed that the mono, di-, tri- and tetra-oxides of N-catenated molecules are less thermodynamically stable than the corresponding isomers [97]. (3) The thermodynamic stability of molecules containing two or multiple N+ –O− bonds depends on relative positions among the bonds, i.e., the farther relative position, the higher molecular stability

4.2 Traditional Energetic Molecular Crystals

127

[97, 98]. (4) Ozonation of azole compounds is favorable, with a regioselectivity of yielding monoxide, as the most thermodynamically stable isomer [99]. Meanwhile, it is also found there are some disadvantages to molecular stability when introducing N+ –O− . For example, the molecular stability of a furazan compound will substantially reduce if oxidized to the corresponding furoxan [100]. This is a main reason why BTF is used as a primary explosive. For another example, the oxidation of an azo group will worsen its stability, as the thermal stability of DAAzF is significantly higher compared to its azo-oxidized product, DAAF. It shows both the advantages and disadvantages of N+ –O− introduction over molecular stability, and thus gives rise to an issue of how we can properly use the N+ –O− introduction as a strategy for stabilizing energetic molecules. Because a high N content suggests higher energy and density [86, 101], Yuan et al. recently studied the effect of N+ –O− introduction on a series of molecules containing C–N heteroaromatic ring with QC calculations [102], including imidazoles, pyrazoles, triazoles, tetrazoles, pentazoles, furazans, pyridines, pyridazines, pyrimidines, pyrazines, triazines, tetrazines, pentazines, and the full-N molecules hexazines [91]. Because N atom is an isoelectronic body of the CH group, these Nrich molecules can be regarded as CH replaced products of C-rich ones. In fact, using N atom to replace CH group is a common strategy for designing molecular skeletons of energetic compounds. Moreover, these compounds containing N+ –O− need less oxygen when combusting, and produce less toxic and lighter combustion products compared to their hydrocarbon analogs, thereby enhancing specifical impulse with more and lighter gas products. In combination with possible high thermal stability, some N-rich compounds may act as promising high-energy candidates [103–107]. Thus, it deserves to study the influence of the N-oxidation on molecular stability. 102 molecules are classified into A-K groups, as shown in Figs. 4.13 and 4.14. The molecular stability of these samples is mainly assessed by bond lengths. First of all, the optimized structures of these heteroaromatic molecules generally keep planar after introducing N+ –O− moieties, suggesting that the N-oxidation has a small effect on π-conjugation over the rings. As exhibited in Figs. 4.13 and 4.14, the bond lengths of N+ –O− are within 1.19 to 1.27 Å, featuring double bonds between N and O atoms [97]. In general, the Noxidization elongates the neighboring bonds, compared to the primary rings without N-oxidization; and shortening and strengthening of N+ –O− bonds appear at the cost of the elongation and weakening of adjacent bonds. For example, the N+ –O− bonds in J1-2, J1-4, J1-8, and K1-2 are strong, with lengths of 1.198, 1.197, 1.186, and 1.186 Å, respectively; while their adjacent N–N bonds are weak, with lengths of 1.404, 1.436, 1.574, and 1.544 Å, respectively, much above the normal. It shows the weakened molecular stability by the N-oxidization. Nevertheless, it exhibits a slight influence on molecular stability in some other cases. That is, short N+ –O− bonds (e.g., 1.194 and 1.193 Å of K1-1 and K1-3, respectively) does not necessarily suggest long N–N bonds (they are elongated by only 0.053 and 0.07 Å for K1-1 and K1-3, respectively). Given the high superiority of N-oxide introduction in OB improvement and density enhancement, several molecules shown in Figs. 4.13 and 4.14 should receive more attention, in spite of a slight decrease in molecular stability.

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

Fig. 4.13 Molecular structures of pyrazoles, triazoles, tetrazoles, pentazoles, furazans, pyridines, and their N-oxides, denoted as Groups A-F, respectively. The bond length is in Å

Owing to the high electron-withdrawing capability of O atom, the lengths of adjacent C–N and N–N bonds increase more or less after N-oxidization introduced. In particular, a N–N bond will be significantly stretched when located between double N–O bonds on a ring. For example, the N–N bonds in I1-6 and K1-2 are stretched by >0.2 Å, resulting in broken hexagon rings. This may be attributed to the repulsion between the adjacent lone pairs of O atoms [108]. Thus, if two neighboring N+ –O− bonds are introduced on an aromatic ring, it will be damaged.

4.2 Traditional Energetic Molecular Crystals

129

Fig. 4.14 Molecular structures of pyridazines, pyrimidines, pyrazines, triazines, tetrazines, pentazines, hexazines and their N-oxides, denoted from Groups G to K. The bond length is in Å

In combination with the analyses of frontier orbitals, aromaticity and NBO charges, and the existing understandings [109–117], Yuan et al. concluded that the introduction of N+ –O− bond weakens molecular stability mostly, as it stretches its neighboring bonds and decreases molecular aromaticity; and it occasionally enhance molecular stability by diminishing the lone-pair repulsion and promoting the σ– π separation [118]. After an overall assessment of both energy and stability, they proposed 19 N-oxides as promising basic high-energy structures with considerable

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

stability, including G2-2, G3-1, G3-2, H1-4, H2-1, H2-2, H2-3, H2-5, H2-6, H3-1, H3-2, I2-2, I2-5, I2-6, I2-7, I3-1, I3-3, I3-4, and J1-9 [91].

4.2.3 Energetic Organic Azides As an explosive group, azide can exist as not only a substituent in an organic compound, but also an ion in an ionic compound. Some organic azides [83, 85, 119–125] are shown in Fig. 4.15. Azide is naturally an electron-acceptor, while it possesses a weak ability to accept electrons, making it less stable compared with fluorides. Moreover, because an azide group can obtain more electrons in ionic salts than in organic compounds, azide salts are usually more stable than organic azides. In fact, some organic azides like DATZ are extremely sensitive and hard to be treated. Besides, azide group is a kind of explosive group as NO2 . However, the initiation mechanisms of two groups are totally different from each other. For a NO2 compound, NO2 is partitioned from the reactants first and an intermediate forms out, then a series of complex subsequent reactions takes place, and finally some stable products like H2 O and N2 generate; while for N3 compound, N3 is also the first to be partitioned to form N3 radicals, but then converted to N2 by a combination of such two radicals. Furthermore, due to the low packing densities and high sensitivities of organic azides, N3 compounds usually do not exhibit detonation performances as high as the nitro compounds and are often applied as primary explosives. O

B

C

A

C

A B

B

O

O

C

AAF

A

DATZ

B

NGA

A

O/C

B

A O B

ANTHA

O/C

C

A

ANB

NADAT

B C C

O O/B

A

A

O A

C

Fig. 4.15 Molecule and crystal packing structures of some organic azides

B

4.2 Traditional Energetic Molecular Crystals

131

4.2.4 Energetic Compounds with Different Heat Resistance In this section, we introduce the intrinsic structures of energetic molecular compounds based on their heat resistance. Some energetic compounds with high heat resistance are used in the formulations of heat-resistant energetic materials. In applications, it is sometimes necessary to deal with high-temperature environments, such as the exploitation of deeply buried fossil fuels of coal, oil and gas, and in-space operations [126, 127]; thus, the pursuit of new thermostable energetic compounds is encouraged. Plenty of energetic compounds with excellent heat resistance have been synthesized and applied already, such as TATB, HNS, LLM-105, PYX, and TACOT, as shown in Fig. 4.16. Their DSC decomposition temperature peaks (Td ) can reach above 573 K [1, 81, 128–130]. In principle, the high molecular stability roots for the high thermal resistance. For example, they usually possess stable molecular frames, such as six- or five-membered conjugated rings, and stable substituents. All these frames and substituents are also the common stable moieties in organic chemistry. In comparsion, these moieties seldom exist in thermally unstable compounds, such as PETN and nitroforms. Besides, it was confirmed that bridged structure facilitates the high heat resistance very recently [131]. Recently, Huo et al. studied the thermal decay of three thermostable energetic compounds of TATB, HNS, and PYX, and found that the clustering was responsible for the high thermostability [132]. Furthermore, they confirmed the close compositions of clusters produced in thermally decay these three compounds, i.e., C always possesses the highest population, followed by O, H, and N atoms. It seems that a high C content facilitates high heat resistance. From Fig. 4.17, one can readily confirm a dependence of Td on OB or the C content, i.e., in general, much negative OB or high C content corresponds to high Td . In fact, the more negative OB generally implies the higher C content. It is well known that C can be hybridized in the patterns of sp, sp2 , and sp3 , and possesses the highest ability to form covalent bonds, but it is prone to cluster in case of insufficient O. Besides, a stable molecular frame roots for the

A

A

B/O

B

O

B C/O

A C

C

TATB

HNS

LLM-105

A A

B/O B

C

C/O

PYX

TACOT

Fig. 4.16 Molecular and packing structures of some highly thermostable energetic compounds

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4 Energetic Molecules and Energetic Single-Component Molecular Crystals

high thermal stability, as all the 28 highly thermostable energetic compounds shown in Fig. 4.17 each possesses a highly stable ring unexceptionally. In comparison, some energetic compounds exhibit low thermal resistance, such as nitroforms and nitricesters shown in Fig. 4.18, including TNMA [23], BTNEDA [30], BTNNA [134], BTNF [134], TNETB [135], NG [31], and PETN [34]. From a point of view of reactivity, these compounds exhibit high reactivity when heated, thanks to a fast monomolecular decomposition or intermolecular decomposition. A

823.15 K -43.1% 27.2% BTDAONAB

711.7 K -95.2% 42.8% m-DNB

709.3 K -95.2% 42.8% P-DNB

688.1 K -54.4% 32.6% DFP-1

685.3 K -56.3% 33.8% 1,3,5-TNB

676.3 K -91.0% 35.5% 2,4-DNCB

676.1 K -82.4% 26.5% DNTCB

659.1 K -102.6% 39.3% 2,6-DNA

653.1 K -52.8% 29.1% PICl

652.2 K -55.8% 27.9% TATB

651.1 K -74.2% 45.6% TACOT

645.1 K -102.6% 39.3% 2,4-DNA

643.6 K -55.4% 32.8% PYX

641.1 K -114.3% 46.1% 2,3-DNT

632.6 K -75.5% 39.6% 3,5-DNBA

629.9 K -114.3% 46.1% 2,6-DNT

627.1 K -50.0% 23.5% LLM-105

620.8 K -67.6% 37.3% HNS

614.1 K -114.3% 46.1% 3,4-DNT

606.1 K -56.0% 29.6% DATB

604.1 K -97.0% 50.6% 2,4-DNANS

603.3 K -89.6% 50.6% 2,4,6-TNX

594.6 K -74.0% 37.0% 2,4,6-TNT

594.6 K -74.0% 37.0% 3,4,5-TNT

588.1 K -24.5% 24.5% DAAF

586.1 K -114.3% 46.1% 2,4-DNT

585.1 K -78.3% 39.1% 2,4-DNP

582.1 K -78.3% 39.1% 2,6-DNP

578.1 K -45.4% 31.4% PA

572.6 K -74.0% 37.0% 2,3,4-TNT

Fig. 4.17 Energetic molecules with different heat resistance. The top-down values below each molecular structure are of Td (at a heating rate of 10 K/min), OB (CO2 supposed as the product of C), and weight fraction of C element in the original molecule

4.2 Traditional Energetic Molecular Crystals

O/A

133

C

C

C

A

B O/A

TNMA

B

C

O/B

BTNEDA

B

O/A

BTNNA

BTNF A

C

B

O/A

B

TNETB

A

O/C

B

O/C

PETN

NG

Fig. 4.18 Packing structures of some low thermostable energetic compounds

recent calculation at the level of B3LYP/6–311 + + G(d, p) shows that the BDEs of TNMA, BTNEDA, BTNNA, BTNF, and TNETB are respectively 29.7, 29.2, 28.8, 31.9, and 30.7 kcal/mol [136], much less than those of highly thermal stable compounds (usually >60 kcal/mol) [132]. Moreover, the ready intermolecular reaction contributes to a low thermal stability too. For example, it was confirmed that the ready intermolecular hydrogen transfer roots for the low heat resistance for a lot of hydroxylammonium-based ionic compounds [137].

4.2.5 Energetic Compounds with Different Impact Sensitivity As for the relationship between the intrinsic structure of energetic compounds and their impact sensitivity, this book will elaborate it in detail in subsequent chapters, but only briefly in this section. Recently, Ma et al. detailed the molecular structures, intermolecular interactions, and packing modes of impact sensitive and low impact sensitive energetic compounds [15, 17]. They found that, for molecules of LSHEMs, all of them each possesses a big π-bond with all non-hydrogen atoms, and intermolecular and intramolecular HB exists mostly and increases their stability. For LSHEMs, their crystal packing is a π-π stacking in principle, with intermolecular HB supporting the layers. It can be classified into six types, to understand it and reveal its influence on impact sensitivity. For the face-to-face stacked crystals, like TATB, most of them are low sensitive or insensitive to impact. When a crystal is impacted, it is easy to have interlayer sliding in molecular layers, owing to only a slight increase in the inter- or intramolecular potential. In contrast, with respect a mixing stacked crystals like TNB, sliding along any orientation is strongly forbidden. This is the crystal packing mode-impact sensitivity relationship [15]. Thus, it is requisite to have face-to-face π-π stacking with the aid of intermolecular HB in the crystal engineering of LSHEMs, as shown in Fig. 4.19 [14].

134

4 Energetic Molecules and Energetic Single-Component Molecular Crystals B/O

A B

C

B

O O/A

C

C

A

TATB

DATB

NTO

C O/B

A

NQ

DNDP

Fig. 4.19 Some low impact sensitive energetic compounds with H 50 > 290 cm (hammer weight, 2.5 kg)

The crystal packing of 9 typical SHEMs has been systemically analyzed. Two structural factors were identified for understanding their high sensitivity: low molecular stability and π-π stacking without the aid of HB, as HNB and BTF shown in Fig. 4.20 [17]. Meanwhile, the role of intermolecular interactions should be paid attention to. For example, owing to the weak intermolecular interaction and the high sliding barrier, π-π stacking in HNB and BTF cannot play a role in buffering external stimuli efficiently. Combining the crystal packing analysis of LSHEMs and SHEMs, it can be concluded that HB-aided π-π stacking is generally necessary for crystal engineering of LSHEMs.

C A

O/B

O

B

C/A C

A

O/B

HNB

PETN

B

A

O/C C

O

BTF B

B

A

ε-CL-20

C/O

α-RDX

NG

B

A

A B C

O/A

C

TNAZ

O B

β-HMX

C

A/O

CE

Fig. 4.20 Some impact sensitive energetic compounds with H 50 < 40 cm (hammer weight, 2.5 kg)

4.3 Energetic Halogen Compounds

135

4.3 Energetic Halogen Compounds This section briefly introduces some energetic halogen compounds. And there are some benefits to introduce halogen elements to energetic compounds. First, it will enhance the molecular stability while stay still highly energetic. For example, the group –CF(NO2 )2 is generally more stable than –C(NO2 )3 and –CH(NO2 )2 . Moreover, because halogen is naturally the remover of chemical and biological warfare agents, energetic halogen compounds have a combined effect of damage and agent-removing. Besides, introducing F atoms into energetic compounds can enhance the working ability of Al-contained formulations, since the Al-F combination will release more energy than Al-O combination and AlF3 (1910 K) possesses a much lower boiling point than Al2 O3 (4000 K).

4.3.1 Energetic Fluorine Compounds There are two advantages of introducing F into the traditional CHON energetic systems. One is to increase the density of the system, because the mass density of F atom is higher than that of any of the CHNO atoms. Replacing O by F will lead to a significant increase in the density of the explosive, for instance, from 1.96 g/cm3 of O2 N–C(NO2 )2 –CH2 –N(NO2 )–CH2 –C(NO2 )3 to 2.05 g/cm3 of F2 N–C(NO2 )2 – CH2 –N(NO2 )–CH2 –C(NO2 )2 NF2 . The other is to increase reaction heat. For the CHNOF energetic systems, F atom will be transformed to be HF after the detonation, with only a low HOF of −184 kcal/mol. This is much lower than that of H–OH, −116 kcal/mol. According to denotation theory, the detonation properties are determined by the density, reaction heat, and gas yield. Thus, the introduction of F will promote the detonation properties when the gas yield remains invariable. There are two forms for F atom in energetic CHONF compounds, –NF2 and –CF(NO2 )2 . The molecules containing NF2 are usually less stable corresponding NO2 compounds. Meanwhile, the oxidation number of F is −1 is less than that of O, −2. Thus, NF2 contributes less to reduce OB to make reaction complete than NO2 . Considering the two reasons, compounds containing NF2 are rarely applied energetic materials. Figure 4.21 demonstrates the intrinsic structures of some fluoronitro compounds [138–147]. In general, these fluoronitro compounds are more stable than corresponding nitroform compounds, as well as the corresponding geminaldinitro compounds. The repulsion among the three NO2 groups of the nitro groups will reduce when replacing a NO2 with a F atom, thereby a molecule with –CF(NO2 )2 group is more stable than –C(NO2 )3 group. Because –CH(NO2 )2 group features weak acidity, the partition of H+ from it will become ready if it meets with a base compound. This will lower its stability. Whereas, no such protonation can take place for the – CF(NO2 )2 group, showing its higher stability. That is, the replacement of the H atom by the F atom avoids the salification and increases the compatibility.

136

4 Energetic Molecules and Energetic Single-Component Molecular Crystals F

C

N

O

H

B A O/B

A

C C

LLM-208

O/B

FDMNTA

FDMTA B

O

C A B

C

A

O

A B

C/O

C

BFOD

O A

FFOYDO

FDNMDO C O/B

C

O/B

A

C

O A

A B

FDNT C

FDNO

2-FDNT

B A

Fig. 4.21 Molecular and packing structures of some energetic fluorine compounds

LLM-208 was first reported by DeHope et al. in 2013 [148]. It possesses low mechanical sensitivity (H50 = 119 cm), while moderate thermal stability (Td = 470 K, at a heating rate of 10 K/min) and detonation properties (vd = 8320 m/s and Pd = 32.9 GPa, predicted by Cheetah). The packing density of LLM-208 is 1.895 g/ cm3 at 130 K, while the density at ambient condition is calculated to be 1.848 g/cm3 [138]. The relatively low melting point, around 425 K, can partly be responsible for its low mechanical sensitivity. FDMNTA and FDMTA are analogs to each other. It is interesting to find that the FDMTA possesses a low melting point of 340 K, lower than that of TNT, showing a potential to be used as a casting explosive [139]. BFOD has a high crystal packing density of 1.960 g/cm3 under common condition, but it is readily analyzed when heated to 444 K, restricting its application [140]. The low thermostability and relatively low melting point are also found for FFOYDO, which is a hydrogen-free compound [141]. There are only the crystallographic information and molecular adsorption spectra reported for FDNMDO [142]. A similar case happens on FDNT, without any other property reported. In terms of the composition, FDNO is an oxidizer with a positive OB [143]. The compound 2-FDNT displays a melting point of 389 K and begins to decompose at 481 K, and its impact sensitivity is less than that of RDX. In addition, its Pd and vd were predicted to be 33.2 GPa and 8400 m/s [144]. –CF(NO2 )2 serves as substituent in both DFMD [145] and FDMDP [146], which possess acceptable thermal stabilities. For FDNMD, the density is found to be 1.886 g/cm3 at 300 K, the impact sensitivity is lower than that of TNT, and the

4.3 Energetic Halogen Compounds

137

friction sensitivity is comparable with RDX and is considerably lower than that of HMX, implying its high application potential [147]. In summary, most synthesized energetic fluorine compounds exhibit relatively low melting points due to the weak intermolecular interactions, and do not have high detonation properties as expected since F element disfavors the gas production. Thus, energetic fluorine compounds can hardly present us a good perspective with respect to high detonation properties.

4.3.2 Energetic compounds with Chlorine, Bromine, or Iodine In comparison with energetic fluorine compounds, the quantity of other halogen compounds is limited. We list some of them in Fig. 4.22, where the chlorine, bromine, or iodine atoms is contained therein [149–155]. Besides the aforementioned combined effect of energetic materials and chemical/biological agent remover, these halogen compounds can also serve as the intermediates in synthesizing the energetic CHNO compounds. For example, TCTNB is an intermediate of one synthetic process of producing TATB by ammonification. Cl, Br, or I atom is a good active group for synthesizing energetic molecules by displacement. It will weaken the C–NO2 bond when introducing Cl, Br, or I on a benzene ring to be adjacent to a NO2 group, because it destroys the conjugation effect between the ring and NO2 group, such as the compounds in Fig. 4.22. Because TCTNB is much sensitive than TATB, its existence as impurity in TATB will significantly affect the safety of the TATB-based formulations. Because of the destructed conjugation structure, Cl C

O

Br

I

C

N

O

B B

A B C/O

C/O

A

DCMO

A

CMTTBII

DTTBII A

O

C

B

A

TNCB

O/B

C

TCTNB

DCTNB A

B C

A

O/B

TBTNB

A

O

C

BOTNB

C

O/B

TITNB

Fig. 4.22 Molecular and packing structures of some energetic halogen compounds without F

H

138

4 Energetic Molecules and Energetic Single-Component Molecular Crystals

the molecular planarity of 1,3,5-trinitrobenzene compounds with the replacement by halogens is much lower than that by –NH2 or the compound themselves. On the other hand, the halogen bonding is a kind of intermolecular interactions consolidating the crystal packing.

4.4 Entropy Explosives: Energetic Peroxides 4.4.1 Energetic Peroxides Energetic peroxides possess a common group of peroxide, serving as an oxidation group. In general, the containing of N atoms in energetic peroxides can faciliate to increase energy content. As shown in Fig. 4.23 [156–161], the energetic peroxides generally possess much negative OB, suggesting much incomplete oxidation of the decomposition reactions due to insufficient oxidizer in these molecules. The decomposition of energetic peroxides usually starts from the breaking of O–O bond. This bond is so weak that the molecular stability of energetic peroxides is even lower than most conventional energetic molecules applied already, and also very sensitive to external stimuli. A known case of the synthesis of peroxides is TATP, by oxidizing acetone with H2 O2 and the aid of catalyzer, as illustrated by Fig. 4.24. TATP was invented in 1895 by a chemist Richard Wolffenstein [162]. He was the first one who used inorganic acid as the catalyst and obtained a patent to synthesize explosives from hydrogen peroxide. In the synthesis, DADP is also produced, and even more unstable than TATP. When the reaction condition features slightly acidic or neutral, the oxidation of acetone will slow down, with more DADP produced.

B

A C

B

O

O/A B

TDHT

C

A/O

C

CTDD

DADP

A

C

O/B

A

HMDD

B

B

C/O O/C

A

TDDD

Fig. 4.23 Molecule and crystal packing structures of some organic peroxides

TATP

4.5 Full Nitrogen Molecules

139

Fig. 4.24 Syntheses of TATP and DATP

4.4.2 Introduction of Entropic Explosion Energetic peroxides are very sensitive. For example, TATP can explode when it is rubbed or heated slightly, thanks to the aforementioned ready cleavage of O–O bond. It was the protagonist of the bombing in Britain on July 7, 2005. Interestingly, it does not produce any flame during the explosion of TATP. The decomposition of TATP molecule can release acetone, O2 and O3 , and one TATP molecule produce four gas molecules, which is the reason why TATP can explode. In a period of shorter than one second, only a few hundred grams of TATP can produce hundreds of kiloliters of gas, while with inconspicuous heat release. Thus, the energetic peroxides like TATP are much different from conventional explosives like TNT, whose decomposition accompanies the release of a large quantity of heat and gas. The explosives that can release much gas but with negligible heat are the entropic explosives. Of course, TATP is not the only explosive with such properties. For example, many azide compounds can generate a lot of N2 when they decompose, while a little heat only. People take advantage of this property of some azides and use them as gas-generator of airbag in cars. It is noteworthy that TATP is calculated to decompose and produce O3 and O2 , which are not intuitively expected oxidation products. The explosion of TATP with large amount of heat released is not highly favored. It rather concludes entropy explosion, yielding four gaseous molecules from each TATP molecule in solid state. As stated by Dubnikova et al., different from common explosive compounds, three isopropylidene units in TATP cannot be oxidized and release heat in decomposition. It seems that three peroxide units of TATP are hold in a close spatial distance and an appropriate orientation for chain decomposition reactions (Fig. 4.25). It shows that the detonation of peroxides is more likely an entropic explosion [163].

4.5 Full Nitrogen Molecules Except for nitrogen molecule (N2 ), there is no other full nitrogen molecule that has successfully been prepared till now. Still, theorists have proposed many possible configurations of all-N molecules based on basic chemical theoretical knowledge. This section focuses upon full nitrogen molecules, as well as ions, which are likely to be stable and/or of interest. Simple calculation methods (usually DFT) were used for the geometric optimization and the relative enthalpy calculation for various isomers at

140

4 Energetic Molecules and Energetic Single-Component Molecular Crystals

(a)

Reaction coordinate

(b)

Reaction coordinate

(c)

Reaction coordinate

(d)

Reaction coordinate

Fig. 4.25 Decomposition paths of TATP to produce O3 (a → b → c) and O2 (a → b → d)

0 K. For a given formula, there may be many isomers with different thermodynamic stabilities. As pointed out in a computational review [164], following objectives should be pursued by theoretical investigations: (1) to locate the PES minimum of various conformers and isomers with a specified structural formula; (2) to confirm the stability of a gaseous molecule; and (3) to determine the properties stabilizing the compound. In fact, the real challenge is to estimate the isomeric stability and give advice to experimentalists. In general, the energy barriers of decomposition of 77 and 120 kJ/mol are seen as thresholds for a lifetime long enough for experimental detection and practical use at common conditions, respectively. It should be noted that polymer nitrogen belongs to atomic crystal, instead of molecular crystal, and therefore will introduced later. (a) N3 . In 1890, HN3 was prepared for the first time, and N3 − was the first stable full nitrogen species except for N2 . The absorption spectral data of linear N3 radicals was first recorded by Thrush in 1956 [165]. There are two stationary structures for N3 radical, one is linear and the other is a ring. In 2003, Wodtke obtained the cyclic N3 radical through the photolysis of ClN3 [166]. He also constructed the PES of N3 radical using CASSCF, CASPT2, and MRCISD(Q) methods and found a very complex converted PES. In addition to the change of the geometric structure, there is also an overlap of the PESs of different

4.5 Full Nitrogen Molecules

141

spins. Overall, the linear N3 radical is the most stable, and the energy of the ring structure is 134.7 kJ/mol, higher than the former [167, 168]. Through high-level theoretical calculations and experimental results, Prasad proved that the linear azide is the most stable when it is an anion [169]. The bond energy of the azide radical containing N=N is very considerable. All the salts formed by azide with metal cations are explosives, among which lead azide is the most representative one and often used as detonator. (b) N4 . Theoretical investigations of the structure of N4 began in the early 1990s. The most widely studied are three possible stable N4 structures, an open chain structure in a C 2h symmetry, square one in D2h and tetrahedral one in T d (Fig. 4.26a). According to the PES (Fig. 4.26b), the energy of D2h N4 and T d N4 are both very high, but the decomposition energy barrier of the former is much lower. The high energy barrier of tetrahedral T d N4 implies a possible long lifetime. However, it is difficult to find a suitable chemical synthesis path to reach this structure. And the energy for the decay barrier to two N2 and the HOF are debatable, because both of them are dependent on the calculation accuracy, as well as the specific decomposition pathway [170–174].

(a)

Td

D2h

C2h

TS2 D2

(b)

TS3 D2d

TS1 D2h

0.61

3.04

Td

2.65

D2h 2N2

2N2

Fig. 4.26 a Diagram of N4 molecular structures and b energy barriers on the minimum energy pathways for dissociating T d N4 and D2h N4 and for their interconversion (energy unit in eV/ molecule)

142

4 Energetic Molecules and Energetic Single-Component Molecular Crystals

Experimentally, it is more challenging to detect the neutral molecule of N4 . The first observation of N4 were related to the formation of the N4 + cation in an electric discharge in N2 [174, 175]. It was an unsuccessful attempt to detect the N4 by discharge in N2 and depositing the products on glass cooled by liquid helium [176]. The first success did not come until 2002. Cacace et al. took an advanced massspectrometric technique, neutralization-reionization mass spectrometry (NRMS), making it possible to record a signal from the N4 molecule [177, 178]. They observed peaks from 15 N2 and 14 N2 , and found that the two species formed a weakly bound N4 open chain complex [177]. Afterward, a comprehensive study supported the observation. Therein, the mass spectra of N4 molecule were measured experimentally and also assigned by detailed quantum chemical calculations [179]. According to these data, the N4 with a lifetime of about 1 μs can be detected by NRMS. However, the experimental and theoretical results of N4 molecule have not reached a full consensus yet, as there may exist multiple N4 structures. (c) N5 . Experimentally determined species of N5 , in a type of ion. Thus, they will be introduced in Sect. 6.3. (d) N6 . N6 was experimentally reported [180, 181], while without further confirmation. In 1995, Workentin et al. synthesized anion N6 − with the N3 radical; in this case, N6 − in acetonitrile was verified as a broad absorption peak ~700 nm and an IR peak at 1842 cm−1 appear [182, 183]. In practice, the structure is a weakly N3 N3 − bound complex. Theoretical studies on the neutral molecule of N6 revealed many isomers. One of the isomers, the benzene analogue (hexa-azabenzene) was predicted, with imaginary frequencies in the vibrational spectrum [184], suggesting an instable structure. Several other N6 molecules were also investigated [184, 185], where the most two energetically favorable forms were the chain-like with C 2h symmetry (Fig. 4.27a) and the twist-boat one (Fig. 4.27b). In addition, the prismatic structure with D3h symmetry (Fig. 4.27c) [188] was found to have both a high barrier to decompose and a high energy content, and was recommended as a candidate for high-energy–density materials. Crystal stability is related to more factors. As noted in an article about N8 molecular crystals [187], three points are required for stabilizing a molecular solid at a macroscopic scale: (1) the molecular building blocks should be stable in gas state; (2) the chemical stability of molecules (or ions) should be kept in crystal; and (3) the intermolecular interactions in crystal should be in the forms of van der Waals and electrostatic ones. In 2016, a computational work to predict the crystal structure of N6 molecules was published and showed that the crystal structure of N6 open chain is stable (Fig. 4.27d) [188]. (e) N7 . For N3 and N5 with an odd number of N atoms, the ionic configuration is more stable than corresponding neutral one. Among all the possible configurations of N7 ion, including the ring and linear structures, open chain N7 − (C 2 ) and N7 + (C 2v ) are two energy minima on the PES [189]. The decomposition products of a N7 − are a N3 − and two N2 , while the products of a N7 + are a N5 + cation and a N2 . At a calculation level of G3 (MP2), their decomposition energy

4.5 Full Nitrogen Molecules

(a)

143

(b)

(c) B

O/A

C

(d) Fig. 4.27 Molecular and crystal structures of N6 . chain-like conformer with C 2h symmetry (a), twist-boat conformer with D2 symmetry (b), prismatic conformer with D3h symmetry (c), and molecular crystal (d)

barriers are calculated to be respectively 1.2 and 3.1 kcal/mol, showing very low stability. (f) N8 . The structure of N8 is so complicated due to various styles of N atom connections. Four N8 molecular conformers were predicted to be stable according to the PES [190]. Among the isomers of N8 without double bonds, Schaefer’s research confirmed that alkane N8 with a caged structure (Fig. 4.28a) was more stable than that with a cubic structure (Fig. 4.28b), and its energy content was still high [191]. It is difficult to detect N8 experimentally according to the theoretical calculations [185, 190, 192–194], which were performed since 1990 and showed that almost all N8 isomers had very low dissociation barriers. Despite the low stability of N8 molecule, N8 crystal is expected to be more stable. A recent prediction confirmed the existence of a molecular crystal of N8 (C 2h ) (Fig. 4.28c) [187]. A N8 chain consists of three single bonds, one double bond and two triple bonds at both ends of the chain. The molecule is also highly energetic despite the triple bond. Enthalpy calculations revealed that this structure is more stable than the cg-N below 20 GPa. Combined with the above N6 crystal, it seems that the linear all-N molecular packing is likely to be the most stable.

144

4 Energetic Molecules and Energetic Single-Component Molecular Crystals

C

O/B

(a)

(b)

A

(c)

Fig. 4.28 Molecular and crystal structures of N8 . the C 2v conformer (a), the Oh conformer (b), and molecular crystal of N8 (c)

We summarize the decomposition barrier and HOF of all-N molecules with no more than 8 N atoms in Table 4.1 and find that all the molecules are highly energetic; meanwhile, the tetrahedral N4 and prismane N8 may be stable with high decomposition barrier. Unfortunately, they have not come into being yet. (g) N9 , N10 , N20 , and N60 . Theoretical prediction shows that both neutral molecule and ionic configuration of N9 have an open chain C 2v structure [195]. Unlike other odd-numbered N structures, neutral N9 molecules are more stable than ions. A DFT calculation shows an energy barrier of 32 kcal/mol for N9 to decompose into N6 and N3 . In contrast, the barrier for N9 + to decompose into N7 + and N2 is 2.1 kcal/mol only. In a search for PES minima of N10 , Ren et al. investigated nine structures that did not contain double bonds, and confirmed seven of them to be minima at a relatively accurate level of MP2 [196]. 11 minima were confirmed at the levels of B3LYP and MP2, but these species were predicted to be kinetically unstable due to the low barrier for dissociation or isomerization [197]. Manaa studied N10 structures with two N5 rings parallel and perpendicular to each other, and found that the N5 –N5 bond was Table 4.1 Summary of the geometries, decomposition barriers, and HOF for several typical all-N molecules Compound

Geometry

Point group

Decomposition barrier (eV/mol)

HOF (eV/mol)

N4

Tetrahedral

Td

2.650 [169]

7.950 [173]

N4

Chain

C 2h

0.571 [171]

6.843 [172]

N4

Square

D2h

0.608 [169]

8.285 [170]

N6

Twist-boat

D2

1.147 [186]

9.202 [185]

N6

Chain

C 2h

0.774 [183]

8.804 [185]

N6

Prismane

D3h

1.494 [186]

14.684 [186]

N8

Chain

C 2h

0.774 [190]

11.180 [187]

N8

Cage

C 2v

–

15.449 [191]

4.5 Full Nitrogen Molecules

145

strong and N10 could be a good block for building N60 ; while, due to the instability of N5 ring, the dissociation of the two N5 radicals is very ready [198]. In 2005, Zhou et al. studied the stability of nine isomers of N10 with G3 and G3MP2 methods, and confirmed the most stable bowl-shaped structure with 3 five-membered rings, indicating that the formation of double bonds plays an important role in molecular stability [199]. It is difficult to obtain reliable data about all-N compounds containing more than ten nitrogen atoms, due to the complex molecular geometry with really large degrees of freedom. Other theoretical researches were performed on large molecules that contain much more N atoms, such as N20 and N60 . Bliznyuk, Shen, and Schaefer showed that N20 has a dodecahedron geometry (Fig. 4.29a) and its energy was 50 kcal/ mol above that of ten N2 molecules [200]. In 1999, Ha et al. [201] also studied N20 isomer using MP2 and B3LYP methods and found three minimums, i.e., the conformers of the dodecahedron cage (Fig. 4.29a), D5v bowl (Fig. 4.29b) and D5 ring (Fig. 4.29c). It was computationally confirmed that cage conformer was about 200 kcal/mol higher than both the bowl and ring ones, and ring conformer was the most energetically stable. Strout’s group [202] confirmed another conformer with a more cylindrical cage by MP4 and DFT calculations (Fig. 4.29d), where the structure was energetically favored than the conformer of dodecahedron cage. They also speculated that more frameworks would be more stable. A calculation study of the N60 molecule was first published by Song et al. in 1997 [203], and they found that the S 6 structure composed of 12 N5 structures was with the greatest stability. Three years later, calculations from Livermore National Laboratory [198] showed that it was possible to form N60 molecules composed of six rings, each ring containing 10 N atoms. Thereby, the “nitrogen fullerene” molecule was hypothesized and could be synthesized experimentally under extremely high

Fig. 4.29 Four conformers of N20 of the icosahedral cage (a), the D5v bowl (b), the D5 ring (c) anda more cylindrical cage (d), and the morphology of N60 (e)

146

4 Energetic Molecules and Energetic Single-Component Molecular Crystals

pressures. Unfortunately, subsequent detailed investigation [204] on N60 molecule confirmed that S 6 structure was metastable and I h structure (like that of C 60 ) was also unstable.

4.6 Conclusions and Outlooks The energetic single-component molecular crystals are the most widely distributed among the applied energetic crystals and have received the most attention. We have discussed them in terms of molecular skeletons and substituents. They are also the basis for other interests that will be discussed in subsequent sections. Although lots of other types of energetic compounds have come into being, most of them have not been applied yet. Thus, single-component molecular crystals retain still as the mainstream currently. In fact, the understanding of this group of energetic materials is the basis for understanding other kinds and still requires many attempts. After all, there are still numerous things we have not known.

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203. Song, L. I., Hong, Q. U., & Qian-Shu, L. I. (1997). Quantum chemical study on N(60) . Chemical Research in Chinese Universities, 68, 59–69. 204. Wang, L. J., & Zgierski, M. Z. (2003). Super-high energy-rich nitrogen cluster N60 . Chemical Physics Letters, 376, 698–703.

Chapter 5

Polymorphism and Polymorphic Transition in Energetic Molecular Crystals

5.1 Introduction Polymorphism is a universal phenomenon of both natural and artificial substances, and refers to that a substance can exist in different crystalline forms. Correspondingly, that one form changes to another is polymorphic transition. It occurs as one form is thermodynamically unstable and kinetically permitted to be transferred to another. Thereafter, molecular and crystal structures, property and performance change more or less. Generally, there is no chemical reaction included during a polymorphic transition. Energetic compounds, usually organic molecules composed of C, H, N, and O atoms, are inherently polymorphic thanks to the variations of molecular conformation and molecular stacking. The polymorphic transition of energetic materials may occur under allowed conditions like heating and pressing, during their lifetime from design and synthesis to crystallization, powder manufacture, machining, transportation, storage, and application. Polymorphic transition is often accompanied by varied structures, properties, and performances, and is a common phenomenon of energetic materials. This section introduces the polymorphism, polymorphic transitions, and molecular and stacking structure variations, and property and performance changes of six traditional energetic compounds applied already, including TNT [1, 2], PETN [3, 4], RDX [5–7], HMX [8, 9], CL-20 [10–12], and FOX-7 [13, 14]. These compounds each consists of energetic neutral CHNO molecules. Although this section does not cover the polymorphism and polymorphic transition for all energetic compounds, it is still expected to be helpful to study others.

© Science Press 2023 C. Zhang et al., Intrinsic Structures and Properties of Energetic Materials, https://doi.org/10.1007/978-981-99-2699-2_5

157

158

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

5.2 Polymorphism and Polymorphic Transition 5.2.1 Polymorphism TNT, as a benchmark of energetic compounds, has two polymorphs at ambient conditions, m-TNT and o-TNT [1, 2]. PETN, an important primary explosive, has been ascertained to have four polymorphs, PETN-I at ambient conditions, PETN-II at high temperatures which is close to the decomposition limit [15], while PETN-III and PETN-IV under high pressures [16]. RDX possess multiple phases [17–19], i.e., the most stable polymorph at ambient conditions is α-RDX, β-RDX is a heat-induced form, and γ -, ε-, δ-, ζ-, and η-RDX belong to high pressure phases. It is reported that there are eight phases for HMX, including α-, β-, ε-, γ -, φ-, ζ-, η-, and δ-HMX, exhibiting multiple phases as RDX [20–23]. α-, β-, and δ-HMX can be stabilized under common conditions, while γ -HMX appears in a hydrated form at ambient conditions [20]. γ -HMX is actually not a phase of HMX according to the strict definition of polymorph, which refers to that molecules with the same chemical structure are arranged orderly in a certain way. γ -HMX is a double-component form with H2 O, different from the single-component ones, and in fact it belongs to a cocrystal according to the recent definition [21, 22]. The other forms, ζ-, ε-, η-, and φ-HMX, stay in the pressure range of 5 ≤ P < 12.6 GPa, 12.6 < P < 16 GPa, 16 < P < 27 GPa, and P > 27 GPa, respectively [23]. Four polymorphs of CL-20 identified. α-CL-20 is also a hydrate as γ -HMX and should be excluded from a polymorph. β-, γ -, and ε-CL-20 [10] exist at ambient conditions, while ζ-CL-20 [24, 25] in high pressures. FOX-7 is also highly polymorphic, as it exists in the α-form at ambient conditions, β-, γ -, and δ-forms at elevated temperatures, and α’- and ε-forms under high pressures [14, 26–28]. All the polymorphs for the six compounds are listed in Table 5.1, with their identified lattice parameters and related measurement conditions. It should be noted that a usual difficulty exists in ascertaining crystallographic information of energetic compounds at extremes, especially some conditions where the compounds are ready to decompose.

5.2.2 Polymorphic Transition The phase diagrams of the six energetic compounds concerned are summarized Fig. 5.1. Arrowed lines a and b therein denote the energetic compounds undergoing a temperature elevation with a small and a significant pressure increases, respectively, so they can roughly represent the evolution of energetic compounds impacted or heated in unconfined and confined environments, respectively. Thereby, what polymorphic transition takes place in practice can be deduced. The reported phase diagram of TNT is rare. At a common condition, m-TNT can be transitioned to o-TNT through solvent crystallization [2]. In addition, the highpressure melting line and chemical stability of molten TNT were carefully studied by

Crystal system

Monoclinic

Orthorhombic

Tetragonal

Orthorhombic

Orthorhombic

Orthorhombic

Orthorhombic

Orthorhombic

Orthorhombic

Monoclinic

Hexagonal

Monoclinic

Monoclinic

Orthorhombic

Polymorphs

m-TNT

o-TNT

PETN-I

PETN-II

α-RDX

β-RDX

ε-RDX

γ -RDX

α-HMX

β-HMX

δ-HMX

ε-HMX

ζ-HMX

β-CL-20

Pb21a

P21 /c

P21 /c

P61

P21 /c

Fdd2

Pca21

Pca21

Pca21

Pbca

Pcnb

P421 c

Pca21

P21 /a

Space group

9.676(2)

6.233

21.799(3)

7.711(2)

6.5400

15.1400

12.5650(19)

7.0324(11)

15.0972(7)

13.182(2)

13.290

9.380

14.910(2)

14.9113(1)

a, Å

13.006(4)

10.474

10.913(2)

7.711(2)

11.0500

23.8900

9.4769(6)

10.530(3)

7.5463(4)

11.574(2)

13.490

9.380

6.0341(18)

6.0340(1)

b, Å

11.649(3)

8.369

10.819(2)

32.553(6)

8.7000

5.9130

10.9297(9)

8.7909(11)

14.4316(6)

10.709(2)

6.830

6.700

19.680(4)

20.8815(3)

c, Å

90

90

90

90

90

90

90

90

90

90

90

90

90

90

α, °

90

124.49

97.43(2)

90

124.30

90

90

90

90

90

90

90

90

110.365(1)

β, °

Table 5.1 Lattice parameters and measurement conditions of the polymorphs of six common energetic compounds

90

90

90

120

90

90

90

90

90

90

90

90

90

90

γ, °

(continued)

10–30 °C, 1 atm

10–30 °C, 6.2 GPa

-73 °C, 1 atm

10–30 °C, 1 atm

10–30 °C, 1 atm

10–30 °C, 1 atm

20 °C, 5.2 GPa

20 °C, 5.7 GPa

0 °C, 1 atom

10–30 °C, 1 atm

136 °C, 1 atm

10–30 °C, 1 atm

−150 °C, 1 atm

−173 °C, 1 atm

Measurement conditions

5.2 Polymorphism and Polymorphic Transition 159

Orthorhombic

Monoclinic

Triclinic

Monoclinic

β-FOX-7

α’-FOX-7

ε-FOX-7

γ -FOX-7

P21 /n

Monoclinic

Monoclinic

ζ-CL-20

α-FOX-7

P21 /n

Monoclinic

γ -CL-20

P21 /n

P1

P21 /n

P21 21 21

P21 /n

P21 /n

Monoclinic

ε-CL-20

Space group

Crystal system

Polymorphs

Table 5.1 (continued)

13.354(3)

6.0745(11)

6.7118(4)

6.9738(7)

6.934(7)

12.579(2)

13.231(3)

8.852(2)

a, Å

6.895(1)

6.6924(7)

6.0361(4)

6.635(1)

6.6228(8)

7.7219(19)

8.170(2)

12.556(3)

b, Å

12.050(2)

6.6972(7)

10.9581(12)

11.6475(16)

11.3119(13)

14.1260(15)

14.876(3)

13.386(3)

c, Å

90

119.505(3)

90

90

90

90

90

90

α, °

111.102(8)

93.913(7)

90.077(4)

90

90.065(13)

111.218(10)

109.17(2)

106.82(2)

β, °

90

110.042(7)

90

90

90

90

90

90

γ, °

– 73 °C, 1 atm

20 °C, 5.9 GPa

20 °C, 4.27 GPa

120 °C, 1 atm

25 °C, 1 atm

20 °C, 3.3 GPa

10–30 °C, 1 atm

10–30 °C, 1 atm

Measurement conditions

160 5 Polymorphism and Polymorphic Transition in Energetic Molecular …

5.2 Polymorphism and Polymorphic Transition

161 600

600

(a) TNT

(b) PETN

Lindemann melt line Hugoniot

600

b

450

II

500

b

PETN-II

PETN-IV

400

PETN-I 0

5

10

15

20

25

300

0

2

6

8

10

γ

δ

α

150

12

0

14

(d) HMX

600

250

β

b

ε

150

Pressure, Pressure /GPa GPa

0.4

50 0

20

25

30

(f) FOX-7

ζ

600

500

400

b

δ γ β

γ 0.3

15

decomposition

α

β 0.2

10

a

decomposition

Temperature, Temperature / K K

Temperature, Temperature / K

b

0.1

5

Pressure, Pressure / GPa GPa 700

(e) CL-20

a

700

α

0

Pressure, Pressure / GPa GPa 350

a Temperature, Temperature / K

a

b

300

PETN-III

4

Pressure, Pressure /GPa GPa 800

500 0.0

ε β

III

I

300

450

know unkown

(c) RDX

Liquid

a

Temperature /KK Temperature,

a

Temperature Temperature,/ KK

Temperature, K Temperature /K

750

ε α'

α 300 1

2

Pressure, Pressure / GPa GPa

3

4

0

2

4

6

8

10

Pressure / GPa Pressure, GPa

Fig. 5.1 Phase diagrams of the six compounds. Red and blue dashed arrowed lines, lines a and b, denote the temperature elevation with a small and a significant pressure increases, respectively. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

Dattelbaum et al., showing a steep melting boundary by 61 K/GPa from the ambient pressure to 2 GPa (Fig. 5.1a). In contrast to the ambient pressure, high pressures narrow the difference between the melting and the decomposition temperatures of TNT, and when pressure reaches at 6 GPa, TNT will be analyzed, not molten instead [30]. The crystalline PETN can exist under the condition up to 14 GPa and 550 K, with phase diagram well established [31]. As shown in Fig. 5.1b, PETN-I exist stably at ambient conditions, and will be transitioned to PETN-II when heated close to its melting point (~414 K) [32]. PETN-I to PETN-II and PETN-I to PETN-III transitions will occur, once the environment varies along lines a and b, respectively. PETN-IV is a phase of high-temperature and high-pressure. Interestingly, it is found that the decomposition temperature of PETN increases along with pressure increasing. The decomposition of PETN starts with the partition of NO2 group by means of O–NO2 bond cleavage, accompanied with a large number of gas production. Thermodynamically, the pressure prevents PETN from the NO2 partition and gas production. RDX appears in multiple forms, as shown in Fig. 5.1c [17, 33–36]. ε-RDX exists in a narrow domain of pressure and temperature. Additionally, η-RDX and ζ-RDX were only reported as high-pressure phases, without any detailed data [17–19]. Hence, further work of the clarification of the diagram of RDX is still required. The most stable phase under common conditions, α-RDX, will be transitioned to β- and ε-RDX if it is evolved along a, and to γ - and δ-RDX along b. Figure 5.1d shows that β-HMX, as the most stable form under common conditions, will undergo a transition to α-HMX if the environment is evolved along a, and retain till the final decomposition along b [37]. Moreover, β-HMX is first converted into αHMX when heated to 375−377 K and subsequently into δ-HMX in the temperature range of 433−437 K [38]. Also, some high-pressure phases, such ζ-HMX (5 GPa),

162

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

ε-HMX (12 GPa), η-HMX (16 GPa), and φ-HMX (27 GPa), were reported [23]. Similar to RDX, HMX possesses an incomplete phase diagram. The phase diagram of CL-20 is shown by Fig. 5.1e [39, 40]. Because the polymorphic transition of CL-20 can weaken the application safety, it has received much attention. The α-, β- and ε-forms of CL-20 are all stable under common conditions, and can be transformed into the γ -form in 428−471 K [41]. Note the existing condition about temperature and pressure for a polymorph that can be different from that for polymorphic transition. Ciezak et al. evidenced the polymorphic transition from ε- to γ -CL-20 under 4.1−6.4 GPa, and further to ζ-CL-20 under about 18.7 GPa [42]. While, another much lower pressure of 0.7 GPa for holding ζ-CL-20 was confirmed by Russell et al. [24]. This difference may be caused by different transition path. Bishop et al. systematically studied the heating- and pressure-induced polymorphic transitions of FOX-7, and achieved a phase diagram covering six phases, as illustrated in Fig. 5.1f. α-FOX-7 exists stably at the ambient condition. The β-, γ -, and δ-formed FOX-7 are of high-temperature phases, while α’- and ε-formed FOX7 are of high-pressure ones [26, 39]. By the way, the crystallographic information on γ -FOX-7 was collected by heating it up to close to 393 K as its decomposition temperature and then annealing to 203 K. It is irreversible for FOX-7 to transform from β-form to γ . Two potential triple points of β + γ + δ and α + β + δ of FOX-7 can be deduced from the diagram. If the condition is evolved along a, the polymorphic transitions will occur from α- to β- and further γ -form; while α-FOX-7 will be changed to the α’- and ε-form in the case of environment changes in a route of b. Phase diagrams of energetic compounds are an important tool for understanding their polymorphic transition and guide the practical application. However, the phase diagrams of energetic compounds remain still incomplete, implying much more attempts required. This can be largely attributed to the high sensitivity of energetic compounds to temperature and pressure, as well as rays.

5.3 Factors Influencing the Polymorphic Transition At a given condition, such as a specific temperature and pressure, it is essentially determined by thermodynamics and accessible kinetics whether a polymorphic transition takes place or not. Nevertheless, kinetic determinations of polymorphic transition may be complex and variable, so there are many challenges should be faced up with. In this section, we focus on the effects of two determining factors, crystal quality and additive, on the polymorphic transition, as they are usually involved in crystallization process of energetic compounds.

5.3 Factors Influencing the Polymorphic Transition

163

Average particle size, um 58

60

62

64

66

160

160

156

156

152

152

148 148

Initial phase transition temperature,

Initial phase transition temperature,

56

144 144 94

95

96

97

98

99

100

Chemical purity, %

Fig. 5.2 Initial transition temperature from the ε- to γ -forms of CL-20 for samples with various chemical purities and particle sizes. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

5.3.1 Crystal Quality The crystal quality of energetic compounds mainly refers to morphology, perfection, chemical purity, and size and size distribution, while the so-called high quality generally means spherical crystal shape, high perfection, and purity, as well as particle sizes with only a narrow distribution [43]. Many experiments evidenced the determination of crystal quality on polymorphic transition. For example, the purity and particle size were related to the polymorphic transition from the ε- to γ -forms of CL-20 [44]. As demonstrated in Fig. 5.2, the initial polymorphic transition temperature increases with increased purity or decreased particle size. Reasonably, the smaller size with the higher specific surface energy facilitates the readier polymorphic transition. Nevertheless, it turns our common sense on head that the polymorphic transition of larger size CL-20 particles process more readily than the smaller ones. This is because the larger particles contain more defects, facilitating polymorphic transition [44]. In general, crystals with higher specific surface are more likely to undergo polymorphic transition.

5.3.2 Additive Numerous works evidenced the determinative effect of additives on polymorphic transition. A possible reason is that the presence of the additives can damage the

164

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

surface integrity of energetic crystals, increase interfaces and defects, and thus shallow the energy barrier for polymorphic transition. Leiserowitz et al. proposed a basic model to describe additive-promoted polymorphic transition. That is, an additive will be selectively adsorbed on the crystal faces of an energetic compound if it is structurally similar to the energetic molecule. Thereby, the adsorption place acts as the starting point for the transition [45, 46]. In fact, it shows a double-side effect of additives. That is, they can also restrict the polymorphic transition. For example, a compact coating on crystals with polymer additives is experimentally evidenced to prevent the polymorphic transition [47]. Besides, it was reported that different inertia additives can also affect the transition from ε-CL-20 to its γ -form [44]. As demonstrated in Fig. 5.3, the initial polymorphic transition temperature decreases with increasing the contents of graphite and paraffin wax; while it remains unchanged after TATB added. Also, it was reported that the polymorphic transition of TNB is promoted by adding trisindane (TI), as a new TIinduced polymorph of TNB from the CCl4 solution was obtained [48]. Furthermore, Zhang et al. studied the influence of additives on CL-20 polymorphic transition temperature, which can be divided into inert, active, and inhibitory effects [49]. 180 100wt% CL-20

90wt% CL-20

80wt% CL-20

Initial phase transition temperature,

175 170 165

165

165 165 160

160

155

155

155 150

150 145 140 CL-20

CL-20+TATB

CL-20+graphite CL-20+paraffin wax

Fig. 5.3 Initial polymorphic transition temperatures for samples containing only CL-20, and CL20 mixed with several inertia additives. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

5.4 Polymorph-Reduced Differences in Structure and Energetics

165

5.4 Polymorph-Reduced Differences in Structure and Energetics 5.4.1 Molecular Structure The molecular conformers in different polymorphs of the same energetic compound are usually different from one another, implying a change of molecular conformer after polymorph transition. As illustrated in Fig. 5.4, in most cases, the molecular conformers of an energetic compound have close skeleton geometries, with only tiny differences between substituent orientations, except for HMX. It shows that the rotation of single bonds linked with the substituents dominate the polymorphic transition mostly. First, we focus on the cases of TNT, PETN, and FOX-7. For these energetic compounds, the difference in molecular conformer of a given polymorphs is caused by the rotation of single bonds, especially the –NO2 . Figure 5.5a shows that the two TNT polymorphs and each one contains two types of molecular conformers. As to PETN, no difference in molecular conformer is found. Figure 5.5b exhibits that, for γ - and ε-forms of FOX-7, each of them has two kinds of molecular conformers, and each of the rest forms (α-, β-, α’-) only has one type. As shown in Fig. 5.5, the NO2 of TNT are always not coplanar with the benzene ring. Different from TNT, the planarity of FOX-7 increases as pressure and temperature increase. Along with the temperature increasing, the maximum torsion angle ϕO−N−C−C of the molecular conformer in αFOX-7, β-FOX-7, γ -FOX-7–1, and γ -FOX-7–2 decreases from 35.6°, 25.6°, 20.2°, and 17.4°, respectively. On the other hand, with the pressure rising, the maximum torsion angle ϕO−N−C−C increases from 35.6° to 37.7° during polymorphic transition

(a) CL-20

(b) HMX α-FOX-7 β-FOX-7 α'-FOX-7 ε-FOX-7-1 ε-FOX-7-2 γ-FOX-7-1 γ-FOX-7-2

(d) FOX-7

α-RDX β-RDX-1 β-RDX-2 ε-RDX γ-RDX-1 γ-RDX-2

α-HMX β-HMX δ-HMX ε-HMX-1 ε-HMX-2 ε-HMX-3

β-CL-20 ε-CL-20 γ-CL-20 ζ-CL-20

(c) RDX

m-TNT-1 m-TNT-2 o-TNT-1 o-TNT-2

(e) TNT

PETN-I PETN-II

(f) PETN

Fig. 5.4 Multiple molecular conformations, superimposed in a plot and distinguished by colors, for the six energetic compounds

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5 Polymorphism and Polymorphic Transition in Energetic Molecular …

(a)

Superposition

m-TNT-1

m-TNT-2

o-TNT-1

o-TNT-2

(b) T increasing ~376 K

β-FOX-7

Superposition

γ-FOX-7-1

γ-FOX-7-2

ε-FOX-7-1

ε-FOX-7-2

α-FOX-7 4.27 GPa

5.9 GPa

P increasing

αí-FOX-7

Fig. 5.5 Comparison in molecular structures of different polymorphs of TNT (a) and FOX-7 (b). The molecular structures in each superposition are distinguished by colors. P and T denote pressure and temperature, respectively. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

from α-FOX-7 to α’-FOX-7 first, and then the angle decreases to 7.2° and 6.6° accompanied by polymorphs ε-FOX-7–1 and ε-FOX-7–2 formed, respectively [49]. Figure 5.6 shows the molecular conformers in various polymorphs of RDX, HMX, and CL-20. Regarding RDX, there are two main molecular conformer types, AAA and AAE, in which A and E respectively denote NO2 oriented at pseudo-axial and pseudo-equatorial directions relative to the plane determined by the neighboring CNC atoms on the molecular frame. The AAE type appears in α-RDX, while the AAA type is exhibited in β-RDX and ε-RDX. Moreover, both the AAE and AAA types appear in γ -RDX. It shows that the molecular conformer will change from AAE type to AAA, and AAA and AAE types if RDX is evolved along a and b, respectively (Fig. 5.6a). The boat-boat and chair types can be used to distinguish the molecular conformers in polymorphic HMX, depending on the NO2 orientations (Fig. 5.6b). The boat-boat type appears in the α- and δ-forms, while the chair-type is exhibited in the three forms of β, ε and ζ [23]. That is, if HMX proceeds along a (from β- to α-from), the molecular conformer will be changed from chair into boat-boat types, while evolution along b (from β- to ε-from) will bring an orientational variation for NO2 groups at 1 and 3 sites (Fig. 5.6b). The molecular conformers of CL-20 are also distinguished according to the orientations of the three NO2 groups at the 1, 2, and 3 sites (Fig. 5.6c), similar to HMX. Thereby, it can be concluded that the difference in molecular conformer of various polymorphs of RDX, HMX, and CL-20 results from the discrepancy between the orientations of NO2 groups, as well as the molecular skeletons [29].

5.4 Polymorph-Reduced Differences in Structure and Energetics

(a)

167

(b)

(c) 1 1

1

1 1 γ-RDX-1

1

3

2

3

2 α-RDX

ε-HMX-1

β-HMX

2

1

2

3

2 ζ-HMX

3

1

γ-RDX-2

3

3

2

1

ε-CL-20

3

γ-CL-20 1

2

1

β-RDX-1

ε-HMX-2

α-HMX

1

1

2

2

2

1

1

3

1

1 3 3

2 β-RDX-2

δ-HMX

ε-RDX

3

β-CL-20

ε-HMX-3

ζ-CL-20

Fig. 5.6 Molecular structures in different polymorphs of RDX (a), HMX (b), and CL-20 (c). Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

Molecular volume Vm , as an important characteristic of molecule, is considered too. Figure 5.7 plots the Vm for the six energetic compounds as well as their differences. It shows that the polymorphic transition caused by temperature elevation does not bring an increase of Vm for PETN and FOX-7, and the pressure enhancement does not decrease Vm for FOX-7, either. There is a rule that materials expand with heat and contract with cold in most cases. Nevertheless, the expansion or contract of a material is not caused by those of molecules themselves, i.e., by intermolecular distances instead, as shown in Fig. 5.7. The Vm varies only in a range from −2.2 to 1.12%. Therefore, Vm changes a little when heated or pressured, compared to common conditions [51], suggesting that, in a certain range of heat and pressure, it is the intermolecular distance that changes, not Vm instead. Most stable phase under common conditions Phase under common conditions

Phase under low T and 1 atm Phase under low T and 1 atm

Phase under room T high P

350 27 4. 3

27 4

27 3. 9

250

20 7. 8

20 5. 5

20 1. 6

20 4. 7

200 10 5. 2

10 4

1. 15

1. 44

1. 12

-0.8 -1.6 -2.4

7

7 X-

FO ε-

7

X-

X-

O

FO

-F α'

X-

7 α-

FO

FO

γ-

β-

-3.2

X-

7

-2 .0 2

-1 .9

-2 .1 4

-2 .1 4

0.0 -0 .5 8

-0 .1 5

0 TN PE II TN -I

PE

-T N T oTN T

-3.2

D X αR D X γR D X εR D X

-2.4

βR

-1 .4 7

-1.6

-2 .2

-0 .3 9

-0.8

m

100 1.6 0.8

βC L20 εC L20 γC L20 ζC L20

0.0

-0 .1 1

0.8

150

2.4

(b)

δH M X αH M β- X H M X εH M X

1.6

0. 06

RD of Vm, %

2.4

10 5. 5

10 3. 4

100

10 1. 9

15 4. 2

300

15 0. 9

150

15 0. 9

15 0. 8

16 6. 1

200

22 4

22 0. 7

250

27 4. 3

350

(a) 16 6. 2

Vm, ≈ 3

300

Fig. 5.7 Vm and their relative differences (RDs) with respect to that of the most energetically favored polymorph. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

168

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

5.4.2 Molecular Packing In addition to the molecular structure, another intrinsic structure refers to molecular packing structure, in which molecular packing pattern, PC, dc , and intermolecular interaction are involved. For a given compound, the crystal structures change with polymorphic transition, resulting in different molecular arrangement in lattice and lattice parameters. Figures 5.8 and 5.9 plot the crystal structures and packing coefficients for the six energetic compounds and their relative differences (RDs), respectively. The existing of the high-pressure phases of RDX, CL-20, and FOX-7 shows good compressibility according to their significant increasement of PC. The compressibility is also related to dc , which is the production of dm and PC. Because molecular weight is invariable for a specified molecule, a small variation of dm or Vm can be deduced based on that of RD. It agrees with the above-mentioned small variation of Vm after a polymorphic transition under no high pressures. Furthermore, the PC always increases as the pressure increases and reduces as the temperature increases, implying that PC governs the pressure-induced increase and heat-induced reduction of dc . Molecular stacking mode plays an important role in governing the safety of energetic compounds, and serves as a basis for designing new LSHEMs [52]. The stacking mode covers face-to-face, wavelike, ladder-like, herringbone, crossing, and mixing types [53, 54]. Remarkably, the face-to-face π-π stacking is the most effective to low impact sensitivity, at a premise of planar π-conjugated molecule. For example, the conjugated frames of TNT and FOX-7, benzene ring, and ethylene, respectively, settle a basis of molecular planarity. The molecules in the two TNT polymorphs are both stacked in a wavelike way (Fig. 5.10a), while the molecules five polymorphs of FOX-7 are differently stacked, i.e., the heat and pressure tend to change the wavelike stacking to the face-to-face stacking (Fig. 5.10b). This stacking pattern change along the polymorphic transition partly roots for the low impact sensitivity of FOX-7 [50]. The layered stacking pattern can be used to describe the molecular stacking modes of RDX, HMX, PETN, and CL-20, which are not π-conjugated molecules. For example, from Fig. 5.11a–d, two modes are found for the four polymorphs of RDX, i.e., parallel stacking of ε-RDX and wavelike stacking of the others. The weak intermolecular interactions support the stacking. Regarding HMX, a higher diversity is exhibited in the five polymorphs (Fig. 5.11e–i), i.e., β-HMX, ε-HMX and ζ-HMX are wavelike stacked, while α-HMX and δ-HMX are ladderlike and parallel channellike, respectively. With respect to PETN, it is wavelike and layered stacked in PETN-I (Fig. 5.11j) and PETN-II (Fig. 5.11k), respectively. Layered stacking appears in all the four CL-20 polymorphs (Fig. 5.11l–o). Reasonably, these stacking modes can cause different mechanical characteristics, which have different influences on impact sensitivity. Numerous experiments and simulations evidenced the important effect of HB on the energy and safety of energetic materials [55]. To illustrate the polymorphic transition-induced HB change, Bu et al. recently studied the variation in the polymorphic transition of the α- → β- → γ -forms of FOX-7 [50]. Figure 5.12a exhibits the

5.4 Polymorph-Reduced Differences in Structure and Energetics a o

o

b

TNT-m-1

169

a b

a

TNT-O-2 c

TNT-O-1

TNT-m-2

a

o TNT-O-2

TNT-O-1 c

o

b

b

c

c

(a) m-TNT

(b) o-TNT

(c) PETN-I

β-RDX-1 c

(d) PETN-II

a

a

o

γ-RDX-2 o

b

a

β-RDX-2 a

γ-RDX-1

b c

o

b b

(e) α-RDX

c

o

c

(g) ε-RDX

(f) β-RDX

(h) γ-RDX

o

b

a

c

a

o

c

a

b c

c

b

(i) β-CL-20

b

o

(j) γ-CL-20

a

o

(k) ε-CL-20

(l) ζ-CL-20 a

a c

o

a c

o

a c

c

b

c o

b

o b

c

(m) α-FOX-7

(n) β-FOX-7

(o) α’-FOX-7

γ-FOX-7-2

ε-FOX-7-2 ε-FOX-7-1

b

γ-FOX-7-1

a o

(p) ε-FOX-7

(q) γ-FOX-7

o

b

ε-HMX-1 a c

a o

ε-HMX-3

ε-HMX-2

c c

a

o

(r) α-HMX a b o

a

(s) δ-HMX

b b

(t) β-HMX

(u) ε-HMX

Fig. 5.8 Crystal structures of the six energetic compounds. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

intralayered HBs in the three forms of FOX-7, among which the α-form possesses the densest HB nets, followed by the γ - and β-forms, showing a first weakening and subsequent strengthening of the HB during heating FOX-7. Interestingly, the intermolecular HBs change the same as the intramolecular ones, which are also weakened (α- FOX-7 to β-FOX-7) and then strengthened (β- FOX-7 to γ -FOX-7) too. At the same time, the averaged distance of H···A varies from 2.293 to 2.558 Å, and then 2.391 Å, while the averaged angle ∠D–H···A changes from 138.9º to 127.9º, and then 135.5º (Fig. 5.12b), showing the weakest intermolecular HBs in β-FOX-7 among the three polymorphs. Besides, these HBs were described by Bu et al. [50] with the Hirshfeld surface method [56, 57]. Figure 5.12c shows that the Hirshfeld surface of all the forms of FOX-7 are block-shaped, and all the red dots are distributed

170

5 Polymorphism and Polymorphic Transition in Energetic Molecular … Most stable phase under common conditions Phase under common conditions

1.1

Phase under room T high P 1.1

(a)

1.0

PC

Phase under high T and 1 atm Phase under low T and 1 atm

0.95

0.93 0.93

0.9 0.8

0.75 0.75

0.72

0.7

0.76

0.73

0.76

0.73 0.75

0.79 0.81

0.99

0.75 0.77

0.8 0.72

0.76

0.8

0.8 0.7 0.6

(b)

22.37 22.37

18.75

23.75

11.69 2.53

L20

L20 γC L20 ζC L20

-6.49

εC

βC

M X

M X

εH

βH

M X

X

0 0 -2.6

-5.06

αH

δH

X

D εR

X

D

X D

D αR

βR

γR

-I

-II

TN

TN

PE

PE

m -T N

-7.6

M X

-3.95

-5.26

-5

35 28 21 14 7 0 -7 -14

γFO X7 βFO X7 αFO X7 α' -F O X7 εFO X7

00

T oTN T

RD of PC, %

0.6 35 28 21 14 7 0 -7 -14

1.0 0.9

0.86

Fig. 5.9 PC of the polymorphs for the six energetic compounds, and their relative differences (RD) with respect to that in most energetically favored polymorph. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

(a)

m-TNT

o-TNT

(b) T increasing ~376 K β-FOX-7

γ-FOX-7

α-FOX-7 5.9 GPa 4.27 GPa P increasing αí-FOX-7

ε-FOX-7

Fig. 5.10 Molecular packing patterns of two polymorphs of TNT (a) and five polymorphs of FOX-7 (b). The dash shows the molecular layers. This representation is also employed in Fig. 5.11. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

at the block edges, suggesting the dominance of intermolecular HBs in the intralayer intermolecular interactions, based on our previous understanding [58]. In addition, the close intermolecular interatomic contacts of all the polymorphs of the six energetic compounds were concerned by Bu et al. [29]. As shown in Fig. 5.13, H···O, O···O, and N···O govern the close contacts of all the cases. For the same compound but with different polymorphs, only a small difference in the contact

5.4 Polymorph-Reduced Differences in Structure and Energetics

171

P increasing T increasing

(a) β-RDX

(b) α-RDX

(c) γ-RDX

(d) ε-RDX

P increasing

(e) δ-HMX

(f) α-HMX

(g) β-HMX

(h) ζ-HMX

T increasing

(j) PETN-І

(i) ε-HMX

(k) PETN-ІІ

(m) γ-CL-20

(n) ε-CL-20

(l) β-CL-20

(o) ζ-CL-20

Fig. 5.11 Molecular stacking in the polymorphs of four energetic compounds: RDX (a–d), HMX (e–i), PETN (j–k) and CL-20 (l–o). Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society (a)

T increasing

~376 K

α-FOX-7 138.9

° Average H···A, A

2.55

2.558

H···A D— H···A

2.50

135.5 2.45

136

134

2.40

2.391

(c)

138

132

2.35

Average D–H···A,

(b)

γ-FOX-7

β-FOX-7 140

2.60

α-FOX-7

β-FOX-7

γ-FOX-7-1

γ-FOX-7-2

130 2.30

2.293 128

127.9 2.25

α-FOX-7

β-FOX-7

γ-FOX-7

Fig. 5.12 Comparison of some characteristics of the three polymorphs of FOX-7: intralayered HBs (a), characteristics of intermolecular HBs (b) and Hirshfeld surfaces (c). Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

12% 10%

11% 10%

52%

51%

12%

13%

58% 9%

56% 8%

9%

9%

61% 9%

58% 8%

35%

37%

30%

58% 10% 8%

36%

25%

19%

19% 42% 37%

16% 44%

44% 35%

64%

9%

20% 10%

19%

63%

9%

9% 20% 63%

14%

21% 63%

20% 59%

12% 21% 58%

13%

13% 13%

17%

61%

55%

14%

13% 18%

Others

16%

57%

12%

16% 10%

32% 10%

18%

33% 10%

H-H

46%

44%

46%

44%

50% 40%

57%

18% 7%

18% 7%

60%

18% 7%

70%

18% 7%

80%

55%

90%

N-O

60%

O-O

57%

H-O 100%

55%

172

20% 10% m -T m NT-T 1 o- NT T N -2 o- T-1 TN T2 PE TN P E -II TN -I εR β - DX R β- DXRD 2 α - X-1 R γ- D X RD γ- XRD 1 X2 δHM α- X H β- MX H ε- M HM X ε- XHM 1 ε - XHM 2 X3 βCL γ- -20 C ε- L-2 CL 0 ζ- -20 CL γ- - 2 0 FO γ- XFO 7X 2 β- -7FO 1 α- XF 7 α' OX - ε- FO 7 FO Xε- X- 7 FO 7X- 1 72

0%

Fig. 5.13 Populations of intermolecular interatomic close contacts of six energetic molecules in crystal. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

populations exists, possibly ascribed to the unchanged molecular construction. On the other hand, the two-dimensional fingerprint plot is only a straightforward and rough tool to describe intermolecular interaction. In fact, a small difference in lattice energy among various polymorphs of each compound [51], also suggesting the close intermolecular interactions therein.

5.4.3 Morphology Polymorphic transition can vary morphology of energetic crystals. Recently, the morphologies of HMX and CL-20 grown in vacuum are predicted, as exhibited in Fig. 5.14 [59]. Big differences were observed among the different morphologies of a same compound. That is, the α-, β-, γ -, and δ-forms of HMX appear in the shapes of needle, diamond, flake, and drum, respectively, while the α- and β-, γ -, and εformed CL-20 are like a thin cake, a peg-top, and a diamond, respectively [59]. It shows the morphologic difference can be used to distinguish polymorphs. Besides, morphology can be significantly influenced by crystallization conditions like solvent, temperature, and agitation. With respect to different polymorphs, they also exhibit a difference in crystal shape even under the same or close crystallization condition.

5.4 Polymorph-Reduced Differences in Structure and Energetics

173

AR=12.24 SP=0.55

AR=1.95 SP=0.89

AR=6.01 SP=0.68

AR=1.52 SP=0.85

(a) α-HMX

(b) β-HMX

(c) γ-HMX

(d) δ-HMX

AR=2.71 SP=0.84

AR=2.60 SP=0.84

AR=1.73 SP=0.98

AR=1.44 SP=0.91

(e) α-CL-20

(f) β-CL-20

(g) γ-CL-20

(h) ε-CL-20

Fig. 5.14 Predicted crystal morphologies of the polymorphs of HMX and CL-20 in vacuum using the attachment energy (AE) model. AR and SP denote aspect ratio and sphericity, respectively. Reprinted with permission from Ref. [59]. Copyright 2013 American Chemical Society

5.4.4 Energetics Generally, polymorph formation is related to the molecular conformer and crystal packing, respectively represented by molecular conformer energy (MCE) and lattice energy (LE) in thermodynamics. Thereby, an issue is given rise to, i.e., which factor dominates the most stable polymorph at common conditions? In principle, the most stable polymorph possesses the lowest total energy (TE), which is determined by both MCE and LE. Thus, the issue becomes whether MCE or LE weights more in TE. The confirmation will deepen the understanding of energetic polymorphs, in combination with previous focuses upon the preparation techniques [60], structural analyses [61], and response to external stimuli [62, 63]. The polymorphs at common conditions, where most of applications of energetic crystals are implemented, usually attract much more attention. The polymorph transformation often takes place under a given temperature and pressure, involving the thermodynamic quantity, Gibbs free energy G. In the case of polymorph transition, the Gibbs free energy variation (ΔG) is approximately equal to the internal energy variation (ΔU ). However, it is generally difficult to calculate ΔG but relatively easy to determine ΔU . Taking the approximation of ΔG ≈ ΔU will make it ready to verify the most stable polymorph at common conditions. Elaborations are as follows. If polymorph 1 can be transitioned to polymorph 2, then ΔG = G 2 − G 1 < 0

(5.1)

ΔG = ΔH − Δ(T S)

(5.2)

174

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

ΔS is very tiny and negligible, in the case of a physical polymorphic transition of a molecular crystal consisting of small organic molecules at common conditions, so we have Δ(T S) ≈ 0

(5.3)

ΔG ≈ ΔH

(5.4)

Thus,

While the enthalpy variation (ΔH) is known to be ΔH = ΔU + Δ( pV )

(5.5)

Next, we will do derivation to obtain ΔH ≈ ΔU , by taking ε-CL-20 [64] as an example. The ε-CL-20 molecule possesses the largest volume among the all polymorphs of the six energetic compounds, 356 Å3 , or 2.143 × 10–4 m3 /mol. Supposing a 10% volume varied by phase transition under common conditions, it would produce the volume work ( pΔV ) of only 0.02 kJ/mol, which is too small to be negligible. Thereby, we have ΔG ≈ ΔH ≈ ΔU

(5.6)

ΔU can be employed to verify the possibility of a physical polymorphic transition at ambient conditions. In principle, U, or TE, includes intramolecular and the intermolecular parts, corresponding to MCE and LE, respectively. U = TE = MCE + LE

(5.7)

For convenience, Liu et al. defined relative molecular conformer energy (RMCE), relative lattice energy (RLE), and relative total energy (RTE) to the minimums of all the polymorphs to study various energies [51]. Thereby, the thermodynamics for polymorph i can be readily compared. RMCEi = ΔMCE = MCEi − MCEmin

(5.8)

RLEi = ΔLE = LEi − LEmin

(5.9)

RTEi = ΔU = Ui − Umin = (MCE + LE)i − (MCE + LE)min = RMCE + RLE (5.10) Similarly, the RTEi difference (ΔRTEi ) can be used to compare RTE of different polymorphs.

5.4 Polymorph-Reduced Differences in Structure and Energetics

ΔRTEi = RTEi − RTEmin

175

(5.11)

The more negative MCE, LE, and TE suggests the higher thermodynamic stability or the stronger intermolecular interactions. Liu et al. [51] performed QC computations on the above thermodynamical quantities with PBE-D2 method [65], which had been validated for energetic molecular and ionic crystals [66, 67]. Two cases, relaxation with (OPT1) and without (OPT2) symmetry fixed, were accounted for. As results, Table 5.2 exhibits a negligible effect of symmetry restriction on cell parameter optimization. Meanwhile, it was also verified the reliability of PBE-D2 to deal with these polymorphs. Both molecular conformer and crystal packing are intrinsic structures for energetic compounds. They will differ more or less in various polymorphs of a same energetic compound, i.e., their RMCE, RLE, and RTE are polymorph-dependent. The three kinds of energies for the six energetic compounds are plotted in Fig. 5.15. It shows a variability of the dominance of MCE or LE in governing the most stable forms at common conditions, with smaller values representing the higher thermodynamic stability. LE governs the most stable forms of CL-20, RDX, PETN, and FOX-7; MCE dominates that of HMX; and MCE and LE contribute the same to TNT [51]. Thereby, we think that the alternatives of either MCE or LE dominating TE is a main reason why it is so difficult in crystal structure prediction currently.

5.4.5 Detonation Property In most cases, different crystal packing for a group of polymorphs results in different dc . For CHON-contained energetic compounds, their vd and Pd , are proportional to 1 + 1.30 dc and dc 2 , respectively, according to Kamlet-Jacobs’s formula. As such, a little variation of dc can cause a rather large change of vd and Pd . For example, the dc of the γ -, β-, and ε-formed CL-20 are 1.916, 1.958, and 2.044 g/cm3 at common conditions, respectively, suggesting the highest detonation properties of the ε-form [10]. Similarly, owing to the highest dc , β-HMX is the most powerful among the polymorphs at ambient conditions [68, 69]. Considering the most compact form for an EM is usually the most powerful but the least impact sensitive among all the polymorphs under common conditions, it is a good way to control the crystal form to alleviate the energy-safety contradiction of energetic materials.

176

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

Table 5.2 Comparison of experimental (EXP) and optimized (OPT1 and OPT2) lattice parameters of polymorphs under common condition or below 0 °C Polymorphs

a, Å

b, Å

c, Å

α, °

β, °

γ, °

V c , Å3

β-CL-20 EXP

9.676(2)

13.006(4)

11.649(3)

90

90

90

1465.98

OPT1

9.6364

13.1360

11.5418

90

90

90

1461.00 (−0.3%)

OPT2

9.6470

13.1201

11.5399

89.78

89.85

89.92

1460.64 (−0.4%)

EXP

8.852(2)

12.556(3)

13.386(3)

90

106.82(2)

90

1424.15

OPT1

8.8790

12.5455

13.3608

90

105.84

90

1431.75 (0.5%)

OPT2

8.8767

12.5398

13.3400

89.97

105.74

89.95

1429.21 (0.4%)

ε-CL-20

γ -CL-20 EXP

α-HMX

β-HMX

δ-HMX

α-RDX

β-RDX

13.231(3)

8.170(2)

14.876(3)

90

109.17(2)

90

1518.89

OPT1

13.1417

8.2458

14.8201

90

108.54

90

1522.66 (0.2%)

OPT2

13.1646

8.2509

14.8957

89.03

109.59

89.78

1524.00 (0.3%)

EXP

15.1400

23.8900

5.9130

90

90

90

2138.70

OPT1

15.0887

23.3328

5.9168

90

90

90

2083.08 (-2.6%)

OPT2

15.1652

23.3650

5.9325

90.09

89.89

91.63

2101.23 (−1.8%)

EXP

6.5400

11.0500

8.7000

90

124.30

90

519.39

OPT1

6.5117

10.8034

8.7199

90

124.61

90

504.90 (−2.8%)

OPT2

6.5126

10.7954

8.7309

89.99

124.65

89.95

504.98 (−2.8%)

EXP

7.711(2)

7.711(2)

32.553(6)

90

90

120

1676.27

OPT1

7.5671

7.5671

32.8001

90

90

120

1626.54 (−3.0%)

OPT2

7.5678

7.5589

32.8305

90

90

119.92

1627.79 (−2.9%)

EXP

13.182(2)

11.574(2)

10.709(2)

90

90

90

1633.86

OPT1

13.2362

11.3943

10.6423

90

90

90

1605.04 (−1.8%)

OPT2

13.2411

11.3942

10.6482

89.99

89.94

89.95

1606.51 (−1.7%)

EXP

15.0972(7) 7.5463(4)

14.4316(6)

90

90

90

1644.16

OPT1

15.0740

14.3886

90

90

90

1627.16 (−1.0%)

7.5021

(continued)

5.5 Polymorph-Dependent Mechanism of Thermal Decomposition

177

Table 5.2 (continued) a, Å

b, Å

c, Å

α, °

β, °

γ, °

V c , Å3

15.0743

7.5034

14.3810

89.99

90

89.99

1626.61 (−1.1%)

6.934(7)

6.6228(8)

11.3119(13) 90

90.065(13) 90

519.47

OPT1

6.9701

6.3257

11.1935

90

92.34

90

493.12 (−5.0%)

OPT2

6.9556

6.3753

11.2811

90.92

90.32

83.57

497.03 (−4.3%)

Polymorphs OPT2 α-FOX-7 EXP

γ -FOX-7 EXP

m-TNT

o-TNT

PETN-I

13.354(3)

6.895(1)

12.050(2)

90

111.102(8) 90

1035.11

OPT1

12.9185

6.9070

12.1447

90

113.483

993.896 (−4.0%)

OPT2

12.8191

6.8915

12.1458

90.0632 111.681

EXP

14.9113(1) 6.0340(1)

20.8815(3)

90

110.365(1) 90

1761.37

OPT1

14.8008

5.8823

21.2839

90

112.26

90

1725.96 (−2.0%)

OPT2

14.9977

5.9698

20.6147

89.91

110.76

89.79

1725.85 (−2.0%)

EXP

14.910(2)

6.0341(18) 19.680(4)

90

90

90

1770.58

OPT1

14.9634

5.9545

19.4049

90

90

90

1728.97 (−2.4%)

OPT2

14.8498

5.9180

19.5500

88.77

86.13

93.50

1725.39 (−2.7%)

EXP

9.380

9.380

6.700

90

90

90

589.495

OPT1

9.3246

9.3246

6.6105

90

90

90

574.771 (−2.5%)

OPT2

9.6614

9.3800

6.7030

90

88.2816

90

607.179 (3.0%)

90

91.5305 996.658 (−3.7%)

Note The percent in brackets shows the relative errors of optimized cell volumes compared to experimental ones

5.5 Polymorph-Dependent Mechanism of Thermal Decomposition Besides the above differences in structure and energetics, the difference in thermal reactivity can also exist among the polymorphs. As one of the most important properties of energetic materials, thermal stability has received much attention, especially on the difference in thermal stability/reactivity among polymorphs. This is a basis to evaluate the applicability of energetic materials. Here, CL-20 and HMX are adopted to exemplify the polymorph-induced difference in thermal reactivity under a condition with volume confined.

178

5 Polymorphism and Polymorphic Transition in Energetic Molecular … Most stable phase under common conditions

Phase under high T and 1atm

Phase under common conditions

Phase under low T and 1 atm

Phase under room T high P

80

80

RMCE

(a) 60

60

40

40

20 0

0.1

0 0

10.3 10.7

00

0.1

0 0

0

0.7

0

0.1

0

4.5 5.2

0

20

10.2 2.3

0 0

2.5 2.6 1.2

0

(b) 60

60

RLE

46.7 45.5

40.2

40

40

23.2 20 0

00

8

0

0.4

8.1

5.7

6

0

0

8.1

7.1

0

2.2 5.8

1.8

0

20

7.3

0

(c)

60

46 44.8

45.9

40

40

22

20

L20

2.5

L20 γC L20 ζC L20

εC

βC

M X

0 0

2.1 3.4

00

20

7.6 0

γFO X7 βFO X7 αFO X7 α' -F O X7 εFO X7

3.6

1 εH

M X

0 0

βH

X M H δ-

M X

X

X

D

D γR

εR

X

X D

D βR

4.6

0 αR

-I

-II

TN

TN

12.5

5

0

PE

PE

m -T N

8.1

0.3

T oTN T

0

00

αH

ΔRTE

60

Fig. 5.15 Energy (in kJ/mol) comparisons for the six interested energetic compounds. Reprinted with permission from Ref. [29]. Copyright 2020 American Chemical Society

5.5.1 Mechanism of Thermal Decomposition of CL-20 Polymorphs CL-20 is currently the most powerful energetic compound commercialized [70–75]. However, its practical application remains still limited, ascribed to its high sensitivity and high cost. Thermal decomposition of CL-20 appears as a consequence of the response against sufficient external stimuli, and have received plenty attention [76–84]. The high sensitivity of CL-20 can be partly attributed to its low molecular stability, which is a result from its low BDE [85]. Besides, the ready polymorphic transition roots for its high sensitivity [86–89]. For CL-20, although the heat-induced polymorphic transition will occur prior to thermal decomposition, an original polymorph can retain till the decay in the case of that they are volumetrically constrained or heated fast. Recently, Liu et al. [90] performed MD simulations on the decomposition mechanism of β-CL-20, ε-CL-20, and γ -CL-20, based on the self-consistent charge density-functional tight binding (SCC-DFTB) methods with 3ob-3–1 parameter set, which had been validated before [69, 91–103]. First, the potential energy (PE) evolution is exhibited in Fig. 5.16 for the three polymorphs of CL-20. In the case of the programmed heating from 300 to 2000 K, as illustrated in Fig. 5.16a, the PEs of all the three polymorphs successively increase and they are overlapped one another for about 17 ps, the PE becomes fluctuant and the curves become differentiable. Based on the PE evolution tendency, we can deduce the weakest thermal stability of γ -CL-20, followed by β-CL-20 and ε-CL-20, as they possess the same order of the first appearance of PE decrease. As to the cases of constant temperature heating at 1000, 1500, and 2000 K, the PE evolutions are shown in Fig. 5.16b–d. In general, the PE undergoes a first increase and then a decrease

5.5 Polymorph-Dependent Mechanism of Thermal Decomposition -CL-20 12

ε-CL-20

(a) 300-2000 K

(b) 1000 K

(c) 1500 K

(d) 2000 K

179 -CL-20

10 8 6

PE, eV

4 2 12 10 8 6 4 2 0

2

4

6

8

10

12

14

16

18

20

2

4

6

8

10

12

14

16

18

20

Time, ps Fig. 5.16 Evolution of potential energies for the three polymorphs of CL-20 when heated. Reprinted with permission from Ref. [90]. Copyright 2019 American Chemical Society

in constant-temperature heating [104]. At 1000 K, the PE decreases after 10 and 16 ps for β-CL-20 and for γ -CL-20, respectively, but ε-CL-20 does not exhibit PE reduction within the timescale of simulation, showing the highest thermal stability of ε-CL-20, followed by γ -CL-20 and β-CL-20. With respect to the cases of 1500 and 2000 K, it always shows the later PE decrease of ε-CL-20, while the order of γ -CL-20 and β-CL-20 is temperature dependent. Meanwhile, Li et al. focused upon the dependence of initial steps of decomposition on the polymorphs of CL-20. First, they confirmed five steps observed in simulations, as shown in Fig. 5.17: the NO2 partitions from the five-membered ring (A) and the six-membered ring (B), the cleavage of C–N bonds of the six-membered ring (C) and the five-membered ring (D), and the C–C bond breakage (E) [90]. These steps have been found in previous work [81–105]. Figure 5.18 shows the percentage of each initial step under four heating conditions. As illustrated in the figure, in the case of β-CL-20, A increases while B decreases with temperature increasing, C is never been observed, D occurs at 1000, 1500, and 2000 K, and E takes place at 1500 and 2000 K. Among these steps, the NO2 partition (A and B) governs the ignition of the thermal decomposition of β-CL-20, while the cleavage of C–N bond (C and D) and C–C bond (E) contributes much less. This differs from the initial steps observed in shocked ε-CL-20, as the ring opening is dominant therein [84]. Also, the dominance of the NO2 partition is found in εand γ -CL-20, and the weights of other steps of these two polymorphs are generally similar to β-CL-20, with the largest difference of that no reaction occurs at 1000 K,

180

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

C-/-N O2N N O2N N O2N

N

NO2

NO2

NO2

N

N

N

N

N

N

NO2

NO2

NO2

C-/-C

E

O2N N O2N N

β-CL-20 ε-CL-20 γ-CL-20

D

O2N

NO2

N

N

NO2

A

N NO2 N NO2

N N

NO2

N-/-N

N NO2

C

C-/-N O2N N O2N N O2N

N

B

N NO2 N NO2 N NO2

N-/-N

O2N N O2N N

O2N

N

N NO2 N NO2 N

NO2

Fig. 5.17 Five initial thermal decomposition steps (from A to E) of CL-20. Reprinted with permission from Ref. [90]. Copyright 2019 American Chemical Society

as pointed out in the analysis of the PE evolution. This can partly explain the lowest impact sensitivity of ε-CL-20. The thermal stability for different polymorphs can also be evaluated by the evolution of some key intermediates and products when heated. In the case of the programmed heating from 300 to 2000 K, the three polymorphs of CL-20 generally exhibit a small difference in the evolution of the chemical species, as illustrated in Fig. 5.19. ε-CL-20 is analyzed the most slowly, followed by β- and γ -CL-20, based on their disappearance time in Fig. 5.19a. Compared Fig. 5.19a–b, it is ready to find the time that NO2 arrives at a peak is just that when the CL-20 molecules disappear. Thereafter, the quantities NO, NO3 , and N2 O increase (Fig. 5.19c–e), i.e., there increase proceeds at the cost of the reduction of NO2 . At the same time, HCN, HONO, and HNO3 are produced in a tiny amount, as demonstrated in Fig. 5.19g–j. At the end of the simulation, it appears a polymorph-induced difference of some of intermediates and products, where more N2 O, CO, and H2 O yield from γ -CL-20 while more NO3 , HCN, and HNO3 from ε-CL-20. The difference can also occur in the cases of constant temperature heating [90].

5.5 Polymorph-Dependent Mechanism of Thermal Decomposition A (N-N) 75 (a) β-CL-20 300-2000 K

B(N-N)

C(C-N)

181

D(C-N)

E(C-C)

(b) β-CL-20 1000 K

(c) β-CL-20 1500 K

(d) β-CL-20 2000 K

(f) ε-CL-20 1000 K

(g) ε-CL-20 1500 K

(h) ε-CL-20 2000 K

(j) γ-CL-20 1000 K

(k) γ-CL-20 1500 K

(l) γ-CL-20 2000 K

50 25 0 75 (e) ε-CL-20 300-2000 K 50 25 0 75 (i) γ-CL-20 300-2000 K 50 25 0

Fig. 5.18 Percentages (%) of the five possible initial thermal decomposition steps of CL-20 under four heating conditions. Reprinted with permission from Ref. [90]. Copyright 2019 American Chemical Society β-CL-20

ε-CL-20

γ-CL-20

10

(a) CL-20

(b) NO2

(c) NO

(d) NO3

(e) N2O

(f) CO

(g) HCN

(h) H2O

(i) HONO

(j) HNO3

8

6

4

Amount

2

10

8

6

4

2

0

5

10

15

20

5

10

15

20

5

10

15

20

5

10

15

20

5

10

15

20

Time, ps

Fig. 5.19 Evolutions of some important small molecules, as well as CL-20, during the thermal decay of the three CL-20 polymorphs under the programmed heating from 300 to 2000 K. Reprinted with permission from Ref. [90]. Copyright 2019 American Chemical Society

182

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

5.5.2 Mechanism of Thermal Decomposition of HMX Polymorphs Liu et al. were also concerned about the initial thermal decomposition mechanism of another polymorphic energetic compound, HMX [105]. There are three forms of HMX exist stably at ambient conditions, including α-, β-, and δ-HMX, among which the β-form has the largest dc , followed by α- and δ-forms [8, 9, 106]. Similar as the polymorphs of CL-20, those of HMX are also different from one another not only in molecular conformer, but also molecular stacking structure, from which the initial thermal decomposition mechanism was discussed. The same (SCC-DFTB) MD simulations as applied to study the thermal decay mechanism of CL-20 were adopted for the three polymorphs of HMX, whose molecular conformers and crystal packing structures are shown in Fig. 5.20. Regarding the molecular conformer, the boat-boat type is involved in the α- and δ-forms of HMX (Fig. 5.20a), while chair-type in the β-form (Fig. 5.20b). These two types of conformers are distinguished by the configuration of molecular skeleton (eight-membered ring) and the relative direction of NO2 to the molecular skeleton. As to the molecular stacking, α- and β-HMX exhibit the layered stacking (Fig. 5.20c– e), while δ-HMX shows the staggered stacking of with channels (Fig. 5.20d). In contrast to δ-HMX, the layered stacking of α- and β-HMX is advantageous to ready shear sliding and further lower impact sensitivity [54, 58]. In fact, the shear sliding energy barrier of β-HMX was predicted to close to that of a low impact sensitive compound TKX-50 [101]. Unlike α- and β-HMX, infinitely extensive frames and channels serve as the molecular stacking characteristic of δ-HMX (Fig. 5.20d), and disfavor the shear sliding. Meanwhile, the channels are much like vacancy in crystal, which generally promote ignition when heated or shocked. All these partly determine its higher sensitivity.

(a) boat-boat type HMX

(c) α-HMX

(d) δ-HMX

(b) chair-type HMX

(e) β-HMX

Fig. 5.20 Molecular conformers and stacking structures of the three polymorphs of HMX. Reprinted with permission from Ref. [105]. Copyright 2021 American Chemical Society

5.5 Polymorph-Dependent Mechanism of Thermal Decomposition

183

As discussed in Sect. 5.4.4, β-HMX possesses the lowest RTE, which is dominated by RLE. Meanwhile, it possesses the largest PC and largest dc among three polymorphs, making it the most desired in practical application. Regarding the decay for an energetic molecule, it involves NO2 partition, H transfer and HONO elimination, C–N bond breakage, rearrangement from NO2 to ONO, and concerted ring cleavage [101, 107–113]. Recently, Liu summarized the barriers of these reactions at a unified level of B3LYP/6-311+(d, p) [105], as listed in Fig. 5.21. First of all, the barrier for overcoming the NO2 partition is slightly molecular conformer-dependent, with a small barrier difference < 4.2 kJ/mol between the two types of molecular conformers. And so are the rearrangement from NO2 to ONO and concerted ring cleavage. Differently, molecular conformer has a significant influence on the energy barrier required for breaking the C–N breakage, i.e., the chair-type require more than the boat-boat one, due to its less ring stress. Similarly, the cooperative reaction of the H transfer and HONO elimination is also significantly conformer-dependent, with a difference in energy barrier of 32.2 kJ/mol. In the MD simulations of heating the three polymorphs of HMX [105], the C–N bond breakage to open the ring (reaction I), the N–NO2 fission (reaction II) followed by a secondary reaction between the intermediates and HMX reactants, and the intermediate-initiated decomposition (reaction III) were all observed to be the first step of the thermal decomposition reaction, as shown in Fig. 5.22. Both reactions I and II take place in all the three polymorphs, showing no orientated NO2 partition and C–N bond breakage, i.e., they can be either axial or equatorial. Reaction III only occurs in the β-formed HMX, due to the frequent intermolecular H transfer therein. All these may be attributed to that the chair-typed molecular conformer possesses a larger Vm and a higher PC, and enhances the probabilities of contact among neighboring molecules and intermolecular reactions.

NO2 N O2N

N

N

NO2

N NO2

NO2 +

O2 N

N

N

NO2

O2 N

N

N

NO2

O2N

O

N

NO2

NO2

154.8 boat-boat axial boat-boat equatorial 146.9

235.1 238.9

158.2 144.8

274.9 263.6

210.0 193.7

NO2

O

N

N N

N

N

chair axial chair equatorial

N

HONHO + N

NO2 N

N

NO2

O2N

N

N

NO2

O2N

N

N

N

N

NO2

NO2

NO2

--225.9

--325.1

boat- 193.7

--325.1

chair- 202.1

N

NO2

Fig. 5.21 Energy barriers (in kJ/mol) of the five possible initial decomposition steps of the HMX molecule calculated at the level of B3LYP/6-311+(d, p). Reprinted with permission from Ref. [105]. Copyright 2021 American Chemical Society

184

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

Reaction II

Reaction I Breakage of equatorial bond

NO2 H2C O2N

N

H2C

N

H2C

Boat-boat type N

N H2C

NO2

NO2

C-/-N

N-/-N

O2N

CH2

CH2 N

N H2C

NO2

N

N

NO2

CH2

NO2

Chair-type

Breakage of axial bond

Reaction III

Chair-type HMX

Intermediates

Fig. 5.22 Starting reactions for the thermal decomposition of HMX observed in MD simulations. In reactions I and II, only one NO2 is retained for clarity. Reprinted with permission from Ref. [105]. Copyright 2021 American Chemical Society

The weights of these three pathways in the constant temperature heating HMX are concerned. In α-HMX, the initial decay is always dominated by reaction I, and its weight enhances with temperature increasing (Fig. 5.23a), while reaction II varies conversely with the temperature. The weights of reactions I and II of δ-HMX proceed the same as α-HMX, with the dominance of reaction II at relatively low temperatures of 2000 and 2200 K (Fig. 5.23b). As pointed out above, the difference of β-HMX from α- and δ-HMX is the occurrence of reaction III, with a weight of 6.25% all along (Fig. 5.23c). It shows the enhancement of the C–N cleavage while the weakening of the NO2 partition with temperature increasing, in an agreement with a previous result arguing a faster C–N bond breakage compared to the N–NO2 partition also caused by the temperature elevation [114]. This case of reactions in solid is much different from those in gaseous state, as it lacks enough space to release the partitioned NO2

5.5 Polymorph-Dependent Mechanism of Thermal Decomposition II (N-NO2)

III (Intermediate-initiated)

Percentages, %

I (C-N)

185

Fig. 5.23 Percentages (%) of the steps in starting reactions for the thermal decomposition of various HMX polymorphs heated at 2000, 2200, and 2500 K. Reprinted with permission from Ref. [105]. Copyright 2021 American Chemical Society

and the C–N bond cleavage becomes dominant. This can be deduced from that the N–NO2 fission always weights more in δ-HMX in contrast to α-HMX, as δ-HMX possesses a lower volume filling degree (VFD). Recently, the effect of VFD on the thermal explosion of RDX was studied, showing a smaller VDF facilitating the NO2 partition, while reducing the possibility of NO2 to react with RDX molecules or other intermediates [115]. All these exhibits a polymorph and temperature dependence in the initial decomposition mechanism of HMX. Furthermore, Liu et al. studied the second- and third-steps in the thermally decaying solid HMX [115]. As shown in Fig. 5.24, they confirmed the cleavage of the adjacent C–N bond always following the N–N bond fission, or the fission of the neighboring N–N bond following the C–N bond rupture, in agreement with a recent work of He et al. [116]. Therein, it was ascertained that the C–N bond rupture dominated the starting step of thermal decomposition of β-HMX, followed by the adjacent NO2 partition.

186

5 Polymorphism and Polymorphic Transition in Energetic Molecular … H2 C O2 N

H2C

N-/-N

NO2 H2C O2N

N

N H2C

N

NO2

NO

CH2

C-/-N NO2

NO2

NO2 CH2 NO2

N NO2

N NO2

NO2

NO2

NO2

CH2 N NO2

CH2

CH2

C-/-N

N

CH2

Small product molecules

NO2 CH2

N-/-N NO2

CH2

N

N

CH2 N

N CH2

C-/-N

N

CH2

CH2 N

CH2

N NO2

N

N CH2

CH2

NO2

N NO2

CH2

C-/-N

NO2

CH2

N

CH2

N

N

CH2

CH2

CH2 N

N

N

N

N

N NO2 + NO2

N CH2

CH2

N

CH2

N-/-N

Fig. 5.24 The first-, second-, and third-steps in decomposition of polymorphic HMX, shown in green, orange, and blue, respectively. Reprinted with permission from Ref. [105]. Copyright 2021 American Chemical Society

5.6 Polymorph Transition-Induced Low Impact Sensitivity of FOX-7 The underlying mechanism responsible for sensitivity of energetic materials against external stimuli is very complicated and related to multiple factors, such as molecular stability, molecular stacking mode, crystal perfection, crystal shape, crystal size, interfacial features, stimulation style, testing condition, etc. [117, 118]. When a stimulation like heat or pressure is loaded, an energetic material may proceed polymorphic transition, which influences the sensitivity too. In this section, we exemplify the influence from the heat-induced polymorphic transformation on the impact sensitivity by the work of Bu et al., which uncovered the heat-induced variation of shear sliding characteristic of FOX-7 [50]. It is a relatively novel low impact sensitive energetic compound with E dr of 30.9 J, close to that of another one, LLM-105, 28.7 J [119–121].

5.6.1 Stacking Structures of FOX-7 Polymorphs In fact, the most stable form under common conditions of FOX-7, α-FOX-7, will suffer from the heat-induced polymorphic transition to β-FOX-7 if temperature increases at about 113 °C and subsequently to γ -FOX-7 at 173 °C [13, 14, 122]. Afterwards, the molecular stacking modes change. It was found that the α- → β- → γ -FOX-7 transition causes the increasingly ready shear sliding. Figure 5.25 exhibits that molecules are stacking more and more planar, i.e., closer and closer to the case of TATB. Because the HB-aided face-to-face π-π stacking generally contributes to low impact sensitivity [52, 53, 58], this polymorphic transition with more planar molecular stacking facilitates the low impact sensitivity of FOX-7. In addition, the FOX-7 molecules themselves become more and more planar thanks to the polymorphic transformation of α- → β- → γ -form caused by temperature increasing, since the maximal torsion angle in molecule varies from 35.6 to 25.6 and 20.2°, facilitating

5.6 Polymorph Transition-Induced Low Impact Sensitivity of FOX-7

187

B

B

O/A

C

O/A

C

(a) α-FOX-7 C/O

(b) β-FOX-7

B C

A/O

B

A

(c) γ-FOX-7

(d) TATB

Fig. 5.25 Crystal packing structures of α-FOX-7 (a), β-FOX-7 (b), γ -FOX-7 (c), and TATB (d). The C, H, N, and O atoms are represented in grey, green, blue, and red, respectively. These representations are also employed in the following figures. Reprinted with permission from Ref. [50]. Copyright 2019 American Chemical Society

the normal face-to-face π-π stacking. The π-π stacking of the three polymorphs of FOX-7 is supported by intermolecular HBs, as usually in low sensitive energetic compounds. That is, each layer in the crystal is in fact a dense HB network, as illustrated in Fig. 5.26, similar to that of TATB. According to Jeffrey’s criterion for ranking HB strength [123], these intermolecular HBs are weak or rather weak. In the heat-induced polymorphic transition of α- → β- → γ -forms of FOX-7, the length of HB increases first and then reduces, with the averaged distance of H···A varying from 2.293 to 2.558 and then 2.391 Å. At the same time, the density of these intermolecular HBs is also weakened and subsequently enhanced, as the numbers of total intermolecular HBs around one FOX-7 molecule in the α-, β-, and γ -forms are 12, 10, and 13, respectively.

5.6.2 Sliding Characteristics of FOX-7 Polymorphs In exploring the variation in FOX-7 molecular stacking induced by heat, the accompanied changes of shear sliding characteristics remind us that the intermediate packing structure in the evolution also plays an important role in influencing the sensitivity and cannot be overlooked. In principle, structures determine properties and performances. There would be a deficiency in understanding the sensitivity mechanism if the structures at ambient conditions are accounted alone, i.e., the intermediate structures should be seriously paid attention to, for reasonably predicting, evaluating, and understanding the performances like the impact sensitivity. During the evolution of an energetic compound from a mechanical stimulus loaded to final combustion and/or detonation, it was ascertained that the characteristic of

188

5 Polymorphism and Polymorphic Transition in Energetic Molecular …

A A B/O B/O

(a) α-FOX-7

A/O

C

C

(b) β-FOX-7

C B

B C/O

(c) γ-FOX-7

A

(d) TATB

Fig. 5.26 Intermolecular HBs represented by green dash in the three polymorphs of FOX-7, and in TATB. Reprinted with permission from Ref. [50]. Copyright 2019 American Chemical Society

shear sliding is a key factor to start its decomposition, as the readier shear sliding facilitate the lower impact sensitivity [52, 53, 58, 124–129]. Among the shear sliding, there are two extremes without volume change: bulk shear sliding and interfacial shear sliding, as shown in Fig. 5.27 [58, 130, 131]. Generally, the increased energy by sliding is adopted to represent the sliding difficulty, i.e., the less the energy increases, the lower the sliding barrier. On the contrary, if the energy increased is above the E a or BDE for chemical decomposition, sliding will be unallowed [129–131]. Recently, Bu et al. [50] performed DFT calculations with PBE formulation [132] and D2 correction of Grimme [133] methods to compute the energy change after slide relative to the original crystal structures (ΔE) for the three polymorphs of FOX-7. Figure 5.25 exhibits the remarkable layered packing structures of the polymorphs, implying that the most energetically preferred sliding is parallel to the AOC plane and along the c axis of α-FOX-7 or β-FOX-7, while parallel to the BOC plane and also along the c axis of γ -FOX-7. After the interfacial shear sliding scanned with a step of a fraction of 0.1 (Fig. 5.28), the ΔE contours of the three polymorphs of FOX-7 were achieved to distinguish there shear sliding characteristics. For comparison, as illustrated in the figure, they also obtained that of TATB slid parallel to the AOB plane and along the a axis by the same calculation methods [50]. For the bulk shear sliding, Bu et al. set a series of slip systems along the most energetically favored sliding orientations of the three polymorphs to calculate ΔE with the same DFT method, including (010)/[001], (010)/[10-1], (010)/[100] and (010)/[101] for both α- and β-FOX-7, and (100)/[011], (100)/[010], (100)/[10-1]

5.6 Polymorph Transition-Induced Low Impact Sensitivity of FOX-7

189

Mechanical FOX-7 stimulation

Fig. 5.27 Model showing the bulk and interfacial shear sliding of an EM. The decreased size of the arrows, from orange to green, denotes the dispersed mechanical energy due to the shear sliding. Reprinted with permission from Ref. [50]. Copyright 2019 American Chemical Society Slid layer

b

=

(0.48, 0.75, 0.61)

(a) α-FOX-7

Fixed layer

a

(0.52, 0.25, 0.39)

o

c

a

o

(0.47, 0.94, 0.87) Slid layer (0.25, 0.5, 0.38) Fixed layer (1.03, 0.06, 0.37)

c

Fixed layer

=

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

o

(0.75, 0.72, 0.50)

a

(0.48, 0.75, 0.61) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

c

Slid structure

o

(0.52, 0.25, 0.39)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(0, 0.75, 0)

c

a (1.03, 0.06, 0.37) (0.47, 0.94, 0.87) (0.25, 0.5, 0.38) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

c

b

Slid layer

o

(0.52, 0.25, 0.39)

a 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

o

(0.25, 0.28, 0.5)

(c) γ-FOX-7

=

c

b

a 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

o Fixed layer

(b) β-FOX-7

a 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

(1.03, 0.06, 0.37) (0.47, 0.94, 0.87)

o 0)0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (0, 0.5,

c

b 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

(0.75, 0.72, 0.50) (0.25, 0.28, 0.5) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

c

o

(0.75, 0.72, 0.50)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(0.25, 0, 0)

c

Initial structure

Fig. 5.28 Scanning models for calculating the energy variations of the interfacial shear sliding of α- (a), β- (b), and γ -forms of FOX-7 (c). In each cell, the molecules involved are grouped into two layers according to the most energetically favored sliding shown in Fig. 5.25. One is the fixed layer in blue, while the other is the sliding layer in red. The factional coordinates are of the centroids of the two layers. Reprinted with permission from Ref. [50]. Copyright 2019 American Chemical Society

190

5 Polymorphism and Polymorphic Transition in Energetic Molecular … [010] [001]

[100]

[100] (010) [001]

a [100]

[100]

[100]

[10-1]

b

[101]

(a) α-FOX-7

(010)

[001] [100]

[10-1]

(100)

[101] c

(b) β-FOX-7

a

b

a [100]

[001]

c

[01-1] c

[011]

[001]

[001]

b [100]

(c) γ-FOX-7

Fig. 5.29 Models for the bulk shear sliding calculation of the three polymorphs of FOX-7. The sliding planes and orientations are shown by shadowed planes and dashes, respectively. Reprinted with permission from Ref. [50]. Copyright 2019 American Chemical Society

and (100)/[001] for γ -FOX-7, as demonstrated in Fig. 5.29. Afterwards, the bulk shear sliding of each polymorph was simulated through a series of step-by-step calculations [52, 134]. It should be noted that this step-by-step static process is close to a dynamic process in a sense, which is much likely to resemble practice. In the successive calculations, the relaxation of one step with shear loaded was performed based on the relaxed structure of a stain loaded cell at the former step. Different from the contours, ΔE profiles were obtained in this case. The ΔE contours of the three forms of FOX-7, as well as TATB, are illustrated in Fig. 5.30. As pointed out above, an energetic compound will decompose if ΔE > BDE. For a FOX-7 molecule, the trigger bond, C–NO2 , possesses the BDE of 271.7 kJ/mol. Thereby, a close energy of 250.8 kJ/mol was adopted as a reference to define a feasible shear sliding region, i.e., ΔE ≤ 250.8, 125.4, and 41.8 kJ/mol are denoted as the criteria for feasible, rather ready, and ready shear sliding, respectively (Fig. 5.31) [50]. From the figure, it can be readily concluded that, from α- to βand γ -FOX-7, the regions of the rather ready and ready shear sliding become wider and wider, i.e., the region of feasible shear sliding increases from 0.48c to 0.62c and 1.0c, and γ -FOX-7 even appears free interfacial shear sliding with ΔE almost always below 41.8 kJ/mol and only two small regions of 41.8 < ΔE < 83.6 kJ/mol (Fig. 5.30c). This variation of sliding characteristic agrees with the above analysis of molecular stackings. γ -FOX-7 is approximately face-to-face π-π stacked and is the closest to that of TATB, compared to other two polymorphs. As to bulk shear sliding, ΔE in Fig. 5.32 is significantly lowered in contrast to the interfacial shear sliding shown in Fig. 5.30, suggesting a readier sliding. Comparing the energy profiles in Fig. 5.32, we find that the ΔE of α-FOX-7 is much different from those of β- and γ -FOX-7. For α-FOX-7, the ΔE corresponding to most shear strains are above 16.7 kJ/mol, except (010)/[100]. As for β- and γ -FOX-7, they are all below 16.7 kJ/mol, suggesting a readier bulk sliding thereof. Of course, TATB almost possesses a ΔE of zero (Fig. 5.32d), showing a much easier bulk sliding and partly rooting for its very low impact sensitivity. Furthermore, the largest ΔE can be seen as energy barrier of sliding. As exhibited in Fig. 5.33, the sliding barriers along various orientation of the three forms are below: 25.1, 24.7, 21.7, and 9.6 kJ/mol along the orientations of (010)/[10-1], (010)/[001], (010)/[101], (010)/[100] of α-FOX-7, 15.9, 14.2, 14.2, and 8.4 kJ/mol along (010)/[001], (010)/[10-1], (010)/[101], and (010)/

5.6 Polymorph Transition-Induced Low Impact Sensitivity of FOX-7

191

α

Fig. 5.30 ΔE (kJ/mol) contours for the interfacial shear sliding of the three polymorphs of FOX-7 and TATB. Reprinted with permission from Ref. [50]. Copyright 2019 American Chemical Society α-FOX-7

β-FOX-7

γ-FOX-7

1.0

width, c

0.8

0.6

0.4

0.2

0.0

ΔE 360 N. Regarding thermal stability, most energetic ionic compounds is inferior to HMX, with Td < 280 °C (the Td of HMX is 279 °C). Similar to energetic molecular crystals, the thermal decomposition mechanism of energetic ionic crystals features complex as well. For example, with respect to the initial step of an ionic compounds, it may be the intramolecular reaction of the cation or the anion, or the intermolecular reaction between the anions, the cations, or the cation and anion. Some of these belong to H transfer will be introduced in Chapter 9. As to the quantity of heat of formation (△θf H ), many of them exceed those of RDX (1.81 kJ/g) and HMX (1.90 kJ/ g), suggesting a good potential of heat release. If we define a comprehensive criterion

6.6 Energetic Organic Ionic Crystals

223

for choosing applicable energetic ionic crystal, with dc > 1.80 g/cm3 (close to that of RDX), vd > 8500 m/s (close to that of RDX), IS > 15 J (close to that of raw TNT), and Td < 220 °C (close to that of RDX), only EIS28 will be satisfactory. It shows the rareness of applicable energetic ionic compounds. To discuss the crystal packing characteristics, two groups of energetic ionic compounds separately based on A2 and A3 are employed, as demonstrated in Figs. 6.19 and 6.20, respectively. These two anions are structurally planar with all atoms conjugated, and possess larger sizes than NH3 OH+ (C1) and NH4 + (C2). A2 and A3 are strong HBAs to non-covalently link with the cation, as HBD. Thus, to a certain extent, what holds the crystal packing is more likely to be the dense and strong intermolecular HB, rather than the ionic bonding, due to weak ionicity of these ions. If the cations are removed, we will confirm the planar stacking in EIS5 and EIS6, wavelike stacking in EIS10, ladder-like stacking in EIS4 and EIS11, crossing stacking in EIS9, herringbone stacking in EIS7, and mixed-type stacking in EIS8. When adding cations, the stacking turns out to be a little irregular and can change to another type. The irregularity stems from the nonplanarity of most cations, while the type change results from the participation of large-sized cations in the stacking. For example, the herringbone stacking of A2 varies to the crossing stacking of practical EIS7, by the participation of C4. As to the small-sized compounds containing NH3 OH+ (C1) and NH4 + (C2), their diffraction patterns are determined by the frames of anions.

6.6.2 Ionic Crystals Containing Triazole Derivative On the whole, the energetic ionic compounds containing triazole derivatives exhibit similar properties to the aforementioned ones containing tetrazole derivatives. They are composed of cations and anions shown in Figs. 6.1 and 6.3, respectively. For dc , EIS62 reaches as high as 1.9 g/cm3 , due to both high PC and dm . As matter of fact, such high dc of 1.9 g/cm3 appear rare for energetic ionic compounds with C, H, N, and O atoms. NH3 OH+ (C1) feature a high ability to form strong HB and A23 has a high dm , so EIS63 formed by the two can have a large dc . Wholly, the energetic ionic compounds containing triazole derivatives exhibit inferior heat of formation to the ones with tetrazole derivatives, with lower △θf H , partly ascribed to the lower energy content of the triazole ring. By comparing Tables 6.5 with 6.6, it seems that the triazole ionic compounds generally possess lower mechanic sensitivity and higher thermal stability, with higher E dr and Td , also partly attributed to the higher molecular stability of the triazole ring. For the crystal packing structures, we adopt four bis-1,2,4-triazole-1,1' -diol (A23) ionic derivatives for discussion, as illustrated in Fig. 6.21. A23 itself is a planar structure. When forming ionic compounds with cations and taking no account of the cations, A23 is stacked in the forms of crossing (EIS64, Fig. 6.21a), wavelike (EIS62, Fig. 6.21b), herringbone (EIS63, Fig. 6.21c), and planar-layer (EIS61, Fig. 6.21d). The cations embellish crystal packing and can also influence the stacking of anions.

224

6 Energetic Ionic Crystals

Table 6.5 Main properties of some energetic ionic compounds containing tetrazole derivatives Compound

Cation

Anion

dc

vd

Pd

IS

FS

△θf H

EIS1 [14]

C2

A5

1.688

8436

26.6

> 50

> 360

2.19

EIS2 [14]

C3

A5

1.695

8759

29.0

46

> 360

2.79

EIS3 [14]

C1

A5

1.803

9100

33.4

> 50

> 360

2.25

EIS4 [4]

C2

A2

1.590

7417

18.9

35

> 360

EIS5 [4]

C3

A2

1.531

8265

23.6

40

360

EIS6 [4]

C1

A2

1.742

8854

31.7

10

240

Td

EIS7 [4]

C4

A2

1.586

7199

17.6

40

> 360

EIS8 [5]

C2

A3

1.664

8212

25.8

10

360

1.26

265

EIS9 [5]

C1

A3

1.822

9264

37.2

3

60

1.65

172

EIS10 [5]

C4

A3

1.633

7752

22.1

> 40

> 360

1.12

331

EIS11 [5]

C5

A3

1.637

8137

24.7

30

> 360

1.79

255

EIS12 [2]

C1

A4

1.785

9236

371

2

40

1.78

172

EIS13 [7]

C2

A1

1.567

7900

22.9

10

300

3.69

220

EIS14 [7]

C1

A1

1.561

8227

25.7

3

40

3.67

136

EIS15 [13]

C2

A6

1.56

7182

16.4

35

0.7

262.9

EIS16 [13]

C3

A6

1.62

8222

23.0

40

2.0

211.5

EIS17 [13]

C1

A6

1.60

7756

17.8

40

1.2

260.4

EIS18 [13]

C2

A7

1.45

7381

17.2

> 40

2.6

239.9

EIS19 [13]

C3

A7

1.68

9050

28.7

35

3.4

212.1

EIS20 [13]

C1

A7

1.68

8839

28.8

20

2.6

237.8

EIS21 [11]

C2

A8

1.617

8074

24.6

10

0.44

205

144

EIS22 [11]

C1

A8

1.614

8298

26.8

15

160

0.71

178

EIS23 [11]

C4

A8

1.624

7775

22.3

> 40

240

0.20

225

EIS24 [10]

C2

A13

1.530

8225

24.5

10

> 360

1.92

195

EIS25 [10]

C1

A13

1.664

9056

32.7

> 40

> 360

2.12

155

EIS26 [9]

C1

A16

1.850

9499

39

4

60

1.33

157

EIS27 [9]

C4

A16

1.698

8201

26.6

> 40

252

0.72

211

EIS28 [60]

C2

A10

1.800

8817

31.6

35

360

1.47

290

EIS29 [60]

C3

A10

1.725

9159

34.0

9

252

2.89

220

EIS30 [60]

C4

A10

1.639

7917

23.3

> 40

> 360

1.42

274

EIS31 [61]

C4

A11

1.596

8141

24.9

13

> 360

0.60

179

EIS32 [62]

C2

A12

1.693

8557

30.3

5

120

0.87

147

EIS33 [62]

C1

A12

1.796

9034

36.4

3

60

1.02

148

EIS34 [62]

C4

A12

1.697

8306

27.4

7

120

0.58

160

EIS35 [63]

C2

A9

1.592

8054

24.0

1

40

2.42

222

EIS36 [63]

C1

A9

1.596

8224

25.8

30

160

0.28

175 (continued)

6.6 Energetic Organic Ionic Crystals

225

Table 6.5 (continued) △θf H

Compound

Cation

Anion

dc

vd

Pd

IS

EIS37 [64]

C2

A17

1.69

7953

23.4

5

212

EIS38 [64]

C3

A17

1.74

8517

29.4

18

242

EIS39 [64]

C1

A17

1.77

8548

30.8

26

243

EIS40 [64]

C4

A17

1.64

7840

23.3

10

EIS41 [65]

C2

A14

1.553

7749

21.7

> 40

> 360

0.16

205

EIS42 [65]

C3

A14

1.594

8284

25.3

> 40

> 252

1.46

196

EIS43 [65]

C1

A14

1.634

9034

32.4

> 40

> 360

1.10

138

EIS44 [65]

C4

A14

1.612

7401

20.7

> 40

> 360

0.06

239

EIS45 [66]

C2

A15

1.757

9111

34.4

3

52

2.20

FS

Td

287

EIS46 [66]

C3

A15

1.678

9102

33.4