Size Exclusion Chromatography (GPC) 9780841205864, 9780841207288, 0-8412-0586-8

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Size Exclusion Chromatography (GPC) Theodore Provder,

EDITOR

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.fw001

Glidden Coatings and Resins

Based on a symposium sponsored by the Division of Analytical Chemistry at the 178th National Meeting of the American Chemical Society Washington, D.C., September 10-14, 1979.

ACS

SYMPOSIUM AMERICAN

CHEMICAL

WASHINGTON, D. C.

SERIES SOCIETY 1980

138

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.fw001

Library of Congress CIP Data Size exclusion chromatography ( G P C ) . (ACS symposium series; 138 ISSN 0097-6156) Includes bibliographies and index. 1. Gel permeation chromatography—Congresses. 2. Polymers and polymerization—Analysis—Congresses. I. Provder, Theodore, 1939- . II. American Chemical Society. Division of Analytical Chemistry. III. American Chemical Society. IV. Series: American Chemical Society. ACS symposium series; 138. QD272.C444S59 ISBN 0-8412-0586-8

547.7'046 ASCMC 8

80-22015 138 1-312 1980

Copyright © 1980 American Chemical Society A l l Rights Reserved. The appearance of the code at the bottom of the first page of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective works, for resale, or for information storage and retrieval systems. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, reproduce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. PRINTED I N T H E UNITED

STATES

OF

AMERICA

Society Library

1155 16th St. N. W. Washington, D. C. 20036

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.fw001

ACS Symposium Series M . Joan Comstock, Series Editor

Advisory Board David L. Allara

W. Jeffrey Howe

Kenneth B. Bischoff

James D. Idol, Jr.

Donald G. Crosby

James P. Lodge

Donald D. Dollberg

Leon Petrakis

Robert E. Feeney

F. Sherwood Rowland

Jack Halpern

Alan C. Sartorelli

Brian M . Harney

Raymond B. Seymour

Robert A. Hofstader

Gunter Zweig

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.fw001

FOREWORD The ACS SYMPOSIUM SERIES was founded in 1974 to provide

a medium for publishing symposia quickly in book form. The format of the Series parallels that of the continuing ADVANCES IN CHEMISTRY SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. Papers are reviewed under the supervision of the Editors with the assistance of the Series Advisory Board and are selected to maintain the integrity of the symposia; however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable since symposia may embrace both types of presentation.

PREFACE

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.pr001

S

ize exclusion chromatography or gel permeation chromatography (GPC) became a practical technique for obtaining the molecular weight distribution of polymers around 1964 through the pioneering efforts of John C. Moore. Since that time, GPC has become the analytical method of choice for fractionating and analyzing the molecular weight distribution of macromolecules. Thefieldhas grown and the output of journal articles has remained at a high level—during the past five years there have been on the order of 400 to 500 papers published annually. Recent technological advances over the past five years have sparked a new level of activity in thefieldof size exclusion chromatography (GPC). These include: (1) the development of high-performance, high-speed column technology; (2) the development and increased use of multiple in-line detectors (for example, differential refractometer, ultraviolet and infrared spectrophotometric detectors, visometry, light scattering, gravimetry, densitometry, etc.); and (3) the application of minicomputer and microcomputer technology for instrument control and data analysis. These developments in turn have led to new and improved applications of size exclusion chromatography (GPC) as well as higher quality information. The topics in this book that reflect some of these new technological advances include particle size analysis of latex by chromatography methods; gel content measurements; determination of polymer chain branching and copolymer composition as a function of molecular weight; high-resolution GPC analysis of oligomers and micellar systems; applications of aqueous GPC; improved data analysis methods; and kinetic modeling of polymerization reactions. These new technological advances also have impacted the work of the American Society for Testing and Materials (ASTM). The ASTM committee D20.70.04 currently is involved in developing new size exclusion chromatography methods (GPC) that incorporate these advances. It is hoped that this book will spur further activity in the field of size exclusion chromatography (GPC). The editor wishes to thank the authors for their effective oral and written communications and the reviewers for their critiques and constructive comments. THEODORE PROVDER

Glidden Coatings and Resins Strongsville, Ohio 41136 May 20, 1980 vii

1 Particle Size Analysis by Chromatography 1

2

A. J. McHUGH , D. J. NAGY , and C. A. SILEBI

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch001

Department of Chemical Engineering and Emulsion Polymers Institute, Lehigh University, Bethlehem, PA 18015

The use of column chromatography for fractionating polymer latex suspensions has been growing rapidly. Figure 1 shows a schematic breakdown of the several methods. One method, developed by Small (1,2), involves pumping the latex suspension through columns packed with nonporous beads. Separation by size results from the interaction between the electrostatically stabilized particles and eluant velocity gradients in the interstices between the packing. Thus the term Hydrodynamic Chromatography or HDC has been used to describe the process. Under conditions where van der Waals attraction between the particles and packing can predominate (such as at high eluant ionic strength), the particles may interact with or deposit onto the packing. The possibility exists for controlling the deposition -reintrainment behavior of the particles in this regime, based on either size or any of the physico-chemical parameters involved in the potential energy of interaction between the particles and packing. The term Potential Barrier Chromatography or PBC has been used to describe this process (3,4). A second chromatographic method, s i m i l a r i n o p e r a t i o n t o HDC, i n v o l v e s the use o f porous packing (as i n GPC) and has been r e f e r r e d t o as L i q u i d E x c l u s i o n Chromatography or LEC. Krebs and Wunderlich (5) were the f i r s t t o r e p o r t the use o f l a r g e pore s i l i c a g e l s f o r the f r a c t i o n a t i o n o f p o l y s t y r e n e and polymethylmethacrylate l a t e x e s . More r e c e n t l y , C o l l (6) and Singh and Hamielec (7.) have i n v e s t i g a t e d the s e p a r a t i o n o f p o l y s t y r e n e l a t e x e s up t o one micron i n diameter u s i n g c o n t r o l l e d - p o r e , s i l i c a g l a s s packing. T h e i r choice of packing s i z e and pore diameters c l e a r l y resembled those of t r a d i t i o n a l GPC systems. As a r e s u l t o f some o f the s t u d i e s t o be d i s c u s s e d i n t h i s paper, a separate regime i s p o s s i b l e when the packing pores are l a r g e Current address: department o f Chemical Engineering University of I l l i n o i s Urbana, I l l i n o i s 6l801 * A i r Products and Chemicals T r e x l e r t o w n , Pennsylvania 18105 0-8412-0586-8/80/47-138-001$06.25/0 © 1980 American Chemical Society

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch001

2

SIZE EXCLUSION CHROMATOGRAPHY

(GPC)

compared t o the p a r t i c l e s i z e . Such a process we r e f e r t o as Porous Hydrodynamic Chromatography. A t h i r d method i n v o l v e s f l o w o f the p a r t i c l e suspension through l o n g , s m a l l bore, open c a p i l l a r y tubes and has been r e f e r r e d t o as C a p i l l a r y Hydrodynamic Chromatography (8^9.). In t h i s process the f l o w s e p a r a t i o n mechanism appears t o be r e l a t e d t o the " t u b u l a r p i n c h e f f e c t " discussed i n the work of Segre and S i l b e r b e r g {10) and the name Tubular P i n c h Chromatography (TPC) has a l s o been a s s o c i a t e d w i t h i t . Since the phenomenon o n l y occurs above a c r i t i c a l Reynolds number ( l l ) , i t may be most a p p l i c a b l e t o p a r t i c l e s l a r g e r than a micron i n diameter. Another area o f r a p i d growth f o r p a r t i c l e s e p a r a t i o n has been t h a t o f F i e l d - F l o w F r a c t i o n a t i o n (FFF) o r i g i n a l l y developed by Giddings (12^, 13,1^,15.) (see a l s o papers i n t h i s symposium s e r i e s ) . L i k e HDC, the s e p a r a t i o n i n f i e l d - f l o w f r a c t i o n a t i o n (FFF) r e s u l t s from the combination of f o r c e f i e l d i n t e r a c t i o n s and the convected motion o f the p a r t i c l e s , r a t h e r than a p a r t i t i o n i n g between phases. In FFF the f o r c e f i e l d i s a p p l i e d e x t e r n a l l y w h i l e i n HDC i t r e s u l t s from i n t e r n a l i n t e r a c t i o n s . This paper w i l l be l i m i t e d t o a d i s c u s s i o n of our packed column s t u d i e s i n which we have addressed a t t e n t i o n t o questions r e g a r d i n g , (a) the r o l e o f i o n i c s t r e n g t h and s u r f a c t a n t e f f e c t s on both HDC and porous packed column b e h a v i o r , (b) the e f f e c t s of pore s i z e and pore s i z e d i s t r i b u t i o n on r e s o l u t i o n , and (c) the e f f e c t s of the l i g h t s c a t t e r i n g c h a r a c t e r i s t i c s o f p o l y s t y r e n e on s i g n a l r e s o l u t i o n and p a r t i c l e s i z e d i s t r i b u t i o n d e t e r m i n a t i o n . The d i s c u s s i o n s i n c l u d e r e f e r e n c e s t o previous p u b l i c a t i o n s which c o n t a i n d e t a i l e d development o f some o f the m a t e r i a l presented here. Nonporous Packing:

HDC

i ) Background. D e t a i l s o f the experimental aspects o f HDC column design and o p e r a t i o n are given i n s e v e r a l references ( l , l 6 , 1/7,18). The b a s i c technique i n v o l v e s pumping a d i l u t e suspension o f l a t e x p a r t i c l e s through beds packed w i t h styrene-divinylbenzene copolymer beads. P a r t i c l e s are detected by monitoring the t u r b i d i t y o f the eluant stream i n a flow-through c e l l at 25U nm. Over a range o f i o n i c s t r e n g t h s , p a r t i c l e s e l u t e from the columns ahead o f a d i s s o l v e d marker species (dichromate ion) w i t h p a r t i c l e residence time decreasing w i t h i n c r e a s i n g diameter. P a r t i c l e s e p a r a t i o n can be c h a r a c t e r i z e d by the s e p a r a t i o n f a c t o r , R , which i s the r a t i o o f eluant t o p a r t i c l e e l u t i o n volumes, o r , by the d i f f e r e n c e i n e l u t i o n volume, AV, between p a r t i c l e and eluant marker t u r b i d i t y peaks. For p o l y s t y r e n e monodisperse standards, a l i n e a r r e l a t i o n s h i p occurs between the l o g o f the p a r t i c l e diameter and AV, w i t h a s e r i e s of p a r a l l e l l i n e s r e s u l t i n g f o r d i f f e r e n t c o n c e n t r a t i o n o f e i t h e r s a l t or s u r f a c t a n t below i t s c r i t i c a l m i c e l l e c o n c e n t r a t i o n (17,18,19). The s e p a r a t i o n f a c t o r has a l s o been shown t o be independent o f eluant F

1.

MCHUGH E T A L .

3

Particle Size Analysis

flow rate (l8,1£). To q u a n t i f y Rp i n terms o f a fundamental model f o r t h e p a r t i c l e r e s i d e n c e time t h e d e f i n i t i o n i n terms o f average v e l o c i t e s i s used,

F

(1)

where v and vg r e f e r t o t h e p a r t i c l e and eluant a x i a l v e l o c i t y , and t h e b r a c k e t s r e f e r t o t h e a p p r o p r i a t e averaging taken over the cross s e c t i o n o f t h e assumed e q u i v a l e n t bed i n t e r s t i t i a l geometry. For t h e c a p i l l a r y bed model ( l 8 )

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch001

p

J

= —

R -R o p

x - 2

E

v i

(11) E

V l

/2+τΕ ] . ( e" 2 ) 2

E

W i

E i

where σ and τ describe the Gaussian and exponential instrument peak broadening parameters often used i n describing SEC column performance.^ For any of the algorithms, i n p r a c t i c e two polymer standards (of the same polymer type) having d i f f e r e n t known [η] values are used to obtain E^ and E using e i t h e r equation 10, 11, or 12. The standards used can be broad or narrow MWD. The l a r g e r the d i f f e r e n c e between the two [η] values, the more accurate the determined E^ and E values w i l l be. The two required standards can be obtained from samples chosen from a series of unknowns, or they can be obtained by c o l l e c t i n g two portions o f a sample from another SEC e l u t i o n experiment. The samples chosen as standards should then be measured c a r e f u l l y by c l a s s i c viscometric techniques to deter­ mine t h e i r [η] values using the same solvent as used i n the SEC experiment. The samples are then chromatographed as the c a l i b r a t i o n standards to e s t a b l i s h the retention volume/intrinsic v i s c o s i t y r e l a t i o n s h i p . Two polystyrene standards were used to demon­ s t r a t e the proposed c a l i b r a t i o n method. One narrowand one broad-MWD sample were purposely selected to show that the method works for both narrow and broad 2

2

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch005

102

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

TABLE 3 VISCOSITY RESULTS OF UNKNOWN SAMPLES

Polystyrene Samples 11B 60917 4B 3B 61124 NBS705 NBS706

MW

[η] Measured

Two Std. Calib. Curve

% Di

4,000 50,000 110,000 390,000 1.8x10 1.793x10 2.578x10

0.06 0.30 0.53 1.40 3.11 0.72 0.94

0.06 0.30 0.53 1.20 2.82 0.74 1.08

0 0 0 0 -14 +3 +15

6

5 5

5.

YAU E T AL.

103

Polymer Viscosity Characterization

standards. The c a l i b r a t i o n curve obtained i s p l o t t e d i n Figure 4 along with the peak p o s i t i o n c a l i b r a t i o n curve. The agreement between the methods by i n s p e c t i o n i s very good. Good agreement i s also observed between measured ^nd c a l c u l a t e d [η] values as shown i n Table 3 for the polystyrene samples. The differences seen between the corresponding [η] values are small con­ s i d e r i n g p o s s i b l e experimental u n c e r t a i n t i e s i n e i t h e r of the two techniques. I t i s i n t e r e s t i n g to note that since [ n l _ _ i s c a l c u l a t e d d i r e c t l y from the SEC SEC e l u t i o n curve and i s a p p l i c a b l e equally well f o r e i t h e r high or low v i s c o s i t y samples, the SEC-[η] approach may, i n f a c t , be able to study samples with v i s c o s i t y values which are too low to be measured accurately by conventional viscometry once a SEC-[η] c a l i b r a t i o n has been e s t a b l i s h e d i n t h i s region. In summary, the unique features of t h i s p r a c t i c a l SEC-[η] approach are as follows:

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch005

0

• knowledge of polymer Κ and α values i s not required; • the method i s not l i m i t e d by the a v a i l a b i l i t y of narrow MWD standards, (broad MWD standards are usually more r e a d i l y a v a i l a b l e f o r a l l polymer types); • knowledge of the molecular weight of the standards i s not required. D. SEC Measurement of Mark-Houwink Constants Using Only Polydispersed Standards. I f the SEC-MW c a l i b r a t i o n curve of the polymer-solvent system i s known i n addition to the [η] c a l i b r a t i o n , the MarkHouwink constants of the polymer-solvent system are e a s i l y c a l c u l a t e d from the c a l i b r a t i o n constants D^, U2, E and E as: 1 #

2

α

=

Κ

=

E /D 2

2

(13)

( 1 4 )

Note that equations 13 and 14 are simple rearrangements of equations 8 and 9. Depending on the a v a i l a b i l i t y of c a l i b r a t i o n standards, the standards f o r the MW c a l i b r a t i o n (D^^ and D ) can be the same or d i f f e r e n t from those used to c a l i b r a t e the [η] (Ε-, and E~) curve. The requirements 2

104

SIZE EXCLUSION C H R O M A T O G R A P H Y

(GPC)

f o r t h e MW c a l i b r a t i o n s t a n d a r d s a r e t h a t M a n d M v a l u e s f o r a s i n g l e b r o a d s t a n d a r d be known o r two different. M and/or M v a l u e s f o r two s t a n d a r d s be k n o w n .vi-t±) The b r o a d - s t a n d a r d l i n e a r c a l i b r a t i o n c u r v e s f o r p o l y s t y r e n e i n THF i n F i g u r e 1 a n d 4 a r e u s e d t o i l l u s t r a t e t h e Κ and α c a l c u l a t i o n s as f o l l o w s . The p a r t i c u l a r c a l i b r a t i o n curves a r e found t o correspond to the f o l l o w i n g c a l i b r a t i o n equations: w

w

n

n

V

R

=

2 2 . 7 5 - 1.76 L o g

V

R

=

1 3 . 0 - 2.5 L o g

M

(15)

[η]

(16)

l Q

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch005

and

Then, D

= 8.44 χ 1 0

1

and

E

1 2

, D

2

1 Q

= 1.309, E

±

= 1.56 χ 1 0

5

=0.92

2

By s u b s t i t u t i n g t h e s e v a l u e s . i n t o e q u a t i o n s ( 1 3 ) a n d ( 1 4 ) , a Κ v a l u e o f 1.28 χ 10 and an α v a l u e o f 0.703 a r e o b t a i n e d w h i c h a r e i n r e a s o n a b l y g o o d a g r e e ­ m e n t w i t h t h e e x p e c t e d v a l u e s o f 1.25 χ 1 0 ~ d l / g a n d 0.72 m e n t i o n e d earlier. The u n i q u e f e a t u r e s o f t h i s m e t h o d o f m e a s u r i n g polymer Κ and αa r e : ψ Only

p o l y d i s p e r s e d standards a r e used;

•

Only

two t o f o u r s t a n d a r d s a r e r e q u i r e d ;

•

Concentration extrapolation i s not necessary s i n c e SEC s a m p l e s a r e a l r e a d y h a n d l e d a s v e r y dilute solutions.

E. U n i v e r s a l C a l i b r a t i o n S t u d i e s . The u s e o f SEC-[η] a n d MW c a l i b r a t i o n u s i n g b r o a d MWD s t a n d a r d s w i l l make i t e a s i e r t o s t u d y t h e a c c u r a c y o f t h e u n i v e r s a l c a l i b r a t i o n concept. By c o m b i n i n g t h e D I / D 2 and E - i / E calibration curves, the universal calibration (Μ[η]Τ c a n b e g e n e r a t e d d i r e c t l y a s i n e q u a t i o n 1 7 . -D V -E9V -(D +E )V Μ[η] = ( D e 2 ) ( E ^ e ) = (DjE-^e (17) 2

D

V

2

Z

2 Z

2

x

w h e r e (D]_Ei) a n d ( D 2 + E 2 ) constants f o r Μ[η].

a r e now t h e c a l i b r a t i o n

5.

Y A U E T AL.

Polymer Viscosity Characterization

105

Conclusions The v a l i d i t y of a p r a c t i c a l method of d i r e c t v i s c o s i t y c a l c u l a t i o n from s i z e exclusion chromato­ graphic analysis i s demonstrated. The method i s con­ venient to use and i s not l i m i t e d by the a v a i l a b i l i t y of narrow MWD standards. I t i s possible to accurately measure polymer Mark-Houwink constants using the sug­ gested broad standard SEC-[η] and SEC-MW c a l i b r a t i o n procedure.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch005

Acknowledgement We thank J . C. Rowell f o r the i n t r i n s i c v i s c o s i t y data f o r the polymer samples used i n t h i s study. ABSTRACT A new d i r e c t method f o r using s i z e exclusion chromatography (SEC) to evaluate polymer i n t r i n s i c v i s c o s i t y [η] is discussed. Sample v i s c o s i t y informa­ t i o n i s obtained by combining SEC e l u t i o n curve data and c a l i b r a t i o n data using d i r e c t SEC-[η] c a l i b r a t i o n procedures without i n v o l v i n g polymer molecular weight calculations. The p r a c t i c a l utility, convenience and the expected p r e c i s i o n of the proposed method are illustrated. Literature Cited 1.

Yau, W. W., Kirkland, J. J., and Bly, D. D . , "Modern Size Exclusion Liquid Chromatography", John Wiley & Sons, N . Y . , 1979, Chapters 9 and 10.

2.

Hellman, M. Y., i n Chromatographic Science Series, Vol. 8, Liquid Chromatography of Polymers and Related Materials, J. Cazes, e d . , Dekker, New York, 1977, p. 29.

3.

Yau, W. W., Stoklosa, H. J. and Bly, D. D . , J. Appl. Polym. S c i . , 21, 1911 (1977).

4.

Fok, J. S. and Abrahamson, Ε. Α . , Chromatographia, 7, 423 (1974).

5.

Yau, W. W., Ginnard, C. R. and Kirkland, J. J., J . Chromatography, 149, 465 (1978).

RECEIVED May 20, 1980.

6 Characterization of Branched Polymers by Size Exclusion Chromatography with Light Scattering Detection R. C. JORDAN and M . L . McCONNELL

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

Chromatix, 560 Oakmead Parkway, Sunnyvale, C A 94086

Size exclusion chromatography (SEC) separates molecules of a polymer sample on the basis of hydrodynamic volume. When the chromatograph is equipped only with a concentration-sensitive detector, i.e. conventional SEC, a molecular weight distribution (MWD) can be obtained from the chromatogram only through use of a calibration function relating molecular weight and elution volume V (1). The calibration technique used in conventional SEC does not always give the correct MWD, however. The molecular size of a dissolved polymer depends on its molecular weight, chemical composition, molecular structure, and experimental parameters such as solvent, temperature, and pressure (2). If the polymer sample and calibration standards differ in chemical composition, the two materials probably will feature unequal molecular size/weight relationships. Such differences also will persist between branched and linear polymers of identical chemical composition. Consequently, assumption of the same molecular weight/V relation for dissimilar calibrant and sample leads to transformation of the sample chromatogram to an apparent MWD. In some cases the r e l a t i o n s h i p between polymer intrinsic v i s c o s i t y ([η]) and molecular weight (M) has been e s t a b l i s h e d f o r the SEC s o l v e n t and temperature c o n d i t i o n s ; i . e . , the e m p i r i c a l Mark-Houwink c o e f f i c i e n t s (2)(K,a) i n the equation

[η>

KM

a

(1)

have been determined. Under these circumstances the " u n i v e r s a l " c a l i b r a t i o n approach can be u t i l i z e d to c a l c u l a t e the c o r r e c t MWD from the sample chromatogram. However, K,a values are not a v a i l a b l e f o r many samples, p a r t i c u l a r l y those with polymer chain branching. A number o f the l i m i t a t i o n s o f conventional SEC can be overcome through use o f a low angle l a s e r l i g h t s c a t t e r i n g (LALLS) d e t e c t o r attached i n s e r i e s with a concentration

0-8412-0586-8/80/47-138-107$05.75/0 © 1980 American Chemical Society

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

108

S I Z E

E X C L U S I O N

C

H

R

O

M

A

T

O

G

R

A

P

H

Y

( G P C )

d e t e c t o r (SEC/LALLS). The p r i n c i p l e s and methodology o f the technique are described i n d e t a i l elsewhere ( 4 - 7 ) . Data from both detectors are used to obtain the absolute molecular weight a t each point i n a sample chromatogram. The SEC/LALLS technique i s capable o f q u i c k l y y i e l d i n g the c o r r e c t MWD o f l i n e a r and branched samples without recourse to the approximate column c a l i b r a t i o n methods used i n conventional SEC. The hydrodynamic volume separation mechanism o f SEC, along with the d i f f e r e n t molecular size/weight r e l a t i o n s h i p s o f branched and l i n e a r polymers o f i d e n t i c a l chemical composition, can be e x p l o i t e d with the SEC/LALLS method to gain information about polymer branching. In the s t u d i e s described i n t h i s paper both conventional SEC and SEC/LALLS a r e used to obtain data about branching i n samples o f p o l y v i n y l acetate) (PVA) and p o l y c h l o r o prene (PCP). Theoretical The d i s c u s s i o n and experimental approach presented here r e l y on the p r i n c i p l e s and use o f universal c a l i b r a t i o n f o r SEC analysis. For a review o f t h i s method the reader i s r e f e r r e d to several useful a r t i c l e s (1_,3,8,9). For i l l u s t r a t i o n considfer SEC chromatograms obtained f o r two polymers on the same chromatographic system. One sample i s a l i n e a r homopolymer while the o t h e r i s a branched polymer with the same chemical composition. In the l a t t e r sample assume that the polymer components o f d i f f e r e n t molecular weight have uniform branching c h a r a c t e r i s t i c s so that a l l have s i m i l a r molecular size/weight r e l a t i o n s h i p s . Compare molecular size/weight c h a r a c t e r i s t i c s o f branched and l i n e a r species e l u t i n g a t V i n each chromatogram. Under the universal c a l i b r a t i o n formalism branched and l i n e a r components have the same hydrodynamic volume a t V: (Cn] M ) = b

b

v

([η] Μ ) 1

1

γ

(2)

where s u b s c r i p t s b and 1 denote branched and l i n e a r polymer components, r e s p e c t i v e l y . I f the f r a c t i o n a t V i s homogeneous with respect to hydrodynamic volume, the polymer molecules a t V w i l l be monodisperse with respect to molecular weight. The r a t i o o f the i n t r i n s i c v i s c o s i t i e s o f branched and l i n e a r species at V i s obtained by rearranging eq 2

(3)

6.

J O R D A N

A N D

M

C

C

O

N

N

E

L

Characterization of Branched Polymers

L

109

However, the q u a n t i t y which i s f r e q u e n t l y discussed and r e l a t e d to s p e c i f i c branching models i s the r a t i o o f i n t r i n s i c v i s c o s ­ i t i e s at constant molecular weight (2)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

(4)

For polymer samples o f the type considered here t h i s parameter r e f l e c t s the reduction i n molecular s i z e o f branched, r e l a t i v e to l i n e a r , material o f i d e n t i c a l molecular weight. The r e l a t i o n s h i p between g and g^ can be found through use o f the Mark-Houwink r e l a t i o n s h i p . n"he i n t r i n s i c v i s c o s i t y o f a l i n e a r polymer o f the same molecular weight (M. ) as the branched polymer i s

D

(5)

where Κ and a are the Mark-Houwink constants f o r the l i n e a r polymer. Equation 3 gives the r e l a t i o n o f M. to M, a t V, so t h a t we can r e l a t e the i n t r i n s i c v i s c o s i t y o f the l i n e a r polymer at V to the i n t r i n s i c v i s c o s i t y o f l i n e a r polymer having the same molecular weight as the branched polymer a t V:

(6)

S u b s t i t u t i o n o f eq 1 i n t o eq 6 gives

(7)

Use o f eq 7 i n eq 4 gives

110

SIZE EXCLUSION CHROMATOGRAPHY (GPC

Since we have e x p l i c i t l y s p e c i f i e d that branched species o f molecular weight M. a r e contained a t volume V, eq 8 can be written:

(Cn] ) b

9

= M

M

—

~

v

a


,10). Values shown in Tables II-IV cover data c o l l e c t e d between acceptable s i g n a l / noise l i m i t s o f the LALLS and DRI detectors a t the low and high molecular weight ends, r e s p e c t i v e l y , o f the chroma tograms. Consequently i n the high molecular weight p o r t i o n o f chromatograms data were processed when the concentration exceeded 1% o f the peak c o n c e n t r a t i o n , whereas i n the low molecular weight region the lowest concentration used represented 10% o f the maximum. For the NBS standard polystyrene SRM 706 Table II presents SEC/LALLS values o f (M^y as well as band-spreading c o r r e c t e d (MjJ) values obtained from processing data i n the conventional sense. The dependences on V o f l o g Î M ^ v and l o g i M ^ y are p l o t t e d i n Figure 1. In a d d i t i o n to the g* values c a l c u l a t e d from ( M Î ) and ( M ) * v a l u e s o f (M*/Mw)y are reported i n Table I I . The parameter (M*) represents the apparent molecular weight o f l i n e a r polymer a t V, given by the GPC1 program, but without a p p l i c a t i o n o f the band-spreading c o r r e c t i o n (Appendix). T h e r e f o r e , the d i f f e r e n c e between g ' and ( M * ^ ) ' at V shows the e f f e c t o f a p p l y i n g the band-spreading c o r r e c t i o n to data processed i n the conventional sense. In a d d i t i o n , Table II n

v

a

V

w

v

v

+ a

J O R D A N

A N D

M

C

C

O

N

N

E

L

L

Characterization of Branched Polymers

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

Table I

Data from the SEC/LALLS A n a l y s i s o f Narrow MWD Polystyrene Standards

SAMPLE

3 R

U\P

w

n

PC600K

6.65xl0

PC390K

3.76x10

PC233K

2.50x10

NBS705

1.73xl0

PC100K

9.08x10

PC50K

4.87x10

PC37K

3.73x10

(corr)]

5

6.54x10

5

3.72xl0

5

2.45x10

5

1.72xl0

4

8.99X10

4

4.79x10

4

3.66x10

5

5

5

5

4

4

4

a

P r e f i x e s PC and NBS r e f e r to the s u p p l i e r s , Pressure Chemical Co. and National Bureau o f Standards, r e s p e c t fully.

b

The quantity R ( c o r r ) i s the SEC/LALLS sample number average molecuTar weight, c o r r e c t e d f o r band-spreading, while 1^ i s the sample weight-average molecular weight.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

116

SIZE EXCLUSION

CHROMATOGRAPHY

(GPC)

6.4

4.2 I

27

I

I

I

ι

I

I

29

31

33

35

37

39

V(ml) m

Figure 1. Dependence on V of \MJA (corr)} for polystyrene calibrants (Table I), and dependence on V of (M„) and (Μ„*) for polystyrene SRM706 (Table II): (A) M -= [MvMJcorr)]" ; (+) M = (M *) ; (O) M = (MJ . The straight line corresponds to Equation 15. n

v

υ

2

w

v

V

6.

JORDAN

Characterization of Branched Polymers

A N D M iti sample \ and band-spreading c o r r e c t e d f L v a l u e s . Data from Table IV are p l o t t e d i n Figure 4 as l o g ( l $ ) and l o g (Μ^γ v s . V; a p l o t o f g ' v s . l o g ( Μ ^ f o r PCP i s shown i n Figure 5. a

n

d

d

a

t

a

f

o

r

P C P

i

n

a

d

d

o

n

t

0

t

h

e

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

ν

ν

Discussion Data i n Figures 3 and 5 show an increase i n g' with de­ c r e a s i n g molecular weight f o r each o f the p o l y d i s p e r s e PVA and PCP samples. However, the data f o r PCP and one o f the PVA samples (0106) a l s o e x h i b i t g ' values g r e a t e r than unity a t the low molecular weight ends o f the molecular weight d i s t r i ­ butions. Since by i t s d e f i n i t i o n g i s expected to equal o r be l e s s than u n i t y , such values are anomalous. A l s o , some g values are s u s p i c i o u s l y low i n the high molecular weight r e ­ gions o f the PVA samples. Examination o f data f o r the NBS standard polystyrene SRM 706 gives i n s i g h t i n t o the behavior o f g' data i n the molecular weight extremes o f the PVA and PCP samples. The SEC/LALLS data i n the l o g i M ^ v vs V p l o t (Figure 1) e x h i b i t l i n e a r b e h a v i o r , along with curvature i n the high and low molecular weight r e g i o n s . This i s i n c o n t r a s t to the l i n e a r dependence on V o f l o g i R ^ ) ' ' which i s shown by the narrow MWD polystyrene c a l i b r a n t s . Diminished molecular s i z e r e s o ­ l u t i o n i n the molecular weight extremes o f SRM 706 i s a probable cause f o r t h i s discrepancy. High molecular weight, unresolved species serve to increase SEC/LALLS ( ^ ) values a t low V, whereas unresolved low molecular weight components decrease (Mu,) a t high V. The other n o t i c e a b l e feature i n Figure 1 i s the dependence o f log(Mj$) on V, obtained by conventional processing o f the d a t a ; log(MjJ) shows the expected l i n e a r v a r i a t i o n with V throughout the chromatogram, except f o r downward curvature in the high molecular weight r e g i o n . These l a t t e r data correspond to points i n the extreme high molecular weight end o f the chromatogram, where the concentration i s only a few percent o f the peak ( R e s u l t s ) . I t i s doubtful t h a t material at points i n the extreme t a i l s o f the chromatogram has a Gaussian d i s t r i b u t i o n o f molecular weights, thus i n ­ v a l i d a t i n g use o f the band-spreading c a l c u l a t i o n (Appendix). 1

1

2

ν

v

v

v

6.

J O R D A N

A

N

D

M

C

C

O

N

N

E

L

L

Characterization of Branched Polymers

121

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

logM

Β

logM

Figure 2. Dependence on V of (MJ and (M *) for (A) PVA 0106 and (B) PVA 0107-066 (data from Table III: (+) Μ = (M *) ; (Ο) M = (MJ ) V

w

v

w

v

V

SIZE EXCLUSION CHROMATOGRAPHY

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

122

6.8

6.4

6.0

5.6

(GPC)

4.4

5.2

log (M )v w

Figure 3. Dependence of g on (MJ for PVA samples (data from Table III: (+) = g for PVA 0106; (O) = g' [= gYU] for PVA 0107-066; note that for PVA 0106, g' = 4.18 has been deleted from the plot) V

logM

Figure 4.

Dependence on V of (MJ and (M *) for PCP (data from Table IV: (+) M = (M *) ; (O) M = (MJ ) V

w

w

v

v

V

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

J O R D A N

A

N

D

Figure 5.

M < C O N N E L L

Characterization of Branched Polymers

Dependence of g on (MJ for PCP (data from Table IV) V

124

SIZE

EXCLUSION

CHROMATOGRAPHY

On the other hand concentration detector (DRI) data represent at l e a s t 10% o f the maximum on the low molecular weight s i d e o f the chromatogram ( R e s u l t s ) , and the Gaussian approximation i s probably a p p l i c a b l e . Since polystyrene SRM 706 i s supposedly a l i n e a r polymer sample, g' i s not expected to deviate s t r o n g l y from u n i t y . I n spection o f Table II shows that g* values c l u s t e r about unity throughout most o f the SRM 706 molecular weight d i s t r i b u t i o n . In the t a i l s o f the d i s t r i b u t i o n , however, decreased r e s o l u t i o n and i n a p p l i c a b i l i t y o f the band-spreading c o r r e c t i o n serve to make g' behave anomalously. * For PVA and PCP the dependences on V o f log(M^) and log ( M ) (Figures 2a, 2b and 4) show s i m i l a r trends as f o r SRM 70o. Noticeable downward curvature o f log(M^)y at low molecular weight occurs i n each c a s e , i n c o n t r a s t to r e l a t i v e l y l i n e a r behavior o f l o g ( M ^ ) . Anomalously l a r g e values o f g r e s u l t (Figures 3 and 5 ) . In the highest molecular weight r e g i o n , a sharp downturn i n the l o g (M^) dependence on V i s apparent which i s accompanied by very low g' v a l u e s . The r e s u l t s found i n t h i s work i n d i c a t e that SEC/LALLS can be used to obtain q u a l i t a t i v e data about polymer branching. As suggested e a r l i e r in the d e r i v a t i o n o f the expression f o r g ' , the assumptions inherent i n using t h i s parameter as an approximation to g should not be overlooked. Caution should be e x e r c i s e d f o r polymers with unknown branching c h a r a c t e r i s t i c s , e . g . , where branching frequency i s suspected to vary with molecular weight. In t h i s case the molecular weight h e t e r o geneity a t V can be s i g n i f i c a n t l y more than allowed f o r by the l i n e a r polymer band-spreading c o r r e c t i o n used here (18). The g' data f o r the PVA samples (Table I I I , Figure 3) i n d i c a t e that branching a f f e c t s the molecular volume o f PVA 0107-066 to a g r e a t e r extent than the lower molecular weight PVA 0106. Except f o r the suspect points i n the extremes o f the MWD the g* values f o r PVA 0106 are l a r g e r than f o r PVA 0107-066, and f o r each sample the data show a decrease i n g with i n c r e a s i n g molecular weight. (The r e p r o d u c i b i l i t y o f the t e c h nique i s shown by the agreement o f g' values obtained f o r successive runs of PVA 0107-066.) Studies (19) have shown t h a t , f o r PVA samples wherein c e r t a i n branching c h a r a c t e r i s t i c s ( e . g . branching frequency) increase with the extent o f r e a c t i o n a general decrease i n g (eq 4) with i n c r e a s i n g molecular weight was found. A s i m i l a r dependence o f g on molecular weight i s found f o r the PCP sample (Table IV, Figure 5 ) . The data suggest the presence o f branching throughout the MWD, which i s c o n s i s t e n t with the known p r o p e n s i t y o f t h i s polymer to e x h i b i t branching under most r e a c t i o n c o n d i t i o n s ( V7)· Anomalous g values in the molecular weight extremes again r e f l e c t the dependence on V o f log(M^) and l o g ( M ) (Figure 4 ) . v

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

(GPC)

w

y

1

v

v

m

1

m

1

1

w

v

6.

JORDAN

AND

Characterization

MCCONNELL

of Branched

Polymers

125

Since the SEC/LALLS technique always yields a weightaverage molecular weight (M^y for the slightly polydisperse fraction at V, a small overestimation of the sample R is expected (5., 10). As noted previously (Results) a 1% to 4% decrease in the narrow MWD polystyrene M values (Table I) accompanied application of the band-spreading correction; Table II shows that for SRM 706 good agreement^*s obtained between SEC/LALLS and conventional SEC sample Pi^ and R values when the band-spreading correction was used. However, the NBS 706 polydispersity index (FL/R ) given by the supplier (ca. 2.1) does not agree with that U . ο ) found here using the SEC/LALLS and conventional SEC techniques. Insensitivity of the LALLS detector to a small amount of low molecular weight material may account for a larger sample M ; however, this is not supported by the conventional SEC data. The reason for the discrepancy remains unclear. n

n

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

n

n

Appendix Yau, et. al_., (11 ) described a computation method, named GPCV2, which corrects for chromatographic dispersion (bandspreading) in the determination of the MWD using SEC. Although developed for use with a single broad standard calibration scheme, the fundamental equations are also valid for a multiple narrow standard calibration. In this study we have composed a minor variation in GPCV2 to f a c i l i t a t e its use with a universal calibration scheme. Also, we have derived a computational method analogous to GPCV2 which can be used to correct for chromatographic dispersion in the determination of the MWD by SEC/LALLS. To employ GPCV2 in SEC, the column calibration is expressed as M* = D ~ 2 (Al) D

V

i e

where M* is the apparent linear (peak position) molecular weight at retention volume V. Because of chromatographic dispersion, the sample fraction in the detector cell is polydisperse. The weight-average and number-average molecular weights of the polydisperse fraction are calculated as =

KK w

D 2 g 2 )

"

· exp[(D c^/2] · M* 2

(A2)

~T(Tj

v

M

( „)

F ( V

=

F

(

V

)

e x

v

2

P [-(0 σ) /2]. M* 2

2

F(V+D o ) 2

(A3)

126

SIZE

EXCLUSION

CHROMATOGRAPHY

(GPC)

where F(V) i s the normalized ( E F ( V ) = l ) chromatogram under the conditions o f chromatographic d i s p e r s i o n ( . . F(V) i s the d e t e c t o r response a t r e t e n t i o n volume V ) . The term σ i s the d i s p e r s i o n constant. The RJJ and P§ o f the t o t a l sample are c a l c u l a t e d as

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

y

fl*

= exp[-(D a) /2] -l[(F(v)D

%

= exp[(D a) /2]/E

2

2

2

2

D i e x p

^)

]

exp(-D V)J

(A4)

2

(A5)

v )

Combination o f eqs (A4) and (A5) y i e l d s

%

= -(D2a) e

2

v)D e- 2 ] · Z[F(V)/D - 2 ] D

E [ F (

v

D

1

v

(A6)

i e

1

Η η

T h e r e f o r e , i f M^/M^ i s known, σ = D"

1

^ ln|(fl*/R*)

σ can be c a l c u l a t e d as

* E[F(V)D -¥] i e

· Z[F(V)/D " 2 ]j D

i e

v

(A7)

In t h i s study we have used an Mj£/M c a l c u l a t e d from s u p p l i e r ' s specifications. The GPCV2 equations were developed f o r conventional log(MW) v s . r e t e n t i o n volume c a l i b r a t i o n s . When used i n conjunction with a universal c a l i b r a t i o n , the slope term (Dp) must be c o r r e c t e d f o r the d i f f e r e n t molecular size/weight r e l a t i o n s h i p s o f the c a l i b r a n t s and the samples as derived i n the f o l l o w i n g equations. To understand t h i s c o r r e c t i o n , c o n s i d e r the con­ ventional c a l i b r a t i o n curve that could be created from the universal c a l i b r a t i o n d a t a . The slope term, Dp, f o r a c a l i b r a t i o n with polymer 1 i s defined a t points a and b on the c a l i b r a t i o n curve as n

6.

JORDAN

AND

Characterization

MCCONNELL

of Branched

Polymers

127

the slope term that must be used to c o r r e c t f o r d i s p e r s i o n o f sample polymer 2 can be s i m i l a r l y defined

,

D

_

1

n

"

2

2 ^

Μ

Ί

" 2,a

.

M

V a V

According to the universal

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

= K

2

2,a

M

"

V a V

concept

(a,+l)

?

a

(A9)

( - f e - )

n

calibration

(a +l) J

1

=

l l,a

K

(A10)

M

where K , a and K] ,a-j are the Mark-Houwink c o e f f i c i e n t s o f polymer 2 and polymer 1, r e s p e c t i v e l y , and J i s the hydrodynamic volume a t r e t e n t i o n volume a . Similarly, 2

2

a

*AT - AT ]

b

j

=

K

{A11)

]

Reconfiguring A10 and A l l we o b t a i n

2,b

M

=

ά

λ)

η

2+1)

ai2

ι*Α χ /^ *

< >

and

2,a

M

=

λ)/Κ

η&2+1)

( A 1 3 )

ίκΑ*Χ Ζ?

therefore 2,b/ 2,a

M

ί ^ / ^ Ψ ^ )

=

M

-

[M , /M 1

b

l i a

3

( a

l

+ 1 ) / ( a 2 + 1 )

(AH)

and In ( M

2 f b

/M

2 > a

)

=

[(a +l)/(a +l)] 1

2

In ( M

l f b

/M

1 > a

)

(A15)

Combination o f eqs A8 and A9 y i e l d s D

2

=

D

2

l

n

( 2,b M

/ M

2,a>

/ l n

( l,b M

/ M

l,a)

(A16)

S u b s t i t u t i o n o f A15 i n t o A16 y i e l d s D' 2

=

D ( +l)/(a +l) 2

a i

2

(A17)

128

SIZE

EXCLUSION

(GPC)

CHROMATOGRAPHY

Therefore to obtain (M*) and (M*) from M* data obtained by universal c a l i b r a t i o n , eqs A2 ana A3 are employed, but ΌΧ c a l ­ c u l a t e d by A17 i s s u b s t i t u t e d f o r the D terms i n A2 and A3. Note a l s o that the value of σ obtained f o r a given l i n e a r polymer c a l i b r a n t i s an approximation to the true value f o r a branched polymer o r a polymer of d i f f e r i n g monomeric composition, since the dispension f u n c t i o n i s 1 i k e l y to vary f o r the various sample types. Under these c o n d i t i o n s , the d i s p e r s i o n c o r r e c t i o n i s a somewhat poorer approximation than the standard GPCV2 corrections. In SEC/LALLS, the molecular weight measured a t any i n s t a n t i s (M ) . Thus the sample M can be c a l c u l a t e d by the standard definition

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

2

w

% = *[F(V) ( M ) w

y ]

(

A

1

8

)

Using gq A2 to e l i m i n a t e M* i n eq A3, and s u b u s t i t u t i n g (M ) f o r (M ) a d i s p e r s i o n - c o r r e c t e d (M ) can be determined i n the StC/LALLS experiment: v

F(V) (M ) n

n

v

V

=

2 2

2

T~ · e x p [ - ( D a r ] * 2

Z

2

F(V+D a ) · F(V-D a ) 2

1

(MJ W

V

(A19)

V

2

then f o r the t o t a l

sample

M (corr) n

= l/Z[F(V)/(H ) ] n

Y

(A20)

where M ( c o r r ) denotes the o v e r a l l sample number-average molecular weight from SEC/LALLS, c o r r e c t e d f o r band-spreading. The 1 i m i t a t i o n s on the a p p l i c a t i o n o f eq A19 to branched p o l y ­ mers and the use o f a constant σ f o r various polymers i n SEC/ LALLS a r e i d e n t i c a l t o the l i m i t a t i o n s c i t e d above f o r GPCV2. Acknowledgements: The authors wish to acknowledge the valuable t e c h n i c a l a s s i s t a n c e o f P h i l i p J . C h r i s t and Frank Chambers.

6.

JORDAN AND McCONNELL

Characterization of Branched Polymers 129

LITERATURE CITED 1. 2. 3.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch006

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

Yau, W. W., Kirkland, J. J., and Bly, D. D., "Modern Size Exclusion Chromatography", John Wiley & Sons, New York Ν. Y., 1979. Flory, P. J., "Principles of Polymer Chemistry", Cornell University Press, Ithaca, Ν. Υ., 1953. Grubisic, Ζ., Rempp, P., and Benoit, H., J. Polym. Sci. B, (1967), 5, 753. Application Notes LS-2, LS-3, LS-5, LS-10, Chromatix, 1977-1979. McConnell, M. L . , Am. Lab., (1978), 10 (5), 63. Ouano, A. C., and Kaye, W., J. Polym. Sci. Polym. Chem. Ed., (1974), 12, 1151. MacRury, Τ. Β., and McConnell, M. L . , J. Appl. Polym. Sci., (1979), 16, 2829. Dubin, P., and Kronstadt, M., in "Plastic Materials Science and Technology", Baijal, M. J., ed., Wiley-Interscience, New York, In press. Weiss, A. R., and Cohn-Ginsburg, Ε., J. Polym. Sci. B, (1969), 7, 379. Hamielec, A. E., Quano, A. C., and Nebenzahl, L. L . , J. Liq. Chromat., (1978), 1 (4), 527. Yau, W. W., Stoklosa, H. J., and Bly, D. D., J. Appl. Polym. Sci., (1977), 2 1 , 1911. Huglin, Μ. Β., in "Light Scattering from Polymer Solutions", Huglin, Μ. Β., ed., Academic Press, New York, Ν. Υ., 1972 p. 165 ff. Application Note LS-7,Chromatix, 1979. Ouano, A. C., J. Chromatogr., (1976), 118, 303. Hellman, Μ. Υ., in "Liquid Chromatography of Polymers and Related Materials", Cazes, J., ed., Marcel Dekker, New York, Ν. Y., 1977, p. 31. Park, W. S., and Graessley, W. W., J. Polym. Sci. Polym. Phys. Ed., (1977), 15, 71. Coleman, Μ. Μ., and Fuller, R. E . , J. Macromol. Sci.-Phys., (1975), B11 (3), 419. Ambler, M. R., Mate, R. D., and Purdon, J. R., Jr., J. Polym. Sci. Polym. Chem. Ed., (1974), 12, 1759. Park, W. S., and Graessley, W. W., J. Polym. Sci. Polym. Phys. Ed., (1977), 1 5 , 85.

RECEIVED May 7, 1980.

7 The Molecular Weight and Branching Distribution Method G. N. F O S T E R — U n i o n Carbide Corporation, Bound Brook, N J 08805 A. E. HAMIELEC—Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4M1

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

T. B. M a c R U R Y — U n i o n Carbide Corporation, South Charleston, W V 25303

Free radical polymerization leads to long chain branching (LCB) in commercial polymers such as polyvinyl acetate (PVAc) and low density polyethylene (LDPE) via a transfer to polymer mechanism (1). The branch lengths and spacings between branch points are most probably random for such polymers. Long chain branching content in commercial PVAc and high pressure LDPE ranges from one to twenty branch points per molecule. It is well known that LCB has a pronounced effect on the flow behavior of polymers under shear and extensional flow. Increasing LCB will increase e l a s t i c i t y and the shear rate sensi­ t i v i t y of the melt viscosity (2). Environmental stress cracking and low-temperature brittleness can be strongly influenced by the LCB. Thus, the a b i l i t y to measure long chain branching and its molecular weight distribution is c r i t i c a l in order to t a i l o r product performance. The use of 1 3 c NMR to measure LCB (3, 4), although absolute, is both time intensive and 1imi ted in that i t provides informa­ tion only on the whole polymer. Existing size exclusion chroma­ tographic (SEC) methods (!5, 6) have attempted to correct the whole polymer molecular weights for long chain branching. How­ ever, both interpretations ignored the fact that the contents of the detector cell are polydispersed and that the LCB is a func­ tion of molecular weight. SEC separates molecules according to hydrodynamic size, which is directly related to the product of the intrinsic viscos­ ity [ η ] and the molecular weight as demonstrated by Benoit et. a l . ( 7 ) . Recently, Hamielec and Ouano (8) proved that for branched polymers, the instantaneous molecular weight in the detector cell is the instantaneous number average molecular weight M^j(V). Therefore, the hydrodynamic size at a given elution volume is equal to the product Ln](V)M^(V). Hence the detector cell will contain a complex mixture of molecules having the same hydrodynamic size but different molecular weights due to long chain branching.

0-8412-0586-8/80/47-13 8-131 $05.00/0 © 1980 American Chemical Society

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

132

SIZE

EXCLUSION

CHROMATOGRAPHY

(GPC)

Ideally one needs on-line detectors for measuring the instantaneous number average molecular weight and weight average molecular weight. Due to the s o l u b i l i t y characteristics of resins 1 ike polyethylene, these detectors must be able to operate at temperatures up to 150°C. Low angle laser light scattering photometry can be used to determine % ( ¥ ) directly at elevated temperatures ( 9 ) . However, high temperature on-1ine viscometers, needed for the indirect measurement of MJ\J(V) from the universal calibration, are not commercially available. Furthermore, the batch type instruments available can not be used with the small elution volumes characteristic of high speed SEC equipment. Therefore, herein is presented a new method for interpreting SEC data which accounts for the instantaneous polydispersity due to LCB within the detector cell and which allows for the c a l culation of LCB content and frequency as a function of the instantaneous number average molecular weight. Hereafter, this method will be referred to as the molecular weight and branching distribution (MWBD) method. Applications of the MWBD method will be highlighted using selected PVAc and high pressure LDPE resins. Development of the MWBD Method As pointed out by Hamielec and Ouano ( 8 ) , the separation of a branched polymer by size in the SEC process results in molecular species of different molecular weights eluting at the same volume. Thus, the molecular weight of these species is not monodispersed and M(V) must be replaced by the instantaneous number average molecular weight when using the universal calibration procedure for branched polymers, ln{[n](V)MN(V)} = A + BV + . . .

(V)

The coefficients A, B, . . . can be determined from f i t t i n g In i [ n ] ( V ) M N ( V ) } as a function of V for 1inear narrow distribution standards for which M (V) = M(V). It is now clear that the molecular weight obtained for branched polymers, when using the universal calibration procedure, is a number average molecular weight and not a weight average molecular weight as has been suggested in the past (5_, 7_, H), 11 ). The choice of My as the proper molecular weight average to couple with the i n t r i n s i c viscosity perhaps evolved from the intuitive feeling that for most polymers the weight average molecular weight is the closest average to the viscosity average molecular weight. Note that for linear polymers Mfl(V) = My(V) = M(V) since the contents of the detector cell are monodispersed. The most direct method for calculating M^(V) across the chromatogram would be to use an on-line viscometer to measure [n](V) and then to calculate M^j(V) from N

7.

FOSTER

ET AL.

MWBD

Method

133

M (V) = exp(A + BV + . . . ) / [ n ] ( V ) .

(2)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

N

U n f o r t u n a t e l y , an o n - l i n e viscometer which can provide i n s t a n t a n ­ eous [η] values at low and high temperatures i s not a v a i l a b l e . Although batch viscometers have been used i n the past ( 1 2 , 1 3 ) the use of high speed S E C makes them useless due to the smaTT e l u t i o n volumes. We, t h e r e f o r e , propose an i n d i r e c t method f o r o b t a i n i n g the v a r i a t i o n of the i n t r i n s i c v i s c o s i t y and number average molecular weight across the chromatogram. F i r s t the i n t r i n s i c v i s c o s i t y molecular weight r e l a t i o n s h i p f o r a polymer with long chain branching ( L C B ) i s assumed to be expressable i n a form s i m i l a r to t h a t used by Ram and M i l t s ( 6 ) , ln(Cn](V)) = InK + alnM (Y) + b ( l n M ( V ) ) N

N

2

(3)

+ c(lnM (V)) . 3

N

Κ and a are the Mark-Houwink constants f o r the l i n e a r homologue in the same solvent and at the same temperature as the S E C measurements. The constants b and c are to be determined. If there i s no L C B below a c e r t a i n molecular weight Μ, , the c i n equation ( 3 ) can be replaced with c = -b/lnM .

(4)

L

The value normally found f o r ( 6 , 1 3 ) .

i s between

M,

5 , 0 0 0

and

10,000

L

Once a value f o r M L i s assumed, t h i s leaves one unknown b which can be determined from the S E C chromatogram and the measured whole polymer i n t r i n s i c v i s c o s i t y i n the f o l l o w i n g manner. First, one estimates a value f o r b, and c a l c u l a t e s M ^ ( V ) and [ n ] ( V ) across the chromatogram using the u n i v e r s a l c a l i b r a t i o n curve and equation ( 3 ) . Then the whole polymer i n t r i n s i c v i s c o s i t y i s obtained from

[η] = jV(V)[n](V)dV,

(5)

where F(V) i s the normalized c o n c e n t r a t i o n d e t e c t o r response. The c a l c u l a t e d [τγ] value i s compared with the measured v a l u e . Further b values are then t r i e d u n t i l the d i f f e r e n c e between the measured and c a l c u l a t e d i n t r i n s i c v i s c o s i t i e s i s minimized. It i s a l s o p o s s i b l e to determine both M L and b i f [η] and M N are known f o r the whole polymer. Having determined b by the above method, the true number average molecular weight and higher moments f o r the whole polymer can be c a l c u l a t e d as f o l l o w s :

134

SIZE

^

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

M

EXCLUSION

N

fF(V)(M (V)) dV/|F(V)M (Y)dV. 2

=

(GPC)

(7)

= fF(V)M (V)dV, z

CHROMATOGRAPHY

N

N

(8)

Note that the weight and Ζ average molecular weights so obtained are only approximate and l e s s than the true v a l u e s . This i s a consequence of the u n i v e r s a l c a l i b r a t i o n method g i v i n g the instantaneous number average molecular weight across the chromatogram. The instantaneous weight average molecular weight My(V) can a l s o be measured by using an o n - l i n e , low angle l a s e r l i g h t scattering device. Such measurements have been performed suc­ c e s s f u l l y both at low temperatures (14, 15) and at high tempera­ tures (9J. When combined with the method presented here f o r determining M^(V), the p o l y d i s p e r s i t y i n the d e t e c t o r c e l l (Mw(V)/M (V)) could be c a l c u l a t e d across the chromatogram. Work on the combination of these two methods w i l l be reported at a l a t e r date. Since our i n d i r e c t method produces both the l i n e a r (b=0) and branched i n t r i n s i c v i s c o s i t i e s across the chromatogram, i t i s p o s s i b l e to estimate several LCB parameters as a f u n c t i o n o f e l u t i o n volume or number average m o l e c u l a r weight. The branch­ ing f a c t o r G(V) can be w r i t t e n as N

G(V) = { [ n ] ( V ) / [ n ] ( V ) } b

1

1 / e l

(9)

where [ n ] ( V ) i s the instantaneous branched i n t r i n s i c v i s c o s i t y , C n l l ( V ) i s the instantaneous 1inear i n t r i n s i c v i s c o s i t y , and the branching s t r u c t u r e f a c t o r ε i s a constant to be determined. For s t a r polymers a value o f ε = 0.5 has been obtained (16, 17) and studies (18) o f model comb polymers i n d i c a t e a value of 1.5. Other work ( 1 9 j has suggested that ε i s near 0.5 at low LCB frequencies. For a random LCB conformation of higher branching frequency an ε value between 0.7 and 1.3 might be expected, i . e . somewhere between a s t a r and a comb c o n f i g u r a t i o n . Zimm and Stockmayer (20) derived a t h e o r e t i c a l r e l a t i o n s h i p between G(V) and the number average number of LCB points per molecule B ( V ) , namely b

N

Therefore by combining equations (9) and (10) and assuming some appropriate value f o r ε , the number average number of LCB points per molecule can be c a l c u l a t e d as a f u n c t i o n of e l u t i o n volume. The corresponding whole polymer number average number of LCB points per molecule i s given by

MWBD

FOSTER ET AL. _ B

N

=

M

135

Method

( F(V)B (V)dV N

N

}

(11)

M (V) N

Another parameter commonly used f o r c h a r a c t e r i z i n g long chain branching i s the number o f branch points ( o r frequency) per 1000 repeat u n i t s . The number average number o f branch points can be c a l c u l a t e d across the chromatogram from x ( v ) = looo Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

(12)

M^m/ry.v)),

N

where M i s the repeat u n i t molecular weight. whole polymer q u a n t i t y i s

The corresponding

R

B. 1000 M D zr N, Ν

(13)

R

In an analogous f a s h i o n , the weight average long chain branching parameters per molecule (By) and per 1000 repeat u n i t s (Xy) can be c a l c u l a t e d . F i r s t B (V) can be determined from the Zimm-Stockmayer equation ( 2 0 ) , W

(2 + B ( V ) )

1

1 / 2

M

G(V) =

Bu(V)

?

_

(B

W

(V))

1

/

2

(2 + B ( V ) )

1 / 2

w

X

+(B (V))

1 / 2

w

- 1

ln{ ((2 + B ( V ) )

1 / 2

W

- (B (V)) W

1 / 2

(14)

'

Then B , X ( V ) , and Ay can be obtained from the f o l l o w i n g expressions : w

w

_ B

_

W

=

M

(F(V)B (V)

N)

W

M (V)

d V

M

(15)

«

X (V) = 1000 M (B (V)/M (V)), W

and

R

M

N

(16)

SIZE

136

EXCLUSION

CHROMATOGRAPHY

(GPC)

It should be noted that In order to calculate the weight average number of LCB points, per 1000 repeat units, one must divide By by M . The use of My here is incorrect. The method outlined above for characterizing branched polymers w i l l hereafter be referred to as the molecular weight and branching distribution (MWBD) method. In the following sec­ tions, its application to the long chain branching in polyvinyl acetate and high pressure low density polyethylene will be demonstrated. N

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

Long Chain Branching in Polyvinyl Acetate Under conditions of low radical i n i t i a t i o n , Graessely (21) has shown that the following set of equations describes the molecular weight and branching development in the bulk polymeri­ zation of vinyl acetate:

dx

c L

M

(18) 1-x

dQ-|

ώΓ dQ2 dx

(19)

= 1,

1 +

kx 1-x

1

+

^ 1-x

+

^ 1-x

(20)

C + -2M 1-x L

(Lx + kQ„ dx

(21)

1-x

where k =

Ρ

Ρ

(22)

In the above equations kf is the transfer to monomer constant, k is the propagation constant, kfn is the transfer to polymer constant, and kp* is the constant for terminal double bond reactions. The quantities Q , Q-|, and Q2 are the zeroeth, f i r s t , and second moments of the molecular weight distribution, respectively. The number average and weight average molecular weights are given simply by m

p

0

(23)

\ - WQi ·

(24)

7.

MWBD

FOSTER ET AL.

Method

137

where M i s the monomer molecular weight. The M M , M , and By values p r e d i c t e d by t h i s k i n e t i c model are p l o t t e d as a f u n c t i o n o f conversion i n F i g u r e 1 . The k i n e ­ t i c parameters used f o r these c a l c u l a t i o n s are CJ^J= 2 . 0 χ 1 0 " * , C = 3 . 0 χ 1 0 " 4 , and k = 1 . 0 ^ Note_that whereas My i s almost independence of c o n v e r s i o n , M and i n c r e a s e r a p i d l y with _ increasing conversion. For conversions o f 50% and 60%, the My, Myy, and By s obtained f o r r e a l i s t i c values of C^, Cp, and k are l i s t e d i n Table I . w

4

P

w

1

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

TABLE I SOLUTION OF KINETIC EQUATIONS FOR LONG CHAIN BRANCHING IN BULK VINYL ACETATE POLYMERIZATION* ÇM(X10 )

Çp(xl0 )

k

2

1.5

0.6

0.54-0.58

1.7-2.2

0.6-0.9

2

2.5

0.6

0.54-0.58

2.1-2.7

0.9-1.2

2

3.0

1.0

0.63-0.71

3.0-4.6

1.3-1.9

2

4.0

1.0

0.63-0.71

3.5-5.4

1.5-2.3

0.63-0.71

3.9-6.2

1.8-2.8

4

2

4

5.0

1.0

\(χΐο-6)

*Values shown are f o r conversions of 50-60%,

B

- N

respectively.

In order to estimate the branching f a c t o r ε f o r p o l y v i n y l acetate we have analyzed the S E C data obtained on sample PVAc-E4 using the MWBD method with v a r i o u s ε v a l u e s . This sample was synthesized under k i n e t i c a l l y c o n t r o l l e d c o n d i t i o n s ( i s o t h e r m a l , Τ = 6 0 ° C , [AIBN] = 1 0 " g - m o l e / 1 , conversion l e v e l o f 4 8 . 5 percent). The S E C measurements were made at 2 5 ° C i n t e t r a h y d r o furan. The Mark-Houwink c o e f f i c i e n t s used f o r l i n e a r p o l y v i n y l acetate are those suggested by Graessley ( 2 1 ) , namely Κ =_5.1 χ 1 0 " dl/gm and a = 0 . 7 9 1 . The whole polymer M^, M , and B^ values obtained are l i s t e d in Table I I . The number average number of branch points per molecule decreases with i n c r e a s i n g ε and the molecular weights are independent of ε . The weight average molecular weight c a l c u l a ­ ted by the MWBD method i s s l i g h t l y l e s s than the value of 1 . 6 χ 1 0 obtained by l i g h t s c a t t e r i n g . This i s c o n s i s t e n t with the f a c t t h a t t h i s method uses a number average molecular weight i n the averaging process. The number average molecular weight obtained i s c l o s e to that p r e d i c t e d by the k i n e t i c model_ with C ^ = 2 . 0 χ 1 0 " , k = 0 . 6 and a conversion of 50%. The By value of 1.1 f o r ε = 1 . 0 i s in the range i n d i c a t e d by the second set of k i n e t i c parameters l i s t e d i n Table I. Thus i t i s f e l t that 5

5

w

6

4

138

SIZE

EXCLUSION

C H R O M A T O G R A P H Y (GPC)

the MWBD method with ε = 1.0 gives good agreement with kinetic predictions and with the weight average molecular weight obtain­ ed by 1ight scattering. TABLE II EFFECT OF EPSILON ON B OF WHOLE POLYMERSAMPLE PVAC-E4 N

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

Epsilon

6

M^xlO )

yxio" )

-6

0.5

2.5

0.51

1.37

0.8

1.4

0.51

1.37

1.0

1.1

0.51

1.37

1.2

0.34

0.51

1.37

We have used the MWBD method with ε = 1.0 to analyze the branching in two commercial PVAc standards supplied by the Aldrich Chemical Company, PVAc - Lot 1 and PVAc - Lot 3. A cut­ off molecular weight of 5,000 was used in the analysis. The whole polymer M , N^, B M , and values obtained are given in Table III. The calculated molecular weight averages are in rea­ sonable agreement with those quoted by the manufacturer. The number average number of LCB points per molecule and per 1000 repeat units are greater for Lot 1 than Lot 3. However, for both these samples, the branching parameters are less than 1.0. N

TABLE III MWBD RESULTS FOR CÛW1ERCÏAL PVAc STANDARDS DISTRIBUTED BY ALDRICH CHEMICAL COMPANY* PVAc - Lot 1 6

PVAc - L o t 2 6

M = 0.092 χ Ί 0 (0.083 χ 1 0 ) N

= 0.300 χ 10 B λ

6

6

(0.331 χ 10 )

+

6

6

6

6

M^ = 0.146 χ 10 (0.103 χ 10 ) M = 0.626 χ 10 (0.840 χ 10 ) w

N

= 0.783

B = 0.601

Μ

= 0.748

% = 0.354

N

H

*Values obtained using M^ = 5,000 and ε = 1.0. +Values in parenthesis are those quoted by the manufacturer.

7.

FOSTER ET AL.

M W B D

139

M e t h o d

For one of the samples, PVAc - Lot 1, the number average molecular weight d i s t r i b u t i o n i s p l o t t e d i n Figure 2. Also shown i s the instantaneous number average number o f LCB points per molecule, p l o t t e d as a f u n c t i o n o f number average molecular weight. Note that By(V) increased r a p i d l y with i n c r e a s i n g num­ ber average molecular weight. The molecular weight and branch­ ing d i s t r i b u t i o n o f PVAc - Lot 3 i s s i m i l a r to Lot 1 and thus not shown.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

A p p l i c a t i o n o f the MWBD Method to LDPE In order to determine the branching s t r u c t u r e f a c t o r ε , Foster (22) s t u d i e d a l a r g e group of high pressure low d e n s i t y polyethylene r e s i n s (HP-LDPE). Using the MWBD method, he c a l ­ culated the whole polymer number average number o f branch points per J000 carbon atoms from SEC data as a f u n c t i o n o f ε . Then the Ay values were compared with those obtained by ^ C NMR. Best agreement was found f o r ε = 0 . 7 5 . An example of t h i s method of determining ε i s shown i n Figure 3 where the λ has been c a l c u l a t e d as a f u n c t i o n o f ε f o r three HP-LDPE r e s i n s , designated LDPE A, B, and C. LDPE A was produced at the highest conversion and LDPE C a t the lowest c o n v e r s i o n . The SEC data used were obtained at 140°C i n 1 , 2 , 4 trichlorobenzene. The Mark-Houwink c o e f f i c i e n t s used f o r 1inear polyethylene were Κ = 5.1 χ 1 0 - dl/gm and a = 0.706. The 13c NMR Ay values are indicated_by open t r i a n g l e s . The whole polymer My, N^, By, and Ay values obtained using the MWBD method and ε = 0.75 f o r these three LDPE r e s i n s are shown i n Table IV. The molecular weights and branching para­ meters are i n agreement with expectations based on the l e v e l s of conversion^ With_increasing conversion My remains constant whereas M^, By, and Ay i n c r e a s e . 3

Ν

4

TABLE IV MWBD RESULTS FOR COMMERCIAL HIGH PRESSURE LDPE SUPPLIED BY UNION CARBIDE CORPORATION*

LDPE

M^xlO" )

A

15.6

Β

15.6

C

19.6

3

•Values obtained using

yxio

- 3

)

h

*N

243

5.05

4.52

116

2.89

2.60

2.44

1.75

83.9 = 2,000;

ε = 0.75

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

140

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

whole polymer

0 . 3

0 . 4

Conversion

F i g u r e m e n t

I. in

S o l u t i o n h u l k

c o n v e r s i o n .

V A c

of

kinetic

é q u a t i o n s

p o l y m e r i z a t i o n .

M o d e l

predictions:

for

M ,

M

N

C

M

=

w

2.0

m o l e c u l a r

,

a n d X

IOGIO M N

F i g u r e p o i n t s (M

N

2. per =

M o l e c u l a r m o l e c u l e ^ 9 0 2 0 0 ;

M

weight ( B

w

s

=

)

as

distribution a

f u n c t i o n

3 0 0 2 0 0 ;

W

N

4

weight

are

s

; C

=

P

a n d

plotted 3.0

L C B

as

a 4

X

10~ ;

d e v e l o p -

f u n c t i o n K==

of

1.0.

(V)

a n d of

W /M

1 0

B

n u m b e r

M (V) =

a v e r a g e

for

N

3.33;

W

P V A c N

=

n u m b e r S a m p l e

0.78;

~

N

of A ,

=

L C B L o t 0.75)

1

7. FOSTER ET AL.

M W B D

141

M e t h o d

The number average molecular weight d i s t r i b u t i o n and LCB frequency A ( V ) are p l o t t e d i n Figures 4 and 5 f o r the highest and lowest conversion r e s i n s . Not only are the molecular weight d i s t r i b u t i o n s q u i t e d i f f e r e n t , but a l s o the LCB d i s t r i b u t i o n are r a d i c a l l y d i f f e r e n t . J F o £ LDPE A the molecular weight d i s ­ t r i b u t i o n i s very broad (Ν^/Μ = 15.5) and λ ( Υ ) increases to about 5 . 0 , remains constant up to about a number average molecu­ l a r weight οf 1_ χ 1 0 , and then r a p i d l y i n c r e a s e s . In c o n t r a s t f o r LDPE C Ν^/Μ = 4.3 and the LCB frequency q u i c k l y increases to a maximum of about 2.3 a t M (V) = 9,000 and then slowly decreases. Some of the p r o p e r t i e s of these three r e s i n s are l i s t e d i n Table V. The agreement between c a l c u l a t e d from the MWBD method with ε = 0.75 and from 13c NMR i s e x c e l l e n t . Long chain branching frequency i s found to c o r r e l a t e well with blown f i l m properties. Increasing LCB, f o r r e s i n s with s i m i l a r d e n s i t i e s , leads to increased haze, decreased g l o s s , and decreased t e a r strength. As i n d i c a t e d by the d i e swel1, melt e l a s t i c i t y increases with i n c r e a s i n g LCB. A more d e t a i l e d d i s c u s s i o n o f the c o r r e l a t i o n of LDPE p h y s i c a l p r o p e r t i e s with the long chain branching frequency can be found elsewhere (22). The MWBD method was a l s o used to determine the long chain branching in the_National Bureau of Standards LDPE SRM #1476. The M M , M , and values c a l c u l a t e d using ε = 0.75 are given in Table V I . Included f o r comparison are the r e s u l t s obtained by Wagner and McCrackin (23) from summing well c h a r a c t e r i z e d f r a c t i o n s o f 1476 and by MacRury and McConnell (9) from coupling a low a n g l e j l a s e r l_ight s c a t t e r i n g photometer to a GPC (LALLSP/ GPC). The M ^ and c a l c u l a t e d from MWBD are in good agreement with those determined by the summing of f r a c t i o n s . The M^ value i s too low as expected. The M value c a l c u l a t e d using LALLSP/ GPC i s too high because an instantaneous weight average molecular weight i s used in the averaging. E x c e l l e n t agreement i s found between the Ά . determined by LALLSP/GPC and that c a l c u l a t e d by the summing of f r a c t i o n s . Thus, as was mentioned e a r l i e r i n t h i s paper, the MWBD method combined with the LALLSP/GPC y i e l d s the c o r r e c t number average and weight average molecular weights across the chromatogram and f o r the whole polymer. The LCB frequency obtained by MWBD i s p l o t t e d i n Figure 6 as a f u n c t i o n of_ number average molecular weight. The open t r i ­ angles are the AN values c a l c u l a t e d by Wagner and McCrackin f o r various f r a c t i o n s . A g a i n , good agreement i s found between the two methods. N

Ν

Ν

6

Ν

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

N

w

N

142

SIZE

15

EXCLUSION

CHROMATOGRAPHY (GPC)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

R

0.5

1.0

15

BRANCHING CONFORMATION ,EPSILON,€

F i g u r e

3.

calculated

Effect for

of

three

the L D P E

b r a n c h i n g resins

structure

u s i n g the by

1

3

C

factor

M W B D N M R )

(t)

o n

m e t h o d

the

L C B

((A)XN

frequency values

(λ ) Ν

o b t a i n e d

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

FOSTER ET AL.

F i g u r e

4.

M

for

N

( V )

M W B D

M o l e c u l a r L D P E

A

weight

(M

N

=

143

M e t h o d

distribution

1 5 6 0 0 ;

M

w

=

a n d

L C B

2 4 3 1 0 0 ;

Xv = 4.52)

frequency M

W

/ M

N

=

as 15.5;

a

function %

=

of 5.05;

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch007

144

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

ιοο,ο*ι {ν) Ν

F i g u r e

5.

M

for

N

( V )

M o l e c u l a r ^weight L D P E

C

( M

=

N

distribution

1 9 6 0 0 ;

M

]

λ. — ν

a n d

=

V

L C B

8 3 9 0 0 ;

M

frequency W

/ M

N

=

as

a

4.29;

function B

N

—

of

2.44;

L 7 5 )

MOLECULAR WEIGHT

F i g u r e using

6. the

C o m p a r i s o n M W B D

of

the

method_(( ((A)

L C B )

λ

Ν

=

1.05

λ*

frequency =

1.47)

( W a g n e r

obtained with

a n d

that

for

N B S

obtained

M c C r a c k i n ) )

by

SRM

# 1 4 7 6

fractionation

85

Gloss 53

% 19 125 200

122 156

6.6 4.8

0.796 0.825 0.925

0.919

0.921

0.923

72

48

39

1.8

2.6

2.1

A

Β

C

Materials

LDPE

Tear Strength, 31000

χ 10

-4

.406

1.04 χ 10

Provder, T., Woodbrey, J.C., C l a r k , J . H . , ACS Sympos i um on GPC, ACS, Houston, Texas February, 1970

.697

> 0.03 lu?

F i g u r e

1.

M e a n

height

values

v a l u e as a

of

c h r o m a t o g r a m s

percent

of

m e a n

vs.

of

P M M A

retention

a n d

v o l u m e

9 5 %

confidence

BALKE AND PATEL

H i g h - C o n v e r s i o n

P o l y m e r i z a t i o n

K i n e t i c

M o d e l i n g

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

8.

F i g u r e used;

2. (àk)

C a l i b r a t i o n f r o m

c u r v e

universal

for

P M M A ,

calibration of

RH

curve;

P M M A

C o l u m n (•,

O)

C o d e f r o m

standard))

25

((

Weiss

) m e t h o d

p o l y n o m i a l (1.88

m g

155

SIZE EXCLUSION C H R O M A T O G R A P H Y ( G P C )

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

156

F i g u r e used; R H

3. (A)

P M M A

C a l i b r a t i o n from

curve

universal

standard);

( O

for

P M M A ,

calibration f r o m

curve;

Weiss

C o l u m n (Oi

M e t h o d

C o d e

from (5.33

28

Weiss m g

of

((

)

M e t h o d

R H

P M M A

p o l y n o m i a l (3.55

m g

of

standard))

BALKE AND

-,

PATEL

H i g h - C o n v e r s i o n

-τ— ι ι ι ι Μ !

P o l y m e r i z a t i o n

Γ~—I I—ΓΤΤΤΤΤ

1

K i n e t i c

Γ~Τ—I I ! I Π

157

M o d e l i n g

' 1

M i l l

1 1

Φ

s 2.0

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

8

Ο

A i

a

Ο

|

|

ι

ι i m

—5"

a Ù j

ι

ι

ι

11111

ι

ι

ι

ι ι i.,.n.i._ I0

ι

ι

ι

ι

ι

ι

ι

ι 111

5

Mn (t) F i g u r e C o d e 27:

4.

25:

(a)

G P C (\, 1-77

a n d

)

1.8

absolute (A)

m g ;

m g ;

(&)

1.81

M

.8

c o m p a r i s o n

n

m g ; (BJ

mg;

(0)3.55

-i

r

T

—

Γ

-

Γ

Τ

Γ

Τ

Γ

- -

y

C o l u m n

γ

3.55

mg;

mg; (Q)

j

j

τ

T

τ

(polystyrene

C o d e

Γ

Τ

26:

(Q)

ι

standards) 1.8

3.99

5.33

- -

(Q)

m g ;

mg;

( C o l u m n

C o l u m n

C o l u m n

C o d e

C o d e

28:

mg)

-

τ

Γ

η

τ τ η—

~ τ~

τ

ΓΤΙΤΤΤ

Φ

1.5

1

m

$

1

g

1.0

g—^t-Q-j

g

ok

s-

§ α 0 I

I

i

I I I 1i I

I

L J - J - 1 J _ L U _

I

I

1 i I I 1H

I

1

I

M

I II

Mw (t)

F i g u r e

5.

G P C

a n d

absolute

M w

c o m p a r i s o n 4

for

(polystyrene

symbols)

standards)

(see

F i g u r e

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

158

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

F i g u r e

6.

heights: using

Effect

M e t h o d 0.2

F i g u r e

of

s y m m e t r i c a l

experimental

7.

2

a n d

with h

=

axial

c h r o m a t o g r a m

dispersion

(——);

s m o o t h i n g :

(

=

0.3;

0.1

oscillations

due

s h o w e d

E x p e r i m e n t a l

C o d e

25;

)

h

c h r o m a t o g r a m s

(-

-

-)

C o d e

correction

o n

c h r o m a t o g r a m s

using

27;

(-

(· to

·

·)

h

=

n u m e r i c a l

different

(W 0.4.

(y)) V a l u e s

obtained of

h=

instabilities.

c o l u m n

) C o d e

c h r o m a t o g r a m N

28)

c o d e s

((

)

8.

BALKE AND PATEL

H i g h - C o n v e r s i o n

P o l y m e r i z a t i o n

K i n e t i c

M o d e l i n g

159

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

molecular weight averages being weighted integrals over the whole curve, are strongly affected. This situation leads to conclusions in the GPC literature that axial dispersion should be corrected for if molecular weight averages disagree with absolute values. However, in polymerization kinetic modeling a very viable option is to model using chromatogram heights. Molecular weight averages, if needed for other purposes, can be obtained from the kinetic model later. C. Chromatogram Interpretation. Tables III and IV show the distinction between using averages and heights of GPC in kinetic modeling. The advantages of utilizing the individual heights are: 1. The need for axial dispersion correction is minimized for broad distributions. 2. Heights from specific areas of the chromatogram can be chosen to maximize reproducibility or to emphasize one range of molecular weights. 3. The change in concentration with time of a given molecular weight can be estimated and used to provide a guide as to choice of model or an approximate estimate of parameters. As previously mentioned, the results of this approach in the polymerization of PMMA have already been published (8) and tested (e.g. (9)). Also, a few workers have recently begun to recognize some of the value of utilizing chromatogram heights

(15* Μ)·

From the axial dispersion viewpoint alone there is no doubt that the experimental reduction of dispersion or its correction would be preferable to assuming it negligible. Either of these options require a simple method for the assessment of axial dispersion which does not depend upon absolute molecular weight averages or assumption of distribution functions (5, 6). Such a method will be shown in Section 3 of this report However, first the problem of copolymer analysis which led to this method as a by­ product will be examined. 3. High Conversion Copolymerization of Styrene η-Butyl Methacrylate. The copolymer analysis problem becomes increasingly more difficult as we progress from conversion and average property determination to property distribution determination. Also, copolymer composition information appears easiest to obtain as opposed to sequence length and molecular weight information which are much more elusive. However, as will be seen in the following sections, conventional GPC analysis of copolymers is fundamentally unsatisfactory because the GPC fractionation accomplishes a molecular size separation and not afractionationuniquely related to any one of the property distributions. In fact, there is considerable ambiguity in what is considered a copolymer composition distribution. In G P C analysis the nature of the fractionation leads to calculation of average copolymer composition at each retention time (W^(V)) as a function of retention time. However, in polymerization kinetics we require the weight fraction of copolymer as a function of the instantaneous copolymer composition (Wj) produced at any reaction time. The first section below deals with the problem of obtaining the concentrations of the individual monomers (styrene and η-butyl methacrylate) and of the copolymer at any reaction time. This is the information required for conversion (X) and overall average composition (Wj). Kinetic modelling focusses on the prediction of conversion versus concentration of unreacted styrene (wj). In the second section, the usual dual detector, analysis is shown to provide a relationship for the area ratios of the dual detector chromatograms versus W^. Through ratios of area segments on each chromatogram the average composition at each retention time can be calculated (W^(V)). The limitations of this approach are discussed and lead to the orthogonal coupling of GPCs. A. Conversion and Average Property Determination for Copolymers. Figure 8 shows chromatogram obtained on the GPC#1 with Column Code A l (Table I). Using new

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

160

TABLE

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

GPC

AND

MOLECULAR

Q

(It

KINETIC WEIGHT

MODEL AVERAGES

K-1

where Κ = 1 f o r M η

= 2 for

M

w

= 3 for

GPC

M

z

MODEL

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

8.

BALKE AND PATEL

High-Conversion

P o l y m e r i z a t i o n

K i n e t i c

Modeling

161

162

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

800 700 830 500

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

F(t)

400 300 200

24

27

30

33

36

39

42

45

48

51

54

t(min.)

F i g u r e mediate

8.

Typical

polystyrene

η-butyl methacrylate

conversions) s h o w i n g m o n o m e r

p e a k s

by

G P C

at

times

c h r o m a t o g r a m 46.2

a n d

(low

49.2

m i n

to

inter­

resolved

®4 0

193

197

©478

475

(5)

^580

F i g u r e

H

P L C

identification:

(1,2,

and

9.

5)

represent

analysis a n d MM A

3) a n d

of

a

m o n o m e r .fraction

represent styrene

MM A , at

2 5 4

styrene, n m ;

(6)

s h o w i n g a n d are

retention

n - B M A THF

at

2 0 0

impurity

times nm; p e a k s

a n d (4

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

8.

BALKE AND PATEL

High-Conversion

P o l y m e r i z a t i o n

K i n e t i c

M o d e l i n g

163

high resolution columns the monomer peaks could be clearly separated from the polymer. There are several examples in the literature of GPC now being utilized for small molecule analysis (17). However, in this case, attempts to obtain monomer concentrations for kinetic modelling were frustrated by irreproducible impurity peak interference with monomer peaks, time varying refractometer responses and insufficient resolution for utilization of a reference peak. This last point meant that injected concentration would have to be extremely reproducible. Alternate ways of obtaining the data were considered. G C appears most promising (18). However, entrapment of monomer, polymer degradation and column degradation for high conversion were evident problem areas. Instead, the idea of Coupled-Column Chromatography was employed (19). Here, this means the manual collection of fractions from one chromatograph and their reinjection into another. Collection of G P C fractions and their analysis by other instruments or re-injection has often been utilized qualitatively in GPC . However, precise quantitative analysis is much less often reported (6). Figure 9 shows the result of injecting 10 μΐ of the total low molecular weight fraction from GPC #1 (Column Code A2) into GPC #2 (Column Code Bl). With this column code, GPC #2 is performing as a High Performance Liquid Chromatograph (HPLC). Separation is based upon solubility (i.e. composition differences) rather than upon molecular size. Methyl methacrylate monomer was used as a reference and added to the solution injected into GPC #1. Concentrations of η-butyl methacrylate, styrene and conversion are readily calculated from the peak areas and initial concentrations. Results are shown in Figures 10 and 11. HPLC is well known as a reproducible and accurate technique for composition measurement From the point of view of kinetic model development however, the following points deserve emphasis. 1. Data points fall in Figure 11 fall between predictions using the two reactivity ratio values quoted by Gruber and Knell (10) in classical kinetics. 2. Very similar variations in average copolymer composition with conversion have recently been observed in the styrene methyl methacrylate system by both Johnson et al (20) and by Dionisio and O'Driscoll (21). The reason for the variation may be due to a viscosity effect on propagation rate constants (20). 3. Fractionation by GPC was assessed by changing injected concentrations and by GPC analysis of polymer before and after fractionation. Efficiency of fractionation of polymer from monomer did not appear to be a source of error. In fact, an advantage of this method over others is that the separation of monomer from the polymer can be clearly monitored and controlled. 4. Total error variance may not be constant with conversion: At 30% conversion a replicate analysis showed that composition could be determined with ±_ 1.4% reproducibility (standard deviation as a % of mean) and conversion with + 2.1%. A duplicate at 52% conversion showed a relative error (difference/mean) of 1.7% and 2.7% respectively. Between 30 and 80% conversion, although no gel effect is evident in the data the polymer/monomer mixture becomes sticky and difficult to handle. Somewhat beyond 80% conversion the η-butyl methacrylate content for these compositions becomes too small to be detected with the procedure developed. Additional optimization of concentration injected and detector utilized is required for very high conversions. B. Measurement of Property Distributions for Copolymers. Figure 12 shows chromatograms of typical products in the copolymerization study (Column Code B2). Since the detector is responding to concentration, composition, and perhaps sequence length, the direct single detector interpretation as described for PMMA is not immediately applicable here. Tacticity variation is yet another consideration but is assumed of second order importance for these samples (22).

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

Figure 11. Conversion vs. weight fraction styrene in monomer, styrene n-butyl methacrylate (samples as for Figure 10) (( ) r, — 0.68, x = 0.45; ( ) = 0.56, r = 0.40) t

T i

f

8.

BALKE AND PATEL

High-Conversion

Polymerization

Kinetic Modeling

165

Interpretation of copolymer chromatograms in the literature does not include axial dispersion correction (3, 6) and little is known regarding it (5). The usual approach® is to utilize dual detectors and to assume that both detectors respond to, at most, both composition and concentration. The two chromatograms then provide two equations in these two unknowns at each retention time. In our case, detector one ( λ = 254 nm) responds only to component one. Therefore, considering a chromatogram slice dt as representing hydrodynamic volumes dV:

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

K

V

d

l,254 ^lOO g( >

V

F

=

l «

d

t

(»

254 is the response constant for component 1 on detector 1 chromatogram from detector 1 average weight fraction of monomer 1 (styrene) in copolymer contained in chromatogram slice t = time g(V)dV = weight of copolymer at V to V + dV

where Fi(t) W|(V)

= =

For detector 2 ( λ = 235 nm) the response is assumed to be a linear combination of the weight fraction of each component in the copolymer. That is: (K

1 2 3 5

W

(V) + K

x

2 e 2 3 5

W (V)) g(V) dV = F (t)dt 2

2

(2)

Integrating each equation over all volumes and times: Κ

1·254 W i = 2 5 4 g A

Kl.235 W i + K

2

2

(3)

3

5

W

2

J ^ 5 _

=

g

where W

W 1

=

(4)

w

10-(1-X) l X

w = ι.-Wi 2

g

=

total weight of copolymer

Usually (e.g. 4, 23) the ratio equivalent to A254/A235 is plotted versus as shown in Figure 13. However, a plot of A235/A254 versus (1/Wj) is also useful. From Equation (3) and (4) the deviation from the straight line derived from the pure homopolymers can then be used to reveal their adequacy of homopolymers for composition calibration and the presence of other variables. Figure 14 shows such a plot. The detector response ratto is elevated with respect to the homopolymer line but very near parallel to it less than = 0.74,or number average styrene sequence lengths less than 4. In this case these particular homopolymer standards could not be used alone for the copolymer calibration. Judging from the literature, styrene sequence length is likely responsible for the deviation QO, 24). If so, then this area ratio as an indicator of sequence length is most sensitive a b o v ë w γ = 0.74. Below this value the change of

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

0.70

0.56

0.42

F (0 Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

N

F i g u r e

12.

c o r r e s p o n d

0.28

h

0.14

h

N o r m a l i z e d to

s a m e

samples curves.

in

G P C

c h r o m a t o g r a m s

T a b l e

V.

S a m p l i n g

U V

t i m e (t ) 8

f r o m

detectors s h o w n

at

references

C o l u m n 2 5 4

a n d

C o d e 2 3 5

n m

C o l u m n C o d e

B 2 .

Letters

p r o v i d e

the

A 3 .

3.0

F i g u r e

13.

A r e a

ratio

f r o m

detectors

vs.

(weight

average fraction)

styrene

c o m p o s i t i o n

in

p o l y m e r

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

8.

BALKE

AND PATEL

High-Conversion

Polymerization

Kinetic Modeling

167

A235 with respect to A254 nearly conforms to that expected from homopolymer mixtures. Using equations (1-4) and Figure (13) the ratio of compositions across the chromatogram can now be obtained from the ratio of the chromatogram heights (i.e. ratios of area segments Fj(t)dt/F2(t)dt). It was observed that the normalized chromatograms (Fj^(t)) for detector 1 shown in Figure 12 were superimposable on those for detector 2. Therefore, when the plot shown in Figure 14 is linear over the range of compositions involved in the sample, then (according to equations (1-4) ) the composition of the sample is the same at each retention volume. If the variation with retention volume is negligible the copolymer can then possibly be treated as is a homopolymer in G PC interpretation. In particular, intrinsic viscosity measurements could then lead to estimates of molecular weight via the universal calibration curve. However, the high conversion chromatogram was superimposable despite that a definite shift of molecular weights to the higher values was observed during the polymerization (Figure 12). Also, the area ratio obtained by experimentally examining only a high molecular weight fraction of the high conversion sample indicated that it was significantly richer in styrene than lower molecular weight fractions. It is evident that the deviation from the linear plot observed in Figure 14 can conceal a composition variation if not somehow taken into account. Furthermore, in the more general case we are concerned with a variation of composition and sequence length distribution not only as a function of retention volume but within each chromatogram area segment (or "slice") at each retention volume. A significant polydispcrsity of one of these properties within a chromatogram slice can easily invalidate the polymer analysis described above. New and multiple detectors are part of the solution to this problem. However, according to the most recent published developments in this area (25,26), alone they have not been able to provide an answer. As will be seen in the following sections, obtaining the desired fractionation by GPC, before multiple detection, offers hope of a general solution. 4. Cross Fractionation by Orthogonal Chromatography. The fundamental limitation of conventional GPC analysis of copolymers is that GPC does not fractionate with respect to any one of the property distributions but rather with respect to molecular size-a characteristic potentially common to all of them simultaneously. In the first of the following sections several previously published major advances related to the problem are associated to synthesize a new approach involving the orthogonal coupling of one GPC to another. This approach is then developed in the second section by first presenting the raw output of the second G P C for different copolymers and then comparing this output to: a. composition and sequence distribution expected on the basis of polymerization kinetics and b. sources of error. In the final section a practical procedure for applying the method is presented along with some initial results(27). A. Synthesis of the Method. A vast amount of literature is pertinent. following major developments were of particular relevance:

The

i. Cross Fractionation. In the literature this refers to a solvent fractionation first with respect to molecular weight and then with respect to composition (6, 28, 29). Here it refers to fractionating first with respect to hydrodynamic volume and then with respect to "non-homopolymer character".

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

168

SIZE EXCLUSION C H R O M A T O G R A P H Y

(GPC)

0.2 h

I

J

2

3

I

4

»

5

(w,)-» Figure 14.

Area ratios plotted to compare with homopolymer calibration

GPC No. 2

1. Threeway valve 2. Injecttonvalve 3. Off/On valve 4. Mixing valve

Figure 15.

GPC No.1

5. Pump 6. UV Detector 7. GPC Columns 8. Rl Detector

Cross fractionation b y orthogonal chromatography: arrangement of GPCs

8.

BALKE

AND PATEL

High-Conversion Polymerization

Kinetic Modeling 169

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

ii. Coupled-Column Chromatography. In the previous section, this referred to the manual collection and analysis of fractions. Here it refers to the actual physical coupling of one GPC to another. It, thus provides a means for obtaining nearly monodisperse slices of chromatogram for analysis by the second chromatograph. The method has been used in a G P C / H P L C mode and not yet successfully with polymers Q9). Here we propose to use it in a G P C / G P C mode and suggest that a general term more descriptive of it is "Orthogonal Chromatography". The use of "steric exclusion" columns in the second instrument provide columns with a stationary phase accessible to polymers, iii. The Universal Calibration Concept With T H F as solvent and silica columns (GPC #1) the G P C is expected to separate the polymer molecules according to hydrodynamic volume (6). With use of a THF/n-Heptane mixture for example, in G P C #2 the hydrodynamic volume of polymer molecules rich in one monomer component can be much more affected than those rich in the other. Steric exclusion separation can then distinguish compsitional differences. iv. Partition and Adsorption Mechanisms in GPC #2. Steric exclusion columns are now known to behave as reverse phase partition columns with suitable solvents in small molecule analysis (30). In analysis of polymers by GPC such non-steric exclusion mechanisms as partition and adsorbtion have been considered undesirable because they cause exceptions to universal calibration. Investigations of such exceptions provide clues as to what solvents can be chosen to enhance a composition or sequence length separation in GPC #2 (31, 32) utilizing these mechanisms. v. Copolymerization Kinetics. Classical copolymerization kinetics commonly provides equations for instantaneous property distributions (e.g. sequence length) and sometimes for accumulated instantaneous (i.e. for high conversion samples) as well (e.g. copolymer composition). These can serve as the basis upon which to derive equations which would reflect detector response for a GPC separation based upon properties other than molecular weight. These distributions can then serve as calibration standards analagous to the use of molecular weight standards. Thus, the strategy underlying this approach is as follows: (a) The solvent in GPC #2 is chosen so as to favour one monomer component (e.g. nbutyl methacrylate) over the other (e.g. styrene). (b) Polymer molecules in the slice taken from GPC #1 will, therefore, be all of the same hydrodynamic volume in pure T H F but in the solvent of GPC #2 they will have different hydrodynamic volume and perhaps different partition/adsorbtion characteristics as well. (c) The chromatogram of GPC #2 should, therefore, reflect heterogeneity in the slice examined and we can attempt to find the separation mechanism and calibrate for the heterogeneity. Figure 15 shows a schematic of the arrangement of the GPCs. Flow from G P C #1 bypassed all columns while awaiting analysis by GPC #2. B. Development of the Method. Figure 16 shows normalized chromatograms for various copolymers from GPC #2 with 57% η-heptane in T H F as its mobile phase. In beginning the development of this technique, two major aspects are important: (i) Variation in Molecular Properties Expected Within a Chromatogram Slice and (ii) Sources of Error in Analyzing for These Properties. These are discussed in turn below. (i) Variation of Molecular Properties According to Polymerization Kinetics

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

170

SIZE

EXCLUSION

CHROMATOGRAPHY (GPC)

t (rninj F i g u r e

16.

g r a m s

o n

G P C # 2 G P C

# 1

c h r o m a t o g r a m s

(letters

c o r r e s p o n d ( +

obtained to

by

s a m p l i n g

s a m p l e s

in

c o p o l y m e r

T a b l e

V

—

(

φ

c h r o m a t o )A ;

( 0 )

) C ; ( 0 ) D ; ( m ) E )

60

50 h

©

40 dX X dW, F

30 h

®

I®

20 h

Ν

10 h Ι

I' ' I ι ι ιI ιιι ι I 1 l i l l l l l 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

ι ι ι I ι ι ' i ι ι

0.10

W.

Figure

17.

T h e o r e t i c a l 0.56,

r

t

=

n o r m a l i z e d

0.40;

letters

c o p o l y m e r c o r r e s p o n d

c o m p o s i t i o n to

sample

distributions

in T a b l e

V)

(ft

B ;

8.

BALKE

High-Conversion

AND PATEL

P o l y m e r i z a t i o n

K i n e t i c

171

M o d e l i n g

(a) Copolymer Composition Distribution Due to Relative Rates of Monomer Consumption. Figure 17 shows that the differential copolymer composition distributions from the classical kinetic model are in the same order as the chromatograms of Figure 16. The normalized differential form shown here can be derived from the cumulative distribution utilized by Hamielec (1):

GOV!) XF

(5)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

where G(Wj)

= cumulative copolymer composition = weight fraction of styrene in the copolymer = final conversion = present conversion

Xp X

by differentiation: dX J

| d G ( W ) | = \l_ 1

dW

X

x

F

The expression of dX

(6)

άΨ

ι

is obtainable from the literature (33).

The distributions are very narrow. This is in accordance with similar theoretical results by Stejskal and Kratochvil (34). (b) Copolymer Composition Distribution Due to Instantaneous Statistical Fluctuations. Stockmayer (35) derived a form for the distribution of copolymer composition from chain to chain caused by statistical fluctuations over an instant of time. For a molecular weight of 1.2 χ 10^ the standard deviation of the Gaussian distribution of compositions expected (36, 34) is 1 χ 10"^. Only for the near azeotropic composition and perhaps for the very high conversion samples where a large shift in Mn occurred would this contribution be significant. All the chromatograms of Figure 16 can be fit by a Gaussian shape (Table V). (c) Sequence Distribution. Figure 18 shows weight sequence distribution for various copolymer samples. The order of increasing sequence length corresponds to the order of the chromatograms in Figure 16. These distributions are obtained by using Harwood's expression for the sequence distribution (37) and accumulating the result with respect to the contribution at each conversion. That is, using the weight distribution function n-1 A

W

1

= . na (1

+a )

where, for any incremental time: Αψι

=

weight of monomer 1 sequences of length η total weight of all monomer 1 sequences

(7)

172

SIZE

fï

=

M|

EXCLUSION

CHROMATOGRAPHY

(GPC)

M /(M -hM ) 1

1

= moles//

2

of monomer 1 in the reaction mixture

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

This can be accumulated in a similar manner to that of instantaneous molecular weight distributions (11, 8):

(8) x

l,f

0

where Χ = ( c χ

10

- c^/c^

C j = gms of styrene in unreacted monomer (c = initial value) Q

X}f

= X^ calculated at final

The number and weight average sequence lengths accumulated with conversion are calculated from:

(9) n

n,l

X

l,f

0

where (38): n

n,l = « +

1

and

(10)

where (38):

= 2a + l

BALKE

AND PATEL

H i g h - C o n v e r s i o n

LA O

m

t*\

\D

_3-

tA

- Ν CO

— Ο « ui CL :

to ο
Λ 4 — oo m co » ·— «Λ — —

174

SIZE

E X C L U S I O N CHROMATOGRAPHY ( G P C )

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

0.75

F i g u r e

18.

Theoretical

T a b l e

V

(ïï„

t

l

weight

W ,

t

s e q u e n c e

a n d

wj

W

W t 1

/n"

distributions are

n t l

( E q u a t i o n

s h o w n

beside

8)

for

each

s a m p l e s

of

curve)

t (min) [ G P O | ] 30 31 32 3334 35 36 37 38 39 40 41 K) F

1 1 I I I

7

I0 l

1

3

300

F i g u r e

1

19.

U n i v e r s a l

i

s a m p l i n g

n a r r o w

in

THF

T a b l e

(B4, THF

o b t a i n e d

(B5, by

calibration

v o l u m e

η - h e p t a n e

in

i

I

1

I

I

I

I

I

320 340 360 380 400 420 440 460 480 500 520 t (sec) [GPC *2]

h y d r o d y n a m i c by

1

I I 1 I -ι 1

I

THF

in

T a b l e

obtained

T a b l e s a m p l i n g

I)

T

H

F

for

) :

direct as

in

into

3

G P C

as

in

#1

1

0.375 2)

a n d

THF

(5) a n d

G P C

(B3,

( A 3 ,

above);

into

above);

C u r v e

# 1

1 0 0 %

injection

( N B S 7 0 6 , using

G P C

(1)

(obtained

by

# 1

( V

injected I)

(obtained G P C

curves

# 1

standards

(B4, 1),

G P C

G P C

T a b l e

(3)

#2;

1 0 0 % 0.750

#2

T a b l e

5 7 % (4)

1);

into

on

o b t a i n e d (2)

5 7 %

η - h e p t a n e

6 2 %

THF m g

based 1)

(A3, G P C

in

n-heptane T a b l e # 1

I), a n d

8.

BALKE

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

(ii)

AND

PATEL

H i g h - C o n v e r s i o n

P o l y m e r i z a t i o n

K i n e t i c

M o d e l i n g

175

Sources of Error.

a. Concentration Effects. Too high a concentration in GPC # 1 can mean overloading and calibration curve shifts which would destroy hope of comparisons in GPC # 2 . Too low a concentration means undetectable concentrations for GPC # 2 . Table V shows the concentrations of polymer (usually in THF/polymer/monomer mixtures), the GPC that they were directly injected into, and the Column Code involved (Ref. Table 1). No effect of different concentration was observed in the chromatograms from GPC # 2 when concentrations of samples A to Ε inclusive were changed by 33%. GPC # 1 chromatograms were too disturbed by sampling to be useful except as a rough guide to sampling position. Figure 19 shows the Universal Calibration Curve obtained for the coupled GPCs in terms of the hydrodynamic volume in T H F (Ref. Table II). The addition of the nHeptane caused a dramatic shift downstream of the polystyrene standards. The difference between curves obtained by sampling GPC #1 and by direct injection into G P C # 2 (e.g. curves (2) and (3), Figure 19) is probably due to the more monodisperse nature of the former rather than to any concentration effect (Concentrations into GPC # 2 are approximately the same.) b. Axial Dispersion. The output of GPC # 2 is affected by axial dispersion in both GPC # 1 and GPC # 2 . Experimentally the resolution in GPC # 1 was increased by the long column lengths and low flow rate but degraded somewhat by the high sample loadings. The high flow rate in GPC # 2 was only necessary because in these exploratory studies many different runs had to be performed and necessitated short analysis times. An important by-product of the development of this approach is that Orthogonal Chromatography provides a direct method of estimating the shape of the chromatogram for extremely narrow molecular weight distributions. This "shape function" is fundamental information for axial dispersion evaluation and is not otherwise easily obtained. Even commercially available "monodisperse" standards synthesized by anionic polymerization are too polydisperse. Some authors have utilized manual collection of fractions and re-injection into the GPC (e.g.: 39, 40). In our case, sampling the chromatogram of a narrow standard at its peak will provide an extremely narrow fraction as input into GPC # 2 . The chromatogram from GPC # 2 then provides a direct measure of the shape function for that GPC. Figure 20 shows an example of its use. As expected, the GPC # 2 chromatogram of a fraction of a monodisperse standard (obtained by sampling it with GPC # 2 at its peak) is narrower than the whole standard which in turn is narrower than chromatograms of slices of broad polystyrene distributions. In Figure 20, two examples of the latter show the difference obtained by improving resolution in GPC # 1 . Although there was some skewing towards low molecular weights particularly for the narrowest distribution, these curves were generally well fit by a Gaussian shape. Furthermore, the same was found for the copolymer fractions shown in Figure 16. Results are summarized in Table V. No polydispersity due to compositional variation can be distinguished. Furthermore, when standard deviations were superimposed on the calibration curves (Figure 19) it was very evident that resolution in both GPCs had to be improved, particularly in GPC # 1 . No attempt was made to optimize sampling of narrow fractions. A smaller injection volume or better resolution in GPC #1 would possibly provide a more optimistic picture of resolution in GPC # 2 . Also, peak broadening appeared to increase with increased concentration of nheptane. It is quite possible that mobile phase composition and/or polymer type affects axial dispersion.

176

SIZE

EXCLUSION

CHROMATOGRAPHY (GPC)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

2.5

t (min)

F i g u r e

2 1 .

Separation

polystyrene;

(

of

poly-n-butyl ) 2 5 4

n m

methacrylate

i n 1:1

((

solution, 0.100

) 2 3 5 total

%

n m by

f r o m

N B S 7 0 6

weight)

8.

BALKE

A N D PATE L

High-Conversion Polymerization Kinetic Modeling

111

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

The position of the peak (Figure 16) is of critical importance in distinguishing a composition based separation. The large axial dispersion in G P C #1 was attributed to the sample loadings being more than the 9 silica filled columns could handle. This had potentially serious consequences in terms of chromatogram sampling effects. c Chromatogram Sampling. When a slice of chromatogram is sampled, because of axial dispersion it will contain molecules from either side of the slice. Furthermore, the number of these misplaced molecules will generally be higher from the peak side of the sampling point than from the tail side. This effect will, therefore, depend upon the location of the slice, the axial dispersion in G P C # 1 and to a lesser extent upon the size of the slice. The analysis by GPC #2 can then reflect an undesirable molecular size polydispersity independent of other properties. In our case sampling was at 37 min. on column code A3. This is approximately equivalent to 11.2 min. on column code B2 and is shown on Figure 12. Trie order of the distributions' peaks in that figure around the sampling point are similar to that found in the GPC #2 chromatograms (Figure 16). The effect could be elucidated by additional axial dispersion characterization of GPC#1. An alternate approach is to utilize only T H F in both G P C #1 and #2 and to observe whether slices exit at the expected hydrodynamic volume. Attempts to do this indicated that differences on the order of 30% of the peak separation shown in Figure 16 were probably due to such effects. At other sampling points, better and worse results were observed likely because the tail heights of distributions were being sampled. Another sampling effect which deserves mention is that since the molecular weight distribution shifts towards higher molecular weights with conversion, a slice will not in general contain proportionate amounts of polymer from all conversions. This shifting can be accounted for in the theoretical predictions by incorporating it into accumulation of the instantaneous property distributions (e.g. Equation 8). C. Practical Implementation. As a cross-fractionation method GPC has one very definite advantage over other methods-it can clearly show the number of variables affecting the results. Thus, despite the complexity of the problem, guidelines which minimize error and begin to provide useful results have been developed. They are summarized as follows: 1. Improved Resolution in GPC #1: Curve G , Figure 20, (sample G in Table V) shows the results of adding columns to GPC #1 (resulting in Code A4, Table I). Now the variance for NBS706 has been reduced by 1/3 with a notable loss of the high molecular weight tail. 2. Use of an Internal Standard and Improved Resolution in GPC #2 Figure 21 shows the result of sampling a 50:50 blend of NBS706 and poly n-butyl methacrylate using Column Codes A4 and B4 (Table I) injecting a total of 1.5 mg into GPC #1. Figure 22 shows the result of sampling a 1.63:1 blend of sample A with NBS706 (Column Codes A4 and B6). In each case both detectors provide strong evidence for the fractionation obtained. Composition is likely the dominant separation mechanism since both homopolymers and copolymers were separated. 3. Checking for Sampling Effects: Running both GPCs with T H F caused all of the curves shown in Figures 21 and 22 to collapse into a single curve. Since in each case the columns used in GPC #2 could readily resolve a molecular weight distribution in the region involved, this together with different responses on each detector is very good evidence of elimination of sampling effects.

178

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

SIZE

EXCLUSION

CHROMATOGRAPHY (GPC)

1.0

0.8 μ­

ι (min) Journal of Polymer Science F i g u r e 12.5

22.

m i n ;

S e p a r a t i o n A

(-

in -

-)

T a b l e 2 5 4

of

V)

n m

polystyrene f r o m

in

N B S 7 0 6

1.63:1

n-butyl

methacrylate

polystyrene

solution, 0.131

(14.5

total

%

(peak m i n )

by

((

weight)

retention ; (27)

2 3 5

time: n m ;

8.

BALKE

AND PATEL

High-Conversion Polymerization Kinetic Modeling 179

D . Recommendations. Cross-Fractionation using Orthogonal Chromatography has high potential in the analysis of complex polymers and even polymer latices (with Hydrodynamic Chromatography). Multi-detector analysis, particularly utilizing spectrofluorometry, should be very useful in developing the technique.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

IV Conclusions GPC is much more than a source of molecular weight averages. Although averages can be a valuable output, particularly since they fit directly to the Method of Moments in kinetic analysis, they are often amongst the most difficult information to obtain accurately and reproducibly from a GPC. This is because they are weighted integrals which are strongly affected by axial dispersion and which emphasize the heights at the tails of the chromatogram. An alternate approach is to utilize the chromatogram heights as representative of individual concentrations of molecular size. From the kinetic modeling viewpoint, this leads to treating the polymerization as a well-characterized, multi-component reaction system. Phrasing kinetic models in terms of instantaneous property distributions which are summed to provide distributions at any conversion is then highly rewarding. The variation of individual concentrations with time from the G P C readily provides significant insight into the model requirements. From the GPC interpretation viewpoint this alternate approach leads to two major operating modes: 1. appraisal of the whole GPC output for the most useful information obtainable and, 2. experimental use of the GPC in unconventional ways to obtain desired fractionation before detection. In this paper the G P C interpretation underlying the kinetic model of methyl methacrylate polymerization previously published and by now shown to be useful is detailed and updated. It provides a prime example of the conventional experimental use of G P C in homopolymerization studies. To study the bulk copolymerization of styrene η-butyl methacrylate both conventional and unconventional G P C analyses were used. The normally obtained chromatograms, (from dual U.V. detectors) primarily provided area ratios indicative of composition as a function of retention volume. However, even this information was only obtainable after average compositions had been otherwise determined. Furthermore, in general, since the GPC normally separates on the basis of hydrodynamic volume, the polydispersity of all polymer molecular properties at each retention time is of serious concern. Two "unconventional modes" of GPC operation utilizing "Orthogonal Chromatography" were utilized to circumvent these problems: 1. Use of GPC to separate all polymer from all monomer and subsequent analysis of the monomer using HPLC: The results obtained using a highly quantitative version of this approach are shown to be reproducible and in reasonable accord with those of other workers. Advantages of the method include monitoring of the polymer fractionation obtained. 2. Use of one GPC coupled to another with the conditions of the second chosen so as to effect a separation primarily on the basis of composition: Property distribution predictions utilizing kinetic equations derived from the classical copolymerization model are shown for copolymer composition and styrene sequence length. These are compared to chromatograms obtained and sources of error are discussed. Development of a practical procedure for minimizing these errors is initiated and very recent results presented. With this work the distinction between the use of GPC and HPLC begins to dissolve as now we can begin to utilize GPC in a cross-fractionation mode for the HPLC of polymers while incorporating our knowledge of multi-detector analysis.

180

SIZE

EXCLUSION

CHROMATOGRAPHY

(GPC)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

Axial dispersion characterization is a valuable by-product of coupling GPCs. By sampling chromatograms with the second GPC, extremely monodisperse fractions can be obtained and the concentration of misplaced molecules in any chromatogram slice revealed.

Abstract Polymerization kinetic model development often depends upon accurate GPC analysis. This paper shows attempts to use GPC to determine conversion, molecular weight distribution, copolymer composition distribution and sequence length distribution. The free radical homopolymerization of methyl methacrylate and copolymerization of styrene n-butyl methacrylate are used as examples. In each case previously published approaches are triedfirstwith new methods developed when necessary. For homopolymers, calibration using hydrodynamic volume is satisfactory and the need for imperfect resolution correction is circumvented. For copolymers, conventional GPC analysis with dual detectors yields only average composition values. To emphasize desiredfractionationas well as detection "Orthogonal Chromatography" was employed. For polymers this is a new method of analysis involving the orthogonal coupling of one GPC to another with the second run so as to obtain a "Cross Fractionation" of the copolymer. Results are compared to kinetic modelling expectations and sources of error are examined. The method enables GPC copolymer analysis to employ separation mechanisms normally reserved for the HPLC of small molecules. It should be generally useful for revealing property distributions of complex polymers and for direct determination of GPC resolution. Nomenclature ^i Αψ ι Κψ ι C| FQ(0 F|(t) Fjsj(t) fj G(Wj) g h

Area under chromatogram obtained at λ = i Instantaneous weight sequence distribution for styrene Weight sequence distribution for styrene gms of styrene in unreacted monomer (C^Q = initial value) Gaussian fit to chromatogram Chromatogram of detector i Normalized chromatogram (Table IV) Molefractionof styrene in unreacted monomer Cumulative copolymer composition (Equation 5) Weight of polymer Resolution factor ( = l./(2 χ variance of chromatogram of truly monodisperse sample)) Ky detector response constant (Equation 1-4) for component i, detector λ = j m Number of heights M Molecular weight M| Moles/ of styrene in unreacted monomer M2 Moles/ of η-butyl methacrylate in unreacted monomer Mn Number average molecular weight Mn(t) Absolute Mn Mn(oo) GPC uncorrected Mn Mw Weight average molecular weight Mw(t) Absolute Mw Mw( 00) GPC uncorrected Mw η Styrene sequence length n ι Instantaneous number average styrene sequence length lY ι Number average styrene sequence lenpth n

n

8. n

BALKE

ι

w

n

w,l r q,r2 t ^ ν V

High-Con version Polymerization Kinetic Modeling 181

AND PATEL

Instantaneous weight average styrene sequence length Weight average styrene sequence length Polymer chain length Reactivity ratios Retention time GPC # 1 retention time at which chromatogram slice was obtained for GPC # 2 Retention volume Hydrodynamic volume of polymer (here considered equivalent to the "separation parameter" K M \ Table II for GPC calibration) V of polymer in T H F in GPC # 1 a

V

T H

p

W Wj Wj Wj(V)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

f

W| X X| X| f Xj X j | a λ

+

Weightfractionof molecules of length r to r + dr instaneously produced Weightfractionof component i in copolymer instaneously produced Average weight fraction of component i in copolymer Average weight fraction of component i in copolymer contained in chromatogram time increment ("slice"). Weightfractionof component i in unreacted monomer (wj = initial value) Conversion (wt. fraction) Conversion of component 1 (wt. fraction) (Equation 8) Final conversion of component 1 (wt.fraction)(Equation 8) Conversions at times I and II (Table IV) Variable defined after Equation 7 U.V. wavelength (nm) Q

Acknowledgement We would like to thank Dr. L. Alexandra for kindly providing one of the computer programs for instantaneous polymer properties used in this study.

Literature Cited 1. Hamielec, A.E., "Introduction to Polymerization Kinetics", "Polymer Reaction Engineering - Intensive Short Course on Polymer Production echnology", McMaster University, Hamilton, Ontario, Canada, June 1977. 2. Hamielec, A.E., "Computer Applications Modeling of Polymer Reactor Systems", Proceedings - Polymer Characterization Conference, Cleveland State University, Division of Continuing Education, Cleveland, Ohio, April 30 - May 1, 1974. 3. Reiss, G. and Callot, P., in Tung, L.H., Ed., "Fractionation of Synthetic Polymers", Marcel Dekker Inc., N.Y., N.Y. (1977). 4. Stojanov, C., Shirazi, Z., Audu, T., Chromatographia, 1978, 11, 274. 5. Friis, N., Hamielec, A. in Giddings, J.C., Grushka, E., Keller, R.A. and Cazes, J., Eds., Advances in Chromatography, Series 13, Marcel Dekker Inc., N.Y., N.Y. 1975. 6. Tung, L.H., Ed., "Fractionation of Synthetic Polymers", Marcel Dekker, Inc., N.Y., N.Y., 1977. 7. Rudin, Α., Samanta, M.C., J. Appl. Pol. Sci., in publication. 8. Balke, S.T., Hamielec, A.E., J. Appl. Pol. Sci., 1973, 17, 905. 9. Friis, N., Hamielec, A.E., J. Appl. Pol. Sci., 1974, 12, 251. 10. Gruber, E., Knell, W., Makromol. Chem., 1978, 179, 733. 11. Balke, S.T., "The Free Radical Polymerization of Methyl Methacrylate to High Conversions", Ph.D. Thesis, McMaster University, August 1972. 12. Weiss, A.R., Cohn-Ginsberg, E., J. Appl. Pol. Sci., A-2, 1970, 8, 148. 13. Ishige, T., Lee, S.I., Hamielec, A.E., J. Appl. Pol. Sci., 1971, 15, 1607.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch008

182

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

14. Kotaka, T., J. Appl. Pol. Sci., 1977, 21, 501. 15. Budtov, V.P., Podosenova, N.G., Polymer Science USSR, 1977, 19, 1881. 16. Braks, J.G., Huang, R.Y.M., J. Appl. Pol. Sci., 1978, 22, 3111. 17. Krishen, Α., J. Chrom. Sci., 1977, 15, 434. 18. Berezkin, V.G., Alishogev, V.R., Nemirovskaya, J.G., "Gas Chromatography of Polymers", Elsevier, N.Y., N.Y., 1977. 19. Johnsen, E.L., Gloor, R., Majors, R.E., J. Chrom., 1978, 149, 571. 20. Johnson, M., Karmo, T.S., Smith, R.R., Eur. Pol. J., 1978 14, 409. 21. Dionisio, J.M., O'Driscoll, K.F., J. Pol. Sci., B, 1979, 17, 701. 22. Podesva, J., Doskocilova, D., Makromol. Chem., 1977, 178, 2383. 23. Probst, J., Cantow, H.J., Kautschuk und Gummi, Kunststoffe, 1972, 25, 11. 24. Stutzel, B., Miyamoto, T., Cantow, H.J., Pol. J., 1976, 8, 247. 25. Ogawa, T., J. Appl. Pol. Sci., 1979, 23, 3515. 26. Garcia-Rubio, L.H., MacGregor, J.F., Hamielec, A.E., "Copolymer Analysis Using GPC with Multiple Detectors", presented at the "Symposium on Recent Developments in Size Exclusion Chromatography", 178th ACS National Meeting, Washington, D.C., September 9-14, 1979. 27. Balke, S.T., Patel, R.D., J. Pol. Sci., B, in publication. 28. Cantow, M.J.R., "Polymer Fractionation", Academic Press, N.Y., 1967. 29. Teramachi, S., Fukao, T., Pol. J., 1974, 6, 532. 30. Mori, S., Yamakawa, Α., Anal. Chem., 1979, 51, 382. 31. Dawkins, J.V., Hemming, M., Makromol. Chem., 1975, 176, 1795. 32. Bakos, D., Bleha, T., Ozima, Α., Brek, D., J. Appl. Pol. Sci., 1979, 23, 2233. 33. Myagchenkov., V.A., Frenkel, S.Y., Vysokomol. soyed., 1969, A11, 2348. 34. Stejskal, J., Kratochvil, P., J. Appl. Pol. Sci., 1978, 22, 2925. 35. Stockmayer, W.H., J. Chem. Phys., 1945, 13, 199. 36. Lamprecht,J.,Stazielle, C., Dayantis,J.,Benoit, H., Makromol. Chem. 1971, 148, 285 37. Harwood, H.J., J. Pol. Sci., C., 1968, 25, 37. 38. Cantow, H.J., Ber. Bunseng., Physik. Chem., 1966, 70, 257, 275. 39. Taganov, N.G., Novikov, D.D., Korovina, G.V., Entelis, S.G.,J.Chrom., 1972, 72, 1. 40. Ehrlich, B.S., Smith, W.V., in Ezrin, M., Ed., "Polymer Molecular Weight Methods", Adv. in Chem. Series, 125, American Chemical Society: Washington, D.C., 1973. RECEIVED May 7, 1980.

9 Molecular Weight and Peak Broadening Calibration in Size Exclusion Chromatography Use of Multiple Broad Molecular Weight Distribution Standards for Linear Polymers

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

A. E. HAMIELEC and S. Ν. E. OMORODION Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada L8S 4M1 Herein are reported improved methods of molecular weight cal­ ibration where simultaneously, peak broadening parameters (σ) are obtained through the use of multiple polydisperse molecular weight standards. There are two basic methods covered. The first and most reliable method employs the universal molecular weight cali­ bration curve obtained using narrow MWD polystyrene standards. The second method assumes that the molecular weight calibration curve is linear on a semilog plot and should be employed where universal calibration is not practical as with aqueous SEC. Seve­ ral variants of these methods involving different molecular weight data for the standards are discussed. The proposed methods have been evaluated using aqueous SEC and polydextran standards and nonaqueous SEC with polyvinylchloride standards. Previous methods of molecular weight calibration using broad MWD standards were of three basic types. Those which employ a broad MWD standard with known molecular weight distribution (1,2, 3,4,5). Those which employ one or more broad MWD standards with known M , M or [η] and assume a linear molecular weight calibra­ tion curve (6,7,8,9) and finally those which employ one broad MWD standard with known M , M or [η] and use the universal molecular weight calibration curve obtained with narrow MWD polystyrene N

W

N

W

standards (10). Y au et a l . were the f i r s t t o suggest t h a t i t i s more general t o search f o r the t r u e molecular weight c a l i b r a ­ t i o n curve r a t h e r than an e f f e c t i v e molecular weight c a l i b r a t i o n curve. T h e i r a p p l i c a t i o n o f t h i s p r i n c i p l e u n f o r t u n a t e l y has two weaknesses. The f i r s t i n v o l v e s t h e i r assumption t h a t the molecular weight c a l i b r a t i o n curve i s l i n e a r . The second i n v o l v e s the use of peak broadening parameters measured w i t h narrow M W D p o l y s t y r e n e standards f o r the polymer i n q u e s t i o n . This assump­ t i o n may l e a d t o s i g n i f i c a n t e r r o r propagation i n the c a l c u l a t i o n of the molecular weight c a l i b r a t i o n curve (11). The present methods o f determining the molecular weight c a l i 0-8412-05 86-8/80/47-138-18 3$05.00/0 © 1 9 8 0 American Chemical Society

184

SIZE EXCLUSION CHROMATOGRAPHY

(GPC)

b r a t i o n curve overcome the d e f i c i e n c i e s i n the method proposed by Yau et a l by simultaneously determining peak broadening parameters f o r the polymer i n q u e s t i o n . In a d d i t i o n , i f the u n i v e r s a l mole­ c u l a r weight c a l i b r a t i o n curve i s a v a i l a b l e , the molecular weight c a l i b r a t i o n curve i s not assumed t o be l i n e a r . I f the u n i v e r s a l curve i s n o n l i n e a r , the molecular weight c a l i b r a t i o n curve f o r the polymer i n question w i l l a l s o be n o n l i n e a r . In the f o l l o w i n g s e c t i o n the t h e o r e t i c a l b a s i s f o r the pro­ posed methods w i l l be e s t a b l i s h e d .

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

Theory Equations ( l ) , (2) and (3) which give the number and weightaverage molecular weights and i n t r i n s i c v i s c o s i t y of a broad MWD standard i n terms of a mass d e t e c t o r response (F^( ν)) , the t r u e molecular weight c a l i b r a t i o n curve (M(v))and the peak broadening parameter ( v a r i a n c e of a s i n g l e - s p e c i e s chromatogram σ ) form the b a s i s f o r the proposed methods of determining the molecular weight c a l i b r a t i o n curve M(v). 2

-1

\

exp

*

F ( v ) M(v)""

Λ

F ( v ) M(v) N

f(aD a) , )

1

dv

N

(1)

dv

2

[η]

exp

2

=

Κ

F ( v ) M(v) N

dv

(3)

'2

where Κ and a are Mark-Houwink constants f o r the polymer i n ques­ tion . % and My or [η] f o r the broad MWD standard are taken as known q u a n t i t i e s . F^(v) i s the normalized chromatogram f o r the broad MWD standard obtained w i t h a mass d e t e c t o r . D i s the slope of the molecular weight c a l i b r a t i o n curve at the peak p o s i t i o n o f the chromatogram (the equation of the tangent i s given by M(v) = Ό\ exp(-D v). σ i s the v a r i a n c e of the s i n g l e - s p e c i e s chromatogram at the peak p o s i t i o n . The c o r r e c t i o n s f o r imperfect r e s o l u t i o n i n equations ( l ) and (2) were f i r s t d e r i v e d by Hamielec and Ray (12). The methods proposed by Yau et a l employ equations ( l ) and (2) and assume t h a t M(v) = Dj exp(-D v) and estimate σ u s i n g p o l y s t y r e n e v a l u e s . They search f o r Ό\ and D constants i n the assumed l i n e a r molecular weight c a l i b r a t i o n curve. We w i l l now develop improved methods one step at a time. 2

2

2

2

2

2

Methods Based on U n i v e r s a l xMolecular Weight C a l i b r a t i o n Curve The n o n l i n e a r u n i v e r s a l molecular weight c a l i b r a t i o n may be expressed as shown i n equation (k).

curve

9.

HAMiELEC AND OMORODiON

Peak Broadening

185

Calibration

(h)

(v) M(v) = Φ(ν)

[n]

The molecular weight c a l i b r a t i o n curve f o r t h e polymer i n question may be expressed as M(v)

=

where 3 = (

α φ(ν)

1 1+a'

β

(5)

and α = Κ

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

Equations ( l ) , (2) and (3) may now be r e w r i t t e n as

MJJ

exp

f-(D a)

2

2

Ir

ρ

F ( v ) φ(ν)" dv

exp

[η] exp where 3 =

dv

(2a)

F ( v ) φ ( ν ) dv

(3a)

F ( v ) φ(ν)

ρ

N

,aD a) 2

and α

1+a

(la)

N

α

Ρ

N

ι- Β

Κ"

U n i v e r s a l Molecular Weight C a l i b r a t i o n Curve - One Broad MWD Stan­ dard. 2

There are t h r e e unknowns, K, a and σ . One might question the a v a i l a b i l i t y o f Mark-Houwink constants f o r t h e polymer i n t h e open l i t e r a t u r e . Mark-Houwink constants i n the l i t e r a t u r e d i f f e r w i d e l y f o r the same polymer and i t i s d i f f i c u l t t o decide on t h e c o r r e c t p a i r t o employ. Another problem which can a r i s e i s t h a t the u n i v e r s a l molecular weight c a l i b r a t i o n curve may not apply e x a c t l y f o r t h e polymer i n q u e s t i o n . The use o f t h e t r u e MarkHouwink constants would t h e r e f o r e i n t r o d u c e an e r r o r i n t h e mole­ c u l a r weight c a l i b r a t i o n . C a l i b r a t i o n w i t h a broad MWD standard should e l i m i n a t e t h i s e r r o r . The Mark Houwink constants obtained i n t h e c a l i b r a t i o n would i n t h i s i n s t a n c e be e f f e c t i v e r a t h e r than true values. In p r i n c i p l e , one could s o l v e equations ( l a ) , (2a) and (3a) f o r K, a and σ . U n f o r t u n a t e l y , % and [η] are o f t e n h i g h l y c o r r e ­ l a t e d and i t i s recommended t h a t only one o f these data be used per standard. A p r a c t i c a l procedure i s t o estimate σ u s i n g nar­ row MWD p o l y s t y r e n e standards l e a v i n g two unknowns, Κ and a. To i l l u s t r a t e the method, suppose MJJ and My data are a v a i l a b l e f o r the s i n g l e broad MWD standard. D i v i d i n g equation (2a) by ( l a ) e l ­ iminates a and one i s l e f t w i t h a s i n g l e - v a r i a b l e search f o r 3. Once 3 i s known a d i r e c t c a l c u l a t i o n u s i n g e i t h e r equation ( l a ) o r (2a) may be done. A s i m i l a r s i n g l e - v a r i a b l e search procedure may 2

2

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

186

be used when and [η] are known. We w i l l now move on and remove the need t o employ peak broadening parameters based on narrow MWD polystyrenes. U n i v e r s a l Molecular Weight C a l i b r a t i o n Curve - Two or More Broad MWD Standards Two Pieces o f Molecular Weight Data Per Standard. T h i s meth­ od uses the f a c t that when equations ( l a ) and (2a) o r ( l a ) and (3a) with proper m o d i f i c a t i o n are m u l t i p l i e d the peak broadening parameter σ vanishes. The equations f o r two broad MWD standards where M^ and My are known f o l l o w : Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

2

_1

F

(ν) φ ( ν )

N

Ρ

F

dv

(ν) φ(ν) "dv

N

i

i

....

(6)

where s u b s c r i p t i represents the standard. A s i n g l e - v a r i a b l e search f o r 3 r e s u l t s when equation (6) f o r i = l i s d i v i d e d by the equation i = 2 , 3, t o e l i m i n a t e a. Once 3 i s found a d i r e c t c a l c u l a t i o n using equation (6) gives α and then once α and 3 are known a d i r e c t c a l c u l a t i o n u s i n g equations ( l a ) or ( 2 a ) gives the peak broadening parameter σ . f o r each o f the broad MWD standards employed. 2

One Piece o f Molecular Weight Data Per Standard. With t h i s amount o f molecular weight i n f o r m a t i o n per standard, one should estimate the peak broadening parameters ( σ ) f o r each standard using narrow MWD p o l y s t y r e n e standards. With t h i s method there are v a r i o u s p o s s i b l e combinations o f molecular weight data, MJJ, My and [η], The r e s u l t i n g equations f o r some o f these combinations follow : 2

% M

and

% f-(D a)?

Ni

2

expI

Ι

w N

M

exp

X

and

exp

l -1

-(Ο,σ) 2

;

[Ta)

(ν) φ(ν) dv c

F

2/,

:7b)

%

( Γ F

w

P

(ν) φ(ν)

dv

(8a)

9.

HAMiELEC AND OMORODiON

M

Peak Broadening

( D a )\2 2 2

exp

/

187

C a l i b r a t i o n

(8b)

ρ

F

(ν) φ ( ν ) dv ^2

M^

and [ η ]

2

ϊ

2

-(D20)!

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

exp

[η]

2

exp

1-1

/

(aD a) ^ 2

2

(9a)

P

F

(ν) (v)~ dv

19b)

ρ

F. (ν) φ ( ν ) dv N T

2

There are many a d d i t i o n a l combinations which may be employed. Any o f these combinations o f molecular weight data permit a s i n g l e v a r i a b l e search f o r a followed by a d i r e c t c a l c u l a t i o n o f K. Methods which assume a l i n e a r molecular weight c a l i b r a t i o n curve w i l l now be b r i e f l y considered. f

f

Methods Based on a L i n e a r Molecular Weight C a l i b r a t i o n The assumed form o f the l i n e a r molecular weight curve i s given i n equation ( 1 0 ) M(v)

=

Curve calibration

(10)

Ώι exp(-D v) 2

where and D are p o s i t i v e constants. The approach used with the l i n e a r c a l i b r a t i o n i s almost i d e n t i c a l with t h a t u s i n g u n i v e r ­ s a l c a l i b r a t i o n except t h a t now the unknowns are Βχ and D r a t h e r than Κ and a, the Mark-Houwink constants. T h i s approach w i l l be i l l u s t r a t e d u s i n g two broad MWD standards with known M and M^. The equations t o be solved i n t h i s example f o l l o w : 2

2

N

-1

exp - ( D a ) J / 2

(10a)

(v) exp(-D v) dv

(10b)

2

i

i

exp

Κ | i

(v) exp(D v) dv

F

= Di

N

2

i

^ F

(v)exp(-D v)dv

N

2

F

(v)exp(D v)dv (10c) * 2

i

i

A s i n g l e - v a r i a b l e search f o r D i s followed by a d i r e c t c a l c u l a ­ t i o n o f Di u s i n g equation ( 1 0 c ) f o r a t l e a s t two broad MWD stand­ ards. A d i r e c t c a l c u l a t i o n u s i n g equations ( 1 0 a ) or ( 1 0 b ) p r o 2

188

SIZE EXCLUSION CHROMATOGRAPHY

(GPC)

a

v i d e s ± f o r each of the broad MWD standards. Methods based on u n i v e r s a l c a l i b r a t i o n - w i l l be i l l u s t r a t e d u s i n g nonaqueous SEC and broad MWD PVC standards. The M^ and % of these standards i s known. Methods based on the l i n e a r molecu­ l a r weight c a l i b r a t i o n w i l l be i l l u s t r a t e d u s i n g aqueous SEC and broad MWD p o l y d e x t r a n standards f o r which M and My are known. N

Experimental C a l i b r a t i o n

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

U n i v e r s a l C a l i b r a t i o n and broad MWD My known

PVC Standards w i t h %

and

Case Study #1 SEC Operating C o n d i t i o n s ___

,

0

5

ο

ο 3

Α+μ-Styragel columns - 10 A, lO^A, 10 A, 500 A Mobile phase - THF c o n t a i n i n g 1% polypropylene g l y c o l Flowrate - 1 ml/min. Detector - d i f f e r e n t i a l r e f r a c t o m e t e r Temperature - ambient.

(PPG)

The molecular weight c a l i b r a t i o n curve f o r p o l y s t y r e n e was measur­ ed w i t h a s e r i e s of narrow MWD p o l y s t y r e n e standards u s i n g the peak p o s i t i o n s of the chromatograms. The c a l i b r a t i o n curve ob­ t a i n e d u s i n g n o n - l i n e a r polynomial r e g r e s s i o n i s shown i n F i g u r e 1. I n t r i n s i c v i s c o s i t i e s f o r the narrow MWD p o l y s t y r e n e standards were measured i n the mobile phase and the r e s u l t s are shown p l o t ­ ted i n F i g u r e 2. These data y i e l d e d the Mark-Houwink constants shown i n the F i g u r e . The o f t e n used Mark-Houwink constants f o r p o l y s t y r e n e i n THF at ambient temperature (K = 1.60xlO~ and a = 0. 706) agree q u i t e w e l l w i t h the v i s c o s i t y data as shown i n F i g u r e 2. I t i s not c e r t a i n whether 1% PPG i n THF has s i g n i f i c a n t l y a l t ­ ered the Mark-Houwink constants or whether the d i f f e r e n c e s noted are l a r g e l y due t o t h e strong c o r r e l a t i o n of Κ and a found i n f i t t i n g molecular weight and i n t r i n s i c v i s c o s i t y data. The u n i ­ v e r s a l molecular weight c a l i b r a t i o n curve based on p o l y s t y r e n e i s e f f e c t i v e l y the same f o r both p a i r s of Mark-Houwink constants. The molecular weight data f o r the two broad MWD PVC standards used i n t h i s i n v e s t i g a t i o n of u n i v e r s a l c a l i b r a t i o n are given i n Table 3

1.

Table I .

Sample PV2 PV3

Broad MWD

PVC

M^xlO"

Standards Employed w i t h U n i v e r s a l C a l i b r a t i o n Methods 3

25-5 hl.O

S u p p l i e d by Pressure Chemical

M^xlO"

3

V\

68.0 118.0

2.67 2.88

Co. , P i t t s b u r g h , PA.

The f i r s t c a l i b r a t i o n i n v o l v e d the use of two broad MWD

PVC

P e a k

B r o a d e n i n g

1

C a l i b r a t i o n

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

H A M i E L E C AND OMORODiON

10* I 19.0

A

21.0

.— t t ι 1 23.0 2S.0 27.0 29.0 RETENTION VOLUME(counts)

ι 33.0

ι 31.0

Figure 1. Molecular weight calibration curve for polystyrene and_ universal molec­ ular weight calibration curve based on polystyrene ((Φ) [η]Μ ; (m) W ) w

w

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

190

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

10 ρ

10* I

ι 10*

t 10·

i 10·

—ι W

1

10·

MOLECULAR WEIGHT

Figure 2. Intrinsic viscosity-molecular weight data for polystyrene and polyvinyl chloride measured by osmometry and by SEC using broad MWD standard calibra­ tion (polystyrene: (φ) [ ] = 7.06 Χ 10 M in THF/1% PPG; (Ο) [η] = 1.60 X 10' M in THF; polyvinyl chloride: ( ) [ ] = 1.63 Χ 10 Μ· in THF(13);(m) M = 0.93 χ ΙΟ M - in THF/1% PPG) 5

0 77

η

4

0 706

A

v

3

0

589

0 766

9.

HAMIELEC AND OMORODiON

Peak Broadening

191

Calibration

s t a n d a r d s w i t h known Mpj a n d My t o g e n e r a t e t h e peak b r o a d e n i n g parameters (σ ) f o r both standards as w e l l as t h e m o l e c u l a r weight c a l i b r a t i o n c u r v e f o r PVC. T h i s was f o l l o w e d w i t h t h e u s e o f one b r o a d MWD PVC s t a n d a r d a t a t i m e t o g e n e r a t e t h e m o l e c u l a r w e i g h t c a l i b r a t i o n c u r v e f o r PVC u s i n g peak b r o a d e n i n g p a r a m e t e r s o b t a i n ­ ed i n t h e f i r s t c a l i b r a t i o n . These r e s u l t s a r e t a b u l a t e d i n T a b l e I I a n d compared i n F i g u r e 2 w i t h a t y p i c a l Mark-Houwink e q u a t i o n f o r p u r e THF p u b l i s h e d i n t h e l i t e r a t u r e . There a p p e a r s t o b e a s i g n i f i c a n t e f f e c t o f t h e 1% PPG on t h e c o i l s i z e o f PVC m o l e c u l e s . The c o r r e c t i o n s f o r i m p e r f e c t r e s o l u t i o n f o r PV2 a n d PV3 a r e 16% and 21% r e s p e c t i v e l y f o r t h e w e i g h t a v e r a g e m o l e c u l a r w e i g h t s . The m o l e c u l a r w e i g h t c a l i b r a t i o n c u r v e s o b t a i n e d f o r PVC a r e shown p l o t t e d i n F i g u r e 3. T a b l e I I I shows a n i n v e s t i g a t i o n o f t h e e f f e c t o f t h e peak b r o a d e n i n g p a r a m e t e r (σ) assumed when a s i n g l e b r o a d MWD PVC s t a n d a r d i s u s e d . The c o r r e c t i o n s f o r i m p e r f e c t r e ­ s o l u t i o n f o r PV2 a n d PVC w i t h a σ = 0.5 a r e now r e d u c e d t o a b o u t h% f o r b o t h s t a n d a r d s . I t i s o f i n t e r e s t t o n o t e t h a t w i t h a r e ­ d u c e d c o r r e c t i o n f o r i m p e r f e c t r e s o l u t i o n t h e Mark-Houwink e x p o n ­ e n t o b t a i n e d i s c l o s e r t o p u b l i s h e d l i t e r a t u r e v a l u e s f o r PVC i n THF ( 1 3 ) . The u s e o f t h e a s s o c i a t e d m o l e c u l a r w e i g h t c a l i b r a t i o n c u r v e f o r PVC w o u l d r e p r o d u c e t h e % a n d My o f t h e PVC s t a n d a r d s w i t h e r r o r s o f a b o u t 15%·

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

2

T a b l e I I . R e s u l t s o f Case S t u d y #1 - U n i v e r s a l C a l i b r a t i o n w i t h One and Two B r o a d MWD PVC S t a n d a r d s w i t h Known M a n d M y N

( [ n ]

P

= 7.06

S

x 10~

5

M° *

7

7

) - 1

Method

a

(counts ) C a l i b r a t i o n Curve S l o p e a t Peak o f Chromât ogram

σ(counts)

KxlO

2-broad MWD S t a n d a r d s

0.861 ( P V 2 ) 0.981 ( P V 3 )

0.930

0.589

0.625

1-broad MWD S t a n d a r d PV2 PV3

0.861 0.981

1.881 1.9

0.522 0.522

0.653 0.653

3

T a b l e I I I .. U n i v e r s a l C a l i b r a t i o n w i t h S i n g l e B r o a d MWD PVC S t a n d a r d w i t h Known M a n d M - E f f e c t o f P e a k B r o a d e n i n g P a r a m e t e r ( a ) N

w

([nips = 7.06 χ 1C5 r

M

0.77) - 1

Sample

PV2 PV3

σ(counts)

KxlO

0.5 0.861 0.5 O.98I

0.231 1.881 0.129 1.9^7

3

a

0.721 0.522 0.767 0.522

(counts ) C a l i b r a t i o n Curve S l o p e a t Peak o f Chromatogram

0.578 0.653 0.563 0.653

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

192 SIZE EXCLUSION CHROMATOGRAPHY (GPC)

9.

HAMiELEC AND OMORODiON

Peak Broadening Calibration

193

We now move on t o aqueous SEC and the use o f the method o f c a l i b r a t i o n based on a l i n e a r molecular weight c a l i b r a t i o n curve and two broad MWD polydextrans with known M^ and M^.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

Case Study #2 SEC Operating Conditions

(See Ref.(lh) f o r f u r t h e r d e t a i l s ) .

- 729/700 Â, 700/500/370 Â, 370/327 Â, 21*0/120 Â , 120/88 Â , 88 Â. - 0.05 M KF/0.02 wt.% NaN /l.0$ CH 0H/l g T e r g i t o l per 2k I H 0 - h.O ml/min - d i f f e r e n t i a l refractometer - ambient

6 CPG10 columns (1*< χ 3/8") Mobile phase (pH = 2.66) Flowrate Detector Temperature

3

3

2

Polydextran standards employed i n t h i s i n v e s t i g a t i o n are l i s t e d i n Table IV. Table IV.

Broad MWD

Sample

M xl0~

T500 T250 T150 T110 T70

173 112.5 86.0 76.0

Polydextran Standards Employed with L i n e a r C a l i b r a t i o n Methods 3

N

28.9 15.00

509 231 151+.0 106.0 70.0 1*1+.1* 22.3

5.70

9.30

1*2.5

TUO

T20 T10

3

M^xlO""

M

rms

xl0~

1.51+ 1.1*9

297 l6l.2 115.1 89.8 5U.5 35.8 18.29

1.63

7.28

2.9I+ 2.05 1.79 1.39

1.65

:

Supplied by Pharmacia L t d .

The r e s u l t s of the c a l c u l a t i o n s o f Ό\ and D and the peak broaden­ i n g parameter ( σ ) are given i n Table V. The agreement found f o r D the slope of the molecular weight c a l i b r a t i o n curve i s remark­ able c o n s i d e r i n g the usual r e p r o d u c i b i l i t y of MJJ and My f o r broad MWD polymers by SEC which i s about ± 5$ at 95$ confidence l e v e l . The r e p r o d u c i b i l i t y seems t o have had a much g r e a t e r e f f e c t on Ό\ the i n t e r c e p t o f the c a l i b r a t i o n curve. The c o r r e c t i o n s f o r im­ p e r f e c t r e s o l u t i o n are n e g l i g i b l e except f o r the highest molecular weight standard T500 where negative σ are somewhat d i s t u r b i n g . O v e r a l l one can conclude t h a t these r e s u l t s f o r aqueous GPC and polydextran standards are very promising. Another i n t e r e s t i n g f a c t was observed when the molecular weight c a l i b r a t i o n curve u s i n g (D )avg = 0.3 and ( D 1 ) = 0.37 10 was compared with t h a t using the M t o obtain the c a l i b r a t i o n curve. T h i s comparison i s made i n Figure h. The e x c e l l e n t agreement suggests t h a t the use o f M values and chromâtogr'am peak p o s i t i o n s f o r broad MWD 2

2

2

2

x

2

a v g

r m s

R M S

9

SIZE EXCLUSION CHROMATOGRAPHY ( G P C )

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

194

10» ι 90.0

ι 105.0

ι 136.0

ι 120.0

-J 150.0

ι 165.0

ι 180.0

< 195.0

R E T E N T I O N VOLUME (counts)

Figure linear vs.

4.

M o l e c u l a r

calibration a n d p e a k

retention

weight

two

b r o a d

v o l u m e

calibration M W D

((m)

curves

standards

M ; RMÊ

(

for

; a n d

polydextran by

plotting

M

r

Μ (ν) = 0.37

obtained m

a

χ

( Λ /

M

N

9

using ·

M) W

ΙΟ exp(-0.3 ν))

9.

HAMIELEC AND OMORODiON

Peak Broadening

195

Calibration

Table V. R e s u l t s o f Case Study #2 - L i n e a r C a l i b r a t i o n w i t h Two Broad MWD Polydextran Standards w i t h Known M ^ and f f y . Sample P a i r s

1

D (Counts" ) 2

T500 T150 T500

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

TllO T500 TTO

T500 TUO

T250 TllO T250

TTO T250

ThO

T150

ThO

TllO TUO

(D ) 2

a v g

DiXlO""

9

2

2

σ (counts )

Imperfect Resolution Correction Factor

0.296

0.339

3.12 0.32

0.87 0.99

0..301+

0.1+06

-2.53 0.89

1.12 0.96

0. .308

0.1+50

2.21

0.90

0,.300

0.376

0..292

-0.37

1.02

-2.77

1.13

-O.O6

1.00

0.295

0.61+ -O.6I

1.03

0..301+

0.397

-o.oU

1.00

0.22

0.99

0,.295

0.317

0.. 30U

O.U16

0. .297

0.33U

= 0.300

-0.1+9

-0.12 0.01 0.17

-Ο.72 0.06

0.97

1.01+ 1.08

1.00 0.99

1.03 1.00

(Dl)avg = 0.370 x 1 0

9

polymer standards i s a u s e f u l approach f o r e s t a b l i s h i n g a molecu­ l a r weight c a l i b r a t i o n curve where narrow MWD standards are not available. Concluding Remarks Two improved methods o f molecular weight c a l i b r a t i o n u s i n g broad MWD standards have been proposed and some e v a l u a t i o n has been done e x p e r i m e n t a l l y f o r aqueous and nonaqueous SEC. The ex­ p e r i m e n t a l e v a l u a t i o n s i n d i c a t e t h a t both methods appear very promising and j u s t i f y f u r t h e r experimental i n v e s t i g a t i o n . I t i s recommended t h a t these new c a l i b r a t i o n methods be evaluated f o r a wide range o f polymers,packings and mobile phases.

196

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

Acknowledgement s

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch009

The authors acknowledge the s i g n i f i c a n t c o n t r i b u t i o n o f Dr. J . Johnston and Dr. T. MacRury o f Union Carbide Corp., South Charleston, W. Va. t o t h i s p u b l i c a t i o n . The SEC analyses o f the broad MWD PVC standards were done i n the Union Carbide Laboratori e s . The authors a l s o acknowledge the a s s i s t a n c e provided by Dr. N. Foster with the i n i t i a l computer programming.

Literature Cited 1. Cantow, M.J.R.; Porter, R.S.; Johnson, J.F. J. Polymer Sci., 1967, A-1, 5, 1391. 2. Weiss, A.R.; Conn-Ginsberg, E. J. Polymer Sci., 1970, A-2, 8, l48. 3. Wild, L . ; Ranganath, R.; Ryle, T. J. Polymer Sci., 1971, A-2, 9, 2137. 4. Swartz, T.D.; Bly, D.D.; Edwards, A.S. J. Applied Polymer Sci. 1972, 16, 3353. 5. Abdel-Alim, A.H.; Hamielec, A.E. J. Applied Polymer Sci., 1974, 18, 297. 6. Balke, S.T.; Hamielec, A.E.; LeClair, B.P.; Pearce, S.L. Ind. Eng. Chem. Prod. Res. Develop., 1969, 8, 54. 7. Frank, F.C.; Ward, I.M.; Williams, T. J. Polymer Sci., 1968, A-2, 6, 1357. 8. Friis, N.; Hamielec, A.E. Advances in Chromatography, 13, (Giddings, J.C.; Grushka, E.; Keller, R.A.; Cazes, J. eds), Marcel Dekker p.41 1975. 9. Yau, W.W.; Stoklosa, H.J.; Bly, D.D. J. Applied Polymer Sci., 1977, 21, 1911. 10. Provder, T.; Woodbrey, J.C.; Clark, J.H. Separation Science, 1971, 6, 101. 11. Pollock, M.; MacGregor, J.F.; Hamielec, A.E. J. Liquid Chromatography, 1979, 2, 895. 12. Hamielec, A.E.; Ray, W.H. J. Applied Polymer Sci., 1969, 13, 1319. 13. Freeman, M.; Manning, P.B. J. Polymer Sci., 1964, A, 2, 2017. 14. Omorodion, S.N.E.; Hamielec, A.E.; Brash, J.L. "Optimization of Peak Separation and Broadening in Aqueous GPC", - to be published in ACS-Proceedings, Washington, September 1979. RECEIVED May 7, 1980.

10 Effect of Solute Shape or Conformation in Size Exclusion Chromatography W. W. Y A U and D. D. B L Y

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

Central Research and Development Department, Experimental Station, Ε. I. Du Pont de Nemours & Company, Wilmington, D E 19898

ABSTRACT The dependence on molecular weight of the size of macromolecules or other l a r g e - p a r t i c l e solutes in s o l u t i o n varies as a function of the shape of the solute molecule or p a r t i c l e . Solute conformation or shape, therefore, affects the slope of the c a l i b r a ­ t i o n curve and range of molecular weight separations a v a i l a b l e i n s i z e - e x c l u s i o n chromatography (SEC). Various theories which have been derived for d i f f e r e n t solute conformations are u n i f i e d i n t h i s work by ex­ pressing the s i z e of the solute i n terms of a reduced s i z e parameter, R , the radius of g y r a t i o n . I t i s pre­ dicted according to the u n i f i e d theory, that a SEC c o l ­ umn containing a single pore-size packing will have about two decades of MW spearation range for random­ -coil polymers, three decades of MW range for s o l i d sphere solutes and only one decade of MW range for rod­ - l i k e p a r t i c l e s or molecules. This indicates that anal­ y s i s of the slope of a SEC-MW c a l i b r a t i o n curve can be used to study the conformation of solute macromolecules. g

0-8412-0586-8/80/47-138-197$05.00/0 © 1980 American Chemical Society

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

198

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

As the scope of s i z e exclusion chromatography (SEC, or gel permeation chromatography, GPC) expands, for example, into p a r t i c l e measurements and biopolymer, gel filtration chromatographic (GFC) separ a t i o n s , increased needs for i n t e r p r e t a t i o n of solute shape are developing (e.g. hard-sphere for p a r t i c l e s and c o l l o i d s , r i g i d - r o d for biopolymers, and random-coil for f l e x i b l e polymers). The SEC retention chara c t e r i s t i c s for solutes with these d i f f e r e n t conformations have been studied separately i n the theoretical treatments by Casassa, Giddings, Ackers and others.(1-4) However, these are b a s i c a l l y mechanistic theories, developed to provide fundamental understanding of SEC retention i n terms of solute s i z e s ; there remains a need to r e l a t e these theories to p r a c t i c a l SEC calibration procedures which are based on solute molecular weight (MW). In t h i s communication are summarized some of the important p r a c t i c a l insights which theory provides about SEC-MW c a l i b r a t i o n ; predictions also have been derived to show the e f f e c t of solute conformation on the slope and molecular weight range of SEC c a l i b r a tion. For s i m p l i c i t y , the radius of gyration, R , was chosen as a common reduced solute s i z e parameter to compare various theories concerned with d i f f e r e n t solute conformations. A more rigorous treatment would require the use of molecular projections as the common SEC s i z e parameter.(5) However, s i g n i f i c a n t insights are still gained through the s i m p l i f i e d approach. These provide a t i e between theory and experimentally observed solute shape e f f e c t s , and lead to a better understanding of SEC c a l i b r a t i o n p r a c t i c e s . g

Background E x i s t i n g SEC r e t e n t i o n t h e o r i e s h a v e b e e n independently developed f o r each o f the m o l e c u l a r s h a p e m o d e l s shown i n F i g u r e 1. The deep h o l l o w c y c l i n d r i c a l p o r e i n t h e f i g u r e ( A , B, a n d C) i l l u s t r a t e s t h e SEC e x c l u s i o n e f f e c t o n t h r e e t y p e s o f s o l u t e molecules, hard-sphere, r i g i d - r o d , and random-coil, r e spectively. The i n d i v i d u a l t h e o r i e s a n d t h e i r bases o f c o m m o n a l i t y a r e now r e v i e w e d b r i e f l y . In the o r i g i n a l works, t h e o r e t i c a l models w e r e d e v e l o p e d t o e x p l a i n t h e SEC c a l i b r a t i o n c u r v e

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

10.

YAU AND BLY

Effect of

S o l u t e

S h a p e

or

Conformation

199

Journal of Physical Chemistry

Figure 1. Exclusion effect in cylindrical cavities (I) ((A) hard sphere of radius r; (B) thin rod of length L , in two orientations in the plane of the cross section; (C) random-flight chain with one end at point 0 showing allowed conformation ( ) and forbidden conformation ( ))

200

SIZE EXCLUSION CHROMATOGRAPHY

(GPC)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

shape as a function of s i z e and shape of the solute and column packing pore. The t h e o r e t i c a l considerations i n t h i s paper are based p a r t i c u l a r l y on the c y l i n d r i c a l pore shape model f o r s i m p l i c i t y i n argument. Actual SEC packings generally have pore s t r u c tures of a random or i r r e g u l a r shape, but i t i s expected that the r e s u l t s of t h i s study as regards solute shape e f f e c t s should be generally applicable using the c y l i n d r i c a l pore shape model. In fundamental SEC studies retention i s often described i n terms of a d i s t r i b u t i o n c o e f f i c i e n t . The t h e o r e t i c a l d i s t r i b u t i o n c o e f f i c i e n t K i s defined as the r a t i o of solute concentration inside and outside of the packing pores under s i z e exclusion conditions. The experimental d i s t r i b u t i o n c o e f f i c i e n t Kg , as defined i n Equation 1, i s a measurable quantity that can be used to check the theory. E

K

=

SEC

i V W V

(1)

where V i s the retention volume f o r any p a r t i c u l a r solute and V Q and are the respective i n t e r s t i t i a l volume and the t o t a l permeation volume of the packed SEC columns tëO R

The exclusion e f f e c t of hard-spheres i s i l l u s t r a t e d i n Figure ΙΑ., which shows a s p h e r i c a l solute of radius r inside an i n f i n i t e l y deep c y l i n d r i c a l cav­ i t y of radius a . Here the exclusion process can be described by straightforward geometrical considera­ tions , namely, solute exclusion from the walls of the c a v i t y . Furthermore, i t can be shown that c

K

E

=

(1-

(2)

c The exclusion e f f e c t of a r i g i d - r o d i n the same c y l i n d r i c a l pore i s shown i n Figure IB., where the length of the rod i s L,. Quantifying the ex­ c l u s i o n process here i s much more complicated than i n the hard sphere case. Exclusion of the rod depends on the rod o r i e n t a t i o n i n three dimensions and s t a t i s t i ­ c a l methods must be used f o r the evaluation. For r i g i d - r o d s i t has been shown that K i s described bycJ F

10. Kj,

Effect of Solute Shape or Conformation

Y A U AND B L Y

=

1 - ~ [ ( 1 - β ) Ε ( | , β ) - (l-β ) F ( | , 3 ) ] 2

where β = L^/2a

2

, w i t h β£ 1, a n d E , F a r e

201

(3) elliptical

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

integrals. F i g u r e 1C. i l l u s t r a t e s two c o n f o r m a t i o n s o f a f l e x i b l e polymer c h a i n w i t h one end f i x e d i n s i d e the c a v i t y . Even w i t h one end f i x e d , t h e c h a i n s t i l l c a n assume a l a r g e number o f c o n f o r m a t i o n s . The presence o f t h e c a v i t y w a l l , however, does e x c l u d e some c o n f o r m a t i o n s , f o r e x a m p l e , t h e d a s h e d o n e s h o w n in thesketch. This restraint o f conformational free­ dom c a u s e s a d e c r e a s e i n b o t h t h e e n t r o p y a n d t h e s o l ­ ute concentration i n s i d e t h e c a v i t y . F o r t h i s case i t h a s b e e n shown t h a t :

K

E

=

4

\ m=l

B " expt-(^—) 1 2

m

(4)

c

where t h e n u m e r i c a l c o n s t a n t β i s the m-th r o o t o f the B e s s e l f u n c t i o n o f t h e f i r s t k i n d o f order zero, a n d Rg i s t h e s o l u t e r a d i u s o f g y r a t i o n . E a c h o f t h e a b o v e e x i s t i n g SEC r e t e n t i o n t h e o r i e s i s u n i q u e l y r e l a t e d t o o n l y one p a r t i c u l a r solute-shape model. Because o f the d i f f e r e n c e s i n t h e b a s i c s o l u t e - s i z e p a r a m e t e r , r , L]_, a n d Rg i n t h e i n ­ d i v i d u a l c a s e s , t h et h e o r y o f each s o l u t e - s h a p e model stands alone. S i n c e , under these c o n d i t i o n s the d i f ­ f e r e n t t h e o r i e s are n o td i r e c t l y comparable, i t i s d i f f i c u l t t o make i n t e g r a t e d o b s e r v a t i o n s o r t o u n d e r ­ stand various p r a c t i c a l i m p l i c a t i o n s i nthese t h e o r i e s . To g a i n m o r e i n s i g h t s i n t o SEC c a l i b r a t i o n , a common s i z e p a r a m e t e r i s n e e d e d t o u n i f y t h e SEC t h e o r i e s . U n i f i c a t i o n o f Theory S i n c e t h e p a r a m e t e r Rg i s known t o b e a b a s i c SEC s i z e p a r a m e t e r f o r r a n d o m - c o i l t y p e m o l e c u l e s (Equation 4 ) , and s i n c e i t i s a l s o a w e l l - d e f i n e d s t a t i s t i c a l average s i z e parameter, a p p l i c a b l e t o s o ­ l u t e s o f any shape i n c l u d i n g t h e sphere and r o d l i k e m o l e c u l e s , Rg h a s b e e n c h o s e n i n t h i s w o r k t o s e r v e a s a common, r e d u c e d , s o l u t e - s i z e p a r a m e t e r f o r d e ­ s c r i b i n g t h e t h e o r y o f SEC s e p a r a t i o n . B y d e f i n i t i o n :

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

202

SIZE EXCLUSION C H R O M A T O G R A P H Y

(GPC)

w h e r e Ν i s t h e number o f m a s s e l e m e n t s i n a s t r u c t u r e a n d X^ i s t h e dd ii s t ca n c e f r o m t h e i - t h m a s s e l e m e n t t o t h e c e n t e r o f mma s s . , F o r s o l i d s p h e r e s and r i g i d r o d s , E q u a t i o n (5) g i v e s : R

g

R

1 / 2

(sphere)

=

(3/5)

r

(rod)

=

(1/12) L . .

(6)

1 / 2

(7)

The c o m p o s i t e p l o t s o f t h e t h e o r e t i c a l K c u r v e s ( E q u a t i o n s 2, 3 a n d 4) f o r t h e t h r e e s o l u t e s h a p e d ) i n t e r m s o f t h e common r e d u c e d s i z e p a r a m e t e r Rq ( E q u a t i o n s 5, 6, a n d 7) a r e s h o w n i n F i g u r e 2. This p l o t shows t h a t on an R b a s i s a l l s o l u t e s o f d i f f e r e n t c o n f o r m a t i o n s s h o u l d b e h a v e v e r y s i m i l a r l y i n a n SEC experiment. (This r e s u l t i s c o n s i s t e n t w i t h the u n i ­ v e r s a l SEC c a l i b r a t i o n c o n c e p t .(S) E

q

The m o l e c u l a r w e i g h t M o f a s o l i d - s p h e r e i s p r o p o r t i o n a l t o t h e v o l u m e o f t h e s p h e r e , i . e . , M 1/2, b u t f o r a n i d e a l i z e d r a n d o m - f l i g h t p o l y m e r , α = 1/2.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

10.

YAU AND BLY

Effect of Solute Shape or

Conformation

203

The values of the exponent f o r M i n Equa­ tions 8, 9, and 10 determine the rate at which the s i z e of the respective macromolecular shapes change with the molecular weight. For example, a tenfold i n ­ crease i n molecular weight roughly corresponds to a 10 χ L p 2 χ r, or 3 χ R change i n molecular s i z e for the three d i f f e r e n t solute conformations under study. I t i s expected, therefore, that the l i n e a r portion of the SEC-MW c a l i b r a t i o n curve (see Figure 3) w i l l be steepest f o r the sphere-like solutes ( i . e . the l e a s t e f f e c t i v e separation or resolution) and the c a l i b r a t i o n slope f o r spheres w i l l be 3/2 of that f o r c o i l e d molecules. The l i n e a r portion of the curve f o r the r o d l i k e solutes i s expected to have the shallowest slope ( i . e . most r e s o l u t i o n ) , only h a l f that of c o i l e d solutes. As expected and i l l u s t r a t e d here i n Figure 3, an SEC column containing a single-pore-size packing should have a MW separation range of about one decade for r o d l i k e molecules and three decades f o r spheres, compared to the usual, approximately two-decade MW separation range f o r random-coil solutes. Experimental Support f o r the U n i f i e d Theory Published data i n support of the above ob­ servations are shown i n Figures 4 and 5. Figure 4 i s the c a l i b r a t i o n curve f o r the SEC analysis of s i l i c a sol p a r t i c l e s as a function of s i z e XU This curve i l ­ l u s t r a t e s the hard-sphere case where about one decade of p a r t i c l e diameter separation i s observed; note t h i s i s equivalent to about 3 decades of MW. The c a l i b r a ­ t i o n curve slopes f o r polybenzyl-L-Glutamate (PBLG) and polystyrene (PS) are compared i n Figure 5. The l e s s e r slope f o r the polybenzyl-L-Glutamate i s con­ s i s t e n t with the expected trend discussed above .(2) This d i f f e r e n c e i n c a l i b r a t i o n curve slope i s expected because of the molecular conformation difference be­ tween PBLG (rod) and PS ( c o i l ) . Conclusions A s i m p l i f i e d analysis of the e f f e c t of p a r t i ­ c l e shape or molecular conformation on SEC c a l i b r a t i o n has l e d to the p r e d i c t i o n that the more open structure of r i g i d rod shaped solutes gives a r e l a t i v e l y f l a t SEC-MW c a l i b r a t i o n curve. As the solute conformation becomes more compact (random-coil to solid-sphere), the SEC-MW c a l i b r a t i o n curve becomes increasingly steep

204

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

7

SPHERE

6

4

1

1

Ο Κ

Figure 3.

SEC

Theoretical SEC calibration curves for various shapes

(GPC)

10.

YAU AND BLY

Effect of Solute Shape or Conformation

205

100 cr

10

1

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

SILICA SOL SIZE, nm

5.0

5.2

5.4

5.6

5.8

6.0

V , ml R

Journal of Chromatography

Figure 4. SEC calibration curve for silica sol separation (hard sphere particles, single pore size column) (1). Column: PSM-1500 (8.9 μ/η), 30 χ 0.78 cm; mobile phase: 0.1M Na HPO -NaH PO pH 8.0 Ë

Figure 5.

k

t

llt

SEC calibration curves: random-coil vs. rigid-rod (&) (SEC column set of several pore sizes, Ν,Ν-dimethylacetamide solvent at 80°C)

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

206

a n d c o v e r s a l a r g e r MW s e p a r a t i o n r a n g e . I t should now b e p o s s i b l e t o u s e t h e s l o p e o f t h e SEC-MW c a l i ­ b r a t i o n curves, generated from s i n g l e pore s i z e c o l ­ umns, t o s t u d y t h e c o n f o r m a t i o n o f t h e s o l u t e m o l e c u l e s . Acknowledgment We t h a n k J . J . K i r k l a n d f o r h i s i n t e r e s t a n d h e l p f u l d i s c u s s i o n s on t h i s work.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch010

References 1.

Ε. F. Cassassa, J. Phys. Chem., 75, 3929 (1971).

2.

J . C. Giddings, Ε. Kucera, C. P. Russell, and M. Ν. Myers, J. Phys. Chem., 72, 4397 (1968).

3.

G. K. Ackers, Biochemistry, 3, 723 (1964).

4.

W. W. Yau and J. J. Kirkland, and D. D. Bly, "Modern Size-Exclusion Liquid Chromatography," Wiley, New York, 1979, Chapters 2 and 9.

5.

E . F . Casassa, Macromplecules, 9, 182 (1976).

6.

C. Tanford, "Physical Chemistry of Macromolecules," Wiley, New York, 1961, Chapters 3 and 5.

7. J. J. Kirkland, J. Chromatography, 185, 273 (1979). 8.

J . V. Dawkins and M. Hemming, Polymer, 16, 554 (1975).

RECEIVED May 20, 1980.

11 High-Performance Gel Permeation Chromatography Characterization of Oligomers Used in Coatings Systems C H E N G - Y I H K U O and T H E O D O R E P R O V D E R

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

Glidden Coatings and Resins, Division of S C M Corporation, 16651 Sprague Road, Strongsville, OH 44136

Over the last five years the Coatings industry has had to develop new technologies to meet the challenges of governmental regulations in the areas of energy, ecology and consumerism. The greatest changes have occurred in the industrial or chemical coatings areas with the development of environmentally acceptable coatings systems such as High Solids, Powder, Water-borne and radiation curable coatings. These new coating technologies require the use of tailor-made low molecular weight polymers, oligomers and reactive additives which when further reacted produce higher molecular weight and crosslinked polymers concomitant with the minimization of the evolution of volatile products. In these types of coatings systems the control of the oligomer/polymer composition and molecular weight distribution (MWD) is critically important. Conventional GPC does not provide the required resolution in the low molecular weight region for the control of MWD in these oligomer/polymer systems. With the advent of high efficiency columns, the resolution in the lower molecular weight region (molecular weights in the range of 200 to 10,000) has been greatly improved and the speed of analysis increased. These f e a t u r e s make h i g h performance GPC (HPGPC) an i n d i s p e n s a b l e c h a r a c t e r i z a t i o n t o o l f o r the a n a l y s i s o f oligomers/polymers i n environmentally acceptable coatings systems. In t h i s paper, we w i l l d e s c r i b e the q u a l i t a t i v e and q u a n t i t a t i v e HPGPC methodolog i e s we have developed f o r the a n a l y s i s o f oligomers and p o l y mers. S p e c i f i c a p p l i c a t i o n s i n c l u d e a) q u a l i t y c o n t r o l of s u p p l i e r raw m a t e r i a l s , b) g u i d i n g r e s i n s y n t h e s i s and p r o c e s s i n g c) modifying r e s i n s y n t h e s i s t o improve end-use p r o p e r t i e s and d) c o r r e l a t i n g oligomer and polymer MWD w i t h end-use p r o p e r t i e s . Experimental The instrument used i n t h i s study was an in-house c o n s t r u c t ed HPGPC composed o f a Waters A s s o c i a t e s M-6000 s o l v e n t d e l i v e r y system, Waters A s s o c i a t e s U6K i n j e c t o r , V a r i a n Instruments f i x e d 0-8412-05 86-8/ 80/47-13 8-207$05.00/0 © 1980 American Chemical Society

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

208

(GPC)

wavelength (254 nm) UV d e t e c t o r , V a r i a n Instruments d i f f e r e n t i a l r e f r a c t o m e t e r (DRI) and Waters A s s o c i a t e s l i q u i d volume counter. The instrument was operated a t room temperature w i t h Burdick and Jackson d i s t i l l e d i n g l a s s THF as the e l u t i n g s o l v e n t . The sample column bank c o n s i s t e d of s i x μ-Styragel columns w i t h t h e f o l l o w i n g p o r o s i t y d e s i g n a t i o n s : 10*, 1 0 , 500» 500, 100, 100A. The f l o w r a t e was adjusted to 0.6 ml/min. A 2.2- m i l l i ­ l i t e r syphon was used to monitor r e t e n t i o n volume. The column p l a t e count was determined from the e x p r e s s i o n 3

o

P l a t e Count - 16 (V /Wb)

2

(1)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

R

where V R i s the r e t e n t i o n volume and Wf> i s the b a s e l i n e w i d t h of the p l a t e count standard. Using o-dichlorobenzene as the p l a t e count standard y i e l d e d 24,000 p l a t e s f o r 180 cm. of column. The r e s o l u t i o n of the column set was determined from the e x p r e s s i o n d e r i v e d by B l y [1] 2 S

C V

V

V

+ W

R

)

I

log

b2

1 ( )

(M!/M )

V

}

2

where VR« and V R ^ are r e t e n t i o n volumes, W^ and W^ are base­ l i n e widths and, and M are peak molecular weights f o r p o l y ­ mer standards 1 and 2, r e s p e c t i v e l y . For t h i s set of columns, a p o l y s t y r e n e standards of molecular weights 37,000 and 2,000, obtained from Pressure Chemical Co., P i t t s b u r g h , Pa., were used f o r standards 1 and 2, r e s p e c t i v e l y . The v a l u e obtained f o r R was 2.2 a t a f l o w r a t e of 0.6 ml/min. This v a l u e of R compares to a value of 1.14 a t a 2 ml/min. f l o w r a t e r e p o r t e d i n the l i t e r a t u r e [ 2 ] . At t h i s f l o w r a t e the column s e t gave the o p t i ­ mum r e s o l u t i o n per u n i t time. T h i s r e l a t i v e l y low f l o w r a t e a l s o i s r e q u i r e d to preserve the column r e s o l u t i o n over an extended p e r i o r of time. This f l o w r a t e c o n d i t i o n corresponds to the minimum i n a Van Deemter p l o t of h e i g h t e q u i v a l e n t t h e o r e t i c a l p l a t e s U 6 . l i n e a r v e l o c i t y and i s i n agreement w i t h other pub­ l i s h e d data on μ-Styragel ® columns [_3,4J . The column s e t was c a l i b r a t e d w i t h Pressure Chemical p o l y ­ styrene standards over the molecular weight range of i n t e r e s t . The c a l i b r a t i o n curve f o r t h i s column set i s shown i n F i g u r e 1. The p o l y s t y r e n e molecular weight s c a l e was used to p r o v i d e quan­ t i t a t i v e estimates of MWD parameters such as number- and weightaverage molecular weight (M , M ) f o r r e l a t i v e comparison pur­ poses i n c o n j u n c t i o n w i t h the a n a l y s i s of the MWD of oligomers and low molecular weight polymers used i n c o a t i n g s systems. 2

s

s

n

w

Data A c q u i s i t i o n and A n a l y s i s The HPGPC has been i n t e r f a c e d to a Data General NOVA Model

κυο AND PROVDER

HPGPC

of

209

O l i g o m e r s

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

11.

30

35

40

RETENTION F i g u r e

1.

Polystyrene

4S VOLUME

m o l e c u l a r

weight

50

Û

(ml) calibration

c u r v e

ώ

210

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

1230 minicomputer f o r r e a l - t i m e data a c q u i s i t i o n and a n a l y s i s . The minicomputer system has been d e s c r i b e d p r e v i o u s l y [ 5 ] . The subsequent_datja r e d u c t i o n and a n a l y s i s provides molecular weight averages (M , M , M , M +i) or the e q u i v a l e n t extended c h a i n l e n g t h averages as w e l l as v a r i o u s p o l y d i s p e r s i t y i n d i c e s . In a d d i t i o n , s t a t i s t i c a l shape parameters such as v a r i a n c e , skewness and k u r t o s i s f o r the number-, weight- and z - d i s t r i b u t i o n s are provided. A t y p i c a l computer generated a n a l y s i s r e p o r t i s shown i n F i g u r e 2. The data a n a l y s i s program provides p l o t s of base­ l i n e - a d j u s t e d height U6. r e t e n t i o n volume as shown i n F i g u r e 3, as w e l l as p l o t s of the w e i g h t - d i f f e r e n t i a l and cumulative d i s ­ t r i b u t i o n s of molecular weight w i t h the l o c a t i o n s of the respec­ t i v e molecular weight averages (Mn, M , M , Μ +χ, M +2> marked on the d i f f e r e n t i a l curve as shown i n F i g u r e 4. The computation of MWD s t a t i s t i c s and p l o t s are based on the method g i v e n by P i c k e t t , Cantow and Johnson [ 6 ] . For o l i g o m e r i c samples w i t h w e l l d e f i n e d peaks as shown i n F i g u r e 5, the r e l a t i v e percentage f o r each component can be ob­ t a i n e d by i n t e g r a t i n g the area under each peak v i a a gas chroma­ tography data r e d u c t i o n package a l s o r e s i d e n t on the NOVA m i n i ­ computer [5] . n

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

(GPC)

w

z

z

w

z

ζ

z

R e s u l t s and D i s c u s s i o n The r e s o l u t i o n c a p a b i l i t y of the y - S t y r a g e l ® column s e t i s shown i n F i g u r e 6. A mixture of p o l y s t y r e n e s w i t h molecular weights ranging from 97,000 to 600 were separated according to t h e i r molecular weights. The unique f e a t u r e of m i c r o p a r t i c u l a t e h i g h e f f i c i e n c y columns, which i n c l u d e μ-Styragel ® , i s the high r e s o l u t i o n i n the low molecular weight r e g i o n [_3,4^,7^,8^,9^, 10]· For the 600 molecular weight p o l y s t y r e n e standard, conven­ t i o n a l GPC columns would g i v e . o n l y a broad peak. However, the μ-Styragel ® columns separated t h i s sample i n t o a t l e a s t s i x w e l l - d e f i n e d peaks as shown i n F i g u r e 6 corresponding to monomer, dimer, t r i m e r and other h i g h e r molecular weight oligomers. Even s m a l l molecules such as ortho-dichlorobenzene and benzene are r e a d i l y separated. The h i g h r e s o l u t i o n i n the low molecular weight regions i s p a r t i c u l a r l y s u i t e d f o r f i n g e r p r i n t i n g the oligomers used i n chemical c o a t i n g s systems. I n F i g u r e 6, both UV and DRI t r a c e s are shown. For c l a r i t y i n comparisons, o n l y UV t r a c e s w i l l be shown f o r examples i n subsequent d i s c u s s i o n unless where s p e c i f i e d otherwise*. Powder Coatings. One of the new c o a t i n g s t e c h n o l o g i e s which has developed as an i n n o v a t i v e response to governmental r e g u l a ­ t i o n i s powder c o a t i n g s . These c o a t i n g s systems are designed to be 100% s o l i d s . The development of c o a t i n g s p r o p e r t i e s are a r e s u l t of r e a c t i n g the low molecular weight polymer w i t h an oligomer c r o s s l i n k i n g agent to produce c r o s s l i n k e d polymer. The

11.

HPGPC

κυο AND PROVDER

GPC:10

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

211

O l i g o m e r s

1/14/80

JOB 30289

OPR:AFK

REV 6.4

OPERATOR SELECTED BASELINE

RERUN OF JOB 30211 SAMPLE ID RUN NO.

of

5299

DETECTOR:

ULTRAVIOLET

MOLECULAR WEIGHT DISTRIBUTION

MEAN VARIANCE SKEWNESS KURTOSIS

NUMBER .723E 03 .3/ΟΕ 06 .292E 01 .154E 02

WEIGHT .124E 04 .102E 07 .238E 01 .105E 02

MEAN WT/MEAN NMBR MEAN Z/MEAN WT MEAN Z+1/MEAN Ζ MEAN Z+2/MEAN Z+l MEAN Ζ * MEAN Z+1/MEAN WT ,144E 03 RANGE

Z+l 2206E .232E .212E .765E

04 07 01 01

. 318E 04

Z+2 .465E 04

1.708 1.667 1.546 1.461 .531E 04 TO .132E 05

RAW CHROMATOGRAM STATISTICS .217E .689E .143E .239E .180E

MEAN VARIANCE SKEWNESS KURTOSIS AREA

02 00 00 01 04

MAX PEAK MAX PEAK MOMENT 3 MOMENT 4

COUNT! HEIGHT ABOUT MEAN ABOUT MEAN

21.56 835.81 .938E-01 .263E 01

COLUMN AND BASELINE PARAMETERS COLUMN SET SOLVENT VOID VOLUME TOTAL VOLUME CALIBRATION CURVE CALIBRATION POLYMER

7 STARTING BASELINE COUNT THF ENDING BASELINE COUNT 8.00 BASELINE SLOPE 28.00 FIRST DATA POINT COUNT 21 LAST DATA POINT COUNT POLYSTYRENE 1/80

#1 count unit * 1 syphon dump of 2.2 milliliters. Figure 2.

Typical computer-generated data analysis report

18.00 28.00 -.0160 19.00 24.80

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

212

30289C3021O

UV

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

JOB

(GPC)

—

r

10.

Figure 3.

I 20. 15. R E T E N T I O N VOLUME

V 25. IN COUNTS

30.

~35.

Typical computer-generated plot of baseline-adjusted height vs. retention volume

11.

κυο AND PROVDER

HPGPC

of

JOB 30289C30211)

Oligomers UV

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

ο

LOG MOLECULAR WEIGHT

Figure 4.

Typical computer-generated plot of weight differential and cumulative distributions of molecular weight

INTERMEDIATE

RETENTION V O L U M E (ml) Figure 5.

HPGPC chromatogram of a model compound of epoxy-ester

213

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

214

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

(GPC)

R E T E N T I O N VOUJME(mi)

Figure 6. HPGPC traces ( U V and DR!) of a polystyrene standard mixture (operating conditions: columns—(xStyragel 1 0 \ J O , (2) 5 0 0 , (2) 1 0 0 A; solvent— 3

THF;

flow—0.6

X-03

X-38

X-.36

X-02 .°

3

mL/min)

.

,°

4

.

y

R E T E N T I O N V O L U M E (ml)

Figure 7.

HPGPC chromatograms of four isocyanate cross-linkers

11.

κυο AND PROVDER

H P G P C

of

215

O l i g o m e r s

powder c o a t i n g u s u a l l y contains a s m a l l amount of an o l i g o m e r i c flow agent to a i d f l o w and l e v e l i n g d u r i n g the baking process. The MWD of the low molecular weight polymer, o l i g o m e r i c c r o s s l i n k i n g agent, and o l i g o m e r i c flow agent must produce a c o a t i n g s system such t h a t a) the powder p a r t i c l e s w i l l not "block (co­ a l e s c e ) upon shipment or storage, b) the r e s i n system w i l l melt and f l o w w i t h a p p r o p r i a t e l e v e l i n g c h a r a c t e r i s t i c s optimum f o r appearance p r o p e r t i e s p r i o r to the c r o s s l i n k i n g r e a c t i o n w i t h i n s p e c i f i c time c o n s t r a i n t s at a given temperature, and c) the c r o s s l i n k i n g r e a c t i o n must occur at the a p p r o p r i a t e p o i n t i n time a f t e r the r e s i n has melted c o n s i s t e n t w i t h the development of both good appearance p r o p e r t i e s and good mechanical p r o p e r t i e s . Thus, the MWD of the polymer, c r o s s l i n k i n g agent and f l o w modi­ f i e r must be c a r e f u l l y designed and c o n t r o l l e d to produce a powder c o a t i n g s system which meets d e f i n e d r h e o l o g i c a l , r e a c t i v ­ i t y and mechanical property c o n s t r a i n t s . Figure 7 i l l u s t r a t e s the use of HPGPC to a i d a r e s i n chemist i n developing an in-house isocyanate c r o s s l i n k e r f o r a powder c o a t i n g system. Isocyanate c r o s s l i n k e r X-02 gave d e s i r e d pro­ p e r t i e s and i s considered the standard. At the e a r l y stage of the development, r e s i n X-03 was i n i t i a l l y made. By changing the types of r e a c t a n t s , molar r a t i o of r e a c t a n t s and r e a c t i o n c o n d i ­ t i o n s , r e s i n X-36 was the next i t e r a t i o n i n the r e s i n s y n t h e s i s process. F i n a l l y , X-36 was f i n e - t u n e d to produce X-38 which matched X-02 i n both i t s chemical r e a c t i o n p r o p e r t i e s and i t s MWD. HPGPC a l s o was used f o r q u a l i t y c o n t r o l of incoming raw m a t e r i a l s . F i g u r e 8 shows the chromatograms of two d i f f e r e n t batches of blocked isocyanate c r o s s l i n k e r s . One was acceptable and the other was too r e a c t i v e . As can be seen from the HPGPC t r a c e s , the l e v e l of the component e l u t e d at r e t e n t i o n volume 40 i s much higher f o r CX-46 than f o r CX-48. This component was a s s o c i a t e d w i t h f r e e isocyanate f u n c t i o n a l i t y which i n excess would make CX-46 too r e a c t i v e . With t h i s i n f o r m a t i o n , e i t h e r the necessary adjustment f o r the presence of e x c e s s i v e f r e e i s o ­ cyanate f u n c t i o n a l i t y c o u l d be made or t h i s p a r t i c u l a r batch from the s u p p l i e r c o u l d be r e j e c t e d . Another example i n v o l v e d a batch of isocyanate c r o s s l i n k e r which was too tacky. Upon comparing the HPGPC t r a c e of t h i s sample w i t h that of a c o n t r o l as shown i n Figure 9, i t i s seen that the major d i f f e r e n c e between these two samples was the l e v e l of f r e e caprolactam. The high content of f r e e caprolactam i n sample CX-006 depressed the g l a s s t r a n s i t i o n temperature (Tg) of the sample to such an extent that CX-006 became too tacky. T h i s method of a n a l y s i s has proved t o be a r e l i a b l e and u s e f u l t e c h ­ nique f o r d e t e c t i n g low l e v e l s of f r e e caprolactam i n t h i s type of o l i g o m e r i c c r o s s l i n k e r . F i g u r e 10 shows the HPGPC t r a c e s of two d i f f e r e n t batches of in-house a c r y l i c r e s i n s f o r powder c o a t i n g s . I t i s seen t h a t due to the presence of high l e v e l s of low molecular weight components

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

11

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

216

SIZE E X C L U S I O N

2 0

L.

AO

3 0 1

ι

1

1

.

1

RETENTION Figure 8.

H P G P C

c h r o m a t o g r a m s

S O

. ι

1

of

CHROMATOGRAPHY (GPC)

- * ι

6

-L.

0

:

V O L U M E (ml)

two

isocyanate

cross-linkers

f r o m

different

batches

20

1

30

40

I

I

50

60

I

1

R E T E N T I O N V O L U M E (ml) F i g u r e

9,

H P G P C

c h r o m a t o g r a m s

of

two

isocyanate

batches

cross-linkers

f r o m

different

11.

κυο

A N D PROVDER

HPGPC

of

217

Oligomers

and r e s i d u a l monomer and s o l v e n t i n sample TG-37, the Tg i s 20°C lower than t h a t of sample TG-57. Reducing the amount of low molecular weight components and r e s i d u a l monomer and s o l v e n t by vacuum s t r i p p i n g gave an i n c r e a s e i n the Tg from 37°C to 48°C f o r sample TG-37. This brought the sample w i t h i n the m i n i ­ mum acceptable Tg l e v e l c o n s i s t e n t w i t h n o n - " b l o c k i n g of the sample.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

M

High S o l i d s . Another technology which has evolved as a r e ­ sponse t o governmental r e g u l a t i o n s i s h i g h s o l i d s c o a t i n g s . High s o l i d s c o a t i n g s are those which are u s u a l l y 62.5% n o n - v o l a t i l e or g r e a t e r on a volume b a s i s . These c o a t i n g s systems c o n t a i n oligomers which are g e n e r a l l y low i n molecular weight, on the order of 500. As i n powder c o a t i n g s , these systems develop mech­ a n i c a l p r o p e r t i e s upon r e a c t i o n w i t h a c r o s s l i n k i n g agent t o p r o ­ duce a c r o s s l i n k e d polymer. The key design parameters i n h i g h s o l i d s c o a t i n g s are low v i s c o s i t y , low v o l a t i l i t y and c o n t r o l l e d r e a c t i v i t y [11,12]. Low c o a t i n g s v i s c o s i t y (100-500 cps) i s r e ­ q u i r e d i n order to be able to apply the c o a t i n g w i t h convention­ a l spray a p p l i c a t i o n equipment. However, v o l a t i l i t y of the r e s i n system at the c u r i n g temperature must be minimal. These c o n s t r a i n t s n e c e s s i t a t e the design of a c a r e f u l l y t a i l o r e d mole­ c u l a r weight d i s t r i b u t i o n to minimize the presence of v o l a t i l e components c o n s i s t e n t w i t h molecular weights h i g h enough to a i d mechanical p r o p e r t y development upon c u r i n g , but not too h i g h to have a d e l e t e r i o u s e f f e c t upon a p p l i c a t i o n p r o p e r t i e s and the u l t i m a t e appearance p r o p e r t i e s of the c o a t i n g . The c u r i n g mech­ anism should be c o n t r o l l a b l e under v a r y i n g r e a c t i o n c o n d i t i o n s to produce c r o s s l i n k e d c o a t i n g s a t temperatures low enough to minimize v o l a t i l e e v o l u t i o n and a t the same time minimize energy usage d u r i n g the cure process. I n order to compensate f o r the decrease i n molecular weight of a polymer designed f o r h i g h s o l i d s c o a t i n g s , there i s an i n c r e a s i n g dependence on the c r o s s l i n k i n g agent f o r the development of mechanical p r o p e r t i e s . I t becomes important to c a r e f u l l y match the c r o s s l i n k i n g agent w i t h the polymer both i n terms of r e a c t i v e f u n c t i o n a l i t y and MWD. For h i g h s o l i d s c o a t i n g s HPGPC i s very u s e f u l f o r s c r e e n i n g v a r i o u s r e s i n s f o r the o p t i m i z a t i o n of c o a t i n g s v i s c o s i t y and cured f i l m p r o p e r t i e s . Among the f i v e p o l y e s t e r r e s i n s shown i n Figure 11, E-17 was f i n a l l y chosen to be scaled-up due to the unique combination of good f i l m p r o p e r t i e s (hardness and s a l t spray r e s i s t a n c e ) and lowest v i s c o s i t y . The three r e s i n s on the r i g h t hand s i d e of F i g u r e 11 (E-44, E-38 & E-42) were not accept­ able because t h e i r v i s c o s i t i e s were too h i g h as a r e s u l t of h i g h molecular weight components. While r e s i n E-13 met the r e q u i r e ­ ment of low v i s c o s i t y f o r h i g h s o l i d s , the f i l m p r o p e r t i e s were not as good as those of E-17 due to the presence of a h i g h l e v e l of unreacted monomer. F i g u r e 12 shows the HPGPC DRI t r a c e s of f o u r h i g h s o l i d s a c r y l i c oligomers. The r e s u l t s of p a i n t performance e v a l u a t i o n

218

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SIZE EXCLUSION C H R O M A T O G R A P H Y ( G P C )

R E T E N T I O N V O L U M E (ml) F i g u r e

20 i

-ι

30 ι

ι

10.

H P G P C

40 ι

»

*

c h r o m a t o g r a m s

50

20

J

'

RETENTION F i g u r e

11.

H P G P C

of

acrylic

resins

30 »

'

40 *

»

V O L U M E (ml)

c h r o m a t o g r a m s

of

high

solids

polyesters

5,0 «

I

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

11.

κυο A N D PROVDER

HPGPC

of

Oligomers

219

on these a c r y l i c s showed that a c r y l i c A-8 possessed s i m i l a r p a i n t v i s c o s i t y , p e n c i l hardness, impact, MEK r e s i s t a n c e and adhesion p r o p e r t i e s to the commercial high s o l i d s a c r y l i c R-42 due to the s i m i l a r molecular weight range. A c r y l i c s A-15 and A-16 possessed two to three u n i t s higher i n hardness than a c r y l i c A-8 due to the presence of l a r g e amounts of h i g h molecular weight components. However, the c o a t i n g s v i s c o s i t y of coatings systems made with A-15 and A-16 was unacceptably too high. HPGPC a l s o was used to analyze the MWD of v a r i o u s amino c r o s s l i n k e r s , which are the most f r e q u e n t l y used c u r i n g agent f o r i n d u s t r i a l c o a t i n g s . I t i s seen from Figure 13 that HPGPC r e ­ solved each c r o s s l i n k e r i n t o s e v e r a l components d e s p i t e the f a c t that the v e n d o r s l i t e r a t u r e s t a t e d that M-03 and M-56 are monomeric. The e f f e c t of these amino c r o s s l i n k e r s i n the p r o p e r t i e s of a c r y l i c high s o l i d s coatings has been s t u d i e d . Using the same set of a c r y l i c r e s i n s , i t has been shown that c o a t i n g s prepared with the M-70 c r o s s l i n k i n g agent had b e t t e r 500 hours s a l t spray r e s i s t a n c e but lower impact r e s i s t a n c e than c o a t i n g s prepared with the M-03 c r o s s l i n k i n g agent. These p r o p e r t i e s are b e l i e v e d to be a s s o c i a t e d w i t h the higher molecular weight of M-70. 1

Water-Borne Coatings. Water-borne c o a t i n g s are r e p l a c i n g solvent-based c o a t i n g s i n such markets as metal d e c o r a t i n g (bev­ erage can l i n e r s ) , c o i l c o a t i n g s and wood c o a t i n g s as a response to meeting government r e g u l a t i o n s with r e s p e c t to allowable amounts of v o l a t i l e s o l v e n t emission during the baking process. These c o a t i n g s u s u a l l y are i n the 5,000-30,000 molecular weight range and are prepared i n water-miscible organic s o l v e n t s up to 70 to 80% s o l i d s by volume. Chemically, these r e s i n s can be p o l y e s t e r s , a l k y d s , a c r y l i c s and epoxy e s t e r s . G e n e r a l l y , these r e s i n s can s e l f - e m u l s i f y i n t o water when t h e i r s o l u t i o n i n organ­ i c s o l v e n t s i s introduced i n t o water c o n t a i n i n g some amine [13]. In the p r o d u c t i o n of epoxy e s t e r water-borne c o a t i n g s , i t becomes important to monitor changes i n the molecular s t r u c t u r e of low molecular weight epoxy r e s i n s during storage. I t i s w e l l known that c a t a l y z e d l i q u i d epoxy r e s i n s w i l l undergo f u r t h e r r e ­ a c t i o n upon aging. HPGPC has been used to monitor r e t a i n s of i n ­ coming shipments from the r e s i n s u p p l i e r and monitor p e r i o d i c samples from storage tanks of p r o d u c t i o n p l a n t s . F i g u r e 14 shows that at the time of sampling the samples that came from the p l a n t storage tank was e s s e n t i a l l y s i m i l a r to the r e t a i n e d samples from the s u p p l i e r . Also shown i n the f i g u r e i s an epoxy sample which has been aged f o r a year. I t i s seen that the low molecular weight components had undergone f u r t h e r r e a c t i o n to form a much higher molecular weight compound. Observation of any changes i n oligomer d i s t r i b u t i o n such as t h i s , at any time, w i l l a l e r t the r e s p e c t i v e p r o d u c t i o n p l a n t to take proper a c t i o n . UV Curable Coatings. T y p i c a l l y , UV c u r a b l e c o a t i n g s c o n s i s t of very low molecular weight m u l t i - f u n c t i o n a l oligomers d i l u t e d

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

220

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

κυο AND PROVDER

HPGPC

of

Oligomers

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

11.

RETENTION V O L U M E (mi) Figure 14.

HPGPC chromatograms of epoxy resins

221

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222

SIZE E X C L U S I O N C H R O M A T O G R A P H Y ( G P C )

A

Β

20

30

40

50

RETENTION V O L U M E (ml) F i g u r e

15.

HPGPC

c h r o m a t o g r a m s

(DRI

traces)

of

polyester

methane

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11.

κυο

AND PROVDER

HPGPC

of

Oligomers

223

with r e a c t i v e monomers and c o n t a i n a p h o t o s e n s i t i z e r to promote the c r o s s l i n k i n g r e a c t i o n . The almost instantaneous r a t e of r e ­ a c t i o n permits very f a s t l i n e speeds. T h i s type of technology i s i d e a l l y s u i t e d f o r f l a t stock such as f l o o r t i l e and i n t e r i o r wood p a n e l i n g . Often such coatings are a p p l i e d by r o l l c o a t i n g a p p l i c a t i o n methods. In order to have acceptable appearance pro­ p e r t i e s a f t e r cure, the MWD of the oligomer system i s one v a r i ­ able along with t o t a l coatings v i s c o s i t y which must be c o n t r o l l e d to have the a p p r o p r i a t e r h e o l o g i c a l p r o p e r t i e s w i t h respect to r o l l t r a n s f e r , flow and l e v e l i n g . The MWD of the oligomer must be maximized c o n s i s t e n t with acceptable r h e o l o g i c a l p r o p e r t i e s i n order to generate acceptable mechanical p r o p e r t i e s i n the cured film. HPGPC i s very u s e f u l f o r g u i d i n g r e s i n s y n t h e s i s and process development. Figure 15 shows the HPGPC t r a c e s of two p o l y e s t e r based urethane oligomers produced by v a r y i n g the order of monomer a d d i t i o n to the r e a c t o r . The d i f f e r e n c e i n the oligomer d i s t r i ­ bution i s c l e a r l y seen i n the 38-45 ml r e t e n t i o n volume r e g i o n . Due to the presence of the high l e v e l of very low molecular weight components, the r e s i n produced from process A d i d not have acceptable mechanical p r o p e r t i e s compared to the r e s i n produced from process B. The coatings system c o n t a i n i n g r e s i n A produced a c l e a r p r o t e c t i v e surface c o a t i n g which when subjected to cure v i a UV r a d i a t i o n d i d not meet hardness s p e c i f i c a t i o n s . Conclusions The emergence of new c o a t i n g s technologies such as high s o l i d s , powder, water-borne and r a d i a t i o n curable coatings as a response to governmental r e g u l a t i o n s has l e d to the development of r e s i n systems where the measurement of the oligomer and low molecular polymer MWD i s c r i t i c a l l y important i n order to c o n t r o l the p r o p e r t i e s of these c o a t i n g s systems. I t has been shown that the HPGPC technique using high e f f i c i e n c y columns provides the necessary r e s o l u t i o n i n the low molecular weight regions of i n ­ t e r e s t f o r these coatings systems. This technique can be extended by use of other d e t e c t o r s . Chromatix [14] have shown that an o n - l i n e l i g h t s c a t t e r i n g de­ t e c t o r , under a p p r o p r i a t e c o n d i t i o n s can provide absolute mole­ c u l a r weight i n f o r m a t i o n i n the low molecular weight r e g i o n . In a d d i t i o n , i t should be p o s s i b l e to unravel the s u b t l e and im­ portant compositional dependence of the molecular weight d i s t r i ­ b u t i o n f o r these systems i n the low molecular weight r e g i o n by use of u l t r a - v i o l e t and i n f r a r e d d e t e c t o r s [15].

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

224 Literature Cited 1.

Bly, D. D.; J. Polym. Sci., Part C, 21, 13 (1968).

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch011

2. Yau, W. W., Kirkland, J. J., and Bly, D. D.; "Modern Size­ -Exclusion Liquid Chromatography", Wiley-Interscience, New York, 1979, p. 111. 3.

Vivilecchia, R. V., Colter, R. L . , Limpert, R. J., Thimof, Ν. Ζ., and Little, J . N.; J. Chromatogr., 99, 407 (1974).

4.

Dark, W. Α., Limpert, R. J., and Carter, J . D.; Polym. Eng. and Sci., 15 (12), 831 (1975).

5. Niemann, T. F., Provder, T., Metzger, V., and Kearney, R. J.; ACS Organic Coatings and Plastics Chemistry Preprints, 38, 133 (March, 1978). 6. Pickett, H. E . , Cantow, M. J . R., and Johnson, J . F.; J . Appl Polym. Sci., 10, 917 (1966). 7. Kirkland, J. J.; and Antle, P. E.; J. Chromatogr. Sci., 15, 137 (1977). 8. Krishen, Α.; J. Chromatogr. Sci., 15, 434 (1977). 9.

Krishen, Α., and Tucker, R. G.; Anal. Chem., 49, 898 (1977).

10.

Majors, R. Ε., and Johnson, E. L.; J. Chromatogr. Sci., 167, 17 (1978).

11.

Antonelli, J. Α.; Am. Paint J., 44 (March 31, 1975).

12.

Koleske, J. V., Smith, O. W., and Kucsona, J . G.; Modern Paint and Coatings, 39 (Dec, 1977).

13.

Myers, R. R., Gardon, J. L . , Lauren, S.; Ed; Proceedings Science of Organic Coatings Workshop, Kent State University, Kent, Ohio; "Gaps in the Current Physical Chemical Chemistry State-of-the-Art Related to New Coatings Systems", J . L. Gardon, 65 (June, 1978).

14.

Chromatix KMX-6 Application Note, LS10, "Molecular Weight Distribution of Low Molecular Weight Polymers".

15.

Provder, T., and Kuo, C.; ACS Organic Coatings and Plastics Chemistry Preprints, 36 (2), 7 (1976).

RECEIVED May 20, 1980.

12 Size Exclusion Chromatography of Some Reversed Micellar Systems PAUL L. DUBIN

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

Memorex Corporation, San Tomas at Central Expressway, Santa Clara, CA 95052

I.

INTRODUCTION

With the development of new instrumental techniques, much new information on the size and shape of aqueous micelles has become available. The inceptive description of the micelle as a spherical agglomerate of 20-100 monomers, 12-30 Å in radius (1), with a 1iquid hydrocarbon interior, has been considerably refined in recent years by spectroscopic (e.g.: nmr, fluorescence decay, quasielastic light-scattering), hydrodynamic (e.g.: viscometry, centrifugation) and classical light-scattering and osmometry studies. From these investigations have developed plausible descriptions of the thermodynamic and kinetic states of micellar micro-environments, as well as an appreciation of the plurality of micelle size and shape. The intermolecular structure of surfactant aggregates in apolar media is at present more obscure. Because the surfactant polar head groups must lie in the interior of these aggregates, they are described as "inverted micelles" or "reversed micelles." While these terms in themselves suggest a high degree of correspondence to the aqueous systems, substantial evidence indicates that the coalescence of surfactants in apolar solvents occurs through step-wise "mass-action-law" aggregation (2). In contrast t o the s i t u a t i o n f o r aqueous m i c e l l e s , t h i s form o f e q u i l i b r i u m i m p l i e s the absence of a sharp c r i t i c a l micelle concentration (CMC) below which only free monomers may be found. On the other hand, s p e c t r a l and other physical p r o p e r t i e s of non-aqueous surf a c t a n t s o l u t i o n s sometimes show modest d i s c o n t i n u i t i e s in t h e i r concentration dependence, and some workers have i n t e r p r e t e d these as " o p e r a t i o n a l " CMC's (3). The c e n t r a l issue i s the d i s t i n c t i o n between the two types of s e l f - a s s o c i a t i o n : nm m (1) n m ^ am2 + bm + . . . (2) n

a n a

3

*Current address:

Clairol

Research, Stamford, CT.

0-8412-0586-8/80/47-13 8-225$05.00/0 © 1980 American Chemical Society

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

226

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

(GPC)

where eq (1) may be used to describe cooperative (CMC-type) mi­ c e l l e formation, while eq ( 2 ) corresponds to i n d e f i n i t e selfassociation ( 4 J . In many e a r l y studies the "monomer η-mer" as­ s o c i a t i o n (4J of eq (1) was an i m p l i c i t assumption behind the i n t e r p r e t a t i o n of conductance (5) or s p e c t r a l [6| data. Recently, the i n d e f i n i t e s e l f - a s s o c i a t i o n model has been found to provide the more r e a l i s t i c explanation of vapor phase osmometry (VPO) data (4) and nmr r e s u l t s ( 7 ) . At the present time, i n t e r e s t in reversed m i c e l l e s is intense f o r several reasons. The rates of several types of reactions in a p o l a r solvents are strongly enhanced by c e r t a i n amphiphiles, and t h i s " m i c e l l a r c a t a l y s i s " has been regarded as a model f o r enzyme activity ( 3 ) . Aside from such "biomimetic" f e a t u r e s , rate en­ hancement by these s u r f a c t a n t s may be important f o r a p p l i c a t i o n s i n s y n t h e t i c chemistry. L a s t l y , the aqueous "pools" s o l u b i l i z e d w i t h i n reversed m i c e l l e s may be s p e c t r a l l y probed to provide s t r u c t u r a l information on the otherwise e l u s i v e state of water in small c l u s t e r s . To i n t e r p r e t studies i n t o the foregoing matters in d e t a i l , a c l e a r understanding of the s i z e and shape of reversed m i c e l l e s is b e n e f i c i a l . M i c e l l e aggregation numbers, i . e . : ^ m i c e l l e ^ m o n o m e r have been obtained by a v a r i e t y of methods, most notably vpo ( 8 ) , but a l s o c l a s s i c a l l i g h t - s c a t t e r i n g ( 9 ) , i n e l a s t i c l i g h t - s c a t t e r ing (10) and c e n t r i f u g a t i o n (11). A l l of these molecular weight methods provide a s i n g l e average value f o r the aggregation number, e . g . , number-average from vpo or weight-average from 1ight s c a t ­ t e r i n g , and thus y i e l d information about m i c e l l e s i z e d i s t r i b u t i o n only i n d i r e c t l y . The same r e s t r i c t i o n has been encountered in the a p p l i c a t i o n of these techniques to the c h a r a c t e r i z a t i o n of syn­ t h e t i c polymers. This l i m i t a t i o n has in large part provided the impetus f o r the development of GPC, which can portray the whole distribution. S i z e e x c l u s i o n chromatography has been s p a r s e l y a p p l i e d to aqueous m i c e l l a r systems. Gel f i l t r a t i o n on Sephadex columns has been used to examine the state of a s s o c i a t i o n of a l k y l and a r y l a l k y l sodium sulfonate s o l u t i o n s ( 1 2 . 1 3 ) and to measure the s i z e of a l k y l p o l y e t h y l e n e o x i d e m i c e l l e s (14). Porous glass was employed to study monomer-micelle e q u i l i b r i a in sodiurn dodecyl s u l f a t e ( 1 5 ) and to f r a c t i o n a t e casein m i c e l l e s ( 1 6 ) . However, no report has appeared d e s c r i b i n g the e x c l u s i o n chromatography of s u r f a c t a n t s in apolar solvents even though such solvents are t y p i ­ c a l l y the ones employed in modern "high e f f i c i e n c y GPC systems. The present work reports p r e l i m i n a r y studies with a v a r i e t y o f amphiphilic s o l u t e s . The r e s u l t s , while somewhat fragmentary at t h i s stage, suggest that GPC may be a rapid and v e r s a t i l e way t o examine the s i z e and s t a b i l i t y of reversed m i c e l l e s . II.

EXPERIMENTAL

Di(2-ethylhexyl)sodium s u l f o s u c c i n a t e ( d i i s o o c y t y l s u l f o s u c c i n a t e , Aerosol 0T, AOT) was obtained from A l d r i c h and p u r i f i e d by

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

12.

DUBiN

Reversed Micellar

227

Systems

r e c r y s t a l l i z a t i o n from e t h a n o l . Hexadecyl-trimethylammonium bro­ mide (CTAB), glycerolmonooleate (GMO) and di-N-octylamine hydrobromide (DNOAHBr) were obtained from the same source and used without f u r t h e r p u r i f i c a t i o n . Commercial Soya L e c i t h i n * was s u p p l i e d by Chemurgy D i v i s i o n of Central Soya (Central 3FUB). This natural product was f u r t h e r p u r i f i e d by p r e c i p i t a t i o n from THF i n t o acetone, which removed the g l y c e r i d e s (soya o i l ) . The p r e c i p i t a t e , which contained the soya phosphatides, was f u r t h e r p u r i f i e d by p r e c i p i t a t i o n from THF into ethanol to y i e l d a super­ natant c o n s i s t i n g predominantly of chemical l e c i t h i n (phosphatidyl c h o l i n e ) henceforth r e f e r r e d to as the e t h a n o l - s o l u b l e f r a c t i o n . GPC was c a r r i e d out with a "main columns" system, or one of two "Oligomer GPC" systems. The former was a Waters ALC/GPC 204 equipped with 1 0 , 10 \ 1 0 and 500 A juStyragel columns with THF as an e l u a n t . The l a t t e r was in one case a s i m i l a r Waters i n ­ strument with a 1 0 % juStyragel column or 500 A + 100 A (uStyra­ ge! columns and benzene as e l u a n t . The second 01igomer GPC was a high-speed, h i g h - r e s o l u t i o n system (25,000 t h e o r e t i c a l plates) u t i l i z i n g a Milton Roy mi ni-pump, a Rheodyne #7120 i n j e c t o r , and two Toyo Soda G2000H columns with THF as mobile phase. (The use of benzene as a mobile phase with the l a t t e r column set was avoided based on the manufacturer's recommendations f o r columns packed with THF.) A Waters R401 d i f f e r e n t i a l refractometer was the d e t e c t o r used in a l l experiments. The usual narrow d i s t r i b u ­ t i o n polystyrene standards were used f o r c a l i b r a t i o n and a l l reported MW values are r e l a t i v e to t h e i r e l u t i o n ( M S ) . III. RESULTS A. Chromatographic Behavior of Amphiphiles in Benzene 5

3

3

p

GPC chromatograms of Α0Τ in benzene obtained with a 500 ft + 100 A fjStyragel column s e t , and over a range of i n j e c t e d sample weights, are shown in F i g u r e 1. The apparent peak molecular weight increases with the amount of sample applied to the columns. At higher sample loads, the value of M p appears to ap­ proach a l i m i t of 1200-1600. The apparent MWs observed a t low concentrations (ca 500) may represent a lower 1imit corresponding to unassociated s o l u t e . The i n f l u e n c e of sample s i z e on the apparent MW of Α0Τ i s shown i n Figure 2 where sample mass in mg i s p l o t t e d against Mp . In the range 5-20 mg, the apparent MW increases in a nearly l i n e a r maiuier with the sample s i z e . At higher solute con­ centrations, Mp appears to a t t a i n a l i m i t i n g value which, i n s p i t e of some s c a t t e r in the d a t a , can be i d e n t i f i e d as 1400 + 200. PS

P S

PS

* Soya l e c i t h i n i s a natural product which contains about 34% g l y c e r i d e s (soya o i l ) , 5% s u g a r s , and 61% phosphatides. The phos­ phatides in turn are comprised of phosphatidyl c h o l i n e , i.e., chemical lecithin (20%), phosphatidyl ethanolamine (20%), and phosphatidyl i n o s i t o l (21%).

SIZE E X C L U S I O N C H R O M A T O G R A P H Y (GPC)

228

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

3mg

F i g u r e

1.

benzene;

G P C

c h r o m a t o g r a m s

c o l u m n s :

5 0 0

A

-j-

100

of

A e r o s o l A

O T

pStyragel;

v o l u m e :

750

at

varying

flow

rate:

μΣ)

s a m p l e

0.58

loads

m L / m i n ;

(solvent: injection

DUBiN

R e v e r s e d

M i c e l l a r

229

S y s t e m s

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

12.

F i g u r e

2.

D e p e n d e n c e

F i g u r e

1 ((Φ)

of

apparent

injection

m o l e c u l a r

v o l u m e

2 5 0

^L;

weight (

o n

) data

s a m p l e for

Α

size, Ο

Ύ in

f r o m

data

THF)

of

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

230

(GPC)

Chromatograms obtained f o r the other compounds e l u t e d in benzene are shown in F i g u r e 3. Concentrations applied to the columns ranged from ça 2 mg/ml, near the l i m i t of d e t e c t i o n , up to the s o l u b i l i t y limit. Over t h i s range, no change could be observed f o r CTAB. B.

Exclusion Chromatography in THF

Samples of AOT were e l u t e d in THF on Toyo Soda 01 igomer Columns at 118 ml/hr. A s i n g l e rather narrow peak was observed f o r sample s i z e s from 0.1 to 31 mg. The dependence of Mp*> on sample s i z e i s shown by the broken l i n e in F i g u r e 2. The chromatogram of the commercial soya l e c i t h i n as shown in F igure 4 suggests a number of components and al 1 subsequent work was done with the e t h a n o l - s o l u b l e f r a c t i o n , i . e . , phosphatidyl c h o l i n e , or the e t h a n o l - i n s o l u b l e f r a c t i o n , comprised p r i m a r i l y of o t h e r phosphatides. Chromatograms of the e t h a n o l - s o l u b l e f r a c t i o n were obtained i n THF on Toyo Soda 01 igomer columns over a range of sample masses, as shown in F i g u r e 5. The e x c l u s i o n l i m i t of these columns i s ca 50,000 and M values above 10,000 are i n a c c u r a t e because the c a l i b r a t i o n curve i s very steep in t h i s r e g i o n . Consequently, chromatograms were a l s o obtained on the "Main Column" GPC with the r e s u l t s shown in Figure 6. The dependence of Mp ^ on sample s i z e f o r the e t h a n o l s o l u b l e f r a c t i o n i s summarized by the s o l i d l i n e s in F i g u r e 7. F o r both column s e t s , the apparent MW of the p r i n c i p a l peak i n creases by nearly an order of magnitude as the mass of the i n j e c t e d sample i s increased from one to four mg. In c o n t r a s t , the e t h a n o l - i n s o l u b l e f r a c t i o n e x h i b i t s a rather narrow chromatogram with Mp = 20,000, essentially independent of the sample mass or the column system.

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

P

P S

p

P

PS

IV.

DISCUSSION

The decrease in r e t e n t i o n time with i n c r e a s i n g sample s i z e , along with the high values of M , i s a c l e a r i n d i c a t i o n of aggregation of these solutes in nonaqueous media. The two solutes s t u d i e d in d e t a i l , AOT and soya phosphatides, both d i s p l a y l i m i t i n g values of M p at high and low concentrations (see F i g ures 2 and 7) that may correspond to the most s t a b l e aggregate and the unassociated s o l u t e , r e s p e c t i v e l y . The concentration dependence of Mp in the intermediate region varies strongly. To some extent t h i s may correspond to aggregates of intermediate size. On the other hand, the process of separation i t s e l f r e s u l t s i n a continuous perturbation of the e q u i l i b r i u m and the p o s i t i o n and breadth of the observed chromatogram may r e f l e c t in a complex way the process of disaggregation as the solute e l u t e s through the column. P S

p

PS

PS

DUBIN

R e v e r s e d

M i c e l l a r

231

S y s t e m s

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

12.

Figure loads A

3.

G P C

(solvent:

pStyragel

c h r o m a t o g r a m s

benzene;

( G M O ) ;

flow

c o l u m n s : rate:

g r a m s

in

for

D N O A H B r

5 0 0

A

0.55

100

-f

m L / m i n ,

A ; injection

a n d A

except

v o l u m e :

G M O

pStyragel 1.13

700

at

m L / m i n

p L )

varying

( D N O A H B r ) for

s a m p l e or

10

s

c h r o m a t o -

SIZE E X C L U S I O N C H R O M A T O G R A P H Y

(GPC)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

232

F i g u r e u m n s :

4. 2

GPC

c h r o m a t o g r a m s

X G2000H m g / m L ;

T o y ο (

S o d a ; ):

2 5 4

of

c o m m e r c i a l

flow n m

rate:

1.96

detection,

0.2

soya

lecithin

mL/min; abs.

(solvent:

injection: units

THF;

col-

50 /xL X 75

full-scale)

D U B i N

R e v e r s e d

M i c e l l a r

233

S y s t e m s

0.5mg

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

13mg

20,000

F i g u r e

5.

GPC

c h r o m a t o g r a m s

(conditions

s a m e

as

for

of

Figure

phosphatidyl 4

except

choline

injection

fraction

v o l u m e :

of

soya

5 0 - 2 5 0

lecithin

yJL)

* 25mg

12,000 12,000

F i g u r e

6.

c o l u m n s ;

GPC 10

5

A

c h r o m a t o g r a m s +

4

W

A

f

10

s

of A

injection

phosphatidyl +

5 0 0

v o l u m e :

A

choline

fxStyragel;

2 5 - 2 5 0

fraction

flow ^ L )

rate:

(solvent: 1.81

THF;

m L / m i n ;

SIZE E X C L U S I O N C H R O M A T O G R A P H Y ( G P C )

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

234

Figure 7. Effect of sample size on apparent molecular weight for soya lecithin phosphatide fractions (conditions same as for Figures 5 and 6; (O) ethanol-soluble fraction (phosphatidyl choline), "oligomer GPC; (%) ethanol-soluble fraction (phosphatidyl choline), "main column"; (A) ethanol-insoluble fraction (other phosphatides), "oligomer GPC"; (±) ethanol-insoluble fraction (other phosphatides), "main column")

12.

Reversed Micellar

DUBiN

Systems

235

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch012

Micelle Size In reviewing the l i t e r a t u r e on reversed m i c e l l a r systems, Kertes (2) has tabulated mean aggregation numbers n, u s u a l l y ob­ t a i n e d by osmometry or l i g h t - s c a t t e r i n g . In order to compare these values with the present f i n d i n g s , we can attempt to c a l c u ­ l a t e η from the r a t i ο of apparent s i z e at high concentration to t h a t at low sample s i z e , assuming that the former value c o r r e s ­ ponds to the s t a b l e m i c e l l a r aggregate. Several measures of molecular s i z e have been proposed f o r the c a l i b r a t i o n of 01igomer GPC columns i n c l u d i n g molecular weight, M (17), the "universal c a l i b r a t i o n parameter" [7|]M ( 1 8 , 1 9 ) , the l a r g e s t molecular dimen­ s i o n t (20), and the molar volume V (21,22). While a l l of these parameters are s a t i s f a c t o r y f o r a homologous s e r i e s of s o l u t e s , only the l a s t two provide reasonable congruence for structurally different solutes in the range of 10 ). A f r a c t i o n c o n t a i n i n g a l l three myosin l i g h t chains was i s o l a t e d as described by H o l t and Lowry ( 1 7 ) . A l l myosin derived p r o t e i n s were d i a l i z e d against mobile phase b u f f e r c o n s i s t i n g o f 50 mM Na3P04 (pH 7 . 4 ) , 0 . 2 M (NH4) S04, 1 mM EDTA, 0.2 mM d i t h i o t h r e c t o ! and 0.02% NaN3* %

2

Assays, Protein concentrations were measured by the method o f Bradford (18) and the various c o n t r a c t i l e p r o t e i n ATPase a c ­ t i v i t i e s by the method o f Martin and Doty (.19). Gel e l e c t r o ­ phoresis was c a r r i e d out by the method o f Ames (20) on 1.5 mm polyacrylamide slabs using the discontinuous SDS b u f f e r system o f Laemmli (2]_). Dried gels were scanned a t 550 nm f o r densiometry measurements. Results and Discussion C a l i b r a t i o n Curves and E f f i c i e n c y . Protein c a l i b r a t i o n curves f o r both the SW-2000 and SW-3000 columns are shown i n Figure 1. Good l i n e a r i t y was e v i d e n t over the range o f molecular weights used with each column. However, cytochrome C which i s a s m a l l , very b a s i c p r o t e i n e l u t e d sooner than expected when chromatographed on the SW-2000 column. The f r a c t i o n a t i o n o f a mixture o f four standard p r o t e i n s ranging i n molecular weight from 15,000 t o 150,000 on the SW-2000 column i s shown i n the same f i g u r e . The recovery o f absorbance units was e s s e n t i a l l y complete and no a d ­ s o r p t i o n o f the proteins t e s t e d was evident a t the concentration of phosphate b u f f e r used ( 0 . 2 M).

16.

SOMACK ET AL.

287

Spherogel TSK-SW-Type Gel

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch016

3

ι ο

ι 1

ι 2

1

3

ι 4

ι 5

111111111

6

7

8

9

10

11

12

13

14

ι 15

111

16

17

18

ι 19

τ­ 20

RETENTION TIME (MINUTES»

PROTEIN S T A N D A R D S 1. Cytochrome C

MW 12500

RETENTION TIME (MINUTES)

Figure 1. Protein calibration curves for the Spherogel TSK-SW 2000 and SW 3000 columns. Ten μΣ containing 10-100 fig of each protein in 0.2M KPO buffer (pH 6.8) was chromatographed in the same buffer at 1.0 mL/min. Detection was at 254 nm X 0.16 AUFS; pressure: 500 psi. A chromatogram of 4 proteins on the SW 2000 column is also shown. f

288

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch016

Figure 2 shows the e f f e c t o f flow r a t e on column e f f i c i e n c y using the SW-2000 column with cytochrome C. The column e f f i c i e n ­ cy expressed as the number o f t h e o r e t i c a l p l a t e s (N) was depend­ ent on flow r a t e , a r e s u l t t y p i c a l o f s i z e e x c l u s i o n chromato­ graphy. F r a c t i o n a t i o n o f Serum and Column C a p a c i t y . A Fractiona­ t i o n o f human serum on the SW-3000 column i s shown i n Figure 3. A d e f i n i t i v e i d e n t i f i c a t i o n o f the p r o t e i n s i n each peak i s not p o s s i b l e , however, the e l u t i o n times o f the peaks a t 13-14 min. and 15 min. are c l o s e t o the times which would be expected f o r gamma-globulins and albumins, two o f the p r i n c i p a l c l a s s e s o f serum p r o t e i n s . These data a l s o i n d i c a t e the l o a d i n g c a p a c i t y o f t h i s column with serum. More than 14 mg. o f u n d i l u t e d serum was i n j e c t e d before evidence o f overloading i n the form o f band broadening and peak d i s t o r t i o n was observed. Milk P r o t e i n s . S i z e e x c l u s i o n chromatography i s commonly used i n biochemistry t o observe i n t e r a c t i v e processes between proteins. We tested the c a p a b i l i t y o f the SW-2000 gel to follow such phenomena i n m i l k . Figure 4 shows the 254 nm absorbing p r o f i l e s obtained a f t e r chromatographing i d e n t i c a l volumes o f three d i l u t i o n s o f non-fat dry milk i n 0.2 M PO4 b u f f e r , a t pH 7. While the data are not amenable t o q u a n t i t a t i v e a n a l y s i s , d i l u t i o n appears t o have caused disaggregation o f higher molecular weight m a t e r i a l i n the f i r s t peak with a concomitant accumulation o f lower molecular weight material i n the t h i r d peak. In order t o e s t a b l i s h t h a t t h i s e f f e c t was not due to the d i f f e r e n c e i n t o t a l mass chromatographed, 10 y l o f u n d i l u t e d whole milk was i n j e c t e d using a 10 y l loop and the r e s u l t compared t o a run where 100 μΐ o f a 1:10 d i l u t i o n was i n j e c t e d using a 100 μΤ l o o p . Although the same sample mass was a p p l i e d i n both c a s e s , the apparent d i s ­ aggregation was s t i l l observed (data not shown). A s i m i l a r e f f e c t was observed i n whole m i l k . Upon rechromatographing m a t e r i a l c o l ­ l e c t e d from the f i r s t peak, a s h i f t o f much o f the material to a l a t e r e l u t i n g p o s i t i o n occurred (Figure 5 ) . A s i m i l a r d i l u t i o n e f f e c t can a l s o be observed by chromatographing a l p h a - c a s e i n alone at d i f f e r e n t concentrations (Figure 6 ) . I n i t i a l l y , the p r o t e i n was chromatographed a t approximately the same concentration a t which i t i s present i n whole m i l k . A f t e r d i l u t i n g the p r o t e i n 1:10, the p r o f i l e c l e a r l y showed the disaggregation o f m a t e r i a l with a molecular weight o f 80,000 daltons o r g r e a t e r . These ob­ s e r v a t i o n s are c o n s i s t e n t with the known p r o p e r t i e s o f a l p h a c a s e i n , the major p r o t e i n found i n m i l k . Dry milk i s 25% casein by weight, h a l f o f which i s a l p h a - c a s e i n ( 2 2 ) . The a l p h a - c a s e i n f r a c t i o n makes up 50% o f the t o t a l milk p r o t e i n and a l l o f the casein i n milk p a r t i c i p a t e s i n complex, r e v e r s i b l e aggregation (23, 2 4 ) . I t seems reasonable t o speculate t h a t these d i l u t i o n e f f e c t s observed i n whole milk are due t o the d i s a s s o c i a t i o n o f high molecular weight casein aggregates. High performance s i z e

Publication Date: November 26, 1980 | doi: 10.1021/bk-1980-0138.ch016

SOMACK ET AL.

0.5

0.6

289

Spherogel TSK-SW-Type Gel

0.7

0.8

Figure 2. Effect of flow rate on the efficiency (N) of the Spherogel TSK-SW 2000 column. The conditions were as indicated in Figure 1 using cytochrome C as test solute.

0.9

FLOW RATE (Ml/Min)

I

1

1

1

1

1

1

ι

Ο

3

6

9

12

15

18

21

MINUTES

Γ 24

Figure 3. Fractionation of human serum proteins on Spherogel TSKSW 3000. The conditions were as in Figure 1. The analyses were made using (Λ) α 50-μΣ, injection loop with an analyticalflowcell; (B) a 100-L loop with a semipreparative flow cell; or (C, D) a 500-L loop with a preparativeflowcell.

290

SIZE EXCLUSION CHROMATOGRAPHY (GPC)

MW 80,000