Adsorption at Interfaces [1ST ed.] 9780841202498, 9780841201743

Table of contents :
Title Page......Page 1
Half Title Page......Page 3
Copyright......Page 4
ACS Symposium Series......Page 5
FOREWORD......Page 6
PdftkEmptyString......Page 0
PREFACE......Page 7
Introduction......Page 12
Gas Adsorption on Parallel Plates......Page 13
Non-electrolyte Mixture Adsorption on Parallel Plates......Page 15
Electrolyte Adsorption on Ideally Polarized Plates......Page 18
Electrolyte Adsorption on Ideally Non-polarizable Plates......Page 23
Literature Cited......Page 26
2 Configurational Behavior of Isolated Chain Molecules Adsorbed from Athermal Solutions......Page 27
The Present Approach......Page 28
The Model......Page 30
Computation......Page 31
Results and Discussion......Page 32
Concluding Remarks......Page 36
Literature Cited......Page 38
Introduction......Page 39
Theory......Page 41
Discussion......Page 49
Literature Cited......Page 57
Introduction......Page 59
Binding of Two Components at the Liquid Interface......Page 60
The Gibbs Adsorption Equation......Page 62
Evaluations of Г2......Page 63
Solute-Solvent Binding Characteristics......Page 64
Conclusions......Page 71
Literature Cited......Page 72
Introduction......Page 74
Experimental - Materials and Methods......Page 75
Wetting Behavior.......Page 76
Results......Page 78
Discussion......Page 82
Literature Cited......Page 88
Introduction......Page 90
Experimental......Page 91
Results and Discussion......Page 92
Literature Cited......Page 103
Introduction......Page 107
Materials and Methods......Page 108
Results and Discussion......Page 112
Literature Cited......Page 117
Introduction......Page 118
Experimental......Page 120
Results......Page 122
Discussion......Page 124
Adsorption at and Below the C.m.c.......Page 128
Adsorption Isotherms above the C.m.c......Page 130
Adsorption Maxima and the Exclusion of Micelles......Page 133
Summary......Page 136
Literature Cited......Page 137
Introduction......Page 140
Background......Page 142
Experimental Procedures......Page 148
Results and Discussion......Page 150
Literature Cited......Page 164
Experimental......Page 168
Results and Discussion......Page 170
Literature Cited......Page 180
Materials and Methods......Page 181
Results......Page 182
Discussion......Page 184
Literature Cited......Page 191
Contact Angles......Page 194
Discussion......Page 195
Literature Cited......Page 200
Introduction......Page 202
Materials and Methods......Page 203
Results and Discussion......Page 204
Literature Cited......Page 208
Critical Surface Tensions of Wetting......Page 210
Steric Configurations......Page 216
Electrostatic Dipoles......Page 218
Literature Cited......Page 219
Experimental......Page 223
Results and Discussion......Page 224
Summary......Page 231
Literature Cited......Page 234
Experimental......Page 236
Results and Discussion......Page 238
Literature Cited......Page 242
Introduction......Page 245
Theory and Calculations......Page 246
Experimental......Page 251
Literature Cited......Page 257
Experimental Data by Smith-Johannsen and Discussion......Page 259
Literature Cited......Page 271
Materials......Page 272
Measurement of Surface and Interfacial Tension......Page 273
Results and Discussion......Page 274
Calculation of Adsorption Using Gibb's Equation......Page 276
Literature Cited......Page 277
Introduction......Page 281
Influence of the Electrical Double Layer on the Removal of Soil Particles......Page 284
The Primary Step of the Removal of Adhering Particles......Page 288
Summary......Page 289
Literature Cited......Page 291
Β......Page 292
D......Page 293
G......Page 294
L......Page 295
Ρ......Page 296
S......Page 297
V......Page 298
Ζ......Page 299

Citation preview

Adsorption at Interfaces

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

Adsorption at Interfaces K. L. Mittal, Editor

Papers from a symposium honoring

sponsored by the Division of Colloid and Surface Chemistry at the 167th Meeting of the American Chemical Society Los Angeles, Calif., April 2-5,

ACS

1974.

SYMPOSIUM

SERIES

AMERICAN CHEMICAL SOCIETY WASHINGTON, D. C. 1975

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

8

Library of Congress

Data

Adsorption at interfaces. (ACS symposium series; no. 8) Companion vol. to Colloidal dispersions and micellar behavior. Includes bibliographical references and index. 1. Adsorption—Congresses. I. Mittal, K. L., 1945- ed. II. American Chemical Society. Division of Colloids and Surface Chemistry. III. American Chemical Society. IV. Series: American Chemical Society. ACS symposium series; no. 8. QD547.A37 541'.3453 74-32040 ISBN 8412-0249-4 ACSMC8 8 1-290 ( 1975)

Copyright © 1975 American Chemical Society A l l Rights Reserved

PRINTED IN THE UNITED STATES OF AMERICA

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ACS Symposium Series Robert F. Gould, Series Editor

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

FOREWORD The A C S S Y M P O S I U M SERIES was founded in 1974

to provide

a medium for publishing symposia quickly in book form. T h e format of the SERIES parallels that of its predecessor, A D V A N C E S IN C H E M I S T R Y 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. As a further means of saving time, the papers are not edited or reviewed except by the symposium chairman, who becomes editor of the book.

Papers published in the A C S S Y M P O S I U M

SERIES

are original contributions not published elsewhere in whole or major part and include reports of research as well as reviews since symposia may embrace both types of presentation.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

PREFACE "Professors R. D . Void and M . J. Void retired in June 1974 after more A

than 30 yrs at the University of Southern California. The annual

meeting of the American Chemical Society in April in near-by Los Angeles provided an ideal opportunity to pay tribute to these two outstanding workers in colloid science by holding a symposium in their honor. When the idea for this symposium was broached to me, I accepted it without hesitation as I such an event would elicit an enthusiastic response both from their former students and fellow colloid scientists.

The response exceeded all expecta-

tions as 57 papers covering a wide variety of interfacial and colloidal phenomena by 98 authors from 14 countries were included in the program, and two papers were considered later on.

Such overwhelming

response certainly testifies to their popularity as well as versatility in this research field. In fact, this symposium turned out to be the second largest one at the meeting. In consideration of the contents of this symposium, it might be more appropriate to name it "International Symposium on Interfacial and Colloid Phenomena honoring Professors R. D . and M . J. Void." This volume of 20 papers documents part of the proceedings of the symposium. T h e other part is contained in a companion volume of 24 papers, entitled "Colloidal Dispersions and Micellar Behavior." The papers in this volume deal with the adsorption of a variety of adsorbates on an array of substrates. Thermodynamics of adsorption, insoluble monolayers, adsorption at low energy solids, adsorption at colloidal particles, adsorption of polymers, and other aspects of adsorption are covered. Adsorption plays an important role in many technological, industrial, natural, and biological processes. Adsorption is truly an interdisciplinary field as is evidenced by the vast amount of literature being published from diverse laboratories.

Adsorption at interfaces ranges from the ad-

sorption of simple molecules ( for example, gases ) on bulk solid substrates to the adsorption of polymeric materials on colloidal particles.

Innumer-

able adsorption applications have produced a proliferation of literature on this topic. W i t h the availability of sophisticated instrumentation, a tremendous progress has been made in understanding the nature of the adsorbed species and the absorbate-adsorbent

interactions, but the sub-

ix In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ject of adsorption is still pregnant with many challenging problems whose solutions will open new vistas in many basic and applied areas. Colloid chemistry, more generally colloid science, has been aptly described by the Voids in their book "Colloid Chemistry" (Reinhold, 1964)

as "the science of large molecules, small particles, and surfaces."

So obviously, adsorption is an integral part of the study of colloids, and many of their characteristics are attributable to the adsorption at colloidal particles. The Voids have been active in a spectrum of research activities.

He

made his research debut in the study of the solubility of organic compounds in aqueous and nonaqueous media while her first paper was on the mechanism of substitution reactions.

After this Robert worked in

industry where he became acutely aware of the inadequacies of the theories of simple system to study the intricacies of colloidal systems.

Subsequently, Marjorie be-

came very interested in studying colloids. They actively pursued the phase rule studies of association colloids ( soaps, greases, etc. ) in aqueous and nonaqueous media using surface chemical, electron microscopic, x-ray diffraction, and thermal analytical ( D T A ) techniques; adsorption at various interfaces; stability of colloidal dispersions; and calculation of van der Waals forces. More recently, their research interests have included understanding the factors influencing emulsion stability using ultracentrifuge; use of computer in floe formation and calculation of the dimensions of coiling type polymers; dispersions of carbon black; phase behavior of lithium stéarate greases; theories of colloidal stability in nonaqueous media; and the hydration of biopolymers like D N A . Obviously, the Voids' research activities have run the gamut from less glamorous colloidal systems like greases to the more fashionable biopolymers. Their work on the phase behavior and properties of nonaqueous soap systems had a significant impact in the petroleum industry (cf. N L G I Spokesman 18, 168

(1964)).

Their research

investigations

have culminated in 136 scientific and technical publications. They have also written the book mentioned above. This small paperback is an extremely good exposition of the principles and the methods of study of colloidal systems.

Owing to its popularity and utility it has been trans-

lated into Japanese. Apart from their research contributions, the Voids have rendered a great service to colloid science by popularizing it on a global basis, and they were very instrumental, along with Professors Adamson, Mysels, and Simha, in establishing an internationally acclaimed center for surface and colloid chemistry in the Chemistry Department at the University of Southern California.

Robert Void organized the Summer Conferences

χ In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

on Colloid Chemistry (1961-1964) at U . S . C . sponsored by the National Science Foundation. The Voids are very meticulous researchers and highly stimulating teachers.

I have found them very adept at inculcating good research

habits in the minds of neophytes in research. N o student can get away with sloppy record keeping.

Furthermore, they know how to bring out

the best in a student. Robert D . Void received his A . B . and M.S. degrees at the University of Nebraska in 1931 and 1932, respectively, and P h . D . degree from the University of California at Berkeley in 1935. During 1935-1937 he was a research chemist with Proctor and Gamble in Cincinnati. H e was a postdoctoral fellow with Professor J. W . McBain at Stanford University from 1937 to 1941.

Since 1941 he has been engaged in teaching and

research at the Universit a Fulbright Senior Research Fellowship with Professor Overbeek at the University of Utrecht, The Netherlands.

In 1955-1957 he served as Visit-

ing Professor of Physical Chemistry at the Indian Institute of Science, Bangalore, India, where he introduced new fields of research and helped to establish a P h . D . program.

In 1965 he served as a consultant for the

Summer Institute at Jadavpur University, Calcutta, India, which is designed to improve the teaching of chemistry in Indian colleges. H e was a member of the advisory board of the Journal of Colloid Science from its inception in 1946 until 1960. Among the various offices he has held in National Associations include Chairman, Southern California Section, A C S , 1967; Committee on Colloid and Surface Chemistry of the National Academy of Sciences, 1964-1967; Chairman,

California Association

of Chemistry

Teachers,

1961; National Colloid Symposium Committee, 1948-1953; and Chairman, Division of Colloid Chemistry, A C S , 1947-1948.

H e was awarded the

Tolman medal of the Southern California Section of the American Chemical Society for his research contributions and service to the profession in 1970. Marjorie J. Void received her B.S. in 1934 and P h . D . in 1936 from the University of California at Berkeley at the unusually young age of 23. She was University Medallist (Class Valedictorian)

at U . C . Berkeley.

After brief experience as a lecturer at the University of Cincinnati and the University of Southern California, she was a research chemist with the Union O i l Co. ( 1942-1946 ). Since then she has held various faculty appointments in the Department of Chemistry of the University of Southern California, with the title of Adjunct Professor for the last 14 yrs. She was awarded a Guggenheim Fellowship in 1953 which was taken at the University of Utrecht, T h e Netherlands.

From 1967 to 1970 she served

xi

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

as a member of the Advisory Board of the Journal of Colloid and Interface Science. She was awarded the Garvan Medal of the American Chemical Society in 1967. Among many other awards and honors include Los Angeles Times "Woman of the Year," 1966; National Lubricating Grease Institute Authors Award for the "Best Paper" presented at the Annual Meeting (in 1967), 1968; and she is listed among the 100 Outstanding Women of the U.S. by the Women's Home Companion 1969. Unfortunately, Mrs. V o i d was struck with multiple sclerosis in the fall of 1958 and has been confined to a wheel chair most of the time since 1960. In spite of her poor health and this terrible handicap, she has shown admirable stamina to deliver advanced colloid chemistry lectures continuously for two hours. O n November 19, 196 Binds" appeared in Los Angele glimpses of the scientific and social lives of the Voids. A special love for science has been maintained in the Void clan for almost a century. Individually speaking, the Voids are different in many respects. Mrs. Void has put it succinctly, "Robert has a sound almost conservative judgment while I tend to go off half-cocked. W e complement each other in our work and our lives." Although the Voids are retiring from active duty, they have no intention of relinquishing their interest in colloid science—a discipline they have cherished for about 40 yrs—as they plan to write a text book on the subject. M a y we join together on this occasion to wish them a very healthy and enjoyable retirement in San Diego. Acknowledgments: First, I am grateful to the Division of Colloid and Surface Chemistry for sponsoring this event. I am greatly indebted tc the management of the I B M Corp., both at San Jose and at Poughkeepsie for permitting me to organize this symposium and edit the volumes Special thanks are due to my manager, E . L . Joba, for his patience and understanding. The secretarial assistance of Carol Smith is gratefully acknowledged. Special thanks are also due to M . J. Dvorocsik and Elizabeth M . Ragnone for helping to prepare this volume for publication. The able guidance and ready and willing help of Paul Becher and K. J. Myseh is deeply appreciated. T h e reviewers should be thanked for their man) valuable comments on the manuscripts. I am thankful to my wife, Usha for helping with the correspondence, proofreading, and above all foi tolerating, without complaint, the frequent privations of an editors wife It would be remiss on my part if I failed to acknowledge the enthusiasn and cooperation of all the participants, especially the delegates fron overseas countries. Poughkeepsie, N.Y., November 19, 1974 K. L . M I T T A L :

xii

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

Adsorption at Interfaces

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

1 Thermodynamics of Adsorption and Interparticle Forces D. H . E V E R E T T School of Chemistry, University of Bristol, Bristol BS8 1TS, England C. J. R A D K E Chemical Engineering Department, Pennsylvania State University, University Park, Penn. 16802

Introduction An understanding of the p r o p e r t i e s of colloidal systems depends critically upon a knowledge of the factors which determine the forces between small particles in a fluid medium. Many systems of practical importance are d i s p e r s i o n s in aqueous e l e c t r o lyte s o l u t i o n s and it was n a t u r a l that the earlier t h e o r i e s of colloid stability were concerned w i t h the way in which e l e c t r o static forces, arising from ions in the s o l u t i o n and the electrical s t a t e of the s u r f a c e , combine w i t h d i s p e r s i o n forces between the particles to determine the thermodynamically s t a b l e (or metastable) s t a t e of the system. With the development of systems (often in non-aqueous media) stabilised by adsorbed molecules, a t t e n t i o n was d i r e c t e d towards the e f f e c t of adsorbed species on interparticle forces. A number of p o s s i b l e contributions to these e f f e c t s were recognised but in earlier treatments they were i n c l u d e d as separate a d d i t i v e c o n t r i b u t i o n s to the interaction energy. The phenomena a s s o c i a t e d w i t h adhesion between particles in powders have been looked upon as u n r e l a t e d problems and no q u a n t i t a t i v e study has been made of the e f f e c t of adsorbed gases on the i n t e r a c t i o n f o r c e s . The present work has sought to provide a u n i f y i n g thermodynamic approach to all these problems. Much of the earlier work on colloid stability was a l s o based on a thermodynamic approach and some of the equations of the present paper have p r e v i o u s l y been a p p l i e d to specific problems, though they were often d e r i v e d by more intuitive methods which l a c k both the r i g o u r and g e n e r a l i t y of a formal approach. There has, as far as we know, been no previous attempt to b r i n g all the above problems together in a s i n g l e general thermodynamic framework. It i s important to s t r e s s that colloidal phenomena are controlled both by thermodynamic and kinetic f a c t o r s and that s i n c e d i f f e r e n t p o s s i b l e processes ( e . g . , the approach of two particles via Brownian motion, and the establishment of adsorption equilibrium at the particle surfaces) may occur on w i d e l y d i f f e r e n t time s c a l e s , the observed phenomena may correspond, in d i f f e r e n t 1

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2

ADSORPTION

AT

INTERFACES

circumstances, to t h e i r e v o l u t i o n along d i f f e r e n t paths. We l i m i t c o n s i d e r a t i o n here to the case i n which adsorption e q u i l i ­ brium i s maintained d u r i n g the approach, encounter, and subsequent aggregation or s e p a r a t i o n of two p a r t i c l e s . For s i m p l i c i t y we deal w i t h the case of the i n t e r a c t i o n between p a r a l l e l p l a t e s . Rather than develop the theory i n i t s f u l l g e n e r a l i t y at once, i t i s more convenient to t r e a t f i r s t the case of s o l i d p a r t i c l e s i n a vapour phase: t h i s r e v e a l s the more important p r i n c i p l e s which are shown l a t e r to have q u i t e general a p p l i c a ­ bility. We then consider i n t e r a c t i o n s i n n o n - e l e c t r o l y t e systems and f i n a l l y the e l e c t r o l y t e case f o r both i d e a l l y p o l a r i z a b l e and non-polarisable electrodes. In the l a t t e r case, we discuss two s p e c i f i c examples: extensions to other systems are r e a d i l y devised. Gas Adsorption on P a r a l l e The e f f e c t of gas a d s o r p t i o n on the f o r c e between i n t e r a c t i n g p l a t e s has been discussed i n an e a r l i e r paper(1) and we summarise the a n a l y s i s here. An a d s o r p t i v e gas and two p a r a l l e l p l a t e s are enclosed i n a p i s t o n - c y l i n d e r arrangement as shown i n Figure 1 and the p l a t e s are p o s i t i o n e d at an e q u i l i b r i u m separa­ t i o n by an e x t e r n a l f o r c e Af ( p o s i t i v e i f the p l a t e s r e p e l one another) which i s p r o p o r t i o n a l to the s u r f a c e area of each p l a t e and which i n an i n f i n i t e s i m a l movement dh c o n t r i b u t e s work -Afdh to the system. The d i f f e r e n t i a l Gibbs f r e e energy of the system, w r i t t e n r e l a t i v e to a reference system having the same temperature bulk pressure and volume as those i n F i g u r e 1 but c o n t a i n i n g no adsorbing p l a t e s , i s shown to be d(G - G*)

=

-(S - S^)dT

σ υ

+

ydn

a

+

2adA

-

Afdh

(1)

v

where η = η - n i s the Gibbs adsorption of the vapour at a chemical p o t e n t i a l of μ and σ i s the d i f f e r e n t i a l surface excess f r e e energy ( i n t e r f a c i a l t e n s i o n ) . I n t e g r a t i o n of Equation (1) at constant Τ, u, σ and h w i t h subsequent d i f f e r e n t i a t i o n and s u b t r a c t i o n from (1) leads to a modified Gibbs adsorption equation 1

-2da

=

fdh

1

+

2rdy

,

(constant T)

(2)

where Γ = n°/2A i s the adsorbate surface excess c o n c e n t r a t i o n per u n i t area of s o l i d p l a t e . I f E q u a t i o n (2) i s r e w r i t t e n i n the l i m i t of zero pressure, i n d i c a t e d by a s u p e r s c r i p t , and sub­ t r a c t e d from ( 2 ) , we o b t a i n

(3)

where Af i s the excess f o r c e over t h a t between the p l a t e s i n vacuum. Thus a change i n the s o l i d / g a s i n t e r f a c i a l t e n s i o n w i t h

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

1.

EVERETT

AND

Adsorption and

RADKE

Interparticle Forces

3

p l a t e s e p a r a t i o n c o n t r i b u t e s to the t o t a l f o r c e . Another more u s e f u l expression f o r Af emerges when the Maxwell r e l a t i o n between f and Γ from Equation (2) i s i n t e g r a t e d w i t h respect to the f u g a c i t y of the adsorbate p*, p*/ 9Γ Af = f - f° = 2RT d In p* (constant T,h) , (4) 9h T,P where the f u g a c i t y i s defined r e l a t i v e to the u n i t - f u g a c i t y i d e a l gas standard s t a t e . This equation presents the a l t e r n a t i v e but e q u i v a l e n t view that changes i n gas adsorption (at constant gas pressure) w i t h p l a t e s e p a r a t i o n i n f l u e n c e the t o t a l f o r c e . The p o t e n t i a l energy between the p l a t e s per u n i t p l a t e area and r e l a t i v e to zero at i n f i n i t e p l a t e s e p a r a t i o n i s defined as the i n t e g r a l of the f o r c e w i t h respect to h at constant Τ and p. A p p l i c a t i o n of t h i s d e f i n i t i o Equatio (3) give V

V

P ' P

=

f

(f

f

" °

)

d

h

=

2 [ ( σ

"

Q 0 )

h

"

( σ

-

a 0 )

«J

(constant Τ,ρ)

· ,

(5)

where ν i s the p o t e n t i a l energy of p l a t e i n t e r a c t i o n i n the zero gas pressure l i m i t and t h e r e f o r e a r i s e s only from the i n t e r molecular forces between the p l a t e s . This vacuum p o t e n t i a l energy may be w r i t t e n approximately as v^ = -k^/l2i\h?- where A^ i s Hamaker's constant f o r the p a r t i c u l a r s o l i d m a t e r i a l ( 2 ) , thus enabling the t o t a l p o t e n t i a l energy curve to be c a l c u l a t e d from knowledge of A^ and the dependence of the i n t e r f a c i a l t e n s i o n on h. A more convenient r e l a t i o n f o r Vp f o l l o w s by combining Equations (4) and (5) and changing the i n t e g r a t i o n order: ΓΡ* ν - v° = 2RT [Γ(«0 - r ( h ) ] d In p* (constant T,h) . (6) Ρ Ρ J 0

Thus the pressure dependence of - Γ(η)] (or the e f f e c t of h on the adsorption isotherm) determines the e f f e c t of the gas adsorbate on the p o t e n t i a l energy of i n t e r a c t i o n . Two opposing e f f e c t s a r i s e when the p l a t e s approach. First the i n t e r m o l e c u l a r p o t e n t i a l f i e l d s emanating from each p l a t e o v e r l a p , causing an increase i n the gas a d s o r p t i o n , and from Equations (4) and (6), i f t h i s increase occurs at a l l pressures an a t t r a c t i v e component to the t o t a l i n t e r a c t i o n ensues. Second, the d i m i n i s h i n g adsorption space decreases the gas adsorption and i f t h i s decrease occurs at a l l p r e s s u r e s , Equations (4) and (6) i n d i c a t e a r e p u l s i v e component to the t o t a l i n t e r a c t i o n . The p r i n c i p l e that an overlapping of force f i e l d s f u r n i s h e s an a t t r a c t i v e increment to the t o t a l p o t e n t i a l energy whereas a d i m i n i s h i n g space f u r n i s h e s r e p u l s i v e increment i s not s p e c i f i c to gas adsorption but, as w i l l be seen l a t e r , can be expressed i n more general terms. These e f f e c t s may be i l l u s t r a t e d q u a n t i t a t i v e l y by con­ s i d e r i n g the adsorption of an i d e a l gas i n the low pressure or Henry's law r e g i o n ( 1 ) . In t h i s model the gas i s d i s t r i b u t e d i n

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

4

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AT

INTERFACES

the i n t e r m o l e c u l a r f o r c e - f i e l d between the p l a t e s , presumed to be a d d i t i v e i n the i n d i v i d u a l p l a t e p o t e n t i a l s , according to a Boltzmann c o n c e n t r a t i o n p r o f i l e ( 3 ) and the p l a t e s e p a r a t i o n dependence of Γ i s determined by i n t e g r a t i n g the excess concentra­ t i o n p r o f i l e over the a v a i l a b l e a d s o r p t i o n space. A p p l i c a t i o n of Equation (6) then permits e v a l u a t i o n of Vp - v . The r e s u l t s of these c a l c u l a t i o n s , using both (10:4) (A) and (9:3) (B) a d s o r p t i o n p o t e n t i a l s , are reviewed i n F i g u r e 2 (compare F i g u r e 5, reference 1) i n which the t o t a l p o t e n t i a l energy curve v i s shown as a f u n c t i o n of h. To estimate the vacuum d i s p e r s i o n - f o r c e p o t e n t i a l Vp ( s o l i d l i n e C) a Hamaker constant of 1 0 " ^ j chosen, corresponding approximately to the experimental value f o r mica (4,5). The dashed curve represents s c h e m a t i c a l l y the short range r e p u l s i o n when the p l a t e s get very c l o s e together. Curves A and Β i n the 0.8-0.9 nm (8-9 X) range i n d i c a t e the e f f e c t of the a d s o r p t i v e gas; they correspon T o r r ) , to a c o l l i s i o n diamete p l a t e a d s o r p t i o n w e l l depth of 8 kT (approximately 22 k J mol"" at room temperature). Although no s t a b i l i s i n g b a r r i e r i s present i n Figure 2, a deep secondary minimum appears even at modest a d s o r p t i o n e n e r g i e s , suggesting t h a t the presence of an a d s o r p t i v e low pressure gas might cause loose f l o c c u l a t i o n of s o l i d a e r o s o l s . At higher pressure, where m u l t i l a y e r a d s o r p t i o n commences, the simple i d e a l gas model i s i n v a l i d and no q u a n t i t a t i v e theory i s p r e s e n t l y a v a i l a b l e to p r e d i c t the v a r i a t i o n of gas a d s o r p t i o n with plate separation. N e v e r t h e l e s s , q u a l i t a t i v e arguments suggest that a r e p u l s i v e f o r c e c o n t r i b u t i o n might occur at a l l separations i n t h i s pressure r e g i o n ( l ) . Adsorbate molecules i n the l a y e r s f u r t h e s t away from the s o l i d surface are not s t r o n g l y i n f l u e n c e d by the s o l i d p l a t e p o t e n t i a l f i e l d and w i l l i n t e r a c t w i t h the outermost molecules adsorbed on the approaching second p l a t e before the p l a t e p o t e n t i a l f i e l d s overlap s i g n i f i c a n t l y . This r e d u c t i o n of a v a i l a b l e adsorption space w i l l decrease at a l l separations and hence lead to a r e p u l s i v e c o n t r i b u t i o n to the t o t a l p o t e n t i a l energy. The p o s s i b i l i t y t h e r e f o r e a r i s e s that at higher gas pressures a p o t e n t i a l b a r r i e r may e x i s t to prevent adhesion of the s o l i d p l a t e s . At pressures between the Henry and m u l t i l a y e r regions intermediate behaviour should be expected (e.g., see F i g u r e 9 of Réf. 1 ) . p

p

w a s

1

N o n - e l e c t r o l y t e Mixture Adsorption on P a r a l l e l P l a t e s The a n a l y s i s of the preceding s e c t i o n i s r e a d i l y extended to the case of a c-component n o n - e l e c t r o l y t e l i q u i d mixture confined between p a r a l l e l p l a t e s ( 1 ) . We review the e s s e n t i a l features by w r i t i n g Equation (2) f o r a multicomponent system and by s u b s t i t u t ­ ing the i s o t h e r m a l and i s o b a r i c Gibbs-Duhem equation of the bulk l i q u i d l e a d i n g to i=c -2da = fdh + 2 £ Γ. dy. (constant Τ,ρ) , (7) i=2 1 , 1

1

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

EVERETT

AND RADKE

Adsorption and Interparticle Forces

Ρ

T,P,V

-L

. Af

Figure 1. Cylinder of volume V containing an amount η of gas at Τ,ρ; and two flat plates each of area A, separated by distance h, held in equilibrium by a force Af

Figure 2. Calculated potential energy curve for two plates in an adsorptive ideal gas A, for 10:4 potential; Β for 9:3 potential at a pressure of 20 Nm' (0.15 Torr) for single plate well depth of 8 kT, and collision diameter 0.34 nm (3.4 A); C van der Waals attraction (Hamaker constant 10' J); dotted line short range repulsion (schematic)

2

19

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

6

ADSORPTION

AT

INTERFACES

c. where Γ. , - Γ. i s the r e l a t i v e adsorption of species i 1,1 ι l w i t h respect to an a r b i t r a r y component 1. Cross d i f f e r e n t i a t i o n of Equation (7) followed by i n t e g r a t i o n w i t h respect to y. y i e l d s a r e l a t i o n analogous to Equation (4) c

1

1

-

f c-1 —00

where

I

dy

3h J

(constant Τ,ρ,η,μ^.

i

i s the f o r c e i n the c-component mixture and f

χ

)

(8) ^ i s the

force i n the l i q u i d mixture from which component i has been eliminated. By a p p l y i n g Equation (8) (c-1) times to e l i m i n a t e s e q u e n t i a l l y the mixtur force e x p r e s s i o n s , we o b t a i far

i=c

-

2

I

3h

i=2

dy. T, ,u P

(constant T,p,h),(9)

ijtl

where f ^ i s the f o r c e between p l a t e s immersed i n the pure l i q u i d of species 1. Equation (9) again r e v e a l s that the i n t e r a c t i o n force i n a l i q u i d mixture i s i n f l u e n c e d by the d i s t a n c e depend­ ence of the a d s o r p t i o n isotherm and contains e i t h e r a t t r a c t i v e terms when ^ increases w i t h decrease i n h or r e p u l s i v e terms when ?i9l decreases w i t h decrease i n h. F i n a l l y , the p o t e n t i a l energy o f i n t e r a c t i o n i n a none l e c t r o l y t e s o l u t i o n r e l a t i v e t o the p o t e n t i a l energy i n pure l i q u i d 1 i s , c f . Equation ( 6 ) , i=c

v (c) p

-

v (l) p

2

I

Κι™

T

~ i , i ^ i

i=2

(constant T,p,h) , (10) where [Γ£ ι(°°) i ( h ) ] i s the change i n the r e l a t i v e a d s o r p t i o n of component i when the two p l a t e s approach at constant Τ,ρ and y£. This r e l a t i o n suggests a means f o r c a l c u l a t i n g the e f f e c t of s o l u t i o n composition on the i n t e r a c t i o n o f p a r t i c l e s i n a l i q u i d medium and, t h e r e f o r e , may provide a path to estimate the v a r i a t i o n of the e f f e c t i v e Hamaker constant w i t h composition. I f we n e g l e c t the e f f e c t of pressure on l i q u i d phase p r o p e r t i e s , [ v p ( l ) - Vp] i s given by Equation (6) when the upper l i m i t o f that i n t e g r a l i s the s a t u r a t i o n f u g a c i t y of component 1. Thus a d d i t i o n o f t h i s l i m i t i n g form o f Equation (6) to (10) gives the p o t e n t i a l energy i n a l i q u i d mixture v ( c ) r e l a t i v e to t h a t i n vacuum v . Q u a n t i t a t i v e a p p l i c a t i o n o f these ideas must await f u r t h e r development i n our understanding of dense gas and l i q u i d mixture a d s o r p t i o n . p

p

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

1.

EVERETT

AND

RADKE

Adsorvtion and

Interparticle Forces

7

E l e c t r o l y t e Adsorption on I d e a l l y P o l a r i z e d P l a t e s E a r l y attempts to e x p l a i n the e f f e c t of e l e c t r o l y t e s on the s t a b i l i t y of lyophobic c o l l o i d s culminated i n the coherent p i c t u r e of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory(6^7)· Extension of the present f o r m u l a t i o n to t h i s problem i s s t r a i g h t ­ forward (8) and provides r i g o r o u s expressions from which, on the b a s i s of a simple model, the DLVO theory i s recovered. Since some of the e a r l i e r work, notably t h a t of 0verbeek(9), was a l s o based on a thermodynamic a n a l y s i s , s e v e r a l of the expressions derived below are c l o s e l y s i m i l a r to p r e v i o u s l y known equations. The present work, however, r e v e a l s some i m p l i c i t assumptions i n e a r l i e r d i s c u s s i o n s , provides a b a s i s f o r f u r t h e r developments, and completes the general account of the forces between c o l l o i d a l p a r t i c l e s immersed e i t h e r i n e l e c t r o l y t e or n o n - e l e c t r o l y t e solutions. Since p o l a r i z e d i f f e r e n t l y , we d i s c u s In the f o l l o w i n g , only an o u t l i n e of theory i s given: a d e t a i l e d account w i l l be p u b l i s h e d s e p a r a t e l y ( 8 ) . By analogy w i t h the s e c t i o n on gas adsorption on p a r a l l e l p l a t e s , two i d e a l l y p o l a r i z a b l e p a r a l l e l p l a t e e l e c t r o d e s are immersed i n an e l e c t r o ­ l y t e s o l u t i o n and enclosed i n a p i s t o n - c y l i n d e r arrangement (Figure 3). The e l e c t r o d e s are h e l d at a s e p a r a t i o n h by the force A f , and are connected to an i n t e r n a l reference e l e c t r o d e , w i t h respect to which the p l a t e s can be h e l d at a p o t e n t i a l E. For convenience we d i s c u s s the p a r t i c u l a r case of a system of platinum e l e c t r o d e s , a d i l u t e aqueous KC1 e l e c t r o l y t e s o l u t i o n , and, s i n c e i t i s r e v e r s i b l e to the e l e c t r o l y t e anion, an i n t e r n a l calomel reference e l e c t r o d e . An e x t e r n a l calomel reference • · Ο e l e c t r o d e c o n t a i n i n g KC1 at a standard c o n c e n t r a t i o n c i s a l s o included. P o t e n t i a l s measured r e l a t i v e to t h i s are denoted by Ε . To describe the system, platinum ions and e l e c t r o n s are chosen a r b i t r a r i l y as the components of the e l e c t r o d e phases, and potassium i o n s , c h l o r i d e ions and water molecules as the com­ ponents of the aqueous phase. Equation (7) may be w r i t t e n i n terms of these components and combined (a) w i t h the bulk e l e c t r o d e and s o l u t i o n Gibbs-Duhem equations, (b) w i t h the i n t e r f a c i a l e l e c t r o - n e u t r a l i t y c o n d i t i o n , Σζ^Γ^ = 0 and (c) w i t h the d i s s o c i a ­ t i o n e q u i l i b r i u m c o n d i t i o n s f o r KC1 and P t ( 1 0 , l l ) . This then y i e l d s the f o l l o w i n g form of the Gibbs adsorption isotherm: β

-2da

=

fdh

where

^

+

2qdE

+

2Γ + Κ

R

Q

du^

(constant Τ,ρ)

,

(11)

i s the r e l a t i v e adsorption of potassium ions w i t h

Q

respect to water at the p l a t i n u m / s o l u t i o n i n t e r f a c e , q i s the i n t e r f a c i a l charge per u n i t area defined by q

=

F(r

p

t

+

-r _) e

=

F(r

c

l

--r

K

+

)

,

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

(12)

8

ADSORPTION

AT

INTERFACES

and Ε i s the c e l l p o t e n t i a l given by fe

=

y . c l

-

y_ e

-

^

-

J y ^ ^

.

(13)

In Equation (13) F i s the Faraday constant and which depends on the e l e c t r i c a l s t a t e of the phase i n which i r e s i d e s ( 1 2 ) , i s the e l e c t r o c h e m i c a l p o t e n t i a l of charged species i ; f o r n e u t r a l components = P£, the o r d i n a r y chemical p o t e n t i a l . When the two p l a t e s are i n f i n i t e l y separated, Equation (11) reduces to the c l a s s i c a l Lippmann equation f o r a p o l a r i z a b l e i n t e r f a c e ( 1 1 ) . By arguments s i m i l a r to those used p r e v i o u s l y , Equation (11) leads to s e v e r a l a l t e r n a t i v e expressions f o r the i n t e r a c t i o n force. I f Equation (11) i s w r i t t e n at the p o i n t (or p o t e n t i a l ) of zero charge (pzc) and, subtracted from Equation ( 1 1 ) , we o b t a i n 3(σ - σ )η f(E) - f f t ) = pzc Sir ·Ρ· · κοι μ

which i s analogous to Equation (3) except that here f at a c e l l p o t e n t i a l Ε i s r e l a t i v e to that i n a s o l u t i o n of the same com­ p o s i t i o n but at the p o t e n t i a l of zero charge. Since the e l e c t r o ­ l y t e c o n c e n t r a t i o n i s constant Ε - E = Ε - E . Three other force expressions are a v a i l a b l e from the Maxwell r e l a t i o n s of Equation ( 1 1 ) * . The c r o s s - d i f f e r e n t i a l between f and q upon i n t e g r a t i o n over the celjj, p o t e n t i a l y i e l d s p z c

f(E)

-

ftt > pzc

p z c

Ε pzc (constant T , p , y

KC1

,h)

.

(15)

V a r i a t i o n of s u r f a c e charge d e n s i t y w i t h p l a t e s e p a r a t i o n at con­ stant c e l l p o t e n t i a l and s o l u t i o n composition w i l l a f f e c t the force. Furthermore, the c r o s s - d i f f e r e n t i a l between f and Γ, on i n t e g r a t i o n w i t h respect to the chemical p o t e n t i a l of potassium c h l o r i d e , gives the force i n a s o l u t i o n having a chemical p o t e n t i a l P K C 1 > r e l a t i v e to that i n a standard reference s o l u t i o n at the same i n t e r n a l c e l l p o t e n t i a l . When the c o n c e n t r a t i o n of potassium c h l o r i d e i s changed at constant E, the p o t e n t i a l of the i n t e r n a l e l e c t r o d e , and hence that of the p l a t e s , changes r e l a t i v e to the e x t e r n a l e l e c t r o d e . An i n c r e a s e i n the c o n c e n t r a t i o n of potassium c h l o r i d e c decreases the p o t e n t i a l of the p l a t e s and by a s u i t a b l e choice of c the p l a t e s can be brought to the p o t e n t i a l o£ zero charge (pzc) which, r e l a t i v e to the e x t e r n a l e l e c t r o d e i s Epzc* We choose t h i s c o n c e n t r a t i o n C p as reference concentra­ t i o n , whence Z C

* There are e i g h t p o s s i b l e Maxwell equations i n v o l v i n g f from Equation ( 1 1 ) . We c i t e only three here.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

1.

EVERETT

AND RADKE

9

Adsorption and Interparticle Forces

Γ pzc

I

Κ +

· 2°Ί 3h J Η

T

E

'P' '\ci

(constant T,p,E,h) (16) DZC where Pj^Cl * 4cCl n e g a t i v e l y charged p l a t e s and i s greater f o r p o s i t i v e l y charged p l a t e s . A t h i r d Maxwell r e l a t i o n r e s u l t s i n d i r e c t l y from Equation (11) by using the i d e n t i t y 3E 3h [SE - - 1 s l e s s

t n a n

f

o

r

(15)

followed by s u b s t i t u t i o n i n the d i f f e r e n t i a l form o f Equation and i n t e g r a t i o n w i t h respec f(q)

-

f(0) =

i3E

l

dq

9h

Γ

(constant Τ , ρ , ν ^ , η )

(17)

,

where the lower l i m i t of i n t e g r a t i o n i s again taken as the p z c . These f o r c e expressions may be i n t e g r a t e d according t o Equation (5) to o b t a i n the p o t e n t i a l energy o f i n t e r a c t i o n r e l a t i v e t o that when the p l a t e s are at the pzc. Thus Equation (14) y i e l d s 2[(σ

σ ) pzc h

- (σ

σ ) 1 pZC (18) ι

(constant Τ,ρ,h)

.

Again the v a r i a t i o n o f the i n t e r f a c i a l t e n s i o n d i f f e r e n c e (σ - CTp ) w i t h p l a t e s e p a r a t i o n determines the p o t e n t i a l energy of i n t e r a c t i o n ( c f . Equation (5)). The d i f f e r e n c e (σ^ -σ^) i s c o n v e n t i o n a l l y c a l l e d the f r e e energy' o f the charged i n t e r a c t i n g p l a t e s 07,9). Equation (15) with i n v e r s i o n o f the order o f i n t e g r a t i o n gives ZC

f

[q(«0

" q(h)] dE

~pzc (constant T,p,h)

,

(19)

where i t i s assumed that E p i s independent of h. An equation s i m i l a r to Equation (19) has been d e r i v e d e a r l i e r both by an i n t u i t i v e argument and by a l e s s e x p l i c i t thermodynamic treatment (7). From Equation (16) we o b t a i n f o r n e g a t i v e l y charged p l a t e s Z C

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

10

ADSORPTION

A T INTERFACES

^KCl V

E

' W

E

-V

O

-

2

tV,H 0 o

( h

(

d

> " V,H 0 ^ ^Cl 9

Z C

U? TCCl (constant T,p,h)

.

(20)

The general p r i n c i p l e enunciated i n the e a r l i e r s e c t i o n on gas adsorption on p a r a l l e l p l a t e s again a p p l i e s to the approach o f charged p l a t e s a t constant i n t e r n a l c e l l p o t e n t i a l and constant bulk c o n c e n t r a t i o n of potassium c h l o r i d e , provided a t t e n t i o n i s focussed on the p r e f e r e n t i a l l y adsorbed i o n ( c o u n t e r - i o n ) . Thus f o r n e g a t i v e l y charged p l a t e s Γ + i s positive. As the p l a t e s approach the d i f f u s e p a r t f th doubl l a y e r begi t overla and s i n c e Ε i s kept constant between the p l a t e s ; Γ (°°) (h) plate κ. >"2 experience a r e p u l s i v e i n t e r a c t i o n . Conversely, f o r p o s i t i v e l y charged p l a t e s Γ + i s negative and increases w i t h decrease i n h, w h i l e Γ -

i s p o s i t i v e and decreases as the p l a t e s approach. fti^J

LI

Thus, i f the adsorption of the counter-ion decreases as the p l a t e s approach, adsorption e f f e c t s w i l l make a r e p u l s i v e c o n t r i b u t i o n t o the p o t e n t i a l o f i n t e r a c t i o n . Superimposed upon the p u r e l y e l e c t r o s t a t i c i n t e r a c t i o n s w i l l be the i n t e r m o l e c u l a r i n t e r a c t i o n s of the ions and the s o l v e n t which are u s u a l l y neglected as a second-order e f f e c t . F i n a l l y , i n t e g r a t i o n of Equation (17) gives V

p

(

q

' W

"

ν

ρ

( 0

'\α

}

=

2 |^[(E(h) - E C ) ] dq (constant Τ,ρ,η)

,

(21)

where v ( 0 ) i s again the p o t e n t i a l energy a t the pzc. For ideally p o l a r i z a b l e p l a t e s , because no charge can be t r a n s f e r r e d across the i n t e r f a c e , i t i s p o s s i b l e to b r i n g the p l a t e s together a t con­ s t a n t charge, and a t the same time to maintain an e q u i l i b r i u m i o n i c distribution. The d i s t a n c e dependence o f the changing c e l l p o t e n t i a l a t constant charge now determines the p o t e n t i a l energy of i n t e r a c t i o n . A q u a n t i t a t i v e i l l u s t r a t i o n of the thermodynamic f o r m u l a t i o n i s provided by the simple model o f p o i n t charges ( K and CI f o r convenience) d i s t r i b u t e d i n a uniform l i q u i d d i e l e c t r i c confined between two conducting p a r a l l e l p l a t e s . Since the p o i n t charges i n t e r a c t only w i t h the f i e l d s emanating from the charged p l a t e s , the e l e c t r o c h e m i c a l p o t e n t i a l o f an i o n i c species may be r i g o r o u s l y separated i n t o a p u r e l y chemical and a p u r e l y e l e c t r o s t a t i c part(12), p

+

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

1.

EVERETT

\

=

μ

AND

+

£

Adsorption and

RADKE

z.F

Interparticle Forces

11

,

(22)

where z. i s the i o n charge and φ i s the l o c a l e l e c t r o s t a t i c potential. This s e p a r a t i o n leads to a Boltzmann c o n c e n t r a t i o n d i s t r i b u t i o n and upon combination w i t h the Poisson equation from c l a s s i c a l e l e c t r o s t a t i c s provides a d i f f e r e n t i a l equation to describe the s p a t i a l v a r i a t i o n of the l o c a l e l e c t r o s t a t i c p o t e n t i a l between the i n t e r a c t i n g p l a t e s ( 1 3 ) . For small e l e c t r o ­ s t a t i c p o t e n t i a l s the Poisson-Boltzmann equation i s r e a d i l y i n t e ­ grated and y i e l d s two expressions f o r the r e l a t i o n between the surface charge d e n s i t y q and the surface e l e c t r o s t a t i c p o t e n t i a l Φ depending on the boundary c o n d i t i o n imposed at the p l a t e surface. F i r s t , i f the surface p o t e n t i a l i s h e l d constant then the reduced surface charge d e n s i t y becomes ο

where c i s the bulk molar c o n c e n t r a t i o n of potassium c h l o r i d e , λ i s the Debye length defined f o r a 1:1 e l e c t r o l y t e i n a l i q u i d solvent of uniform d i e l e c t r i c constant, ξ = Ρφ /RT i s a reduced surface p o t e n t i a l and h = h/λ i s the reduced d i s t a n c e between the charged plates. SeconSly, i f the surface charge d e n s i t y remains constant then the surface p o t e n t i a l must vary according to q

W

r ΊΓ

=

C 0 t h

(

V

(constant q)

.

(24)

F i n a l l y , the reduced surface excess c o n c e n t r a t i o n (Γ ) of potassium ions i s Γ

+

Κ ,Η 0

A,

2

F

=

r

TZ

=

ξ

- ο

t a n h

(25)

I "

The reduced surface excess c o n c e n t r a t i o n of c h l o r i d e ions i s equal and opposite. Equations (22) to (25) supply the r e q u i r e d r e s u l t s from the point-charge model. S u b s t i t u t i o n of Equations (23) and (22), w r i t t e n once f o r c h l o r i d e ions and once f o r e l e c t r o n s , and Equation (12) i n t o Equation (19) y i e l d s -

y^w

- y pzc>w E

r

-

°

2XcRT =

ζ [ΐ 2 ο

[q l ) and ν ( f ^ ^ ) are e q u a l , since the P t e l e c t r o d e s ρ pzc ρ Q both have the same p o t e n t i a l E , r e l a t i v e to the e x t e r n a l standard reference e l e c t r o d e wnen the pzc i s independent o f c. As shown i n Figure 4 the p l a t e s experience a r e p u l s i o n a t a l l distances. I t may be noted that whereas i n the case o f gas a d s o r p t i o n , r e p u l s i o n force i n the case o f e l e c t r o l y t e case, from e l e c t r o s t a t i c f o r c e s : i o n s i z e e f f e c t s may a l s o appear as a second c o n t r i b u t i o n . A p p l i c a t i o n of the point-charge model to Equation (21) pro­ vides a constant-charge p o t e n t i a l energy of i n t e r a c t i o n which, because of the d i f f e r e n t i n t e g r a t i o n path, i s d i s t i n c t from Equation (26). From Equations (13), (21), (22) and (23) we obtain Z C

p Z

0

i

z c

E

K C 1

p z c

y^w - y^w 2 cRT

^o

( h

r

9

" 5

)

f

= ξ^(-)[ ο^ 0

o

( 0 O )

^

d q

1 J q -i] Λ h

0

(constant T,p,h)

.

(27)

This r e s u l t i s that of the DLVO theory a p p l i e d to c o l l o i d a l p a r t i c l e s which c o l l i d e w i t h a constant surface charge(14). To maintain constant charge when two charged polarïzable p l a t e s approach, the e f f e c t of o v e r l a p p i n g of the d i f f u s e p a r t s of the double l a y e r s which tends to decrease the adsorption of the counter-ions has to be o f f - s e t by an increase i n the p o t e n t i a l . Thus, from Equation (27), a r e p u l s i v e p o t e n t i a l energy i s generated. We note (Figure 4) that the r e p u l s i v e e f f e c t i s more pronounced f o r the constant charge i n t e g r a t i o n path and that a t small separations the constant-charge p o t e n t i a l energy approaches infinity. Since the present l i n e a r i s e d point-charge model equations apply only f o r s m a l l values of the surface p o t e n t i a l , Equation (27) must break down f o r s e p a r a t i o n distances near zero. E l e c t r o l y t e Adsorption on I d e a l l y Non-polarizable P l a t e s To discuss the i n t e r a c t i o n between r e v e r s i b l e ( i . e . , i d e a l l y n o n - p o l a r i z a b l e ) p a r t i c l e s the platinum e l e c t r o d e s i n F i g u r e 3 are replaced by s i l v e r / s i l v e r c h l o r i d e e l e c t r o d e s . Since s i l v e r and

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

EVERETT

A N D RADKE

Adsorption and Interparticle Forces

Ρ

A -

A f

c

H 02

KCI(c) Hg Ci 2

r

1] +0 Ε ~?

KCKc^K 5-

metric aqueous electrolyte (potassium chloride) and two plates charged to a potential Ε relative to an internal ref­ erence calomel electrode and to a potential F? relative to an external standard calomel electrode

Figure 4. Calculated effect of a dilute point-ion electrolyte on the potential energy for two charged plates from Equations 26 and 27

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14

ADSORPTION

AT

INTERFACES

c h l o r i d e ions are present i n the aqueous s o l u t i o n to an extent determined by the s o l u b i l i t y product o f s i l v e r c h l o r i d e K^gCl they both serve as p o t e n t i a l determining ions f o r the s i l v e r c h l o r i d e electrodes. F o l l o w i n g the e a r l i e r procedure, the modified Gibbs a d s o r p t i o n equation f o r the r e v e r s i b l e e l e c t r o d e system i s -2da

=

fdh +

2Γ +

άμ^

χ

(constant Τ,ρ)

.

(28)

Comparison o f Equation (28) w i t h Equation (11) d i s c l o s e s the absence of the c e l l p o t e n t i a l as an independent v a r i a b l e . For r e v e r s i b l e e l e c t r o d e s a t constant temperature and pressure the c e l l p o t e n t i a l cannot be v a r i e d s i n c e Ε i s determined by the chemical p o t e n t i a l s of pure phases o n l y : F E

-

%

+

% c i -

Because the i n t e r n a l c e l l p o t e n t i a l i s no longer an independent v a r i a b l e , n o n - p o l a r i z a b l e e l e c t r o d e s cannot approach r e v e r s i b l y under the c o n d i t i o n of constant charge. By r e p e t i t i o n of the thermodynamic development given i n the preceding s e c t i o n , the p o t e n t i a l energy o f i n t e r a c t i o n between n o n - p o l a r i z a b l e e l e c t r o d e s becomes pzc ^kci = 2 [V,H 9 0 ( h > " V,H 9 0 ( T O >J%:ci

y w - v©

y

KCl (constant T,p,h)

,

(30)

which i s analogous to Equation (20) and again i n d i c a t e s the r o l e of e l e c t r o l y t e a d s o r p t i o n i n determining the e l e c t r o s t a t i c p a r t o f the t o t a l p o t e n t i a l energy curve f o r i n t e r a c t i n g r e v e r s i b l e electrodes. A p p l i c a t i o n of the point-charge model to Equation (30) y i e l d s a r e s u l t s i m i l a r to t h a t of the constant p o t e n t i a l DLVO theory. S u b s t i t u t i o n of the e l e c t r o c h e m i c a l p o t e n t i a l e q u a l i t y c o n d i t i o n of the c h l o r i d e (or s i l v e r ) ions i n the aqueous and s o l i d s i l v e r c h l o r i d e phase, Equations (22), ( 2 5 ) , and the r e l a t i o n t h a t 2

dy

R C 1

=

RT d I n

( 1

τ

+

Ζ

1

+

/ 4 K AgCl] — 2 - j r

J

g i v e s , as a f i r s t order approximation o f a s e r i e s expansion,

-κ

jxzxt

ξ

=

0

& -

t a n h

[tJJ I·

1

+

- V J

·

( 3 1 )

We n o t i c e , however, a c o r r e c t i o n term t o the constant p o t e n t i a l DLVO theory i n v o l v i n g the s o l u b i l i t y product of the r e v e r s i b l e electrodes. For substances such as s i l v e r c h l o r i d e ( s o l u b i l i t y product M O " ( m o l d m " ) the c o r r e c t i o n term i s unimportant f o r added K C l concentrations of > 10"^ mol dm" . The c o r r e c t i o n 1 0

3

2

3

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

1.

EVERETT A N D RADKE

15

Adsorption and Interparticle Forces

f a c t o r w i l l not be n e g l i g i b l e f o r more s o l u b l e substances, e.g., MgC0 , K = 2.6 χ 10~-> when c i s l e s s than 5 χ 10"" mol dm"". The present thermodynamic treatment thus provides a means f o r extending the DLVO theory to i n c l u d e i n t e r a c t i o n s between more s o l u b l e dispersed s o l i d s . 2

3

3

s

Conclusions A general thermodynamic treatment i s presented t o d e s c r i b e the e f f e c t of adsorption o f gases and mixtures o f both e l e c t r o ­ l y t e s and n o n - e l e c t r o l y t e s on the i n t e r a c t i o n o f s o l i d p a r t i c l e s . The f o r m u l a t i o n provides a coherent p i c t u r e o f the e f f e c t o f a d s o r p t i o n i n terms o f the opposing tendencies o f the overlap o f the i n t e r p a r t i c l e f o r c e f i e l d s ( i n t e r m o l e c u l a r o r e l e c t r o s t a t i c ) and o f the a v a i l a b i l i t y o f adsorption space. The two i d e a l i s e d cases o f p o l a r i z a b l e an to d e s c r i b e the i n t e r a c t i o medium. A q u a n t i t a t i v e point-charge model a p p l i e d t o both types of i n t e r a c t i n g p a r t i c l e s y i e l d s , under d i f f e r e n t c o n d i t i o n s , the constant p o t e n t i a l and constant charge Derjaguin-Landau-VerweyOverbeek t h e o r i e s . Extension o f the DLVO theory t o the case o f less sparingly soluble solids i s outlined.

Literature Cited 1. Ash, S.G., Everett, D.H. and Radke, C.J., J.Chem.Soc.Faraday Trans.II, (1973), 69, 1256 2. Hamaker, H.C., Physica (l937), 4, 1058 3. Barker, J.A. and Everett, D.H., Trans.Faraday Soc., (1962), 58, 1608 4. Tabor, D. and Winterton, R.H.S., Proc.Roy.Soc. (1969), 312A, 435 5. I s r a e l a c h v i l i , J.N. and Tabor, D., Proc.Roy.Soc., (1972), 331A, 19 6. Derjaguin, B.V. and Landau, L., Acta Physicochem.USSR (1941) 14, 633 7. Verwey, E.J. and Overbeek, J.Th.G., "Theory of the S t a b i l i t y of Lyophobic Colloids", Elsevier, Amsterdam, 1948 8. Everett, D.H. and Radke, C.J., i n preparation 9. Overbeek, J.Th.G., in "Colloid Science", H.R.Kruyt, Ed., Vol. I , Chap. 4,6, Elsevier, Amsterdam, 1952 10. Parsons, R., "Thermodynamics of E l e c t r i f i e d Interfaces", i n 'Source Book of Colloid and Surface Chemistry', H. van Olphen, Ed., to be published 11. Newman, J . , "Electrochemical Systems", Prentice-Hall, Englewood Cliffs, New Jersey, 1973 12. Guggenheim,E.A.,"Thermodynamics",5th ed., North-Holland, Amsterdam, 1967 13. Parsons, R., in "Modern Aspects of Electrochemistry", J.O'M. Bockris,Ed.,Vol. 1, Chap. 3, Academic Press, New York, 1954 14. Usui, S., J. Colloid InterfaceSci.,(1973), 44, 107

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2 Configurational Behavior of Isolated Chain Molecules Adsorbed from Athermal Solutions M.

LAL

and M . A. T U R P I N

Unilever Research, Port Sunlight, Cheshire L62

4XN,

England

K. A. R I C H A R D S O N Department of Polymer and Fibre Science, University of Manchester, Institute of Science and Technology, Manchester, England D. S P E N C E R Unilever Computing Services Ltd., Bromborough Port, Cheshire, England

Models which have been considered i n the various a n a l y t i c a l treatments of s t a t i s t i c a l thermodynamic and conf i g u r a t i o n a l behaviour of adsorbed polymer layers most often ignore such important c h a r a c t e r i s t i c s of the adsorbate molecules as the excluded-volume e f f e c t and bond r o t a t i o n a l hindrance (1,2,3,4,5). Further, the procedures used for introducing solvent and concentration e f f e c t s are less s a t i s f a c t o r y (6). The present a n a l y t i c a l developments are thus limited to oversimplified models that would have only a little correspondence with r e a l systems. It i s , therefore, desirable to investigate alternative approaches which would be e f f e c t i v e i n the study of more r e a l i s t i c models. The success of Monte Carlo computer simulation method i n investigating the configurational and thermodynamic behaviour of systems involving polymer molecules assuming models of varying complexity i s well established (7,8,9). This approach i s based on the assumption that it i s possible to generate a random sample of molecular configurations which would adequately simulate the canonical ensemble corresponding to the model assumed. Then the mean values of various properties over such a sample would converge to the canonical ensemble averages. The extension of the Monte Carlo method to polymers i n t e r a c t i n g with interfaces has so f a r been c a r r i e d out only to a limited extent (10,11). This i s because of a serious d i f f i c u l t y pertaining to sample convergence that one would encounter i n the case of strongly i n t e r a c t i n g systems, i f the usual techniques are used. The first objective underl y i n g the present work i s to introduce a more sophisticated Monte Carlo scheme i n t h i s area with the aim of overcoming the d i f f i c u l t y just mentioned. The successful application of such a scheme should lead to r e l i a b l e studies on the models which adequately take into account the solvent and concentration effects. This i s the first of a series of papers on our 16

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2.

LAL E T AL.

Isolated Chain Molecules

s t u d i e s of the c o n f i g u r a t i o n a l s t a t e of c h a i n molecules i n the a d s o r b e d s t a t e . H e r e we d e s c r i b e t h e p r e s e n t a p p r o a c h and p r e s e n t i t s a p p l i c a t i o n t o an i s o l a t e d e x c l u d e d - v o l u m e c h a i n i n t e r a c t i n g with a surface. T h i s m o d e l may be c o n s i d e r e d t o r e p r e s e n t a polymer m o l e c u l e adsorbed from an e x t r e m e l y dilute athermal solution. The

Present

Approach

The e q u i l i b r i u m v a l u e o f a q u a n t i t y , q, q, c a n i d e n t i f i e d w i t h the c a n o n i c a l ensemble a v e r a g e :

be

q exp(-U/KT) d i l fexp(-U/KT) dSL where e x p ( - U / K T ) i s t h v a l u e q of the q u a n t i t y integration e q u a t i o n extend o v e r t h e t o t a l c o n f i g u r a t i o n a l phase space, of the system. L e t us draw a random sample o f c o n f i g u r a t i o n s f r o m t h e p h a s e s p a c e SI. The mean o f t h e q u a n t i t y q, , over such a sample i s g i v e n as exp(-UVKT)

= S

where S i s t h e m a g n i t u d e o f t h e s a m p l e . The Monte C a r l o a p p r o a c h assumes t h a t f o r l a r g e S, w o u l d c o n v e r g e t o q . For systems i n v o l v i n g s t r o n g i n t e r a c t i o n s , sampling procedures b a s e d on p u r e l y random c o l l e c t i o n o f c o n f i g u r a t i o n s w i l l n o t be s a t i s f a c t o r y a s t o a c h i e v i n g c o n v e r g e n c e t h a t w i l l p r o d u c e estimates w i t h i n reasonable l i m i t s of u n c e r t a i n t y . The way t o o b t a i n samples w i t h a c c e p t a b l e c o n v e r g e n c e i n such c a s e s i s t o u t i l i s e a s a m p l i n g scheme w h i c h f a v o u r s t h e h i g h d e n s i t y r e g i o n s o f the p h a s e s p a c e . I n a p r e v i o u s p u b l i c a t i o n we p r e s e n t e d a scheme s u i t a b l e f o r t a c k l i n g c h a i n m o l e c u l a r models i n v o l v i n g i n t e r - s e g m e n t a l i n t e r a c t i o n s ( 1 2 ) . This scheme c a n be m o d i f i e d so a s t o be c o n g e n i a l t o t h e m o d e l under the p r e s e n t c o n s i d e r a t i o n . The p r e s e n t method i n v o l v e s g e n e r a t i n g a homogeneous markov s e q u e n c e o f c o n f i g u r a t i o n s w i t h o n e - s t e p t r a n s i t i o n p r o b a b i l i t i e s ( p . .) g i v e n s u c h t h a t t h e c o n f i g u r a t i o n s a m p l e thus o b t a i n e d assumes Boltzmann d i s t r i b u t i o n i n t h e l i m i t of a l o n g sequence. Hence t h e s i m p l e means o v e r s u c h a s a m p l e c a n be i d e n t i f i e d w i t h t h e c a n o n i c a l e n s e m b l e a v e r a g e s . The d e s i r e d c o n f i g u r a t i o n s e q u e n c e s c a n be g e n e r a t e d f o l l o w i n g t h e commonly u s e d a s y m m e t r i c p r o c e d u r e a c c o r d i n g t o w h i c h t h e t r a n s i t i o n p r o b a b i l i t i e s a r e g i v e n as (13)

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

18

ADSORPTION

1 f o r U. J

x

INTERFACES

V

±

1-P

The s e q u e n c e c a n s t a r t f r o m any a l l o w e d c o n f i g u r a t i o n c h o s e n arbitrarily. L e t the e n e r g y c o r r e s p o n d i n g t o t h i s c o n ­ f i g u r a t i o n be U. Consider another c o n f i g u r a t i o n , with e n e r g y 'U, w h i c h c a n be d e r i v e d f r o m t h e p r e v i o u s one by some random p r o c e s s . I f 1J i s l e s s t h a n o r e q u a l t o U, a c c e p t t h e new c o n f i g u r a t i o n i n t h e s e q u e n c e . E l s e , c h o o s e a random number, x, b e t w e e n 0 and 1 and compare i t w i t h r = [exp(-U/KT)/exp(-U/KT)] . I f r > x, a l s o t h e n t h e new c o n f i g u r a t i o n assume O t h e r w i s e , r e j e c t th r e t u r n t o t h e p r e c e d i n g one, w h i c h means t h a t t h e same c o n ­ f i g u r a t i o n i s counted a g a i n i n the sequence. Repeat the above p r o c e s s t o a c q u i r e f u r t h e r moves. I n t h i s way t h e s e q u e n c e c a n be e x t e n d e d t o any l e n g t h . I n t h e p r e v i o u s scheme t h e mechanism by w h i c h t h e s y s t e m moved f r o m one c o n f i g u r a t i o n t o a n o t h e r i n v o l v e d t h e r o t a t i o n of a s i n g l e bond i n t h e c h a i n . T h i s r e s u l t e d i n the changes i n t h e p o s i t i o n s of a l l the segments s u c c e e d i n g t h e r o t a t i n g bond. T h i s scheme, a l t h o u g h s u c c e s s f u l i n c a s e of f r e e chains, i s u n s u i t a b l e i n the p r e s e n c e of an i n t e r f a c e . F o r t h e p r e s e n t m o d e l we d e v e l o p e d a mechanism b a s e d on t h e c o n s i d e r a t i o n t h a t t r a n s i t i o n f r o m one c o n f i g u r a t i o n t o a n o t h e r o c c u r s as a c o n s e q u e n c e o f c h a n g e s i n t h e r o t a t i o n a l p o s i t i o n s o f o n l y a few c o n s e c u t i v e b o n d s . L e t us t e r m s u c h a s e q u e n c e o f b o n d s a s t h e t r a n s i t i o n r e g i o n (figure 1). The p o s i t i o n o f t h e t r a n s i t i o n r e g i o n i n t h e m o l e c u l e i s assumed t o be s t o c h a s t i c i n n a t u r e . In the p r e s e n t scheme t h e number o f bonds c o n s t i t u t i n g t h e t r a n s i t i o n region is four. T h i s i s t h e minimum s i z e o f t h e r e g i o n w h i c h must be c o n s i d e r e d i n o r d e r t o g e n e r a t e a l l t h e p o s s i b l e c o n f i g u r a t i o n s w h i c h c a n be assumed by a l i n e a r c h a i n m o l e c u l e confined to a tetrahedral l a t t i c e . We f u r t h e r assume t h a t b e y o n d t h e t r a n s i t i o n r e g i o n no c h a n g e s i n t h e p o s i t i o n s o f t h e segments w i l l o c c u r . In o r d e r t h a t the samples a c h i e v e the r e q u i r e d convergence, i t i s n e c e s s a r y t h a t t h e e r g o d i c i t y and s t e a d y s t a t e c o n d i t i o n s a r e met. In simple terms, the e r g o d i c i t y c o n d i t i o n s t i p u l a t e s t h a t s t a r t i n g f r o m a c o n f i g u r a t i o n i t i s p o s s i b l e t o r e a c h any p e r m i s s i b l e c o n f i g u r a t i o n i n a f i n i t e number o f s t e p s , and t h a t t h e sample c o n t a i n s no p e r i o d i c i t i e s . The s t e a d y s t a t e c o n ­ d i t i o n states that

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2.

LAL E T AL.

Isolated Chain Molecules

ZJ i

u. p.. ι J

=

u. J

a

19

for a l l j

where u . a n d u . a r e t h e a b s o l u t e p r o b a b i l i t i e s o f t h e o c c u r r e n c e o f s t a t e s i and j i n t h e sample. We r e c k o n t h a t t h e s a m p l e s g e n e r a t e d by o u r scheme a r e i n r e a s o n a b l e a c c o r d w i t h t h e above c r i t e r i a . J

The

Model

The g e o m e t r y c o r r e s p o n d i n g t o t h e f o u r v a l e n c e bonds o f t h e c a r b o n atom i m p l i e s t h a t p o l y m e r m o l e c u l e s w i t h -C-C-C"back-bone" can be a d e q u a t e l y r e p r e s e n t e d by t h e t e t r a h e d r a l chains. Our model i s t h u s b a s e d o n a t e t r a h e d r a l l a t t i c e i n which t h e l a t t i c e s i t e o r by s o l v e n t m o l e c u l e s C-C^" bond a n g l e s i n such c h a i n s i s 109.28°, a n d t h e v a l u e s o f t h e r o t a t i o n a l a n g l e s w h i c h t h e bonds c a n assume a r e 0 ( t r a n s ) , 120° ( g a u c h e ) and 240° (gauche"). The l a t t i c e m o d e l assumes t h a t t h e a b o v e v a l u e s o f t h e bond a n g l e s a n d t h e bond r o t a t i o n a l a n g l e s a r e i n v a r i a n t . This approximation seems n o t u n r e a s o n a b l e . I t i s necessary t o s t i p u l a t e that t h e c h a i n s w i l l assume o n l y t h o s e c o n f i g u r a t i o n s w h i c h do n o t c o n t a i n m u l t i p l e occupancies (the excluded-volume c o n d i t i o n ) . The a d s o r b e n t i s r e p r e s e n t e d by a t w o - d i m e n s i o n a l s u r f a c e i n the l a t t i c e with t h e a d s o r p t i o n s i t e s l o c a t e d a t the l a t t i c e points. +

In s o l u t i o n s t h e r e e x i s t t h r e e k i n d s of i n t e r a c t i o n s : ( 1 ) segment/segment i n t e r a c t i o n s , ( 2 ) s o l v e n t / s o l v e n t i n t e r a c t i o n s and (3) segment/solvent interactions. Let ^22' with

^12

d e n c r t e

>

respectively,

t h e segment/segment,

pairs.

The e n e r g y

segment/segment

segment/solvent

change a c c o m p a n y i n g t h e f o r m a t i o n

pair,

Δ € = € 1

the energies associated

s o l v e n t / s o l v e n t and

Δ β^,

11

+ €

of a

w i l l be

22

- 2 €

12

Δ^ serves as t h e s o l v e n t parameter i n t h e model. Good s o l v e n t s o p p o s e t h e f o r m a t i o n of segment/segment p a i r s , w h i c h i m p l i e s t h a t f o r such s o l v e n t s Δ ^ assumes p o s i t i v e v a l u e s . I n b a d s o l v e n t s t h e f o r m a t i o n o f segment/segment p a i r s w i l l be f a v o u r e d , hence Δ ^ w i l l be n e g a t i v e . Δ ^ = 0 corresponds t o athermal s o l u t i o n s . The s e c o n d e n e r g y p a r a m e t e r c h a r a c t e r i s i n g o u r m o d e l i s the segment/surface b i n d i n g energy Δ C » which i s d e f i n e d as

a

2

IS

2S

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

20

ADSORPTION

where and

£ ^ *

i s the ^ ^ s

AT

INTERFACES

energy a s s o c i a t e d with a segment/surface a s s o c i a t e d w i t h a s o l v e n t / s u r f a c e bond.

n a

bond

s

Thus * t h e e n e r g y c h a n g e due t o t h e f o r m a t i o n o f a s e g m e n t / s u r f a c e bond a t t h e e x p e n s e o f a s o l v e n t / s u r f a c e b o n d . The a d s o r p t i o n c a n o n l y t a k e p l a c e i f Δ ^ i s negative. Computation A c o m p u t e r p r o g r a m was d e v e l o p e d f o r g e n e r a t i n g c o n f i g u r a t i o n s e q u e n c e s f o l l o w i n g o u r scheme a s s u m i n g t h e m o d e l d e s c r i b e d i n s e c t i o n 3. The p r o g r a m p r o c e e d e d a s follows : 1.

Read t h e Ν

following

= total

of

data:

segment

M L

= l e n g t h of th = l e n g t h of i n t e r v a l i n the sequence c o r r e s p o n d i n g the output of data i n i n t e r m e d i a t e stages Δ€^Δ€ : the energy parameters.

to

2

2.

G e n e r a t e an

i>y f

x

±

initial

x

configuration

;

z ±

; *N> N> V

N]

[_ l ;

(

n

±

, y

i

, z

Χ

l>

>y * ±

z

±

2'^2^2'

····

)

define

the

p o s i t i o n of

3.

Define

the

adsorbent

4.

D e t e r m i n e t h e v a r i o u s q u a n t i t i e s o f i n t e r e s t ( e . g . number o f s e g m e n t s on t h e s u r f a c e , s q u a r e o f t h e e n d - t o - e n d d i s t a n c e , s q u a r e o f t h e r a d i u s of g y r a t i o n , e t c . ) .

5.

G e n e r a t e a new c o n f i g u r a t i o n by r a n d o m l y s e l e c t i n g f o u r c o n s e c u t i v e bonds i n any p a r t of t h e c h a i n and m o v i n g t h e s e bonds t o an a l t e r n a t i v e c o n f i g u r a t i o n , w h i l s t t h e remainder of the molecule i s u n a l t e r e d .

6.

Check t h e new c o n f i g u r a t i o n f o r e x c l u d e d - v o l u m e . c o n f i g u r a t i o n i n v o l v e s m u l t i p l e o c c u p a n c y of any s i t e , go t o 14.

7.

C a l c u l a t e Δϋ, the d i f f e r e n c e between the p r e v i o u s and t h e new configuration.

8.

I f Δυ

9.

Calculate r =

10.

Generate a

11.

I f r > x,

12.

Go

13.

Calculate

to

i s p o s i t i v e or

a

Z

plane such t h a t

zero,

go

to

y = x+

constant.

energies

I f the lattice

of

the

13.

exp(AU/KT).

random number go

segment i .

to

( x ) b e t w e e n 0 and

1.

13.

14. the

desired

q u a n t i t i e s f o r the

new

configuration.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2.

LAL E T AL.

21

Isolated Chain Molecules

14.

Accumulate the

calculated

15.

I f the i s any

16.

Print

17.

I f the t o 5.

18.

C a l c u l a t e the simple over the sample.

19.

P r i n t the

number of integer), the

quantities.

configurations go t o 5.

desired

number o f

g e n e r a t e d Φ AL

(where

A

information. configurations

a v e r a g e s of

computed a v e r a g e s and

g e n e r a t e d increases r a p i d l y with the increase i n ( - Δ ^ 2 ^ ^ -Δ € / K T = 0.5, l e s s t h a n 1 0 % o f t h e s e g m e n t s a r e a d s o r b e d , while a t -Δ62/ΚΤ 1·4, a p p r o x i m a t e l y 7 5 % o f t h e segments w o u l d be o n t h e s u r f a c e . The < V> v e r s u s - Δ ^ 2 ^ e x t r a p o l a t e d t o d e t e r m i n e t h e p o i n t b e l o w w h i c h < V> i s z e r o . S u c h a p o i n t i s known a s t h e c r i t i c a l p o i n t , and t h e c o r r e s p o n d ­ ing energy i s the c r i t i c a l energy of a d s o r p t i o n . For the p r e s e n t s y s t e m (-à € /KT^ f o u n d t o b e ~0.45. To o u r k n o w l e d g e no c a l c u l a t i o n s h a v e h e r e t o f o r e b e e n r e p o r t e d o n a model i d e n t i c a l t o t h e o n e u n d e r t h e p r e s e n t consideration. However, M c C r a c k i n c a r r i e d o u t Monte C a r l o c a l c u l a t i o n s on t h e s y s t e m chains constrained t o f w i t h r e g a r d t e n e r g y o f a d s o r p t i o n f o u n d by M c C r a c k i n i s q u a l i t a t i v e l y s i m i l a r t o t h a t g i v e n by f i g u r e 3. T h e r e i s , however, a p p r e c i a b l e q u a n t i t a t i v e d i f f e r e n c e i n t h e two r e s u l t s : t h e c r i t i c a l energy f o r the t e r m i n a l l y anchored chains c o n s i d e r e d by M c C r a c k i n was f o u n d t o b e a p p r o x i m a t e l y 0.25 KT, w h i c h i s c o n s i d e r a b l y lower than t h a t o b t a i n e d f o r t h e p r e s e n t system; a l s o , o u r v a l u e s of < V > tend t o be lower than those which would b e o b t a i n e d by e x t r a p o l a t i n g M c C r a c k i n s r e s u l t s t o t h e corresponding adsorption energies and t h e chain length. This may b e due t o t h e r e a s o n t h a t a " t r a i n " i n t e t r a h e d r a l c h a i n / / κ τ

:

a

2

=

K T

i

D

l

o

t

c

a

n

D

e

s

2

1

can e x i s t o n l y i n a s i n g l e c o n f i g u r a t i o n tttt . Hence i t i s i n t h e s t a t e of zero c o n f i g u r a t i o n a l entropy. This means t h a t o n a d s o r p t i o n a s e q u e n c e o f s e g m e n t s w i l l h a v e t o l o s e whole c o n f i g u r a t i o n a l e n t r o p y a s s o c i a t e d w i t h i t i n the s o l u t i o n phase. The a d s o r p t i o n i s , thus, o n l y p o s s i b l e i f t h e segment/surface i n t e r a c t i o n energy i s so l a r g e t h a t i t would more t h a n c o m p e n s a t e t h e e n t r o p y l o s s . Secondly, s y s t e m s s u c h a s t h o s e s t u d i e d by M c C r a c k i n h a v e a l r e a d y l o s t some e n t r o p y o n a c c o u n t o f t h e a d d i t i o n a l c o n s t r a i n t o f one chain-end permanently anchoring t o the s u r f a c e . Thus t h e segment/surface energy r e q u i r e d f o r a d s o r p t i o n t o take p l a c e would be lower, a s i t has lower e n t r o p y t o overcome. F i g u r e 4 g i v e s t h e mean f r a c t i o n s o f segments i n t h e s u c c e s s i v e l a y e r s a b o v e t h e s u r f a c e computed f o r v a r i o u s v a l u e s o f -Δ We n o t e t h a t i n t h e c a s e o f Δ € = -0.5 KT the d i s t r i b u t i o n i s markedly d i f f e r e n t from those o b t a i n e d for higher segment/surface b i n d i n g energies. For Δ β = -0.5 KT, t h e segment d e n s i t y v a r i e s l i t t l e i n t h e f i r s t f e w l a y e r s adjacent t o t h e s u r f a c e , and then d e c l i n e s s l o w l y as the d i s t a n c e from t h e s u r f a c e i n c r e a s e s . For higher i n t e r a c t i o n e n e r g i e s , o n t h e o t h e r hand, t h e i n i t i a l d e c r e a s e i n t h e d e n s i t y with d i s t a n c e i s very r a p i d , which subsequently slows down a s t h e d e n s i t y a p p r o a c h e s z e r o . The t h i c k n e s s o f a d s o r b e d 2

2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

24

ADSORPTION

A T INTERFACES

Figure 3. Mean fraction of segments bound to the surface () vs. energy of adsorp­ tion per segment (—Ae /kT) 2

-*e / 2

kT

—^ Ο·70η

0-60 -fl

0-50 Η

j Figure 4. Mean fraction of segments () vs. height above the surface (h). 1: —Ae /KT = 0.5. 2: -A* /KT = 0.7. 3: -Ae /KT = 0.9. 4: -Ae /KT = 1.2. 2

2

2

0-40-

4* 0·δΟ -ft

2

Ο

2

4

6

6

10

12

14

h

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

16

18

20

LAL E TAL.

25

Isolated Chain Molecules

l a y e r ( * G ) c a n be d e f i n e d a s t h e d i s t a n c e f r o m t h e s u r f a c e a t which the segment-density vanishes, v i z . the d i s t a n c e a t which a d i s t r i b u t i o n c u r v e i n f i g u r e 4 meets t h e a b s c i s s a . The v a l u e s ofthus d e t e r m i n e d a r e p l o t t e d a g a i n s t - Δ £ / K T i n f i g u r e 5. T h i c k n e s s o f a d s o r b e d l a y e r i s f o u n d t o b e a r a p i d l y decreasing f u n c t i o n of the segment/surface i n t e r a c t i o n energy. The m a g n i t u d e o f C O a t -Δ € = 0.5 (~20 u n i t s ) 2

2

KT s u g g e s t s t h a t when t h e i n t e r a c t i o n e n e r g y i s s m a l l , t h e m o l e c u l e i n t h e a d s o r b e d s t a t e w o u l d assume d i m e n s i o n s s i m i l a r t o t h o s e i n s o l u t i o n . B u t a t e n e r g i e s e x c e e d i n g -1.0 KT t h e a d s o r b e d m o l e c u l e w o u l d be c o n s i d e r a b l y f l a t t e n e d , a s i s i n d i c a t e d by t h e s m a l l v a l u e s of4"£7. A n a l y s i s of the s i z e d i s t r i b u t i o n s of " t r a i n s " , "loops" and " t a i l s " r e v e a l s t h a narrow d i s t r i b u t i o n s wherea e x t r e m e l y w i d e s h o w i n g l a r g e f l u c t u a t i o n s . The mean s i z e s o f " t r a i n s " ( < L > ) , " l o o p s " (), a n d " t a i l s " ( < L > ) c a l c u l a t e d at s e v e r a l values of Δ ^ a r e p l o t t e d i n f i g u r e 6. The mean " t r a i n " s i z e v a r i e s between t h r e e and s i x i n t h e e n e r g y r a n g e considered. At Δ € = -0.5 KT, t h e mean " l o o p " s i z e i s a s l a r g e a s about 20 u n i t s b u t f o l l o w s a s h a r p d e c r e a s e a s - Δ β increases. As e x p e c t e d , t h e mean " t a i l " l e n g t h d e c r e a s e s w i t h the i n c r e a s e i n -Δ C . i n t e r e s t i n g f e a t u r e which our a n a l y s i s brings out i s that, except a t very high - Δ € , a large p r o p o r t i o n o f u n a d s o r b e d segments c o n s t i t u t e " t a i l s " , and t h a t t h e " t a i l s " c o n t r i b u t e most s i g n i f i c a n t l y t o t h e t h i c k n e s s o f adsorbed layer. t

e

2

2

T

n

e

2

2

P i c t u r e of an i s o l a t e d adsorbed molecule emerging from t h e p r e s e n t s t u d y i s t h a t a t low s u r f a c e / s e g m e n t i n t e r a c t i o n e n e r g i e s o n l y a s m a l l f r a c t i o n o f t h e segments i s bound t o t h e s u r f a c e , and t h e shape and d i m e n s i o n s o f t h e a d s o r b e d m o l e c u l e a r e c o m p a r a b l e t o t h o s e assumed i n s o l u t i o n . A t i n c r e a s e d v a l u e s o f t h e i n t e r a c t i o n e n e r g y , however, t h e number o f s e g m e n t s on t h e s u r f a c e i s s i g n i f i c a n t , a n d t h e c o n f i g u r a t i o n a l s t a t e assumed i s s u c h t h a t s m a l l " t r a i n s " a n d s m a l l " l o o p s " are favoured while " t a i l " lengths are r e l a t i v e l y l a r g e . Most important c o n t r i b u t i o n t o the thickness of adsorbed l a y e r d e r i v e s from " t a i l s " . Concluding

Remarks

I n t h i s s t u d y we h a v e d e l i b e r a t e l y assumed a n e x t r e m e l y s i m p l e m o d e l , f o r o u r m a i n p u r p o s e h e r e was t o a s c e r t a i n t h e v i a b i l i t y o f t h e M e t r o p o l i s s a m p l i n g method i n t h e c a s e o f c h a i n m o l e c u l a r systems i n t e r a c t i n g with a s u r f a c e . Notwithstanding the l a r g e magnitude o f the samples r e q u i r e d f o r s a t i s f a c t o r y c o n v e r g e n c e , t h e Monte C a r l o a p p r o a c h c o n s i d e r e d may b e r e g a r d e d a s s u c c e s s f u l i n t a c k l i n g t h e p r e s e n t s y s t e m s . We hope t h a t t h i s method p r o v e s e q u a l l y s u c c e s s f u l when

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION

Δ

ι °·β € /kj 2

, ι·ο

ι ι·2

Figure 5. Mean thickness of adsorbed layer () as a function of the energy °f

I 1-4.

—

0 4

0*6

A T INTERFACES

O ô

Ι Ό

1-2

Figure 6. Mean values of "train' (), "loop" (), and "tail" () lengths correspond­ ing to various values of the adsorption energy per segment t

e

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2.

LAL ET AL.

Isolated Chain Molecules

27

m o d i f i c a t i o n s such as the trans/gauche bond conformational energy d i f f e r e n c e and non-athermal solvents a r e introduced i n the model. We s h a l l deal with such models i n f u r t h e r studies. An important extension of t h i s work that we envisage concerns the i n v e s t i g a t i o n of the c o n f i g u r a t i o n a l behaviour of adsorbed polymer molecules as the s u r f a c e coverage v a r i e s . This can be achieved by i n t r o d u c i n g p e r i o d i c boundaries i n the system (14). Literature Cited 1.

F r i s c h , H.L., Simha, R., and E i r i c h , F.R., J . Chem. Phys., (1953), 21, 365.

2.

Hoeve, C.A.J., DiMarzio Phys., (1965), 42

3.

Rubin, R.J., J . Chem. Phys.,

4.

Roe, R.J., Proc. N a t l . Acad. Sci., (1965), 53, 5 0 .

5.

Motomura, K., and Matuura, R., J . Chem. Phys., (1969), 50, 1281.

6.

S i l b e r b e r g , Α., J . Chem. Phys., (1968), 48, 2835.

(1965), 43, 2392.

7. Lal, M., R.I.C. Rev., (1971), 4, 97. 8.

L a l ,Μ.,and Spencer, D., J . Chem. Soc. Faraday Trans. I I , (1973), 69, 1502.

9.

L a l ,M.,and Spencer, D., J . Chem. Soc. Faraday Trans. I I , (1974), 70, 910.

10.

Bluestone, S., and Cronan,

J . Phys. Chem., (1966), 70, 306.

11.

McCrackin, F.L., J . Chem. Phys., (1967), 47, 1980.

12. 13.

L a l , M., Mol. Phys., (1969), 17, 57. Wood, W.W., i n "Physics of Simple L i q u i d s " , pp 117-230, North Holland P u b l i s h i n g Co., Amsterdam, 1968.

14.

C l a r k , A.T., and Lal, Μ., t o be p u b l i s h e d .

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3 Equilibrium Film Pressure on a Flat, Low-Energy Solid R O B E R T J. G O O D Department of Chemical Engineering, State University of New York at Buffalo, Buffalo, Ν. Y. 14214

Introduction The equilibrium f i l m pressure of an adsorbate, πe, i s defined as πe

=

Y

S -

Y

SV

(1)

where ΥS i s the surface free energy of the s o l i d i n vacuum, and YSV i s the surface free energy of the s o l i d i n contact with the saturated vapor of the ad­ sorbate. The value of this property for an adsorbate which, as a l i q u i d , forms a non-zero contact angle on the s o l i d , has been a matter of uncertainty for some time (1-9). This fact has detracted from the use­ fulness of measurements of contact angle, θ, for the estimation of s o l i d surface free energies (2,3). See r e f s . (5) and (6) for an important discussion of the problem as it has existed in recent years. The measurement of πe i s not p a r t i c u l a r l y easy; and up to very recently (8) the only determinations that had been reported for low-energy s o l i d s were made on powders (4,5,6), while reported contact angle measurements were made on e s s e n t i a l l y f l a t surfaces. Fox and Zisman (1) found reason to conclude that πe, i s probably n e g l i g i b l e ; and this assumption i s basic to t h e i r "Yc" method of t r e a t i n g contact angle data. Adamson (3) has pointed out that the existence of a t h i c k adsorbed f i l m , and consequent non­n e g l i g i b l e value of πe, are compatible with the e x i s ­ tence of a non-zero contact angle, provided the ma­ terial in the adsorbed f i l m has a structure that i s s i g n i f i c a n t l y d i f f e r e n t from the bulk l i q u i d . He hypothesizes a degree of "structure" i n a m u l t i l a y e r f i l m , which decays with distance from the surface. If such t h i c k , structured multilayers e x i s t , the low 28

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

GOOD

Equilibrium

29

Film Pressure

entropy associated with such a structure could account for the existence of a non-zero contact angle. But of course, one cannot argue that the existence of a non­ zero contact angle proves the presence of a thick, structured f i l m . And indeed, i t i s hard to imagine that a m u l t i l a y e r f i l m of, say, CCl^ on Teflon could have a "structure that would meet the requirements noted i n Ref. 3. Whalen (6) pointed out that the Hill-deBoer equation (11,12,13), with empirical con­ stants obtained from measurements with hexane and octane on Teflon TFE i n the low-coverage region, pre­ d i c t s a submonolayer l i m i t i n g adsorption at saturation. The purpose of this paper i s to develop a method of estimating 7r , a p r i o r i , on a molecularly f l a t , homogeneous, low-energy surface f o r adsorbates of l i q u i d s f o r which θ physical i n t e r a c t i o n quantitative expressions are a v a i l a b l e i n well-known physical theory (10). As a f i r s t step i n this a n a l y s i s , an attempt was made to compute, by methods which w i l l be described below, the constants for a BET m u l t i l a y e r adsorption isotherm for CCI/, on a homogeneous, molecularly smooth fluorocaroon surface. I t was found that the BET "c" constant was very small. I f the adsorbent were a powder instead of a f l a t surface, a very low value of c would indicate a BET type I I I isotherm, the f i n a l up-turn of which (near ρ = p ) was due to enhanced adsorbate-solid i n t e r a c t i o n s at points of s o l i d - s o l i d contacts, e.g. as pendular r i n g s , which Wade and Whalen (.5,(5) have discussed. Such s t r u c t u r a l features are, by d e f i n i t i o n , absent from a molecularly smooth surface. These preliminary r e s u l t s led us to turn to a Langmuir model, as being f a r easier to treat than a BET model. It was a n t i c i p a t e d that a s t r i c t l y Langmuirian model might break down when some possible values of molecular parameters were assumed — for example, the model might p r e d i c t high enough coverage that l a t e r a l i n t e r a c t i o n s would be important. For such a regime, a Hill-deBoer isotherm would be more s u i t a b l e . However, i n the present computations, we confined that aspect of the study to the estimation of the conditions under which the Langmuir postulates break down. To a n t i c i p a t e some of our r e s u l t s , a breakdown of the Langmuir assumptions was i n f a c t found, and i n a very i n t e r e s t i n g region of the range of chain-length for n-alkanes, on Teflon. 11

e

Q

ff

11

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

30

ADSORPTION

AT

INTERFACES

Theory Consider the low-coverage sub-monolayer region of an adsorption isotherm on a uniform s o l i d . We w i l l estimate the energy and entropy of adsorption, with the bulk l i q u i d as the reference state. The p a r t i a l molal entropy of the adsorbed molecules, i n a Langmuir adsorbed f i l m on a s o l i d , i s given by (14). S - - Rln [ x / ( l - x ) l a

(2)

a

where x i s the "θ" of the Langmuir adsorption equa­ t i o n , i . e . the mole f r a c t i o n of surface s i t e s that are occupied. This entropy term i s c o n f i g u r a t i o n a l ; i t arises from the p o s s i b i l i t y of permuting the molecules among the occupied molal entropy of transfer, liqui sorbed f i l m , i s given by, X W AS = - Rln τ — + Rln ^r- + AS. . - S (3) l-x W internal ql ' The l a s t two terms i n Equation 3 can probably be neglected. These correspond, r e s p e c t i v e l y , to the changes i n i n t e r n a l , molecular degrees of freedom, and to the configurational entropy of the l i q u i d , considered as a q u a s i - l a t t i c e with occupied and vacant s i t e s . The l a t t e r term i s small, probably less than 0.5 entropy unit (15). The second term on the r i g h t involves the number of angular configurations accessible to a molecule i n the l i q u i d (W^) and i n the adsorbed state (W ). For a quasi-spherical molecule such as C C I 4 , this term i s zero. For an elongated molecule, such as an n-alkane longer than propane or η-butane, we may estimate this term as follows: The molecule i s treated as a r i g i d c y l i n d e r , of length I and diameter d. In the l i q u i d , i t s axis may be at any angle, r e l a t i v e to a fixed coordinate system; i n e f f e c t , i t has a volume 0.75ΤΓ(Ί/2)3 accessible to i t . In the adsorbed state, the energy of a t t r a c t i o n between the s o l i d and the extended molecule renders i t improbable that the molecule w i l l have i t s axis i n any plane that i s at an appreciable angle to the surface. So i t may be r e ­ garded as having, accessible to i t , a volume 2ir(l/2)^d. This entropy term, then, i s approximately Rln(3d/4^). A further refinement on t h i s term can be made by counting the numbers of bent configurations e x p l i c i t l y . These are tedious to enumerate, but t h e i r e f f e c t on the equilibrium w i l l be to predict even lower coverage than that estimated with t h e i r neglect. a

Q

Q

Ί

Ί

v

a

L

a

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

Equilibrium

GOOD

31

Film Pressure

Thus, we can write as a reasonable approximation, f o r the entropy of transfer per mole between l i q u i d and adsorbed state: N k t l n ^ J - - ln(ff)] (4) a where Ν i s the Avogadro number. For symmetrical ad­ sorbate molecules, the l a s t term i n the brackets i s omitted. Volume changes are small, i n transfer from l i q u i d to adsorbed state, so we may estimate the enthalpy change as follows: The p a r t i a l molal energy change, i n transfer from the pure l i q u i d to the adsorbed state, i s : AS = -

Δϋ « AU

V

- ÂÏÏ

V

Here, AU i s the molar energy of vaporization, and AU the p a r t i a l molal energy of adsorption from the vapor. For the purpose of a s t r i c t l y Langmuir-type computation, we assume A U to be constant. Estimates of A U have not been b r i l l i a n t l y successful i n the past; but we are not d i r e c t l y interested i n the heat of adsorption from the gas. Rather, we are interested i n the energy of transfer from the l i q u i d . Thus, i f we use a model that i s moderately reasonable to estimate AU , and the same model to estimate AU * , we w i l l have a good probab i l i t y of making a better estimate of the difference between these two terms. It w i l l develop that we use the macrospic heat of vaporization of the pure l i q u i d as our experimental parameter i n p r e d i c t i n g coverage. Molecular considerations w i l l enter only i n regard to estimating the energy of i n t e r a c t i o n between unlike molecules or segments, and to taking molecular shape into account. Thus, we can write, for substance i , taking the l i q u i d as the reference state, a d s

a d s

acis

V

ac

A

U

N

€

z

/

s

2

( 6 )

i " ii iL Here, ζΐχ i s the coordination number for substance i i n the l i q u i d , and €±± i s the energy at the minimum of the pair p o t e n t i a l function, f o r substance i . Let the molecules of the l i q u i d be designated 1, and those of the s o l i d 2. Then the energy change per mole, on transfer of molecules of type 1 from the l i q u i d to the adsorbed state, i s : Δϋ ^ N < *

1 L

€ /2 u

- «

l a

€

1 2

/2)

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

(7)

ADSORPTION

32

AT

INTERFACES

Here €^2 i s the energy at the minimum of the p o t e n t i a l function, f o r 1-2 bimolecular i n t e r a c t i o n , and z ^ i s the number of nearest neighbor surface molecules, or groups, that can i n t e r a c t with a molecule of adsorbate, The l a s t term the brackets i n Equation 7 corresponds to the energy of adsorption from the vapor, estimated according to the same model used f o r Equation 6· Equating Δϋ and TAS, we obtain a

-

NkTUn^-H

ln(|f)] = N ( N Z

1L

Z l L

€ n

z

l a

€

flafl2

11

1 2

)/2

(8)

I f the dominant types of a t t r a c t i v e forces f o r the two species are the same, i t has been shown that 6^2 *- given, approximately, by ( 1 0 ) : s

(9)

'12

The r i g h t side of Equation 8 then becomes: Ν

ζ

η Λ ι

(10)

τ

I f the coordination number of a molecule (or group) of type 1, i n the l i q u i d , z ^ , i s the same as that of a molecule (or group) of type 2 i n i t s l i q u i d state, ζοτ, and i f there i s the same degree of v a l i d ­ i t y f o r trie assumption of pairwise a d d i t i v i t y of energies f o r substances 1 and 2, and the same f r a c t i o n ­ a l contribution due to neighbors outside the f i r s t coordination s h e l l , then, L

€

ll

/ €

22

Ξ

(ID

AUJf/AUj

Combining Equations 6, 10 and 11 with Equation 8, we obtain: log1-x.

2.3RT

^la

1 Z

(12)

1 L VAUj

A simple case, to which we can apply Equation 12, i s C C I 4 on polytetrafluorethylene (Teflon TFE). We estimate the r a t i o of energies, ^22^11 > a

s

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

A U

Equilibrium

GOOD

£C1//

a u

$FO

β

Film Pressure

F

o

r

t

h

i

s

P

33

u r

P°se,

A U

ÏFo

2

i

s

estimated

z

from ^heat of vaporization data for CF4 (16). Using the experimental energy of vaporization f o r CCI4, i t i s found that χ = 3 χ 10"^. The f i l m pressure f o r a d i l u t e monolayer can be computed from s,™ x 7Γ (13) e l-x o

σ

a

where a i s the area per molecule i n a close-packed monolayer. For CCIA on Teflon, assuming σ = 30A , the r e s u l t i s ir = 4 χ 10"^ ergs/cm . Thus we obtain a f i r s t , important conclusion: For one l i q u i d that forms a non-zero contact angle on a low-energy s o l i d (!) > ^e should be n e g l i g i b l e , provided the s o l i d i s homogeneous and molecularl An important syste applied i s the series of homologous n-alkanes on polytetrafluoroethylene. For t h i s purpose, we must modify Equations 8 to 12. We may assume the T e f l o n surface to consist of extended chains. The zigzag structure of the fluorocarbon chain j u s t matches the period of zigzag i n a saturated hydrocarbon chain. We may neglect the h e l i c a l configuration of the f l u o r o ­ carbon, because the p i t c h i s small, about 14 carbons for a turn of the h e l i x . The fact that the l a t e r a l spacing between ( C F 2 ) n chains i s wider than between ( C H o ) chains does not a f f e c t t h i s computation. For an n-alkane, the methyl groups must be treated separately from the methylenes, because the p o l a r i z a b i l i t y of a C H 3 i s considerably greater, and a terminal C H 3 w i l l have more nearest neighbors i n the l i q u i d than w i l l a mid-chain C H 2 . For a long-chain hydrocarbon, most of the neighbors of a C H 3 i n the l i q u i d state are C H 2 groups, so the energy of i n t e r a c t i o n between C H 3 groups i n the l i q u i d may be neglected. Then Z - Q ^ H , Equation 7, may be replaced with the expression Z

n

^ LCH2

and z

l a

( n

€

"

1 2

2 ) z

CH2 9

L

C

H

^

L

C

H

^

,

^

^

, by €

aCH CH ,CF 2

2

+ 2

2z

G

aCH CH ,CF 3

3

With t h i s model, the expression i n Equation 10, becomes

2

for AU,

(15) employed

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

34

ADSORPTION

Δϋ - f

+ 2z

^

^ LCH^ CH^CH^

LCH,

CH2CH2

CH^CH^

1 -

'aClk

"CF CF

'LCH.

•CH C

2

0

2

C

H

'aCH.-

-CF CF

'LCH,

:

2

A T INTERFACES

2

2

2

(16)

CH2 CH„

We can estimate the 6's for methylene and methyl groups i n terms o f energies of vaporization, as was done f o r use i n Equation 1 2 . As before, we approximate the r a t i o s under the square roots by the r a t i o o f energies of vaporizatio the r e s u l t with the /Δυ

'aCR-, log-

1-x

1

(η-2)Δυ;

2.3RT

'LCH,,

«2

2 y

A

U J

,

AU,

CH,

1

CH„

A U

CH

4

i

/Δυ,

'aCH, +

CF.

-

CF.

- log(|f) ( 1 7 )

-

Δϋ,CH.

'LCH-

We have c a r r i e d out computations f o r n-alkanes on Teflon, using A U C H 3 2 5 0 joules/mole and ΔΗ^Ηβ = 8 2 0 0 joules/mole, from vapor pressure data ( 1 6 ) , and 2

Z

/ z

2

/

4

=

z

/ z

1

,

1

T

h

e

r

a

t

i

o

d

/

l w

a

s

aCH LCH " ' aCH LCH = ' estimated assuming the van der Waals diameter of a n-alkane to be 4.8A, and the projection of the C-C distance on the chain axis to be 1.252A. Table I shows the r e s u l t s of this c a l c u l a t i o n . Values f o r pentane and butane are i n parentheses because the assumptions that most of the neighbors of a C H 3 group are C H 2 groups, and that the molecule l i e s f l a t on the surface, break down f o r short-chain alkanes. We note at once, from Table I, that x and are e s s e n t i a l l y zero f o r the higher hydrocarbons. Below hexane, χ increases r a p i d l y ; and the assumption of no l a t e r a l interactions quickly becomes inapplicable. So this computation leads d i r e c t l y to a p r e d i c t i o n of the region where the method of computation should break down. Thus, i t 2

2

3

3

a

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

Equilibrium

GOOD

Film Pressure

35

Table I. n-alkane

2

X

octadecane

1.4 χ

a 10~

hexadecane

4.2 χ

decane

1.1 χ

TT ,ergs/cm e

6

4.4 χ

10~

5

10"

6

1.5 χ

10"

4

10~

4

5.6 χ

10"

3

10"

2

octane

4.0 χ

10"

4

hexane

1.7 χ

10"

3

pentane

(2.9 χ

2.3 χ 0.12

(0.23)

3

10" )

butane i s as expected, that the computed values f o r butane and pentane are much below those observed (4). It i s possible that the estimates of z çHo d aCH3 used above may, f o r c e r t a i n kinds of s i t e s , be too Small. For a r e a l surface, i t i s highly probable that step or ledge s i t e s e x i s t , for which z cHo y ke 3 and z Q^ may be as 5. Such s i t e s could w e l l constitute 5 or 10% of an experimental surface. Examination of models shows that, for elongated molecules, i t i s u n l i k e l y that z cH2 l d be as large as 3 f o r the e n t i r e chain, together with z çH2 s large as 5 for every terminal C H 3 . Indeed the values of these two z's w i l l depend on chain length, and on the l a t e r a l spacing of fluorocarbon chains. I t i s only for convenience that we approximate them by constants, and we w i l l assume average values of 2.5 f o r z çjj2 * 4 for z ç7io. An aiicane molecule i n a s i t e such as j u s t described w i l l not have freedom to take up any angular o r i e n t a t i o n p a r a l l e l to the plane of the surface; indeed there w i l l be just two orientations which have the same energy. So the term, log (3d/4t), i n Equation 17 must be replaced by log (3d2/£ ) Table II shows the r e s u l t computations of this type: The f r a c t i o n x ( tep}°f step s i t e s on Teflon TFE covered by n-alkane molecules, and the contribut i o n to the f i l m pressure due to t h i s coverage, assuming 5% of the surface i s accounted for as step sites. a n

a

z

m a

a

a

c o u

a

a

a

a n c

a

a

2

e

a

s

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

36

ADSORPTION

AT

INTERFACES

Table I I : Estimate of f r a c t i o n a l coverage of step s i t e s on t e f l o n TFE by n-alkane molecules, and c o n t r i b u t i o n of t h i s coverage to equilibrium f i l m pressure, assuming 5% of surface i s accounted f o r as step s i t e s . Table II n-alkane octadecane

χ , a(step) 8.5 χ 10

hexadecane

1.8 χ 10

fc

0.05ττ , ergs/cm e' 1*3 χ ΙΟ"

N

4

3

3.2 χ 10

decane

2.2 χ 10~

2

octane

5.2 χ 10"

2

hexane

1.5 χ

(pentane)

(2.0 χ 10" )

(butane)

2

&

2

5.8 χ 10"

1.5 χ 10 " 1

(0.8)

1

(1.3)

(3.0 χ 10" )

1

The values f o r pentane and butane are given i n paren­ theses because of the breakdown of an assumption ( i n addition to those noted regarding Table I) that was made i n the s t e p - s i t e model. This i s , that the aver­ age values of ζ , τ τ and z ~ are less than 3 and 5, respectively. 2 3 We note at once, from Table I I , that the comput­ ed contributions to ir f o r the higher n-alkanes i s not a p p r e c i a b l e — j u s t as was seen i n Table I. And for the lower alkanes, f o r which the model breaks down, the computed contribution to ir i s s t i l l r e l a t i v e l y small — only 1.9 erg/cm2 for butane, for which i t i s computed that about 30% of the step-sites are occupied. F i n a l l y , we w i l l treat water on Teflon and on polyethylene, using Equation 12 with omission of the term, log(3d/4£). To evaluate ^^_2 * relations : ο Γ

u

a C H

a C H

e

y w

€

d

+

"

+

6

μ

e

u

s

=

e

t

le

" C " )

Κ

1

+

B

«A

+

1

~TET

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

GOOD

Equilibrium

e

2 2

Film Pressure

= ^22

fc

12

Here

37

*12

(

J4l

€

2

0

)

21

22

< >

i s computed by the equation

*

d

22

- -r+M-

< >

where I i s i o n i z a t i o n energy. These r e l a t i o n s are discussed i n d e t a i l i n Ref. (10). The superscripts d, i and μ,, i n Equations 18 - T 2 r e f e r r e s p e c t i v e l y to dispersion, inductio components of intermolecula energy polariz a b i l i t y , I i s i o n i z a t i o n energy, μ i s dipole moment, and Β i s a constant which, f o r molecules c o n s i s t i n g of atoms i n the second and t h i r d rows of the periodic table, i s close to 0.66 (10). For water, the r a t i o computed by Equation 19 i s close to 0.20 (10). Equations 18 and 19, are i m p l i c i t i n the discussion of Fowler and Guggenheim (17,18). Equation 21 can be put i n the form, e

"- "fe-% €

€

- 11

° '

2

(23>

v

< > 24

The reduction i n average coordination number, ùz , f o r water, on going from bulk l i q u i d to adsorbed state, i s probably about 1, i . e . from something near 4, to about 3. Polyethylene i s treated as extended (CH2) chains. The r e s u l t s are given i n Table I I I . It should be emphasized that these computations are f o r water on i d e a l Teflon TFE and polymethylene surfaces, i . e . assuming the s o l i d s to be smooth and homogeneous* n

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

38

ADSORPTION

AT

INTERFACES

Table I I I . Estimates of f r a c t i o n a l coverage and of equilibrium f i l m pressure f o r water on a fluorocarbon s o l i d and on a polymetheylene surface, both assumed to be smooth and homogeneous. Solid

χ a

7Γ , ergs/cm e 7-

Teflon TFE

6 χ 10

2.5 χ 10

Polyethylene Discussion

7 χ 1θ"

6

3 χ 1θ"

5

(a) The Approximations. We must now make a c a r e f u l examination of the important approximations that we have introduced The f i r s t and possibly the most important, approximatio Langmuir equation i t s e l f y computed show that these systems (except for the lower hydrocarbons) should be within the coverage region where the Langmuir equation can s a f e l y be used. We have, of course, neglected l a t e r a l interactions so far; and we now examine the v a l i d i t y of that neglect. For a quasi-spherical molecule such as CCl^, the energy term — i . e . the r i g h t side of Equation 12 — becomes ΔΙΙν

^la

lia

273RT

5

IL

AU;

5

(25)

1L

where z"£ i s the average number of " l a t e r a l " nearest neighbors of an adsorbed molecule. ^ In a perfect 2-dimensional, hexagonal l a t t i c e , z'i would be 6. For CH2 groups i n an n-alkane, z £ i s at most 2 . The entropy of adsorption w i l l be less than the Langmuir entropy (14), so to use the expression ,(25) instead of the corresponding term i n Equation 1 2 w i l l y i e l d the maximum value of x : a

v

a

a

a

l-x-

exp

ΔΙΙ JL RT

'ΔΙΚ

1 - 'la 1L

'la S

5

(26)

1L

For C C I 4 on Teflon TFE, with zî /ziL =0.5, this treatment y i e l d s x < 10" . Thus, the refinement of computing x^ with allowance f o r l a t e r a l i n t e r a c t i o n s does not bring the estimated coverage s e r i o u s l y outside the region of the isotherm where l i n e a r i t y i s a

2

a

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

GOOD

Equilibrium

Film Pressure

39

expected. Hence, the use of the Langmuir isotherm as an acceptable approximation, f o r molecules such as C C I 4 , appears to be j u s t i f i e d . (For step s i t e s , the s i t e s themselves w i l l be i s o l a t e d from each other, and so there i s no l a t e r a l i n t e r a c t i o n of adsorbate molecules even when most of the step s i t e s are covered). For l i q u i d s having much lower b o i l i n g points than CCl^, however, i t i s to be expected that l a t e r a l interactions and two-dimensional condensation w i l l be important, and hence that larger values of ττ w i l l be found. A second approximation i s the assumption of chemical uniformity of the s o l i d surface. It has been established (19) that hydrophilic s i t e s e x i s t on at l e a s t some, ancT possibly a l l samples of Teflon TFE Such s i t e s are, no doubt the majority of s i t e s containing groups are l i k e l y to be present at the surface; and on other low-energy surfaces, i t i s to be expected that high-energy heterogeneities should commonly be present i n a f i n i t e concentration. Such s i t e s would i n t e r a c t with water molecules, and could contribute to a large value of ττ as computed from water adsorption, yet not make an excess c o n t r i b u t i o n to hydrocarbon adsorption. Heterogeneity w i l l also be present for geometric reasons, such as microscopic roughness or microporosity beyond the l e v e l of the step-sites considered above. So some adsorbed molecules w i l l have more nearest neighbors, i n terms of groups such as C F 2 , C F 3 etc. on Teflon, than w i l l others. But i n general, i t i s very u n l i k e l y that z-^ w i l l be larger than 5 or 6. So the r a t i o z^ /z-n w i l l be, at most, about 0.5; and the large values or this r a t i o w i l l pertain to only a very small f r a c t i o n of surface s i t e s , on a surface which i s smooth enough for contact angle measurements to be made. The r a t i o , ^ 2 2 ^ 1 1 ' ^ l° " §y s o l i d , 2, i n contact with any l i q u i d , 1, w i l l seldom be very large; for a hydrocarbon on a fluorocarbon, i n the computations given above, i t turned out to be at most 1.25. There w i l l be no more than a small f r a c t i o n of the s i t e s for which the energy term i n Equation 12 or 17 i s , for geometric reasons, very much larger than that computed above. And f o r elongated molecules on such s i t e s , i t has already been noted that the angular entropie term (the l a s t term i n Equations 12 and 17) w i l l be much more negative, because to occupy such a high-energy s i t e , an extended molecule w i l l have at most two configurations access­ i b l e to i t . Hence, the coverage of an e s s e n t i a l l y Β

Θ

a

a

o r

a

w

e n e r

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

40

ADSORPTION

AT

INTERFACES

f l a t surface w i l l not be s e r i o u s l y l a r g e r than that c a l c u l a t e d here. Of course, surfaces can be prepared which are very much more heterogeneous, f o r geometric reasons, than j u s t indicated, e.g. by abrasion. But as pointed out by Neumann and Good (20), such surfaces are not suitable for contact angle measurements ; and the r e p r o d u c i b i l i t y of data obtained would be very poor, and the hysteresis extremely large. Also, the heterogeneity of a surface that has been modified, by p a r t i a l oxidation or by g r a f t i n g short hydrophilic chains onto i t , w i l l be much more serious than that of an unmodified surface. The f i l m pressure on such surfaces i s a very d i f f e r e n t problem from that on an e s s e n t i a l l y homogeneous low-energy surface and i t w i l l not be discusse The term Rln(W /WL) rigorou expressio the change i n entropy associated with angular conf i g u r a t i o n s . The approximation of evaluating i t as Rln(3d/4£) has already been discussed. The error thus introduced r e s u l t s i n p r e d i c t i o n of too high an adsorption; so the conclusion as to the n e g l i g i b l e value of ir f o r higher hydrocarbons i s not weakened by i t . Regarding the expressions containing the €'s, e.g. Equation 10, i t may be seen at once that € ^ i s by f a r the most important parameter, because the r a t i o , la/ 1L generally small, e.g. 3/12, or r a r e l y larger than perhaps, 5/11. Since i s evaluated from AUÏ, i t i s c l e a r that the dominant energetic component of the computation i s the heat of vapori z a t i o n of the l i q u i d . There i s considerably less energy than A U "recovered , on adsorption, because the coordination number i s so much lower, f o r the adsorbed molecule with the groups i n the adsorbent surface. The estimation of €^2 from >/€^^Z2 3 i ° 9, i s i f anything, on the high side, even f o r systems where the cohesion of the bulk l i q u i d and of the s o l i d are both dominated by the London force. A more exact expression, replacing Equation 9, i s a

e

Z

Z

i s

V

11

9

€

1 2 = * - ^ Λ 2 "

E


where Φ can be computed a p r i o r i , from molecular properties (10), e.g., by Equation 22 f o r nonpolar molecules. The fact that we express the €'s i n terms of A U s (e.g. Equations 11 to 17) i s , i n a p r a c t i c a l V f

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

GOOD

Equilibrium

Film Pressure

41

sense, a strong point of this theory. We have already noted the assumptions m a d e — s e e the paragraph preceding Equation 11. The main factor leading to inequality of z^j and (see above) i s , differences i n decree of expansion or the l i q u i d s , considered as f r a c t i o n of q u a s i - l a t t i c e s i t e s that are vacant, at the temperatures where the heats of vaporization are measured. Since the b o i l i n g point i s , to a f a i r approximation, a "corresponding temperature within the meaning of the theory of corresponding states, we can conclude the equality of coordination numbers i s a good approximation. Even i f these errors do not cancel t o t a l l y , they should do so p a r t i a l l y . And since this r a t i o appears under a square root sign Equation 12 and then i s m u l t i p l i e d by a facto the s e n s i t i v i t y of y i s small. Equations 16 and 17 introduce approximations needed to treat highly asymmetric molecules. The asymmetry cannot be handled i n terms of any e x i s t i n g , macroscopic treatments which use heats of vaporization d i r e c t l y . These assumptions are, however, a p r i o r i , reasonable, and so can be counted on as leading to a v a l i d p r e d i c t i o n of the trends. Equations 18 to 22 are based on Good and Elbing (10) and (as already noted) on the e a r l i e r treatments of Good and G i r i f a l c o (2.,Z>18) and Fowler and Guggen­ heim (17). A notation basecPon that of Fowkes (21) has been employed; but the quantities are not obtain­ able from empirical treatment of surface tension data, as i s the case with Fowkes Y '. Indeed, the dispersion component of the t o t a l surface energy can­ not i n general be evaluated from contact angle data, because of the lack of thermodynamic uniqueness of the U function, i n a binary system. (It i s only when there i s no i n t e r f a c i a l excess mass of e i t h e r . component that U i s unique. In general, U ( '£ U ( ), where the superscript designates the Gibbs d i v i d i n g surface: (1) r e f e r s to the surface located such that Γ\ = 0, and (2), to the Γο = 0 surface.) Thus, i s a function which has physical meaning only i n terms of the components of intermolecular a t t r a c t i o n constants as computed from molecular properties, e.g. by Equation 18 and 19. The c o e f f i c i e n t , 0.2, i n Equation 24, arises from t h i s treatment of the energy components f o r i n t e r a c t i o n of water and a nonpolar s o l i d . I t s use i n the theory for water depends f o r accuracy, not so much on the v a l i d i t y of Equation 18 or 19, as on the assumptions 11

1

lf

df

s

s

S

L

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

s

2

42

ADSORPTION

AT

INTERFACES

about coordination number and second-nearestneighbors, which j u s t i f y the use of the r a t i o of^ energies of vaporization i n Equation 24. We estimate the uncertainty here, as no worse than 50% i n ^i\l^22 which means an uncertainty that i s less than 25% a f t e r the square root i s extracted. The q u a l i t a t i v e conclusion that x and rr are n e g l i g i b l e , f o r H2O on Teflon and polyethylene, are not s e r i o u s l y changed by allowance for such uncertainty, because A U i s so large, f o r water, and as a consequence, the computed values of x and ΊΤ are so small. In summary, the approximations of t h i s theory are probably not serious; and indeed, the majority of the approximations contribute errors i n the d i r e c t i o n of too high an estimate of x and ττ · It would take very much greater c o r r e c t i o l i k e l y to appear, i the q u a l i t a t i v e conclusion that x and ττ are generally small for l i q u i d s that b o i l above room temperature. It must be emphasized, however, that these compu­ tations are not intended as quantitative predictions of x arri 7r for these systems. The approximations made above, including those about structure of the s o l i d surface, are s u f f i c i e n t l y serious that quanti­ tative agreement cannot be expected. But for the p r e d i c t i o n of trends, as with the n-alkanes, and for the conclusion that ττ i s small for high b o i l i n g l i q u i d s , the approximations should not detract from the v a l i d i t y of this theory. (b) Comparison with Experiments: i r for Organic Compounds on Teflon. Graham (4) has found ir to be much smaller, f o r η-octane on powdered Teflon TFE, than for alkanes having surface tension below Y , e.g. butane. ir has been reported to be large f o r low-boiling gases such as N on Teflon. Graham (4) noted a d i f f i c u l t y a r i s i n g from bulk s o l u b i l i t y of an alkane i n the substrate, such that the quantity sorbed could not be uniquely assigned as between adsorption and absorption. (This trouble was not encountered by Whalen and Wade (5,6.)). Graham concluded that his value of ir for octane on Teflon, about 1.7 erg/cm^, was an upper l i m i t ; he could not estimate the r e a l value. Wade and Whalen (5,j5) also used a powder form of Teflon, and also oBtained a small value for i r : 3.3 f o r hexane and 2,9 for octane. They e x p l i c i t l y corrected for pendular r i n g condensation, and i n so doing, they obtained estimates of ir i n t h e i r systems that were very probably more v a l i d than Graham's were f o r h i s . Our computations are lower than these experimental r e s u l t s y

a

e

V

a

θ

a

a

e

e

e

c

e

2

e

e

e

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

Equilibrium

GOOD

Film Pressure

43

e.g. ττ =0.1 f o r hexane i n the absence of step s i t e s . The r e s u l t , 7 r =0.5 for Teflon with step s i t e s accounting for 5% of the area, shows the d i r e c t i o n of change i n the computed r e s u l t s when a more complex surface i s postulated. The preliminary computations made f o r CCl^ indicate that the e x p l i c i t employment of a two-dimensional van der Waals equation (11,12) would be worthwhile with the lower hydrocarbons. We w i l l investigate such two-dimensional condensation i n another communication. We note, however, that our equations have successfully predicted the observed trend of ir with chain length. As has already been noted, water adsorption measurements at Lehigh (19) have shown that the surface of Teflon powder i s heterogeneous and about 0.757 of the surface of the sampl which adsorbed wate t i o n of water, reported i n Table I I I , i s f o r the 99% of the surface exclusive of the hydrophilic s i t e s . The Lehigh measurements (19) could not q u a n t i t a t i v e l y d i s t i n g u i s h the increment of water adsorption due to t h i s f r a c t i o n of the surface. The water isotherm was described as resembling a type II isotherm, with surface area less than 1% of the nitrogen area, superimposed on a type I I I isotherm. We have not attempted to analyse the contribution to the adsorption of hydrocarbons or other nonpolar molecules, due to the hydrophilic s i t e s on Teflon. Wade (6) has discussed the evidence f o r interactions of high-energy s i t e s on Teflon with hydrocarbon molecules. Whalen (22) has recently measured the adsorption of water on Teflon powder, and estimated a value of 1.9 ergs/cm for ?r . He estimates the hydrophilic s i t e s on this s o l i d to account f o r 3%> of the surface area (6,23). Adsorption measurements on Teflon powders are of l i m i t e d d i r e c t pertinence to the contact angle question because there i s every reason to suspect that the surface of a powder i s quite s i g n i f i c a n t l y d i f f e r e n t from that of a smooth slab that i s suitable for contact angle measurement. This point i s hard to v e r i f y d i r e c t l y , however, because while electron microscopic examination of a grossly smooth s o l i d could reveal pores, i t would not reveal chemical heterogeneity, p a r t i c u l a r l y that i n the form of i s o ­ l a t e d , high-energy s i t e s ; and the p r e c i s i o n measure­ ment of contact angle on a powder i s not easy. e

e

2

e

(c) Comparison With Adamson's Model, and Results For Water On Polyethylene.

His

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

44

ADSORPTION

AT

INTERFACES

(1) Theory. Our model i s , i n p r i n c i p l e , not incompatible with that of Adamson and Ling (3), i n that t h e i r isotherm graph, i n i t s lower pressure region, resembles a BET type I I isotherm. I t i s w e l l known that, by lowering the value of the " c " constant, a type I I I isotherm i s obtained which, i n i t s lowcoverage region, i s not experimentally d i s t i n g u i s h a b l e from the Henry's law region of a Langmuir isotherm. Figure 1 shows a schematic graph of the isotherm we propose. Since the coverage at saturation i s f a r below a monolayer, there i s no need to make any hypotheses about the structure of the absorbed mater­ i a l i n the region above monolayer coverage. (2) Experiment Adamson i n 1973 reported (8,9.) a value of 42 ergs/c These r e s u l t s appea I I I . They are also i n apparent c o n f l i c t with the w e l l known conclusion (24) that the Y polyethylene i s i n the neighborhood dF"31 ergs/cm . The use of Equation 28, [Y (cos0+l)- 7Γ 2 ] •Li e Y c

2

T

S

4Λ

\

(28)

Y (cose+i)

2

L

4Φ

2

with Φ about 0.9 to 0.95 (1,10) leads to an estimate of about 36 ergs/cm f o r Yg. I t would be rather anomalous f o r polyethylene i n water vapor to have a negative surface free energy Ygy, which would be obtained by subtracting 42 from"36 as Equation (1) would seem to prescribe. A r e c o n c i l i a t i o n can be achieved by hypothesizing that water on the polyethylene sample that was used (8.,9.) behaved i n a s i m i l a r fashion to water on Teflon TFE, (19) noted above. The water molecules might adsorb i n clusters on i s o l a t e d hydrophilic s i t e s , y i e l d i n g a f i l m with the observed average thickness and the reported ττ^. With respect to water adsorption, the e f f e c t i v e Y g of this s o l i d would then be, not the value derived from contact angles of nonpolar l i q u i d s , but a larger value: 2

Y

S

=

Y

+

S ^e(water) -36+42 , = 78 ergs/cm

(29)

2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

GOOD

Equilibrium

Film Pressure

45

Figure 1. Schematic: A possible isotherm for adsorption of a liquid such as carbon tetrachloride or hexadecane on a molecularly smooth, homogeneous solid such as Teflon TFE. Extrapohtions shown on log-log plot are speculation, and no physical reality is intended, particularly beyond the region where the curve starts to swing to the left.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

46

ADSORPTION

AT

INTERFACES

1

I f the water c l u s t e r s on Adamson s p o l y e t h y l e n e were i s o l a t e d from each o t h e r , t h e i r p r e s e n c e would not reduce t h e water c o n t a c t a n g l e t o z e r o . And i n the h y d r o p h o b i c r e g i o n s between c l u s t e r s , t h e amount o f water adsorbed p e r u n i t a r e a , and ττ , would be n e g l i g i b l e — a s computed above, f o r T a b l e I I I . β

Conclusions The e q u i l i b r i u m f i l m p r e s s u r e , 7 r , s h o u l d be n e g l i g i b l e on a smooth, homogeneous s u r f a c e o f a lowenergy s o l i d such as T e f l o n , f o r most l i q u i d s t h a t form non-zero c o n t a c t a n g l e s , and p a r t i c u l a r l y f o r those w i t h h i g h h e a t s o f v a p o r i z a t i o n . ir s h o u l d be large f o r l o w - b o i l i n g substances such as N 2 ethane e t c . , on t h e s e s o l i d s d i c t i o n s are i n accor e

e

Acknowledgement T h i s work was s u p p o r t e d by t h e N a t i o n a l S c i e n c e F o u n d a t i o n under Grant GK10602. Literature

Cited

1.

Fox, H.W. and Zisman, W.A., (1950) 5, 514.

2.

Good, R.J. and (1960) 64, 561.

3.

Adamson, A.W., and L i n g , I . , in " C o n t a c t A n g l e , Wettability and A d h e s i o n " , p. 57, Advan. Chem. S e r No. 43, American C h e m i c a l S o c i e t y , Washington, D.C., 1 9 6 4 .

4.

Graham, D.P., J. Phys. Chem., (1965), 69, 4387.

5.

Wade, W.H., and Whalen, J.W., J . Phys. Chem. (1968), 72, 2898.

6.

Whalen, J.W., J . Colloid (1968), 28, 443.

7.

Good, R.J., in " C o n t a c t A n g l e , W e t t a b i l i t y and Adhesion", Advan. Chem. S e r . No. 43, American C h e m i c a l S o c i e t y , p. 74, Washington, D.C., 196 4 .

8.

Adamson, A.W., 4 7 t h N a t i o n a l Ottawa, Canada, June, 1973.

Girifalco,

J.

Colloid

Sci.,

L.A., J. Phys. Chem.,

and

Interface

Colloid

Sci.,

Symposium,

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3.

9. 10.

GOOD

EquilibriumFilmPressure

47

Adamson, A.W., 167th National Meeting of the American Chemical Society, Los Angeles, April, 1974. Good, R . J . and Elbing, Ε . , Ind. Eng. Chem. (1970), 62, (3), 54.

11.

de Boer, J . H ., "The Dynamical Character of Adsorp­ tion," Oxford University Press, London, 1953.

12.

Ross, S., and O l i v i e r , J . P . , "0n Physical Adsorp­ tion," Interscience Publishers, New York, 1964.

13.

Hill, T . L . , "Introduction to S t a t i s t i c a l Thermo­ dynamics," Addison-Wesley Publishing Co., Reading, Mass., 1960.

14.

Everett, D.H., Proc. Chem. Soc., Feb., 1958, p. 57.

15.

Glasstone, S., L a i d l e r , K.J., and Eyring, Η., "Theory of Rate Processes," McGraw-Hill, N . Y . , 1941.

16.

C.R.C. Handbook, 51st ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1970.

17.

Fowler, R . H . , and Guggenheim, E . A . , " S t a t i s t i c a l Thermodynamics," Cambridge University Press, London, 1952.

18.

Berghausen, P . E . , Good, R.J., Kraus, G . , Podolsky, Β., and S o l l e r , W., "Fundamental Studies of the Adhesion of Ice to S o l i d s , " WADC Technical Report 55-44, 1955.

19.

Chessick, J.J., Healey, F . H . , and Zettlemoyer, A . C . , J . Phys. Chem. (1956), 60, 1345.

20.

Neumann, A.W. and Good, R.J., J . Colloid and Inter­ face Sci., (1972), 38, 341.

21.

Fowkes, F . M . , J. Phys. Chem. (1957), 61, 904.

22.

Whalen, J.W., Vacuum Microbalance Techniques, A.W. Czanderna, E d . , v. 8, p. 121, Plenum Press, 1971.

23.

Whalen, J.W., (personal communication,

24.

Zisman, W.A., i n "Contact Angle, Wettability and Adhesion," Advan. Chem. Ser., No. 43, pp. 1-51, American Chemical Society, Washington, D.C., 1964.

1974).

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

4 Binding of Solute and Solvent at the Interface and the Gibbs Surface Excess D. K. C H A T T O R A J and S. P. M O U L I K Department of Food Technology and Biochemical Engineering and Department of Chemistry, Jadavpur University, Calcutta-32, India

Introduction With the help of an imaginary mathematical plane placed at the interfacial region, a liquid-gas system, according to the Gibbs concept, may be divided into two phases. From the thermodynamic analysis of such a system, Gibbs also derived his well­ -known equation relating the surface excess of solute with the surface tension and bulk activity of the solute in solution. The physical concepts associated with the Gibbs surface excess have been examined more critically by Guggenheim and Adam (1) and also by Defay and Prigogine (2). Guggenheim (3) has also given an alternative derivation of the Gibbs adsorption equation assuming certain arbitrary but finite values for the physical thickness of the interfacial phase. In some cases, the interfacial thickness may be estimated from the experimental data (4). Goodrich (5) has recently analyzed the Gibbs adsorption equation with the help of an algebric method in which no mention is made of the mathematical dividing surfaces. Surface excesses of solute and solvent in a two-component system are, however, relative to each other and their values may be positive or negative. An attempt will be made in this paper to obtain relations between the surface excesses and the absolute amounts of solvent and solute bound to the interfacial layer. It is well-known that the surface tension of water increases with addition of various inorganic electrolytes to its bulk. In the dilute region of electrolyte concentrations, this increase is explained in terms of image forces (6^Z.>jL) * ^ extensive application of the Gibbs adsorption equation for the highly concentrated electrolyte solutions did not attract many workers because interpretation of the negative surface excess of electrolyte in terms of its interfacial adsorption is difficult. An attempt will also be made here to estimate the composition of the interfacial phase of an electrolyte solution from the observed negative value of the solute surface excess. T

48 In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ie

4.

cHATTORAj A N D MOULiK

Binding of Solute and Solvent

Binding o f Two Components at the L i q u i d I n t e r f a c e Let us imagine t h a t a c e r t a i n amount of a l i q u i d component 1 i s mixed w i t h a d e f i n i t e amount of another l i q u i d or s o l i d component 2 as a r e s u l t o f which a b i n a r y s o l u t i o n i n the shape of a column (Figure 1) i s formed. With the help o f a plane set a r b i t r a r i l y at p o s i t i o n P j p j , t h i s column may be d i v i d e d i n t o two d i s t i n c t regions A and B. The exact nature and the charac­ t e r i s t i c f e a t u r e of t h i s d i v i d i n g plane w i l l be discussed l a t e r on i n d e t a i l . Region B, composed s o l e l y of the bulk l i q u i d phase, contains ηχ and T12 moles of components 1 and 2 respec­ t i v e l y . The components i n the bulk phase are s a i d t o remain i n the f r e e s t a t e of mixing. In region A, nj and τΐ2 moles of two components are present as a whole. Out o f these, ηχ and η 2 moles e x i s t i n g i n the f r e e s t a t e of mixing may form the bulk phase. Remaining Δ n with moles of componen 2 because of the existence of the i n t e r f a c i a l energy at the upper extreme top s i d e o f t h i s r e g i o n . They are termed to remain i n the bound s t a t e o f mixing and considered to form one square centimeter of an i n t e r f a c e . ?

Let Γ ι and Γ 2 be the r e l a t i v e excesses of components 1 and 2 r e s p e c t i v e l y i n r e g i o n A which may be d e f i n e d by the r e ­ l a t i o n s (2) ,

1 *2

= n{ - n^

Τ

= n2 - ni jh_

2

...

χ

Γ^

...

(1) (2)

*i where and X2 are bulk mole f r a c t i o n s of the r e s p e c t i v e com­ ponents i n r e g i o n B. The concentrations o f s o l u t e and solvent i n the gas phase are neglected i n w r i t i n g Equations (1) and (2). Γ j and Τ2 w i l l be zero when the composition n^Av? of r e g i o n A becomes equal to the bulk composition X1/X2 of region B. Combining r e l a t i o n s (1) and (2), Equation (3) w i l l be obtained. f

Χ

χ

Τ2

+ X

Γ 2

1

= 0

...

(3)

For given values o f X^ and X2, the values o f ^ \ and Γ 2 are thus r e l a t e d t o each other according to Equation (3) and o b v i o u s l y the two excesses a r e o p p o s i t e i n s i g n . F u r t h e r , a t d e f i n t e values o f X^ and X2, n^ and n2 i n Equations (1) and (2) are not f i x e d but are s i g n i f i c a n t l y dependent on the a r b i ­ t r a r y p o s i t i o n o f the d i v i d i n g plane. The absolute composition of the surface cannot t h e r e f o r e be expressed i n terms o f Γι, f

Γ2,

ni

f

a n c

* 2· η

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

50

ADSORPTION

AT

INTERFACES

Let us now assume f u r t h e r t h a t the d i v i d i n g plane at p-^p^ behaves as a semi-permeable membrane which allows o n l y the com­ ponents i n t h e i r f r e e s t a t e o f mixing t o pass from r e g i o n A to r e g i o n Β and v i c e v e r s a . However, the components i n t h e i r bound s t a t e o f mixing i n r e g i o n A are not allowed t o permeate through t h i s membrane. The chemical p o t e n t i a l M 2 °f component 2 i n r e g i o n A, remaining i n the f r e e s t a t e may be given by the r e ­ lation, If

=

β 2

μ

2

+

R

T

l

n

f

2

n

2

Π n

=

M°

If +

l

n

2

+

(nj

-

&n{)+in

2

-

Δη ) 2

(4)

a r e

t n e

Here f and μ. r a t i o n a l a c t i v i t y c o e f f i c i e n t and standard chemical p o t e n t i a l o f component 2 i n the f r e e phase r e s p e c t i v e l y . The chemical p o t e n t i a l o f the same component i n r e g i o n Β i s s i m i l a r l y given by Equation ( 5 ) . 2

2

μ

=

2

μ

+

2

RT l n f X 2

...

2

(5)

From^the p r i n c i p l e o f membrane e q u i l i b r i u m , JLt i s equal t o U>2 t h a t combining Equations (4) and ( 5 ) , one w i l l o b t a i n 2

s o

n

2

nj

-

Δη

-

Δη*

X

2

...

2

(6)

X

1

Rearranging t h i s , n

2

-

n{

x

2

=

Δη

2

-

X

2

An[

...

(7)

Equation (7) i s s i m i l a r i n form to t h a t used by B u l l and Breese (9) f o r the c a l c u l a t i o n s o f the extents, o f s o l u t e and.solvent b i n d i n g on the p r o t e i n boundary. I n s e r t i n g Equation (7) i n Equation ( 2 ) ,

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

4.

CHATTORAJ

AND

Γ

=

2

Binding, of Solute and Solvent

MOULiK

Δη

2

-

An

x

x

2

51

...

(8)

I t may s i m i l a r l y be shovm t h a t

Γι

=

AnJ

-

Δη

*1_

2

...

(9)

X2 For given values o f and X , Δ η | and Δη? (and hence 1^ and Γ ) are not dependent on the p o s i t i o n o f the d i v i d i n g membrane. Absolute composition o f the bound phase a t the i n t e r face may be obtained i experimental data. Equation (2) may a l s o be w r i t t e n i n the form, 2

2

Γ

2

=

(Δη^ -

Δη[

X

2 x

}

l

+ (n' 2

X

2 j

..

(10)

X

From the comparison r e l a t i o n s (8) and (10), one w i l l a t once f i n d , X

η'' 2

η" 1

2

...

(10a)

X. 1

This means t h a t the mole r a t i o n o f the components i n the f r e e phases o f regions A and Β are i d e n t i c a l . I n the r i g h t s i d e o f Equation ( 2 ) , two equal and opposite v a r i a b l e s η and η Xo/Xj become i m p l i c i t l y i n c l u d e d owing t o the a r b i t r a r y placement o f the d i v i d i n g plane i n c l u d i n g a p a r t o f the bulk region. The numerical values o f these v a r i a b l e s then depend upon the p o s i t i o n o f t h i s d i v i d i n g plane. The terms i n r e l a ­ t i o n s (8) and (9) are independent o f the p o s i t i o n o f the d i v i d i n g membrane. The Gibbs Adsorption Equation Let us now imagine t h a t the d i v i d i n g plane i s r a i s e d from p o s i t i o n p-jP-[ t o P P s l o w l y and r e v e r s i b l y , so t h a t a l l the f r e e components from r e g i o n A permeate t o region B. Region Β i s now occupying the t o t a l bulk o f the l i q u i d system whereas r e g i o n A, s o l e l y composed o f Δ η ^ and Δ η ^ moles o f the bound components, may be regarded t o form the surface phase o f one square centimeter i n t e r f a c i a l area. The s p e c i a l mixing o f the components a t the i n t e r f a c e i s o b v i o u s l y due t o the e x i s t e n c e 2

2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

52

ADSORPTION

AT

INTERFACES

o f the i n t e r f a c i a l energy. In the absence of the imaginary membrane a l s o , the bound s t a t e should remain as a p h y s i c a l r e a l i t y because the i n t e r f a c i a l f r e e energy does not disappear under t h i s c o n d i t i o n . The surface bound phase may thus be imagined t o be separated e n t i r e l y from the l i q u i d i n b u l k , by an imaginary p h a s e - d i v i d i n g plane placed at the p o s i t i o n P P 2 Applying the Gibbs-Duhem r e l a t i o n s f o r the surface (bound) and bulk phases separated w i t h such a plane set a p p r o p r i a t e l y , we can o b t a i n the f a m i l i a r expressions f o r the Gibbs adsorption equation which at constant temperature and pressure w i l l read (3), ?

2

Γ

2

=

( Δη

=

f

-

2

x

Δη|

2

)

2

RT

d f X 2

2

and (

Δ

Δη.

Π ι

X

=

- f x x

RT

2

dy

x

d

... X £ 1

(12)

1

Here y stands f o r the s u r f a c e t e n s i o n o f the l i q u i d mixture corresponding t o a given bulk mole f r a c t i o n X o f the s o l u t e , f l and f , the r a t i o n a l a c t i v i t y c o e f f i c i e n t s of the s o l v e n t and s o l u t e r e s p e c t i v e l y , R the gas constant and Τ the absolute temperature. In the conventional forms of the Gibbs equation, Γι and Γ are r e l a t e d to n j and n according to Equations (1) and (2) r e s p e c t i v e l y which on t h e i r t u r n depend s i g n i f i ­ c a n t l y on the p o s i t i o n of an a r b i t r a r y d i v i d i n g plane P i P i . Δηj and Δη are, however, independent of the p o s i t i o n o f the d i v i d i n g plane. 2

2

2

2

1

2

Evaluations of

^2

The surface t e n s i o n , y , o f water u s u a l l y increases w i t h increase i n c o n c e n t r a t i o n o f an i n o r g a n i c e l e c t r o l y t e provided the s o l u t e content i n the aqueous s o l u t i o n i s high. For the present a n a l y s i s , the data on the surface t e n s i o n o f water f o r d i f f e r e n t high concentrations of an e l e c t r o l y t e have been c o l l e ­ cted form the l i t e r a t u r e . These e l e c t r o l y t e s are the f o l l o w ­ ing: L i C l (10) 25°C; NaCl (11) 25°C; KC1 (12) 25°C; NaBr (10)

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

4.

CHATTORAJ

AND

53

Binding of Solute and Solvent

MOULiK

25°C; NaN0 (10) 20°C; K S 0 (12) 25°C; M g C l (10) 20°C; MgS0 (13) 25°C and A l (S04)3 (10) 25°C The surface t e n s i o n data of n o n - i o n i c sucrose (10) s o l u t i o n s have a l s o been considered here s i n c e t h i s s o l u t e i s observed t o increase the boundary t e n s i o n o f water. The p r a c t i c a l a c t i v i t y c o e f f i c i e n t s (on the m o l a l i t y s c a l e ) f o r v a r i o u s concentrations o f these e l e c t r o l y t e s and sucrose can be obtained from the l i t e r a t u r e (14). The values o f t h e corresponding r a t i o n a l a c t i v i t y c o e f f i c i e n t s ( f ) of these s o l u t i o n s may e a s i l y be c a l c u l a t e d u s i n g a p p r o p r i a t e conversion f a c t o r s (14). Here water and s o l u t e stand f o r com­ ponents 1 and 2 r e s p e c t i v e l y . For each s o l u t e , y has been p l o t t e d against f X and t h e slopes d y /d (f2X2) o f curve f o r v a r i o u s v a l u e s o f f2X2 have been c a l c u l a t e d u s i n g the chordarea method o f slope a n a l y s i s (15). The negative surface excesses - Γ 2 , o f the e l e c t r o l y t e s f o r v a r i o u s values o f X have been c a l c u l a t e d w i t h t h e hel and 5, - Γ 2 f o r v a r i o u against the mole r a t i o X / X i . The open and c l o s e d signs i n the f i g u r e s represent data obtained from experiments and from i n t e r p o l a t i o n o f 7-f2X2 curves, r e s p e c t i v e l y . 3

2

4

2

4

2

2

t

2

n

e

2

2

Solute-Solvent Binding C h a r a c t e r i s t i c s I t i s o f i n t e r e s t t o note t h a t i n a l l these p l o t s i n Figures 2, 3, 4 and 5 increases l i n e a r l y w i t h i n c r e a s i n g mole r a t i o , X 2 / X 1 , provided the s o l u t e content i n the s o l u t i o n i s not too high. The slope and i n t e r c e p t o f such l i n e a r p l o t s may e v i d e n t l y represent the r e s p e c t i v e values o f Δ η ι and Δ 2 according t o Equations (8) o r (11). The l e a s t square values o f Δηχ and Δ η f o r v a r i o u s systems are presented i n Table I along w i t h t h e i r r e s p e c t i v e s t a n d a r d d e v i a t i o n s . From t h e values o f Δ η ^ i n Table I , i t may be observed t h a t one square centimeter o f a s o l u t i o n i n t e r f a c e may bind s i g n i f i ­ cant amount o f water whose magnitude may be o f t h e order 1 0 " ° t o 10" moles. Δη{ f o r a l k a l i c h l o r i d e s f o l l o w the order: L i C l < NaCl < KCl. The water b i n d i n g c a p a c i t i e s o f the i n t e r ­ face i n the presence o f u n i - u n i v a l e n t sodium s a l t s (NaCl, NaBr and NaN03) do d i f f e r from each other widely. The magnitudes of Δ η ^ f o r u n i - u n i v a l e n t and u n i - b i v a l e n t s a l t s ( K S 0 , M g C l ) are a l s o comparable t o each other. However, Δ η ^ f o r p o l y v a l e n t e l e c t r o l y t e s , A l ( S 0 ) 3 and MgS0 , are s i g n i f i c a n t l y high. The agreement o f t h e order o f Δ η ! f o r v a r i o u s e l e c t r o l y t e s w i t h that t o be expected from the t y o t r o p i c s e r i e s i s o n l y p a r t i a l . From Figures 2, 3, 4 and 5, i t may a l s o be noted t h a t the p l o t o f - Γ against Χ /Χχ d e v i a t e s from l i n e a r i t y f o r L i C l , NaBr (not shown i n f i g u r e ) , NaNU3, K S 0 (not shown), and A l (S0 )3 when t h e mole r a t i o n r e l a t i v e l y high. This may i n d i c a t e t h a t t h e surface bound components Δη^ and Δ η are not constant but become v a r i a b l e f u n c t i o n s o f X A i a t r e l a t i v e l y higher s o l u t e c o n c e n t r a t i o n s . When X A l f o r NaNU3, K S 0 , K C l , η

2

f

n

o

t

2

2

2

4

4

2

4

2

2

a

r

4

2

e

4

2

2

2

2

4

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

5.57

KC1 (cone)

(b)

3.74

K2SO4 (cone)

155

MgSÛ4 (cone)

00

52.7

MgS0 ( d i l )

8 (a)

4

MgCl

7

(b)

6.66

4.71

K2SO4 ( d i l )

6 (a)

2

8.36

NaNU3 (cone)

00

3.28

NaN0 ( d i l )

5 (a)

3.06

NaBr

4

3

5.05

KC1 ( d i l )

3 (a)

3.70

NaCl

2

2.95

+

+

+

+

+

+

+

+

+

+

+

+

9

0.83

0.90

0.29

0.04

0.96

0.70

0.07

0.05

0.18

0.01

0.07

0.31

2

A n j χ 10 moles/cm

LiCl

Electrolytes

1

Serial No.

-0.05

0.10

0.51

-0.01

-0.08

57.7

-0.39

0.01

-1.51

-1.31

-0.15

0.34

+

+

+

+

+

+

+

+

+

+

+

+

0.61

0.35

0.23

0.03

0.12

9.24

0.08

0.08

0.79

0.39

0.12

1.04

2

1 1

A n j x 10 moles/cm s

Δη

93.0

31.6

3.99

2.24

2.82

3.45

1.97

1.83

3.33

3.02

2.21

1.77

L

Table I . Least Square Values o f Δ η { and

0.069

^ J L Δ ηj

2

s

3.90

m

S

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

s

2.60 9.00

2.62 +_ 1.70 18.8 + 1.86

15.1 +_ 0.89

Sucrose

19.2

L

4.34 +_ 1.73

1 1

Sucrose ( d i l )

(cone)

(cone)

*not l e a s t square v a l u e s .

(b)

10(a)

0

2

χ 10

moles/cm

2

10.5

32.0

2

Δη

4.66 + 4.23

3

Al2(S04)

(b)

*(dil)

9

mo l e s / c m

Δ n{ χ 1 0

17.6 +_ 2.92

3

4

A1 (S0 )

2

Electrolytes

9(a)

No.

Serial

Table I . (Contd.)

1

2

s

0.33 0.69

0.0124

0.14

m

0.0060

0.0026

Δη 1

Δ n

ο

a

Si"

IT

56

ADSORPTION

P

2

AT

INTERFACES

y///////7777}\ P2

p; θ

Figure 1. Hypothetical binary solution in the shape of a column

5 10

10 20

15 50

20 40

( X /X|> X I 0 2

25 SO

90 60

I Π

3

Figure 2. Surface excess of solute as a function of mole ratio. 1: KCl (Scale I-I). 2: KCl (Scale I-II). 3: MgSO (Scale II-II). 4: MgSO (Scale I-I). h

/f

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

CHATTORAJ

AND

Binding of Solute and Solvent

MOULiK

CM

(X /X,

Figure 3.

) Χ ΙΟ

Surface excess of solute as a function of mole ratio. 1-4: LiCl, NaBr, NaCl, MgCl . 2

I

π

m

-3 -60 L

Figure 4. Surface excess of solute as a function of mole ratio. 1: NaN0 (Scale II-II). 2: NaNO, (Scale I-I). 3: K SO (Scale III-III). 4:K,SO,,(ScaleUl-l). 3

2

h

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

58

ADSORPTION

AT

Figure 5. Surface excess of solute as a function of mole ratio. 1: Sucrose (Scale I-I). 2: Sucrose (Scale II-I). 3 and 4: Al (SO., ), (Scale I-I). 2

t

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

INTERFACES

4.

CHATTORAJ

AND

MOULiK

Binding of Solute and Solvent

59

MgSU4, A l (S04)3 and sucrose are very h i g h , - Γ v s X / X i p l o t s become again l i n e a r having d i f f e r e n t slopes and i n t e r ­ cepts. The l e a s t square values o f Δ I L and Δ η , c a l c u l a t e d again from Equation (11) a t these regions o f h i g h s o l u t e con­ t e n t , are a l s o i n c l u d e d i n Table I . Compared t o Δ η | , values o f Δ η f o r d i f f e r e n t e l e c t r o ­ l y t e s are indeed q u i t e s m a l l . Δ η o f NaNC3 (concentrated) i s very h i g h and the s u r f a c e m o l a l i t y (m ) i n t h i s case i s as h i g h as 4 molal compared t o i t s bulk m o l a l i t y v a r y i n g between 5 t o 10. For A l (SU4)3 and sucrose, Δ η i s s i g n i f i c a n t and m l i e s between 0.10 t o 0.70. For a l l other cases, Δ η and m are l e s s than 1 0 " and 1 0 ~ r e s p e c t i v e l y . The observed experimental e r r o r f o r the e v a l u a t i o n o f Δ η are q u i t e high so t h a t the signs and magnitudes o f Δ η f o r these e l e c t r o l y t e s have no p h y s i c a l meaning. For these e l e c t r o l y t e s one may e a s i l y neg­ l e c t Δ η i n Equatio i n the e v a l u a t i o n o f Δ η ^ . £ni i s o f the order 10 and i t s signs are p o s i t i v e both i n the nigh and low ranges o f mole r a t i o . Δ η | f o r low and high KCl concentrations are found t o be 5.0 χ 10"" and 5.6x10 moles per u n i t area r e s p e c t i v e l y . Since negative values f o r Δη do not bear any p h y s i c a l meaning, probably Δ η i n Equation (11) f o r KCl i s a l s o n e g l i g i b l e but Δ η | instead of remaining constant s l o w l y i n c r e a s e s w i t h gradual increase o f X / X j . The i n i t i a l slope r e p r e s e n t i n g Δ n-^ o f KCl i n a short range o f e l e c t r o l y t e c o n c e n t r a t i o n w i l l not be, however, t o o f a r o f f from the observed v a l u e 5.0 χ 10"^. In g e n e r a l , we conclude t h a t o n l y a small amount o f e l e c t r o l y t e i s a s s o c i a t e d w i t h the surface-bound water even when a l a r g e amount o f the same e l e c t r o l y t e remains d i s s o l v e d i n the bulk water phase. I n t e r f a c i a l water f o r these cases i s h i g h l y s u r f a c e - a c t i v e and i t has a strong d i s l i k e f o r i n o r g a n i c e l e c t r o l y t e s and sucrose. The r e l a t i v e p o s i t i v e surface excess o f water i n the con­ v e n t i o n a l i n t e r p r e t a t i o n o f the Gibbs equation may be i d e n t i f i e d w i t h the amount o f water adsorbed on one square centimeter o f the l i q u i d i n t e r f a c e when the adsorbed s o l u t e i s a r b i t r a r i l y taken as zero. In many o f the cases considered here, Δ η i s i n f a c t n e g l i g i b l y small so t h a t according t o Equations ( 3 ) , (8) and ( 9 ) , Γι i s v e r y c l o s e t o Δ η | . R e s u l t s i n Table I f o r NaN03 and a few e l e c t r o l y t e s a l s o i n d i c a t e t h a t Δ η ^ may be s i g n i f i c a n t l y g r e a t e r thann i f Δ η i s not n e g l i g i b l y s m a l l . F u r t h e r , the r e l a t i v e excess r which i s negative i s observed t o increase c o n s i d e r a b l y w i t h increase o f Χ?/Χχ. Under these c o n d i t i o n s , e l e c t r o l y t e a c t u a l l y bound, Δ η , i s e i t h e r n e g l i ­ g i b l y small o r s i g n i f i c a n t l y p o s i t i v e and at c e r t a i n range o f e l e c t r o l y t e c o n c e n t r a t i o n , i t becomes independent o f the mole r a t i o X /X^. Assuming the e f f e c t i v e c r o s s - s e c t i o n a l area o f a water molecule t o be 1 nm a t the i n t e r f a c e , the moles ( Δη·^) o f water r e q u i r e d t o form one square centimeter (6) o f an i n t e r 2

2

2

2

2

2

s

2

2

s

2

11

s

2

2

2

2

9

2

2

2

2

2

2

2

2

2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

60

ADSORPTION

AT

INTERFACES

9

f a c i a l monolayer i s 1.7 χ 10" . Neglecting the c o n t r i b u t i o n o f Δ η , the number ( L ) o f water l a y e r s i n the bound i n t e r f a c i a l region may be estimated from the r a t i o Δη·[/ Δ η ^ . L f o r v a r i o u s e l e c t r o l y t e s and sucrose are a l s o included i n Table I . The r e s u l t s i n d i c a t e that the surface bound water i s m u l t i molecular f o r a l l s o l u t e s . For u n i - u n i v a l e n t and u n i - b i v a l e n t e l e c t r o l y t e s , as w e l l as f o r non-ionic sucrose, the number o f such surface bound l a y e r s may l i e between the values 2 t o 6. Values o f L , f o r A l ^ 0 4 ) 3 and sucrose (concentrated) are moderately high whereas those f o r MgS0 i n both high and low concentration ranges are u n u s u a l l y l a r g e . Higher values o f L f o r p o l y v a l e n t e l e c t r o l y t e s may be r e a l . I t may a l t e r n a t i v e l y be p o s s i b l e that these p o l y v a l e n t e l e c t r o l y t e s undergo consider­ able h y d r o l y s i s o r i o n - a s s o c i a t i o n a t high s o l u t e concentrations. Under these c o n d i t i o n s , s e v e r a l types o f s o l u t e components w i l l e x i s t i n the system s needed f o r the c a l c u l a t i o o f the Gibbs adsorption equation (16). 2

s

s

s

2

4

s

Conclusions I t i s evident from a l l these d i s c u s s i o n s t h a t a l i q u i d column i n Figure 1 may be d i v i d e d by a phase demarcating plane 2 2 every part o f the bulk phase below t h i s plane has the mole r a t i o composition Χ /Χι· Above t h i s plane, t h e mole r a t i o o f any part o f the surface-bound l i q u i c i phase mav deviate from Χ /Χχ because o f the b i n d i n g o f Δ η ^ and Δ η moles o f the components. S i m i l a r r e a l concept f o r the surface phase has a l s o been discussed by others (_2, 3 ) . With the help of the Gibbs Equations (11) and (12), the a c t u a l composition o f the surface region i n terms o f Δ η * and Δ η may be evaluated from the surface t e n s i o n - c o n c e n t r a t i o n data. This e v a l u a t i o n i s only p o s s i b l e when the composition o f the surface bound l i q u i d phase becomes independent o f the bulk mole r a t i o so that - Γ becomes a l i n e a r f u n c t i o n o f Χ /Χι· The l i q u i d column i n Figure 1 may f u r t h e r be d i v i d e d by p l a c i n g a semipermeable membrane a t an a r b i t r a r y p o s i t i o n P^Pj so that region A now contains the bulk and the surface-bound phases r e s p e c t i v e l y below and above the phase d i v i d i n g plane P P . The r e l a t i v e surface excesss Γ y thus be shown t o be equal t o e i t h e r o f the expressions o c c u r r i n g on the l e f t or r i g h t s i d e o f Equation (7). The magnitudes o f the terms n j and n^ i n t h i s equation depend s i g n i f i c a n t l y on the a r b i ­ t r a r y p o s i t i o n o f P-^Pjwhereas those o f Δ η | and Δ η are i n ­ v a r i a n t t o ΡχΡχ. In the conventional d e r i v a t i o n o f the Gibbs adsorption equation, sometimes the p h a s e - d i v i d i n g plane i s a r b i t r a r i l y s h i f t e d from i t s f i x e d p o s i t i o n P P t o a v a r i a b l e p o s i t i o n 1 1* r e g i o n o f A i s then a r b i t r a r i l y imagined t o be the surface phase composed o f n j and n moles o f the components. P

P

s u c n

t n a t

2

2

2

2

2

2

m

2

a

2

2

2

2

P

P

T

n

e

2

w n o l e

2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

4.

CHATTORAJ

AND

MOULiK

Binding of Solute and Solvent

61

The i n d i v i d u a l values o f n] and n^ w i l l not bear any p h y s i c a l s i g n i f a n c e . However, the r e l a t i v e surface excess Γ2 defined i n terms o f n^ and n^ according t o Equation (2) may be c o r r e c t l y c a l c u l a t e d from the 7-X2 data s i n c e the r e l a t i v e surface ex­ cess does not depend on the p o s i t i o n o f Ρ ι Ρ χ . The i n v a r i a n t character o f the r e l a t i v e excess may be c l e a r from the c l o s e s c r u t i n y o f Equations ( 7 ) , (10) and (10a). U n l i k e t h e long-chain i o n s , the c a t i o n s and anions o f the i n o r g a n i c e l e c t r o l y t e s are not s p e c i a l l y adsorbed and o r i e n t e d at the i n t e r f a c e o f water. Both surface and bulk phases d i v i d e d by the plane P2P2 should be i n d i v i d u a l l y e l e c t r o n e u t r a l (2) i n terms o f the net charge o f c a t i o n s and anions. With the help o f the Gibbs Equation (11), one can o n l y c a l c u l a t e the macroscopic composition o f the surface phase i n terms o f the water and e l e c ­ t r o l y t e components bound t o each other The m i c r o s c o p i c f e a t u r e of the i o n i c double l a y e i n the i n t e r f a c i a l r e g i o analysis. From the values o f L i n Table 1, i t may be concluded that the i n t e r f a c e s o f d i f f e r e n t e l e c t r o l y t e s o l u t i o n s u s u a l l y poss­ ess p h y s i c a l t h i c k n e s s o f the order 1 t o 10 nm. This order i s i n agreement w i t h t h a t suggested by Guggenheim (17) f o r the t h i c k n e s s o f the p h y s i c a l l y defined surface phase. In c o n t r a s t to the uniform composition o f the bulk r e g i o n , the s o l u t e and solvent bound s u r f a c e r e g i o n should be p h y s i c a l l y inhomogeneous (17, 18). Assuming t h i s p h y s i c a l p i c t u r e o f the surface and bulk phases, Guggenheim (17, _18) has deduced the Gibbs a d s o r p t i o n equation which i s s i m i l a r i n form t o Equations (11) and (12). However, the i n d i v i d u a l amounts o f the s o l u t e and s o l v e n t com­ ponents bound a t the i n t e r f a c e i n h i s treatment remain a r b i t r a r y and u n c e r t a i n s i n c e the bulk phase i s separated from surface phase by a r b i t r a r y placement o f a d i v i d i n g plane. From the d i s ­ cussions presented above, i t i s noted t h a t Δ η } and Δ η ^ a r e independent o f the imaginary placement o f the d i v i d i n g plane. T h e i r values are absolute and under c e r t a i n c o n d i t i o n s may be evaluated w i t h i n the l i m i t s o f experimental e r r o r . In a separate paper i t w i l l be shown t h a t t h e present approach can a l s o be use­ f u l t o c a l c u l a t e the i n t e r f a c i a l b i n d i n g o f components r e s u l t i n g from the mixing o f an organic l i q u i d w i t h water. s

Acknowledgement The authors a r e g r a t e f u l t o Dr. Κ. K. Kundu f o r many h e l p f u l discussions. Literature Cited 1.

Guggenheim, E.A. and Adam, N.K., Proc. Roy. Soc. London, Ser. A, (1933) 139, 231.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

62

2.

3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

ADSORPTION AT INTERFACES

Defay, R., P r i g o g i n e , I . , Belleman, A. and E v e r e t t , D.H., "Surface Tension and A d s o r p t i o n " , John Wiley and Sons, Inc., New York, 1966. Guggenheim, E.A., Trans. Faraday Soc., (1940), 36, 397. C h a t t o r a j , D.K. and C h a t t e r j e e , A.K., J . C o l l o i d I n t e r f a c e Sci., (1966) 21, 159. Goodrich, F.C., Trans. Faraday Soc., (1968) 64, 3403. Randles, J.E.B., i n "Advances in E l e c t r o c h e m i s t r y and E l e c t r o c h e m i c a l E n g i n e e r i n g " , P. Delahay, Ed., V o l . 3, p.1, I n t e r s c i e n c e , New York 1963. Onsager, L. and Samaras, N.N.T., J. Chem. Phys., (1934) 2, 528. Buff, F.P. and Stilbinger, F.H., Jr., Chem. Phys., (1956) 25, 312. B u l l , H.B. and Breese Arch Biophys Biochem. (1970) 137, 299. "Hand Book o f Chemistry and P h y s i c s " , 47t ed., F25, The Chemical Rubber Company, C l e v e l a n d , Ohio, 1966-67. Jones, G. and Ray, W.A., J . Amer. Chem. Soc., (1941) 63, 3262. Jones, G. and Ray, W.A., J . Amer. Chem. Soc., (1937) 59, 187. Jones, G. and Ray, W.A., J . Amer. Chem. Soc., (1942) 64 2744. Robinson, R.A. and Stokes, R.H., " E l e c t r o l y t e S o l u t i o n s " , 2nd ed. ( r e v i s e d ) , B u t t e r w o r t s , London, 1959. C h a t t e r j e e , A.K. and C h a t t o r a j , D.K., J . C o l l o i d I n t e r f a c e Sci., (1968) 26, 140. C h a t t o r a j , D.K. and P a l , R.P., Indian J. Chem., (1970) 10, 417. Guggenheim, E.A., "Thermodynamics", North H o l l a n d , Amsterdam, 1961. Adam, N.K., "The P h y s i c s and Chemistry o f S u r f a c e s " , Dover P u b l i c a t i o n s , New York, 1968.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

5 Mechanism o f Sulfonate A d s o r p t i o n at the Silver Iodide-Solution Interface K. OSSEO-ASARE, D. W. F U E R S T E N A U , and

R. H . O T T E W I L L *

Department of Materials Science and Engineering, University of California, Berkeley, Calif. 94720

Introduction The e a r l y work on silver i o d i d e d i s p e r s i o n s (1) showed that the s o l s prepared in the presence of an excess of i o d i d e ions were more s t a b l e than those prepared w i t h silver ions present in ex­ cess. This was found to be due to the f a c t that the p o i n t of zero charge d i d not c o i n c i d e w i t h the equivalence p o i n t , i.e. in the presence of potential determining ions only, the equivalence p o i n t was found to be at pAg 8 whereas the net charge on the s u r f a c e became zero at pAg 5.5. Historically silver i o d i d e has been clas­ sified as a hydrophobic sol, a definition l a r g e l y based on the f a c t that silver i o d i d e s o l s are not r e v e r s i b l e , i.e. coagulated s o l s cannot be redispersed by diluting w i t h water (see Frens and Overbeek (2)). R e c e n t l y , s t u d i e s of the a d s o r p t i o n of water vapor on silver i o d i d e powders have shown t h a t the s u r f a c e is a l s o hydrophobic in terms of the u s u a l definition of wettability. Zettlemoyer et al. (3) found that the s u r f a c e area r a t i o s water/ argon and water/nitrogen were much l e s s than u n i t y and concluded that approximately three out of five s u r f a c e s i t e s were hydro­ phobic; they a t t r i b u t e d the h y d r o p h i l i c - h y d r o p h o b i c balance to oxide i m p u r i t i e s . The r e s u l t s of P r a v d i c and M i r n i k (4) showed that at pI 5 (pAg 11) and pH 5 hexylamine can reverse the charge of a silver iodide particle. This behavior i s in marked c o n t r a s t to the e f f e c t of alkylamine on q u a r t z , a h y d r o p h i l i c s u b s t r a t e , where as far as a d s o r p t i o n is concerned the octylammonium i o n appears to behave in the same way as an ammonium i o n ( 5 ) . Long chain alkyl sulfates, even at low c o n c e n t r a t i o n s , a l s o a f f e c t the z e t a p o t e n t i a l of the silver i o d i d e s u r f a c e ( 6 ) . Moreover, according to B i j s t e r b o s c h and Lyklema (7) even short c h a i n a l c o h o l s , e.g. η-butyl, adsorb w i t h t h e i r hydrophobic p a r t s towards the silver i o d i d e . Recently measurements of the contact angle of silver i o d i d e surfaces in water have shown that values of ca. 23° can be obtained (8,9). These f a c t o r s all suggest t h a t there i s strong hydrophobic i n t e r a c t i o n between hydrocarbon chains and 63

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

64

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INTERFACES

s i l v e r i o d i d e surfaces which can play an important r o l e i n s i l v e r i o d i d e - s u r f a c e a c t i v e agent s o l u t i o n i n t e r a c t i o n s . In a d d i t i o n , recent s t u d i e s u s i n g e l e c t r o n microscopy have shown that a l k y l p y r i d i n i u m compounds appear t o undergo a chem­ i c a l r e a c t i o n w i t h s i l v e r i o d i d e surfaces at s u r f a c t a n t concen­ t r a t i o n s approaching the 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 (10). I t appears t h e r e f o r e that the a d s o r p t i o n of surface a c t i v e agents at a s i l v e r i o d i d e s u r f a c e may i n v o l v e a complex i n t e r p l a y of e l e c t r i c a l , hydrophobic ( d i s p e r s i o n f o r c e s ) and chemical i n t e r ­ actions . The purpose of the present paper i s t o e l u c i d a t e a d s o r p t i o n mechanisms i n the a l k y l s u l f o n a t e - s i l v e r i o d i d e system through e l e c t r o p h o r e t i c m o b i l i t y measurements. The s u l f o n a t e s used i n t h i s study ranged from p e n t y l to t e t r a d e c y l . Further i n f o r m a t i o n on the nature of the A g i s u r f a c e and s u l f o n a t e a d s o r p t i o n was obtained through study systems. Experimental

- M a t e r i a l s and Methods

M a t e r i a l s . T r i p l y d i s t i l l e d water used f o r a l l s o l u t i o n s was prepared by f i r s t passing tap water through a Barnstead Laboratory s t i l l followed by a two-stage Haraeus quartz s t i l l . The f i n a l d i s t i l l a t e was kept under p u r i f i e d n i t r o g e n u n t i l used. S i l v e r n i t r a t e and potassium i o d i d e of A.R. grade were used to prepare the s i l v e r i o d i d e s o l . Iodine was obtained as resublimed c r y s t a l s from M a l l i n c k r o d t and s i l v e r w i r e of 99.5 to 99.8% p u r i t y was obtained from Sargent-Welch. The sodium s a l t s of C m , 12> 10> 8 s u l f o n i c a c i d s were s u p p l i e d by A l d r i c h Chemical Company w h i l e the C 5 was from Κ & Κ L a b o r a t o r i e s . c

c

a n d

c

P r e p a r a t i o n of S i l v e r Iodide S o l . A stock s o l was prepared by adding 50 ml of 1 0 " Μ ΚΙ s o l u t i o n to an equal volume of 1 0 ~ M AgNÛ3 s o l u t i o n w i t h s t i r r i n g . A f t e r aging f o r 12 - 18 hours, t h i s was d i l u t e d to a s o l c o n c e n t r a t i o n of 10~** M Agi f o r e l e c t r o ­ phoresis measurements. The i o n i c s t r e n g t h was c o n t r o l l e d w i t h 10~ M KNO3 and a p p r o p r i a t e volumes of AgNU3 and s u r f a c t a n t s o l u ­ t i o n s were added to g i v e t h e r e q u i r e d pAg and s u r f a c t a n t concen­ tration. z

2

3

E l e c t r o p h o r e s i s . The e l e c t r o p h o r e t i c measurements were con­ ducted w i t h the R i d d i c k Zetameter (11), a product o f Zetameter I n c . , New York. Room temperature was maintained a t 20 ± 2°C f o r most of these experiments. I n g e n e r a l , twenty m o b i l i t y readings were taken f o r each system and averaged; the p o l a r i t y of t h e a p p l i e d v o l t a g e was reversed f o r a l t e r n a t e measurements. U s u a l l y 100 V was used; however, f o r slower p a r t i c l e s i t was o f t e n neces­ sary to go to v o l t a g e s as high as 300 V to observe any a p p r e c i ­ able motion. Care was taken not to keep the s o l too long before use s i n c e on standing f o r extended periods of time, the s o l

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

5.

OSSEO-ASARE

ET

Sulfonate Adsorption

AL.

65

p a r t i c l e s have been found to decrease i n m o b i l i t y - probably a r e s u l t of the desorption which accompanies c o a g u l a t i o n ( 6 ) . The average diameter of the s o l p a r t i c l e s , 2a, was found by e l e c t r o n microscopy (12) to be 20 nm. The i o n i c s t r e n g t h was c o n t r o l l e d u s i n g ΙΟ" M KNO3; t h i s gave a Debye-Huckel r e c i p r o c a l l e n g t h 1/K of 9.5 nm. Based on the f a c t that under these c o n d i ­ t i o n s the product Ka has a v a l u e of 1.05, the r e s u l t s of Wiersema et a l . (13) can be used to convert the measured e l e c t r o p h o r e t i c m o b i l i t i e s to z e t a p o t e n t i a l s . Below a m o b i l i t y , u , of 2 urn/ sec per volt/cm, as a good f i t to the c a l c u l a t i o n s of Wiersema et a l . , the m o b i l i t y can be converted i n t o zeta p o t e n t i a l by 3

ζ = 20u

(1)

Q

e

where ζ i s the z e t a p o t e n t i a l i n m i l l i v o l t s b i l i t y v a l u e s , however zeta p o t e n t i a l becomes Wetting

At the higher

mo­

Behavior.

P r e p a r a t i o n of t h i n A g i f i l m s . F o l l o w i n g the method of B i l l e t t and O t t e w i l l ( 8 ) , g l a s s microscope s l i d e s , cut i n t o pieces approximately 1 cm χ 2.5 cm χ 0.1 cm, were cleaned w i t h aqua r e g i a and stored under t r i p l y d i s t i l l e d water. To p l a t e the g l a s s w i t h s i l v e r , a watch g l a s s w i t h the s l i d e s i n i t , was p o s i t i o n e d 3 cm v e r t i c a l l y below a s i l v e r source (approximately 6 cm s i l v e r w i r e ) held i n a tungsten basket. The vacuum u n i t was pumped down to about 666.6 yPa through a l i q u i d n i t r o g e n t r a p . The s i l v e r m i r r o r s were t r a n s f e r r e d q u i c k l y from the vacuum evap­ o r a t o r and immersed i n a 0.0025 Ν s o l u t i o n of i o d i n e i n 0.01 Μ ΚΙ s o l u t i o n f o r 20 - 30 seconds. The f i l m s were then aged i n 10" * Μ ΚΙ s o l u t i o n f o r 1.5 hours and kept under d i s t i l l e d water u n t i l used. I t was found that l e a v i n g a t h i n l a y e r of s i l v e r between the g l a s s p l a t e and the Agi f i l m improved the adhesion of the f i l m to the s u b s t r a t e . This procedure was t h e r e f o r e followed i n the p r e p a r a t i o n of the f i l m s . 1

Measurement of contact angle. The c a p t i v e bubble technique (8) was used to determine the contact angles. For making the measurement, the s o l u t i o n to be s t u d i e d was f i r s t added to a c e l l made of o p t i c a l g l a s s and then the s l i d e w i t h the A g i f i l m was placed i n t o the d e s i r e d s o l u t i o n f o r about 15 minutes before t a k i n g measurements. A g l a s s c y l i n d r i c a l tube of 3 mm i n t e r n a l diameter was placed above the f i l m s u r f a c e and the a i r pressure i n the bubble was regulated by means of a screw arrangement at the upper end of the tube. A telescope supplied w i t h an o c u l a r p r o t r a c t o r was used to observe the bubble p r o f i l e . The bubble was allowed to touch the f i l m surface by g e n t l y i n c r e a s i n g the pressure, then a f t e r s i t t i n g on the f i l m f o r about 15 seconds, the pressure was increased by a s m a l l amount. This

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION

A T INTERFACES

Figure 1. The effect of pAg on the electro­ phoretic mobility of silver iodide in the pres­ ence of sodium pentyl sulfonate at millimolar ionic strength with potassium nitrate

3

4

5

6

7

8

ρ Ag

Figure 2. The effect of pAg on the electro­ phoretic mobility of silver iodide in the pres­ ence of sodium octyl sulfonate at millimolar ionic strength with potassium nitrate

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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ossEOASARE E T A L .

Sulfonate Adsorption

67

s i t u a t i o n y i e l d s the receding angle θ^. The pressure was then r e l e a s e d u n t i l the contact boundary on the p l a t e j u s t moved. The r e s u l t i n g angle i s the advancing angle, θ^. S u r f a c t a n t s o l u ­ t i o n s of a given c o n c e n t r a t i o n were prepared and the contact angles were measured as a f u n c t i o n of pAg f o r C I Q and C ^ . In a l l cases, i n c l u d i n g the experiments i n the absence of s u r f a c t a n t , the i o n i c s t r e n g t h was c o n t r o l l e d w i t h ΙΟ" M KNO3. The contact angles reported here are the average of s i x or more values ob­ tained by p l a c i n g the bubbles on d i f f e r e n t samples or on d i f f e r ­ ent p o s i t i o n s on the same sample. 3

Results E l e c t r o p h o r e s i s . Figures 1 to 5 present the e l e c t r o p h o r e t i c m o b i l i t y of Agi as a f u n c t i o f pA f o v a r i o u a l k y l s u l f o n a t concentrations and d i f f e r e n s u r f a c t a n t , the p o i n t o charg Ag at pAg 5.6, i n agreement w i t h previous values reported i n the l i t e r a t u r e ( 1) . I n a l l cases, w i t h i n c r e a s i n g concentrations of s u r f a c t a n t at any pAg values below the pzc, the p o s i t i v e m o b i l i t y of the s o l p a r t i c l e s decreased, passed through z e r o , and then became i n c r e a s i n g l y negative. The most i n t e r e s t i n g f e a t u r e s of these r e s u l t s are (1) The short c h a i n s u l f o n a t e s are able to reverse the z e t a p o t e n t i a l on A g i although much higher concentrations are r e q u i r e d than f o r longer chain s u l f o n a t e s . (2) A l l the curves appear to c o i n c i d e i n the neighborhood of pAg 7 independent of chain l e n g t h or s u r f a c t a n t c o n c e n t r a t i o n . (3) The zeta p o t e n t i a l goes through a maximum at higher concentrations of s u r f a c t a n t , an e f f e c t which increases w i t h chain l e n g t h . Wetting Behavior. The magnitude of the contact angles ob­ t a i n e d both i n the absence of s u r f a c t a n t and i n the presence of v a r i o u s concentrations of and C\q have been p l o t t e d as a f u n c t i o n of pAg i n Figures 6 to 8. In the absence of s u r f a c t a n t , both the receding and advanc­ ing contact angles go through a maximum at about pAg 5.4. The curves shown i n F i g u r e 6 are drawn through the weighted average of the experimentally determined contact angle values f o r each pAg. The spread i n the θ values f o r a given pAg i s l a r g e l y the r e s u l t of the inherent d i f f i c u l t y of o b t a i n i n g p e r f e c t l y r e p r o ­ d u c i b l e s u r f a c e s . These r e s u l t s are i n good agreement w i t h those reported by B i l l e t t and O t t e w i l l (14) who a l s o observed a maximum at about pAg 5.4, which i s c l o s e to the pzc. Figures 7 and 8 show that when the b u l k c o n c e n t r a t i o n of the s u r f a c t a n t i s low, the w e t t i n g behavior i s very s i m i l a r to that of the s u r f a c t a n t - f r e e system except at higher p o s i t i v e s u r f a c e charge (low pAg) where a s i g n i f i c a n t r i s e i n contact angle i s observed. In other words, i n F i g u r e 8, the receding contact

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION

3

4

5

6

7

A T INTERFACES

8

Ρ Ag

Figure 3. The effect of pAg on the electrophoretic mobility of silver iodide in the pres­ ence of sodium decyl sulfonate at millimolar ionic strength with potassium nitrate

3

4

5

6

7

PAg

Figure 4. The effect of pAg on the electrophoretic mobility of silver iodide in the pres­ ence of sodium dodecyl sulfonate at millimolar ionic strength with potassium nitrate

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

5.

OSSEO-ASARE

ET AL.

Sulfonate Adsorption

Figure 5. The effect of pAg on the electrophoretic mobility of silver iodide in the presence of sodium tetradecyl sulfonate at millimolar ionic strength with potassium nitrate

Figure 6. The contact angle on silver iodide in the absence of surfactant as a function of pAg at millimolar ionic strength with potassium nitrate

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

69

ADSORPTION

120

AT

Γ

—ι C S0 No 0

3

( Ι 0 " Μ KNO3) 3

100 h

0 Δ

Ι«Ι0" Μ 4

ο 801

60|

ο

ο < 40|

2 Ο

5

pAg

6

Figure 7. The contact angle on silver iodide in the presence of sodium decyl sulfonate as a func­ tion of pAg at millimolar ionic strength with potassium nitrate

120

100 Ul UJ

ο ω 80(-

ζ


ιο

υ

•H i-H Ο

Ο ·Η ^

Φ r-t

i—t

i

&

Ctf CO

CO

10

u ιο

CM σ » t o t o CM t o

e υ

rt

to

ο to

to

CM to

Ο to

L O CM V O Ι Ο to to to to

σ>

νΟ

to

Η

I ι

ctf

«H 10 Oj

U

b

C

Q>

bû G

C •H

3

e ^ •H i-3

Ο CO

bO

6

d (LiDS) > d (NaDS). A l s o common ( n o n - s t r a t i f i e d ) f i l m s are s l i g h t l y t h i c k e r w i t h L i than w i t h N a (22). T h i s can be explained by the l e s s e r s p e c i f i c ad­ s o r p t i o n o f L i on the s u r f a c t a n t surface w i t h the ensuing stronger e l e c t r o s t a t i c r e p u l s i o n . T h i s e x p l a n a t i o n agrees w i t h the observed CMC-order o f LiDS and NaDS, but not f o r NH^DS (see above). The i n f l u e n c e o f the s u r f a c t a n t c o n c e n t r a t i o n ( c p ) i s two­ f o l d . I n the f i r s t p l a c observable.This i s probabl cooperative s t r u c t u r e formation. The second e f f e c t , the decrease of d w i t h i n c r e a s i n g c p i s more d i f f i c u l t t o e x p l a i n . B r u i l and Lyklema (3.) found a dependence on c ' ^ f NaDS-films. We found the same dependence f o r NH^DS. The v a r i o u s orders are roughly e q u i d i s t a n t . The d i f f e r e n c e s d - d j = Ad decrease w i t h i n c r e a s i n g c p . At the highest s o a p s t u d i e d ( 0 . 3 0 M f o r LiDS, 0 . 6 0 f o r NaDS and 0 . 5 0 f o r NH^DS) they are 6 . 6 , 5.5 and 6 . 3 nm r e s p e c t i v e l y . The mutual d i f f e r e n c e s are not s i g n i f i c a n t . These increments decrease f u r t h e r w i t h c p and upon e x t r a p o l a t i o n c _ « a t t a i n l i m i t i n g values of 5 . 2 ± 0 . 6 nm. T h i s tends t o the t h i c k n e s s o f a Newton f i l m . Under these c o n d i t i o n s the s t r a t i f i e d f i l m i s apparently b u i l t as r e ­ p e a t i n g Newton-like l a y e r s . +

+

+

s o a

g o a

1

o r

s o a

c

s o a

g o a

E f f e c t o f E l e c t r o l y t e s . The i n f l u e n c e o f added e l e c t r o l y t e s ( c o n c e n t r a t i o n c ) can be summarized i n t o two p o i n t s : ( i ) For a given o r d e r , d decreases somewhat w i t h c . For example, i n a f i l m drawn from a 0.2U M LiDS s o l u t i o n d-j decreases from 8 . 8 t o 7 . 8 nm and dg from 15-9 t o 1 5 · 5 nm i f L i C l i s added up t o 0.12 M. I n a f i l m , drawn from 0.2k M NH^DS, d^ decreases from 9 . 3 t o 8 . 0 nm i f NH^Cl i s added up t o 0 . 3 M. The decrease i s roughly l i n e a r . The measurements are not accurate enough t o say whether the steepness o f t h i s f a l l - o f f i s d i f f e r e n t f o r the d i f ­ f e r e n t o r d e r s . A p o s s i b l e e x p l a n a t i o n i s sought i n terms o f e l e c t r o s t a t i c s h i e l d i n g . Note t h a t the c o n c e n t r a t i o n s are s o h i g h t h a t the Debye-Huckel l i m i t i n g law, which would p r e d i c t a c | de­ pendency, i s no longer v a l i d . ( i i ) E l e c t r o l y t e s i n h i b i t s t r a t i f i c a t i o n , but the i n h i b i t i n g e f f e c t i s s t r o n g l y dependent on thé nature of the c a t i o n . Con­ s i d e r i n g the occurrence o f the second order above the f i r s t , i t appears t h a t o n l y 0 . 0 0 8 M o f added NaCl s u f f i c e s t o subdue i t s occurrence i n NaDS-films, whereas as much as 0.1k M L i C l i s need­ ed t o suppress the occurrence o f more than one l a y e r i n LiDSs t a b i l i z e d f i l m s . For the NH^ -case t h i s f i g u r e i s 0.16 M. g

s

n

+

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

196

ADSORPTION A T INTERFACES

Figure 1. Probable thickness dependency of the Gibbs . . . etc. represent 2nd . . . order. high surfactant concen­ tration, low surfactant concentration. d/nm 40

5th order

•

NaDS

*

Li DS

ο

NH DS 4

30

20h

^- —

- A

4th

order

3rd

order

2nd order

10 Γ·

0

0.2

0.A*

1st

0.6 Surfactant

order

cone/M

Figure 2. Metastable equilibrium thicknesses of stratified films, stabilized by LiDS, NaDS, or NH^DS. No electrolyte added, Τ = 25°C.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

13.

KEUSKAMP AND LYKLEMA

Free Liquid Films

197

There i s a certain parallelism with the influence of elec­ trolytes on common (not-stratified) black films: salts decrease d, and L i - and NH^ -films are s l i g h t l y thicker than Na -films, but i t depends c r i t i c a l l y on the nature of the cation whether or not a jumpwise t r a n s i t i o n to the Newton film occurs. The d i f f e r ­ ence i s that i n t h i s case Na promotes Newton film formation, whereas Na i n h i b i t s s t r a t i f i c a t i o n . The nature of t h i s contra­ diction i s not c l e a r , but phenomenologically i t can be i n t e r ­ preted as a blunting of the activation energy humps i n Figure 1, and more strongly so i n Na than i n L i , so that for common films with L i s t i l l one high barrier remains, preventing the Newton f i l m formation. The behavior of NH^ compares better with that of L i than that of N a . The dramatic differences between L i and Na point out to a very specific ionic effect I t i s not known to us whether these occur also i n concentrate these phenomena deserv +

+

+

+

+

+

+

+

+

+

+

S t r a t i f i c a t i o n of free l i q u i d films i s the occurrence i n i t of l a y e r - l i k e structures. I t can be observed i f free f i l m s , drawn from concentrated surfactant solutions, are drained. In such films after some time several regions can then be seen, d i s t i n ­ guishable i n reflected l i g h t as different shades of gray. These regions are denoted as orders, the lowest order being the t h i n ­ nest f i l m . The thicknesses of the various orders have been o p t i c a l l y determined for films drawn from NaDS, LiDS or NH^DS, both i n the absence and presence of added electrolytes. The orders differ between each other by an increment ΔςΙ that i s roughly constant at given surfactant concentration. For extremely high surfactant concentrations Ad (as well as the thickness of the f i r s t order film) approach that of a Newton (also known as a Perrin or second black) f i l m . Electrolytes i n h i b i t the s t r a t i f i c a t i o n , but Na -ions do so far more effectively than L i - or NH^ -ions. +

+

+

Ac knowledgement The authors acknowledge the s k i l l f u l technical assistance of Mr. R . A . J . Wegh.

Literature Cited 1. Johonnott, E.S., Phil. Mag. (6) (1906) 11, 746 2. Perrin, J., Ann. Phys. (1918) 10, 160 3. Bruil, H.G. and Lyklema, J., Nature Phys. Sci. (1971) 233, 19 4. Jones, M.N., Mysels, K.J. and Scholten, P.C., Trans. Faraday Soc. (1966), 62, 1336 5. Ingram, B.T., J . Chem. Soc. Faraday Trans. I (1972) 68, 2230

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

198

ADSORPTION AT INTERFACES

6. De Feijter, J.A., Ph.D. Thesis, State Univ. Utrecht (1973) 7. Dreger, E.E., Keim, G.I., Miles, G.D., Shedlovsky, L. and Ross, J., Ind. Eng. Chem. (1944) 36, 610 8. Mukerjee, P. and Mysels, K.J. "Critical Micelle Concentrations of Aqueous Surfactant Systems," NSRDS-NBS 36, p.51 Superintendent of Documents, Washington, D.C., 1971 9· Lyklema, J., Scholten, P.C. and Mysels, K.J., J . Phys. Chem. (1965) 69, 116 10. Frankel, S.P. and Mysels, K.J., J . Appl. Phys. (1966) 37, 3725 11. Reiss-Husson, F. and Luzzati, V., J . Phys. Chem. (1964) 68, 3504 12. Lyklema, J., Recl. Trav. Chim. Pays-Bas (1962) 81, 890

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14 Surface Chemical Properties o f H i g h l y Fluorinated Polymers MARIANNE K. BERNETT and W. A. ZISMAN Laboratory for Chemical Physics, Naval Research Laboratory, Washington, D.C. 20375

Introduction Highly fluorinated linear polymers are characterized by a low free surface energy and concomitant low wettability, as evidenced by the large contact angles of drops of organic and aqueous liquids. A comprehensive set of workable principles had been built up by Zisman and co-workers relating the chemical and spatial constitution in the outermost surface of a polymer with its surface energy (1, 2). During the last few years Wall, Brown, and Lowry of the National Bureau of Standards synthesized several new highly fluorinated ethylene polymers and copolymers (3-8) and established (4) that according to Wunderlichs "bead" theory and "rule of constant heat increment" (9, 10), the ethylenic polymers with fluorinated side groups generally contribute two carbon atoms to the backbone chain. This 2-carbon moiety plus the sub­ stituent constitute the smallest unit whose oscillations affect surface lattice equilibrium in a polymeric material, which repre­ sents the lowest free energy configuration. This paper discusses the critical surface tensions of several of these radiation-induced polymers and copolymers, and compares them to those of polymers with related structures and surface constitutions. '

Critical Surface Tensions of Wetting Table I lists the experimental fluoropolymers and the data on their structural formulae, intrinsic viscosities [η] in hexafluorobenzene, and glass transition temperatures Tg (3-8), along with the code numbers used for this report. By casting a polymer from solution in hexafluorobenzene as a film on a clean glass slide, a smooth surface is obtained which is characterizable for wetting properties by contact angle (θ) measurements with freshly percolated liquids. Table II shows the average values of the advancing contact angles (± 1°) obtained from such liquids of two homologous series, the n-alkanes and the 199 In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3

2

3

n

2

61

4 2

6

i n hexafluorobenzene;

2

6

5

5

n

+ [-CF^CF,,-]^

b e i n acetone; i n benzene

n

n

[-CF -CF(C F )-]

2

XIV

1 1

[-CF -CF(C H )-]

5

XIII

2

[-CH -CH(C F )-] 2 6 ρ η

a

3

[-CF -CF(n-C F )-]

3

XII

XI

n

[-CHF-CH(CF )-]

X

3

n

2

[-CH -CF(CF )-]

2

IX

2

3

+ [-CF^CF^]^

16.5 16.5 18.8 17.5

29 21 49 87

1.63 1.30

e

0.27

1.0

4.0

α 25000

0.23

25

2

2

194

25.4

202

17.8

22.5

14.1 105

235

16.2

45

[-CH -CH(CF CF CF )-]

n

15.5

58

VIII

2

3

3

52

2

2

2

[-CH -CH(CF CF CF )-]

2

2

VII

2

2

0.74

VI

V 79

Μ

16.3

41

0.33

18.0

9

2.10

21.1

19

21.5

5.00

[-CH -CH(CF CF CF )-]

+ [-CFg-CFg-]^

2

2

0.63

[-CH -CH(CF CF CF )-]

2

2

[-CF -CF -]

+ C-CF -CF -]

[-CH -CH(CF CF )-]

2

+

c

7 , dyn/cm 27

a

1.10

[η], d l / g

n

IV

39

[-CH -CH(CF )-]

III

3

5Ô

2

[-CH -CH(CF )-]

n

II

3

[-CH -CH(CF )-]

2

Polymer and Composition. mol%

I

Code

Table I . P h y s i c a l P r o p e r t i e s of E t n y l e n i c Fluoropolymers

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

n-ALkanes Hexadecane Tetradecane Trideoane Dodecane Undecane Decane Nonane Octane .methylsiloxanes DC200 3.0 c S t DC200 2.0 c S t DC200 1.5 c S t 12 (DM3) 10 (OMS) 9 (DMS) 8 (DMS) 7 (DMS) 6 (DMS) 5 (DMS)

Liquids

19.4 18.9 18.1 19.7 19.5 19.3 19.1 19.0 18.6 18.2

27.8 26.7 26.0 25.4 24.6 23-9 23.1 21.8

(dyn/cm)

56

42 35 29

45

36 29

50 47

63

III

51

II

50

I

41 40 39 38 37 33 32

50 46 42

55

61 58

IV

54 51

44 40 36

43 40 36

59

64

VI

55 51

61

67

V

Code

48 44

37 33 29

37 33 28

53

59

48 45

55

61

VII VIII

19 16 14 10 7 6 5

39 36 30

45

52 49

IX

30 29 28 26 24 22 18

44 41 36

49

56 53

Χ

51 50 49 48 47 45 43

55 53 49

60

66 64

XI

< 5

22 13 9

31

41 37

XII

Table I I . Advancing Contact Angles (Deg) of L i q u i d s on Fluoropolymers (25°C)

< 5

< 5

14 10

XIII

40 38 36 34 33 29 27

32 28 25

46

52 50

XIV

202

ADSORPTION A T INTERFACES

d i m e t h y l s i l o x a n e s , where the l a t t e r were e i t h e r the Dow Corning 200 s e r i e s o r the w e l l - c h a r a c t e r i z e d s e r i e s c o n t a i n i n g from 6 t o 12 d i m e t h y l s i l o x a n e (DMS) -units. (11, 12). When the cos θ of each member of such a homologous s e r i e s of l i q u i d s on a smooth, c l e a n , s o l i d , low-energy surface i s p l o t t e d a g a i n s t the s u r f a c e t e n s i o n (ïjJ) f o r each of those l i q u i d s , a s t r a i g h t l i n e r e s u l t s ; the i n t e r c e p t a t cos θ = 1 (θ = 0°) i s r e f e r r e d t o as the c r i t i ­ c a l s u r f a c e t e n s i o n of w e t t i n g (7 ) f o r t h a t p a r t i c u l a r s u r f a c e (13). Figure 1 shows such a grapn f o r polymer IV, [-CHp-CHiCpF^)-] , and i s r e p r e s e n t a t i v e o f the graphs f o r t h e other polymers w i t h the e x c e p t i o n of the p e r f l u o r o p h e n y l s u b s t i t u t e d polymers X I I and XIV. Here the s t r a i g h t l i n e f o r the n-alkanes d i s p l a y s a marked d i s c o n t i n u i t y i n the r e g i o n of 7 = 24-25 dyn/cm, r e s u l t i n g i n two values of 7 , d i f f e r i n g by 1 dyn/cm. Experimental phenomena suggest t h a t tne s m a l l e r mole­ c u l e s a r e capable of s l i p p i n adlineated structures o and b u l k i e r molecules are r e t a i n e d on the s u r f a c e , thus b e i n g more r e l i a b l e r e p r e s e n t a t i v e s f o r the t r u e value of 7 . Values of 7 thus obtained f o r each polymer f i l m are given i n Table I . Wettability f o r low-energy s u r f a c e s , as d e f i n e d by 7 , i s determined e s s e n t i a l l y by the nature and packing of the exposed surface atoms of t h e s o l i d and i s otherwise independent o f the nature and arrangement of the u n d e r l y i n g atoms and molecules ( l , 2). The arrangement o f the s u r f a c e atoms, of course, must represent the lowest f r e e energy c o n f i g u r a t i o n f o r a given s e t of r e s t r a i n i n g c o n d i t i o n s such as the nature, s i z e of the u n d e r l y i n g atoms, l e n g t h of the c h a i n , e t c . I n p a r t i c u l a r , f o r polymeric m a t e r i a l s i t depends on d e f i n i t i o n of the s m a l l e s t u n i t , which f o r ethylenic polymers c o n s i s t s o f 2 carbons i n the backbone (Sb IQ) p l u s the s u b s t i t u e n t . Table I I I l i s t s 7 values of f l u o r i n e - c o n t a i n i n g e t h y l e n i c homopolymers, wherS the formulae shown are the r e p e a t i n g u n i t s i n the polymer s t r u c t u r e , as they would appear i f a l l c o n s t i t u e n t s were present i n the s u r f a c e . The order o f s t r u c t u r e s i s arranged t o show p r o g r e s s i v e s u b s t i t u ­ t i o n s of e i t h e r a hydrogen o r a f l u o r i n e atom i n the backbone c h a i n by e i t h e r a f l u o r i n e atom or a p e r f l u o r o group. S e v e r a l observations can be made from i n s p e c t i o n of values of 7 : (a) When the ethylene c h a i n i s f u l l y hydrogenated, replacement of one hydrogen by a - C F group lowers 7 a p p r o x i ­ mately 10 dyn/cm. (Compare XV and i f XVI and IX, and XVI and X.) (b) When one carbon atom i n the 2-carbon moiety of the ethylene c h a i n i s f u l l y f l u o r i n a t e d , replacement of a hydrogen by a -CF^ group on the other carbon atom lowers 7 o n l y about 5 dyn/cm. (Compare XVII and XIX.) (c) Nearly equSl y values a r e observed on s e v e r a l p a i r s of monomers of u n l i k e molecular c o n s t i t u t i o n s , such as I and X V I I , I X and X V I I I , and X and XIX. I n s p e c t i o n o f S t u a r t - B r i e g l e b molecular models shows t h a t , i n c e r t a i n s t e r i c arrangements, the 7 -determining packing of f l u o r i n e atoms a t the s u r f a c e o f these paîrs could be v e r y s i m i l a r , s i n c e the pendant ?

Q

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14.

BERNETT

AND

Highly Fluorinated Polymers

zisMAN

203

Table I I I . E f f e c t on C r i t i c a l Surface Tensions of Wetting by Replacement of Hydrogen w i t h F l u o r i n e and/or Pendant Group Code

7 (dyVcm)

Polymer

31

XV

[CH -CH -]

I

[CH -CH(CF )-]

IV

[-CH -CH(CF -CF )-]

V

[-CH -CH ( C F ^ C F ^ C F ^ ) -]

15.5

XVI

[-CH -CFH-]

28

IX

[-CH

X

[-CH(CF )-CFH-]

XVII

[-CF -CFH-]

n

22

XVIII

C-CF -CF -]

n

18.5

XIX

[-CF -CF(CF )-]

XI

[-CF -GF(nC F

XX

[-CH -CH(C H )-]

XII

[-CH -CH(C F )-]

XIII

[-CF -CF(C H )-]

n

25.4

XIV

C-CF -CF(C F )-]

n

17.8

2

2

2

n

3

2

21.5

n

2

3

2

n

b

2

3

2

2

2

2

3

2

2

2

2

2

Reference 14;

16.3

n

n

2

a

5

6

6

6

6

i:L

17.5

n

17

n

)-]

5

5

5

5

n

n

n

b

C

d

14.1 33-35

e

22.5

Reference 15; °Reference 13; Reference 16;

References 17, 18

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

Macromolecules

Figure 2. Various configurations of polymer [—CHz—CHtCeFs)—']». (a) (top left) syndiotactic, exposure of flat side; (b) (top right) syndiotactic, exposure of edge; (c) (bottom left) isotactic (12).

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14.

BERNETT

AND

Highly Fluorinated

zisMAN

205

Polymers

-CF^ groups may be so l o c a t e d as t o p a r t i a l l y obscure the hydro­ gen atoms . The t o t a l e f f e c t achieves a balance between the hydrogen and the -CF- c o n t r i b u t i o n s which approximates the s u r ­ face c o n s t i t u t i o n of the l i n e a r unbranched c o n f i g u r a t i o n . (d) Polymers IX and X demonstrate a c o n f i r m a t i o n of the c o n c l u ­ s i o n of Pittman and co-workers ( 1 £ ) , t h a t i n a p a r t i c u l a r f l u o r i n a t e d polymer y i s not n e c e s s a r i l y dependent on the t o t a l f l u o r i n e content: deSpite the i d e n t i c a l f l u o r i n e content, the molecular s t r u c t u r e s d i f f e r s u f f i c i e n t l y t o r e s t r i c t f r e e r o t a t i o n of the -CF~ groups i n polymer X w i t h the n e t r e s u l t of c l o s e r surface packing of the f l u o r i n e atoms and thus a lower y . (e) As a n t i c i p a t e d , the lowest y , 14-1 dyn/cm, i s obtained f o r polymer X I which i s not only fulîy f l u o r i n a t e d but a l s o d i s p l a y s the l o n g e s t pendant p e r f l u o r i n a t e d group. The i n c r e a s e i n l e n g t h from 1 carbon t o 5 carbons decreases 7 about 3 dyn/cm (XIX and XI) because of b e t t e r a d l i n e a t i o longer c h a i n , ( f ) Fo hydrogen w i t h f l u o r i n e i n e i t h e r the phenyl group, X I I , or the backbone c h a i n , X I I I , lowers 7 about 10 dyn/cm from the 33-35 dyn/cm of p o l y s t y r e n e . V a r i a t i o n s o r spread of y values f o r a given polymer can be now explained by the v a r i o u s o r i e n t a t i o n s of the phenyl group i n the s u r f a c e , such as exposure of the f l a t s i d e o r the edge, or the t a c t i c i t y of the arrangement (Figure 2 a, b, c ) . T o t a l f l u o r i n a t i o n , as i n polymer XIV of course r e s u l t s i n even lower 7 , s i n c e only f l u o r i n e atoms a r e exposed i n the s u r f a c e . An i n t e r e s t i n g p a r a l l e l can be observed and i s demonstrated i n F i g u r e 3: When the hydrogen atoms i n the e t h y l e n i c backbone are r e p l a c e d by f l u o r i n e atoms, r e g a r d l e s s of whether the pendant group i s the a l k y l -CF~ or the aromatic -CvF , 7 i s lowered by about 4 · 5 dyn/cm. When, on the other hand, ?he S l k y l -CFo group i s r e p l a c e d by the aromatic -C,F group, whether on a f u l l y hydrogenated or f u l l y fluorinaïed backbone, 7 i s r a i s e d by approximately 1 dyn/cm. Q

c

5

6

0

S t e r i c Configurations The problem o f determining the arrangement of the atoms and s u b s t i t u e n t s of the f i r s t l a y e r of the s o l i d s u r f a c e of a polymer or copolymer needs t o be s o l v e d before we can r e l a t e the observed value of 7 t o the most probable surface composition of the polymeric s o l i d . F o r simple u n s u b s t i t u t e d polymers such as [-CF -CF -] o r [-CH ~CH -] the surface conformation can be r a t i o n a l i z e d by S t u a r t - B r i e g l e b molecular models arranged i n p o s s i b l e conformations on a f l a t t a b l e . However, where s i d e chains a r e introduced i n t o the model, s t e r i c hindrances are a l s o i n t r o d u c e d . I t i s obvious from Figure 4, where only some of the p o s s i b l e arrangements of the atoms and s u b s t i t u e n t s i n the f i r s t l a y e r of the s o l i d [-CH -CH(C F^)-] polymer surface a r e shown, t h a t i n a three-dimensional a r r a y a m u l t i t u d e of a l t e r n a t e 2

2

2

2

2

n

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION A T INTERFACES

206

- CH, - CH(CF ) -

- CF - CF(CF,) -

}

2

21-5

l+l.O

4.5 17.0

+0.8 I

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14.

BERNETT AND

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Highly Fluorinated Polymers

207

conformations are p o s s i b l e , l i m i t e d o n l y by s t e r i c considerations. Lacking s p e c i f i c i n f o r m a t i o n on the t a c t i c i t y of the r a d i a t i o n induced polymer, we assumed them t o be a t a c t i c , i . e . , randomly o r i e n t e d . Any p r e d i c t i o n of surface p a c k i n g i s thus p r o b l e m a t i c . In a d d i t i o n t o the s p a t i a l arrangements, polymers such as X a l s o e x h i b i t c i s and trans isomerism w i t h respect t o the o r i e n t a t i o n of the -F and -CF^ s u b s t i t u e n t s on the backbone, f u r t h e r compli­ c a t i n g and expanding the number of p o s s i b l e c o n f i g u r a t i o n s . Electrostatic

Dipoles

A t the juncture of the -CH CH< backbone and the - ( C F j F s i d e group there exists an uncompensated e l e c t r o s t a t i c d i p o l e . I f one assumes t h a t the s i d e group i s d i r e c t e d away from the polymer s o l i d surface i n t closer t o the interfac have shown t h a t as χ becomes s m a l l e r , θ a l s o becomes s m a l l e r . Thus, when χ changes from 1 t o 3, 7 i s lowered from 21.5 t o 15.5 dyn/cm (Figure 5), w i t h the l a r g e r Secrease of 5.2 dyn/cm when 1 < χ < 2 and the s m a l l e r decrease of 0.8 dyn/cm when 2 < χ < 3· I n t h e i r study of adsorbed monolayers of p r o g r e s s i v e l y f l u o r i n ­ ated f a t t y a c i d s of the general formula F ( C F ) ( C H j ^ C O O H and 2

p

F

C F

C H

C 0 Q H

&

Γ

Γ

Ϊ

η

z

i

s

m

a

n

^ 2^ 2^10 ' ^ · ^ (20)/sSowed TOat the uncompensated d i p o l e has a l a r g e e f f e c t on w e t t i n g when χ < 7, but becomes l e s s s i g n i f i c a n t when χ ^ 7. Measurements of e l e c t r i c a l and mechanical p r o p e r t i e s of i n s o l u b l e monolayers on water by Bernett and Zisman (21), supported t h e i r view a l s o . S h a f r i n and Zisman a l s o n o t i c e d an abrupt r e v e r s a l of the e f f e c t of homology a t 2 < χ < 3 where the d i f f e r e n c e i n y was only 0.8 dyn/cm because of random t i l t i n g , of the fluoroSarbon group. A s i m i l a r abrupt d i s c o n t i n u i t y a t 2 < χ < 3 f o r the e t h y l e n i c polymers can be explained by r e s t r i c t i o n of r o t a t i o n of the s u b s t i t u e n t and the subsequent s h i e l d i n g of the e l e c t r o ­ s t a t i c d i p o l e . The l a t t e r i s accentuated by the f a c t t h a t the e t h y l e n i c hydrocarbon, t o which the p e r f l u o r o a l k y l s i d e groups are connected, imposes r e s t r i c t i o n s on the p a c k i n g of these s u b s t i t u e n t groups, n e c e s s i t a t i n g p r o g r e s s i v e l y l a r g e r i n t r a ­ molecular r o t a t i o n s and bending w i t h i n the c h a i n . This r e s u l t s i n exposure of the -CF - atomic grouping i n an outermost surface of randomly o r i e n t e d perfluoroethyl o r -propyl groups. I t would be i n t e r e s t i n g t o study polymers w i t h p r o g r e s s i v e l y longer p e r f l u o r o a l k y l s i d e groups t o a s c e r t a i n whether r e g u l a r decreases i n y can be observed or whether a l i m i t i n g value has been approacheS. When the ethylene backbone i s f u l l y f l u o r i n a t e d , no l a r g e uncompensated d i p o l e s are present, and a gradual and u n i n t e r r u p t e d decrease i n y i s observed w i t h i n c r e a s e i n χ (Figure 5 ) . The shape o f tne two curves i n Figure 5 seems t o p o i n t t o an eventual asymptotic approach t o the y -vs-x curve obtained from adsorbed monolayers o f f u l l y f l u o r i n a t e d c a r b o x y l i c ?

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION AT

208

INTERFACES

a c i d s , as shown i n Figure 6 (20). Since t o date no curve of anyother f a m i l y or s e r i e s of r e l a t e d compounds (22), i n c l u d i n g the two present ones, has crossed or gone beyond the curve of the p e r f l u o r o a c i d s , i t i s suggested t h a t the l a t t e r represents an envelope of l i m i t i n g v a l u e s . Copolymers

I n t h e i r study on copolymers, Hu and Zisman (11) p l o t t e d y f o r each polymer a g a i n s t the mole % of [-CF -CF -] i n the copolymer (Figure 7 ) . The three graphs show the comparative case of p r e d i c t i n g the e f f e c t on y of c o p o l y m e r i z a t i o n of [ C F - C F - ] w i t h [-CH -CH -] (upper curve) (22) and the greater d i f f i c u l t y (middle graph predictin y c o p o l y m e r i z a t i o n w i t h [-CH c

2

2

C

2

2

n

2

2

n

F

e f f e c t w i t h [ - C H - C H ( C o ) - ] ("bottom c u r v e ) . I t should be evident t h a t we are d e a l i n g w i t h s e v e r a l e f f e c t s of adding f l u o r i n a t e d carbon atoms: (a) those due t o London d i s p e r s i o n f o r c e changes (upper graph) and (b) those combining e l e c t r o s t a t i c e f f e c t s and s t e r i c hindrance e f f e c t s (lower two graphs). I t i s obvious from the multitude of p o s s i b l e s t e r i c c o n f i g ­ u r a t i o n s and d i p o l e c o n t r i b u t i o n s t h a t we face the d i f f i c u l t problem of r a t i o n a l i z i n g how t o compute the c o r r e c t molecular conformation t o a r r i v e a t a minimum s u r f a c e energy f o r s u b s t i ­ t u t e d ethylene f luoropolymers and copolymers. 2

7

n

Summary

Wetting p r o p e r t i e s of new, w e l l - c h a r a c t e r i z e d , h i g h l y f l u o r i n a t e d l i n e a r e t h y l e n i c polymers and copolymers w i t h t e t r a f l u o r o e t h y l e n e were i n v e s t i g a t e d . F l u o r i n a t i o n i n the p o l y ­ ethylene backbone was v a r i e d by degree of f l u o r i n e atom s u b s t i t u ­ t i o n ; n - a l k y l s i d e chains of i n c r e a s i n g number were f u l l y f l u o r i n a t e d , whereas phenyl s i d e groups were e i t h e r f u l l y or nonf l u o r i n a t e d . C r i t i c a l s u r f a c e tensions of w e t t i n g obtained on t h i n c a s t f i l m s of these fluoropolymers were compared t o those of polymers w i t h r e l a t e d s t r u c t u r e s and surface c o n s t i t u t i o n s . Because of the presence of the b u l k y f l u o r i n e atoms and aromatic s i d e groups, some of these molecules are extremely s t e r i c a l l y blocked, which makes the p r e d i c t i o n of an e q u i l i b r i u m surface conformation very d i f f i c u l t . The r e s u l t s are discussed i n terms of s o l i d s u r f a c e c o n s t i t u t i o n , s t e r i c hindrance, and e l e c t r o ­ s t a t i c dipole contribution. Literature Cited

1.

Zisman, W. Α., in "Contact Angle Wettability and Adhesion," Adv. Chem. Ser., No. 43, p. 1, Am. Chem. Soc., Wash., D.C., 1964.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14.

BERNETT

0

J

AND ZISMAN

I 2

L

4

Highly Fluorinated Polymers

J 6

1

ι 8

209

Ο

F(CF ) C00H

Δ

F ( C F ) ( C H ) C 0 0 H (FROM SOLUTION)]

•

F ( C F ) ( C H 2 ) C 0 0 H (FROM MELT)

•

H(CH ) C00H

ι

2

2

x

2

2

X

2

I 10

(FROM SOLUTION)

X

| 6

|6

(FROM SOLUTION)

| 7

I

l 12

L

X=NUMBER OF FLUORINATED CARBON ATOMS PER

14

I

I 16

I

18

MOLECULE Journal of Physical Chemistry

Figure 6.

Effect of fluorination of the adsorbed acid monolayer on y ( 20 )

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

c

ADSORPTION A T INTERFACES

Macromolecules

Figure 7. Effect of copolymerization with [—CF -CF —] on y { 11) ?r

2

n

c

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

14.

Highly Fluorinated Polymers

BERNETT AND ZISMAN

211

2. Zisman, W. Α., J. Paint Tech., (1972), 44, 42. 3. Brown, D.W., Wall, L. Α., J . Polym. Sci. A-1, (1968), 6, 1367. 4. Brown, D. W., Wall, L. Α., J . Polym. Sci. A-2, (1969), 7, 601. 5. Brown, D. W., Lowry, R. E . , Wall, L. Α., J . Polym. Sci. A-1, (1970), 8, 2441. 6. Brown, D. W., Lowry, R. E . , Wall, L. Α., J. Polym. Sci. A-1, (1970), 8, 3483. 7. Brown, D. W., Lowry, R. E . , Wall, L. Α., J . Polym. Sci. A-1, (1971), 9, 1993. 8. Brown, D. W., Lowry, R. E . , Wall, L. Α., J. Polym. Sci. (Polym. Chem. Ed.) (1973), 11, 1973. 9. Wunderlich, B., J. Phys. Chem., (1960), 64, 1052. 10. Wunderlich, B., Bodily, D. M., Kaplan, H. M., J . Appl. Phys., (1964), 35, 95. 11. Hu, W. Κ. H., Zisman 12. Bernett, M. K., Macromolecules (In Press) (Sep 1974), 7. 13. Fox, H. W., Zisman, W. Α., J. Colloid Sci., (1950), 5, 514. 14. Fox, H. W., Zisman, W. Α., J. Colloid Sci., (1952), 7, 428. 15. Ellison, A. H., Zisman, W. Α., J . Phys. Chem., (1954), 58, 260. 16. Bernett, M. K., Zisman, W. Α., J . Phys. Chem., (1961), 65, 2266. 17. Ellison, A. H., Zisman, W. Α., J. Phys. Chem., (1954), 58, 503. 18. Fox, R. F., Jarvis, N. L . , Zisman, W. Α., in "Contact Angle Wettability and Adhesion," Adv. Chem. Ser., No. 43, p. 317, Am. Chem. Soc., Wash., D.C., 1964. 19. Pittman, A. G., Sharp, D. L . , Ludwig, Β. Α., J. Polym. Sci. A-1, (1968), 6, 1729. 20. Shafrin, E. G., Zisman, W. Α., J . Phys. Chem., (1962), 66, 740. 21. Bernett, M. K., Zisman, W. Α., J . Phys. Chem., (1963), 67, 1534. 222. Pittman, A. G. "Fluoropolymers," p. 419, Wiley Interscience Press, N.Y., 1972. 23. Fox, H. W., Zisman, W. Α., J . Colloid Sci., (1952), 7, 109. ;

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

15 Effect o f Surface O x y g e n Complexes o n Surface Behavior o f Carbons BALWANT RAI PURI Department of Chemistry, Panjab University, Chandigarh, 160014, India

Introduction It is now well know that microcrystalline carbons contain appreciable amounts of combined oxygen which gives rise to stable carbon-oxygen surface complexes (1). The work reported from our laboratories (2,3) and from elsewhere (4,5) indicates that there are definite surface groups or complexes which evolve carbon dioxide and, similarly, there are distinct surface entities which evolve carbon monoxide on evacuation at increasing temperatures. The effect of combined oxygen on various surface properties, such as wettability (6), heats of immersion in various liquids (7-9), adsorbability of water and other polar vapours (10-12), selectivity in adsorption from binary mixtures (13,14) has been reported. However, the effect of the individual oxygen complexes such as acidic CO2-complex (15), nonacidic CO2-complex (16) and CO-complex (3) on some of the surface properties mentioned above has not received adequate attention. An attempt has been made in the present paper to spell out the effect of each complex on (i) selective adsorption from mixtures of methanol and benzene, and (ii) adsorption of (a) benzene vapour, (b) dry ammonia, and (c) phenol from dilute aqueous solutions. Experimental Mogul (a colour black), Spheron-6 (a channel black) and a charcoal prepared by the carbonisation of recrystallised cane sugar (17) were used as such as well as after (i) outgassing at different temperature upto 1000°C, and (ii) treatment with aqueous hydrogen peroxide or potassium persulphate (l6) so as to get materials associated with different amounts of surface oxygen complexes. The amount of combined oxygen and the form of its disposition was obtained by evacuating 0.5 g portion in a resistance tube furnace, raising the temperature to 1200°C and analysing the gases evolved in the usual manner (17). 212 In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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213

The base a d s o r p t i o n c a p a c i t y , estimated by t i t r a t i n g against aqueous barium hadroxide (17), f i x e d the amount o f a c i d i c CO2complex. This when subtracted from the amount o f carbon d i o x i d e evolved on evacuation gave the amount o f n o n - a c i d i c C0 -complex (l6) which a r i s e s through the f i x a t i o n o f oxygen at unsaturated s i t e s (17). The amount o f CO-complex was obtained from the amount o f carbon monoxide evolved on evacuation. The n i t r o g e n surface areas and the t h r e e main types o f surface oxygen com­ plexes of the v a r i o u s samples are recorded i n Table I . S e l e c t i v e a d s o r p t i o n from methanol-benezene s o l u t i o n s was s t u d i e d by mixing 0.25 g carbon w i t h a known weight (5-6 g) o f the s o l u t i o n i n a s m a l l g l a s s tube drawn out a t one end. The l a t t e r was s e a l e d , a f t e r c o o l i n g i n a f r e e z i n g m i x t u r e , t o min­ imise evaporation. Several such tubes c o n t a i n i n g 0.25 g carbon mixed w i t h s o l u t i o n s o f d i f f e r e n t c o n c e n t r a t i o n placed i a shaker (12 rev/min) h e l 0.05°C f o r ho hours. Th chang compositio liqui was determined i n t e r f e r o m e t r i c a l l y . Adsorption isotherms o f benzene as w e l l as d r y ammonia were determined at 35 + 0.05°C by u s i n g McBain's t o r s i o n balance technique. A d s o r p t i o n isotherms of phenol from aqueous s o l u t i o n s were determined by mixing 0.5 g p o r t i o n s w i t h a known weight ( ~ 5 g) o f s o l u t i o n s of v a r i o u s c o n c e n t r a t i o n s , shaking the suspensions i n a r e v o l v i n g wheel h e l d i n a thermostat a t 35 + 0.05°C f o r 2k hours. The change i n c o n c e n t r a t i o n o f the s o l u t i o n was determined i n t e r f e r o m e t r i c a l l y . The experiments were conducted i n the low c o n c e n t r a t i o n range upto 20 m m o l e s / l i t r e . 2

R e s u l t s and D i s c u s s i o n The composite a d s o r p t i o n isotherms, reproduced i n F i g u r e 1 from a recent r e p o r t from the author's l a b o r a t o r y (l8), show how the preference o f Mogul f o r a d s o r p t i o n from methanol-benzene mix­ t u r e s of v a r i o u s c o n c e n t r a t i o n s i s a l t e r e d i n the presence o f v a r i o u s surface oxygen complexes. I t i s seen t h a t 1000°-outgassed Mogul, which i s e s s e n t i a l l y f r e e o f combined oxygen, shows strong preference f o r benzene at a l l c o n c e n t r a t i o n s , g i v i n g a t y p i c a l l y U-shaped isotherm (marked A ) . The 7 0 0 ° - outgassed Mogul, which i s f r e e o f COg-complex but r e t a i n s over 2.5 per cent oxygen capable o f e v o l v i n g carbon monoxide (C0-complex), shows, s u r p r i s i n g l y enough, even g r e a t e r preference f o r benzene, the l e s s p o l a r component of the m i x t u r e , a l l along the c o n c e n t r a t i o n range. This i s c o n t r a r y t o the view g e n e r a l l y h e l d (l3 lh) t h a t combined oxygen imparts g r e a t e r preference f o r the more p o l a r component o f the mixture. I t appears t h a t the presence o f q u i nonic groups which form a p a r t of the C0-complex (l£) promotes preference f o r benzene due t o p o s s i b i l i t y of i n t e r a c t i o n o f e l e c ­ t r o n s of benzene r i n g w i t h the p a r t i a l p o s i t i v e charge on the carbonyl carbon atom (20). The l*00°-outgassed and the o r i g i n a l samples of Mogul, which c o n t a i n i n c r e a s i n g amounts o f CO2 com9

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION A T INTERFACES

214

Table I . Surface Area and Surface Oxygen Complexes o f the Carbons used i n t h e Present Work.

D e s c r i p t i o n o f the sample

Surface area m /g 2

Acidic CO2complex moles/ 100 g

NonC0acidic complex CO2mmoles/ complex 100 g mmoles/ 100g

Mogul Original 30 30 Outgassed a t 1*00°C 3lk Outgassed at 600°C 325 Outgassed at T00°C 318 Outgassed at 850°C Outgassed a t 1000°C 326 Original, treated 310 w i t h aq.H 02 Original, treated with K S 08 312 Outgassed at 1000°, t r e a t e d w i t h aq. H 02328 2

2

2

2

269 198 163 52

1 nil nil nil nil

nil nil nil nil

nil

1*5

nil

281*

189

nil

315

nil

120

20

15.5

nil nil nil nil

122.5 108 nil

nil

135

Spheron-6 Original Outgassed at 600°C Outgassed at 850°C Outgassed a t 1000°C Original, treated w i t h aq.H202 Outgassed a t 1000°, t r e a t e d w i t h aq.H202

110 112 109

116 11^

2.5 nil nil

61

51

106

nil

10

1*

1*12 51* 502

355 51 nil

nil nil nil

1*91

1*1*3

*53

nil

56Ο

488

nil

165

20

Sugar Charcoal Original Outgassed a t 600°C Outgassed a t 1000°C Original, treated w i t h aq.H202 Outgassed a t 1000° t r e a t e d w i t h aq.H 02 2

531 nil

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

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p l e x , though n e a r l y equal amounts o f CO-complex ( c f . Table I ) , show, on the other hand, p r e f e r e n t i a l a d s o r p t i o n o f methanol over a p p r e c i a b l e range o f c o n c e n t r a t i o n ( c f . isotherms marked C and D). This remarkable change i n the preference may be a s c r i b e d t o the presence o f a c i d i c C02-complex. This view r e c e i v e s support from the f a c t t h a t when the amount of the a c i d i c complex i s r a i s e d from 6 8 . 5 mmoles t o 1*5 mmoles on treatment w i t h aqueous hydrogen peroxide and 189 mmoles on treatment w i t h potassium per­ s u l p h a t e , the preference o f the s u r f a c e i s s h i f t e d i n c r e a s i n g l y i n favour of methanol ( c f . isotherms Ε and F ) . The comparison o f the isotherms Β and F shows c l e a r l y how the presence o f a l a r g e amount o f a c i d i c C02-complex has brought about almost complete r e v e r s a l of the preference o f the carbon s u r f a c e . I t i s a l s o i n t e r e s t i n g t o note t h a t the 1000°-outgassed Mogul y i e l d s almost i d e n t i c a l isother a f t e f i x a t i o f about * per cent o f oxygen, a aqueous hydrogen p e r o x i d e , y oxyge (cf. isotherms marked G and A ) . The presence of n o n - a c i d i c com­ p l e x , e v i d e n t l y , produces l i t t l e o r no e f f e c t on the preference o f the s u r f a c e . Thus the view h e l d by p r e v i o u s workers ( 1 3 » 1 * ) t h a t the e n t i r e combined oxygen imparts p o l a r i t y t o the surface and p r o ­ motes preference f o r the more p o l a r component o f a b i n a r y mixture needs r e v i s i o n i n the l i g h t o f the observations d i s c u s s e d above. A d s o r p t i o n o f Benzene Vapour. The above c o n c l u s i o n s were checked by s t u d i n g a d s o r p t i o n of benzene vapour d i r e c t l y on a number o f carbon b l a c k s (21). The s o r p t i o n - d e s o r p t i o n isotherms (35±0.05°C) on some of the samples o f Mogul ( F i g u r e 2 ) almost superimpose showing almost complete r e v e r s i b i l i t y o f the process. The amount o f s o r p t i o n a t each r e l a t i v e vapour pressure i s seen to i n c r e a s e a p p r e c i a b l y as Mogul i s outgassed at i n c r e a s i n g tem­ p e r a t u r e s . The maximum e f f e c t i s produced when the b l a c k i s out­ gassed at 600°C. I t appears t h a t w i t h the e l i m i n a t i o n o f the p o l a r C02-complex and the emergence o f CO-complex as the o n l y predominant s u r f a c e oxygen complex, the s o r p t i o n o f benzene i n ­ creases a p p r e c i a b l y on account of reasons advanced i n the p r e ­ v i o u s paragraph. The outgassing o f Mogul a t 850°C lowers the amount o f CO-complex c o n s i d e r a b l y and t h e r e i s s i g n i f i c a n t f a l l i n the s o r p t i o n v a l u e at a l l r e l a t i v e vapour pressures. With the complete e l i m i n a t i o n o f the complex at 1000°C, t h e r e i s a f u r t h e r f a l l i n the s o r p t i o n of benzene. A d s o r p t i o n of Dry Ammonia. A d s o r p t i o n o f dry ammonia on m i c r o c r y s t a l l i n e carbons at d i f f e r e n t temperatures has been i n ­ v e s t i g a t e d by a number o f workers amongst which mention may be made of the work o f Anderson and Emmett ( 2 2 ) , V o s k r e s e n s k i i (23.), Holmes and Beebe ( 2 * ) , Studebaker ( 2 5 ) and Dupupet e t a l ( 2 6 . There i s a g e n e r a l agreement t h a t a d s o r p t i o n i s enhanced appre­ c i a b l y i n the presence o f combined oxygen. However, the exact

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

216

ADSORPTION A T INTERFACES

1-2

0·8

OA

Ε

OO

•fraction

Methanol->-

8

c° - 0 - 4

-1-2

Figure 1. Composite adsorption isotherms of methanolbenzene mixtures on Mogul before and after various treat­ ments. A = Mogul outgassed at 1000° C, Β = Mogul out­ gassed at 700°C, C = Mogul outgassed at 400°C, D = Mogul original, Ε = Mogul original, treated with aq. H 0 , F = Mogul original treated with acidified K S 0 , G = Mogul outgassed at 1000°C, treated with aq. H 0 . 2

2

2

8

2

~ΟΛ

0·2 0·3 0 4 0 5 0 6 0·7 Ο θ 0·9 Relative vapour pressure—*:

2

PÔ"

Figure 2. Adsorption isotherms of benzene on Mogul. The solid points denote desorption data. Ο = original, Δ = outgassed at 600°C, • = outgassed at 850°C, · = oxygen-free.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

2

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Surface Oxygen Complexes

217

r o l e o f the v a r i o u s surface oxygen complexes, which c o n s t i t u t e t h i s oxygen, has not "been e l u c i d a t e d . Adsorption isotherms o f ammonia on sugar c h a r c o a l , Mogul and Spheron-6 "before and a f t e r v a r i o u s treatments are shown i n Figures 3» h and 5, r e s p e c t i v e l y . I t i s seen t h a t , i n each case, there i s a considerable f a l l i n the s o r p t i o n o f ammonia a t each pressure on outgassing and t h a t the e f f e c t i s r e l a t i v e l y more when a carbon i s outgassed a t 600°C, causing e l i m i n a t i o n o f most of C02-complex ( c f . Table I ) , than t h a t when i t i s outgassed i n 600-1000° temperature range, causing e l i m i n a t i o n o f CO-complex. This shows t h a t the s o r p t i o n o f ammonia i s i n f l u e n c e d more by the former than by the l a t t e r s u r f a c e oxygen complex. The treatment of o r i g i n a l samples w i t h aqueous hydrogen peroxide which r e s u l t s i n an a p p r e c i a b l e r i s e i n the amount o f the a c i d i c complex w i t h ­ out a f f e c t i n g much the valu f C0-comple ( c f Tabl I ) i t o cause increase i n th sure, as can be seen o compariso of the F i g u r e s . The treatment o f 1000° - outgassed carbons w i t h aqueous hydrogen peroxide r e s u l t s i n a p p r e c i a b l e f i x a t i o n o f oxygen which, however, gives r i s e mostly t o non-acidic C02-comp l e x ( c f . Table I ) . The isotherm on t h i s sample i s seen t o be almost i d e n t i c a l w i t h t h a t on the corresponding oxygen-free sam­ p l e . These observations show c l e a r l y t h a t the e n t i r e combined oxygen does not have a uniform e f f e c t on the s o r p t i o n o f dry ammonia by carbon. The oxygen present as a c i d i c C02-complex i n ­ f l u e n c e s the s o r p t i o n o f ammonia t o a r e l a t i v e l y l a r g e r extent than t h a t present as C0-complex w h i l e the oxygen-present as nona c i d i c C02-complex has h a r d l y any e f f e c t a t a l l . Adsorption isotherms on sugar c h a r c o a l , Mogul and Spheron-6, a l l p r e v i o u s l y outgassed a t 1000° and t h e r e f o r e e s s e n t i a l l y f r e e of oxygen, are p l o t t e d i n F i g u r e 6. I t i s seen t h a t the v a r i o u s p o i n t s f i t around a s i n g l e curve showing t h a t the extent o f sorpt i o n / m o f carbon surface when f r e e o f oxygen i s about the same i n every case i r r e s p e c t i v e o f d i f f e r e n c e s i n p o r o s i t y o f these m a t e r i a l s . I t appears t h a t ammonia, being a s m a l l molecule w i t h t h i c k n e s s equal t o 2.36 A, becomes e a s i l y a c c e s s i b l e t o the inner surface o f carbons as w e l l . 2

Adsorption o f Phenol from Aqueous S o l u t i o n s . Adsorption o f phenol from aqueous s o l u t i o n , b e i n g o f i n t e r e s t from the standpoint o f water treatment,was s t u d i e d u s i n g Mogul,Spheron-6,Graphon(ahighl y g r a p h i t i s e d carbon b l a c k ) and sugar c h a r c o a l . The isotherms (35° C) p l o t t e d on the b a s i s o f amounts adsorbed ( μ moles)per m o f surface i n the v a r i o u s carbons i n the o r i g i n a l s t a t e are pre­ sented i n Figure 7. I t i s seen t h a t the extent o f a d s o r p t i o n a t a given c o n c e n t r a t i o n i s maximum i n the case o f Graphon which i s f r e e o f oxygen and decreases i n the order Graphon>Spheron-6 > Mogul > Sugar c h a r c o a l . This i s a l s o the order o f decreasing oxy­ gen content o f these m a t e r i a l s . The r o l e o f chemisorbed oxygen i n adversely a f f e c t i n g the amount o f a d s o r p t i o n i s , t h e r e f o r e , q u i t e evident. 2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION A T INTERFACES

Figure 3. Adsorption isotherms of ammonia on various samples of sugar charcoal. Ο = original, Δ = 600°-out­ gassed, • = 1000°-outgassed, · = original, treated with aq. H 0 , A = 1000°-outgassed, treated with aq. H 0 . 2

2

2

2

Figure 4. Adsorption isotherms of ammonia on various samples of Mogul. Ο = original, Δ = 600°-outgassed, • = 1000°-outgassed, · = original, treated with aq. H 0 , A = 1000°-outgassed, treated with aq. H 0 . 2

2

2

2

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

15. puni

Surface Oxygen Complexes

219

Figure 5. Adsorption isotherms of ammonia on vanous samples of Spheron-6. Q = original, Δ = 600°outgassed, • = 1000°-outgassed, · = original, treated with aq. H O , A = 1000°-outgassed, treated with aq. H O . 2

z

2

g

Pressure ^ T o r r ) — • ·

Figure 6. Adsorption isotherms of ammonia on oxy­ gen-free (1000°-outgassed) samples of sugar charcoal, Mogul and Spheron-6. Q = 1000°-outgassed sugar charcoal, Δ = 1000°-outgassed Mogul, • = 1000°outgassed Spheron-6.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

220

ADSORPTION A T INTERFACES

I n order t o study the e f f e c t of CO2- and CO-complexes, sep­ a r a t e l y , the isotherms were a l s o determined on 6 0 0 ° - and 1 0 0 0 ° outgassed samples. The r e s u l t s are p l o t t e d i n F i g u r e s 8, 9 and 10 f o r Spheron-6, Mogul and Sugar Charcoal. I t i s h i g h l y s i g n i f ­ i c a n t t o note t h a t when the a c i d i c CO2- complex i s e l i m i n a t e d s u b s t a n t i a l l y on outgassing a t 600° and CO-complex becomes the predominant surface complex, the extent of a d s o r p t i o n a t each c o n c e n t r a t i o n i n c r e a s e s a p p r e c i a b l y i n the case o f each carbon and even surpasses the corresponding values f o r the oxygen-free ( i . e . , 1000°-outgassed) samples. This shows t h a t the adverse e f f e c t o f combined oxygen, as r e p o r t e d by previous workers (27, 28), can not be t r u e f o r the whole o f the oxygen. A p a r t o f the oxygen disposed o f as carbon monoxide, i n f a c t , enhances adsorb a b i l i t y o f phenol t o an a p p r e c i a b l e extent. The p o s i t i v e e f f e c t of a p a r t o f the combine i enhancin sorptio phenol i s being r e p o r t e d s u l t s c l e a r l y i n d i c a t e t h a t when the a c i d i c C02~complex i s pre dominant, the surface p r e f e r s the s t r o n g l y p o l a r molecule o f water (the s o l v e n t ) , which a d v e r s e l y a f f e c t s the a d s o r b a b i l i t y o f phenol. However, w i t h the e l i m i n a t i o n o f t h i s complex and w i t h the emergence o f CO-complex, as the predominant surface complex, the preference o f the surface f o r phenol r i s e s a p p r e c i a b l y . This appears t o be due t o i n t e r a c t i o n o f OH groups o f phenol w i t h p h e n o l i c and quinonic oxygens a s s o c i a t e d w i t h CO-complex. Summary The e f f e c t o f carbon-oxygen surface complexes on s e l e c t i v e a d s o r p t i o n from methanol-benzene mixtures as w e l l as adsorb­ a b i l i t y of benzene vapour, dry ammonia and phenol from d i l u t e aqueous s o l u t i o n s by a few samples o f m a c r o c r y s t a l l i n e carbons has been i n v e s t i g a t e d . The view o f previous workers t h a t the combined oxygen a f f e c t s these p r o p e r t i e s more or l e s s u n i f o r m l y has not been s u b s t a n t i a t e d . Thus, w h i l e the presence o f a c i d i c C02-complex enhances preference of the surface f o r methanol, the more p o l a r component o f methanol-benzene s o l u t i o n s , t h a t o f COcomplex enhances preference f o r benzene, the l e s s p o l a r component of these s o l u t i o n s . The presence o f non a c i d i c C02-complex has h a r d l y any e f f e c t . Again, w h i l e the a c i d i c C02-complex supresses the s o r p t i o n o f pure benzene from vapour phase, t h a t of CO-com­ p l e x enhances i t a p p r e c i a b l y and t h a t o f non a c i d i c complex has h a r d l y any e f f e c t at a l l . Adsorption o f d r y ammonia, which f o r oxygen-free carbons i s l a r g e l y a f u n c t i o n o f surface a r e a , i s enhanced c o n s i d e r a b l y by a c i d i c C02-complex, t o a much smaller extent by CO-complex and not a l a l l by non a c i d i c C02-complex. Adsorption o f phenol from d i l u t e aqueous s o l u t i o n s i s i n f l u e n c e d a d v e r s e l y by a c i d i c C02-complex, f a v o u r a b l y by CO-complex but not by non a c i d i c complex. S u i t a b l e explanations have been o f f e r e d f o r the apparent anamolies.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

15. puRi

Surface Oxygen Complexes

Equilibrium concentration^ moles/litre J —>-

Figure 7. Adsorption isotherms of phenol on Graphon, sugar charcoal, Mogul, and Spheron-6. X = Graphon, • = sugar charcoal, Δ = Mogul, • = Spheron-6.

Equilibrium concentration (m moles/litre) —

Figure 8. Adsorption isotherms of phenol on Spheron-6 before and after outgassing at 600 and 1000° C. · = original Spheron-6, Δ = 600°-outgassed Spheron-6, • = 1000°-outgassed Spheron-6.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

221

ADSORPTION A T INTERFACES

Figure 9. Adsorption isotherms of phenol on Mogul before and after outgassing at 600 and 1000°C. · = original Mogul, Δ = 600°-outgassed Mogul, • = 1000°-outgassed Mogul.

τ q2>q3 are the three roots of the cubic term in the denominator then ««ι-i - t o Y

q

2

=

2

= !

c

o

s

t

+

i

4 COS (| + |2L)+ 1

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

(

1

9

)

(20)

238

ADSORPTION AT INTERFACES

ν ! where

+

(21)

^t

(22)

c o s

cos ψ = 1 -

2

and the solution of Equation (18) as given by Grohner and Hofreiter (10) for q^iq^l is q i F ( M ) - (q! - q )E(k,) 3

'a(qi - q3)'

0

+

(qi - q3)(tan Φ)

/l - k

s i n ψ"

2

2

(23)

where F and Ε are e l l i p t i defined by: de

F(k,4>) and

ο Λ - k Φ

, A - k

E(M)

2

2

(24)

sin e' 2

sin

2

, θ de

(25)

where k

=

2

and

q2 - ^3

Π - qi [1 - q

Φ = Arcsin

(26)

qi - q3 0 < ψ < ϊ

(27)

2

The volume of the drop is obtained by taking Equation (8) in the form . 1 = Y[l - f Y ] (28) [1 + (dY/dX) ]* 2

2

4

If one differentiates this equation with respect to Y and inte­ grates with respect to X one has

_d ο dY

1

Y dX 2

[l+(dY/dX) ]2 2

The l e f t hand side of Equation (29) can be integrated i f the substitution dY = tan τ is made. This yields dX

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

(29)

17. CAYIAS ET AL.

Low Interfacial Tension

239

cos τ dT = 1

(30)

and V "P

2π

3

Y dX = 2

ψ fr

y

(31)

where r is the radius of a sphere of the same volume as the drop. Then combining Equations (29),(30), and (31) yields

r(r)

ο

£

( x

o-i>

(«)

r\

v

This can be reduced to

3 =

J

Combining Equations (6) and (33) yields Cr

Ύ Ϊ3

3

1

(34)

which will be an important equation in computing γ. With the aid of a high speed computor (CDC 6600), one can construct a table of values for r/p , C r , x^/r, yg/r, and x / y with α as the independent variable by the r o l l owing scheme: 3

Q

0

1.

Assign value to a.

2.

Calculate Y for 0 < Y

by Equation (11) or Equation (19)

0

< \

0

3.

Calculate X Q by Equation (23).

4.

Calculate —

by Equation (33).

o

p

5.

Calculate Cr

6.

Calculate x / r by X t (r/p ).

7.

by Equation (34)

3

q

Q

0

Calculate y /r by Y * ( r / p ) Calculate xjy„ by X * Υ ο ο 0 0 n

8.

0

A

n

Λ

This produces Princen s table except the authors have expanded and extended i t to x / y = 4.0 (a = .592589328), and because of the ease of extracting f u l l accuracy from a computer, 1

0

0

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

240

ADSORPTION AT INTERFACES

the values are recorded to ten significant figures, this accuracy however is not necessary.* The authors method of using the table to obtain a value of γ is to take the ratio of the length to width (2x /2y = ο/^ο) P determine the parameter C by using the table; then calculate γ from Equation (7). A flow diagram of the procedure is as follows: 1

0

χ

o

f

t

h

e

d r o

a

n

0

d

When the ratio of the length to width is greater than 4.0, the authors assumed that the shape can be adequately described by assuming a cylindrical tube with hemispherical ends. This is Vonneguts method and equation (15) can be used to determine γ with less than 0.05% error. The error in calculating the volume is less than 0.1%, using this geometry. Experimental The apparatus used (Figure 2) is a refined version of that employed by Princen et a l . A hysteresis synchronous motor was used. Its speed was controlled by varying the frequency from a frequency generator. The rotational s t a b i l i t y was 1 part in 10 as determined by a period averaging counter stable to 1 part in 10 . The range of speeds used was from 1,200 RPM to 24,000 RPM. A Gaertner traveling microscope with a f i l a r eyepiece was used to measure the length and width of the drop and to calibrate the glass tubes for their magnification of the drop diameter. This effect was determined to be a constant for the experiment of y measured/y true=1.332 for a l l aqueous phases studied. The tube housing and assembley (Figure 3) was designed to accept a precision ground .245"0.D. pyrex glass tube (C) rounded on one end and sealed against a rubber septum (G) on the other. A glass cell enclosed the apparatus to permit temperature studies. Thermostating of the system to + 0.5C° was obtained. The procedure for loading the cell is to f i l l the glass tube and metal cap (H) completely with the more dense phase. Holding the tube upside down (capillary pressure retains the more dense phase in the tube), the less dense phase is then injected with a microliter syringe, the tube is then placed in the cap and the 5

8

*

A copy of the program is available from the authors on request

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

Low Interfacial Tension

CAYiAS E T A L .

TUBE

WALL

MOTOR

POWER

CONTROL

AMPLIFIER

BOX

H

y

SCOPE

ROTOR FREQUENCY

TEMPERATURE

COUNTER

CONTROLLER

SIGNAL

ASS'Y

STROBE

GENERATOR

SUPPLY

SPINNING-DROP

Figure 2.

APPARATUS

Schematic of spinning-drop apparatus

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

242

ADSORPTION A T INTERFACES

Figure 3. A = less dense phase (drop), Β = more dense phase, C = glass tube, D = shaft O-rings, Ε = shaft, F = cap O-ring, G = silicone rubber septum, H = cap, I = ball bearings, J = outer support housing, Κ = O-ring for loading bearings, L = load adjusting cap, M = Bakélite plate, Ν = aluminum box tubing, Ο = non-slip positive drive belt, Ρ = pully, R = motor shaft adaptor, and S = threads for heater wire windings

PLOT OF G vs H FOR BENZENE vs. WATER

0

1

2

3 H= Δ < 1 ω / 4 2

Figure 4.

xlO"

AT 27 C e

4 4

Plot for obtaining a using the alternate Princen et al. method

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

17.

CAYIAS ET A L .

Low Interfacial Tension

243

whole assembly placed in the shaft and secured by screwing the cap onto the shaft. A small hypodermic needle is inserted into the cell through the septum to release any pressure buildup caused by screwing the cap on. This method, though d i f f i c u l t at f i r s t , is easily mastered after a few attempts. In a test of the equipment using the benzene/water system with a literature value (11) for the interfacial tension of 35.0 dynes/cm at 20°C the authors obtained at 27°C 34.50 dynes/cm using the principal Princen et a l . method of length and volume measure­ ment and 34.65 dynes/cm using the alternate Princen et a l . method of frequency differences (Figure 4). Figure 5 is a photograph of the drop. The slightly lower values could possibly be due to im­ purities in the system or the higher temperature or both. As a final test of the system, the butanol/water system was measured and a tension of 1.80+.0 pares very well with th at 20°C To check the applicability of the system for measuring low interfacial tensions a commercial surfactant, Petronate TRS 10-80 obtained from Witco Chemical Company, was used. A stock solution was made up with the following components in water: 0.2 wt. % Petronate and 1.0 wt. % NaCl. This solution was then compared against several hydrocarbons at 27°C The results of this exper­ iment are in Figure 6. A picture of one of these drops is included in Figure 7. The octane/surfactant system verified the capability of the apparatus to measure low tensions. The reproducibility of the measurements was 2% but a confidence l i m i t of 10% is probably more r e a l i s t i c for tensions in this range. Using the 10% confidence limit, tensions of 10" dyne/cm could be measured with the Gaertner f i l a r eyepiece (accurate to 5 Χ 10" cm) with some d i f f i c u l t y . This is not a lower limit of the method, only of the optical equipment used. The limit could possibly be extended by choosing a different measuring system. The main d i f f i c u l t y encountered was to deliver small volumes of 10" cc or less. The discharge as a single drop of such small volumes from a syringe was found to be very d i f f i c u l t . The drop has a tendency to stay attached to the needle and quick removal of the needle from the more dense phase caused the drop to detach i t s e l f from the needle partially. This partial detachment made accurate volume measurements almost impossible. A further complication of the problem was that as the needle was retracted from the liquid, some small drops of the less dense phase would be l e f t behind and after starting the rotation these small drops could coalesce with the large drop changing its volume. Another d i f f i c u l t y with the measured volume method is i f the drop breaks up after injection then the experiment would have to be term­ inated. The last d i f f i c u l t y with measuring the volume of the drop was volume change due to solubilization. For low interfacial 6

5

3

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

ADSORPTION A T INTERFACES

SURFACE

TENSION OF HYDROCARBONS

vs. 0.2% PETRONATE / 1.0% Να CI AT 27 °C AFTER

24 HOURS OF STIRRING

NUMBER OF CARBON ATOMS Figure 6.

Results of hydrocarbon studies against the surfactant

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

Figure 7.

Octane surfactant system at 6,000 RPM

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

246

ADSORPTION AT INTERFACES

tensions, where the drop was composed of several components, solubilization could result in indeterminate drop composition. For example the volume of the drop in the octane/surfactant system when the two phases were not pre-equilibrated, initially increased and then slowly decreased from the initial volume making the measured volume method useless and the frequency difference method inaccurate since the volume was not constant. For these reasons it was necessary to abandon the Princen et al. methods and use the authors' method described previously of measuring both the length and diameter of the drop and from this calculating.the tension. Both Vonnegut and Princen et al. observed a rippled surface for an air buble in water. Princen et al. suggested it was probably due to the vibration from the motor drive, however the authors in examining thi t found distortion f th surface but had vibration possible explanation of the lack of these ripples is the small size of the authors' system in comparison to that of Princen et al. Conclusions The spinning drop method for measuring low surface and interfacial tensions using the methods described in this paper is one of simplicity and ease of operation as compared to other methods. The method does not involve a third (solid) phase in contact with the interface of the drop as Ryden and Albertsson (9) pointed out. The Princen et al. method works well in systems where accurate determination of the volume is possible but for systems the authors examined where accurate determination of the volume is a difficult task, the method of measuring both the length and width of the drop is more accurate. Acknow!edgement The authors wish to express their appreciation to the Robert A. Welch Foundation and the National Science Foundation for sponsoring this research and their special thanks and apprécia* tion to H.M. Princen for valuable discussions and furnishing the authors with some of his original data. The authors also wish to express their gratitude to James Gardner for the drawings which appear in the text.

Literature Cited 1.

Plateau, J.A.F., "Statique Experimentale et Theorique des Liquides, etc.", Gauthier-Villars, Paris, 1873.

2.

Beer, Α., Annalen der Physik und Chemie von Poggendorff, (1855) 96, 210.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

17. CAYIAS ET AL.

Low Interfacial Tension

247

3.

Raleigh, Lord, Phil. Mag., (1914) 28, 161.

4.

Vonnegut, Β., Rev. Sci. Instrum. (1942) 13, 6.

5.

Silberberg, Α., Ph.D. Thesis, Basel University, Switzerland, 1952.

6.

Rosenthal, D.K., J. Fluid. Mech., (1962) 12, 358.

7.

Princen, H.M., Zia, I.Y.Z., and Mason, S.G., J. Colloid Interface Sci., (1967) 23, 99.

8.

Patterson, H.T., Hu, K.H., and Grindstaff, T.H., J. Polymer Sci., (1971) 34, 31.

9.

Ryden, Jan and Albertsson Sci. (1971) 37, 219.

10.

Grobner, W. and Hofreiter, N., "Integraltafel," 3rd ed., Vol. I, p. 78, Springer Verlag, Vienna, 1961.

11.

Adamson, Arthur W., "Physical Chemistry of Surfaces," 2nd ed., pp. 44-45, Wiley, New York, 1967.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

18 Adhesion of Ice Frozen from Dilute Electrolyte Solutions H. H. G. JELLINEK Department of Chemistry, Clarkson College of Technology, Potsdam, Ν. Y. 13676

Introduction The adhesion of ice has long been studied but a satisfactory solution, from the practical standpoint of decreasing adhesion or increasing abhesion, has not yet been found. Complete abhesion can be achieved un­ der laboratory conditions but in practice any surface becomes rapidly contaminated after a few abhesions have taken place and the adhesion of ice continually i n ­ creases with further abhesions. Experimental Data by Smith-Johannsen and Discussion Smith-Johannsen (1) studied the effect of impuri­ ties in water on the adhesion of ice by freezing such solutions to various substrates. He ascertained that small i n i t i a l concentrations (1 X 10 mole/liter(M) or less) of electrolytes (salts) decrease ice adhesion considerably. The adhesive strength was measured by the force per square centimeter needed to shear the ice off the substrate. The experiments were carried out at -10°C. The freezing point lowering of water by elec­ trolytes of such concentrations is only about 0.005°C. The ice was frozen rapidly enough so that the electro­ lyte remained homogeneously distributed throughout the frozen system, and did not have sufficient time to dif­ fuse away from the substrate/solution interface. Air bubbles appeared during the freezing process. Table I gives relevant data (S = salinity of i n i t i a l solution; p = salinity of grain boundary solution). The effectiveness of decreasing adhesion, or i n ­ creasing abhesion, varies considerably with the partic­ ular electrolyte in solution. Thus 1 Χ 1 0 Μ Th(NO ) decreases adhesion by 97% on a wax-treated aluminum -3

-3

3 4

248 In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

In Adsorption at Interfaces; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.

3

h

2

2

2

3

3

3

3

s

2.91 3.08 1.95 4.00 1.93 2.99 1.17 1.40 1.15 0.88 1.54 1.20 1.27 2.17

10 2,45 2.20 0.85 0.65 0.76 2.78 0.39 1.38 1.30 0.11