Colloidal dispersions and micellar behavior: Papers from a symposium honoring Robert D. Vold and Marjorie J. Vold (ACS symposium series ; 9)

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Colloidal Dispersions and Micellar Behavior

In Colloidal Dispersions and Micellar Behavior; Mittal, K.; ACS Symposium Series; American Chemical Society: Washington, DC, 1975.


Colloidal Dispersions and Micellar Behavior K. L. Mittal, Editor

Papers from a symposium honoring Robert D. Vold and Marjorie J. Vold sponsored by the Division of Colloid and Surface Chemistry at the 167th Meeting of the American Chemical Society Los Angeles, Calif., April 2-5, 1974.

ACS

AMERICAN WASHINGTON,

SYMPOSIUM

CHEMICAL D.

SERIES

SOCIETY C.

1975


9

Library of Congress

Data

Colloidal dispersions and micellar behavior. (ACS symposium series; no. 9) Includes bibliographical references and index. 1. Colloids—Congresses. 2. Micelles—Congresses. I. Mittal, K . L., 1945- ed. II. American Chemical Society. Division of Colloid and Surface Chemistry. III. Series: American Chemical Society. ACS symposium series; no. 9. QD549.C62 ISBN 0-8412-0250-8

541'.3451

74-34072 ACSMC8 9 1-353

Copyright © 1975 American Chemical Society All Rights Reserved PRINTED IN THE UNITED STATES OF AMERICA


ACS Symposium Series Robert F . Gould, Series Editor


FOREWORD The ACS SYMPOSIU

a medium for publishing symposia quickly in book form. The format of the SERIES parallels that of its predecessor, ADVANCES IN CHEMISTRY SERIES, except that in order to save time the papers are not typeset but are reproduced as they are sub mitted 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 ACS SYMPOSIUM 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.


PREFACE "professors R. D. Void and M . J. Void retired in June 1974 after more -*· 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 knew of their global popularity and knew that such an event would elici former students and fellow colloid scientists. The response exceeded all expectations as 57 papers covering a wide variety of interfacial and col loidal 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 the International Symposium on Interfacial and Colloidal Phenomena Honoring Professors R. D. and M . J. Void. This volume of 24 papers chronicles part of the proceedings of this symposium. The other part is contained in a companion volume of 20 papers entitled "Adsorption at Interfaces." The papers in this volume deal with the formation, stability, and other aspects of a variety of col loidal dispersions and micelles in aqueous and nonaqueous media. 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." This description encompasses a variety of phenomena both in the animate and inanimate world. Colloid science has experienced fluctuations of popularity among researchers. To some people, it is an academic stigma to study colloidal systems as they think that only researchers with cloudy thinking can engage in these cloudy systems. This reminds me of an anecdote which happened in 1966. After finishing my M.Sc. hi India in 1966, I had de cided to join the University of Southern California to carry out my grad uate research in colloid chemistry. One day one of my professors asked me what kind of graduate work I would do at U.S.C. I replied, "Colloid ix


science." He looked at me as though I had said something unpalatable and retorted, "Don't you have anything better to do?" Apparently, he never bothered to probe into the beauty of the ubiquitous colloidal systems. Fortunately, the myths about colloid science are now being dispelled, and the field has gained respectability both in industrial as well as aca demic circles. In the last decade, the researchers have increased the interest in colloidal systems as is evidenced by the proliferation of journal articles, books, and collective volume series, and all available signals indicate that this trend will continue. With the advent of sophisticated instrumentation and the development of quantitative theories of colloids, much progress has been made in understanding colloidal systems. But it is still a long way before the World of Neglected Dimensions is fully understood. The Voids have been active in a spectrum of research activities. He made his research debut in the study of the solubility of organic com pounds in aqueous and nonaqueous media while she published her first paper 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 systems to practical industrial problems and decided to study the intricacies of colloidal systems. Subsequently, Marjorie became very interested in studying colloids. They actively pursued the phase rule studies of association colloids (soaps, greases, etc.) in aqueous and nonaqueous media employing 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 inter ests have included understanding of the factors influencing emulsion stability using ultracentrifuge; use of computer in floe formation and cal culation 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 DNA. Obviously, the Voids' research activities have run the gamut from less glamorous colloidal systems like greases to the more fashionable bio polymers. Their work on the phase behavior and properties of non aqueous soap systems had a significant impact in the petroleum industry (cf. NLGI 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 ex tremely good exposition of the principles and the methods of study of χ


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 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. No 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 Ph.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. He 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 re search at the University of Southern California. In 1953-1954 he held 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 Ph.D. program. In 1965 he served as a consultant for the Summer Institute at Jadavpur University, Calcutta, India, which is de signed to improve the teaching of chemistry in Indian colleges. He 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 in clude Chairman, Southern California Section, ACS, 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, Di vision of Colloid Chemistry, ACS, 1947-1948. He was awarded the Tolman medal of the Southern California Section meeting 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 Ph.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. xi


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 Oil Co. (1942-1946). Since then she has held various faculty appointments in the Department of Chemistry of the University of South ern 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, The Netherlands. From 1967 to 1970 she served 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 So ciety 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 Void 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. On November 19, 1967 an article entitled "Science: A Tie That Binds" appeared in Los Angeles Herald Examiner which presented a few 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. We complement each other in our work and our lives." Although the Voids are retiring from active duty, they have no inten tion of relinquishing their interest for colloid science—a discipline they have cherished for about 40 yrs—as they plan to write a text book on the subject. May 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 to the management of the IBM 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 pub lication. The able guidance and ready and willing help of Paul Becher xii


and Κ. J. Mysels is deeply appreciated. The reviewers should be thanked for their many valuable comments on the manuscripts. I am thankful to my wife Usha, for helping with the correspondence, proofreading, and above all for tolerating, without complaint, the frequent privations of an editor's wife. It would be remiss on my part if I failed to also acknowledge the enthusiasm and cooperation of all the participants, especially the delegates from overseas countries. K . L. MITTAL

IBM Corp. Poughkeepsie, N.Y. November 19, 1974

xiii


1 A Third of a Century of Colloid Chemistry ROBERT D. V O L D and MARJORIE J. V O L D Department of Chemistry, University of Southern California, Los Angeles, Calif. 90007

Our work in colloid chemistry began in 1936 at the Procter and Gamble Company. Th seen many changes, very considerable progress, and a great in crease in our knowledge and understanding of colloidal systems. In this paper an attempt will be made to contrast the present state of the science with that existing in the middle thirties, and sketch some of the changes which have occurred. Although we arrived on the scene too late to meet the founders we were privileged to have a warm personal acquaintance with many of their immediate successors, since colloid and surface chemistry is still a relatively young science. Among these should be men tioned Holmes, Hauser, LaMer, Debye, Bartell, Jerome Alexander, Weiser, and most of all McBain, none of whom are any longer with us. These were great men as well as great scientists. We shall never forget Hauser's consideration at a Colloid Symposium in lunching with a couple of then unknown young sprouts, and intro ducing us to the leaders in the f i e l d , or McBain's talent for raising the self-esteem and bringing out the best in even the least gifted of his students. It is difficult now to put one's self back into the environ ment of 1935. Then there was no BET equation, no general method for determining molecular weight by light scattering, no DLVO theory of stability, and considerable uncertainty as to whether colloidal behavior could be described completely by the usual relations of physical chemistry, or whether special new vari ables would have to be introduced. The ultracentrifuge and the electron microscope were in their infancy, and unavailable ex cept in a very few specialized centers. In fact there was l i t t l e commercially available instrumentation suitable for col loidal studies, as contrasted with the present time when the limitation is usually financial rather than lack of availability. In the old days one had to improvise and construct out of what ever components could be located. Now, provided one has funds, one can simply buy a differential scanning calorimeter or a zeta meter, or a BET apparatus, or a scanning electron microscope, 1


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C O L L O I D A L DISPERSIONS A N D M I C E L L A R BEHAVIOR

etc. Since i t is impossible in the available space to cover the whole f i e l d , the present article will be primarily a personal odyssey describing research in fields in which we have been active at the Procter and Gamble Company to 1937, at Stanford to 1941, and subsequently at the University of Southern California except for Marjorie Void's wartime employment at the Union Oil Company, a year in Professor Overbeek's laboratory in Utrecht, two years at the Indian Institute of Science in Bangalore, and nine months at the California Institute of Technology (RDV). At Procter and Gamble and at Stanford our concern was primarily with the phase behavior of soap-salt-water systems with peripheral in volvement in the nature and properties of surfactant solutions. At U.S.C. we were f i r s t interested in the phase behavior of heavy metal soap-hydrocarbon systems, with a later expansion to study their colloidal structur tion phenomena, and laying a foundation for understanding the be havior of lubricating greases. Simultaneously studies were com menced on adsorption of surfactants at the water-solid interface with particular reference to detergency, suspendability, and electrical double layer theory. The year in The Netherlands focussed attention on the over riding importance of obtaining an understanding of the nature and magnitude of the attractive and repulsive forces operative between colloidal particles suspended in a medium, a problem which is s t i l l not completely solved but on which rapid progress is being made at the present time. Studies of adsorption of surfactants at the oil-water interface were then undertaken as a necessary prerequisite for investigating quantitatively the stability of emulsions. At the same time an active program on the stability of suspensions was undertaken, the zeta potential being the most im portant variable in the case of aqueous suspensions, with entropie and enthalpic effects the important factors with non-aqueous sus pensions. The latter could be investigated most f r u i t f u l l y through a study of flocculation kinetics, while a computer simu lation of the sedimentation process further increased our under standing. With the availability of an ultracentrifuge for study ing emulsion stability, i t was also possible to undertake a study of the physical chemistry of DNA in magnesium salt solutions, with particular interest in the fate of the water of hydration of the magnesium ion on binding to the DNA, and to changes in conforma tion of the DNA molecule, resulting from the binding of magnesium ion or changes in the thermodynamic activity of the water. Simultaneously we have been much concerned with the status of the teaching of colloid chemistry in American universities. Des pite its importance in industry, biology, and fundamental theory, the field has been relatively neglected for the last several years because of the glamorous excitement attending recent developments in the unravelling of molecular structure, as has been eloquently pointed out by several authors (1.2^2). The mother is in danger


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of being devoured by her offspring. Material scientists, biophysicists, polymer chemists, theoreticians dealing with interparticle forces, catalyst chemists, and many others, are all dealing with colloidal phenomena but a l l too often have no con cept of the central organization of the whole field which is pro vided by a series of coherent courses in colloid, surface and polymer chemistry. Many former centers, such as that at Colum bia, have declined because of neglect due to running after the latest fashion. However, there is hope for the future as evi denced by the rapid recent growth of new centers such as those at Clarkson and Lehigh. But at most universities, unfortunately, colloid and surface chemistry are regarded as being too special ized and applied by the chemical purists, and too theoretical by the chemical engineers. Returning to a chronologica of the art in 1936 is strikingl that time space was s t i l l found in the Journal of the Aiterican Chemical Society for a paper of which the main point was simply that the ordinary laws of physical chemistry applied to soap sys tems. This was an off-shoot of my work at the Procter and Gamble Company attempting to apply the phase rule to systems of soaps and water. In certain composition regions liquid crystalline middle soap exists in equilibrium with isotropic solution, and hence the vapor pressure should be independent of composition. Although all now believe that the phase rule applies without ex ceptions the experimental demonstration left much to be desired, since the vapor pressure is near that of water, and variations due to changes in temperature tend to be larger than those due to variation in composition. James W. McBain was one of the giants in the field of col loid chemistry at that time, so I jumped at the opportunity to spend four years in his laboratory as a postdoctoral fellow. It is of interest to recapitulate the problems under investigation in his laboratory in view of its reputation. These included development of an air-driven ultracentrifuge, determination of the surface area of soap curd by adsorption of methylene blue, attempts to measure the range of surface forces from the effect of different substrates on the strength of adhesive joints, d i rect experimental determination of the surface excess and com parison with the results predicted by the Gibbs equation, deter mination of phase diagrams of soap-salt-water systems, character ization of dodecylsuTfonic acid as a colloidal electrolyte through measurement of properties such as diffusion constant, conduc t i v i t y , osmotic coefficient, etc., and "solubilization" of dyes. Tests of the Gibbs adsorption isotherm are perhaps particu larly interesting. A "railroad" was built on which a springdriven cart with a razor edge scoop collected a surface layer 0.05 mm deep from a trough f i l l e d with soap solution (1 ml from 1000 cm of surface), with the concentration difference between bulk and surface solution determined by interferons try. This was 2


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COLLOIDAL DISPERSIONS A N D M I C E L L A R BEHAVIOR

an attempt to explain what was known as McBain's paradox. All curves of surface tension versus concentration of colloidal elec trolyte known at the time went through a minimum, with the sur face excess calculated from the Gibbs equation being necessarily zero at that concentration. But the surface tension of the water was lowered by 50 dynes/cm. or so despite the calculation that no soap was adsorbed at the surface. Various experimental dif f i c u l t i e s , particularly the problem of preventing evaporation from the trough, made i t impossible to obtain really definitive results. It was not until much later, and after several fanci ful attempts by other authors to explain the minimum in the sur face tension-concentration curve theoretically, that i t was shown to be an artifact due to the presence of trace impurities, lauryl alcohol in the case of sodium lauryl sulfate solutions. The electron microscope was a relatively exotic tool in 1937. It was with considerabl pared a sample of the curd fiber phase of sodium laurate in water for McBain to send to a friend of his in the RCA research labora tories to be actually photographed with an electron microscope. The pictures were duly taken with a direct magnification of 8000 diameters and returned to us for interpretation. They showed a fibrous network with an angle between the branches invariably 62-65° which is just the angle to be expected i f the fibers were crystalline in nature and grown together at junction points somewhat like crystal twins. Evidence was also found that their widths were simple multiples of the molecular length. Our own work at Stanford was concerned primarily with the phase diagrams of the sodium soaps with water, and with salt and water, and with the polymorphism of the solvent-free soaps. On heating sodium palmitate in a sealed tube the f i r s t definite visible change is a sintering and increase in trans!ucency at 256° C. This was often listed as the melting point in the early literature, although some of the more persistent investigators went right on heating to higher temperatures, and were rewarded by being able to observe true melting at 292° to 305° C , with a substantial increase in fluidity and transparency. So the question arose as to what was really going on. How many phases of sodium palmitate were there? Could they dissolve water? What is the binary phase diagram like? We put samples of sodium palmitate and water in a dilatometer to observe changes in slope of the curve of volume versus temperature when phase boundaries were crossed, and found that the curve was f u l l of wiggles. Even with anhydrous sodium pal mitate flats were found at 117, 135, 208, 253 and 295° C , prov ing the existence of five polymorphic phases in addition to the isotropic liquid. Microscopic examination between crossed Niçois in sealed f l a t glass capillaries in a microfurnace confirmed the result. This was a rewarding kind of experiment in yet another way: the liquid crystalline structures that separate from the liquid are beautiful to behold.


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The idea was born that the various polymorphic forms of the sodium soaps could be considered to result from the melting pro cess taking place in steps instead of all at once at a single temperature. So we undertook to measure the heats of transition between the various phases. It turned out that some were inde pendent of the length of the paraffin chain of the soap, indicat ing that the structural change involved in the transition was concerned with interactions of the polar head groups. Others were linear functions of the number of carbon atoms in the chain. The sum of the heats of a l l the transitions was very nearly the same as the heat of fusion of the corresponding fatty acid. The method adopted for measuring the heats of transition was differential thermal analysis. Now one can purchase DTA appara tus but this was not the case in 1941. Sample and reference material were sealed in pear-shaped glass cells into which a thermometer well had bee polyisobutylene to effect good contact between the glass cell and the thermometer bulbs. The two cells were placed side by side in a furnace made by wrapping resistance wire around a can insulated with asbestos paper. The rate of heating was con trolled manually, readings of sample and reference thermometers were taken at frequent intervals on heating, and their difference plotted as a function of the temperature of the reference c e l l . Despite the crudity of the equipment, the thermograms obtained were not too bad compared to those obtained today with apparatus provided with an electronically controlled rate of heating and continuous automatic recording of the differential temperature. In 1941 I joined the faculty of the University of Southern California where, among other things, I had the responsibility for organizing and teaching a course in colloid chemistry. For tunately, while at Stanford we had attended McBain's lectures on the subject. McBain had used no text, drawing on his own wide knowledge and personal experience. He had a large number of ex cellent demonstrations but there was no laboratory associated with the course. I did not have sufficient self confidence to proceed in this fashion, and after much casting around finally settled on "Colloid Chemistry" by Harry B. Weiser for the lecture course, and Floyd Bartell's "Laboratory Manual of Colloid Chemis try" for the laboratory. Looking at Weiser's book today is quite a shock. For ex ample, of the f i r s t 113 pages devoted to adsorption, less than half is concerned with the adsorption of gases. Of these 43 pages only ten are concerned with adsorption isotherms. The Freundlich isotherm is given and the Langmuir isotherm, together with its derivation from elementary kinetic considerations. Polanyi's theory is mentioned but is essentially dismissed on the grounds that i t requires van der Waal's forces to be effec tive over a considerable distance whereas "everybody knows" they can extend only over distances of the order of magnitude of mole cular sizes, and usually the Freundlich or Langmuir isotherms


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A N D M I C E L L A R BEHAVIOR

generally f i t the data better anyway. Heats of adsorption cal culated from the Clausius-Clapeyron equation are presented but there is no treatment of their variation with surface coverage. Although the book was copyrighted in 1939, the BET equation, published in 1938, s t i l l had not found its way into the text books . The Gibbs adsorption equation, relating adsorption and the concentration dependence of the surface tension, is given, ac companied by some results of McBain's microtome method purpor ting to show actual adsorption substantially higher than pre dicted by the equation. It is surmised that the Gibbs equation is to be viewed as a "limiting law". One might well ask in view of the vast amount of work on adsorption since then what could be found to say about i t thirty years ago. The answer i rule about the least solubl Traube's rule concerning the increase in sorbability as one as cends a homologous series; Paneth and Fajan's rules regarding the adsorbability of ions on ionic solids; and the SchulzeHardy rule relating the coagulating power to the valence of the ion of opposite charge to that of the colloidal particle. There are a host of other intriguing relations, so that one is led to wonder a bit uneasily whether the newly acquired and highly touted rigor of modern colloid science has been attained at the cost of the loss of some of the beauty of the earlier qualitative observations. In many practical industrial situations a thorough understanding of the qualitative behavior may serve the per plexed chemist better than knowledge of the details of the mathe matical derivation of an equation applicable only to simple or idealized systems. Actually, for most effective performance, familiarity with both approaches is necessary. What is true about the treatment of adsorption is also true of other topics as well, such as stability of lyophobic sols, lyophilic systems including biocolloids, and association colloids. What has been discovered in the last thirty years or so makes the best of the treatments of 1941 seem very much out of date. There are not only sins of omission but also those of commission as well. For instance, Freundlich believed that the electric charge on the particles had to be neutralized by ad sorption of ions of the opposite charge in order to bring about coagulation. Weiser surmized that charge neutralization did not have to be complete in view of the existence of a non-zero value of the zeta potential below which rapid coagulation occur red, and related the phenomenon to contraction of the double layer. But that was as far as he got; there wasn't any quanti tative description. An important feature of academic research in 1941 which should be borne in mind is that there was no National Science Foundation, no Atomic Energy Commission, no Environmental Pro tective Agency, etc. By and large most research in the univer-


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si ties was unsponsored. Some industrial firms, however, would give funds to the university for work under the direction of a given individual. There would be no strings on the nature of the research, but frequently there was an implied understanding that the professor concerned would be interested in the technical problems of the company. I was fortunate in having funds to sup port two such fellowships, one from the Lever Brothers Company, and one from the Col gate-Palmolive-Peet Company. So to a con tinuing interest in soap phases we began also to become interest ed in the characteristics of dilute soap solutions and the pro blems of detergency. Understanding of the mechanism of detergent action involves many of the basic processes of colloid science, such as solu bilization, adsorption, wetting, pore structure, the role of mechanical action, and th soils the mechanical agitatio the dirt from the substrate. The detergent acts by becoming ad sorbed on the surface of both the dirt and the substrate, thus effectively preventing redeposition of the dirt when the agita tion is stopped. In some of our simpler experiments we merely determined the effect of concentration of detergent on the amount of powdered manganese dioxide or carbon black remaining in sus pension in the detergent solution after four hours settling time. The amount suspended passed through a maximum with increasing concentration of detergent but there was no correlation with the critical micelle concentration of the detergent solution. The results could, however, be rationalized in terms of attain ment of a limiting zeta potential resulting from adsorption of the detergent. However, even without the added complexity of a fiber-liquid interface, there are s t i l l many unsolved problems. For the work with solid sodium soaps we went to x-ray dif fraction. Since single crystals of these substances recalcitranly refused to form, the x-ray was used essentially as a finger print device. Several polymorphs can be realized at room temp erature, unimaginatively labelled as alpha, beta, gamma and delta. The alpha form, deposited from aqueous alcohol, turned out to be a hemihydrate. Martin Buerger of M.I.T. did succeed in growing i t as a single crystal, and determined its space group. About this time we became enamoured of the idea of studying the behavior of metal soaps ( i . e . , a l l the soaps except those of sodium and potassium) in oils by the techniques which had been so relatively successful in unravelling the mysteries of the soap-water systems. In the latter case i t had been definitely established that such important use properties as formation of lather, tendency of a bar to crack on aging, et cetera, are de termined by which of several polymorphs is actually present; moreover, the whole process of soap boiling could be described in terms of plotting a course through the phase map of the sys tem. Lubricating greases are made by dispersing metal soaps in o i l , or reacting fats or fatty acids dispersed in o i l with


8


a l k a l i , diluting the resultant concentrate with more o i l , and extensive milling. Just as the art of soap boiling could be reduced to a science by determination of soap-salt-water phase diagrams, i t seemed possible that the art of grease making would be similarly clarified by determination of the phases present at each stage. By this time the Office of Naval Research had un dertaken limited support of fundamental research - i t was s t i l l prior to the date of the National Science Foundation - and un derwrote our f i r s t ventures in this f i e l d . Even prior to these studies i t had become desirable to re place our makeshift differential calorimeter with something bet ter. Differential thermal analysis had been used extensively in studying the dehydration of clays, with an apparatus consist ing of a block of metal with holes bored in i t to contain sample and reference materials with thermocouples in each well. But very rapid rates of heatin 25° C. per minute - and we needed a much lower rate since phase transitions in the soaps can occur fairly slowly. And we needed vapor-tight containers both to prevent oxidation of the soap sample and to maintain constancy of composition in use with solvent-containing systems. We also wanted to automate the in strument. The time-temperature controller we developed was very d i rect. The desired pattern for a given thermal program, say a steady rate of heating of 1 1/2° C./min., was plotted in polar coordinates and cut out on a thin aluminum cam. A lever arm followed the cam as i t turned. The actual temperature of the furnace was measured by a thermocouple located in the reference sample, and the signal fed to both a circular chart recorder and to the controller. Here the difference between the actual furnace temperature and the programmed temperature activated an air valve and set a pneumatic motor to raise or lower an arm which was attached to a cord wound around the stem of a variable transformer supplying heating current to the furnace. The temperature difference between sample and reference cell was measured with a five junction thermopile, and recorded continu ously on a strip chart recorder. For all its Rube Goldberg ap pearance, this apparatus, developed with the collaboration of Todd Doscher, worked very well. With the use of this apparatus, and the polarizing micro scope, systematic measurements were made of the thermal transi tions of most of the heavy metal soaps, and the binary phase diagrams determined for lithium stéarate in cetane and in decalin. The result of a l l this work was the definitive, although negative, demonstration that the use properties of greases could not after a l l be explained in terms of phase diagrams. The phase diagrams of soap in petroleum oil are extremely simple. Each of the successive phases of the solvent-free soap is some what soluble in o i l , with the solubility varying from nearly zero at room temperature to nearly complete miscibility in some


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cases at higher temperatures, but the soap phases do not swell to an appreciable extent. The physical properties of a grease are determined primarily not by what phase or phases are present, but by the structure of the mix of colloidal soap fibers with the o i l . Thus the problem of explaining such physical properties as resistance to shear breakdown, hardness as related to soap and additives present, resistance to syneresis, or consistency and other rheological properties, is as complicated as the phase diagrams are simple. It appeared that explanations would have to be sought in such properties as the type of interconnected gel network formed, the strength and nature of the "bonds" at the contact points, the anisometry of the fibers, the size and tortuosity of the channels, etc. These are difficult to observe and to quantify: an endeavor which is s t i l l far from complete although some progress has been made. Study of such propertie plication of a variety of different techniques, including the penetrometer for measuring consistency, the electron microscope for observing fibers and "structures", the exudation of liquid from the gel under pressure, and the effect on properties and characteristics of differing thermal pretreatments. Although empirical correlations had been developed between the lengthwidth ratio of the soap fibers recoverable from greases and measurable in the electron microscope, i t seemed important to us to attempt to characterize the properties of the structural skeleton formed by these fibers in the soap-oil gel i t s e l f . At the time there was s t i l l considerable controversy even as to the existence of such a three-dimensional structure, since i t was possible to "explain" most observations equally plausibly in terms of a solvate shell of variable thickness. The situation then is reminiscent of the present situation where phenomena otherwise d i f f i c u l t to explain are rationalized in terms of a change in the structure of water. The reality of a three dimensional structure of soap fibers held together at contact points by van der Waal's forces was beautifully demonstrated by the observation by Browning that the oil in a grease could be replaced by other organic liquids with no change in the dimensions of the sample, and l i t t l e change in its rheological characteristics. Peterson and Bondi confirmed and extended this conclusion by making an aerogel from the grease by a similar perfusion technique with liquid butylène and liquid ethylene successively, followed by heating under pressure above the critical temperature, and allowing the ethylene to escape. The resultant aerogel had the same volume and shape as the original blob of grease but was very hard and b r i t t l e , certainly a long way from a loose pile of separate soap crystallites. Electron microscopy showed the presence of an interconnected brushheap of soap fibers. Oil could be sucked back into the aerogel under vacuum, but the reconstituted grease was much harder than the original until i t was subjected to


10



mechanical working, when i t regained its original consistency. The observations are consistent with the concept that oil or ad ditive molecules separate the individual soap fibers at their junction points, and that van der Waal's forces act through the o i l layer making flexible joints which deform when the grease is made to flow. Some further progress was made by borrowing a technique from the biologists, i.e. study of thin sections in the electron microscope, working with Henry Coffer. By cooling a grease to dry ice temperatures i t was possible to prepare sections of about 0.1 ym thickness by slicing with a microtome. Marked dif ferences were found in the appearance of the fibers bound in the continuous network as contrasted with those seen in samples prepared by the more common solvent extraction and smear techni que. The difference is skeleton rather than a pil with the additional complication of inducement of right-handed or left-handed, twisted, rope-like aggreagates in the smears dependent on the direction of smearing. However, no one has yet been able to prepare sections of sufficient quality to per mit any quantitative characterization of the colloidal structure. A grease may be converted into a suspension of soap crystal lites by diluting i t with a solvent for the o i l , such as benzene or heptane. The resulting suspension forms a very weak gel which slowly compacts to a final volume containing only a small amount of solids. This behavior suggested another approach to charac terizing the gel structure through calculation of a theoretical value for the per cent solids in the settled gel. The method employed was a computer simulation of the settling process using the Monte Carlo technique. First the sediment volume was calculated for a sediment composed of spherical particles treated as cohering to each other on f i r s t contact. Then a parameter was introduced giving the particles a specified probability of cohesion on contact - analogous to the existence of an inter action potential between the particles - , and otherwise lett ing them roll over each other to achieve more efficient packing. For moist glass beads settling in a non-polar solvent the ex perimental value of the volume per cent solids in the sediment was 12.9% while the calculated value from the model chosen was 12.8%. The calculations became more d i f f i c u l t and less unam biguous as the model is altered to conform better to real sys tems by making the particles anisometric and introducing longer range attractive forces, although promising in the sense that these alterations reduce the solid content in the sediment to lower values coming closer to those found with real greases. A book appeared in 1948 which changed the entire state of colloid chemistry with respect to understanding of colloidal stability: "Theory of the Stability of Lyophobic Colloids" by E.J.W. Verwey and J . Th. G. Overbeek. It set forth the mathe matical foundation for showing that the tendency of fine parti-


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cles to remain dispersed was due to the mutual repulsion of their electrical double layers being sufficient to overcome the van der Waal's attractive forces pulling them together. The addition of electrolyte reduces the repulsion, thus permitting the van der Waal's forces to dominate the interaction so coagulation occurs. It was just that simple. It turned out subsequently that the Russian investigators, Landau and Derjaguin, had had much the same idea, actually publishing the electrical double layer repulsion part in 1941, although i t did not become known until after the war. So the total treatment is now known as the DLVO theory. Hauser had already understood this qualita tively in 1939 (4), but i t had seemed very contrived to most chemists of that period since any desired prediction could be obtained by shifting around the position of attraction and re pulsion curves on a potentia nor we realized that the ties. In fact, so great was the scepticism that at one meeting of the Colloid Symposium Hauser laid a revolver on the table at the beginning of his talk with the remark that people were going to have to listen to him whether they wanted to or not. At that time i t was s t i l l difficult to accept the idea that van der Waal's forces could be significant at distances of the order of colloidal dimensions. It was in fact not new, having been suggested by Willstatter in the early thirties and worked out in detail for spherical particles by Hamaker in 1936-37. In actual fact i t now turns out that the inverse sixth power at traction of atoms is not additive, so the Hamaker approach is now being replaced by the more complex but more nearly accurate Lifshitz treatment. The proximate cause of our enlightenment was the Ph.D. thesis of Sparnaay working with Overbeek, which purported to give a direct experimental measurement of the magnitude of long range van der Waal's forces between macroscopic objects; two glass plates in a vacuum. The value of the Hamaker constant obtained, while a l i t t l e too large, was of the right order of magnitude to f i t with the Verwey-Overbeek theory. We found the work of Sparnaay and Overbeek exciting - so much so that we wanted to make a pilgrimage to Overbeek's laboratory to see with our own eyes, and perhaps to repeat and extend the measure ments. It became feasible for us to go to Utrecht in 1953-54, thanks to Guggenheim (MJV) and Fulbright (RDV) Fellowships. In Sparnaay's apparatus one glass plate was held on a three point support, movable for levelling purposes by air pressure, with a very fine micrometer screw to raise i t toward a second plate suspended by a spring. The top plate was attached to a silvered disc which formed a part of a condenser, the capacity of which depended on the distance through which the spring was pulled down by the lower plate, thus permitting calculation of the effective force. The distance between the plates was deter mined from the interference colors.


12

COLLOIDAL DISPERSIONS


The three fold enemies of the measurement were vibrations, dust, and stray electrification. Vibrations were minimized by mounting the apparatus on a tombstone on springs in the base ment of the building, since the laboratory was only three blocks from the central railroad station. Dust was minimized by meti culous cleanliness and careful polishing. There was always some vibration. If i t ceased abruptly one could be sure the plates had come to rest with a dust particle between them, ne cessitating that the set-up be dismantled, the plates cleaned once more, and the experiment started over again. An attempt not always successful - to avoid stray electrification was made by including a radioactive mineral in the vacuum chamber to ionize the residual air so as to make i t conducting, thus permit ting dissipation of static charges. Ten months proved t Sparnaay's apparatus and obtain more accurate results worth publishing. The most that we accomplished experimentally was to convince ourselves that the attraction between the plates was real, and really was due to van der Waal's forces. Probably the greatest effect the year in Utrecht had on us, through the close collaboration and friendship of Professor Overbeek, was to redirect our thinking towards the importance in colloidal sys tems of the forces operative between colloidal particles on close approach or contact, and the effect of the size and shape of the particles on the properties of the system. So far, this backward look over the growth of colloid chemistry has been rather narrowly confined to our own interest. What of the rest of the science? In 1954 alone there were some 715 papers dealing with colloid and surface chemistry, even ex cluding such prolific branchés as adsorption of gases, high poly mers, proteins, chromatography, ion exchange, and membrane phenomena. These 715 purported to be fundamental work and did not include a very extensive trade literature. So how does one pick out from these the more significant contributions? One way is to let the contemporary investigators do i t for you - by examining to see to whom they gave various awards and for what kind of work. Colloid chemists who have been awarded the Nobel Prize in clude Zsigmondy, Svedberg for the ultracentrifuge, Tiselius for his beautiful work on separation and characterization of proteins by electrophoresis, Langmuir for his work on films giving the f i r s t definitive measurement of molecular dimensions, and Debye. But Debye was recognized primarily for his work in a different f i e l d . Further insight into what was regarded as being impor tant can be gained by looking to see to whom we gave our own Ken dall Award, a task facilitated by the initiative of Karol J . Mysels, who recently arranged for the publication of the Award addresses (5) of the last twenty years. A paragraph quoted from its Introduction says i t a l l . "The variety of topics covered and techniques discussed is


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enormous. Even when nominally the subject is the same, such as the contact angle, the earlier approach of Bartell has l i t t l e in common with that of Zisman and, s t i l l later, Zettlemoyer touches upon i t again from a different point of view. The solid surface has also been treated by Emmett, Brunauer, Halsey and Zettlemoyer, but with emphasis on various aspects of its interaction with gases, its function in catalysis, the importance of proper area determinations, the mutual interference of adsorbed molecules, and the characteristics of hydrophobic behavior. The liquid-gas surfaces are the subjects of Mysels and of Hansen, but one is concerned with thin films and the other with ripples on bulk liquid. Aqueous dispersions are studied by Matijevic and serve him as a tool to solve problems of inorganic chemistry. The f i r s t monodisperse aerosols were discussed by LaMer, and Kerker reported recently on advances made by light scattering and other modern techniques in thei tering in general, and especially of x-rays, was the subject of Debye. Williams discussed the role of the ultracentrifuge and, later, Vinograd its improvement and uses in studying DNA. Mus cular contraction was the concern of H i l l , and biological prob lems also were very much on Scatchard's mind. Holmes ranges, in his review, from vitamin A to the contraction of the s i l i c a gels which others use as model surfaces. Ferry and Mason both discuss rheology, one from the macroscopic point of view, the variety of personalities, areas of interests, approaches and points of view, as well as the gradual evolution of the whole f i e l d , are manifest from the printed page." As has been well said in the preface to the book, during the last twenty years "we see the last vestiges of art leave the study of colloid and surface chemistry, the technological matur ity is seen; mathematics, physics and the biological sciences be come home ground for the colloid and surface chemists and their territories now extend to the whole world of science". It is a far cry from the opinion in the last century, quoted in J . Chem. Educ. 46, 690 (1969) from A. Conte., "Philosophie Positive" (1830): "Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly i r r a tional and contrary to the spirit of chemistry. If mathematical analysis should ever hold a prominent place in chemistry - an aberration which is happily almost impossible - i t would occa sion a rapid and widespread degeneration of that science". During the last ten or fifteen years my own work (RDV) has involved three major interests; stability of oil-in-water emul sions, stability of non-aqueous dispersions, and the interaction between DNA and magnesium ions. Fundamental work on emulsions became possible as a fringe benefit resulting from pressure on the Northern Regional Research Laboratory of the Department of Agriculture to do something to help the midwestern growers of flax when their market for linseed oil was threatened by the suc cessful utilization of synthetic resin emulsions in paints for


14



exterior use. Limited funds were made available for university research in addition to a large coordinated industrial program to solve the practical problems. The f i r s t difficulty to be overcome was the lack of a re liable, rapid method for measuring stability quantitatively. Groot in our laboratory, Rehfeld at the Shell Development Com pany, and Garrett at the Upjohn Company, independently hit on use of the rate of separation and amount of o i l separated from an emulsion in an ultracentrifuge for this purpose. This method, however, while useful for studying the factors affecting coale scence, is limited in its application to real emulsions, in which both flocculation and coalescence may be important, by the fact that in the ultracentrifuge the emulsion is already floccu lated when measurements begin, and is in a physical state resemb ling a foam rather than an emulsion. The basic question whether the rate-determining step in demulsification leading to coalescence and separation of the oil phase, involves the rheological properties of the adsorbed film of emulsifier, or the rate of drainage of the aqueous phase from the lamellae separa ting the deformed oil "drops". Experiments too extensive to sum marize in a brief report were carried out with the assistance of an able group of collaborators (Robert Groot, Kashmiri Mittal, Ulhee Hahn, Milagros Acevedo, Miodrag Maletic) determining the dependence of the rate of separation of oil on the nature of the oil and the emulsifier, the concentration of the emulsifier, the temperature, the magnitude of the centrifugal f i e l d , and the con centration of added electrolyte present, augmented by determina tion of adsorption isotherms and surface area by adsorption and by drop size distribution. It was soon shown that the s t a b i l i zing action of the emulsifier reached its maximum value when the equilibrium concentration of surfactant in the aqueous phase reached the critical micelle concentration, and a good correla tion was found between stability and fraction of the total o i l water interface covered by adsorbed emulsifier. Some of our most recent findings in this study are being reported in other papers in this symposium. Another group (Paul Hiemenz, Pranab Bagchi, Victor Dunn) worked in turn on the problem of attempting to develop an experi mental method capable of testing the various theories which had been proposed to account for the stability of non-aqueous col loidal suspensions. The unhindered action of van der Waal's forces, as in aqueous systems, would soon coagulate them, and in these cases the stabilizing effect of interpenetrating elec trical double layers is absent. Possible mechanisms suggested i n i t i a l l y to account for the stability of such systems involved, besides the possibility of small residual charges, the decrease in entropy which would result from decrease in the number of con figurations available on overlap of the adsorbed layer of sta bilizing molecules surrounding each particle. Later i t was re-


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cognized that there might also be an enthalpic contribution to the stability because of the increased concentration of s t a b i l i zer molecules in the overlap region. Both theory and experiment are d i f f i c u l t in this problem, since i t is necessary to make many assumptions in order to make theoretical calculations, and measurements attempting to characterize aggregates as contrasted with ultimate particles tend to give results varying with the experimental method. Moreover, in the case of "particles" in the micron size range mechanical action rather than Brownian motion is likely to be the dominant force causing collisions. The method we employed essentially is that of determining the value of the stability ratio, defined as the ratio of the rate of flocculation of the unprotected sol to that of the sta bilized system. Rates of flocculation were obtained by an opti cal method, and the result the Smoluchowski equatio ing a theoretical calculation of the balance between a van der Waal's attraction and a repulsion arising from the decrease in entropy occurring on overlap of the adsorbed layers of stabilizer molecules. Obviously there are d i f f i c u l t problems as to the o r i entation of the adsorbed molecules, the thickness of the adsorbed layer, etc., in addition to the fact that the energy barrier to flocculation is a small term determined as the difference between the very large and somewhat poorly known attraction and repul sion energies. Our conclusion was that actual flocculation be havior could not be predicted by the entropie (or steric hind rance) theory alone, although kinetics of flocculation data could be used to calculate backwards to give a reasonable value for the van der Waal's constant. Use of polymeric stabilizers in these experiments greatly extend their versatility, since i t is then possible to utilize the information available from the ex tensive work on polymer statistics and change of configuration with change of solvent. As is treated in one of the other pa pers in this symposium, however, there are here too d i f f i c u l t experimental problems of attainment of equilibrium and of relat ing the conformation of the adsorbed polymer to the thickness of the adsorbed layer. Meanwhile Bheema Vijayendran, Basappa Chincholi, and Anton Havlik, successively, were studying the effect on DNA molecules of replacement of sodium ions by magnesium ions. Our earlier work on this problem involved use of the ultracentrifuge by the density gradient method of Meselson, Stahl and Vinograd to de termine the buoyant density of magnesium DNA, and by the sedi mentation velocity method to determine its sedimentation coeffi cient, related to its molecular weight. The results obtained indicated a qualitative change in behavior commencing at a water activity of about 0.90, which was tentatively ascribed to a change in the conformation of the molecule resulting from par tial dehydration. Independent support for this hypothesis is being sought from light scattering measurements on the same DNA


16



in magnesium salt solutions, since such a change in shape might be expected to give rise to a measurable change in the radius of gyration obtainable from a Zinm plot of the scattering data. But what of the future? What are now regarded as being the most important topics for investigation in colloid and surface chemistry? Any even remotely complete listing would be impos sibly long for this review. It seems best merely to summarize the conclusions of three authoritative statements which have appeared recently. Professor Overbeek, reporting for a Science Research Council panel of The Chemical Society, recommended the following areas of study (6). The effects of wetting and adsorption on the energy of sur face layers on solids. Study of adsorbed layers by spectroscopic and optical methods. Thermodynamics of colloids layer theory and theory of interfacial layers, particularly of steric stabilizers. Direct measurement of forces between surfaces and the effect of adsorbed layers on such forces. Effects of hydrodynamic factors on stability, stability of emulsions and foams, and the effect of polymeric stabilizers. Further development of optical and spectroscopic techniques for studying colloidal properties; determination of rheological properties of model systems. Catalysis of chemical or biochemical reactions by colloids. Further studies of liquid crystals and association colloids. Chemical formation and stabilization of aerosols. Study of membranes, and cell and particle adhesion. There has just appeared (7) Volume 1 of Colloid Science in the new series of Specialist Periodical Reports of the Chemical Society. Chapters by specialists reviewing recent important literature on the following topics are included: Adsorption at the gas-solid interface; Adsorption at the solid-liquid inter face, non-aqueous systems; Polymer adsorption at the s o l i d - l i quid interface; Capillarity and porous materials, equilibrium properties; Particulate dispersions; Emulsions; Non-aqueous sys tems. Additional volumes are contemplated to cover most of the important areas of colloid science. Even in this country colloid science is once again becoming a more fashionable field of research, partly because of its in volvement in numerous biological processes, and partly because of the energy c r i s i s . Thus i t has recently been spotlighted (8) by the National Science Foundation as one of the basic research areas that will receive special attention in the energy research and development program. Here attention has been directed p r i marily to research on both homogeneous and heterogeneous nucleation, evaporation and growth rates of aerosols, coagulation kinetics, chemical reaction in aerosols, the preparation and stability of colloidal dispersions, emulsions, and surfactants.


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With all this on the immediate agenda i t is surely an excit ing time to be involved in colloid research. For ourselves, we would like to discover the Fountain of Youth, and start all over again. Literature Cited 1. 2. 3. 4. 5. 6. 7.

8.

Ross, S . , "Chemistry and Physics of Interfaces", pp. vii-viii, American Chemical Society, Washington, D. C., 1965. Hansen, R. S . , and Smolders, C. Α., J. Chem. Educ. (1962) 39, 167. Mysels, K. J., J . Chem. Educ. (1960), 37, 355. Hauser, Ε. Α., "Colloidal Phenomena", pp. 217-226, McGraw -Hill Book Company, New York, 1939. Mysels, K. J., Ed., Chemistry - The Kendal Society, Washington, D. C., 1973. Overbeek, J. Th. G., Chemistry in Britain (1972), 8, 370. Everett, D. H., Ash, S. G . , Haynes, J. M., Ottewill, R. H., Sing, K. S. W., and Vincent, B., "Specialist Periodical Re ports. Colloid Science, Volume 1", The Chemical Society, London, 1973. Anon., Chem. and Eng. News (1974), 52, (30), 14.


2 Macrocluster Gas-Liquid and Biliquid Foams and Their Biological Significance FELIX SEBBA Department of Chemistry, University of the Witwatersrand, Johannesburg, South Africa

Introduction In a c o n s i d e r a t i o n of s t a t e s of matter such as crystals or liquids, i t i s usual t o assume t h a t they are composed of u n i t s such as i o n s , atoms or molecules and to i n t e r p r e t the bulk property as a c o - o p e r a t i v e summation of the p r o p e r t i e s of the individual units. However, there are a number of p h y s i c a l systems which could be b e t t e r understood by c o n s i d e r i n g them as c o n s i s t i n g o f u n i t s which are themselves s t a b l e o r metastable aggregates of s m a l l e r units, the m o l e c u l e s , and i t i s suggested t h a t such systems should be named " m a c r o c l u s t e r s y s t e m s " . ( U n f o r t u n a t e l y , the term "cluster" which would be s u i t a b l e has a l r e a d y been a p p r o p r i a t e d by statistical mechanics w i t h a very d i f f e r e n t meaning.) Examples of macrocluster systems are gas -foams, biliquid foams, scums, flocs, concentrated e m u l s i o n s , living t i s s u e , cell cytoplasm and probably biomembranes. A m a c r o c l u s t e r system i s d e f i n e d as a heterogeneous a s s o c i a t i o n composed o f u n i t s , each capable o f independent e x i s t encse but organised in such a way that they c o n s t i t u t e a more advanced system which has p h y s i c a l p r o p e r t i e s a d d i t i o n a l to the p r o p e r t i e s of the i n d i v i d u a l u n i t s . Foams provide a u s e f u l example of a macrocluster system. It w i l l be shown t h a t gas foams c o n s i s t of u n i t s which are bubbles of gas encapsulated in a t h i n f i l m of surfactant s o l u t i o n . However, i n d i v i d u a l gas bubbles are not foams, and do not e x h i b i t the s e m i - s o l i d behaviour of some foams nor t h e i r f l o w p r o p e r t i e s . It i s because these bubbles are held together by t h i n aqueous f i l m s , the adhesion being a consequence of such f i l m s , t h a t the advanced system, the foam i s produced which has p r o p e r t i e s which are more than those of the i n d i v i d u a l u n i t s . As d e f i n e d i n t h i s way, many composite m a t e r i a l s would q u a l i f y as m a c r o c l u s t e r systems, as would those a l l o y s whose p r o p e r t i e s depend upon interphase d e p o s i t s even i f these be metastable s t a t e s . On the other hand, e m u l s i o n s , w i t h the e x c e p t i o n , perhaps, of very concentrated o i l - i n - w a t e r e m u l s i o n s , 18


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are not macrocluster systems. T h i s Is because the p h y s i c a l p r o p e r t i e s of a d i l u t e emulsion are e s s e n t i a l l y those of the continuous aqueous phase. Gas Foams Many a u t h o r i t i e s compare gas foams to emulsions c l a i m i n g that the only d i f f e r e n c e i s that the d i s p e r s e l i q u i d phase in an emulsion i s replaced by a gas. T h i s i s i n c o r r e c t and i t w i l l be shown that the s t r u c t u r e of a foam must be very d i f f e r e n t from that of an e m u l s i o n . However, i t i s p o s s i b l e to make emulsions of a gas in w a t e r , but f a l l i n g i n t o the same t r a p , t h i s author m i s t a k i n g l y c a l l e d them "microfoams" 0 ) · B u t , apart from the common f a c t o r t h a t gas i s the dispersed phase, t h i s system has no foam p r o p e r t i e s and to avoi in f u t u r e , t h i s system b Another misconception i s that a foam c o n s i s t s of gas separated o n l y by a continuous aqueous s k e l e t o n , the l a m e l l a , (Figure 1 ) . This naive model cannot e x p l a i n some simple f a c t s of foam behaviour as w i l l be d i s c u s s e d . It must be recognised that no matter what process i s used to generate a gas foam, e s s e n t i a l requirements must be f u l f i l l e d . F i r s t l y , there must be a s u r f a c t a n t d i s s o l v e d in the l i q u i d , and secondly the gas has to generate a surface w i t h i n the l i q u i d and then break through a second s u r f a c e . Consider the case of a foam generated by passing a i r through a narrow o r i f i c e i n t o a d i l u t e aqueous s o l u t i o n of the foaming agent. The f i r s t step i s the formation of a g a s - f i l l e d hole in the l i q u i d . In the absence of a foaming agent, any such holes which c o l l i d e d , w h i l e s t i l l under the surface of the l i q u i d , would immediately c o a l e s c e . T h i s i s because the l a r g e r hole thus formed would expose a s m a l l e r i n t e r f a c i a l area than the sum of the two i n t e r f a c i a l areas of the two holes from which i t was formed. However, in the presence of a s u r f a c t a n t , coalescence i s l e s s probable because of the energy b a r r i e r produced by the o r i e n t a t e d molecules at the i n t e r f a c e and consequent double l a y e r . The r e p u l s i o n of the two double l a y e r s i s the p r i n c i p a l component of the s o - c a l l e d " d i s j o i n i n g pressure which r e s i s t s t h i n n i n g of the aqueous f i l m jammed between two col 1 i d i n g h o l e s . Under the i n f l u e n c e of g r a v i t y , the g a s - f i l l e d hole r i s e s to the s u r f a c e of the s o l u t i o n . Here i t meets an o b s t a c l e to i t s p r o g r e s s , because i t has to break through the s u r f a c e . If the hole i s very small so that i t does not have enough k i n e t i c energy to penetrate the s u r f a c e , i t may be r e f l e c t e d back into the i n t e r i o r of the l i q u i d . U s u a l l y , however, i t i s l a r g e enough to have s u f f i c i e n t energy to penetrate the s u r f a c e . This i s not a simple break-through because the s u r f a c e i s a l r e a d y covered w i t h a l i q u i d expanded monolayer of the foaming agent accompanied by i t s own double l a y e r . T h e r e f o r e , r e p u l s i v e f o r c e s w i l l operate preventing the gas from d i s r u p t i n g the s u r f a c e c o m p l e t e l y . If 11


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It d i d s o , the gas would simply d i s p e r s e i n t o the outer atmos phere and a foam would not be formed. However, the buoyancy of the g a s - f i l l e d hole i s enough to form a " b l i s t e r on the s u r f a c e , covered by a t h i n aqueous f i l m which owes i t s s t a b i l i t y to the d i s j o i n i n g f o r c e s induced by the p r o x i m i t y o f the charged heads o f the s u r f a c t a n t m o l e c u l e s , (Figure 2). The net r e s u l t i s that the gas encapsulated by the t h i n aqueous s h e l l , f l o a t s on the s u r f a c e very s l i g h t l y immersed and i t i s p r o p e r , a t t h i s s t a g e , to r e f e r to i t as a bubble which i s a volume of gas encapsulated in a t h i n f i l m sandwiched between two expanded monolayer s u r f a c e s , (Figure 3). Should the bubble be l a r g e enough, and there be enough momentum, i t could leave the s u r f a c e as a f r e e f l o a t i n g bubble of the kind painted by John M i l l a i s , i . e . , a sphere o f gas encapsulated in a s h e l l o f s u r f a c t a n t s o l u t i o n w i t h a monolayer of s u r f a c t a n t absorbed at both inner and outer s u r f a c e s of the s h e l l . As the bubble f l o a t s on th whether the bubble i s complete. It would appear to be s o , because i f a f r e e bubble from a i r i s introduced to the s u r f a c e o f a s u r f a c t a n t s o l u t i o n , i t a d j u s t s i t s e l f to f l o a t on the s u r f a c e seemingly in p r e c i s e l y the same way as a bubble generated d i r e c t l y in the bulk o f the l i q u i d . Thus the bubble s i t s in a hollow in the s u b s t r a t e l i q u i d as shown in Figure 3. When two such f l o a t i n g bubbles get c l o s e enough, they move towards each other w i t h i n c r e a s i n g v e l o c i t y u n t i l they almost t o u c h , being separated s t i l l by a very t h i n aqueous f i l m . The e x i s t e n c e o f t h i s f i l m , which i s c r i t i c a l to the behaviour of foams of a l l t y p e s , i s dependent upon the d i s j o i n i n g f o r c e s which must be overcome before the f i l m can be d i s r u p t e d . The pressure d r i v i n g the bubbles together i s o f t e n r e f e r r e d to as the Laplace c a p i l l a r y pressure which e x i s t s because o f the tendency f o r any l i q u i d s u r f a c e to expose the minimum s u r f a c e a r e a . T h i s i s the same pressure as that which causes two p a r t i a l l y immersed p l a t e s to adhere, whereas two completely immersed p l a t e s show no such tendency. In the previous c a s e , the pressure P»2X where γ i s the s u r f a c e t e n s i o n and d i s the d i s t a n c e between the p l a t e s . In the case of the bubbles which are not s p h e r e s , Ρ has not been d e r i v e d , but presumably w i l l s t i l l vary i n v e r s e l y w i t h d i s t a n c e a p a r t . The f i n a l p o s i t i o n of the b u b b l e s , t h e r e f o r e , i s determined by the balance of three f o r c e s , the Laplace f o r c e s which increase as the bubbles approach, the long range Vaif der Waal s f o r c e s which tend to t h i n the i n t e r v e n i n g f i l m and the double l a y e r r e p u l s i v e f o r c e s which r e s i s t t h e s e . The r e s u l t a n t of the l a s t two produces the d i s j o i n i n g f o r c e which prevents the f i l m t h i n n i n g to disappearance. The f a c t t h a t Laplace pressure e x i s t between bubbles on water leads to an important but unexpected c o n c l u s i o n . Because they owe t h e i r o r i g i n to the tendency of l i q u i d s to minimise t h e i r s u r f a c e a r e a , there must be an i n t e r f a c e exposed, such as a meniscus. On the other hand, the l i q u i d must adhere to another phase, otherwise i t would simply r o l l up i n t o a sphere. When 1 1


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GAS

ΔΞ=/

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GAS

GAS

Figure 1. Conventional representation of foams. Ρ represents plateau borders. Hatched areas rep resent thin aqueousfilmof surfactant with mono

WATER Figure 3. Bubblefloatingon surface. è represents surfactant molecules.


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two p l a t e s are completely immersed in a l i q u i d , there is no meniscus and thus no Laplace p r e s s u r e . Immediately, the p l a t e s become p a r t l y immersed, a l i q u i d - a i r i n t e r f a c e e x i s t s and the tendency to minimise t h i s i n t e r f a c e p u l l s the p l a t e s t o g e t h e r . However, the problem of a t t r a c t i o n between two f l o a t i n g bubbles i s not as s i m p l e . The f a c t that they do a t t r a c t one another i s obvious to anyone who has watched the bubbles on h i s cup of t e a . The water meniscus cannot j u s t adhere to the g a s , so i t must adhere to the f i l m e n c a p s u l a t i n g the bubble. T h i s f i l m , c l e a r l y , must have d i f f e r e n t i n t e r m o l e c u l a r a t t r a c t i o n s o p e r a t i n g w i t h i n i t than does the bulk water otherwise i t would simply merge w i t h the bulk and the bubble would b u r s t . It f o l l o w s , t h e n , that e f f e c t i v e l y the e n c a p s u l a t i n g f i l m behaves as though i t were a separate phase from bulk water. Though t h i s might seem at v a r i a n c e w i t h the usual d e f i n i t i o e x i s t s that the molecule d i f f e r e n t p r o p e r t i e s from bulk water. T h i s has been explained as being due to a more i c e - l i k e s t r u c t u r e because of the hydrogen bonding induced by the i n t e r f a c e , and f u r t h e r evidence i s provided by the f a c t that the surface of a s u r f a c t a n t s o l u t i o n has a very much higher v i s c o s i t y than the bulk phase. As water in a t h i n f i l m would have two i n t e r f a c e s , t h i s e f f e c t should be enhanced. A surface boundary implies an abrupt change of i n t e r molecular a t t r a c t i v e f o r c e s , and i t might at f i r s t seem strange that t h i s could r e s i s t the normal k i n e t i c energy tending to mix the molecules. However, once t h i s p o s s i b i l i t y is accepted many phenomena to be described l a t e r become e x p l i c a b l e , and there are two a d d i t i o n a l experimental f a c t s , h i t h e r t o unreported which s u b s t a n t i a t e the view that s u r f a c e phases have a r e a l i t y . These are the e x i s t e n c e of bridges between microgas emulsion bubbles and the e x i s t e n c e of monolayer membranes. To avoid d i s c o n t i n u i t y these w i l l be discussed as two subsections l a t e r . For two equal s o l i d spheres of radius r, a n d , w i t h a drop of water between, the adhesive f o r c e i s 2πτγ where γ i s the s u r f a c e tension of the i n t e r v e n i n g l i q u i d , but t h i s formula does not s a t i s f y the c o n d i t i o n s of the f l o a t i n g bubbles as they are f l a t t e n e d underneath and the undersurface i s completely surrounded by a l i q u i d . A l s o the spheres are not r i g i d , but deformable gas. However, as an approximation, i t can be assumed that when they get c l o s e enough t o g e t h e r , the approaching surfaces w i l l be deformed enough to become p a r a l l e l s i d e s i . e . s i m i l a r to two wet p l a t e s , p a r t l y immersed, so the adhesional pressure w i l l be γ / d where d i s the d i s t a n c e a p a r t . T h i s w i l l be r e s i s t e d by the d i s j o i n i n g f o r c e s . If the bubbles are very s m a l l , the i n t e r n a l pressure in the bubbles which i s i n v e r s e l y p r o p o r t i o n a l to t h e i r r a d i i , w i l l become g r e a t e r , so d i s t o r t i o n w i l l be l e s s than in the case of the l a r g e r bubbles. The behaviour of monolayers of such bubbles is e a s i l y seen on a blackened Langmuir t r o u g h , by blowing a i r through a small j e t under the s u r f a c e . The sheet of bubbles i s almost mono-


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d i s p e r s e . Though they adhere l o o s e l y , such f l o a t i n g bubbles do not yet c o n s t i t u t e a foam. In order to convert them into a t y p i c a l polyederschaum, i t i s necessary to crowd the bubbles, and t h i s can r e a d i l y be achieved by compressing them between b a r r i e r s , when the bubbles w i l l climb over one another forming a m u l t i - l a y e r o f bubbles which soon d i s t o r t s to a foam. More u s u a l l y , a foam i s formed because the v e s s e l in which the bubbles are being formed has a l i m i t e d a r e a . A foam w i l l not s t a r t to form u n t i l the s u r f a c e i s completely covered by a l a y e r o f bubbles. As the bubbles are u n s t a b l e , the average l i f e - t i m e depending i n t e r a l i a on the nature and c o n c e n t r a t i o n of s u r f a c t a n t s and other s o l u t e s in the w a t e r , one of the p r e r e q u i s i t e s f o r the production of a foam i s that the r a t e of generation of bubbles must be g r e a t e r than the rate of d e s t r u c t i o n of bubbles moving from the point of generation to the w a l l s o from the packing of a numbe space causes the spheres to d i s t o r t to polyhedra and the areas of c l o s e s t approach of two polyhedra are p l a n a r . The regions o f l i q u i d confined by these planar i n t e r f a c e s c o n s t i t u t e the lamellae. It should be noted that t h i s model o f independent bubbles forming a macrocluster system foam s t i l l r e t a i n s the Plateau borders as regions of low pressure because of the curvature. If the b a r r i e r s which created a foam on the trough by compression are then moved a p a r t , the foam breaks down, the bubbles s l i p back onto the water s u r f a c e and the monolayer of bubbles i s r e - e s t a b l i s h e d . In other words, there i s complete r e v e r s i b i l i t y between s p h e r i c a l bubbles and the c e l l s in a foam. It i s d i f f i c u l t to v i s u a l i s e t h i s happening i f the l a m e l l a were a s i n g l e uniform f i l m . While i t i s c o n c e i v a b l e that the outer s u r f a c e of the two approaching bubbles could be destroyed under adhesional pressure and thus produce the homogeneous l a m e l l a d e p i c t e d in t e x t b o o k s , i t i s not easy to see t h a t the reverse process could occur spontaneously. However, there i s no such d i f f i c u l t y i f the e n c a p s u l a t i n g f i l m round each bubble remains unbroken, but t h i s does mean that the l a m e l l a i s complex and c o n s i s t s of two bubble f i l m s separated by a t h i r d t h i n aqueous f i l m , (Figure k). Further evidence f o r t h i s model of a foam i s provided by the f o l l o w i n g experiment. If a v i s c o s i t y i n c r e a s i n g substance such as POLYOX i s added to the s u r f a c t a n t s o l u t i o n , the foam s t a b i l i t y i s s u f f i c i e n t l y increased f o r i t to become p o s s i b l e to remove i n d i v i d u a l bubbles from the foam w i t h a s p a t u l a , f l o a t such bubbles on a c l e a n s u r f a c e o f the s o l u t i o n , and then r e p l a c e them on the foam. A bubble r e - i n s e r t e d i n t o i t s o r i g i n a l s i t e resumes i t s o r i g i n a l shape. If a small amount of microgas emulsion i s inserted beneath a foam, the small gas bubbles w i l l r i s e through the foam bed, and i f observed i t w i l l be seen that they never penetrate a c e l l s u r f a c e d i r e c t l y , but always r i s e through the l a m e l l a e in s p i t e o f the f a c t that t h i s o f t e n means


24

C O L L O I D A L DISPERSIONS A N D M I C E L L A R BEHAVIOR

a longer path or along paths that are o n l y i n c l i n e d s l i g h t l y from the h o r i z o n t a l . The i m p l i c a t i o n i s that l e s s work i s needed to separate the bubbles than break c e l l w a l l s . When a foam whose foaming agent i s an a n i o n i c s u r f a c t a n t i s contacted w i t h one produced u s i n g a cat i o n i c s u r f a c t a n t , the foams mutually d e s t r o y each other (2). Though t h i s i s d i f f i c u l t to e x p l a i n on the conventional model of the s i n g l e l a m e l l a , i t i s easy to see how two bubbles, because of the o p p o s i t e l y charged s h e l l s , w i l l a t t r a c t one a n o t h e r , i . e . , w i l l r e i n f o r c e the Laplace pressures instead of r e s i s t i n g them as in a normal foam. F i n a l l y , there i s a well e s t a b l i s h e d technique f o r c o n c e n t r a t i n g ions known as foam f r a c t i o n a t i o n . This is i n e x p l i c a b l e on the c l a s s i c a l model o f a foam but can be e a s i l y under stood on the macrocluster model. The technique i s simply a p a r t i t i o n chromatography round the b u b b l e s , and th between the bubbles. Bridges Between Bubbles. Figure 5 i s a microphotograph of a microgas emulsions ( U , which i s not a macrocluster systems. However, the photograph i s o f an emulsion which i s s u f f i c i e n t l y concentrated in gas bubbles that they a c t u a l l y touch and i t w i l l be observed that whenever two bubbles meet there i s seemingly a bridge between them. They are always there no matter from what point they are i l l u m i n a t e d and a r e , t h e r e f o r e , not o p t i c a l i l l u s i o n s . The s t r u c t u r e has the same appearance as the meniscus that would be seen i f two wettable g l a s s spheres had a drop of water between them. The microgas emulsion c o n s i s t s of g a s - f i l l e d h o l e s , w i t h the s u r f a c t a n t monolayer at the i n t e r f a c e between the hole and the aqueous phase. However, i f t h i s were s o , there would not be the c o n d i t i o n s f o r forming the meniscus. In some c a s e s , the bubbles are seen to be d i s t o r t e d which means that there must be an adhesive f o r c e strong enough to achieve t h i s . This adhesive f o r c e can only be the r e s u l t of Laplace p r e s s u r e s , and such pressures can o n l y e x i s t i f there i s an i n t e r f a c e between the surface phase and the bulk water phase, and the meniscus i s formed by the s u r f a c e phase. By analogy w i t h two equal spheres of r a d i u s , γ , separated by a drop o f l i q u i d , where the adhesive f o r c e i s 2irry, the adhesive f o r c e w i l l be 2·πτγ. where r i s radius of bubble and yj the i n t e r f a c i a l t e n s i o n between s u r f a c e water and bulk water. Since i t i s the s u r f a c e water which i s producing the meniscus, the a t t r a c t i o n between i t s molecules must be g r e a t e r than t h a t between bulk water m o l e c u l e s . This i s c o n s i s t e n t w i t h the suggestion that the s u r f a c e phase i s more hydrogen-bonded than bulk water. The i n t e r f a c i a l t e n s i o n between ice and water i s of the order of 25 dynes c m " ( 3 ) · The i n t e r f a c i a l t e n s i o n between s u r f a c e phase and bulk phase must, t h e r e f o r e , l i e somewhere between 0 and 25 dynes c m " ' . As the adhesive f o r c e i s p r o p o r t i o n a l to the radius o f the bubble d i s t o r t i o n of the bubbles i s o n l y observed in the l a r g e r bubbles. 1


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The interface between shell film and continuous film is effectivily a bimolecular film layer e.g.

CONTINUOUS F . L M \

Figure 5.

F

|

G

M

F

E

4

F

m

m

U

m

Microgas emulsion


d

U

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It should be noted that there i s a d i s t i n c t d i f f e r e n c e between f l o a t i n g bubbles and microgas emulsion bubbles. This is because the former are encapsulated in a f i l m bounded on both faces by monolayer and which i s tenacious and e l a s t i c whereas the l a t t e r i s not. It i s , t h e r e f o r e , c o n c e i v a b l e that in the case of the microgas emulsion the meniscus w i l l draw the bubble s u r f a c e w i t h i t thus forming a tube between the two gas bubbles. When two bubbles of a d i f f e r e n t s i z e t o u c h , as the pressure in the bubble i s i n v e r s e l y p r o p o r t i o n a l to the r a d i u s , the l a r g e r bubble grows a t the expense of the s m a l l e r one. This growth can a c t u a l l y be observed under the microscope. However, the growth i s not by a coalescence mechanism i . e . the w a l l s between the bubbles do not c o l l a p s e . The t r a n s f e r of gas does not proceed as might be expected u n t i l the s m a l l e r bubble v a n i s h e s , but i t seems to stop a t a minimum s i z e s l o w l y , i f at a l l . The consequenc are observed to become coated by a l a r g e number o f t i n y b u b b l e s , which because of t h e i r s i z e , must be under higher pressure and, t h e r e f o r e , r e l a t i v e l y r i g i d . T h i s phenomenon might be caused by the connecting tube being pinched o f f below a c e r t a i n s i z e of bubble. This i s an unusual example o f a two u n i t macrocluster system. Monolayer Membranes. The s u r f a c e of a s u r f a c t a n t s o l u t i o n has s u f f i c i e n t l a t e r a l cohesion to form the b a s i s o f membranes which can be several centimetres a c r o s s , and which are remark a b l y p e r s i s t e n t . To make such a membrane a s u r f a c t a n t s o l u t i o n has to be placed upon an i d e n t i c a l s o l u t i o n without d i s t u r b i n g the s u r f a c e . Microgas emulsions provide one way of a c h i e v i n g t h i s , because they are much l e s s dense than w a t e r . If a microgas emulsion generated from a s o l u t i o n such a s , f o r example, 5 x l O ' ^ M sodium dodecyl benzene sulphonate c o n t a i n i n g 1 χ 10"3M sodium sulphate is g e n t l y placed upon an i d e n t i c a l s o l u t i o n , c o n t a i n i n g a small q u a n t i t y of i n d i c a t o r d y e , such as bromocresol b l u e , in a g l a s s c y l i n d e r , i t w i l l f l o a t upon i t . The gas s l o w l y r i s e s and escapes, u n t i l the upper s o l u t i o n becomes f r e e of gas. However, i t does not spontaneously mix w i t h the lower s o l u t i o n , as can be seen by the e x i s t e n c e of a boundary between the dyed lower s o l u t i o n and c o l o u r l e s s upper s o l u t i o n . What i s remarkable i s the r e s i s t a n c e o f the boundary to d i s t u r b a n c e such as t i l t i n g . One such membrane l a s t e d three weeks and r e s i s t e d t r a n s p o r t a t i o n from one room to another. The membranes are s l i g h t l y more e a s i l y made i f the lower s o l u t i o n i s made f r a c t i o n a l l y more dense than the upper, by i n c o r p o r a t i n g s l i g h t l y more s a l t . The s a l t appears to s t a b i l i s e the membrane. The membrane i s e l a s t i c and i f a g l a s s rod i s made to d i s r u p t the membrane to the depth of about 1 mm., on removal of the rod the membrane returns to i t s o r i g i n a l p o s i t i o n . As i n d i c a t o r dyes are themselves s u r f a c e a c t i v e , membranes have been made in which one of the s o l u t i o n s was coloured w i t h iodine and s t i l l the iodine did not d i f f u s e through


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the membrane. Though these membranes are impermeable to d y e s , they appear to be s l o w l y permeable to hydroxyl i o n s . This can be demonstrated by adding some a l k a l i to the lower s o l u t i o n and a l i t t l e p h e n o l p h t a l e i n to the upper one, and observing the pink c o l o u r developing in the upper l a y e r . However, the p o s s i b i l i t y of creep along the w a l l s of the vessel past the membrane cannot be d i s c o u n t e d . With c a r e , sandwich l a y e r s can be made such as blue and red separated by a c o l o u r l e s s s o l u t i o n . The nature of the membranes has not yet been determined and i t is impossible to say whether they are monomolecular or b i m o l e c u l a r , nor is there any assurance that the a i r may not c o n t r i b u t e to the s t a b i l i t y . What i s c l e a r i s that they are very impermeable so cannot serve as a model f o r biomembranes. What they do confirm i s that membranes such as these r e s i s t mechanical d i s t u r b a n c e and k i n e t i c bombardment, r e i n f o r c i n those postulated f o r foam B i 1 i q u i d Foams. In the f o l l o w i n g d i s c u s s i o n s , i t becomes necessary to make a c l e a r d i s t i n c t i o n between two very d i f f e r e n t types of surface a c t i v e agent. On the one hand, there i s the water s o l u b l e s u r f a c t a n t , u s u a l l y ionised and t y p i f i e d by the a l k a l i soaps and water s o l u b l e d e t e r g e n t s . For b r e v i t y , t h i s type w i l l be r e f e r r e d to as WATSSA. On the other hand, there are the o i l s o l u b l e s u r f a c e a c t i v e m o l e c u l e s , s p a r i n g l y or i n s o l u b l e in w a t e r , such as f a t t y a c i d s , amines, long chain a l c o h o l s and cholesterol. These w i l l be r e f e r r e d to as OILSSA. Biliquid foams, which d i f f e r from gas foams, o n l y in that the holes are now f i l l e d w i t h a l i q u i d , owe t h e i r s t a b i l i t y to s i m i l a r f o r c e s to those o p e r a t i v e in gas foams. The technique f o r t h e i r production has been d e s c r i b e d by Sebba ( i ) . There are two d i s t i n c t types depending on whether the hole c o n t a i n s an aqueous s o l u t i o n or an oil. In order to make a b i l i q u i d foam where the d i s p e r s e phase i s water encapsulated in a t h i n f i l m of o i l , advantage i s taken o f the f a c t that a microgas emulsion w i l l f l o a t on an o i l , so a microgas emulsion i s placed on top of an o i l such as Nujol or k e r o s i n e . As the gas leaves the microgas e m u l s i o n , i t s d e n s i t y s l o w l y r i s e s and when i t i s j u s t above that of the o i l i t s i n k s through i t . In doing s o , i t penetrates the two i n t e r f a c e s required f o r forming a foam, f i r s t l y the upper o i l - w a t e r inter face and then on l e a v i n g the o i l , i t gets i t s e n c a p s u l a t i n g o i l film. T h i s produces a b i l i q u i d bubble, and the macrocluster system, held together by the Laplace pressures i n a t h i n water f i l m between the bubbles, c r e a t e s the b i l i q u i d foam. It i s p o s s i b l e w i t h a hypodermic s y r i n g e to i n j e c t coloured s o l u t i o n s and v a r i o u s s o l u t e s i n t o the water core o f the b u b b l e s , but there i s no d i f f u s i o n outwards, showing t h a t the o i l s h e l l c o n s t i t u t e s an impermeable b a r r i e r to d i f f u s i o n . Thus, though i t was a t f i r s t thought t h a t these foams might serve as a useful model f o r b i o l o g i c a l t i s s u e , c l e a r l y the e n c a p s u l a t i n g o i l f i l m does not have the p e r m e a b i l i t y p r o p e r t i e s of a bio-membrane.


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The general behaviour of such water encapsulated b i l i q u i d foams resembles that of gas f i l l e d foams so c l o s e l y t h a t i s reasonable to t r e a t them as s i m i l a r macrocluster systems. There i s as yet no evidence to decide whether the o i l f i l m is coated w i t h an aqueous s u r f a c e l a y e r in c o n t a c t w i t h a t h i n continuous water f i l m or not. The aqueous phase c o n t a i n s WATSSA because i t s presence i s e s s e n t i a l f o r the production o f the microgas emulsion. If a small amount of OILSSA i s added to the o i l phase, the c h a r a c t e r o f the b i l i q u i d foam changes c o m p l e t e l y . The bubbles are very much s m a l l e r and more d e l i c a t e and the a d h e s i o n a l s t r e n g t h i s reduced so t h a t the bubbles e a s i l y f l o a t away as o i l encapsulated b i l i q u i d bubbles. It was t h i s o b s e r v a t i o n which led to the suggestion that something s i m i l a r , w i t h c h o l e s t e r o l as the OILSSA, was a f a c t o r in c a n c e r , Sebba {$) . It i s not c l e a r how the OILSSA reduces the a d h e s i o n , but as the Laplace pressure i s p r o p o r t i o n a l to the i n t e r f a c i a reduce t h i s , the e x p l a n a t i o n may be the simple one of reduction of the Laplace pressures and hence the a d h e s i o n . The second type of b i l i q u i d foam i s one in which the d i s continuous phase i s o i l and the e n c a p s u l a t i n g phase i s aqueous. To produce such a foam, a microgas emulsion i s allowed to f l o a t on the o i l , j u s t as in the p r e p a r a t i o n of the f i r s t t y p e . If, however, some more o f the o i l i s poured onto the microgas e m u l s i o n , because the o i l i s heavier i t w i l l f a l l through as drops which get coated w i t h the aqueous s o l u t i o n . At the bottom of the microgas e m u l s i o n , i t passes through the second i n t e r f a c e , and completes the requirements f o r a foam. This now c o n s i s t s of o i l c e l l s in a t h i n aqueous s h e l l , the u n i t s , which have a formal resemblance to the gas f i l l e d soap b u b b l e , being separated by a t h i n f i l m of aqueous s o l u t i o n which resembles the continuous aqueous f i l m in a gas f i l l e d foam. Thus, i t i s seen that these foams are more a k i n to g a s - f i l l e d foams than i s the f i r s t type of b i 1 i q u i d foam. It i s necessary to emphasize the d i s t i n c t i o n between o i l in-water emulsions and o i l c e l l b i l i q u i d foams. In the former, there i s a s i n g l e i n t e r f a c e between the o i l drop and the c o n t i n uous aqueous medium, the e m u l s i f y i n g agent at t h i s i n t e r f a c e p r o v i d i n g an energy b a r r i e r which prevents c o a l e s c e n c e . There are none of the c o n d i t i o n s f o r a macrocluster system except in cases of very concentrated emulsions. In the b i l i q u i d foam, the o i l c e l l i s encapsulated by a t h i n aqueous f i l m producing the u n i t f o r the macrocluster system, the adhesion now being provided by the Laplace pressures a c r o s s the t h i n aqueous f i l m which c o n s t i t u t e s the continuous phase. B i l i q u i d foams of t h i s s o r t are o f t e n met w i t h in chemical and h y d r o m e t a l l u r g i c a l processes when o i l as w e l l as aqueous phases are i n v o l v e d . They have been looked upon as e m u l s i o n s , but o f t e n prove r e s i s t a n t to d e s t r u c t i o n using techniques which should destroy emulsions. It would appear that the c o r r e c t procedure would be to use techniques which are known to destroy


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foams, although t h i s i s a d m i t t e d l y an a r t and not always predictable. It w i l l be shown p r e s e n t l y that o i l encapsulated b i l i q u i d foams may provide a model f o r biomembranes and i n t r a c e l l u l a r s t r u c t u r e s may c o n s i s t o f n o n - m i s c i b l e l i q u i d s o p e r a t i n g a c c o r d i n g to the r u l e s f o r macrocluster b i l i q u i d foams. M a c r o c l u s t e r Systems and L i f e . The behaviour of lenses o f o i l spreading on water s u r f a c e s has been f u l l y d e a l t w i t h by Langmuir (6) and Harkins (7). However, t h e i r treatment concerns o n l y pure water and the behaviour o f lenses when spread on d i l u t e WATSSA s o l u t i o n s i s very d i f f e r e n t . The i n t e r a c t i o n o f two such lenses i s an example of a two-unit macrocluster system, and an understanding o f such behaviour may lead to b i o l o g i c a l i n s i g h t . A highly viscous o i not spread on water o r d i l u t some OILSSA i s incorporated i n t o the N u j o l , i t w i l l spread in a strange way. The nature of the spreading depends upon the c o n c e n t r a t i o n o f WATSSA in the s u b s t r a t e and as a l l the c o n d i t i o n s have not been f u l l y i n v e s t i g a t e d , a d e s c r i p t i o n of behaviour under o n l y one set o f c o n d i t i o n s i s g i v e n . The s u b s t r a t e i s water c o n t a i n i n g 0.2 g/1 o f sodium benzene sulphonate plus 0.1 g/1 of sodium sulphate decahydrate. The spreading lens i s Nujol c o n t a i n i n g \0% by volume of the TERGITOL 15-S-3. This i s a n o n - i o n i c s u r f a c t a n t , an a l k y l p o l y (ethyleneoxy) ethanol of HLB number 9 s u p p l i e d by Union Carbide C o r p o r a t i o n . The behaviour i s more dramatic i f the nujol i s coloured by an o i l s o l u b l e dye such as SUDAN 111 or WAXOLINE g r e e n , but the same behaviour can be observed in the absence of dye. The spreading behaviour i s r e a d i l y observed i f the s u b s t r a t e i s placed in a g l a s s d i s h , such as a pyrex baking d i s h , which i s i l l u m i n a t e d from below by a powerful lamp. If a drop of the Nujol s o l u t i o n i s placed on a c l e a n s u r f a c e , i t spreads r a p i d l y , but not as a c i r c u l a r lens but much more i r r e g u l a r l y . If now, a second drop i s placed on the s u r f a c e , which presumably now has a f i l m of OILSSA on i t s s u r f a c e , i t w i l l spread w i t h low contact angle more s l o w l y to a f a i r l y r e g u l a r d i s c , a couple of c e n t i metres in diameter. Spreading w i l l c o n t i n u e f o r a few moments and then suddenly the lens w i l l r e t r a c t , reducing a few m i l l i m e t e r s in diameter and w i t h an obvious increase in c o n t a c t a n g l e . From t h i s moment, spreading i s much slower and very i n t e r e s t i n g . Sometimes, a rhythmic expansion and c o n t r a c t i o n w i l l be o b s e r v e d , again w i t h i n a few m i l l i m e t r e s range o f diameter. T h i s may continue f o r a w h i l e , but i s o f t e n so s l i g h t as to be unobserved. T h i s i s not a new phenomenon. It has been observed w i t h c e t y l alcohol on water (8), and was e x p l a i n e d as due to a changing e x t e r n a l s u r f a c e pressure due to s o l u t i o n of the c e t y l a l c o h o l i n the s u b s t r a t e . As the s u r f a c e pressure dropped, the contact angle became l o w e r , and spreading of the lens could proceed r a i s i n g the s u r f a c e pressure to a point at which the contact angle


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was r a i s e d s u f f i c i e n t l y f o r spreading to s t o p . When that occurred the s u r f a c e pressure dropped once again because of s o l u t i o n of the c e t y l a l c o h o l s u f f i c i e n t l y f o r spreading to be recommenced. A s i m i l a r mechanism wi11 e x p l a i n the rhythmic p u l s i n g of the Nujol l e n s . A f t e r a short t i m e , the lens c o n t a i n i n g OILSSA begins to spread a g a i n , but t h i s time i t does not do so uniformly in a l l directions. Sometimes, many f u z z y l i k e processes w i l l appear g i v i n g the lens the appearance of a m u l t i c i 1 i a t e d organism. These " h a i r s " w i l l g r a d u a l l y grow u n t i l a f t e r some minutes they w i l l have extended from the c e n t r a l lens to a d i s t a n c e o f many centimetres as f i l a m e n t - l i k e processes o f t e n w i t h b r a n c h i n g , (Figure 6). The appearance very much resembles r o o t - h a i r s . A f t e r a t i m e , the f i l a m e n t begins to d i s i n t e g r a t e i n t o t i n y g l o b u l e s of o i l w i t h high contact a n g l e . There has thus been an enormous increase in i n t e r f a c i a almost impossible to avoid convection c u r r e n t s or s i m i l a r d i s t u r b a n c e , the p a t t e r n soon becomes very i r r e g u l a r and an i n f i n i t e v a r i e t y of patterns i s o b t a i n e d , the c e n t r a l lens d e p a r t i n g markedly from i t s o r i g i n a l c i r c u l a r p a t t e r n . Neverthe l e s s , growth continues and o f t e n the p u l s a t i o n is n o t i c e a b l e , so the odd " c r e a t u r e " f l o a t i n g on the water appears to be a l i v e . It i s p o s s i b l e to increase the rate at which the outgrowths extend by sucking o f f from the s u r f a c e a c o n s i d e r a b l e d i s t a n c e away, a t r i c k o f t e n employed f o r c l e a n i n g contamination from s u r f a c e s . The e f f e c t of t h i s i s to reduce the surface pressure of the monolayer, thus i n c r e a s i n g the rate of spreading of the lens. Sometimes, the lens does not grow " w h i s k e r s " , but develops a puckered perimeter. As t h i s occurs when the s u r f a c e i s o l d e r and c o n t a i n s a very large number of t i n y g l o b u l e s , presumably the d i m i n u t i o n of surface pressure i s s l o w e r , being replaced from a l l the small d r o p s , so spreading from the lens i s reduced, and there i s l e s s tendency f o r outgrowths to appear. However, a complete d e s c r i p t i o n and e x p l a n a t i o n of these s t r u c t u r e s must await a separate communication as these are not themselves macrocluster s t r u c t u r e s , although they can be the u n i t s which b u i l d up to macrocluster s t r u c t u r e s . The resemblance of some o f the s t r u c t u r e s found in s p r e a d ing lenses to c y t o l o g i c a l patterns may be more than a c o i n c i d e n c e and of these the most s t r i k i n g are resemblances to the s t e l l a t e c e l l s in nerve t i s s u e , the chromosomes and the endoplasmic r e t i c u l u m systems. Each p a t t e r n i s determined by a balance of a number of f a c t o r s which have not yet been q u a n t i t a t i v e l y d e t e r mined, but the f o l l o w i n g are some of them:1) Nature of WATSSA 2) Concentration of WATSSA in s u b s t r a t e 3) Nature of OILSSA k) Concentration o f OILSSA in o i l , which determines 5) Spreading pressure of lens 6) E q u i l i b r i u m surface pressure of OILSSA on s u b s t r a t e which


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i s determined by Rate of s o l u b i l i t y or s o l u b i 1 i s a t i o n of OILSSA in WATSSA solution 8) Nature and c o n c e n t r a t i o n of d i s s o l v e d s a l t s in s u b s t r a t e 9) Temperature 10) V i s c o s i t y of lens m a t e r i a l 11) Convection c u r r e n t s in s u b s t r a t e or a i r c u r r e n t s above substrate 12) Free area between lens and neighbours or o t h e r o b s t a c l e s 13) S i z e and shape of lens 14) Reaction to spreading f o r c e s 15) Age of WATSSA s o l u t i o n . With respect to ( 1 4 ) , the momentum o f these spreading lenses i s remarkable, and can themselves s t i r up c u r r e n t s o f c o n s i d e r a b l e magnitude which in turn ca l e n s e s . When these get c l o s c l u s t e r systems which in appearance s t r o n g l y resemble endoplasmic r e t i c u l u m s t r u c t u r e s . Perhaps, the most s t r i k i n g macrocluster system i s t h a t produced by two adjacent l e n s e s , because i f the c o n d i t i o n s are c o r r e c t , they can simulate the b i o l o g i c a l phenomenon of endoc y t o s i s to a remarkable degree. Endocytosis i s the process by which a c e l l e n g u l f s f o r e i g n matter and embraces p i n o c y t o s i s and phagocytosis. In the f o l l o w i n g d i s c u s s i o n the term endocytosis w i l l be used to d e s c r i b e the phenomenon, although i t does not here r e f e r to l i v i n g c e l l s . The s i g n i f i c a n t property which determines t h i s behaviour i s a d i f f e r e n c e of c o n c e n t r a t i o n of OILSSA in the two l e n s e s . It i s best observed by using d i f f e r e n t c o l o u r s f o r the two l e n s e s , one of which i s c a l l e d the gobbler and the other i s the prey. For example, a good gobbler i s a 10% by volume s o l u t i o n o f TERGITOL 15-3-3 in N u j o l , coloured red w i t h a WAXOLINE dye. A good prey i s a s o l u t i o n of T e r g i t o l in Nujol l e s s concentrated than the g o b b l e r , coloured green w i t h WAXOLINE green. A 2% s o l u t i o n works w e l 1 , but Nujol without any OILSSA w i l l a l s o work. A lens of gobbler about 2 cm. diameter i s l a i d on the WATSSA s o l u t i o n in w a t e r , and when i t has almost reached a metastable e q u i l i b r i u m w i t h the s u r f a c e , i . e . spreads s l o w l y , a small d r o p , about 2 mm. diameter of prey i s placed a few m i l l i metres away from the g o b b l e r . They begin to a t t r a c t one a n o t h e r , and each moves towards the o t h e r , but because of i t s s m a l l n e s s , the prey moves f a s t e r . As they get c l o s e r , the gobbler may extrude some t e n t a c l e s , but these a r e not e s s e n t i a l . The two lenses are being drawn towards one another by Laplace pressures modified by the f a c t that the p r e y , having a lower c o n c e n t r a t i o n of OILSSA, w i l l absorb OILSSA from the i n t e r v e n i n g s u r f a c e on the s u b s t r a t e , inducing a lower s u r f a c e pressure i . e . higher s u r f a c e t e n s i o n , thus i n c r e a s i n g the Laplace p r e s s u r e . When the two lenses get very c l o s e , the Laplace pressure i s high enough to deform the g o b b l e r , so the gobbler envelops the prey which very soon i s completely engulfed by the g o b b l e r , and moves inwards 7)


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A N D M I C E L L A E BEHAVIOR

towards the c e n t r e of the g o b b l e r , but does not merge w i t h i t . T h i s shows t h a t there i s an envelope surrounding the prey which protects i t . In f a c t , It i s o f t e n p o s s i b l e to see a t h i n r e s i d u a l strand of prey connecting i t w i t h the o u t s i d e of the g o b b l e r , (Figure 7). If the s u r f a c e pressure o u t s i d e the gobbler i s c a r e f u l l y reduced by s u c t i o n , i t i s p o s s i b l e to open up the c a v i t y and the prey w i l l re-emerge unscathed. P h i l o s o p h e r s may muse on the f a c t that when the amoeba eats i t s v i c t i m , i t i s the v i c t i m which f o r c e s i t s way i n t o the amoeba, thus h a p p i l y committing s u i c i d e . Figure 8 shows s c h e m a t i c a l l y the mechanism for endocytosis. If the c o n c e n t r a t i o n o f OILSSA i s the same in the two l e n s e s , there i s no a t t r a c t i o n , and i f they are placed c l o s e t o g e t h e r , they may adhere but do not e n g u l f . The c o n t a c t angle seems to play a part as d r o p l e t s whic angle i . e . i s not l e s s tha there i s no s a l t in the s o l u t i o n , i t seems not to o c c u r , but a d d i t i o n of 3 x 10~^ sodium sulphate enables i t to proceed. This i s understandable on the hypothesis t h a t in order f o r the prey to d i s t o r t the gobbler the Laplace pressure must be high i . e . the two lenses must approach w i t h i n a minimum d i s t a n c e before i t can overcome the r e p u l s i v e f o r c e s caused by the double l a y e r . Salts w i l l reduce the t h i c k n e s s o f the double l a y e r a n d , t h e r e f o r e , enable the lenses to get c l o s e r . The prey does not have to be a l e n s . If a platinum wire or t h i n g l a s s rod i s inserted i n t o the s u b s t r a t e c l o s e to the g o b b l e r , provided the contact angle i s c o r r e c t , the gobbler w i l l s t a r t moving towards the s o l i d and engulf i t . Presumably even the small increase of s u r f a c e area provided by the platinum o r g l a s s i s enough t o lower the s u r f a c e pressure s u f f i c i e n t l y f o r a t t r a c t i o n to o c c u r . D i f f e r e n c e s of spreading pressures may a l s o o f f e r a mechanism f o r the b i o l o g i c a l phenomenon of c y t o p l a s m i c movement. Lenses a f t e r spreading end up as innumerable small g l o b u l e s immersed in a monolayer of OILSSA, there c l e a r l y being e q u i l i b r i u m between the spreading pressure o f the g l o b u l e s and the s u r f a c e pressure of the monolayer. If to such a system, a drop of o i l , Nujol o r k e r o s l n e , low in OILSSA Is added, e x t r a o r d i n a r y a c t i v i t y commences. It s t a r t s w i t h the nearest small g l o b u l e s moving towards the low pressure o i l , but t h i s movement soon spreads and even the most d i s t a n t g l o b u l e s begin to p a r t i c i p a t e . As movement i s r a r e l y uniform in a l l d i r e c t i o n , soon a streaming movement i s observed and t h i s may develop i n t o a s p i r a l movement. If there are s t i l l s t r a n d - l i k e lenses on the s u r f a c e , these f o l l o w the s p i r a l movement, and wind-up l i k e a c o i l e d s p r i n g so that c o n c e n t r i c l a y e r s of lens w i t h the low pressure o i l at the centre r e s u l t . These s t r o n g l y resemble the endoplasmic r e t i c u l u m observed in c e l l s . The motive energy i s o b v i o u s l y the movement of OILSSA from the higher pressure on the s u b s t r a t e s u r f a c e i n t o the low pressure o i l . What i s i n t e r e s t i n g i s that the small g l o b u l e s when they reach the c e n t r e o i l l e n s , o f t e n rebound from M


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Figure 6.

Lens spreading on water

Water.

Figure 7. Model for endocytosis. Hatched circle represents victim lens. Note neck to periphery.

WATER Figure 8. Mechanism of endocytosis. OILSSA moves from lens I to lens II thus tending to increase X , This increases Laplace pressure which is 8 so lens I and lens II are attracted. Spreading pressure of I > spread ing pressure of II so when they touch I spreads around II. The higher the concentration of WATSSA, the less marked the effect of OILSSA on * so attraction is reduced.


34



i t , or e n c i r c l e i t but r a r e l y merge i n t o i t . In other words, although a macrocluster system i s formed, i t i s not a strong one. On the c o n t r a r y , there i s o f t e n a sudden spurt of a c t i v i t y at one p o i n t , and a l l the e n c i r c l i n g small g l o b u l e s get swept to a d i s t a l point on the l e n s , from which p o i n t they again s l o w l y form a r i n g around the l e n s . The reason f o r t h i s e x p l o s i v e p o l a r i z a t i o n i s not obvious but i t almost looks at though an enveloping bubble had burst. The general movement i s remarkably r a p i d , and i s an example of conversion of s u r f a c e energy i n t o movement. It i s , of c o u r s e , the same phenomenon as the camphor c r y s t a l d a r t i n g about the s u r f a c e of water. When there are thousands of l i t t l e g l o b u l e s , a l l moving and a l l a l s o showing r e a c t i o n , i . e . j e t p r o p u l s i o n , as they lose OILSSA, i t i s c l e a r that the movement i s complex, but i t must in i t s t u r n c o n t r i b u t e to the p a t t e r n and shape of other lenses which are developing or packing i n t o macroc l u s t e r systems. Not o n l y i s endocytosis simulated in t h i s way, but so too i s e x o c y t o s i s . This i s b e t t e r shown by o i l s not as v i s c o u s as N u j o l , although the Nujol w i l l show i t more s l o w l y . If some dyed k e r o s i n e , c o n t a i n i n g say 2% o f TERGITOL OILSSA i s spread on the aqueous s u b s t r a t e , i t forms a t y p i c a l lens w i t h a f a i r l y even c i r c u m f e r e n c e . T h i s s l o w l y deforms, i s l a n d s o f monolayer appear and dark zones on the circumference of the kerosine appear. This i n d i c a t e s t h i c k e n i n g of the l e n s , and i t i s i n t e r e s t i n g t h a t these regions of d i f f e r e n t t h i c k n e s s appear showing that pressure i s not u n i f o r m l y d i s t r i b u t e d , (Figure 9). If in the i n t e r i o r of such a l e n s , a drop o f kerosine of d i f f e r e n t c o l o u r , but c o n t a i n i n g a higher c o n c e n t r a t i o n of OILSSA i s p l a c e d , a f t e r a very short period the f o l l o w i n g sequence i s observed. The new lens r a p i d l y expands and then r e t r a c t s to form i s l a n d s o f o i l in a monolayer o f OILSSA. These i s l a n d s may or may not merge. They move towards the t h i n n e s t part of the lens where the monolayer, being at higher s u r f a c e pressure than o u t s i d e , causes a bulge and e v e n t u a l l y breaks through c a r r y i n g the added k e r o s i n e as a lens or lenses out with i t . The lens then reforms to an approximately c i r c u l a r shape w h i l e the added lenses remain o u t s i d e j u s t touching the reformed lens which they then because of t h e i r higher OILSSA content attempt to e n g u l f . What i s s i g n i f i c a n t i s t h a t the s u r f a c e generated w i t h i n the i n t e r i o r of the l e n s , in the readjustment now forms part of the e x t e r n a l s u r f a c e of the l e n s . T h i s i s p r e c i s e l y the o p p o s i t e to what happens in the e n d o c y t o s i s , and simulates what happens in many types of c e l l , (Figure 10). To summarise, i n t e r a c t i o n of two l e n s e s , and presumably of two c e l l s , i s in essence the formation o f a two u n i t macroc l u s t e r system, w i t h endocytosis o c c u r r i n g when the OILSSA c o n c e n t r a t i o n in gobbler i s g r e a t e r than t h a t in the p r e y , and r e j e c t i o n o f the c e l l ( e x o c y t o s i s ) when the OILSSA c o n c e n t r a t i o n i s g r e a t e r in r e j e c t e d c e l l than in the host c e l l . Fertilisation of an ovum by a spermatozoon i s presumably a s p e c i a l case of endocytosis. It i s easy to envisage a s i t u a t i o n in which the



35

Water surface.

Figure 9. Spreading lens. Lens break ing up. M represents monolayer. Rest of lens is thicker. Note sites of thickening at perimeter as lens retracts.

Figure 10. Mechanism of exocytosis. Note that internal surface of A generated near Β becomes part of the external surface of A after Β has been ejected.


36



spermatozoon introduces i n t o the ovum some chemical which i n a c t i v a t e s the OILSSA in the ovum. The e f f e c t of that would be to reduce the spreading p r e s s u r e , and hence increase the contact a n g l e , w i t h the consequence that a second spermatozoon would not be a t t r a c t e d to enter the ovum. In a previous communication (5) i t was suggested that cancer occurred because the c o n c e n t r a t ion of c h o l e s t e r o l , a t y p i c a l OILSSA, was above t h a t in normal c e l l s due t o an Induced g e n e t i c d e f e c t . It Is easy to see now why such c e l l s are I n v a s i v e , i t Is because they behave as t y p i c a l gobbler c e l l s , normal c e l l s having l e s s OILSSA becoming the prey. If, however, these are not m o b i l e , but the cancer c e l l s a r e , the consequence would be i n f i l t r a t i o n by the cancer c e l l along the aqueous lamellae between the t i s s u e c e l l s . Two-Dîmensional Biliqui a d i l u t e WATSSA s o l u t i o n as Nujol c o n t a i n i n g some OILSSA i s r e l e a s e d , i t does not have time to break i n t o d r o p l e t s but u s u a l l y reaches the s u r f a c e as a thread of o i l . On p e n e t r a t i n g the s u r f a c e , the thread spreads to f l a t l e n s e s , and these adhere to form two-dimensional b i l i q u i d foams, the c o n d i t i o n s of breaking two surfaces a p p l y i n g in t h i s case as w e l l . A s i m i l a r e f f e c t w i t h s m a l l e r u n i t s i s obtained by beating a lens Into the s u b s t r a t e . The threads produced by an expanding lens w i l l o f t e n adhere In the same way to form s i m i l a r s t r u c t u r e s . These foams d i s p l a y some of the c h a r a c t e r i s t i c s of s i n g l e l e n s e s . For example, the endocy t o s i s process can o c c u r . If the o u t s i d e s u r f a c e pressure i s reduced by sucking o f f the s u r f a c e , the i n d i v i d u a l lenses w i l l move a p a r t , and reform again on s t a n d i n g . It i s suggested t h a t biomembranes are s p e c i a l examples of two dimensional b i l i q u i d foams. It i s now b e l i e v e d t h a t the Davson-Daniel1i model f o r a biomembrane i s not s a t i s f a c t o r y . E l e c t r o n microscopy r e v e a l s the e x i s t e n c e of p o r e s . A twodimensional b i l i q u i d foam, in which the lenses are very t h i n , and may even be b i m o l e c u l a r , seems to s a t i s f y some o f the conditions. One of the problems of biomembranes i s how penetration is regulated. It i s suggested t h a t r e g u l a t i o n could be achieved by metabolic c o n t r o l o f OILSSA c o n c e n t r a t i o n , as i l l u s t r a t e d In F i g u r e 11 and 12. If the OILSSA c o n c e n t r a t i o n i n c r e a s e s , the lenses w i l l tend to expand and the OILSSA w i l l spread to the i n t e r - l e n s aqueous s u r f a c e , u n t i l the s u r f a c e pressure equals the h o r i z o n t a l component of the spreading pressure. If the OILSSA goes i n t o the aqueous phase f a s t e r than i t moves out o f the spreading l e n s , the lenses w i l l expand and the pores w i l l c l o s e . If It Is produced in the lens f a s t e r than i t d i s s o l v e s In the aqueous phase, the s u r f a c e pressure w i l l b u i l d up, and the lens w i l l r e t r a c t , opening the p o r e s . In f a c t , there i s s i m i l a r i t y between t h i s mechanism and the opening and c l o s i n g of stomata except that in the l a t t e r case i t i s threedimensional pressures in the g u a r d - c e l l s and not two-dimensional


2.

SEBBA

37


AIR

Figure 11. Opening of pores. OILSSA moves more slowly into aqueous phase so concentration on surface builds up. Effect is to decrease V and β rises so lenses contract and pores open up.

AIR

OILSSA

OILSSA

WATER Figure 12. Closing of pores. OILSSA moves via surface into aqueous phase faster than it is spread onto surface. Effect is to increase # and to compensate & drops, lenses expand and pores close.


38



pressures that are i n v o l v e d . In another p u b l i c a t i o n , suggestions w i l l be made as to the nature of the OILSSA in l i v i n g systems and how i t s c o n c e n t r a t i o n i s c o n t r o l l e d . Conclus ions In t h i s paper, the attempt i s made to show that the behaviour of many types of two phase systems can be b e t t e r explained by c o n s i d e r i n g them as macrocluster systems. In order to understand t h e s e , i t i s necessary to assume that the t h i n f i l m of water adjacent to another phase, gas or l i q u i d , behaves as though i t i t s e l f was a d i f f e r e n t phase to bulk water. The behaviour of l e n s e s , spread on water shows remarkable resemblance to c y t o l o g i c a l behaviour. There i s no proof that t h i s behaviour can n e c e s s a r i l y be e x t r a p o l a t e might be u s e f u l to assum spread on w a t e r , the t h i r d phase i s a i r , whereas presumably there i s not gas in c y t o p l a s m , though the question could be asked whether the absence of gas has been unequivocably proven. In c y t o p l a s m , the three phases would be an o i l - p h a s e , an aqueous phase and the s u r f a c e phase, but one of the fundamentals of any phase study is that thermodynamics i s not concerned w i t h the nature of the phases but o n l y w i t h the number of phases. However, there i s one q u a l i t a t i v e f a c t that would j u s t i f y the e x t r a p o l a t i o n from two-dimensional to three-dimensional systems and that i s that when experimenting w i t h b i l i q u i d foams whenever three d i f f e r e n t f l u i d phases met, there was e x t r a o r d i n a r y motion between them resembling the simulated protoplasmic motion described in the twodimensional model. (No attempt has yet been made to e x p l a i n the problems met w i t h in industry in f l o t a t i o n , f l o c c u l a t i o n , and f i l t r a t i o n in terms of the concepts introduced h e r e , but these approaches might very w e l l prove p r o f i t a b l e ) . T h i s paper can o n l y be considered as a p r e l i m i n a r y i n v e s t i g a t i o n , but i t does suggest that the s e c r e t s of l i f e l i e in the behaviour of immiscible l i q u i d s under the i n f l u e n c e of t h e i r interfacial forces. Acknowledgements Thanks are expressed to Mrs. F. Horwitz who helped w i t h the b i l i q u i d experiments and to Mr. T. Ambrose who helped w i t h the photographs. Literature Cited 1. 2. 3.

Sebba, F . , J . C o l l o i d Interface Sci., (1971), 35, 643 Sebba, F., Nature (London), (1963), 197, 1195 Adamson, A.W., " P h y s i c a l Chemistry of S u r f a c e " 2nd ed., pp. 348, 383, I n t e r s c i e n c e , New Y o r k , N.Y. 1967


2.

SEBBA


4. Sebba, F., J. C o l l o i d I n t e r f a c e Sci., (1972), 40, 468 5. Sebba, F., J. Colloid Interface Sci., (1972), 40, 479 6. Langmuir, I., J. Chem. Phys., (1933), 1, 756 7. H a r k i n s , W.D., "Colloid Symposium Monograph", 6, p.24, Chemical Catalog C o . , New York, N . Y . , 1928 8. Sebba, F. and B r i s c o e , H . V . A . , J. Chem.Soc., (1940), 114.


39

3 Mechanical and Surface Coagulation W. H E L L E R Department of Chemistry, Wayne State University, Detroit, Mich. 48202

Introduction

It is well known that colloidal suspensions may coagulate partially or even completely under the influence of agitation, such as stirring or shaking. In concentrated systems, particu l a r l y in those of originally uniform more or less pastelike or creamy consistency, such as concentrated latices or paints this may manifest itself p r i m a r i l y by the formation of microscopic or macroscopic lumps or crums and an increase in f l u i d i t y of the systems. In a more dilute system, separation into a more or less water clear upper layer and a concentrated lower layer will occur, the latter consisting p r i m a r i l y of coagulated colloid. This phenomenon of coagulation of colloidal systems by agitation, is generally referred to as "mechanical" coagulation. The present article is concerned with this type of coagulation. Survey o f the

Literature

The first to point out that agitation should affect the rate of coagulation in a system which is already coagulating (as a result of the addition of coagulating electrolyte) was Smoluchowski (1_). According to his theory, the collision number in a coagulating system is increased under the influence of flow and, therefore, the number of successful collisions also is increased. The actual effect of agitation upon a coagulating system was investi gated systematically first by Freundlich and Basu who used C u O sols of relatively low stability towards electrolyte (2). Figure 1 shows a sample of the quantitative data obtained by these authors on the coagulation of a C u O - s o l after addition of a sodium sulfate solution so that the mixture contained 0. 125 mmoles per liter sol. Curve 1 shows the progress of coagulation in absence of 40


3.

HELLER

Mechanical and Surface Coagulation

41

stirring and Curve 2 that observed on stirring the coagulating system. (The ordinate gives the actual sol concentration, in grams of C u / l i t e r sol, the abscissa gives the time in minutes elapsed since the electrolyte had been added. ) It is apparent that stirring accelerates the coagulation considerably except in its final stage. Although no reference was made to this fact, it is clear from this figure that the effect of agitation was far too large to be accounted for on the basis of the Smoluchowski theory. The same authors found subsequently that addition of electrolyte made these sols susceptible to coagulation by agitation although the amount added was too small to produce coagulation in the system at rest. Freundlich and K r o c h (3) investigated for the first time this "pure" mechanical coagulatio reproduced in Figure 2. Two facts clearly emerge: (1) the co agulation by stirring is faster the higher the rate of stirring; (2) the residual colloid concentration declines linearly with the time of agitation suggesting a zero order reaction. The same linear relationship was found in a subsequent paper by Freundlich and Loebman (4) on the mechanical coagulation of Goethite (a-FeOOH)sols. They were the second type of system found to be suscepti ble to mechanical coagulation. The ordinate in Figure 3, i l l u s trating their results, gives the residual concentration in mg F e / liter and the abscissa the time of agitation in hours. The curve refers to an α - F e O O H sol which had been stirred at 1000 r p m . A n intriguing and as yet unexplained new fact, indicated by this figure, is that the coagulation by stirring alone may not go to completion but may stop after coagulation has progressed sufficiently far. The original assumption that one was dealing with a purely mechanical coagulation did not readily agree with the finding already made by K r o c h and extensively verified by Freundlich and Loebmann that the rate of coagulation increased roughly with the square of the velocity of stirring. The latter relation, they reasoned, would follow naturally, in the case of a surface coagu lation if the water-air surface, created in the middle of the sample by the revolving s t i r r e r , were cylindrical and if the height of this cylinder increased in direct proportion to the speed of the s t i r r e r . (The actual contours of the liquid-air interface are more complex). This idea of a surface coagulation seemed to be reasonable also in view of the interesting effect found by Zsigmondy many years earlier (5) that shaking certain aqueous sols with inert organic liquids produced coagulation. Further support for this explanation of the nature of mechanical coagula-


42


Ή I ! -*»t

ι 10

t ZO

30

t HO

i

t 50

60

ι

f

f

70

SO

90

Zeitschrift fur Physikalische Chemie

Figure 1. Acceleration by stirring of coagulation of CuO-sols by elec trolyte (2). Ordinate: residual sol concentration (g Cu/l.). Abscissa: time, t, in minutes, elapsed since addition of Na SO^ solution without stirring (curve 1) and with stirring during entire time, t (curve 2). NU^SO* concentration: 0.125 mmol/l. sol. 2

n,=mg CuO im Liter

1W

Zeitschrift fur Physikalische Chemie

10 ZO 30 UO SO 60 70 80 90 t Ruhrzeit in δ fun den =

Figure 2. Coagulation of CuO-sols by stir ring alone (3). Ordinate: residual sol con centration (mg CuO/L). Abscissa: time of stirring in hrs. v: number of rotations of stirrer/min.


3.

HELLER


43

tion as a surface coagulation was provided by subsequent investi gations by Freundlich and Recklinghausen (6). They compared the effect of stirring in presence and absence, respectively, of a liquid-air interface at appreciable rates of rotation (700-1000 rpm). The straight line A in Figure 4 shows that the C u O - s o l , used again in these experiments did not coagulate at all if the stirring was done in absence of a water-air interface. Curve Β on the other hand, obtained on admitting one single air bubble into the system, shows that coagulation occurred and progressed until the air bubble was removed (approximately 10 minutes after the start of the experiment) whereupon coagulation stopped c o m pletely. Freundlich and Recklinghausen furthermore found in v e r i f i cation of Zsigmondy's qualitativ occurs also, in absence of a liquid-air surfaceôn stirring a C u O - s o l in presence of mechanically emulsified br omnaphthalene, i . e . in presence of a liquid-liquid interface only. Representative results are shown in Figure 5. Here Curve A pertains to 600 r p m and Curve Β to 1000 r p m . The faster rate of coagulation in the latter case was explained by assuming the formation of smaller emulsion droplets (of br omnaphthalene). Further support for the explanation of mechanical coagula tion as a surface coagulation may be derived from independent work carried out about the same time by Stark. This author (7) investigated the coagulation produced by bubbling gas through especially prepared sols of f e r r i c oxide. He explained the appre ciable coagulation found not as a surface coagulation, but by assuming that the colloid was merely adsorbed at the surface of the rising gas bubbles and that coagulation took place after the gas bubbles burst, due to a critical increase, in the upper region of the sol,of the bulk colloid concentration. Figure 6 gives some representative results obtained by Stark with gas bubbles whose diameter was somewhere between 1-17 m m . The time indicated on the abscissa is the time elapsed after bubbling of gas (probably air) had started and the ordinate indicates the residual concen tration of uncoagulated colloid in grams of iron per l i t e r . Curve 1 represents the coagulation curve in absence of added electro lyte. The other curves show the effect of various concentrations of potassium sulfate on the rate of coagulation. In the quantitative investigations of Freundlich and collabora tors only two types of sols were coagulated "mechanically", those of α-FeOOH and CuO. Both of these, and also the iron oxide sols used by Stark, while perfectly stable at rest, required only small amounts of electrolyte to cause coagulation even in


44

C O L L O I D A L DISPERSIONS A N D M I C E L L A R

BEHAVIOR

Kolloid Beihefte

Figure 3. Coagulation of an a-FeOOH sol by stirring (4). Ordinate: residual sol concentration in mg Fe/l. Abscissa: time of stirring in hrs. Rate of stirring: 1000 rpm.

Elektrochemische Zeitung

Figure 4. Effect of stirring upon a CuO-sol in presence and absence of a liquid-air interface (5). Ordinate: residual sol concentration (mg Cu/l). Abscissa: time of stirring in hrs at 1000 rpm. A: no liquid-air interface is present. B: air bubble present during first 10 hrs.



45

Zeitung fur Physikalische Chemie

Figure 5. Effect of stirring on a CuO sol in presence of a liquid-liquid interface and absence of a liquid-air interface (6). Ordinate: residual sol concentration (mg Cu/l). Abscissa: time of stirring in hrs.

Ο

>v

\

0

10

20 30 Time in hours.

40

50

Journal of the American Chemical Society

Figure 6. Coagulation of iron oxide sol prepared ac cording to Sorum [J. Am. Chem. Soc. (1928) 50,1263] by bubbling air through it (7). Ordinate: residual col loid concentration. Abscissa: duration of bubbling. Curve 1: no electrolyte added to sol. Curves 2-6: in creasing amounts of K SO, added to sol at time zero. 2

t


46


BEHAVIOR

absence of agitation. This led Heller (8) to suspect that the type of coagulation reviewed here may be produced in any colloidal solution provided its natural stability is reduced sufficiently. To check this, eight colloidal solutions were used whose "coagulation value" (9) was systematically reduced f r o m 300 to 2. 0 m m o l of N a C l per liter. By using differing methods of preparation and differing degrees of dialysis it was found that a coagulation value of about 20 m m o l / l i t e r of a 1:1 electrolyte (such as NaCl) made the sols subject to "mechanical" coagulation. These results together with subsequent results on freeze coagulation (10) led to the following tentative explanation of "mechanical" coagulation (10):due to the difference in the dielectric constant in the interior of a colloidal solution and in the liquid-air interface, a critically reduced sol stability ma particle collisions in the interior of the sol are successful while they may be i n the interface. This importance of the dielectric constant for sol stability i n general, was subsequently verified on a quantitative basis by Verwey and Overbeek (11 ). While therefore the explanation of the "mechanical" coagulation as a surface coagulation appeared reasonable also f r o m the theoretical point of view, magneto-optical investigations (still unpublished at that time, see Section VIII) made it most likely that strong turbu lence in the interior of a sol of critically low stability may lead to successful particle collisions due to a c r i t i c a l momentary predominance of the attractive London dispersion forces over the repulsive Coulomb forces as a result of a momentary deformation of the electrostatic double layer (10). The later quantitative theory(11) of colloid stability seemed to give substance also to this alternate possible cause of "mechanical" coagulation. The proposition that a critically low sol stability is necessary and sufficient to make "mechanical" coagulation possible no matter whether it may be a surface coagulation or true mechani cal coagulation resulting from turbulence, was strengthened more recently by interesting experiments by Roe and B r a s s (12). These authors added to polystyrene latices which could be coagu lated mechanically, more potassium palmitate or potassium laurate than had been necessary for the purpose of p o l y m e r i z a tion. They found that this addition increased the resistance of the system to mechanical coagulation appreciably, more the larger the soap concentration. This follows from Figure 7 in which these authors summarize their results. The ordinate gives a measure of the mechanical stability by indicating the time of stirring needed (at 14, 000 rpm) in order to produce 100% coagu lation. It is apparent that not only an increase in concentration


3.

HELLER


47

of the long chain ions adsorbed at the surface of the polystyrene but also an increase in their chain length increased the mechani cal stability. In more recent years the interest in "mechanical" coagula tion has been limited essentially to exploring the potential practical usefulness of the effect in order to remove colloids from aqueous systems. Comprehensive studies on this aspect were c a r r i e d out by Mokrushin and collaborators (13-21) who concentrated on expanding the work of Stark (7) referred to above. The colloid coagulated by bubbling air through the systems was collected in a foam produced at the top of the liquid by addition of a suitable foaming agent. Further contributions to this practical aspect of "microflotation" were made subsequently by Matijevic and collaborators (22-24) Objectives o f the Studies Reviewed i n the Following Sections of T h i s Paper

There was little doubt in view of the literature results r e viewed above that the liquid-gas and liquid-liquid interface, under certain conditions, might be capable of promoting coagulation (25). In absence of any quantitative theory, a decisive test of this reasonable hypothesis was not possible. It appeared most desirable to provide such a test. With the aid of such a test it could be hoped, in addition, to decide whether and when the "mechanical" coagulation may be a pure surface coagulation or a bulk coagulation, due for instance to turbulence, or may be a c o m bination of the two possibilities. A careful scrutiny of the literature data showed that a series of results reported appeared contradictory. A resolution of the respective problems also appeared mandatory. The first prob l e m here concerns the kinetics of coagulation by stirring, shaking or by air bubbles. Figures 2, 3 and 4 show a linear decrease in colloid concentration as a function of time of agitation. This suggests that the coagulation is a zero order reaction. On the other hand, Figures 1, 5 and 6 show more complicated rate curves. The fact that Figures 2, 3 and 4 were obtained in absence of electrolyte while Figure 1 and all curves except curve 1 of Figure 6 were obtained in presence of electrolyte, cannot explain the differences because the curves in Figure 5 also were obtained in absence of electrolyte. Moreover curve 1 of Figure 6 is not a straight line either. Stark believed that the experimental results given in Figure 6 indicate that the theory of Smoluchowski applies. In this theory the coagulation process is considered as a second

American Chemical Society Library 155 15thandSt., N.W. In Colloidal 1 Dispersions Micellar Behavior; Mittal, K.; ACS Symposium Series; American D.C. Chemical Society: Washington, DC, 1975. Washington, 2803S

48


BEHAVIOR

order reaction which differs, however, from the conventional second order reaction by the fact that the reaction products themselves are reactants. In other words, after one individual colloidal particle has aggregated with another, this secondary particle may in turn aggregate again with either another p r i m a r y or secondary particle and so forth. On scrutinizing closely Stark's experimental results, it is seen that the rate constant derived on the basis of the Smoluchowski theory is not really a constant but varies considerably with the progress of coagulation both in presence and absence of additional electrolyte. That the Smoluchowski theory is not applicable to mechanical coagulation by stirring alone had in fact been found already by Freundlich and K r o c h . A n approach to applicability of the Smoluchowski equation was indicated onl To complicate things even more, it may be mentioned that Mokrushin found that the colloid extraction by air bubbles followed the rate of a first order reaction (15) and that the Schulze-Hardy rule did not apply (15 ). A second intriguing problem is the effect of electrolyte addition to the stability of a sol which can be coagulated mechani cally. In the work by Freundlich and Basu (2) and by Freundlich and K r o c h (3) the addition of electrolyte promoted coagulation. In the work by Freundlich and Loebmann (4) on the other hand, the rate of mechanical coagulation was found to be reduced at low electrolyte concentrations while it was increased at higher ones. In the experiments by Stark (7), finally, only promotion of coagu lation was found on adding electrolyte. Theory of Surface Coagulation Theoretical equations for the reaction rate expected of the surface coagulation were developed by J . Peters and the writer (26). The equations a r r i v e d at are based on the following assumptions: 1) The coagulation proceeds exclusively in the liquid-air surface, and it is a bimolecular reaction. 2) The contribution of aggregates to the rate of coagulation (Smoluchowski rate increment) is neglected. In addition, the aggregates, by their return to the bulk, are assumed not to affect significantly the surface area available for occupancy by unreacted p r i m a r y colloidal particles. 3) There is sufficient convection to exclude diffusion of particles to and f r o m the surface as a rate-determining factor in surface coagulation.


3.


HELLER

49

4) There exists a definite steady state for the distribution of p r i m a r y colloidal particles between bulk and surface. This dis tribution is assumed to follow a Langmuir adsorption isotherm. 5) The rate of adsorption is assumed to be large enough relative to the rate of mechanical surface renewal so that the adsorption equilibrium is not affected. The resulting differential equation is fÈ£ " dt

2

§. τ*V 0 (Κ

=

χ

e +K c)

m 2

* '

2

Here, S is the surface area at constant rate of surface renewal; V is the volume of the solution; c is the concentration of the colloid in solution (moles/ml) constants. Equation (1) can be rearranged to 1/2 (-dc/dt) ™

=

(i^s)

( K

K

C

2

1 * 2 >

for the purpose of convenient graphical checks of the validity of Equation (1). Consequently, the plot of [c/(-de/dt)*/2] i d be linear and the ratio of slope to intercept should represent K / K j . Equation (1) has the following properties which are of inter est in connection with the reaction order of surface coagulation: v

s

c

s n o u

2

-dT

=

k

'CI)

i

f

k

2

C »

K

I

This shows that the equation derived for a bimolecular s u r face reaction may also satisfy an apparent z e r o - o r d e r reaction, an apparent f i r s t - o r d e r reaction being an intermediate possibility. The apparent reaction order depends therefore, (1) on the colloid concentration and (2) on the value of the constants K j and K , which depend on the distribution of the colloidal particles between bulk and surface. F o r a given value of K j and K , one would expect that the apparent order of reaction increases with i n c r e a sing degree of coagulation, the initial period of an apparent zero-order reaction covering a larger portion of the coagulation process, the lower the initial colloid concentration, C Q . Moreover at equal CQ and c, the probability of an apparent z e r o - o r d e r reaction would be higher, the higher the affinity of the colloidal 2

2


50

COLLOIDAL DISPERSIONS A N D M I C E L L A R

BEHAVIOR

particles is for the liquid-air surface (the more hydrophobic the particles are in case of a water-air surface). On integrating Equation (1), one obtains on introducing f for c/c

0

i f i

+

2c £? 0

i n i ^ ' d - f )

= K.t

(3)

2 where K = C K Q S / K | V . F r om this equation it follows readily that with an increase in K / K j the reaction rate at any stage of the coagulation changes gradually from the typical second-order reaction to that of a typica again the puzzling fact mentioned in the preceding section that different authors found different orders for the reaction rate of coagulation induced in different systems by mechanical agitation or bubbling of gases. g

0

2

Experimental Test of the Theory of Surface Coagulation The first tests of the theory of surface coagulation were c a r r i e d out by Peters (26) studying the coagulation produced by bubbling nitrogen gas through a colloidal solution of a - F e O O H prepared in the same manner as the sols used by Freundlich and Loebmann (4). The strongly anisometric crystals of a - F e O O H had an average length of 83 nm, a width of 10 n m and the stan dard deviation from these dimensions was sufficiently small to characterize the systems as nearly monodisperse, disregarding a relatively minor amount of nearly cubical crystals present at the same time. Figure 8 in which c represents the concentration of the uncoagulated (residual) colloid in percent of C Q , shows that equation (2) satisfies the coagulation process extremely well down to a residual concentration of merely 5% of the starting concen tration. The slope of the straight line increases, as one expects, with the rate at which nitrogen gas is bubbled through the colloi dal solution, the two cases considered being a flow rate of . 65 and of 1. 65 cm^/sec. On taking into account the difference in the experimentally determined bubble sizes in cases I and II and the differences of the rate of bubbling in the two cases one arrives at a result that is the same within ±4%. This further supports the theoretical equation. Although the probability of a "mechanically" effective turbu lence is rather remote on bubbling gas through a solution, special tests were c a r r i e d out (26) where even the possibility of minor r


51


Journal of Colloid Science

Figure 7. Effect of soaps upon the "mechanical sta bility" of polystyrene latex (12). Abscissa: concentra tion, in the water—air interface of K-palmitate (O) and K-laurate (Δ). Ordinate: number of seconds re quired to produce complete coagulation by high speed stirring (14000 rpm) of a 60 ml sample contain ing 24 volume percent of polymer. Parameter: par ticle "size" in Angstrom units.


3

I: 0.65 cm /SEC. JL 1.65 cm /SEC. 3

Figure 8. Coagulation of a-FeOOH sol by nitrogen bubbles. Test of equation (2) (26). c : colloid concentration of residual sol in percent of original colloid concentration, c (370 mg Fe/L). Average particle diameter: 83 nm. pH: 6.5. Parameter: rate of N -flow. r

0

2


52


BEHAVIOR

turbulence was eliminated by extending experiments over a period of 2000 hrs replacing bubbling of gas through a solution by gentle mechanical renewal of the liquid-air interface. These experi ments also were fully satisfied by the equation of surface coagu lation given above. The same systems were used for coagulation by stirring (27) using the same technique used by Freundlich and Loebmann (4). The curves obtained were essentially the same (for details r e f e r ence (27) should be consulted). It is apparent that the equation for surface coagulation given above again applies very well as is evident from Figure 9. The only deviations occur in the final stage of the coagulation when the residual concentration has fallen to less than 15% of the starting concentration. The cause of these deviations in the final stag This final stage may represent a manifestation of a coagulating effect due to turbulence overshadowed at higher concentrations by the effect of surface coagulation. Special experiments [(see Figure 4 in reference (27)] excluded the possibility that at this stage secondary particles or tertiary particles or still larger aggregates may participate in the coagulation process by providing an additional reaction locus in the interior of the colloidal solution. The Role of Turbulence In order to detect whether and to what extent turbulent flow may actually produce or participate in coagulation - a possible theoretical reason for it having been mentioned in Section II experiments had to be c a r r i e d out in which surface coagulation could be excluded as a factor. To this effect, the same type of colloidal solutions discussed above were circulated, by DeLauder (28), in a closed ring of Tygon tubing by means of a Sigma Motor Finger pump. Since Tygon tubing was found to contain impurities which have a s m a l l but distinct stabilizing effect on aqueous colloidal solutions, the tubing was subjected to a very rigorous cleansing process prior to use. On leaving the same colloidal solution, as used for the other experiments, for extended periods of time in the thoroughly cleaned and closed circular Tygon tubing ring, no coagulation could be detected by checking the turbidity of the system. On the other hand, on operating the pump - which had no contact whatever with the colloidal solution - a definite particle aggregation occurred although the effect was far too small to be detectable by any means other than by light scattering (turbidity) measurements, the aggregates formed being u l t r a -


3.

HELLER


53

microscopic in size. Figure 10 shows that the turbidity deter mined at 6250 A increased by a little more than 10% in 10 hrs of pumping. Since air bubbles, however small, had been rigorously excluded, the only possible causes of particle aggregation were either the turbulence created at the point where the squeezing action of the pump at the Tygon tubing took place, or the interface between the Tygon tubing and the colloidal solution. It could be shown that the solid-liquid interface in fact can be a locus of particle aggregation (28). It becomes detectable, how ever, only if sufficient turbulence is created in the system so that the fine skin of coagulum of ultramicros copie thickness formed at the solid-liquid interface is removed so as to free the solid-liquid interface as a site for further aggregation. Since the colloidal solution i n the not show any change in turbidity in absence of pumping, the coag ulation produced as evident from curve section I in Figure 10, was therefore due either to turbulence directly or to the turbulence induced removal of a colloidally-thin layer of coagulum from the liquid-solid interface. A differentiation between these two p o s s i bilities is not possible at the present time. No matter whether the contribution of turbulence was thus direct or indirect, it is evident that the effect is very small compared to the effect of a coagulation at the liquid-air interface. This is particularly well demonstrated by Section II of the curve in Figure 10. H e r e , at the time t j , a small air bubble was introduced into the system and kept at the point of maximum turbulence (where the pumping action took place). Immediately a steep increase in turbidity was observed. Additional experiments (28) showed that placing and keeping the air bubble rather at the top of a vertical section of the loop where it remained quiescent and undeformed did not produce any increase in turbidity. T h i s , therefore, proved that the increase in turbidity observed in Section II of Figure 10 was due to the constant removal, due to the turbulence induced continu ous deformation of the air bubble, of an ultramicroscopic layer of aggregates.


54


BEHAVIOR


Figure 9. Coagulation of a-FeOOH sol by stirring. Test of equation (2)(27). I: 600 rpm. II: 900 rpm. c : 205 mg Fe/l 0


0.29 I 1 1 1 1 I 1 1 1 1 > 1 L. 0 10 20 FLOW TIME (HRS.)

Figure 10. Coagulation of a-FeOOH sol during locally turbulent flow in loop of Tygon tubing (28). i . In absence of any liquid-gas interface. II. In presence of single air bubble in turbulent section of flow. t : time at which bubble is introduced. Flowrate: 150 ml/min. t


3.

HELLER


55

Factors which Promote or Impede Surface Coagulation Aggregation of two colloidal spheres in a dilute system becomes likely when the positive maximum of the potential energy curve is less than 15 k T (9 kcal/mol)(l 1). Investigation (27) of the temperature-dependence of the coagulation produced by stirring in the α-FeOOH sols discussed above led to the result that the apparent activation energy of surface coagulation is 8. 9 3 k e a l / m o l , remarkably close to the theoretical value for sphere coagula tion. The potential energy maximum was evidently lower in the water-air interface than in the interior of the sol stable at rest. Since a decrease in the height of the potential energy maximum occurs on raising the value of the Debye-Huckel c o n s t a n t , χ , it was expected in line wit (8, 10) that i n very stable systems in which neither bubbling of gases through the solution nor stirring produces coagulation, one may bring it about by adding suitable electrolytes in a concentra tion sufficient to depress the potential energy maximum to the critical value in the water-air interface but not yet in the interior of the system. This was tested successfully on polychlorostyrene and polystyrene latices. Results obtained on the former are illustrated by Figure 11 (28a). Up to a concentration of 0. 15 mol KC1/liter latex s t i r r i n g had little effect on the latex whose concentration was chosen at 185 m g / l i t e r . At still higher KC1 concentration stirring coagulation occurred, more the larger the electrolyte concentration. It is important to note that only from about 0. 2 m o l / l i t e r KC1 on significant bulk coagulation made its appearance, complicating the entire process. Completely analogous results were obtained on bubbling nitrogen through the latex rather than by employing stirring (28a). The situation is not quite this simple in the case of colloidal solutions of inorganic crystals. Thus, in the α - F e O O H systems discussed here p r i m a r i l y one observes at low Κ CI concentrations first an increase in the stability of the systems toward coagulation by stirring or bubbling until at a KC1 concentration - which is still below that at which bulk coagulation becomes pronounced - the trend is reversed. A n example of stabilization is given in Figure 12 (29). At more than 1. 14 m m o l KC1 the trend is reversed, i . e. the electrolyte then promotes coagulation by stirring. The small increase to 1. 17 mmol KC1 was sufficient in this case to reverse the trend at the same r p m (900)* E s s e n tially the same results were obtained more recently (30) by DeLauderfor other than 1, 1 electrolytes, the only difference being that in the case of higher valent gegen-ions the concentra-



100

"

0.15

I

ο

90

\\Ρ·

1 7

—J
15 nm

valid for H < 15 nm The i n t e r a c t i o n V can be c a l c u l a t e d from the t o t a l number o f p a r t i c l e s a s s o c i a t e d w i t h a given p a r t i c l e i . e . the degree of a g gregation. D , can be computed from

3

2

D = 4 ft n a J S exp (-V/kT) ds


(4)


Figure 1.

Characteristic interaction energy profiles in the light of the D.L.V.O. theory

*v 25 kT

Hydrocarbon Droplet

Figure 2. Diagrammatic representation of the coalescence of the coated emulsion droplets


BEHAVIOR

7.

SRivASTAVA

Macwmoleculaf Emulgents

113

where TIQ i s the number o f d r o p l e t s per u n i t volume o f the suspen sion and s = 2 + H / a . The i n t e r g r a n d i s evaluated g r a p h i c a l l y . In case o f r e v e r s i b l e f l o c c u l a t i o n under study, a s i n g l e t doublet e q u i l i b r i u m t e m p o r a r i l y e x i s t s i n the system and the extent o f f l o c c u l a t i o n can be determined from the formula JJ =

number of doublets number of singlets + number of doublets

For the above c a l c u l a t i o n s the value o f the van der Waals cons t a n t , A i s needed which was c a l c u l a t e d from the equation.

where of the to the lowing

^ i s the number o f atoms of k i n d i contained i n 1 c . c . matter of i t h kind and i s the London constant r e l a t i v e same substance, the l a t t e r being c a l c u l a t e d from the f o l three equations: 2

(a) The London e q u a t i o n ,

= 3/4 Q> hV^

(b) The Slater-Kirkwood B _

W

= 11.25 χ ΐ ο " "

2 4

2

3

^^ » ^

2

S—Κ (c ) The Slater-Kirkwood-Moelwyn-Hughes Β

l/2 2 . = 3/4 (s η) ηV α

S-K-M

'

κ

1 ' e where a i s the p o l a r i z a b i l i t y , V i s the c h a r a c t e r i s t i c London ^ frequency η i s the number o f valency e l e c t r o n s , V the e l e c t r o n i c v i b r a t i o n frequency and S i the e f f e c t i v e number o f d i s p e r s i o n e l e c t r o n s i s given by the e m p i r i c a l r e l a t i o n S i = 0.39n. Because the emulstion d r o p l e t s are immersed i n an aqueous medium, the net constant i s given by A = {A,. . + A„ -2A_. I (10) \ disperse phase H o disp.ph-Bô J Q

e

2

A i s thus i n v a r i a b l y p o s i t i v e and hence f o r two p a r t i c l e s o f any species embedded i n a second medium there w i l l always be a net a t t r a c t i v e f o r c e . Employing the above mathematical formulations the i n t e r a c t i o n o f emulsion d r o p l e t s s t a b i l i z e d by macromolecular sub stances such as bovine serum albumin (BSA), p e p s i n , sodium and gum a r a b i c has been examined q u a n t i t a t i v e l y i n the l i g h t of the s t a b i l i t y theory. The orthodox range o f c o l l o i d a l dimensions ( l - 100 nm) has been d e l i b e r a t e l y excluded and the range of the p a r t i c l e s i z e chosen i s such t h a t the f l o c c u l a t i o n i s r e v e r s i b l e and occurs i n the secondary minima of i n t e r a c t i o n energy p r o f i l e s . Since such i n t e r a c t i o n s may be a l t e r e d by adsorbed macromolecules an attempt has a l s o been made to study the i n f l u e n c e of a d s o r p t i o n


114


BEHAVIOR

on van der Waals interaction using the following equation from Void's mathematical treatment (12) described elswhere (13) A

MS

2

= "

H

A

H

H

2A

H

[ < V P S > P M ± {( P- PS) PM-< S A

(2R+H )

2

Q

i s u s u a l l y between 1 and 1/2 as p o i n t e d o u t by McGown and P a r f i t t (33J, which a c c o u n t s f o r s m a l l d i f f e r e n c e s between e x p e r i m e n t a l f a s t c o a g u l a t i o n r a t e s and t h e Smoluchowski c o a g u l a t i o n r a t e . I t i s important t o note t h a t Equations (2), ( 3 ) , and (4) c o r r e s p o n d t o a g g r e g a t i o n a t t h e p r i m a r y m i n i mum, i . e . , t h e p o i n t o f c o n t a c t i s a t H = 0. However, i n t h e c a s e o f secondary minimum f l o c c u l a t i o n , t h e equilibrium distance of separation a t contact i s a t a v a l u e o f H where t h e secondary minimum o c c u r s . Thus the f l o c c u l a t i o n r a t e c o n s t a n t a t t h e secondary minimum a c c o r d i n g t o t h e Smoluchowski,theory w i t h F u c h s cor r e c t i o n s h o u l d be g i v e n by k as Q

Q

1


148


k

BEHAVIOR

(5) S

2R

where 2L i s t h e v a l u e o f H a t which the secondary minimum o c c u r s . Hence, the e x p e r i m e n t a l l y o b s e r v e d s t a b i l i t y r a t i o , W ' , f o r secondary minimum f l o c c u l a t i o n , d e f i n e d as t n e r a t i o o f the f l o c c u l a t i o n r a t e c o n s t a n t o f u n p r o t e c t e d p a r t i c l e s t o t h a t i n the p r e s e n c e o f p r o t e c t i o n , s h o u l d be g i v e n by Q

p

2R

kT

J2L

(2R+H )

2

0

(6) A G

f ° / exp

2R J

0

dH

(

" A V" kT

Q

(2R+H )

2

Q

I t has a l r e a d y been p o i n t e d o u t t h a t the two i n t e g r a l s i n E q u a t i o n (6) a r e s m a l l because A G i s n e g a t i v e . A l s o the c o n t r i b u t i o n s of these i n t e g r a l s f o r small v a l u e s o f H where A G i s s u b s t a n t i a l l y n e g a t i v e , a r e e x t r e m e l y s m a l l compared t o the v a l u e o f t h e s e i n t e g r a l s (34). In o t h e r words, t h e c o n t r i b u t i o n s t o t h e s e i n t e g r a l s m a i n l y come from A G . a t l a r g e d i s t a n c e s o f s e p a r a t i o n , where A G . i s s t i l l n e g a t i v e b u t s m a l l i n magnitude. Thus the i n t e g r a t i o n s o f the above f u n c t i o n s from 0 t o oo o r 2L t o oo s h o u l d make v e r y i n s i g n i f icant difference. ( T h i s i s easy t o r a t i o n a l i z e c o n c e p t i o n a l l y i n terms o f the f a c t t h a t when two p a r t i c l e s a r e s e p a r a t e d by v e r y s m a l l d i s t a n c e s , t h e p r o b a b i l i t y o f c o l l i s i o n by d i f f u s i o n i n a g i v e n l e n g t h of time i s so h i g h t h a t the p r e s e n c e o f a l a r g e a t t r a c t i v e p o t e n t i a l r e a l l y does n o t enhance t h e p r o c e s s t o any e x t e n t . Whereas, f o r p a r t i c l e s s e p a r a t e d by l a r g e d i s t a n c e s t h e p r o b a b i l i t y o f c o l l i s i o n by d i f f u s i o n i n the same l e n g t h o f time i s much s m a l l e r t h a n i n the p r e v i o u s c a s e and hence any a t t r a c t i v e p o t e n t i a l , even i f s m a l l , enhances t h e p r o c e s s o f b r i n g i n g the two particles together.) Thus, a c c o r d i n g to the foregoing arguments, a

Q

A


10.

BAGCHi

Slow Flocculation

149

Therefore, W = 1 f o r s e c o n d a r y minimum f l o c c u l a t i o n a c c o r d i n g t o t h e p r e d i c t i o n s o f t h e Smoluchowski t h e o r y w i t h Fuchs' c o r r e c t i o n . I n terms o f t h e u n c o r r e c t e d Smoluchowski E q u a t i o n (2) such a p r e d i c t i o n i s e a s i e r t o s e e . I n t h e c a s e o f secondary minimum f l o c c u l a t i o n , the e q u i l i b r i u m d i s t a n c e o f s e p a r a t i o n a t c o n t a c t i s a t H = 2L. T h e r e f o r e , one c a n say t h a t t h e e f f e c t i v e r a d i i o f t h e p a r t i c l e s a r e R+L r a t h e r t h a n R i n such a case. A c c o r d i n g t o E q u a t i o n ( 2 ) , k i s independent o f R, which i n d i c a t e s t h a t such secondary minimum f l o c c u l a t i o n r a t e s s h o u l d be independent o f t h e p o s i t i o n o f the secondary minimum. The above d e d u c t i o n u s i n g Smoluchowski t h e o r y i s , however, n o t c o n s i s t e n t w i t h e x p e r i m e n t a l o b s e r v a t i o n s of s e c o n d a r y minimum f l o c c u l a t i o n . F r e n s and Overbeek (35-37) have o b s e r v e d i n c o l l o i d a l s i l v e r s o l s t h a t v a r i o u s degrees o f r e v e r s i b l e i n s t a b i l i t y a r e produced at various e l e c t r o l y t e concentrations. They have con c l u d e d t h a t such v a r i e d d e g r e e s o f i n s t a b i l i t y can be a t t r i b u t e d t o f l o c c u l a t i o n a t t h e secondary minima o f v a r i o u s depths. In n o n i o n i c s t a b i l i z a t i o n , the s t a b i l i t y o f A g i d i s p e r s i o n s i n water and i n t h e p r e s e n c e of p o l y ( v i n y l a l c o h o l ) [ i n v e s t i g a t e d by F l e e r e t a l . ( 3 £ , 3 9 Π and p o l y ( s t y r e n e ) (PS) l a t e x d i s p e r s i o n s s t a b i l i z e d by n - d o d e c y l h e x a o x y e t h y l e n e monomer (C-ioEg) i n water i n v e s t i g a t e d by O t t e w i l l and Walker (15) was i n t e r p r e t e d by B a g c h i (19,21) i n terms o f t h e depths o f the secondary minima. The b a s i c argument o f H e s s e l i n k , V r i j , and Overbeek (IB) i n such an i n t e r p r e t a t i o n i s t h a t i f t h e d e p t h o f t h e s e c o n d a r y minimum i s 1 kT o r l e s s , s u s p e n s i o n s would be i n f i n i t e l y s t a b l e as an energy o f 1 kT i s a v a i l a b l e t o a p a r t i c l e i n d i f f u s i o n a l motion. I n systems where t h e d e p t h o f t h e s e c o n d a r y minimum i s 5 kT o r l a r g e r , s u s p e n s i o n s would be Q

Q

The average k i n e t i c energy o f a p a r t i c l e a c c o r d i n g t o s t r i c t s t a t i s t i c a l t h e o r y i s 3/2 kT r a t h e r than 1 kT, as f r e q u e n t l y used i n an approximate sense and as used i n t h i s paper. As t h e u s e o f 3/2 kT i n p l a c e o f 1 kT would make o n l y v e r y minor d i f f e r e n c e s i n t h e computed r e s u l t s p r e s e n t e d i n t h i s paper, 1 kT would be used as the average k i n e t i c energy o f a p a r t i c l e .


150


BEHAVIOR

t o t a l l y u n s t a b l e as 5 kT i s about t h e maximum energy t h a t may be i m p a r t e d t o a p a r t i c l e owing t o t h e r m a l motions o r by s h a k i n g . C o n s e q u e n t l y , i f t h e d e p t h o f t h e secondary minimum i s l a r g e r than 5 kT, f a s t aggre g a t i o n would t a k e p l a c e g i v i n g r i s e t o a s i t u a t i o n which i s k i n e t i c a l l y s i m i l a r t o p r i m a r y minimum f a s t c o a g u l a t i o n . ^However, i f t h e d e p t h o f t h e secondary minimum, |ΔΘ^"| , i s between 1 and 5 kT, slow f l o c c u l a t i o n would o c c u r as o b s e r v e d e a r l i e r (4,16,17). I t s h o u l d always be remembered t h a t t h e v a l u e o f |AG | = 1 kT between s t a b l e and r e d i s p e r s i b l e systems i s a thermodynamic q u a n t i t y whereas t h e v a l u e o f | àG^. | = 5 kT f o r t h e boundary between r e d i s p e r s i b l e and uns t a b l e systems, i s an approximate p h y s i c a l e s t i m a t e (18). The v a l i d i t y t h e secondary minim b i l i t y o f n o n i o n i c s t a b i l i z a t i o n i s a g a i n i n d i c a t e d by t h e r e c e n t work o f Long e t a l . (4£) i n which they have shown q u a l i t a t i v e l y t h a t t h e weak f l o c c u l a t i o n o f l a t e x p a r t i c l e s i s d e t e r m i n e d by t h e depths o f such secondary minima. The r a t h e r l e n g t h y i n t r o d u c t i o n o f t h i s paper was meant f o r p o i n t i n g o u t t h e f o l l o w i n g two f a c t s : 1. The importance o f t h e secondary minimum i n s u s p e n s i o n s t a b i l i t y , e s p e c i a l l y i n t h e c a s e o f nonionic stabilization. 2. The Smoluchowski t h e o r y o r Smoluchowski t h e o r y w i t h Fuchs' c o r r e c t i o n i s i n c a p a b l e o f p r e d i c t i n g t h e r a t e o f slow f l o c c u l a t i o n a t t h e secondary minimum. Thus, i n t h i s paper a t h e o r y i s d e v e l o p e d f o r t h e p r e d i c t i o n o f t h e slow f l o c c u l a t i o n r a t e a t t h e s e c o n d a r y minimum i n l i g h t o f t h e e x p e r i m e n t a l work o f O t t e w i l l e t a l . (15). W

Theory The p r i m a r y r e a s o n why Smoluchowski t h e o r y does n o t work i n t h e c a s e o f secondary minimum f l o c c u l a t i o n i s because o f i t s b a s i c assumption t h a t a l l c o l l i s i o n s l e a d t o permanent c o n t a c t . As t h e secondary minimum i s n o t i n f i n i t e l y deep, such an assumption f o r t h e f l o c c u l a t i o n a t t h e secondary minimum i s i n c o r r e c t . Also i n t h e c a s e o f Fuchs' t h e o r y , i t i s c o n s i d e r e d t h a t a g g r e g a t i o n n e c e s s a r i l y means c o n t a c t between t h e p a r t i c l e s u r f a c e s , whereas s e c o n d a r y minimum f l o c c u l a t i o n imp l i e s t r a p p i n g o f two p a r t i c l e s a t t h e secondary m i n i mum, which o c c u r s a t d i s t a n c e s o f s e p a r a t i o n l a r g e r than the p o i n t o f p a r t i c l e - p a r t i c l e contact.


10.

BAGCHi

Slow Flocculation

151

F i g u r e 1 shows a t y p i c a l c u r v e o f t o t a l p o t e n t i a l as a f u n c t i o n o f H ~ , the minimum d i s t a n c e o f s e p a r a t i o n o f the p a r t i c l e s u r f a c e s , w i t h a secondary minimum a t H = 2 L . In t h i s f i g u r e the depth o f the secondary minimum i s d e s i g n a t e d as | A G | / k T . The average energy o f d i f f u s i o n i s 1 kT w i t h a a i s t r i b u t i o n o f e n e r g i e s v a r y i n g from z e r o t o i n f i n i t y a c c o r d i n g t o the Boltzmann d i s t r i b u t i o n o f e n e r g i e s . Thus the e n e r g i e s o f a l l b i m o l e c u l a r c o l l i s i o n s a r e a l s o g i v e n by a Boltzmann d i s t r i b u t i o n o f e n e r g i e s as f o l l o w s ( £ 1 ) : Q

w

df =

exp

(-E/kT)

dE ,

(8)

where d f i s the f r a c t i o n o f c o l l i s i o n s w i t h energy E . Thus, i n a c o l l i s i o d e p t h | A G I , i f the ( | Â G | / k T j - 1 , the p a r t i c l e s w i l l bounce back and no attachment w i l l take p l a c e . An energy o f 1 kT i s s u b t r a c t e d from ( A G - J / k T because an energy o f 1 kT i s a v a i l a b l e to a p a r t i c l e i n t r a n s l a t i o n a l or d i f f u s i o n a l motion. A l s o i f | A G . J = 1 kT and c o l l i s i o n s t a k e p l a c e w i t h an energy Ε l e s s than 1 k T , the p a r t i c l e s w i l l not s t i c k t o g e t h e r because r o t a t i o n a l o r t r a n s l a t i o n a l d i f f u s i o n energy a v a i l a b l e t o such p a r t i c l e s w i l l p u l l them a p a r t . I f the c o l l i s i o n e n e r g y , E , i s l e s s than ( | A G | / k T ) - l , permanent c o n t a c t w i l l t a k e p l a c e . Hence t h e f r a c t i o n s o f c o l l i s i o n s , A f , w i t h energy l e s s than ( | A G - J / k T ) - l l e a d i n g t o permanent c o n t a c t w i l l be g i v e n by the f o l l o w i n g i n t e g r a l , W

W

w

à

f

=

kl f

e

where Ë = ( | A G | / k T ) - l w

x

p

("~E/kT) dE ,

(9)

f o r | A G | £ l kT and W

Ε = 0 f o r I A G U l kT w

Hence, G

A f = 1 - exp

l* wl

(1 - i - j g ^ ) .

(10)

I t i s i m p o r t a n t t o note t h a t i n the c a s e o f d i f f u s i o n c o n t r o l l e d b i m o l e c u l a r r e a c t i o n r a t e s one c o n s i d e r s the overcoming o f a p o t e n t i a l b a r r i e r i n o r d e r t o make permanent c o n t a c t . C o n s e q u e n t l y , one has t o c o n s i d e r o n l y t h o s e c o l l i s i o n s w i t h energy l a r g e r than the v a l u e o f t h e p o t e n t i a l maximum f o r r e a c t i o n t o take p l a c e . In such a c a s e the i n t e g r a t i o n o f E q u a t i o n (9) i s c a r r i e d o u t from 0 t o t h e v a l u e o f the p o t e n t i a l b a r r i e r (or t h e a c t i v a t i o n e n e r g y ) . However, i n the c a s e


152


BEHAVIOR

o f secondary minimum f l o c c u l a t i o n , the c o l l i d i n g p a r t i c l e s a r e t r a p p e d i n a p o t e n t i a l t r o u g h , i n which c a s e i n t e £ r a t i o n o f E q u a t i o n (9) i s c a r r i e d o u t between 0 and E . The b i m o l e c u l a r f l o c c u l a t i o n r a t e i s g i v e n by t h e general equation, -

af -

k

s'

(

Δ

£

)

*

2

*

3 where ψ i s the number o f p a r t i c l e s p e r cm , t i s t i m e , and k i s t h e c o l l i s i o n f r e q u e n c y g i v e n i n t h e most r i g o r o u s form by t h e Smoluchowski e q u a t i o n w i t h F u c h s ' c o r r e c t i o n f o r the secondary minimum by E q u a t i o n ( 5 ) . Since AG., i s constan w r i t e the f l o c c u l a t i o secondary minimum as f o l l o w s (42): g

(12) The r a t e c o n s t a n t f o r the c o a g u l a t i o n o f the u n p r o t e c t e d p a r t i c l e s w i l l be g i v e n by E q u a t i o n (3) as i n such a c a s e a g g r e g a t i o n t a k e s p l a c e i n t h e p r i m a r y minima. So t h e e x p e r i m e n t a l s t a b i l i t y r a t i o , as d e f i n e d p r e v i o u s l y , i n t h e c a s e o f secondary minimum f l o c c u l a t i o n would be g i v e n by W as: p Y P

P l e a s e n o t e t h a t i n E q u a t i o n (13) the e f f e c t o f t h e hydrodynamic d r a g on t h e c l o s e approach o f the two p a r t i c l e s , f o r m u l a t e d by Spielman (53) and Honig e t a l . (54) and r e c e n t l y e x p e r i m e n t a l l y s u b s t a n t i a t e d by H a t t o n e t a l . (55), has been n e g l e c t e d . The r e a s o n behind t h i s i s t h a t the c o r r e c t i o n f a c t o r s f o r R = 30 nm and R = 30 + δ nm ( w h e r e δ ~ 0 — 5 nm) a r e not t o o d i f f e r e n t from each o t h e r such t h a t i n the c a l c u l a t i o n o f W p , which i n v o l v e s the l o g o f the r a t i o s o f t h e two c o r r e c t i o n f a c t o r s , c o n t r i b u t e i n s i g n i f i c a n t l y to the value of l o g W _ , c a l c u l a t e d n e g l e c t i n g the hydrodynamic d r a g e f f e c t T 5 6 ) . E X

p x


10.

BAGCHi

Slow Flocculation

153

AG (H ) r oo 2R / exp kt ^2L L i

W. EXP

p A G

r

2R J

A

e x

( H

0

o

l-exp(l

(2R+H ) Q

dH, (2R+H )'

P[-kT-

Q

r

dH,

0

(13)

I AG. Wi kT

Since the approximation i n d i c a t e d i n Equation s t i l l v a l i d , one g e t s

W. EXP exp(l

-

(7)

is

(14)

J3ç w kT

E q u a t i o n (14) i n d i c a t e s t h a t the r a t e o f f l o c c u l a t i o n i s s o l e l y d e t e r m i n e d by the d e p t h o f the s e c o n d a r y minimum, IAGÎ. I t i s o b s e r v e d by i n s p e c t i o n o f E q u a t i o n (14) t h a t as | AG-J g e t s l a r g e r W approaches 1; t h a t i s , f o r a deep secondary minimum f l o c c u l a t i o n r a t e approaches the Smoluchowski r a t e o r the f a s t f l o c c u l a t i o n s i t u a t i o n . χ

C a l c u l a t i o n s and

ρ

Results

F i g u r e 2 shows a p l o t o f W „ as a f u n c t i o n o f AG c a l c u l a t e d using Equation ( i f ; . I t i s observed t h a t f o r A G = -1 kT, W = oo. As A G d e c r e a s e s , EXP ^ s e s and becomes one a t a v a l u e o f AG., o f aêout -5.5 kT, i n comparison w i t h the t o t a l i n s t a b i l i t y l i m i t o f 5 kT as e s t i m a t e d by H e s s e l i n k , V r i j , and Overbeek (18). I t has been p o i n t e d o u t p r e v i o u s l y t h a t the s t a b i l i t y l i m i t s o f PS l a t e x d i s p e r s i o n s i n water and i n the p r e s e n c e o f C E as i n v e s t i g a t e d by O t t e w i l l and Walker (16) can be r e a s o n a b l y w e l l i n t e r p r e t e d i n terms o f the d e p t h s o f the s e c o n d a r y minima (21) . Total s t a b i l i t y i n the s c a l e o f time means a s t a b i l i t y r a t i o o f i n f i n i t y and t o t a l i n s t a b i l i t y i n the s c a l e o f time means a s t a b i l i t y r a t i o o f u n i t y . For c o n d i t i o n s i n t e r m e d i a t e between t h e s e two l i m i t s , slow f l o c c u l a t i o n was o b s e r v e d f o r t h e PS-LatexC,-Eg-water system by O t t e w i l l and Walker (15) . The s t a b i l i t y r a t i o s as x p

W

W

W

χ

ρ

W

e c r e a

1 2

g


154

C O L L O I D A L DISPERSIONS A N D M I C E L L A E

ondary minimum

Secondary Minimum

£-5 -

-2

-3

-4

-5

-6

-7

-8

-9

-10

-II

Depth of the secondary minimum in kT (AG ) W

Figure 2.

Plot of W XP as a function of AG according to Equation (14) E

W


BEHAVIOR

10.

BAGCHi

Slow Flocculation

155

measured by them f o r t h i s system i n the p r e s e n c e o f e l e c t r o l y t e beyond the c r i t i c a l f l o c c u l a t i o n concen t r a t i o n was p r e v i o u s l y (21) termed as t h e l i m i t i n g s t a bility ratio. These e x p e r i m e n t a l s t a b i l i t y r a t i o s a r e d i r e c t l y comparable t o the t h e o r e t i c a l v a l u e s p r e d i c t e d by E q u a t i o n (14) s i n c e such e x p e r i m e n t a l v a l u e s c o r r e spond t o the s t a b i l i t y due t o the n o n i o n i c s t a b i l i z e r , which a r e known t o g i v e r i s e t o o n l y s e c o n d a r y minima. I t i s a d v i s e d t h a t the r e a d e r examine r e f e r e n c e (21_) i n o r d e r t o u n d e r s t a n d the a p p l i c a b i l i t y o f E q u a t i o n (14) t o t h e d a t a d e r i v e d i n r e f e r e n c e (21) from t h e paper o f O t t e w i l l and Walker (15) . T a b l e I l i s t s the v a l u e s o f the a d s o r p t i o n l a y e r t h i c k n e s s e s of C 6 Latex (radius =30 nm), the depths o f the secondary minima as c a l c u l a t e d by B a g c h i (21), t h e e x p e r i m e n t a l limiting s t a b i l i t y r a t i o s as (15), and t h e t h e o r e t i c a l l y c a l c u l a t e d v a l u e s o f t h e s t a b i l i t y r a t i o s from t h e v a l u e s o f |AG-J using E q u a t i o n (14) a t v a r i o u s l o g molar e q u i l i b r i u m concen t r a t i o n s of C , c Latex-C-. 6 ~ system i n v e s t i g a t e d by O t t e w i l l and Walker TI5;. In t h i s c a l c u l a t i o n the Hamaker c o n s t a n t used f o r the PS L a t e x water system was 5 χ 1 0 ~ e r g as used by O t t e w i l l and Walker (15). F i g u r e 3 shows a d i r e c t comparison o f t h e experimental W t o the t h e o r e t i c a l l y c a l c u l a t e d W as a f u n c t i o n or the l o g molar e q u i l i b r i u m c o n c e n t r a tions of C E . The e r r o r l i m i t s i n T a b l e I and F i g u r e 3 c o r r e s p o n d t o an e r r o r o f +1 nm i n the d e t e r m i n a t i o n o f t h e a d s o r p t i o n l a y e r t h i c k n e s s as i n d i c a t e d by O t t e w i l l and Walker ( L 5 ) . E

o

n

t

e

p

s

1 2

E

f

o

r

t

n

e

p

2

s

E

w

a

r

2

1 4

p

1 2

p

6

F i g u r e 5 shows the p a r t i c l e s i z e dependence o f the s t a b i l i t y r a t i o o f PS l a t e x d i s p e r s i o n s as a f u n c t i o n of the e q u i l i b r i u m c o n c e n t r a t i o n of j 2 6 The v a l u e s o f W_ i n F i g u r e 5 were c a l c u l a t e d f o r p a r t i c l e r a d i i r a n g i n g between 10 and 480 nm w i t h a q u i t e l e g i t i m a t e assumption t h a t the a d s o r p t i o n l a y e r t h i c k n e s s e s o f CjoE/: as a f u n c t i o n o f i t s e q u i l i b r i u m c o n c e n t r a t i o n a r e i d e n t i c a l f o r PS l a t i c e s o f a l l sizes. c

E

e

xp

Discussions The agreement o b s e r v e d i n F i g u r e 3 between t h e e x p e r i m e n t a l l i m i t i n g s t a b i l i t y r a t i o and t h e o r e t i c a l l y c a l c u l a t e d s t a b i l i t y r a t i o using Equation (14) can be c o n s i d e r e d t o be r a t h e r good c o n s i d e r i n g the u n c e r t a i n t i e s i n v o l v e d i n the e s t i m a t i o n o f t h e Hamaker c o n s t a n t used i n r e f e r e n c e (21) t o c a l c u l a t e the v a l u e s o f IAG | . As p o i n t e d o u t p r e v i o u s l y , the t h e o r e t i c a l v a l u e o f W^^ i s s o l e l y dependent upon the



c

a

•5.7 •5.5 •5.2 •4.6

-5.3 -4.8 -4.4 -3.9 -3.5 -3.1

E

12 6

0( 0— 0.8( 0— 2.8(1.8— 8.0(7.0— 8.6(7.69.2(8.2—

15.

erg.

U s i n g E q u a t i o n (14)

5 χ 10~

1 3

W

-3.13(- « -0.66(-1.18— -0.13(-0.16— -0.1K-0.14— -0.10(-0.12-

*

0 0 1.4

Q

3

W

3

1.2

0 (0 0.06(0 — oo (0.77— 00 00 00

(1 - | AG / k T | ) = 0 f o r G / k T < l .

c

0.12) 0.80) 00 )

W

the c o r r e s p o n d i n g values of | A G |

E X p

System

Theoretical log W using

g

used f o r t h e PS L a t e x - w a t e r system

-2.42) -1.18) -0.43) -0.10) -0.09) -0.08)

l

EXP FlocDepths o f t h e Floccula- culasecondary minima, t e d by t e d by AG , in k r La(N0 ) HNO-

Hamaker c o n s t a n t

and t a k i n g

21.

1.0) 1.8) 3.8) 9.0) 9.6) 10.2)

Calculated i n reference

T a k e n from r e f e r e n c e

d

Twice the adsorp tion layer thicknessesj 2L i n nm

Experimental

2

V a l u e s o f 2 L , A G . . , and S t a b i l i t y R a t i o s f o r t h e PS L a t e x - C , E - W a t e r a t V a r i o u s Log M o l a r C o n c e n t r a t i o n s o f C ,

Log molar equilibrium concentra tions of

T a b l e 1.

10.

BAGCHi

Slow Flocculation

157

v a l u e o f | A G - J [ E q u a t i o n ( 1 4 ) ] . Hence, the a c c u r a c y w i t h which p r e d i c t i o n s can be made u s i n g E q u a t i o n (14) w i l l depend e n t i r e l y on t h e a c c u r a c y w i t h which t h e depths o f t h e secondary minima can be c a l c u l a t e d . S i n c e the o b j e c t i v e o f t h i s paper i s b a s i c a l l y t o d e v e l o p the t h e o r y and t o p r e d i c t t h e o b s e r v e d t r e n d , no e x t e n s i v e e f f o r t was made on an a c c u r a t e e s t i m a t i o n o f t h e Hamaker c o n s t a n t . Nor was the V o i d e f f e c t (43) , whose importance i n e s t i m a t i n g t h e l o n g - r a n g e i n t e r a c t i o n s has been shown r e c e n t l y (44-46), c o n s i d e r e d i n the c a l c u l a t i o n o f t h e vw a t t r a c t i o n f o r t h e PS L a t e x 12 6~ system. However, i t was shown p r e v i o u s l y (21) t h a t t h e i n c l u s i o n o f the V o i d e f f e c t t o c a l c u l a t e the vw a t t r a c t i o n i s w e l l w i t h i n t h e e r r o r o f e s t i m a t i o n o f the Hamaker c o n s t a n t f o r the PS L a t e x - w a t e r system. I t i s e x t r e m e l y i n t e r e s t i n g t o note t h a t t h e l i m i t s of s t a b i l i t y (W = 1 for unstable-redispersib l e and ^ = oo f o r r e a i s p e r s i b l e - s t a b l e ) a r e i n e x c e l l e n t agreement w i t h the t h e o r e t i c a l p r e d i c t i o n s as o b s e r v e d i n F i g u r e 3. T h i s i s t r u e f o r the f o l l o w i n g reasons. In t h e s t a b i l i t y l i m i t o f W = «> f o r s t a b l e d i s p e r s i o n s t h e e q u i l i b r i u m v a l u e o f ÈJ[=2L) i s large. I t i s w e l l known (21_) t h a t the vw a t t r a c t i o n s a t l a r g e d i s t a n c e s a r e much b e t t e r r e p r e s e n t e d by c o n v e n t i o n a l t h e o r i e s than a t s m a l l e r d i s t a n c e s of s e p a r a t i o n . Also a t t h e l i m i t o f i n s t a b i l i t y and r e d i s p e r s i b i l i t y (W = 1) where | A G . J i s about 5 kT, t h e r a t e o f dec r e a s e o f t h e vw a t t r a c t i o n i s so sharp compared t o t h a t f o r l a r g e r d i s t a n c e s o f s e p a r a t i o n (H ) t h a t the e r r o r i n t h e v a l u e o f 2L has v e r y l i t t l e e r f e c t on W ; as f o r | â G - J l a r g e r than 5 kT, W i s essent i a l l y e q u a l t o u n i t y ( F i g u r e 2 ) . Thus f o r a r e d i s p e r s i b l e system where | A G . J i s between 5 kT and 1 kT, a more q u a n t i t a t i v e agreement between E q u a t i o n (14) and e x p e r i m e n t a l r e s u l t s may be o b s e r v e d o n l y i f a more a c c u r a t e e s t i m a t i o n o f the vw a t t r a c t i o n can be made. The P a r s e g i a n and Ninham (48) t y p e o f c a l c u l a t i o n s h o u l d be p a r t i c u l a r l y u s e f u l f o r such e s t i m a t i o n s . I t i s i n t e r e s t i n g t o note t h a t i f a v a l u e o f 2.3 χ 1 0 ~ e r g i s used f o r t h e Hamaker c o n s t a n t o f t h e PS L a t e x water system (shown i n F i g u r e 4) a much b e t t e r f i t o f the theory with the experimental r e s u l t s i s observed. However, t h i s . d o e s n o t , i n any way, mean t h a t the v a l u e o f 2.3 χ 10 f o r t h e Hamaker c o n s t a n t i s any b e t t e r than t h e v a l u e o f 5 χ 1 0 ~ e r g as used by O t t e w i l l and Walker (15). In F i g u r e 5, i t i s i n t e r e s t i n g t o note the t h e o r e t i c a l p r e d i c t i o n s o f the p a r t i c l e s i z e dependence o f t h e s t a b i l i t y r a t i o o f t h e PS l a t e x d i s p e r s i o n s as a f u n c t i o n of the e q u i l i b r i u m c o n c e n t r a t i o n of C, E . It C

E

w a t e r

E X p

Ε

χ

ρ

χ

ρ

E

Q

1 4

1 4

?


fi

158

COLLOIDAL

DISPERSIONS

A N DM I C E L L A R

BEHAVIOR

I**- Present Theory

Experimental values of limiting log W

EXP

x Flocculated by La(N0 ) Ο Flocculated by HN0 3

3

Ι ι Theoretically calculated ^ valves of log W^p

Figure 3.

Comparison of the experimen

and Walker with the theoretical values of the stability ratio calculated using Equation (14) and the values of \AG \ from Table I as a function of the log molar equilibrium concentration of C E . The error bars correspond to an error of ±1 nm in the values of the adsorption layer thicknesses. Hamaker constant used for the calculation of \AG \ is 5 X 10r erg as used by Ottewill and Walker. Particle radius = 30 nm. W

i2

Smoluchowski Theory and / Smoluchowski Theory with Fuchs Correction

6

u

W

-5

-4

-3

Log molar equilibrium concentration of C, Eg 2

Present theory

4

Experimental values of limiting log W

EXP

x Flocculated by La(N0 ) Ο Flocculated by HN0 3

3

ι Theoretically calculated valves of log W EXP

Smoluchowski Theory and / Smoluchowski Theory with Fuchs Correction -6

-5

-4

-3

Log molar equilibrium concentration of C E )2

Figure 4. Same plot as Figure 3 except the Hamaker constant used for these cal culations of \AG \ is 2.3 χ 10 erg 14

6

W


10.

BAGCHi

159

Slow Flocculation

Log molar equilibrium concentration of C | E 2

6

Figure 5. Size dependence of the stability ratio of dispersions of PS latex in water as a function of the equilibrium concentration of


160

COLLOIDAL DISPERSIONS AND

MICELLAR BEHAVIOR

i s observed t h a t f o r p a r t i c l e s of r a d i i l e s s than 1 2 0 nm one i s a b l e t o v a r y the s t a b i l i t y r a t i o between 0 and oo as a f u n c t i o n o f C, r a d s o r p t i o n such t h a t | A G | ranges between 5 . 5 ana I kT. However, f o r p a r t i c l e s o f r a d i i l a r g e r t h a n 1 2 0 nm, the depths o f the secondary minima a t s a t u r a t i o n a r e between 5 . 5 and 1 kT. C o n s e q u e n t l y i n such c a s e s , a f t e r s a t u r a t i o n , one has d i s p e r s i o n s w h i c h f l o c c u l a t e a t c o n s t a n t r a t e s s l o w e r t h a n the Smoluchowski r a t e and never r e a c h com plete s t a b i l i t y . F o r p a r t i c l e s l a r g e r t h a n 4 8 0 nm the depths o f t h e s e c o n d a r y minima, even a t s a t u r a t i o n , are l a r g e r than 5 . 5 kT. Hence, under a l l c o n d i t i o n s such systems would undergo f a s t f l o c c u l a t i o n . So f a r the d i s c u s s i o n has been on the i n t e r p r e t a t i o n o f the p e r i k i n e t i t i o n u s i n g the d e p t h s o f such minima. Hiemenz and V o i d (49) have o b s e r v e d s i m u l t a n e o u s f l o c c u l a t i o n d e f l o c c u l a t i o n i n carbon black - p o l y ( s t y r e n e ) - t o l u e n e and c a r b o n b l a c k - p o l y ( s t y r e n e ) - c y c l o h e x a n e systems obeying the f o l l o w i n g k i n e t i c e q u a t i o n : E

2

w

- II

= kN

2

- 0N

,

(15)

where k i s the f l o c c u l a t i o n r a t e c o n s t a n t and β i s the d e f l o c c u l a t i o n rate constant. In l i g h t o f the p r e s e n t d i s c u s s i o n s , the q u e s t i o n i s whether one can equate k with k and i n t e r p r e t d e f l o c c u l a t i o n i n terms o f the unsuccessful c o l l i s i o n s . In t h e work o f Hiemenz and V o i d ( 1 0 , 2 3 ) the k i n e t i c u n i t s t h a t underwent f l o c c u l a t i o n and d e f l o c c u l a t i o n were l a r g e f l o e s o f r a d i u s above 2 0 0 t o 3 0 0 nm. F o r such l a r g e f l o e s i z e s , as has been p o i n t e d out p r e v i o u s l y , c o n d i t i o n s f o r o r t h o kinetic flocculation prevails. Thus the Smoluchowski c o l l i s i o n f r e q u e n c y as used i n the d e r i v a t i o n of E q u a t i o n (12) i s inapplicable. C o n s e q u e n t l y , f o r such l a r g e f l o e s t h e f l o c c u l a t i o n r a t e c o n s t a n t k may not be compared w i t h k . The f l o e s i n such systems a r e o f random s t r u c t u r e as t h e o r e t i c a l l y deduced by V o i d (50) and M e d a l l i a ( 5 1 , 5 2 ) and e l e c t r o n microscopically demonstrated f o r graphon s u s p e n s i o n s i n heptane by B a g c h i and V o i d ( 1 0 ) . The d e f l o c c u l a t i o n o f such l o o s e l y bound and randomly s t r u c t u r e d f l o e s i n t h i s system has been r i g h t l y i n t e r p r e t e d by Hiemenz and V o i d ( 2 4 , 4 9 ) t o be due t o s h e a r i n g i n t h e r m a l g r a d i ents. Thus such a d e f l o c c u l a t i o n p r o c e s s cannot be r a t i o n a l i z e d i n terms o f u n s u c c e s s f u l c o l l i s i o n s . How e v e r , the o b s e r v a t i o n t h a t such f l o e s d e f l o c c u l a t e i n t h e r m a l g r a d i e n t s perhaps i n d i c a t e s t h a t the b i n d i n g energy o f such f l o e s comes from a g g r e g a t i o n a t s e c o n d a r y minima o f depths l e s s t h a n 5 . 5 kT. g

g


10.

BAGCHi

Slow Flocculation

161

Acknowledgments The a u t h o r would l i k e t o g r a t e f u l l y acknowledge the t h o u g h t f u l comments o f P r o f e s s o r Egon M a t i j e v i c ' o f C l a r k s o n C o l l e g e o f T e c h n o l o g y , Potsdam, Ν. Υ . , on t h i s work. Thanks a r e a l s o g i v e n t o D r . G . J . Robersen o f the v a n ' t H o f f L a b o r a t o r i u m , U t r e c h t , f o r v e r y k i n d l y p r o v i d i n g the hydrodynamic d r a g c o r r e c t i o n s mentioned i n c o n n e c t i o n w i t h E q u a t i o n (13) and p o i n t i n g o u t an e r r o r i n E q u a t i o n (2). The a u t h o r would a l s o l i k e t o v e r y g r a t e f u l l y acknowledge the t h o u g h t f u l s u g g e s t i o n s o f P r o f e s s o r s R o b e r t D. and M a r j o r i e J . V o i d d u r i n g the p r e p a r a t i o n o f t h i s p a p e r . Summary I t i s w e l l known t h a t the i n s t a b i l i t y o f a s u s p e n s i o n can be due t o slow f l o c c u l a t i o n a t a secondary minimum i n the p a r t i c l e - p a r t i c l e p o t e n t i a l p r o f i l e , f o r b o t h i o n i c and n o n i o n i c s t a b i l i z a t i o n . In most c a s e s o f i o n i c s t a b i l i z a t i o n , the p o t e n t i a l b a r r i e r t o the p r i m a r y minimum i s n o t h i g h enough and c o n s e q u e n t l y one o b s e r v e s f a s t a g g r e g a t i o n a t t h e p r i m a r y minimum. However, i n the n o n i o n i c c a s e , where the d i s p e r s i o n medium i s a good s o l v e n t f o r the s t a b i l i z e r , c a l c u l a t i o n s i n d i c a t e t h a t u n s t a b l e systems always e x h i b i t a secondary minimum, which i s the p r i m a r y cause o f i n s t a bility. The measure o f such i n s t a b i l i t y i s t h e a g g r e gation rate. The Smoluchowski t h e o r y o f a g g r e g a t i o n i s n o t g e n e r a l l y v a l i d f o r secondary minimum f l o c c u l a t i o n , s i n c e i t makes the i m p l i c i t assumption t h a t e v e r y c o l l i s i o n l e a d s t o permanent c o n t a c t . Such an assumption i s c o r r e c t o n l y i n the c a s e o f p r i m a r y minimum c o a g u l a t i o n where the a t t r a c t i o n p o t e n t i a l , a t the p o i n t o f c o n t a c t , goes t o i n f i n i t y . Fuchs theory i s i n a p p l i c a b l e t o secondary minimum f l o c c u l a t i o n b e cause i t c o n s i d e r s o n l y t h o s e c o l l i s i o n s w i t h e n e r g i e s h i g h enough t o overcome the p o t e n t i a l b a r r i e r t o make c o n t a c t a t the p r i m a r y minimum as s u c c e s s f u l c o l l i sions. In t h e c a s e o f secondary minimum f l o c c u l a t i o n s , o n l y t h o s e c o l l i s i o n s w i t h e n e r g i e s l e s s t h a n the d e p t h o f the secondary minimum w i l l l e a d t o permanent c o n t a c t o r , i n o t h e r words, s u c c e s s f u l f l o c c u l a t i o n . On t h i s a s s u m p t i o n , a k i n e t i c t h e o r y f o r the secondary minimum f l o c c u l a t i o n i s d e v e l o p e d i n t h i s paper and a p p l i e d t o the p o l y ( s t y r e n e (PS) l a t e x - n - d o d e c y l h e x a o x y e t h y l e n e monomer ( Ο , - Ε ^ ) w a t e r system as i n v e s t i g a t e d by O t t w i l l and W a l k e r . Tne t h e o r e t i c a l l y p r e d i c t e d dependence o f the l i m i t i n g s t a b i l i t y r a t i o due t o the n o n i o n i c s u r f a c t a n t as a f u n c t i o n o f t h e e q u i l i b r i u m 1


162

COLLOIDAL DISPERSIONS AND MICELLAR BEHAVIOR

c o n c e n t r a t i o n o f C , E seems t o agree f a i r l y w e l l w i t h the e x p e r i m e n t a l o b s e r v a t i o n s o f O t t e w i l l and W a l k e r . 2

Literature 1.

2. 3. 4. 5. 6. Colloid 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

g

Cited

Verwey, E.J.W., and Overbeek, J. T h . G . "Theory o f the Stability o f Lyophobic Colloids," Elsevier, Amsterdam 1948. Overbeek, J. T h . G., in "Colloid S c i e n c e , " H . R. K r u y t , Ed., Vol. II, Elsevier, Amsterdam, 1952. F i s c h e r , E . W . , Kolloid Z., (1958) 160, 120. J a c k e l , K., Kolloid-Z. Z. P o l y m . , (1964) 197, 143. Mackor, E. L., J. Colloid Sci., (1951) 6, 942. Mackor, E. L., and van d e r W a a l s , T. H., J. Sci., (1952) 7, 535. Clayfield, E. J., I n t e r f a c e Sci., (1966) 22, 269, 285. Clayfield, E. J., and Lumb, E. C., Macromolecules, (1968) 1, 133. M e i e r , D. J., J. P h y s . Chem., (1969) 73, 3488. B a g c h i , P., and Vold, R. D., J. Colloid I n t e r f a c e Sci., (1970) 33, 405. B a g c h i , P., and V o l d , R. D., J. Colloid I n t e r f a c e Sci., (1972) 38, 652. Bagchi, P., J. Colloid Interface Sci., (1972) 41, 380. A s h , S. G., and F i n d e n e g g , G . H., T r a n s . F a r a d a y Soc., (1971) 62, 2122. Evans, R., and Napper, D. H., Kolloid-Z. Z. P o l y m . , (1973) 251, 329, 409. Ottewill, R. Η., and Walker, T., Kolloid-Z. Z. P o l y m . , (1968) 227, 108. H e s s e l i n k , F . Th., J. P h y s . Chem., (1969) 73, 3488. H e s s e l i n k , F . Th., J. P h y s . Chem., (1971) 75, 65. H e s s e l i n k , F . Th., Vrij, Α . , and Overbeek, J. T h . G., J. P h y s . Chem., (1971) 75, 2094. B a g c h i , P., J. Colloid I n t e r f a c e Sci., (1974) 47, 86. Bagchi, P., J. Colloid Interface Sci., (1974) 47, 100. B a g c h i , P., J. Colloid I n t e r f a c e Sci., i n p r e s s . D o r o s z k o w s k i , Α . , and Lambourne, R., J. Colloid I n t e r f a c e Sci., (1973) 43, 97. LaMer, V . K., J. Colloid Sci., (1964) 19, 291. Hiemenz, P . C . and V o l d , R. D., J. Colloid Sci., (1965) 20, 635. L e w i s , Κ. Ε., and Parfitt, G . D., T r a n s . Faraday Soc., (1967) 62, 1652.


10. 26. 27. 28. 29. 30. 31. 32. 33. 34.

35. 36. 37. 38.

39. 40. 41. 42.

43. 44. 45. 46.

BAGCHI

Slow Flocculation

163

O t t e w i l l , R. H., and Shaw, J. Ν . , D i s c . Faraday Soc., (1966) 42, 154. Smoluchowski, N . V o n , P h y s i k . Z., (1916) 17, 557, 585. Smoluchowski, N . V o n , Z . P h y s i k . Chem., (1917) 92, 129. van Arkel, A . E., and K r u y t , H . R., Rec. T r a v . C h i m . , (1920) 39, 656. O t t e w i l l , R. H., and Wilkins, D. J., T r a n s . Faraday S o c . , (1966) 62, 1652. Lawrence, S. Α., and Parfitt, G . D., J. Colloid I n t e r f a c e Sci., (1971) 35, 675. F u c h s , Ν . , Z . P h y s i k . , (1934) 89, 436. McGown, D. N . L., and Parfitt, G . D., J. P h y s . Chem., (1967) 71, 449. B a g c h i , P., P h Southern California, Los A n g e l e s , California, 1970. F r e n s , G., P h . D. Dissertation, University of U t r e c h t , The N e t h e r l a n d s , 1968. F r e n s , G . and Overbeek, J. T h . G., K o l l o i d - Z . Z . P o l y m . , (1969) 233, 922. F r e n s , G., and Overbeek, J. T h . G., J. Colloid I n t e r f a c e Sci., (1972) 38, 376. F l e e r , G . J., P h . D. Dissertation, Laboratory f o r P h y s i c a l and Colloid C h e m i s t r y , Agricultural University, Wageningen, The N e t h e r l a n d s , 1971. F l e e r , G . J., K o o p a l , L . Κ., and L y k l e m a , J., Kolloid-Z. Z. P o l y m . , (1972) 250, 689. L o n g , J. Α . , Osmond, D . W. J. and V i n c e n t , B., J. Colloid I n t e r f a c e Sci., (1973) 42, 545. Adamson, A . W . , "A Textbook o f P h y s i c a l Chem istry," Academic P r e s s , New Y o r k , 1973. S m i t h , A . L., D u r i n g his visit t o t h e Kodak Research L a b o r a t o r i e s (March 1974), P r o f . A . L. Smith o f t h e L i v e r p o o l C o l l e g e o f T e c h n o l o g y , E n g l a n d , has disclosed t o me t h a t a s i m i l a r e x p r e s s i o n has been i n d e p e n d e n t l y d e r i v e d by him and h i s c o w o r k e r s , F . W. McDowell (Ph.D. T h e s i s 1971) and W. Hatton (Ph.D. T h e s i s 1973). They might be p u b l i s h i n g their d e r i v a t i o n in t h e future. V o l d , M. J., J. Colloid Sci., (1961) 16, 1. Osmond, D.W.J., V i n c e n t , B., and W a i t e , F . Α., J. Colloid I n t e r f a c e Sci., (1973) 42, 262. V i n c e n t , B . J. Colloid I n t e r f a c e Sci., (1973) 42, 270. B e c h e r , P., J. Colloid I n t e r f a c e Sci., (1973) 42, 645.


164

47.

48. 49. 50. 51. 52. 53. 54. 55. 56.


BEHAVIOR

Padday, J. F., in " T h i n L i q u i d F i l m s and Boundary L a y e r s , " Spec. D i s c . Faraday Soc., Vol. I., p . 64, Academic P r e s s London, 1970. P a r s e g i a n , V . Α., and Ninham, B . W . , J. Colloid I n t e r f a c e Sci., (1966) 21, 470. Hiemenz, P . C., and V o l d , R. D., J. Colloid I n t e r f a c e Sci., (1966) 2 1 , 470. V o l d , M. J., J. Colloid Sci., (1963) 18, 684. M e d a l l i a , A . I., J. Colloid I n t e r f a c e Sci., (1967) 24, 393. M e d a l l i a , A . I., J. Colloid I n t e r f a c e Sci., (1970) 36, 115. S p i e l m a n , L. Α., J. Colloid I n t e r f a c e Sci., (1970) 33, 562. H o n i g , E. P., Robersen P . H., J. Colloid I n t e r f a c e Sci., (1971) 36, 97. H a t t o n , W . , McFadyen, P., and S m i t h , A . L., J. Chem. S o c . , F a r a d . T r a n s . I , (1974) 70, 655. R o b e r s e n , G . J. p e r s o n a l communications (1974).


11 Stability of Sterically Stabilized Dispersions at High Polymer Concentrations F. K. R. LI-IN-ON and B. VINCENT School of Chemistry, University of Bristol, Bristol BS8 ITS, England F. A. WAITE I.C.I. (Paints Div.) Ltd., Slough SL2 5DS, England Introduction The use of polymer stabilise colloidal dispersions against coagulation has been widely practised i n industry, and is of fundamental importance in many natural processes, both biological and environmenta1(1). At present there is a need for a wide range of experimental work in this f i e l d , on well characterised systems, in order to test the several models and theories of steric s t a b i l i s a t i o n . One can distinguish at least two classes of experimental approach. F i r s t l y , one may compare the s t a b i l i t y of the dispersion in the presence and absence of polymer (at a given concentration). Stability is perhaps best defined in this context in terms of the ratio of the rate constants for aggregation in the two cases. Secondly, one may observe under what conditions a s t e r i c a l l y stabilised dispersion w i l l aggregate. There are perhaps four basic requirements for a dispersion to be effectively stabilised by adsorbed or anchoredt polymer chains : a) high surface coverage, i . e . no "bare" patches at the surface b) strong adsorption c) a "thick" adsorbed layer, to prevent the particles coming within a separation where the van der Waals interaction becomes effective. d) the stabilising chains should be i n "good" solvent environment. Such requirements may be met by using AB block and AB comb structures ( 1 - 3 ) · Here the (insoluble) A chains are the adsorbing t by "adsorbed" we refer to the case where the stabiliser is physically adsorbed to the particle surface; by "anchored", where the stabiliser is chemically bonded to the surface, or even (partially) incorporated into the bulk structure of the p a r t i c l e . n

165


166


BEHAVIOR

(anchoring) component and serve to f u l f i l conditions (a) and (b) above, w h i l s t the (soluble) Β chains provide the a c t u a l s t e r i c b a r r i e r , f u l f i l l i n g conditions (c) and ( d ) . In p r i n c i p l e , a s t e r i c a l l y s t a b i l i s e d d i s p e r s i o n can be aggregated by a d j u s t i n g conditions such that one o r more of the p r e - r e q u i s i t e s (a) - (d) i s no longer met. Examples f o r each one are as f o l l o w s : a) at low surface coverages b r i d g i n g , f l o c c u l a t i o n may o c c u r . (In some cases polymer may be d i s p l a c e d l a t e r a l l y to create bare s p o t s ) . b) weakly adsorbed polymers, e . g . horaopolymers, may be d i s placed e n t i r e l y from the p a r t i c l e surface by s m a l l e r molecules, e . g . i o n i c s u r f a c t a n t s , which are themselves more s t r o n g l y adsorbed but which do not themselves provide adequate s t e r i c s t a b i l i s a t i o n . c) the thickness of th determining the dept p a r t i c l e - p a r t i c l e i n t e r a c t i o n c u r v e . I t has been shown by Long, Osmond and Vincent (4) that a c r i t i c a l depth f o r t h i s p o t e n t i a l energy minimum e x i s t s , f o r a given p a r t i c l e number c o n c e n t r a t i o n , at and beyond which aggregation begins to o c c u r . Thus s u b t l e changes i n the thickness of the s t e r i c b a r r i e r , e . g . by changes i n molecular weight or solvency, can change a system from being s t a b l e to being (weakly) aggregated. d) i n a s e r i e s of papers (5-6) Napper has shown that by changing the solvency conditions f o r the s t a b i l i s i n g Β chains from a good solvent environment to a Θ - or near θ - s o l v e n t , l a t e x d i s p e r s i o n s s t a b i l i s e d by AB block copolymers may be aggregated. In a l l the systems s t u d i e d to date, as f a r as we are aware, the e f f e c t of the c o n c e n t r a t i o n of polymer i n the continuous phase on d i s p e r s i o n s t a b i l i t y has not been c o n s i d e r e d . Indeed i n most systems, the bulk polymer concentration i s n e g l i g i b l y s m a l l . However, t h i s i s a s i g n i f i c a n t point to consider i n many p r a c t i c a l d i s p e r s i o n s , e . g . i n drying l a t e x paint films where the concentration of polymer i n the continuous phase o b v i o u s l y must reach a high value as solvent evaporates. In t h i s work we set out to i n v e s t i g a t e whether high con c e n t r a t i o n s of homopolymer Β i n the continuous phase (approaching 100% polymer i n f a c t ) l e d to changes i n the s t a b i l i t y of d i s p e r s i o n s s t a b i l i s e d by AB comb polymers. The s p e c i f i c system i n v e s t i g a t e d was an aqueous polystyrene (PS) l a t e x , plus a comb s t a b i l i s e r with A • PS, Β » poly(ethylene oxide) (PEO), molecular weight 750, to which was added homopolymer PEO, of v a r i o u s , r e l a t i v e l y low molecular weights (200-4000), over a wide concentration range. Above a c e r t a i n c r i t i c a l PEO c o n c e n t r a t i o n , for a given molecular weight, i t was found that aggregation o c c u r r e d . We present a p r e l i m i n a r y report of the r e s u l t s obtained. I t i s intended that a more d e t a i l e d report and d i s c u s s i o n of other r e s u l t s w i l l be p u b l i s h e d s h o r t l y .


11.

LI-IN-ON E T A L .

167

Sterically Stabilized Dispersions

Experimental Materials. A l l solvents and monomers were r e d i s t i l l e d before use. The polyethylene oxides used were the polyethylene g l y c o l s e r i e s 200, 400, 600, 1000, 1500, 4000, ex B r i t i s h Drug House, plus polyethylene g l y c o l 800 ex S h e l l Chemicals L t d . Carbowax 750 was obtained from Union Carbide L t d . These m a t e r i a l s were used without f u r t h e r p u r i f i c a t i o n . Latex D i s p e r s i o n s . The polystyrene l a t e x used was prepared by a method which i s c u r r e n t l y the subject of a patent a p p l i c a t i o n by I . C . I . (Paints D i v i s i o n ) L t d . Nevertheless i t can be s t a t e d here that a free r a d i c a l p o l y m e r i s a t i o n route was used, and t h i s gave a polystyrene l a t e x d i s p e r s i o n , the p a r t i c l e s of which were s t a b i l i s e d b styrene backbone i s p h y s i c a l l the polystyrene p a r t i c l e s . The methoxy-terminated poly(ethylene oxide) (M.W. 750) chains are therefore t e r m i n a l l y anchored at the surface. C h a r a c t e r i s a t i o n of the L a t e x . The mean p a r t i c l e diameter of the l a t e x from e l e c t r o n microscopy was 140 nm. Although not as monodisperse as some of the c h a r g e - s t a b i l i s e d polystyrene l a t i c e s that have been prepared i n the absence of added s u r f a c t a n t s or polymers (7), we do not consider t h i s to be a s i g n i f i c a n t feature i n i n t e r p r e t i n g the r e s u l t s of the experiments we r e p o r t . M i c r o e l e c t r o p h o r e s i s and conductimetrie t i t r a t i o n i n d i c a t e d that the p a r t i c l e s c a r r i e d only a very small surface charge. The c a l c u l a t e d zeta p o t e n t i a l i n 10~ KC1, using the t a b l e s of O t t e w i l l and Shaw (8), was less than 15 mV, i . e . not s u f f i c i e n t to p l a y any s i g n i f i c a n t r o l e i n determining the s t a b i l i t y of the particles. 3

Flocculation. F l o c c u l a t i o n k i n e t i c s were followed using a conventional t u r b i d i m e t r i c technique (9-10), i n which the o p t i c a l density (OD) of the l a t e x was recorded continuously as a f u n c t i o n of time on the a d d i t i o n of a known amount of polymer s o l u t i o n . A Unicam SP 1800 spectrophotometer l i n k e d to a Unicam AR 25 pen recorder was used f o r t h i s purpose. A wavelength of 540 nm was used, and the c e l l - h o u s i n g of the spectrophotometer was thermos t a t t e d at 2 5 ° C . The i n i t i a l number concentration of the p a r t i c l e s Ν , was kept f i x e d at 3.5 χ Ι Ο p a r t i c l e s per ml (corresponding to a p a r t i c l e volume f r a c t i o n of 4 χ 10" *) f o r a l l the runs · Oster (11) has shown that f o r an aggregation d i s p e r s i o n i n which the p a r t i c l e s are Rayleigh s c a t t e r e r s , the t u r b i d i t y , τ , as a f u n c t i o n of time, t , i s given b y . 1 0

1


168


BEHAVIOR

2

τ - AN V ( l + 2N k t ) ο ο

(1)

where A i s an o p t i c a l constant r e l a t e d to the r e f r a c t i v e index o f the p a r t i c l e s and the medium, V i s the volume of a p a r t i c l e , and k the rate constant f o r the aggregation p r o c e s s . As i n d i c a t e d i n the I n t r o d u c t i o n , one may define the s t a b i l i t y , W, o f a d i s p e r s i o n as follows W - k /k ο

(2)

where k i s the rate constant under conditions o f r a p i d coagulation (maximum rate) i n the absence of added s t a b i l i s e r , and i s given by the Smoluchowsk (3) 1

where k and Τ are the Boltzmann constant and absolute and η i s the v i s c o s i t y o f the continuous phase. Combining Equations ( 1 ) , (2) and (3) leads to

temperature

8N k ' T τ = τ (1 • ο where τ or

—2— 3w

.t/η)

i s the i n i t i a l t u r b i d i t y (t

dOD

du7n)

(4) s

0) of the d i s p e r s i o n ,

8N k ' T =

( 5 )

~3w-

where ODr » 0D/0Dο = τ / τ ο . Thus the slope ν of a p ^l o t of OD versus t / η should d i r e c t l y r e f l e c t changes i n W, e f f e c t s due to changes i n A and η , on changing the bulk polymer c o n c e n t r a t i o n , having been e l i m i n a t e d . Since the conditions f o r Rayleigh s c a t t e r i n g are normally only f u l f i l l e d during the i n i t i a l stages of aggregation, and thus n o n - l i n e a r p l o t s are g e n e r a l l y obtained, i t i s normal p r a c t i c e to take the l i m i t i n g slope as t-*0, i . e . i n t h i s case r

dOD /d(t/n)

t-K)

V i s c o s i t y . The v i s c o s i t i e s o f the various PEO-water mixtures were determined at 25°C using a Cannon-Fenske c a p i l l a r y viscometer. The data obtained are shown i n F i g u r e 1.


11.

Li-iN-ON E T A L .


169

Results A t y p i c a l p l o t of 0 D versus t / η i s shown i n F i g u r e 2 f o r the l a t e x i n the presence of PEO 200. Below about 70% (by weight) PEO the system i s s t a b l e . Between 70 and 80% there i s a r a p i d increase i n the i n i t i a l aggregation r a t e . T h e r e a f t e r , the rate of aggregation decreases a g a i n . As discussed above these e f f e c t s cannot be a t t r i b u t e d to v i s c o s i t y or r e f r a c t i v e index changes i n the continuous phase, since these are e l i m i n a t e d i n the method of p l o t t i n g the d a t a . F i g u r e 3 shows the e f f e c t s described more c l e a r l y . Here (dOD / d C t / n ) . ) ^ i s p l o t t e d versus r

PEO c o n c e n t r a t i o n f o r various molecular weights. F o r each M.W. there i s a c r i t i c a l minimum PEO c o n c e n t r a t i o n and only above t h i s i s aggregation observed. This c r i t i c a l c o n c e n t r a t i o n i s p l o t t e d as a f u n c t i o n of PEO molecula i t can a l s o be seen that the f a l l o f f i n aggregation rate at higher polymer concentrations occurs f o r a l l the molecular weight samples s t u d i e d . P r e l i m i n a r y r e s u l t s have been obtained with a polystyrene l a t e x dispersed i n n-hexane, f o r which the s t a b i l i s e r was a p o l y s t y rene-polyisoprene (PIP) block copolymer. The PIP chains i n the block had a molecular weight of the order of 1000, and homo polymer PIP of the same molecular weight was added to the continuous phase at i n c r e a s i n g c o n c e n t r a t i o n s . Again i t was observed that above a c r i t i c a l minimum PIP c o n c e n t r a t i o n , aggregation o c c u r s . Discussion Of the four mechanisms, o u t l i n e d i n the I n t r o d u c t i o n , concerning the various ways i n which a s t e r i c a l l y s t a b i l i s e d d i s p e r s i o n may be d e - s t a b i l i s e d , one can probably only r u l e out with any confidence at t h i s stage mechanism ( b ) , i . e . desorption of the s t a b i l i s e r on p a r t i c l e c o n t a c t . I t would seem (3) that the s t a b i l i s e r i s w e l l anchored at the s u r f a c e . Any of the other three mechanisms, e i t h e r s i n g l y or i n combination, or indeed some other mechanism not so f a r considered, could be responsible f o r the behaviour observed. However at t h i s stage much more work needs to be done on the e f f e c t s of e . g . molecular weight of the s t a b i l i s i n g group, number concentration of the p a r t i c l e s i n d i s p e r s i o n , p a r t i c l e s i z e and temperature, before any firm conclusions can be reached. I t would a l s o seem e s s e n t i a l that other systems be s t u d i e d . Work i n a l l these d i r e c t i o n s i s c u r r e n t l y underway, and i t i s hoped to report these r e s u l t s i n the l i t e r a t u r e i n the near f u t u r e . Acknow1edgement s The authors would l i k e to acknowledge the many u s e f u l and


170


BEHAVIOR

Figure 1. Viscosity of aqueous poly(ethylene oxide) solutions

Figure 2. Corrected OD v s . time plots for the latex in the presence of various concen trations of PEO 200


11.

LI-IN-ON ET

AL.


25

50

75

%PEO

171

100

Figure 3. Stability curves for the latex as a function of poly(ethylene oxide) concentration

Figure 4. Critical poly(ethylene oxide) concen trations for flocculation as a function of molec ular weight


172

C O L L O I D A L DISPERSIONS A N D M I C E L L A R B E H A V I O R

s t i m u l a t i n g d i s c u s s i o n s w i t h M r . D . W . J . Osmond ( I . C . I . , P a i n t s D i v i s i o n ) concerning t h i s work. One of us ( F . K . R . L . ) would l i k e to thank the U n i v e r s i t y of E r i s t o l f o r the award of a U n i v e r s i t y S c h o l a r s h i p to help finance t h i s work. Literature 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11.

Cited

V i n c e n t , Β., A d v . C o l l o i d I n t e r f a c e Sci., (1974) 4 , 193 Waite, F . A . , J.Oil Colour Chem.Ass., (1971) 54, 342. B a r r e t t , K . E . J . , Br.Polymer J., (1973) 5, 259. Long, J.A., Osmond, D.W.J. and V i n c e n t , B . , J.Colloid Inter face Sci. (1973) 42, 545. Napper, D.H. and Hunter, R.J. i n " M . T . P . I n t e r n a t i o n a l Review of S c i e n c e , P h y s i c a l Chemistry, Surface Chemistry and Colloids, S e r . 1 , Vol.7",M. London, 1972. Napper, D . H . , Ind.Eng.Chem.Prod.Res.Dev., (1970) 9 , 467. Goodwin, J.W., Hearn, J., Ho, C . C . and Ottewill, R.H., Br.Polymer J (1973) 5 , 347. O t t e w i l l , R . H . and Shaw, J.N., J.Electroanal.Chem. Interfacial Electrochem. (1972) 37, 133. R e e r i n k , H. and Overbeek, J.Th.G., D i s c . F a r a d a y S o c . (1954) 18, 74. O t t e w i l l , R . H . and Shaw, J.N. D i s c . F a r a d a y S o c . , (1966) 42, 154. Oster, G . , J.Colloid Sci., (1960) 15, 512.


12 Stability of Aqueous Dispersions in Polymer-Surfactant Complexes. Ethirimol Dispersions in Mixtures of Poly -(Vinyl Alcohol) with Cetyltrimethylammonium Bromide or Sodium Dodecyl Benzene Sulfonate TH.

F. TADROS

Plant Protection Limited, Imperial Chemical Industries Ltd., Jealott's Hill Research Station, Bracknell, Berkshire RG12 6EY, England

In a previous paper (1), the interaction of cetyltrimethyl ammonium bromide (CTABr) and sodium dodecvlbenzene sulfonate = (NaDBS) with poly(vinyl alcohol (PVA) (12% acetate groups, 42,000) has been investigated i n aqueous solution. A polymer surfactant 'complex' or polymer nucleated micelle was postulated to form by oriented adsorption of the surfactant ions on the nonionic polymer chain, through some sort of 'hydrophobic' bonding between the hydrophobic end of the surfactant ion and the hydrophobic part of the polymer molecule. Adsorption isotherms on a hydrophilic surface such as silica (1), showed that at high pH, preadsorbed CTA+ ions increased the adsorption of PVA possibly by 'anchoring' the dissociated -SiO- groups with the PVA chains. Provided there were sufficient CTA ions to create enough hydrophobic sites on the silica surface, the PVA could increase to an amount beyond that required for monolayer coverage (assuming flat orientation) and PVA 'loops' with a proportion of PVA segments attached to the hydrophobised s i l i c a surface, result at the silica solution interface. At low pH, a silica surface with preadsorbed PVA also increased the adsorption of CTA above that obtained i n absence of PVA. The same increased adsorption of PVA was also observed on addition of NaDBS. This paper extends previous work on the adsorption of these complexes to organic surfaces, an area of interest i n the dyestuffs, pharmaceuticals, pesticides and other f i e l d s . Organic materials do not necessarily behave i n a similar way to c l a s s i c a l model systems such as s i l i c a and s i l v e r halides but adsorption behaviour i s of great importance i n these systems of industrial interest. We have therefore investigated the adsorption of these polymer-surfactant complexes on ethirimol C2), an organic pesticide having essentially hydrophobic characteristics but containing polar grouping and their effect on s t a b i l i t y against flocculation. One would expect the surfaces of such a material to be heterogeneous with possibly varying degrees of adsorption +

+

173


174


BEHAVIOR

on the various surfaces. I t has a s o l u b i l i t y of ~ 160 ppm i n water. Due to the polyelectrolyte nature of the polymersurfactant complex, one would expect a strong double layer repulsion force besides the steric force. Moreover, the chainsolvent interaction of the resulting polymer-surfactant complex i s expected to be stronger than that of the nonionic polymer. This was proved before (1) by an increase of the cloud point of PVA on addition of NaDBS or CTABr. Therefore, one would expect a greater osmotic repulsive force for the polymer-surfactant stabilised system relative to that of the nonionic polymer. Experimental 1. Materials. Ethirimol was twice recrystallised from ethanol and then dry ground i n a coffee mixer. The surface area of the resulting powder, which was homogenised by mixing i n a large container over r o l l e r s for 24 hours, was measured by BET Krypton adsorption, after degassing at room temperature i n a helium atmosphere for 12 hours. The BET surface area was found to be 0·29 m*/g. CTABr, NaDBS, sodium lauryl sulfate, bromophenol blue were the same materials described before (1). Analar sodium chloride, which was roasted i n a s i l i c a crucible to constant weight, was used to control the ionic strength of the solutions. Doubly d i s t i l l e d water from a l l glass apparatus was used for preparation of a l l solutions, which were always freshly made (kept f o r no longer than two weeks). 2. Preparation of Aqueous Ethirimol Dispersions. For the mobility experiments dispersions were prepared either by directly dispersing 0 · ! g of ethirimol powder i n 50 ml of the appropriate solution using ultrasonic irradiation, followed by f i l t r a t i o n through a No. 2 sintered glass crucible to remove large particles or by dilution from a stock concentrated dispersion previously prepared by a wet milling process. In the latter case 7 g of ethirimol powder were dispersed i n 400 ml doubly d i s t i l l e d water using ultrasonic irradiation followed by milling for 30 minutes to reduce the particle size. The resulting dispersion was stored i n a constant temperature room at 20 ± 1°C to reduce crystal growth and kept continuously stirred using a magnetic s t i r r e r . The resulting dispersion was heterodisperse and microscopic investigation showed that a significant proportion of the particles were asymmetric. An average particle diameter was estimated by sizing about 400 particles from a picture taken under the optical microscope. In the case of the asymmetric particles, the minor axis length was used to represent the diameter of the p a r t i c l e . The arithmetic mean particle diameter was found to be 1·65 um.


12.

175

Aqueous Dispersions

TADROS

3. Determination of the Hamaker Constant of Ethirimol* The Hamaker constant was calculated from refractive index measurements at various wavelengths. The refractive indices were measured at 25°C for four different wavelengths by the Becke line method (3) using characteristic immersion liquids supplied by R.P. Cargille laboratories Inc. Since the refractive indices observed depend on the orientation of the crystal fragments i t was only possible to determine the two extreme values. The refractive index values are shown i n Table 1. The figures are accurate to ^ 0*001. By convention ι\χ i s the lower and ηγ the higher. The third index ηβ (immeasurable) has an intermediate value, α, β and γ represent the various crystallographic planes of the ethirimol crystal. Prom the above data, the London dispersion constant B ^ and Hamaker xonstant were calculated using the method described by Gregory (£). The effective Hamaker constant for interaction across an aqueous medium was calculated from the equation, A

A

A

e f f " < 11* » 3 3 *

>2

where A33 i s the effective Hamaker constant for water (4), taken to be 4 χ 10~20j. T n calculated constants are shown i n Table 2e

Table I.

Refractive Indices of Ethirimol at Various Wavelengths X(nm) 486 546 589 656

Table LT.

11

A

1*557 1*554 1*549 1*544

1*723 1*705 1*696 1*677

α

γ

5*43 χ Ι Ο "

ΛΑ

Α

ηγ

London and Hamaker constants

Orientation Β

ηα

76

6

J m"

-20 6*52 χ 10 ^ J

ι α

3*1 χ 1 0 "

e f f

Average A

r f f

21

J

6*47 χ Ι Ο "

76

6

J m"

-20 7*76 x 10 * J 6*2 χ 1 0 "

21

J

-21 4*6 x 10 J

4. Adsorption Isotherms. 100 ml of CTABr (concentration range 5 χ 10-=> - 4 χ 10-3 mole/1 ) or NaDBS (10-4 - 2*5 χ 10-3 mole/1) solutions with ionic strength controlled to 10-2 with NaCl were added to 2 or 4 g of ground ethirimol. The mixtures were dispersed by ultrasonics at intervals of 30 sec (to avoid heating) with a maximum period of 2 minutes. The dispersion was l e f t stirred overnight using magnetic s t i r r e r s i n a constant


176


BEHAVIOR

temperature cabinet at 25 1°C. The samples were allowed to stand for one hour at the same temperature and the supernatant liquid quickly f i l t e r e d at room temperature (about 22°C) through a 0·22 μη» millipore f i l t e r . The f i r s t few ml were discarded to eliminate errors from possible adsorption on the f i l t e r paper. The equilibrium concentration of CTABr solutions was determined by two phase t i t r a t i o n against standard sodium lauryl sulfate (5). That of NaDBS was determined by t i t r a t i o n against standard CTABr (5). For measurement of adsorption of PVA, 50 ml of PVA i n the concentration range 0-300 ppm were added to 1 g of ethirimol powder and the same adsorption procedure applied. The method of analysis of PVA i s based on measurement of colour intensity of the complex formed with a reagent of iodine + potassium iodide + boric acid, at 670 nm (£, 7)· However, the presence of trace quantities of dissolved ethirimol i n the equilibrium solution (ethirimol has a s o l u b i l i t y of / 160 ppm i n water that i s only very s l i g h t l y increased i n the presence of up to 300 ppm PVA), a turbidity i n solution after addition of the I •»· KI + boric acid reagent obscured measurement of the colour intensity. Extraction of ethirimol using polar and non-polar organic solvents could not be applied as i t was found from blank experiments that some PVA was also extracted into the organic phase. Finally, we found that the turbidity could be removed by adjusting the pH of the equilibrium solution to 9-10 before adding the iodine reagent. For that purpose the pH of the PVA solutions used for the calibration curve were also adjusted to pH 9-10. PVA adsorption was also measured i n the presence of NaDBS (2 χ 10"^ mole/1) and the same procedure of analysis of PVA was adopted. As mentioned before (1), NaDBS did not interfere with the colorimetric method of analysis of PVA. 2

5. Electrophoresis Experiments. The electrophoretic mobility was measured using a commercial microelectrophoresis apparatus (Rank Bros., Bottisham, Cambridge, England). A c y l i n d r i c a l c e l l was used and the mobility of 20 particles was determined at each stationary level, reversing the polarity for successive timings. The average electrophoretic mobility was calculated from the average reciprocal time for a l l 40 measure ments. Mobilities were measured as a function of CTABr or NaDBS concentration (choosing concentration ranges below and above the cmc) and i n the same solutions containing varying amounts of PVA (100-400 ppm). Also the mobility of ethirimol particles was measured as a function of PVA concentration (0-300 ppm without addition of surfactants). In a l l cases, the ionic strength was controlled to 10~ with NaCl. From the electrophoretic mobility the zeta potential was calculated using the c l a s s i c a l Smolukowski equation (this i s j u s t i f i e d since fta»100). 2

6. Flocculation Kinetics. Flocculation kinetics was followed by manual counting technique using a Haemocy tome ter


cell

12.

TADROS

177

Aqueous Dispersions

(Hawskley ) having an etched graticle of 25 χ 10-4 mra2 and a depth of 0*1 mm. A Leitz Qrtholux microscope was used under bright f i e l d illumination and a magnification of 500 x. The eye piece of the microscope was connected to a television camera and the f i e l d of view shown on a television screen* In this way counting was less tedious and the number of particles i n 40 squares of the graticule which were chosen at random was counted. For these experiments the milled stock dispersion was diluted i n the appropriate solution to give a particle concentration of P J 10 particles/ml. The dispersion was sonified and kept i n a constant temperature bath at 25 ^ 0-05°C f o r 15 minutes to attain the temperature of the bath. I t was then quickly sonified and the i n i t i a l count taken immediately after redispersion by ultrasonics, sampling 1 cm below the surface of the dispersion. Countin of time (8-12 minutes) over a period of 1-2 hours, an aggregate being counted as one particle. Prior to sampling the dispersion was gently inverted 3-4 times to counteract sedimentation. The experiments were carried out at the same concentration range of CTABr, NaDBS and PVA used f o r electrophoresis. Also the ionic strength was controlled to 10-2 with NaCl. In order to measure the c r i t i c a l flocculation concentration and the fast flocculation rate, the kinetics of flocculation of the aqueous ethirimol dispersion was followed as a function of NaCl concentration i n the range 10" - 10~^ mole/1. 8

3

Results and Discussion 1. Adsorption Isotherms. Figure 1 shows the adsorption isotherm of CTABr on ethirimol, a two step isotherm with saturation adsorption of 1·8-2·0 χ 10"" mole/g and 3*5 χ 10-6 mole/g ethirimol respectively. Using the BET surface area (0*29 m2/g) the area f o r CTA+ ion was calculated to be 0·27 nm and 0·14 nm at the f i r s t and second plateau respectively. The stepwise isotherm could be due to bilayer adsorption of CTA+, the f i r s t layer with the charge pointing towards the surface and the second layer forming by hydrophobic bonding between the hydrocarbon chains of the surfactant ions. However, the results of electrophoresis (see below) has shown the isoelectric point to occur at much lower concentration (1 χ 10-5 mole/100 ml) than that at which the step occurs (8 χ 10-5 mole/100 ml). We would therefore favour the following picture for adsorption of CTA ions on ethirimol t i l l the f i r s t plateau. I n i t i a l l y the surface has a negative surface charge (as indicated by a negative zeta potential of - 22 mV) which could be due to some s p e c i f i c a l l y adsorbed anions. In the i n i t i a l adsorption stages these charges are neutralised with CTA+ ions, with the positive charge pointing towards the surface, leaving uncovered hydrophobic regions i n between. The subsequent CTA ions w i l l now adsorb on the hydrophobic sites, with the positive charges now pointing towards 6

2

t

2

+

+


178

C O L L O I D A L DISPERSIONS A N D

MICELLAE

BEHAVIOR

the solution. The adsorption process continues u n t i l a v e r t i c a l l y oriented monolayer of CPA"" ions i s reached which i s complete at the f i r s t plateau. However, the area/CTA* ion at this plateau (0·27 nm ) i s lower than expected from models of a close packed trimethy1ammonium ions namely 0·35 nm . Robb and Alexander (8) found on polyacrylonitrile latices an area of 0·35 nm /CTA ion, whereas Conner and Ottewill (9) found an area of 0·47 nm on polystyrene latex i n 10*" M KBr and 0*35 nm i n 5 χ 10-2 mole/1 KBr. In view of the possible error of the BET area our value of 0*27 nm seems reasonable. As the surface of ethirimol becomes f u l l y saturated with CTA ions, there i s s t i l l the p o s s i b i l i t y of association of CTA ions on the surface which could result i n a rapid increase i n adsorption. This explains the step i n the isotherm. Therefore, association or 'hemimicelle' formation as depicted by Fuersteanau et a l . (10) could account for this rapid increase. Figure 2 shows the adsorption isotherm of NaDBS on ethirimol. The isotherm i s more or less of a Langmuir type with a saturation adsorption of ^ 3·5 χ 10-6 mole NaDBS/g ethirimol which i s similar to that obtained with CTABr at the second plateau. However, this saturation adsorption i s reached at a much lower equilibrium concentration of NaDBS and there i s a tendency of further increase i n adsorption beyond this value as indicated by the dotted l i n e on the isotherm. Using the BET area, the area/DBS" ion at the i n i t i a l plateau i s 0*14 nm which i s smaller than that to be expected for a v e r t i c a l l y oriented close packed monolayer of dodecyl benzene sulfonate ions. However i f one uses the area calculated from CTABr adsorption (see below) an area/DBS" ion of *v* 0*18 nm that i s close to that for a close packed monolayer of DBS" ions (0*20 nm ) i s obtained. Adsorption of an anionic surfactant on the negative ethirimol surface should have occurred by the hydrophobic part of the molecule pointing towards the hydrophobic ethirimol surface. Association or hemimicelle formation could account for the increased adsorption beyond the amount required to form a close packed monolayer. A similar type of isotherm has been found by Kudryavtseva and Larionov (11) for adsorption of sodium lauryl sulfate on hydrophobic gold hydrosol. These authors found an adsorption amount corresponding to 3 monolayers of sodium dodecyl sulphate assuming an area of 0·20 nm per dodecyl sulphate ion. Figure 3 shows the adsorption isotherm of PVA on ethirimol (curve A) and the effect of addition of NaDBS on PVA adsorption (curve B). In the absence of NaDBS, the i n i t i a l part of the isotherm i s what to be expected for the adsorption of a nonionic macromolecule, being of the high a f f i n i t y type. However, as the concentration of PVA i s increased, the adsorption continues to increase and a sudden increase i n PVA adsorption i s observed above an equilibrium concentration of 140 ppm. The shape of the isotherm i s markedly different from that recently obtained on polystyrene latex (12). A similar increase i n PVA adsorption on 4

2

2

2

+

2

3

2

2

+

+

2

2

2

2


12.

Aqueous Dispersions

TADROS

179

4h

•

1

Ο

10

;

ι -

20 3

5

Equilibrium Concentration Π mole /100 cm ) x l 0 l Figure 1. Adsorption isotherm of CTABr on ethirimol ι—ι

0

2

4

6

8 3

5

Equilibrium CorKentration [(mole/100cm ) x l O ] Figure 2. Adsorption isotherm of NaDBS on ethirimol


180


MICELLAR

BEHAVIOR

carbon black has been found by Johnson and Lewis (13). Using the BET surface area, the amount of adsorption at the i n i t i a l plateau i s ~ 8 mg/m, which i s considerably higher than that recently obtained on polystyrene (12) for a similar PVA sample, namely 2·8 mg/m. However, the BET area could be underestimated i n view of the low surface area of the sample which could result i n significant error. An area could be calculated from CTABr adsorption assuming an area/CTA of 0·35 nm f o r a close packed monolayer; this would give 0·38 m /q. Using this value PVA adsorption would amount to ^ 6 mg/m, about twice the value obtained on polystyrene. I t seems therefore from these results as well as those of Johnson and Lewis (13) that PVA adsorption depends on the substrate. In the presence of NaDBS, the adsorption of PVA at the i n i t i a l plateau has dropped to half i t s value i n absence of NaDBS. However, the shape of the isotherm i s maintained and the two curves A and Β cross each other at the intermediate PVA concentration. The f i n a l value of adsorption i s lower i n presence of NaDBS than i n i t s absence. The drop i n adsorption of PVA i s what to be expected i n view of the more hydrophilic nature of the PVA-DBS"" complex. Recently, Fleer, Koopal and Lyklema (14) demonstrated that the adsorption of PVA on s i l v e r iodide decreases as the degree of hydrolysis of the polymer (which leads to an increase i n polymer-solvent interaction) increases. The decrease i n adsorption as the chain solvent interaction increases i s readily explained i n terms of Hoeve (15) and Silberberg (16) models. According to these theories, relatively larger loops and consequently r e l a t i v e l y higher adsorption i s expected from poorer solvents. The lower adsorption i n a good solvent i s due to the high osmotic pressure created within the loops (due to the repulsive force between the segments i n the loop region) which hinders the formation of thick loops and large amounts of adsorption i n good solvents. One of course cannot rule out the weaker a f f i n i t y of the more hydrophilic PVA-NaDBS to the hydrophobic surface of ethirimol relative to that of PVA. 2

2

+

2

2

2

2. Zeta Potentials. Figure 4 shows the variation of zeta potential with PVA concentration i n the range 0-300 ppm (in 10-2 mole/1 NaCl). The gradual decrease of zeta potential with increase i n extent of PVA adsorption i s what to be expected for a nonionic macromolecule. In the i n i t i a l stages of adsorption the macromolecule w i l l attain a f l a t t e r conformation, which as adsorption proceeds leads to thicker adsorbed layers. As a result of this a s h i f t i n shear plane towards the solution leads to a lowering of zeta potential and eventually a limiting value (-7 mV) i s reached at the limiting adsorption value. However, one cannot rule out the p o s s i b i l i t y of displacement of some s p e c i f i c a l l y adsorbed ions from the Stern plane on adsorption of PVA segments. Figure 5 shows the variation of zeta potential with CTABr concentration i n presence and absence of PVA, where Figure 6


12.

TADROS

181

Aqueous Dispersions

Equilibrium Concentration (ppm)

Figure 3.

Adsorption isotherm of PVA on ethirimol in the presence (curve B) and absence of NaDBS (curve A)

100

200

300

Concentration of PVA (ppm) Figure 4. Variation of zeta potential with TVA concentration


182



BEHAVIOR

12.

TADROS

Aqueous Dispersions

183

shows the results for NaDBS. In absence of PVA, the i n i t i a l negative zeta potential decreases i n magnitude with increase i n CTABr concentration and at a concentration of ^ 1 χ 10~ mole/1 reversal of charge occurs and the positive zeta potential increase gradually and then more rapidly at and beyond the cmc of CTABr and eventually i t reaches a plateau ahove 5 χ 10" mole/1. With NaDBS, the i n i t i a l negative zeta potential continues to r i s e with increase i n concentration and a limiting value (-85 mV) i s reached at 10-2 mole/1. Addition of PVA, at a given surfactant concentration, always resulted i n lowering of zeta potential to a value below that obtained i n absence of PVA. With CTABr, the reduction i n zeta potential was higher at 200 ppm PVA than at 100 ppm. However, the zeta potentials started to increase again at 300 and 400 ppm PVA, above the value obtained i n 200 ppm. With NaDBS, there was a continual decrease of zeta potential with increase i n PVA concentration u n t i l 400 ppm PVA. The decrease i n zeta potential on addition of PVA to a given surfactant solution could be due to several reasons. Partial displacement of CTA+ or DBS" ions from the surface could be the casue of this drop. However, there i s enough evidence to show that this has not occurred. F i r s t l y , i n the case of CTABr-PVA system, the drop i n zeta potential did not continue by gradually increasing the PVA concentration. If displacement of CTA+ ions would have occurred, one would expect more displacement at higher PVA concentrations. Secondly, our recent adsorption measurements on s i l i c a (1) has shown that adsorption of CTA+ or DBS" ions i s enhanced by addition of PVA. The drop i n zeta potential could therefore be best explained i n terms of interaction between PVA and CTA or DBS" ions at the ethirimol/solution interface with the result of s h i f t i n shear plane. As a result of this interaction an 'association* polyelectrolyte between PVA chains and CTA+ or DBS" i s formed; the resultant complex now adsorbing at the interface. This picture i s supported by the fact that i n the case of PVA-CTA"" ions, the particles always maintained their positive charge above the i.e.p. of ethirimol. Due to the thicker adsorbed layer formed by the polymer surfactant complex compared to that i n absence of polymer, the shear plane i s shifted towards the solution and a lower zeta potential i s obtained. The thicker the layer, the more the extent of the drop, as i l l u s t r a t e d for NaDBSPVA system. However, with CTABr-PVA system, there i s a tendency of increase i n zeta after reaching a minimum at 200 ppm PVA. (Xiing to the complexity of polymer surfactant interaction with the result of having various conformations and/or mixed micelle formation, a change i n adsorbed layer thickness or overall charge of the complex could explain this apparent r i s e . 4

3

+

1

3. Stability Measurements. The quantitative assessment of s t a b i l i t y against flocculation of a dispersion i s usually complex, particularly when extended over a long period of time. However,


184


BEHAVIOR

the direct particle counting method usually carried i n the i n i t i a l period i s the simplest method to interpret i f one considers flocculation as a bimolecular process* In this case the rate of decrease of p a r t i c l e number with time i n the i n i t i a l period follows the Equation - π

-

k

2

n 2

(

1

)

where Ν i s the number of particles per unit volume of dispersion, after time t and Κ i s the second order rate constant. On integration, f

s

êΝ

êNo

+ K^t 2

(2)

A plot of 1/N versus t gave lines which were i n i t i a l l y straight and then started to curve at longer periods of time and i f the counting was carried long enough, the curve reached a limiting value with an apparent zero slope. This i s the behaviour to be expected for secondary ndnimum flocculation. Prom the i n i t i a l slopes, values of K were calculated for every dispersion studied. I t i s the normal practice i n c o l l o i d s t a b i l i t y studies to express s t a b i l i t y i n terms of a s t a b i l i t y ratio W, that i s equal to the ratio between the rate constant K obtained i n absence of any barrier (fast flocculation rate) to the experimental value K. K he calculated using von Smolukowski theory (17) o f rapid flocculation which considers flocculation to be a diffusion controlled process with K = 4/^DR, where D i s the diffusion coefficient and R the c o l l i s i o n radius (2 χ particle radius a). Replacing D by the Einstein coefficient (D = kT/e^ra ^ , where 1 i s the viscosity, k the Bokmann constant and Τ the absolute temperature) gives K = 6·15 χ 10-12 3 sec~1 at 25°C. When the long range van der Waals attraction i s taken into consideration (18), K ,o increases by about 3% using the measured A i value of ethirimol of 4*6 χ 10-21 j . However, taking the hydrodynamic correction (19) into consideration reduces K to about 3 χ 10-12 cm sec" . It i s well known that polydispersity and asymmetry of the particles increase K significantly (20,21). For that reason we could not use the theoretical value of K for calculation of the W value. Instead, we measured the f a s t flocculation rate for our polydisperse system, by measuring the rate of flocculation as a function of NaCl concentration. The fastest rate was obtained at NaCl concentration equal to or greater than 10-2 mole/1. A plot of log W versus log C N C I i s shown i n Figure 7. The c r i t i c a l flocculation concentration i s 0*01 mole/1 NaCl and the fastest rate was found to be 1*05 χ 10-1° cm sec"" , a value that i s about 20 times higher than the theoretical value i f one neglects Spielman effect (19) and about 40 times higgler than the 2

2 ? 0

c

2

a

n

2 f 0

2 f 0

2 0

c m

2

2

2 f Q

3

1

2 f Q

2 f Q

8

3

1


12.

TADROS

185

Aqueous Dispersions

theoretical value i f the Spielman hydrodynamic correction i s taken into consideration. This i s not surprising i n view of the polydispersity and asymmetry of the particles i n our system. Figure 8 shows the variation of W versus PVA concentration. As i s clear W increases gradually with increase i n PVA concentration and then reaches a limiting value of *M 31 above 150 ppm PVA. This i s what to be expected from a build-up of adsorbed layers. The concentration at which W reaches i t s limiting value i s nearly the same at which the zeta potential has reached i t s limiting value and also roughly the same at which the limiting value of adsorption of PVA has occurred before the sudden increase i n adsorption (see Figure 3). If one assumes that the lowering of zeta potential on polymer adsorption to be solely due to s h i f t i n shear plane i . e . assuming H> *° be the same before and after adsorption, one can calculate the thickness of the adsorbed layer from the magnitude of lowering of zeta potential using the equation tanh

fr^ 4kT

»

tanh

-~r 4kT

-£(Δ - S ) e

y 1 μιη these values correspond to 0*8 and 8*2 kT for two particles interacting i n a secondary minimum. Figure 9 shows the variation of W with CcTABr * presence and absence of PVA. In absence of PVA, fast flocculation (W = 1) i s maintained u n t i l a concentration of ^ 4 χ 10-4 mole/1 CTABr, after which i t increases gradually and a maximum i s reached above the cmc after which W drops again. In the i n i t i a l part of the s t a b i l i t y curve, neutralisation of charge has occurred and a zero zeta potential i s obtained at *J 1 χ 10-4 mole/1. This explains why the fast flocculation process was maintained up to this concentration. With further increase i n CTABr concentration up to 4 χ 10-4 the particles acquired a small positive charge which was not sufficient to impart s t a b i l i t y to the particles. The following increase i n W i s what to be expected from the increase i n the positive zeta potential of the particles. The energy of interaction between two particles, assumed to be represented by f l a t plates, covered with a surfactant layer of thickness 2 nm has been calculated at various zeta potential values. In these calculations, the Void effect (24) and retardation were taken into consideration (23), assuming A for the adsorbed layer to be roughly equal to that of liquid paraffin namely A ; 6 χ 10~ J (25). The Fischer osmotic term was neglected as the adsorbed layer thickness i s rather small. Proceeding i n this way, the secondary minimum depth was estimated at various values of zeta potentials. The results are summarised i n Table 3, which also gives the secondary minimum depth assuming ah area of contact of 1 μιη between the particles. As i s clear a secondary minimum depth below that obtained i n absence of surfactant (8*2 kT) i s obtained as the zeta potential increases significantly above 20 mV. 2

n

22

20

2

Table HI. Secondary Minimum Depth for Interaction Two Ethirimol Particles Assumed to be Represented by Flat plates. Zeta potential (mV)

Secondary minimum depth 2

kT/μιη

2

kT/cm 20 40 60 80

Separation at which the minimum occurs (nm)

8-1 χ 10

8

8-1

34· 5

5·2 x 10

8

5·2

40· 5

4·2 χ 10

8

4·2

44·0

3·8 χ 10

8

3·8

45·5

The drop i n W after reaching a maximum value i s d i f f i c u l t to explain. Some years ago, Ottewill and Rastogi (23) observed a drop i n s t a b i l i t y of Agi after reaching a maximum, with increase i n cationic surfactant concentration. This drop occurred at a


188


MICELLAR

BEHAVIOR

concentration below the croc of the surfactant. The authors explained the drop as due to a mutual coagulation process between larger positive micelles induced by the sol particles and the negative sol particles* In the present case, however, both the ethirimol particles and micelles are positively charged and therefore coagulation by this mechanism does not take place* In the presence of PVA, W i s higher at CTABr concentration lower than the cmc. However, above the cmc of the surfactant, W i s lower i n presence of PVA than i n i t s absence except for the 100 ppm PVA curve. As i s clear from Figure 9, the pattern of W-log CçtpABr curves i s rather complex. At the low CTABr concentration, addition of PVA i s expected to increase the s t a b i l i t y of the particle by forming a polymer-surfactant adsorbed layer, which i n absence of PVA was only caused by a low positive charge from CTA concentrations the presence of a thick adsorbed layer of PVA-CTA* complex did not compensate for the reduction i n charge due to s h i f t i n shear plane. This i s d i f f i c u l t to explain* From the above calculations, the secondary minimum depth was higher i n presence of a surfactant layer even at the maximum value of zeta potential, as compared to that obtained with a nonionic PVA layer 40 nm thick. Of course one would expect a thinner layer for the PVA-CTA* layer, but i t i s unlikely that this layer w i l l be thin enough to deepen the secondary minimum beyond that obtained i n presence of CTABr alone. One possible reason for the decrease i n s t a b i l i t y could be due to the presence of the polymer-surfactant mixed micelles which increase the number of c o l l i s i o n s between the various particles i n solution and hence increase the rate of flocculation. Figure 10 shows the variation of W versus C i n the presence and absence of PVA* In the absence of PVA, W i s much higher at low NaDBS as compared to the W values at comparable CTABr concentration. This i s to be expected since addition of NaDBS always resulted i n an increase i n the negative charge on the particles. Also, a maximum, although shallower than that observed with CTABr i s observed i n the W-log C curve. The higher s t a b i l i t y of the ethirimol dispersion obtained with NaDBS as compared to that obtained with CTABr i s clear from the secondary minimum depth results (Table 3). Owing to the higher measured zeta potentials obtained with NaDBS, a shallower minimum i s obtained, leading to a decrease i n the rate of flocculation. Addition of PVA always resulted i n an increase i n the W values above that i n the absence of PVA except i n few cases. Moreover, the maximum i n the W-log C curve became more pronounced on addition of PVA. An enlargement of the graphs i n the region of the maximum i s shown i n the insert of Figure 10. Most striking* i s the sudden increase i n s t a b i l i t y of ethirimol particles at low NaDBS concentration i n the presence of 400 ppm PVA. Actually the W values i n this range (10~ - 10~ mole/1) are greater than those obtained i n absence of NaDBS. This i s inspite of the fact N a D B S

4

3


TADROS

Aqueous Dispersions

189

Figure 10. W—log C

s at various PVA additions

NaDB


190


BEHAVIOR

that i n the presence of NaDBS, less adsorption of PVA and consequently less thick layer i s to be expected (see Figure 3). The increase i n s t a b i l i t y must be due to the combined effect of electrostatic and steric force due to the presence of a polymersurfactant polyelectrolyte l i k e adsorbed layer. This i s more effective i n s t a b i l i s i n g the particles against flocculation than the nonionic polymer alone. As a result of the combined effect of double layer and osmotic repulsive terms, a shallower secondary minimum could be obtained with PVA-DBS" complex relative to that obtained with the nonionic polymer alone. This may occur inspite of the thinner adsorbed layer of PVA-DBS"" complex. Due to the d i f f i c u l t y of assigning an adsorbed layer thickness and owing to the complexity of the double layer repulsion term i n the presence of a polyelectrolyte, we have not attempted to calculate the energy of interaction curves between the particles i n the presence of the polymer-surfactant complex. I t i s surprising, however, to find that the PVA-CTA** complex did not result i n a similar increase i n s t a b i l i t y above that observed with PVA alone. In the region, where the maximum i n the W-log C curve i s observed (see insert of Figure 10), one finds that the increase i n W values above that observed i n absence of polymer i s greatest at 100 ppm PVA. Above this concentration, W begins to decrease again. Possibly the greater decrease i n electrostatic force at higher PVA concentrations i s the result of this decrease i n W values. 1

Summary The adsorption of cetyltrimethylammonium bromide (CTABr), sodium dodecyl benzene sulfonate (NaDBS) and poly(vinyl alcohol) (PVA) was studied on a hydrophobic organic surface, namely ethirimol. For the surfactants, there was some indication of association or hemimicelle formation after formation of a v e r t i c a l l y oriented close packed monolayer- PVA adsorption (6-8 mg/m ) was greater than that recently obtained on polystyrene latices. On addition of NaDBS, the PVA adsorption decrease as a result of the greater chain-solvent interaction of the PVA-DBS" complex. The zeta potential of ethirimol particles measured at various concentrations of CTABr or NaDBS decreases on addition of PVA. This was ascribed to a s h i f t i n shear plane as a result of the presence of the PVA-surfactant complex at the solid-solution interface. The s t a b i l i t y against flocculation of ethirimol dispersions was measured as a function of PVA, CTABr and NaDBS concentration and also i n surfactant solutions with various additions of PVA. In the simpler cases for polymer or surfactant alone, the s t a b i l i t y could be analysed using the potential energy of interaction curves. Qualitatively, the s t a b i l i t y could be related to the secondary minimum depth. At low surfactant concentrations (below the cmc), addition of 2


12.

TADROS

Aqueous Dispersions

191

PVA always increased the s t a b i l i t y above that obtained with the surfactant alone. With the PVA-DBS" system, the s t a b i l i t y ratio W exceeded i n some cases the value obtained with PVA alone, inspite of the expected thinner adsorbed layer of the PVA-DBS"" complex. At high surfactant concentration (above the cmc) W-log C curves were complex leading to an increase followed by decrease i n W values as the PVA concentration increases. Acknowl edgements The author i s indebted to Mr. D. Heath for carrying out most of the experiments described i n this paper. He i s also grateful to Mr. M.J. Garvey for his help i n the computation of the potential energy of interaction curves. Permission by the Management for publicatio Literature Cited 1.

Tadros, Th. F., J . Colloid Interface Sci., (1974), 46, 528.

2.

Ethirimol is 5-n-butyl-2-ethylamino-4-hydroxy-6-methyl pyrimidine. For further details see: "Pesticide Manual" B r i t i s h Crop Protection Council 1972, H. Martin, Ed., p. 243.

3.

Wahlstrom, Ε. E., "Optical Crystallography" 4th ed. Wiley, N.Y., (1969).

4. Gregory, J., Adv. Colloid Interface Sci. (1969), 2, 396. 5.

Barr, T., Olivier, J . and Stubbings, W. V., J . Soc. Chem. Ind. (1948), 67, 45.

6.

Zwick, M. M., J . Appl. Polym. S c i . (1965), 9, 2393; J . Polym. Sci. A-1, (1966), 4, 1642.

7. Horacek, J . Chem. Prumysl., (1962), 12 385; C.A. 58, 10305 f . Chene, Μ., Martin-Barret, O. and Clery, M., (1966), 273; Monte-Vobi, A. J., (1969), J . Ass. Offic. Anal. Chem. 52 891. 8.

Robb, D. J . M. and Alexander, Α. E., Society of Chemical Industry Monograph No. 25, 292 (1967).

9.

Conner, P., and Ottewill, R. Η., J . Colloid Interface S c i . (1971) 87, 642.

10.

Gaudin, A. M. and Feursteanau, D. W., Trans. AIME (1955) 202, 958.



192

11.

Kudryavtseva, Ν. M. and Larionov, O. G., Russian J . Phys. Chem. (1971) 45, 657.

12.

Garvey, M. J., Tadros, Th. F. and Vincent, B., J . Colloid Interface S c i . , (1974) i n press.

13.

Johnson, G. A. and Lewis, K.E.,B r i t i s h Polym. J . (1969) 1, 266.

14.

Fleer, G. J . , Koopal, L. K. and Lyklema, J . , Kolloid Z.Z. polym. (1972) 250, 689.

15.

Hœve, C. A. J . , J . Polym. S c i . (C), (1971) 34 1.

16·

Silberberg, Α., J

17. 18.

Von Smoluchowski Z-physik. Chem. (1917) 92, 129. McGown, D. N. L. and P a r f i t t , G. D., J . Phys. Chem. (1967) 71, 449.

19.

Spielman, L. Α., J . Colloid Interface Sci. (1970) 33, 562; Honig, E. P., Roebersen, G. J . and Wiersema, P. H., J . Colloid Interface Sci. (1971) 36, 97.

20.

Müller, H., Kolloid Z, 38, 1 (1926); Kolloid Beih (1928) 26, 257.

21.

Booth, Faraday Soc. Discussions (1954) 18, 104.

22.

Fischer, E. W., Kolloid Z. (1958) 160, 120.

23.

Garvey, M. J . and Tadros, Th. F., i n Proceedings VI International Congress Surface Activity Vol. II (2) p.715, published 1973.

24.

Vold, M. J., J . Colloid Sci. (1961) 16, 1.

25.

Visser, J . , Adv. Colloid Interface Sci. (1972) 3, 331.

26.

Ottewill, R. H. and Rastogi, M. C., Trans. Faraday Soc. (1960) 56, 866.


13 Rheological Studies of Polymer Chain Interaction ROBERT J. HUNTER, PAUL C. NEVILLE, and BRUCE A. FIRTH Department of Physical Chemistry, University of Sydney, Sydney, N.S.W. 2006, Australia

Introduction In t h i s paper w behaviour of latex particles coated w i t h a h y d r o philic polymer. The core particle is a poly(methyl m e t h a c r y l a t e ) sphere and the adsorbed trib l o c k copolymer i s p o l y - ( e t h y l e n e o x i d e - b - m e t h y l m e t h a c r y l a t e ) i n which the end h y d r o p h o b i c m o i e t i e s a c t as anchors and p e r m i t the e t h y l e n e oxide u n i t s to form a loop which s t r e t c h e s i n t o the s u r r o u n d i n g solution. These systems are t h e r m o d y n a m i c a l l y s t a b l e (1) below a c e r t a i n t e m p e r a t u r e , c a l l e d the critical flocculation temperature (c.f.t.), because the c l o s e approach o f the core particles i s p r e v e n t e d by a r a p i d rise in Gibbs Free Energy as the adsorbed polymer c h a i n s on the colliding particles b e g i n to i n t e r a c t (2-4) . The total energy o f interaction, V , c o n s i s t s o f the van der Waals energy o f a t t r a c t i o n between the core particles, V, and the polymer interaction energy V = ΔG = ΔH - TΔS where ΔH and ΔS are the e n t h a l p y and entropy changes which o c c u r when the adsorbed polymer c h a i n s i n t e r p e n e t r a t e . Both are p o s i t i v e i n t h i s system so t h a t at the c.f.t, ΔG has presumably been reduced to a v a l u e comparable with V . Tne r h e o l o g i c a l b e h a v i o u r o f a c o l l o i d a l s u s p e n s i o n i s d i r e c t l y a f f e c t e d by the i n t e r a c t i o n e n e r gy between the p a r t i c l e s . Systems which are u n s t a b l e or o n l y m a r g i n a l l y s t a b l e , e x h i b i t p s e u d o p l a s t i c or p l a s t i c b e h a v i o u r (5_,6J and the t o t a l energy d i s s i p a t i o n , E ^ , c o n s i s t s of a purely viscous p a r t , E ^ , and a p a r t which may be a t t r i b u t e d to the overcoming of i n t e r p a r t i c l e i n t e r a c t i o n s , E j . L i k e w i s e the shear s t r e s s at h i g h shear r a t e s can be d i v i d e d i n t o a v i s c o u s p a r t , τ ^ , and an a d d i t i o n a l t e r m , τ , c a l l e d the Bingham y i e l d v a l u e s i n c e : T

A

R

R

R

R

R

R

R

A

β

193


194


= Ε

v

+

E

i

BEHAVIOR

(1)

•

F i g u r e 1 shows the b e h a v i o u r which i s a n t i c i p a t e d . To c h a r a c t e r i s e t h i s curve we need to be a b l e to i n t e r p r e t (a) the y i e l d v a l u e , τ , (b) the s l o p e o f the l i n e a r p a r t o f the graph ( u s u a l l y c a l l e d the p l a s t i c v i s c o s i t y , η ) , (c) the shear r a t e at which the r e l a t i o n becomesÎinear and (d) the d e t a i l e d shape o f the n o n - l i n e a r p a r t o f the τ-D c u r v e . In some cases the systems showed at low shear r a t e s , a more c o m p l i c a t e d , Ostwald type (7) flow b e h a v i o u r ( F i g u r e 2 ) , the o r i g i n o f which i s d i s c u s s ed below. β

Theory (i) Ostwald Flow B e h a v i o u r . The g r a d u a l r e d u c t ion i n v i s c o s i t y w i t h i n c r e a s e i n shear r a t e i s u s u a l l y a t t r i b u t e d to a breakdown i n " s t r u c t u r e " i n the system and v a r i o u s attempts have been made to quantify this idea. We propose t h a t Ostwald b e h a v i o u r o c c u r s when the shear f i e l d has to d e s t r o y not o n l y the s h e a r - i n d u c e d d o u b l e t s , but a l s o some o f those c r e a t e d by Brownian m o t i o n . Doublets which s e p a r a t e by Brownian motion ( i r r e s p e c t i v e o f how they are formed) make no c o n t r i b u t i o n to the i n t e r a c t i o n energy. Thus Ε = n ( D ) E D

(2)

g

where n ( D ) i s the number o f d o u b l e t s d e s t r o y e d by shear per u n i t volume p e r second at shear r a t e D, and Ε i s the energy which the shear f i e l d must s u p p l y i n o r d e r to s e p a r a t e the p a r t i c l e s i n the d o u b l e t . The t o t a l energy d i s s i p a t i o n per u n i t volume per second i s then n

E

2

T

= D n (l s

+ 2 . 5 φ ) + n (D) D

E

$

(3)

where η „ i s the s o l v e n t v i s c o s i t y and φ i s the volume f r a c t i o n o f p a r t i c l e s . Here we have assumed t h a t Ε i s g i v e n by the s i m p l e E i n s t e i n r e l a t i o n . Smoluchowski (8) showed t h a t the t o t a l number o f d o u b l e t s produced by both Brownian motion and shear was (4)

+ D where a i s

the p a r t i c l e r a d i u s .

In o r d e r to

determine


13.

HUNTER ET AL.

Polymer Chain Interaction

195

Industrial and Engineering Chemistry

Figure 1. The basic shear diagram for a plastic ma terial showing the contributions to the total stress, as suggested by Michaels and Bolger (21)

Figure 2. Ostwaldflowcurves for thermo dynamically stable suspensions of the same radius (116 nm), showing the effect of temperature on the curved region. The tem peratures were (a) 35°C and (b) 43°C respectively and the theta temperature 47 °C for MgSO, (0.39M). t


196


BEHAVIOR

the f r a c t i o n o f these which are d e s t r o y e d by the shear f i e l d , we must know the average l i f e t i m e o f a doublet i n the shear f i e l d . If this is greater than the Brownian motion l i f e t i m e , we w i l l assume t h a t t h a t d o u b l e t i s not broken by the shear f i e l d . Smoluchowski showed t h a t the Brownian motion l i f e t i m e was t

B = 3n /4kTN

(5)

s

where Ν i s the number o f p a r t i c l e s per u n i t volume. The s h e a r - f l o w l i f e t i m e t , depends on the a n g l e , Φ , between the d o u b l e t a x i s p r o j e c t e d onto the shear p l a n e and the d i r e c t i o and Mason (9) d e r i v e d the r e l a t i o n g

t

s

= (5/D)

tan"

1

(6)

(% tan Φ)

Thus t h e r e e x i s t s a c r i t i c a l angle Φ below which the shear l i f e t i m e i s s h o r t e r than t and t h i s w i l l be g i v e n (from E q u a t i o n s 5 and 6) by: 0

g

Φ

= tan"

0

(2 tan (3n

1

D/20 kT N))

g

(7)

The f r a c t i o n o f c o l l i s i o n s w i t h angle l e s s than Φ was shown by G o l d s m i t h and Mason (10) to be g i v e n by sin Φ . Hence the f r a c t i o n , B, o f c o l l i s i o n s d e s t r o y e d by the shear f i e l d i s : 0

2

0

2

Β = sin (tan" The

v a l u e o f n^(D)

π a and

1

is

, „

V

1

(8)

J

g

w i t h E q u a t i o n s (1)

.

„

. _ § * ! . (, .

At h i g h shear r a t e s straight line:

this

τ = DTigCl

φ)

+

D/20 kT N)))

§

then

M n a

combining t h i s τ

(2 tan ( 3 η

2.5

"

and (3) )

gives

Β Β,

e q u a t i o n degenerates to a E

+

s

ΤΓ a since

(

k T / 4 η a ΏΉ) and B-*l . s


1

0

)

13.

HUNTER

Extrapolation of this straight the Bingham y i e l d v a l u e : τ

Β

197


ET AL.

E

- - F T " 7Γ a

line

to D = 0 g i v e s

s

W

E q u a t i o n 12 has been d e r i v e d p r e v i o u s l y (11) S u b s t i t u t i o n o f E q u a t i o n (12) i n E q u a t i o n (11) Dn

(1 + 2.5 Φ )

s

τ

Β

B|

gives

kT 1 +4 n a"D

(13)

s

which i s the e q u a t i o n we would expect to d e s c r i b e Ostwald f l o w . τ i the e x p e r i m e n t a l data and φ i s c a l c u l a t e d as a hydrodynamic volume f r a c t i o n , φ „ , from the measured d i f f e r e n t i a l v i s c o s i t y at h i g h shear r a t e , u s i n g the E i n s t e i n r e l a t i o n : β

n

= n

P L

s

(1 + 2.5

φ )

(14)

Η

The i n t e r p r e t a t i o n o f Φ i n terms o f the volume f r a c t i o n w i l l now be d e a l t w i t h . Η

expected

(ii) The Hydrodynamic Volume F r a c t i o n . The e f f e c t i v e volume o f the p a r t i c l e i s augmented by the presence o f the adsorbed polymer and the hydrodynamic volume f r a c t i o n , φ^, i s r e l a t e d to the volume f r a c t i o n o f core p a r t i c l e s , φρ, by the simple r e l a t i o n

V*P

=

C ( a

o

+

where δ i s t h e ^ e x t e n s i o n o f the polymer loops i n t o the s o l u t i o n ; 6 depends on the b a l a n c e between the heat o f d i l u t i o n (κ ) and the entropy o f d i l u t i o n (ψ^) f a c t o r s f o r the polymer - s o l v e n t i n t e r a c t i o n . For the s o l u t i o n to behave i d e a l l y these parameters must be equal and at t h i s p o i n t the change i n f r e e energy f o r i n t e r p é n é t r a t i o n and compression o f the polymer i s equal to z e r o , and hence, so too i s the r e p u l s i o n energy V . These are c a l l e d the t h e t a c o n d i t i o n s f o r the polymer i n t h a t s o l v e n t and i t then assumes i t s u n p e r t u r b e d r o o t - m e a n - s q u a r e e n d - t o end d i s t a n c e h i n f r e e s o l u t i o n . The dimensions under o t h e r c o n d i t i o n s may be r e p r e s e n t e d thus R

2

< r >

where a ,

h

the

2

= α <x

Q

> **

i n t r a m o l e c u l a r expansion

(16)

factor,

is


a

198


BEHAVIOR

measure o f the s o l v e n c y o f the d i s p e r s i o n medium f o r the s t a b i l i z i n g m a c r o m o l e c u l e s . The PEO polymer i s under t h e t a c o n d i t i o n s i n 0.39 M MgSO. at a temper a t u r e o f 320 Κ and i n 0.45M K S 0 at 308 Κ and these are the d i s p e r s i o n media used i n the p r e s e n t studies. A d s o r p t i o n o f the polymer onto an i m p e n e t r a b l e s u r f a c e r e s t r i c t s the segments i n such a way as to i n c r e a s e the mean e x t e n s i o n . We may w r i t e 2 > % (17) δ α < 6l δ < r ο 2

4

r

where δ i s a d i m e n s i o n l e s s parameter which element ary s t a t i s t i c a l n o t i o n s would suggest s h o u l d be equal to about 2. (iii)

The Bingham Y i e l d V a l u e ,

τ .

In o r d e r

β

to

1

(a„ + δ ) use E q u a t i o n (12) we now s u b s t i t u t e a where a i s the r a d i u s o f the core p a r t i c l e and φ= φ „ . The energy o f s e p a r a t i o n o f a p a i r o f p a r t i c l e s i s equal to the d i f f e r e n c e between the van der Waals and the r e p u l s i o n energy: (18) A a N

Q

V

12H

R ο and the a n a l y s i s o f Evans and Napper (1_) p r o v i d e s an e x p r e s s i o n f o r V_ which when combined w i t h E q u a t i o n s (12) and (18) g i V e s :

3ΦH

A a

o 12H

2 3 π a

2

-(2ir) / > 27 5

2

3 / 2

2

2

5

3

u> a N ( a - a ) k T S ο A J

1

(19)

M

where ω= c o n c e n t r a t i o n o f s t a b i l i s e r s u r f a c e (assuming 100% c o v e r a g e ) ;

i n g cm

-2

of

m o l e c u l a r weight o f PEO (here 96000). segment d e n s i t y f u n c t i o n .

= A v o g a d r o s number; M f

= a dimensionless

H , the d i s t a n c e o f c l o s e s t approach can be expressed as a m u l t i p l e o f the u n p e r t u r b e d r . m . s . l e n g t h : Q

Η

o

= δ

o

α < r

2

ο

>h = δ

ο

< τ

2

>h

since i s c a l c u l a t e d f o r v a r i o u s v a l u e s o f the d i s t a n c e p a r a m e t e r ^ , and δ i s the minimum v a l u e o f δ c o r r e s p o n d i n g to c l o s e s ? a p p r o a c h .


13.


HUNTER E T A L .

199

At the (iv) The van der Waals c o n s t a n t , A. t h ê t a - t e m p e r a t u r e , θ , the v a l u e o f α i s u n i t y and so the r e p u l s i o n energy i s z e r o . The y i e l d s t r e n g t h at t h i s temperature c a n , t h e r e f o r e , be used to e s t i m a t e a v a l u e f o r the van der Waals c o n s t a n t : A =

, π2a3 4

τ Β (0) (21) *H o p r o v i d e d t h a t [ can be e s t i m a t e d . A l t e r n a t i v e l y , the v a l u e o f A / H may be o b t a i n e d from the v a l u e o f τ D at the t h e t a temperature ( T ( 8 ) ) and t h i s used __-,_..·,_ — δ — We c o u l d then for c a l c u l a t i o n s a write ^3/2 2 5/2 < r > ω a N^(a - & ) kT S. o A τ (β) - Η (2ir) 3 27 Χ π a a

Ό

r

5

3 φ

K

2

Β

(22)

= τ ( θ ) - Β (Τ) f (α) Β

where Β ( Τ ) i s a s l o w l y v a r y i n g f u n c t i o n o f a t u r e and f(o)-

1

temper-

h ^ T i L " - " Jv a r i e s

r a p i d l y w i t h temper / Vi a t u r e , c h i e f l y because o f the second t e r m . For Τ > θ , α < 1 and so f ( a ) i s n e g a t i v e . The y i e l d s t r e n g t h s h o u l d , t h e r e f o r e , always be g r e a t e r than i t s v a l u e at the t h e t a t e m p e r a t u r e , but s i n c e f ( a ) goes through a maximum ( i n a b s o l u t e v a l u e ) , so too does T g . I t o c c u r s at about the same p o i n t as the minimum i n α - α ( i . e . at a s ( 3 / 5 ) ^ ) . It should be p o i n t e d o u t , however, t h a t the t h e o r y from which the v a l u e o f V i s c a l c u l a t e d i s u n l i k e l y to be v e r y r e l i a b l e above the θ - t e m p e r a t u r e . Polymer s c i e n t i s t s show l i t t l e i n t e r e s t i n the r e g i o n where α< 1 s i n c e i n f r e e s o l u t i o n t h i s corresponds to such poor s o l v e n c y t h a t the polymer i s thrown out as a s e p a r a t e phase. Here i t merely s e t t l e s down onto the p a r t i c l e s u r f a c e . The p h y s i c a l reason f o r the maximum i n τ i s not d i f f i c u l t to f i n d . I f T i s w r i t t e n i n t e form Β k

3

d

T

2

r

- Ε ( Φ ) E
) s

(24)

2

where η i s the apparent v i s c o s i t y ( η = τ / D ) and k^ = 2.5 f o r n o n - i n t e r a c t i n g spheres at i n f i n i t e dilution. I n c r e a s e d v a l u e s o f k^ f o r charged spheres are a t t r i b u t e d to the p r i m a r y e l e c t r o v i s c o u s effect (12) which we may her the h i g h i o n i c s t r e n g t h . k i s e v a l u a t e d by c o n s i d e r i n g ( i ) the p a r t i c l e s e l f c r o w d i n g e f f e c t and ( i i ) the secondary e l e c t r o v i s c o u s e f f e c t due to the i n t e r a c t i o n between particles. P a r t i c l e s e l f c r o w d i n g becomes i m p o r t a n t for φ > 0.20 a p p r o x i m a t e l y (13) and w i l l not be considired further here. A model f o r the secondary e l e c t r o v i s c o u s e f f e c t has been proposed by Chan, B l a c h f o r d and G o r i n g (14, 15). I t a t t r i b u t e s the enhanced v i s c o s i t y to an i n c r e a s e i n the s i z e o f the r o t a t i n g d o u b l e t due to the r e p u l s i o n between the particles. T h i s term would be c o n t a i n e d w i t h i n the parameter Ε which we e v a l u a t e from the e x p e r i m e n t a l Tg. E q u a t i o n (10) and (24) combine to y i e l d 2

ν = 3B 2 - f x π a Dn

f,

K

1

c

i

A +

kT

1

c E

1 S 4 ru a D /

Experimental. The PMMA l a t e x p a r t i c l e s were p r e p a r e d by a m o d i f i e d K o t e r a p r o c e d u r e (16) and monodisperse s p h e r i c a l p a r t i c l e s w i t h s i z e s i n the range 0.09 - 0.2μιη were o b t a i n e d . The t r i b l o c k s t a b i l i s i n g polymer was made by the method o f Napper(3) u s i n g p o l y e t h y l e n e oxide o f v i s c o s i t y average m o l e c u l a r weight 96,000 (polyox WSRN10, Union Carbide), The copolymer was adsorbed on to the PMMA p a r t i c l e s by adding a p p r o x i m a t e l y 100 times the amount o f PEO r e q u i r e d f o r 100% coverage to a c o l d d i s p e r s i o n o f PMMA. A f t e r a 24-hour e q u i l i b r a t i o n the excess was removed by c e n t r i f u g a t i o n . C r i t i c a l f l o c c u l a t i o n temperatures o f the s u s p e n s i o n s were determined by t u r b i d i m e t r i c measure ments at 655 nm and were found to be v e r y c l o s e to


13.

HUNTER


E T AL.

201

the t h e t a temperatures o f the f r e e polymer i n the corresponding s o l u t i o n . The expansion f a c t o r , α , r e q u i r e d f o r E q u a t i o n (19) was c a l c u l a t e d from the approximate F l o r y (17) equation : α

5

- α

3

= 2 C

ψ

M

χ

(26)

(1 - Θ / Τ ) yfe

for temperatues below the θ temperature; is a constant. Above the t h e t a temperatureoCwas d e t e r mined from the r e l a t i o n s h i p (18)

is

where

the

l i m i t i n g v i s c o s i t y number.

Results (i) Ostwald Flow B e h a v i o u r . F i g u r e 2 shows the b e h a v i o u r e x h i b i t e d by a s t a b i l i s e d s u s p e n s i o n i n 0.39 M MgS0 f o r which the θ - t e m p e r a t u r e i s 320K. At lower temperatures these samples showed a s m a l l y i e l d v a l u e and an Ostwald Type flow c u r v e . The f u l l l i n e s i n F i g u r e 2, are the t h e o r e t i c a l curves from E q u a t i o n (13) and they o b v i o u s l y g i v e a f a i r r e p r e s e n t a t i o n o f the e x p e r i m e n t a l d a t a , c o n s i d e r i n g the p o s s i b l e e r r o r s i n v o l v e d . F i g u r e 2 shows the same s u s p e n s i o n at two d i f f e r e n t temperatures below the t h e t a t e m p e r a t u r e , w h i l s t F i g u r e 3 shows a comparison o f two d i f f e r e n t suspensions w i t h d i f f e r e n t v a l u e s o f Ν and a at the same t e m p e r a t u r e . 4

Q

(ii) Hydrodynamic Volume F r a c t i o n . The s l o p e o f these curves at h i g h shear r a t e g i v e s an e x p e r i m e n t a l v a l u e f o r η . which when s u b s t i t u t e d i n E q u a t i o n (14) g i v e s an e x p e r i m e n t a l v a l u e f o r φ„. T h i s v a l u e was used i n a l l o t h e r e q u a t i o n s i n p l a c e o f the p a r t i c l e volume fTSLCtion^^. When s u b s t i t u t e d i n E q u a t i o n (15) i t corresponded to a δ v a l u e o f 55 nm which g i v e s a value o f =2.1 from E q u a t i o n (17) . T h i s i s i n very s a t i s f a c t o r y agreement w i t h the expected v a l u e o f about 2. ρ

1

(iii) The Bingham Y i e l d V a l u e , τ . A c c o r d i n g to E q u a t i o n (19) τ s h o u l d be p r o p o r t i o n a l to φ^, and F i g u r e 4 shows t h a t t h i s i s a p p r o x i m a t e l y t r u e even f o r the τ - φ r e l a t i o n . F i g u r e s 4,5 and 6 show how i m p o r t a n t t h e ^ e f f e c t o f temperature i s on τ i n the neighbourhood o f the t h e t a t e m p e r a t u r e . The r e s u l t s f o r MgS04 were l e s s r e l i a b l e because £

β

2

β

β



BEHAVIOR

Figure 3. Comparison of Ostwaldflowcurves for particles of different radii (116 nm (a) and 164 nm (b), respectively) at the same temperature (35°C). Note that the shear rate at which the linear region begins de creases with increase in particle size.

Figure 4. The effect of volume fraction on yield value for two systems of the same particle radius (167 nm); φ = 0.072, φ = 0.055. The dotted line shows the square of the ratio of the gravi metric volume fractions which should be equiva lent to the τΒ ratios at that particular temperature. The points (O) give the experimental values for this ratio. ί

2


13.

203


HUNTER ET A L .

1.5

I-

30

40 Temperature PC)

50

Figure 5. n— temperature curves for a series of particles in K SO (0.45M). The effect of particle radius on the position of the maximum in the curve is described in the text. The particle radii were (a )i = 164 nm; (a ) = 116 nm; (a ) = 103 nm. T

2

0

fl

0

2

0

40 Temperature

3

SO (°C)

Figure 6. Comparison of theoretical (1) and experimental (2) τ —temperature data for a particular size (116 nm) par ticle using a Hamaker constant of 1 X 10~ J n

20


204


BEHAVIOR

the h i g h e r temperatures i n v o l v e d made measurements more d i f f i c u l t but they showed the same q u a l i t i v e b e h a v i o u r p a t t e r n as the K S 0 systems i l l u s t r a t e d in Figures 4 - 6 . The r i s e i n the v a l u e o f τ at about the t h e t a temperature and i t s r e a c h i n g a maximum v a l u e at s l i g h t l y h i g h e r temperatures are i n q u a l i t a t i v e a c c o r d w i t h E q u a t i o n s (19) and ( 2 2 ) . Note t h a t f o r most o f the systems the Tg v a l u e never f a l l s below i t s v a l u e at the t h e t a temperature ( c f . E q u a t i o n 2 2 ) . Note p a r t i c u l a r l y t h a t the e x t e n t o f the r i s e and f a l l in f o r Τ > θ i s c r i t i c a l l y dependent on the core p a r t i c l e r a d i u s ( F i g u r e 5 ) . Figure 6 gives a comparison between th curves. 2

4

β

(iv) The van der Waals c o n s t a n t , A . Values o f A c a l c u l a t e d from τ ( θ ) u s i n g E q u a t i o n (21) depend c r i t i c a l l y on the c h o i c e o f the d i s t a n c e o f c l o s e s t approach. The s m a l l e s t p o s s i b l e v a l u e i s set by the c o n d i t i o n t h a t the i n t e r v e n i n g polymer chains are compressed to t h e i r normal d e n s i t y i n the s o l i d . T h i s would o c c u r at Η = 4 nm which i s o b v i o u s l y too s m a l l f o r i t w o u l â r e q u i r e the e x p u l s i o n o f a l l s o l v e n t from around the polymer c h a i n s . For avalue o f 5 nm the van der Waals c o n s t a n t comes out to be 1 χ 10"20j which i s v e r y r e a s o n a b l e . The much l a r g e r v a l u e s o f H which are c a l c u l a t e d f o r s t a b l e systems by e q u a t i n g the hydrodynamic compressive f o r c e w i t h the e l e c t r o s t a t i c r e p u l s i o n (14) , would require correspondingly higher values for A. That model, however, does not a t t r i b u t e the e x t r a energy d i s s i p a t i o n to van der Waals a t t r a c t i o n (see b e l o w ) . β

Discussion. The s e p a r a t i o n energy which appears i n E q u a t i o n (10) f o r the Ostwald flow curves does not a r i s e from van der Waals a t t r a c t i o n energy between core p a r t i c l e s . These systems are s t a b l e and so the r e p u l s i o n s h o u l d i n any case dominate over a t t r a c t i o n . Also, F i g u r e s 2 and 3 and T a b l e I show t h a t the s e p a r a t i o n energy i s independent o f core r a d i u s but dependent on temperature which i s the o p p o s i t e of the b e h a v i o u r expected o f a van der Waals energy. We b e l i e v e t h a t the s e p a r a t i o n energy i s due to the n e c e s s i t y f o r the shear f i e l d to t e a r p a r t i c l e s apart at a r a t e which i s f a s t e r than the r e l a x a t i o n time o f the i n t e r a c t i n g polymer c h a i n s . The r e l a x a t i o n time f o r the PEO chains can be expected to be (19, 20) about 5 χ 10" s e c . The l i f e - t i m e o f a 4



δ

*

ΕΡ*

3

suspension

SP*

2

SP:

SP*

3

polymerisation

35

43

35

25

0

160

116

116

116

r

Latex P r e p a r - Temperature a a t i o n Method °C ° . (nm)

SP*

No.

190

150

160

170

^

* ΕΡ:

a = a + Hδ* inm9 (nm? « - 2ι

0.05

0.06

0.05

-1

polymerisation.

6

8

6

4

c

Field. E /kT

—§

0.03-.01

N m

Β

τ„

by Shear

Emulsion

0.20

0.12

0.14

0. 15

Ρ

φ

Energy R e q u i r e d f o r S e p a r a t i o n o f Doublets

2

Fig.

—

Table 1.

206


BEHAVIOR

shear d o u b l e t , t g , i s g i v e n by E q u a t i o n (6) and even f o r D = 10^ sec i t i s about 7 χ 10-3 c; i t w i l l be even l o n g e r f o r lower shear r a t e s , so t h e r e i s ample time f o r the chains to f i n d t h e i r time averaged c o n f i g u r a t i o n s as the p a r t i c l e s approach and r o t a t e around one another i n a d o u b l e t . Suppose t h a t the p a r t i c l e s are b e i n g s e p a r a t e d by a simple l a m i n a r shear f i e l d w i t h a v e l o c i t y g r a d i e n t o f 300 s e c " . I f the p a r t i c l e c e n t r e s are d i s p l a c e d by one diameter i n the d i r e c t i o n o f the v e l o c i t y g r a d i e n t , then the v e l o c i t y o f one p a r t i c l e w i t h r e s p e c t to the o t h e r i s 3 χ 10~3 χ 300 = 1 0 ' cm s e c " . I f the d i s t a n c e o f polymer interpénétration i the d o u b l e t a p a r t i or an o r d e r o f magnitude f a s t e r than the polymer c h a i n s can r e l a x . Hence the shear f i e l d has to "tear the p a r t i c l e s a p a r t . On the o t h e r hand, when s e p a r a t i o n o c c u r s by Brownian m o t i o n , the p r o c e s s can o c c u r s l o w l y enough to a l l o w the polymer c h a i n s to r e l a x (tg > 10" sec). In our a n a l y s i s o n l y the energy r e q u i r e d f o r shear s e p a r a t i o n i s i m p o r t ant and T a b l e I shows t h a t i t has a v a l u e o f a few times k T . As a f u r t h e r p i e c e o f c i r c u m s t a n t i a l evidence f o r the h y p o t h e s i s t h a t c h a i n : c h a i n i n t e r a c t i o n s are r e s p o n s i b l e f o r the Bingham y i e l d v a l u e , we show i n F i g u r e 7 a p l o t o f E a g a i n s t (1 - Θ / Τ ) . A c c o r d i n g to F l o r y s a n a l y s i s (17), the f r e e energy change which o c c u r s on m i x i n g polymer chains i s -

1

s e

1

2

1

11

g

f

δ(Δ G/kT) -

constant

ψ ( 1 - Θ/Τ)δν 1

and a l t h o u g h the d a t a i s s u b j e c t to a wide margin o f e r r o r i t does appear to c o r r e l a t e w i t h F l o r y s equation. The s u g g e s t i o n t h a t the f a l l o f f i n x at temperatures above θ i s due to a r e d u c t i o n i n the e f f e c t i o n c o l l i s i o n frequency (and hence f(<j>2) i n E q u a t i o n (23)) i s s u p p o r t e d by the d a t a i n F i g u r e 5. For s m a l l p a r t i c l e s , i n c r e a s e s i n temperi have a p r o p o r t i o n a t e l y l a r g e r e f f e c t than fo l a r g e p a r t i c l e s because S*-/a. i s l a r g e r and hence f ( a ) i n E q u a t i o n (22) undergoes l a r g e r changes with t e m p e r a t u r e . The i n t e r p r e t a t i o n o f enhanced v i s c o s i t y i n terms o f the u s u a l d e s c r i p t i o n (14,15) o f the secondary e l e c t r o v i s c o u s e f f e c t ( E q u a t i o n (25)) p r e s e n t s some d i f f i c u l t i e s . A l t h o u g h the e l e c t r o s t a t i c r e p u l s i o n f o r c e s are e s s e n t i a l l y zero i n 1

g

Q


13.

HUNTER

ET

AL.


207

Figure 7. Energy of separation E vs. (1 — θ/T). The straight line suggests that the energy of separation is due to polymer chain interactions. s


208

C O L L O I D A L DISPERSIONS A N D M I C E L L A E B E H A V I O R

these systems t h e r e are s t i l l r e p u l s i v e f o r c e s between the p a r t i c l e s , as i s e v i d e n t from the s t a b i l i t y o f the s o l . A c c o r d i n g to Chan et a l (14) t h i s would cause an i n c r e a s e i n the hydroïïynamic energy d i s s i p a t i o n because the r o t a t i n g d o u b l e t i s i n c r e a s e d i n s i z e and the e f f e c t s h o u l d i n c r e a s e w i t h i n c r e a s e i n V . Yet we f i n d t h a t r a i s i n g the temperature (which reduces V ) causes an i n c r e a s e i n the v a l u e o f E i n E q u a t i o n (24) (see F i g u r e 7 ) . T h i s i s e s p e c i a l l y t r u e o f the u n s t a b l e s u s p e n s i o n s above the t h e t a temperature where the i n t e r a c t i o n i s wholly a t t r a c t i v e . The c o l l i s i o n doublet would i n t h a t case presumably be s m a l l e r than i t i s at lower t e m p e r a t u r e s One e f f e c t o l i m i t the approach o f two p a r t i c l e s d u r i n g a c o l l i s i o n because the outflow time f o r the i n t e r v e n i n g f l u i d i s l o n g compared to the c o l l i s i o n t i m e . T h i s i s e s p e c i a l l y t r u e f o r l a r g e r p a r t i c l e s and above a = 5 ym i t becomes the dominant e f f e c t . The b e h a v i o u r o f s m a l l e r p a r t i c l e s ( a < 1 ym) i s not known w i t h such c e r t a i n t y but i t i s c l e a r t h a t i f the hydrodynamic f o r c e s are to be l a r g e enough to s e p a r a t e a c o l l i s i o n d o u b l e t , the p a r t i c l e s i n v o l v e d cannot be p e r m i t t e d to approach to the p o t e n t i a l energy minimum. Perhaps the d i f f e r e n c e i n b e h a v i o u r o f these s t e r i c a l l y s t a b i l i s e d systems can be t r a c e d to the f a c t t h a t the r e p u l s i v e f o r c e does not appear u n t i l polymer c h a i n i n t e r p é n é t r a t i o n i s s i g n i f i c a n t . The d e t a i l e d c a l c u l a t i o n o f the energy d i s s i p a t i o n as the d o u b l e t r o t a t e s and s e p a r a t e s would pose v e r y c o n s i d e r a b l e d i f f i c u l t i e s i n t h i s c a s e , s i n c e the flow b e h a v i o u r o f the i n t e r v e n i n g f l u i d i s undoubted l y i n f l u e n c e d by the l o c a l polymer segments. Some a s p e c t s o f t h i s work are p u b l i s h e d elsewhere {22_, 23) . R

R

g

0

ç

Summary Latex p a r t i c l e s s t a b i l i z e d by adsorbed h y d r o p h i l i c polymers e x h i b i t both p s e u d o p l a s t i c and Ostwald type flow b e h a v i o u r i n the neighbourhood o f the c r i t i c a l f l o c c u l a t i o n temperature ( c f . t . ) , which corresponds c l o s e l y to the t h e t a - t e m p e r a t u r e o f the adsorbed p o l y m e r . Ostwald flow occurs below the t h e t a temperature i n s t a b l e systems w i t h a f i n i t e , though s m a l l , y i e l d v a l u e . I t can be e x p l a i n e d q u a n t i t a t i v e l y by c a l c u l a t i n g the excess energy which the shear f i e l d must s u p p l y to d e s t r o y a l l


13.

HUNTER

209


ET AL.

d o u b l e t s not broken down by Brownian m o t i o n . At and above the c . f . t . a l l systems e x h i b i t a y i e l d v a l u e , τ „ , and the dependence o f τ on temper a t u r e can be q u a l i t a t i v e l y e x p l a i n e d by c o n s i d e r i n g both the i n t e r a c t i o n energy and the p r o b a b i l i t y o f c o l l i s i o n between p a r t i c l e s . The energy o f i n t e r a c t i o n i s independent o f core p a r t i c l e r a d i u s and i s o f the o r d e r o f a few times k T . The p l a s t i c v i s c o s i t y o f the system obeys the E i n s t e i n r e l a t i o n w i t h an e f f e c t i v e volume f r a c t i o n which suggests t h a t the adsorbed polymer chains are s t r e t c h e d to about twice t h e i r normal r . m . s . length. β

Acknowledgements. T h i s work was supported by g r a n t s from the A u s t r a l i a n Research Grants Committee and by an A u s t r a l i a n Government Post Graduate S t u d e n t s h i p B.A.F. Literature

for

Cited.

1.

E v a n s , R., Napper, D . H . (1973), 251, 329, 409.

2.

Napper, D . H . 21, 168.

J.

Colloid

Interface

Sci.

(1969),

3.

Napper, D . H . 32, 106.

J.

Colloid

Interface

Sci.

(1970),

4.

Napper, D.H., N e t s c h e y , A . face Sci. (1971), 37, 528.

J.

Colloid

5.

Hunter, R.J., N i c o l , S.K. Interface Sci., (1968), 28,

J. 250

Colloid

6.

Friend, J.P., Hunter, R.J. face Sci. (1971), 37, 548.

J.

Colloid

7.

O s t w a l d , W.

8.

Smoluchowski, M. von (1917), 92, 129.

9.

G o l d s m i t h , H.L., Mason, S.G., i n "Rheology Theory and A p p l i c a t i o n s " , F . R . Eirich, Ed.Vol.4, p . 167, Academic P r e s s , New Y o r k , 1967.

10.

ibid,

11.

Gillespie, 66, 1077.

p.

Kolloid-Z.Ζ.Polym.

Kolloid-Z.Z.Polym.

(1925),

Z. phys.

Chem.

Inter

Inter 36,

99.

(Leipzig)

173. T.,

Wiley,

R.,

J.

Phys.

Chem.(1962)



210

BEHAVIOR

12.

Conway, B.E., D o b r y - D u c l a u x , Α . , i n "Rheology Theory and A p p l i c a t i o n s " , F . R . Eirich Ed., V o l . 3 C h a p . 3 , Academic P r e s s , New Y o r k , 1960.

13.

Krieger, I.M., Advan. (1972), 3, 111.

14.

Chan, F.S., Blachford, J. Colloid Sci. (1966),

15.

Stone-Masui, J., Watillon, Α., J. Interface Sci. (1968), 28, 187.

16.

Kotera, Α . , Kolloid-Z.Z.

17.

Flory, P.J. " P r i n c i p l e s o f Polymer Chemistry," Chapter 14, C o r n e l l u n i v e r s i t y p r e s s , New Y o r k , 1953.

18.

ibid.

19.

T h u r s t o n , G.B., S c h r a g , J.L. (1968), P a r t A - 2 , 6, 1331.

20.

Thurston, (10), 421.

21.

M i c h a e l s , A.S., Chem. Fundam.

B o l g e r , J.C. 1, 153.

22.

Neville, P.C., I n t e r f a c e Sci.

Hunter, R.J. J. (1974) ( i n p r e s s ) .

23.

Firth, B.A., Neville, J. Colloid Interface

Furusawa, Polym

Colloid

Interface

J., G o r i n g , 22, 378.

K.,

Sci.

D.A.I. Colloid

Takeda, Y .

p . 606

G.B.,

Morrison,

J.

J.D.

Polym. Polymer

(1962)

Sci. (1969)

Ind. Eng. Colloid

P.C., H u n t e r , R.J. Sci. (1974) ( i n p r e s s ) .


14 Nonaqueous Dispersion: Carbon Black in Heptane Solution of Manganese and Zinc Salts of 2-Ethylhexanoic Acid B. R. VIJAYENDRAN Copier Products Division, Pitney Bowes, Inc., Norwalk, Conn. 06852

Introduction Nonaqueous d i s p e r s i o n s have drawn c o n s i d e r a b l e amount o f a t t e n t i o n r e c e n t l y b o t h from t h e academic and industrial chemists. S e v e r a l papers (1-10) have been p u b l i s h e d in this a r e a c o v e r i n g v a r i o u s a s p e c t s such as c o a g u l a t i o n , origin o f c h a r g e , stability, theoretical studies, e t c . , of the interesting as w e l l as industrially u s e f u l nonaqueous d i s p e r s i o n s . Patent literature i s abundant w i t h v a r i o u s com p o s i t i o n s o f nonaqueous d i s p e r s i o n s useful in organic c o a t i n g s and paints. One a r e a where nonaqueous d i s p e r s i o n s have found some new a p p l i c a t i o n s has been in electrostatic c o p y i n g as well as in electro - d e p o s i t i o n o f paints. The electrical characteristics of the dispersed particles a r e o f paramount impor t a n c e in such a p p l i c a t i o n s . We shall restrict to this a s p e c t o f nonaqueous d i s p e r s i o n s in this s t u d y . In the electrostatic copying process using liquid development (11), t h e latent electrostatic images a r e toned from a s u s p e n s i o n (commonly called t o n e r ) c o n s i s t i n g o f charged c o l o r e d particles ( c a r r y i n g electrical c h a r g e o p p o s i t e t o t h a t o f t h e latent image) in a low dielectric and insulating s o l v e n t . The charged t o n e r particles m i g r a t e t o t h e o p p o s i t e l y charged image a r e a s on t h e p h o t o c o n d u c t o r through e l e c t r o p h o r e t i c m o b i l i t y . I n some c a s e s , t h e r e i s a l s o some d i e l e c t r o p h o r e s i s due t o t h e inhomogenous e l e c t r i c f i e l d around t h e image. E l e c t r o s t a t i c c o l o r c o p y i n g has been a h c i e v e d by a s i m i l a r process using the photoelectrophoresis p r o p e r t y o f some m a t e r i a l s (12). As one c a n s e e , t h e charge on t h e t o n e r p a r t i c l e i s v e r y i m p o r t a n t f o r e l e c t r o s t a t i c copying process. Besides, the charge on t h e p a r t i c l e a l s o i m p a r t s t h e n e c e s s a r y 211


212


MICELLAR

BEHAVIOR

s t a b i l i t y t o the toner d i s p e r s i o n s . Table I l i s t s some o f the t y p i c a l p r o p e r t i e s o f t o n e r s based on carbon black. Table I

(13,

35)

T y p i c a l P r o p e r t i e s and P r o c e s s Parameters f o r E l e c t r o p h o r e t i c Development o f L a t e n t Images

Particle size Average t o n e r charge Zeta p o t e n t i a l D i e l e c t r i c constant o f medium Volume r e s i s t i v i t y o f medium

0.05 - 2 micrometers 10"" - 10-13 m i c r o c o u l 20 - 75 mV 10

2-3 10*°

χ 5-40 cm' sec.volt

Electrophoretic mobility Apparent s u r f a c e potential

ohms-cms

150

- 250

10-5

volts

The a c t u a l mechanism r e s p o n s i b l e f o r c h a r g i n g t h e suspended p a r t i c l e s i n low d i e l e c t r i c c o n s t a n t and h i g h l y i n s u l a t i n g l i q u i d s i s n o t w e l l u n d e r s t o o d . In g e n e r a l , charges on p a r t i c l e s i n l i q u i d s a r e p r o duced by one o f t h r e e phenomena (1£) : Contact e l e c t r i f i c a t i o n , p r e f e r e n t i a l adsorption of ions and p r o t o n t r a n s f e r . C o n t a c t p o t e n t i a l o c c u r s when e l e c t r o n s move between two s o l i d s , two l i q u i d s , o r a s o l i d and l i q u i d as a r e s u l t o f a d i f f e r e n c e i n t h e work f u n c t i o n s . E l e c t r o n s move from the m a t e r i a l w i t h t h e lower work f u n c t i o n t o the m a t e r i a l w i t h the h i g h e r work f u n c t i o n , and the s u r f a c e s a c q u i r e p o s i t i v e and n e g a t i v e c h a r g e s , r e s p e c t i v e l y . Such a c h a r g i n g mechanism i s r e s p o n s i b l e f o r t h e f i r e h a z a r d i n t h e p e t r o l e u m i n d u s t r y (15). T h e r e a r e s e v e r a l e x p e r i m e n t a l s t u d i e s t o show t h a t s e l e c t i v e a d s o r p t i o n o f i o n s g e n e r a t e s charge on the p a r t i c l e . J u s t t o mention a few: Koelmans and Overbeek (16) r e p o r t e d e l e c t r o p h o r e t i c m o b i l i t y v a l u e s o f s e v e r a l s u b s t a n c e s i n x y l e n e and found 2°3 BaSO^ i n x y l e n e became p o s i t i v e l y c h a r g e d by the a d s o r p t i o n o f o l e i c a c i d , f a t t y a c i d s , Cu (17, 18) O l e a t e and A e r o s o l OT; S i 0 and CaCO became p o s i t i v e by the a d s o r p t i o n o f A e r o s o l OT; Carbon b l a c k i n benzene became p o s i t i v e by the adsorption of calcium s a l t of d i - i s o p r o p y l s a l i c y l i c a c i d (19). The n a t u r e and magnitude o f the charge i s i n f l u e n c e d s t r o n g l y by the p r e s e n c e o f t r a c e amounts o f water i n the system. T h i s i s v e r y p r o F e

a

n

d

9

J


14.

vijAYENDRAN

Nonaqueous Dispersions

213

nounced f o r p a r t i c l e s h a v i n g p o l a r groups such as Ti0 # A 1 0 and F e 2 Û . Papers r e l a t i n g t o t h i s a s p e c t (ίθ_, 21) o f nonaqueous s u s p e n s i o n s have been published. I t i s i n t e r e s t i n g t o note t h a t the normal z e t a p o t e n t i a l o f 50 - 125 mV o b s e r v e d i n nonaqueous systems i s g e n e r a t e d by something l i k e 10 - 30 i o n s adsorbed p e r p a r t i c l e . Because o f such low c o n c e n t r a t i o n s needed f o r the c h a r g i n g o f p a r t i c l e s , v e r y s m a l l q u a n t i t i e s o f i m p u r i t i e s w i l l a f f e c t the results drastically. T h i s i s p r o b a b l y one r e a s o n why r a t h e r c o n t r a d i c t o r y e x p e r i m e n t a l r e s u l t s on s i m i l a r systems have been r e p o r t e d i n the l i t e r a t u r e . Fowkes and a s s o c i a t e s (22) have p r o p o s e d a p r o t o n t r a n s f e r mechanism i n an attempt t o e x p l a i n the n a t u r e o f s u r f a c appears t o e x p l a i n th p a r t i c l e s suspended i n h y d r o c a r b o n l i q u i d s i n the p r e s e n c e o f polymers c a p a b l e o f u n d e r g o i n g a p r o t o n t r a n s f e r w i t h the p a r t i c l e s u r f a c e . T h i s view i s c o n f i r m e d i n a r e c e n t s t u d y (23). The aim o f t h i s paper i s t o p r e s e n t the d a t a o b t a i n e d i n the study o f a c a r b o n b l a c k ( S t e r l i n g R) i n heptane i n the study o f manganese and z i n c octoates ( s a l t s of 2-ethylhexanoic a c i d ) . Data on the e l e c t r i c a l c o n d u c t i v i t i e s o f the heptane s o l u t i o n s o f the two o c t o a t e s , a d s o r p t i o n i s o t h e r m o f the two o c t o a t e s on S t e r l i n g R as w e l l as z e t a p o t e n t i a l o f S t e r l i n g R i n the heptane s o l u t i o n s c o n t a i n i n g the s a l t s a r e r e p o r t e d . I t i s accepted i n t h i s work, t h a t i o n p a i r s a r e i n e q u i l i b r i u m w i t h f r e e i o n s d e s p i t e the f a c t t h a t the d i e l e c t r i c c o n s t a n t o f the medium i s low. Z i n c o c t o a t e was chosen f o r t h i s s t u d y , s i n c e c o n d u c t i v i t y s t u d i e s of m e t a l soaps i n nonaqueous media ( 2 £ , Z 5 , 26) have shown t h a t z i n c soaps behave d i f f e r e n t l y because o f the weaker i n t e r a c t i o n s o f the z i n c - c a r b o x y l a t e bond. S i n c e t h i s p r o p e r t y o f z i n c soaps i n n o n aqueous l i q u i d s p l a y s a r o l e i n d e t e r m i n i n g i t s solution properties, v i z . , equivalent conductivity, i t appears t h a t i t i s r e a s o n a b l e t o assume here t h a t i t s h o u l d a l s o a f f e c t the e l e c t r o p h o r e t i c p r o p e r t y o f the suspended p a r t i c l e s . Manganese o c t o a t e was chosen as the r e p r e s e n t a t i v e o f m e t a l soaps h a v i n g f a i r l y s t r o n g p o l a r bond. Hopefully, the d i f f e r e n c e s i n the e l e c t r o p h o r e t i c b e h a v i o r o f c a r b o n b l a c k i n the two m e t a l o c t o a t e s , i f a n y , would shed some l i g h t on the mechanism o f c h a r g i n g of c a r b o n b l a c k i n the p r e s e n t system. 2

2

3 #

3

Experimental


214

COLLOIDAL

DISPERSIONS A N D

MICELLAR

BEHAVIOR

Materials. Manganese 2 - e t h y l h e x a n o a t e ( r e f e r r e d to as manganese o c t o a t e - M n ( o c t > 2 ) and z i n c 2 - e t h y l hexanoate ( z i n c o c t o a t e - Z n ( o c t ) ) were o b t a i n e d from R e s e a r c h O r g a n i c / I n o r g a n i c C h e m i c a l Corp., Sun V a l l e y , C a l i f o r n i a . These were used w i t h o u t any further purification. The m e t a l c o n t e n t o f t h e two o c t o a t e s d e t e r m i n e d u s i n g atomic a b s o r p t i o n a g r e e d w e l l w i t h t h e t h e o r e t i c a l m e t a l c o n t e n t assuming M n ( o c t ) 2 and Z n ( o c t ) t o be t h e i r c o m p o s i t i o n s . The r e s u l t s were as f o l l o w s ( t h e o r e t i c a l v a l u e s i n parenthesis): Mn(oct) : Μ η 15.91 (16.11%); Z n ( o c t ) 2 : An 18.2% (18.5%). The s a l t s were k e p t o v e r P 0 p r i o r t o b e i n g used. Reagent grade η-heptane was r e f l u x e d o v e r P 2 Û 5 and f r a c t i o n a l l y d i s t i l l e d . S t e r l i n g R o f t h e Cabo o f c a r b o n b l a c k . Th b l a c k was e x t r a c t e d w i t h a c e t o n e and heptane. The washed sample was d r i e d a t 100 - 110°C f o r 2-3 hours b e f o r e the p r e p a r a t i o n o f the suspension. The BET s u r f a c e a r e a o f S t e r l i n g R has been found t o be 21 m^/g and t h e s u r f a c e showed p r e s e n c e o f some v o l a t i l e >CO g r o u p s . 2

2

2

2

5

Procedure. S o l u t i o n s of the metal octoates i n heptane were p r e p a r e d by a d d i n g known amounts o f t h e s a l t t o a c o n v e n i e n t volume o f heptane. Electrical c o n d u c t i v i t i e s of the metal octoate s o l u t i o n s i n heptane were measured u s i n g a 1620A G e n e r a l Radio c a p a c i t a n c e assemblv and Balsbaugh p r e c i s i o n t h r e e t e r m i n a l c e l l a t 25 C. Extreme c a r e was t a k e n t o e l i m i n a t e any p o s s i b l e m o i s t u r e c o n t a m i n a t i o n d u r i n g the c o n d u c t i v i t y as w e l l as o t h e r measurements. A d s o r p t i o n i s o t h e r m s o f t h e two o c t o a t e s from heptane on S t e r l i n g R a t 25°C were d e t e r m i n e d . Carbon b l a c k s u s p e n s i o n s i n heptane c o n t a i n i n g v a r i o u s known amounts o f manganese and z i n c o c t o a t e s were p r e p a r e d by a d d i n g a s m a l l q u a n t i t y o f t h e c a r b o n b l a c k t o 100 ml o f heptane s o l u t i o n and t h e n s u b j e c t i n g t o a brief ultrasonic radiation. Then t h e s u s p e n s i o n s were shaken f o r 24 h o u r s t o a t t a i n e q u i l i b r i u m . The c o n c e n t r a t i o n o f the metal o c t o a t e i n the s o l u t i o n a f t e r t h e a t t a i n m e n t o f a d s o r p t i o n e q u i l i b r i u m was determined. I n t h e c a s e o f manganese o c t o a t e , a s i m p l e a b s o r p t i o n v s . c o n c e n t r a t i o n p l o t a t 600 nm was used t o d e t e r m i n e t h e r e s i d u a l c o n c e n t r a t i o n o f manganese o c t o a t e . I n t h e case o f z i n c o c t o a t e , atomic a b s o r p t i o n was used t o d e t e r m i n e t h e z i n c content. M i c r o e l e c t r o p h o r e s i s on t h e S t e r l i n g R s u s p e n s i o n s were c a r r i e d o u t t o o b t a i n z e t a p o t e n t i a l .


14. vijAYENDRAN

215


The f l a t c e l l used was c o n s t r u c t e d o f q u a r t z and has been d e s c r i b e d elsewhere (27_) · S u s p e n s i o n s o f S t e r l i n g R i n heptane c o n t a i n i n g v a r i o u s concen t r a t i o n s o f manganese and z i n c o c t o a t e s f o r t h e e l e c t r o p h o r e s i s experiments were p r e p a r e d by d i l u t i n g the s u s p e n s i o n s made f o r a d s o r p t i o n s t u d i e s w i t h t h e appropriate metal octoate s o l u t i o n such-that the c o n c e n t r a t i o n i s about 10 p a r t i c l e s / c m . Immediately b e f o r e f i l l i n g t h e c e l l t h e d i s p e r s i o n s were s u b j e c t e d t o u l t r a s o n i c r a d i a t i o n f o r 5 m i n u t e s . Carbon b l a c k p a r t i c l e s d i s p e r s e d by t h e m e t a l o c t o a t e s were a g g r e g a t e s which were n e a r l y s p h e r i c a l and t h e mean d i a m e t e r o f which were 1 - 3 ym. Experiments were done a t 2 5 ° C The c r i t e r i a f o o b s e r v e d and t h e d i s t r i b u t i o n o f v e l o c i t i e s , from w a l l t o w a l l was p a r a b o l i c i n a l l c a s e s (2£) . Only a f t e r a s t e a d y s t a t e had been r e a c h e d w i t h i n t h e c e l l (=30 - 45 minutes) measurements o f t h e e l e c t r o p h o r e t i c m o b i l i t y were made. Between 6 - 1 0 p a r t i c l e s were t r a c k e d o v e r a d i s t a n c e o f 48 pm and the f i e l d p o l a r i t y was o f t e n r e v e r s e d t o e n s u r e . absence o f p o l a r i z a t i o n . F i e l d s as h i g h as 15Ov cm"" were used i n t h e p r e s e n t work w i t h o u t any e v i d e n c e o f polarization. T h i s i s i n agreement w i t h t h e f i n d i n g s o f van d e r Minne and Hermanie (28) and P a r r e i r a (27) who used h i g h f i e l d s w i t h c a r b o n b l a c k i n benzene. The e l e c t r o p h o r e t i c m o b i l i t y μ i s r e l a t e d t o the z e t a p o t e n t i a l ζ by t h e E q u a t i o n , l e

ζ = K-f ( K a ) " y i r « n / e

(1)

where f (ica) i s t h e Henry f a c t o r , η i s t h e v i s c o s i t y o f t h e medium, ε i s t h e d i e l e c t r i c c o n s t a n t o f t h e medium, and Κ i s t h e c o r r e c t i o n f a c t o r due t o t h e r e l a x a t i o n e f f e c t o f the double l a y e r . The a p p r o p r i a t e v a l u e o f f (ica) depends on t h e shape o f t h e p a r t i c l e and a l s o t h e r e l a t i v e magn i t u d e s o f t h e " t h i c k n e s s o f t h e double l a y e r " κ " and t h e p a r t i c l e r a d i u s a . I n nonaqueous systems the d o u b l e l a y e r i s q u i t e extended (jc-l. i s o f t h e o r d e r o f s e v e r a l micrometers) and as a r e s u l t Ka i s found t o be s m a l l . Under t h e s e c o n d i t i o n s , Henry (29) has shown t h a t f (ica) = 1/6 f o r spheres and i s 1/4 o r 1/8 f o r c y l i n d e r s w i t h t h e i r axes p a r a l l e l o r p e r p e n d i c u l a r t o t h e f i e l d , r e s p e c t i v e l y . The c o r r e c t i o n f a c t o r due t o r e l a x a t i o n (K) i s c l o s e t o u n i t y when Ka i s s m a l l and t h e z e t a p o t e n t i a l i s o f the o r d e r o f 100 mV ( 3 0 ) . Hence E q u a t i o n (1) r e d u c e s t o Henry's e q u a t i o n . 1


216


ζ = 6πη·μ/ε

(2)

f o r spheres. Most a u t h o r s have used f Oca) = 1/6, which i m p l i e s a s p h e r i c a l shape f o r t h e p a r t i c l e s , even though van d e r Minne and Hermanie (28) assumed a v a l u e o f 1/4 w i t h o u t an a p p a r e n t r e a s o n . Recently, Lewis and P a r f i t t (31) f e l t t h a t a v a l u e o f 1/6 c o u l d n o t be j u s t i f i e d s i n c e t h e r e was e l e c t r o n m i c r o s c o p e e v i d e n c e t o show t h a t l i n e a r a g g r e g a t i o n o f p a r t i c l e s r e s e m b l i n g r i g i d c y l i n d e r s w i t h t h e i r axes p a r a l l e l t o t h e f i e l d were formed, b e f o r e t h e e l e c t r o p h o r e t i c measurements were made. Hence t h e y used a v a l u e o f f ( K a ) = 1/4. As mentioned above f ( K a ) can v a r y from 1/4 t o 1/8, t h e r e f o r e , t h e t r u e v a l u e o f f (fca) must l i e between t h o s e l i m i t s . Thus, the v a l u e o f 1/6 used i n t h i s , and o t h e r works, appears t o r e p r e s e n t b e s t v a l u e f o r f ( K a ) d e s p i t e an assumed s p h e r i c a l shape f o r t h e c a r b o n b l a c k p a r t i c l e s . Results F i g u r e 1 shows the v a r i a t i o n i n c o n d u c t a n c e w i t h concentration of Mn(oct) and Z n ( o c t ) 9 s a l t s i n heptane. F i g u r e 2 shows t h e e f f e c t o f c o n c e n t r a t i o n on t h e e q u i v a l e n t conductance. The most s t r i k i n g f e a t u r e s of the r e s u l t s a r e , f i r s t , the r e l a t i v e l y h i g h c o n d u c t i v i t i e s o f t h e m e t a l o c t o a t e s i n such a non p o l a r s o l v e n t as heptane and, s e c o n d l y , t h e u n u s u a l form o f the e q u i v a l e n t c o n d u c t a n c e c o n c e n t r a t i o n r e l a t i o n i n the case o f Z n ( o c t ) . We s h a l l discuss this later. Conductance o f t h e magnitude o b s e r v e d h e r e has been r e p o r t e d by o t h e r s i n t h e f o l l o w i n g systems : A e r o s o l OT i n heptane (20); m e t a l soaps i n t o l u e n e (2E[, 26) and o t h e r s (24) ; t h i s shows t h a t the c o n d u c t i o n i s due t o i o n s and/or o t h e r c h a r g e d s p e c i e s such as m i c e l l e s o r t r i p l e i o n f o r m a t i o n o f t h e m e t a l o c t o a t e s i n heptane. F i g u r e 3 shows the a d s o r p t i o n i s o t h e r m o f t h e two m e t a l o c t o a t e s on S t e r l i n g R. The manganese s a l t appears t o be adsorbed more so t h a n t h e z i n c salt. F i g u r e 4 g i v e s the z e t a p o t e n t i a l of S t e r l i n g R i n t h e two o c t o a t e s o l u t i o n s . S t e r l i n g R i s charged p o s i t i v e l y i n a l l the s o l u t i o n s . I n p u r e heptane no e l e c t r o p h o r e t i c m o b i l i t y i s o b s e r v e d . This i s i n agreement w i t h t h e o b s e r v a t i o n o f o t h e r s (31, 32^, 33). The z e t a p o t e n t i a l i s found t o d e c r e a s e , a f t e r an i n i t i a l s h a r p i n c r e a s e , w i t h i n c r e a s i n g concen t r a t i o n o f t h e o c t o a t e s . The maximum i n t h e z e t a p o t e n t i a l a t low c o n c e n t r a t i o n has been o b s e r v e d by 2

2


217


0

100

200

300

Metal Octoate Concentration

mM/1

Figure 1. Effect of metal concentration of metal octoate on conductivity. Q: Mn(oct) ; Δ: Zn(oct) . 2

2

Figure 2. Effect of metal concentration on equivalent conductance. 0 Mn(oct) ; A' Zn(oct) . :

2

2



15

30

45

Metal Octoate

Concentration

60 mM/1

Figure 4. Effect of metal octoate concentra tion on the zeta potential of Sterling R in heptane. Q: Mn(oct) ; Δ: Zn(oct) . 2

2


BEHAVIOR

14.

vijAYENDRAN


219

o t h e r s working w i t h c a r b o n b l a c k i n nonaqueous media (19, 31, 32, 3 3 ) . The maximum has n o t been f u l l y u n d e r s t o o d , even though a few h y p o t h e s i s have been advanced. B e l l and L e v i n e (3£) a s c r i b e d t h e maximum t o a d i s c r e e t n e s s o f charge e f f e c t . The p r e s e n c e o f water has been i n v o k e d . I t i s also possible that i t may be caused by t h e d i f f e r e n c e s i n conductances between t h e b u l k and t h e s u r f a c e p h a s e s , p a r t i c u l a r l y a t low s a l t c o n c e n t r a t i o n s , where t h e maximum generally occurs. An i n t e r e s t i n g s p e c u l a t i o n (32) t h a t may be worth c o n s i d e r i n g h e r e i s whether t h e 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 (cmc) o f t h e s a l t s i s r e l a t e d t o t h e maximum. I n t h e c a s e o f Mn(oct)2 t h e maximum i s seen t o o c c u r a t a lower c o n c e n t r a t i o n as compared t o t h a t i n Z n ( o c t ) . The z e t a p o t e n t i a l i s seen t o be lower i n Z n ( o c t ) t h a n i n M n ( o c t ) . Discussion The r e l a t i v e l y h i g h c o n d u c t i v i t i e s o f t h e m e t a l o c t o a t e s i n heptane c l e a r l y i n d i c a t e t h e r e i s some degree o f d i s s o c i a t i o n o f t h e s e s a l t s i n heptane. Such o c c u r e n c e o f i o n i c conductance i n m e t a l soaph y d r o c a r b o n systems have been r e p o r t e d exhaustively (24, 25, 26) . C o n d u c t i v i t y b e h a v i o r and m i c e l l e f o r m a t i o n o f m e t a l soaps i n nonaqueous l i q u i d s r e s u l t s from t h e i n t e r p l a y o f a wide v a r i e t y o f intermolecular forces. The c o n d u c t i v i t y o f soaps depend on t h e m e t a l - c a r b o x y l a t e bond (whether i t i s p o l a r , i o n i c o r n o n - p o l a r ) and t h e tendency t o form micelles. Increasing p o l a r i t y of the metal-carboxyl a t e bond has been found t o i n c r e a s e c o n d u c t i v i t y (25, 2 6 ) , b u t soaps h a v i n g i o n i c t y p e m e t a l - c a r b o x y l a t e bond a r e o f t e n found t o be i n s o l u b l e i n n o n p o l a r liquids. The m i c e l l e f o r m a t i o n i n nonaqueous l i q u i d s (the m i c e l l e s a r e o f i n v e r s e s t r u c t u r e , namely, t h e p o l a r groups a r e i n t h e c o r e and t h e non p o l a r h y d r o c a r b o n c h a i n s f a c i n g t h e s o l v e n t ) depends on t h e a c i d ( s o f t o r hard) and base c h a r a c t e r i s t i c s o f t h e soap as w e l l as t h e s o l v e n t . These f a c t o r s g o v e r n i n g m i c e l l e s f o r m a t i o n i n nonaqueous l i q u i d s have been t r e a t e d (24). N e l s o n and P i n k (25, 26) measured c o n d u c t i v i t i e s and a g g r e g a t i o n numbers o f d i v a l e n t soaps i n t o l u e n e and found t h a t t h e c o n d u c t i v i t y i n c r e a s e d i n t h e order o f increasing p o l a r i t y of the metal-carboxylate bond i n t h e approximate o r d e r o f z i n c , c o p p e r , n i c k e l , manganese, magnesium and c a l c i u m . They a l s o found t h a t t h e a g g r e g a t i o n numbers t o be l e s s i n z i n c soaps as compared t o n i c k e l o r magnesium s o a p s . The h i g h e r


220

C O L L O I D A L DISPERSIONS A N D M I C E L L A E

BEHAVIOR

degree o f a s s o c i a t i o n i n n i c k e l o r magnesium soaps as opposed t o z i n c has been e x p l a i n e d by s t r o n g e r a c i d base i n t e r a c t i o n s i n t h e former c a s e l e a d i n g t o l a r g e r m i c e l l e s (24_) . I n our c a s e , we o b s e r v e s i m i l a r conductance behavior i n Mn(oct) (oct) s o l u t i o n s o f heptane. The manganese o c t o a t e appears t o behave l i k e a s a l t w i t h f a i r l y p o l a r Mn-carboxylate i n t e r a c t i o n s l e a d i n g t o h i g h e r conductance a t lower c o n c e n t r a t i o n and p r o b ably larger m i c e l l e s . I n t h e case o f z i n c o c t o a t e , t h e conductance i s low (compared t o t h a t i n M n ( o c t ) up t o a c e r t a i n c o n c e n t r a t i o n b u t i n c r e a s e s r a p i d l y (more so t h a n M n ( o c t ) ) a t h i g h e r c o n c e n t r a t i o n . This i s more a p p a r e n t i n F i g u r e 2 where i t i s seen t h a t t h e e q u i v a l e n t conductance i n c r e a s e s d r a m a t i c a l l y w i t h concentration i n th p r o b a b l y due t o t h e much lower tendency o f z i n c soaps t o d i s s o c i a t e and form m i c e l l e s i n nonaqueous media ( m i c e l l e s i z e s a r e s m a l l e r and m i c e l l e s a r e n o t o b s e r v e d a t lower c o n c e n t r a t i o n s ) . In the case o f M n ( o c t ) t h e d i s s o c i a t i o n as w e l l as m i c e l l e f o r m a t i o n appears t o be more f a v o r a b l e . The much lower tendency t o form m i c e l l e s i n t h e case o f z i n c i s due t o t h e f a c t t h a t i t i s a s o f t type lewis a c i d (zinc i s a b o r d e r l i n e c a s e and i s a l e s s s t r o n g e r l e w i s a c i d t h a n manganese) and cannot b i n d s t r o n g l y t o t h e c a r b o x y l a t e groups. The a d s o r p t i o n i s o t h e r m o f t h e two o c t o a t e s on S t e r l i n g R r e f l e c t s the d i f f e r e n c e s i n s o l u t i o n p r o p e r t i e s o f t h e two s a l t s i n heptane. Mn(oct) b e i n g more d i s s o c i a t e d t h a n Z n ( o c t ) , i t i s a d s o r b e d more s t r o n g l y t h a n t h e l a t t e r . I t i s r e a s o n a b l e t o assume from t h e c o n d u c t i v i t y d a t a t h a t t h e m e t a l o c t o a t e s d i s s o c i a t e s i n heptane as f o l l o w s : a

n

d

Z n

2

2

2

2

2

2

2

M(oct)2

=

M

(°

c t

)

+

+

oct"

1

S i n c e t h e p a r t i c l e s a r e p o s i t i v e l y c h a r g e d as o b s e r v e d from m i c r o e l e c t r o p h o r e s i s , i t i s a l s o r e a s o n a b l e t o assume t h a t t h e a d s o r p t i o n i s b r o u g h t about by t h e i n t e r a c t i o n o f the p o s i t i v e l y charged ions o f the s a l t s and t h e n e g a t i v e l y c h a r g e d > CO groups p r e s e n t on S t e r l i n g R. T h i s a g a i n would e x p l a i n why M n ( o c t ) i s a d s o r b e d more s t r o n g l y t h a n Z n ( o c t ) . Of c o u r s e , t h e r e w i l l be a d s o r p t i o n o f o t h e r s p e c i e s such as m i c e l l e s on t h e c a r b o n b l a c k which a l s o has some h y d r o p h o b i c s i t e s . Now l e t us l o o k a t t h e z e t a p o t e n t i a l i n t h e two o c t o a t e s o l u t i o n s . Both e x h i b i t a maximum i n t h e 2

2


14.

221


vijAYENDRAN

z e t a p o t e n t i a l b u t t h e maximum i s found t o o c c u r a t a h i g h e r c o n c e n t r a t i o n i n Z n ( o c t ) as compared t o Mn(oct) . As mentioned e a r l i e r , i f t h e maximum i s r e l a t e d t o t h e cmc o f t h e s a l t s then t h i s would be consistent with the observation that m i c e l l e s are formed more e a s i l y i n M n ( o c t ) t h a n i n Z n ( o c t ) ? . However, t h e maximum i n t h i s c a s e i s found t o Be around 1 0 " moles/1 whereas t h e cmc i n nonaqueous media a r e around 1 0 ~ moles/1. T h i s d i s c r e p a n c y may be due t o t h e f a c t t h e o c t o a t e s h a v i n g s h o r t e r c h a i n l e n g t h p r o b a b l y have a h i g h e r cmc. F u r t h e r work i s needed t o u n d e r s t a n d t h e maximum i n z e t a p o t e n t i a l a t low c o n c e n t r a t i o n , which has been o b s e r v e d i n s e v e r a l nonaqueous systems (19, 31, 32,, 33) . I t i s a l s o see i n Z n ( o c t ) as compared t o t h a t i n M n ( o c t ) . This i s c o n s i s t e n t w i t h t h e a d s o r p t i o n i s o t h e r m as w e l l as c o n d u c t i v i t y b e h a v i o r o f t h e s a l t s , namely, M n ( o c t ) i s more d i s s o c i a t e d and adsorbed s t r o n g l y on S t e r l i n g R s u r f a c e thus c r e a t i n g a higher charge. P a r r e i r a (32) i n h i s s t u d i e s on t h e e l e c t r o p h o r e s i s o f c a r b o n b l a c k i n benzene i n t h e p r e s e n c e o f a l k a l i n e e a r t h s u l f o s u c c i n a t e s s a l t s found c a r b o n b l a c k t o be p o s i t i v e l y c h a r g e d and t h e p o s i t i v e charge t o i n c r e a s e i n t h e o r d e r o f BaCO groups and t h e metal. F u r t h e r , he showed t h a t t h e i n t e r a c t i o n energy or the three a l k a l i n e earth metals i s i n the order o f Mg> Ca> Ba. The energy o f i n t e r a c t i o n i s dependent on t h e i o n i c r a d i u s o f t h e m e t a l element, v i z . , s m a l l e r i o n s have a h i g h e r i n t e r a c t i o n e n e r y i n k e e p i n g with the theory t h a t the small i o n i s the p r e f e r e n t i a l l y a d s o r b e d s p e c i e s (16). The same type o f argument can be made t o e x p l a i n t h e a d s o r p t i o n a s w e l l as t h e z e t a p o t e n t i a l r e s u l t s o b t a i n e d i n t h i s s t u d y . G r e a t e r a d s o r p t i o n and h i g h e r z e t a p o t e n t i a l a r e o b s e r v e d w i t h M n ( o c t ) as compared t o Z n ( o c t ) because Mn b e i n g s m a l l e r than Zn +, t h e former i s p r e f e r e n t i a l l y a d s o r b e d and t h e energy o f t h e i o n i n d u c e d d i p o l e i n t e r a c t i o n w i t h >CO groups o f t h e c a r b o n b l a c k w i l l be such t h a t Mn> Zn. Other s i m i l a r s t u d i e s (35) o f c a r b o n b l a c k i n nonaqueous media i n t h e p r e s e n c e o f v a r i o u s m e t a l soaps seem t o agree w i t h t h i s e x p l a n a t i o n . Of c o u r s e t h i s i s a v e r y s i m p l i s t i c p i c t u r e o f the v a r i o u s i n t e r a c t i o n s t a k i n g p l a c e a t t h e i n t e r f a c e o f S t e r l i n g R and heptane i n t h e p r e s e n c e o f m e t a l octoates. One s h o u l d a l s o p r o b a b l y c o n s i d e r t h e n e g a t i v e i o n a d s o r p t i o n as t h e c o n c e n t r a t i o n i n c r e a s e s . 2

2

2

2

4

2

2

E

E

2

+ +

2

+

E

E


222

COLLOIDAL

DISPERSIONS A N D M I C E L L A R

BEHAVIOR

C a r e f u l examination of F i g u r e 4 suggests t h a t zeta p o t e n t i a l decreases with increase i n c o n c e n t r a t i o n and t h i s cannot be c o m p l e t e l y due t o d o u b l e l a y e r compression e f f e c t s s i n c e such e f f e c t s a r e n e g l i g i b l e i n low p e r m i t i v i t y l i q u i d s . T h i s i s p r o b a b l y why Lewis and Parfitt (31) and o t h e r s (2) have found c a r b o n b l a c k s c o n t a i n i n g >C0 groups t o n e g a t i v e l y c h a r g e d by A e r o s o l OT. One cannot a l s o i g n o r e o t h e r hydrophobic i n t e r a c t i o n s a t the i n t e r f a c e . These f a c t o r s a r e d i f f i c u l t t o s e p a r a t e and s t u d y i n d i v i d u a l l y , because o f the complex n a t u r e o f t h e systems. Acknowledgements The a u t h o r wishes t o thank Mr. G. Brana f o r some o f t h e e x p e r i m e n t a l work and Mr. H. H a z e l t o n f o r p r e p a r i n g the graphs. Thanks a r e due t o P i t n e y Bowes f o r p e r m i s s i o n t o p u b l i s h t h i s work. Summary Adsorption isotherm, micro e l e c t r o p h o r e s i s of a S t e r l i n g R c a r b o n b l a c k d i s p e r s e d i n heptane, i n t h e p r e s e n c e o f v a r i o u s c o n c e n t r a t i o n s o f manganese and z i n c s a l t s o f 2-ethylhexanoic a c i d (octoate) are reported. C o n d u c t i v i t y o f t h e two o c t o a t e s i n heptane a r e a l s o r e p o r t e d . D i f f e r e n c e s o b s e r v e d i n the c o n d u c t i v i t y , a d s o r p t i o n and z e t a p o t e n t i a l c h a r a c t e r i s t i c s between t h e two o c t o a t e s a r e a s c r i b e d t o t h e d i f f e r e n c e s i n the metal-carboxylate i n t e r a c t i o n s as w e l l as i o n i c s i z e . The z e t a p o t e n t i a l i s found t o be p o s i t i v e and d e c r e a s i n g w i t h i n c r e a s e i n con c e n t r a t i o n w i t h an i n i t i a l sharp i n c r e a s e . The g e n e r a t i o n o f charge on t h e c a r b o n b l a c k has been found t o be due t o t h e p r e f e r e n t i a l i o n i c a d s o r p t i o n from s o l u t i o n caused by an i o n i n d u c e d s u r f a c e d i p o l e mechanism. Literature 1 2

3 4

Cited

Lyklema, J., Adv. Colloid I n t e r f a c e Sci., (1968), 2, 65. Meadus, F. W., P u d d i n g t o n , I . E . , Sirianni, A. F., and S p a r k s , B. D., J. Colloid I n t e r f a c e Sci., (1969), 30, 46. Koelmans, Η., Phillips R e s e a r c h R e p o r t s , (1955), 10, 161. Parfitt, G. D., and Willis, E., J. Colloid I n t e r f a c e Sci., (1966), 22, 100.


14.

vijAYENDRAN

5

Lawrence, S. G., and Parfitt, G . D., J. Colloid I n t e r f a c e Sci., (1971), 3 5 , 675. Parfitt, G . D . and Wodd, J. Α., J. Chem. S o c . F a r a d a y T r a n s . I., (1973), 69, 1908. B a g c h i , P . and Vold, R. D., J. Colloid I n t e r f a c e Sci. (1970), 33, 405. Beuche, F., J. Colloid I n t e r f a c e Sci. (1972) 4 1 , 374. B a y l i s , R. L., T r a n s . I n s t . M e t a l Finishing (1972), 50, 80. Dowbenko, R., and H a r t , D . P., I n d . E n g . Chem. P r o d . R e s . D e v . , (1973), 12, 14. M e t c a l f e , Κ. Α., J. Sci. Instr., (1955), 32, 74. T u l a g i n , V., J. O p t . S o c . A m e r . , (1969), 59, 328. Envall, A . D . Rev 118. R e i f , R. B., I n d . R e s e a r c h . , (1971), D e c . , 48. K l i n k e r b e r g , Α., and v a n d e r M i n n e , J. L. "Electrostatics i n the P e t r o l e u m I n d u s t r y " , Elsevier, Amsterdam, 1958. Koelmans, H . and Overbeek, J. T h . G., D i s c . F a r a d a y S o c . , (1954), 18, 52. D a r m e r e l l , V . R., and U r a b a n i c , Α., J. P h y s . C h e m . , (1944), 48, 125. D a r m e r e l l , V . R., and M a t t s o n , R . , J. P h y s . Chem., (1944), 48, 134. v a n d e r M i n n e , J. L. and Hermanie, P . H . J., J. Colloid Sci., (1953), 8, 38. K i t a h a r a , Α., Karasawa, S. and Yamada, Η . , J. Colloid I n t e r f a c e Sci., (1967), 25, 490. McGown, D . N . L., Parfitt, G . D., and Willis, E., J. Colloid Sci., (1965), 20, 650. Fowkes, F. Μ . , A n d e r s o n , F . W . , and Moore, R. J., Preprints, 150th American C h e m i c a l S o c i e t y M e e t i n g , City, S e p t . 1965. T a m a r i b u c h i , Κ., and S m i t h , M . L., J. Colloid Inter f a c e Sci., (1966), 22, 404. S h i n o d a , Κ., Ed., " S o l v e n t P r o p e r t i e s o f S u r f a c t a n t S o l u t i o n s " , Chap. 3 , M a r c e l D e k k e r , Inc., N.Y., 1967. N e l s o n , S. M., and P i n k , R . C., J. Chem. S o c . , (1952), 1744. N e l s o n , S. M . and P i n k , R. C., J. Chem. S o c . , (1954), 4412. Parreira, H . C., J. Colloid I n t e r f a c e Sci., (1969), 29, 432. v a n d e r M i n n e , J. L., Hermanie, P . H . J., J. Colloid Sci., (1952), 7, 600. H e n r y , D . C., P r o c . Roy. Soc. London, (1931), A 133, 106.

6 7 8 9 10 11 12 13 14 15

16 17 18 19 20 21 22 Atlantic 23 24

25 26 27 28 29



223

224

COLLOIDAL

DISPERSIONS A N D M I C E L L A R

BEHAVIOR

30 Wiersema, P. Η., Loeb, A. L., and Overbeek, J . Th., G., J . Colloid I n t e r f a c e Sci., (1966), 22, 78. 31 Lewis, Κ. E., and Parfitt, G. D., T r a n s . F a r a d a y Soc. (1966), 62, 1652. 32 Parreira, H. C., J . Electroanal. Chem., (1970), 25, 69. 33 Parreira, H. C., J . Colloid I n t e r f a c e Sci., (1973), 43, 382. 34 Bell, G. M. and L e v i n e , S., D i s c . Faraday Soc., (1966), 42, 97. 35 V i j a y e n d r a n , B. R., (1971), u n p u b l i s h e d work.


15 Micelle Formation in Nonaqueous Media AYAO KITAHARA and KIJIRO KON-NO Science University of Tokyo, Kagurazaka, Shinjiku-ku, Tokyo, Japan

Introduction Experimental facts about micelle formation of oilsoluble surfactants in nonaqueous media have been recently compiled(1-3). Thus micelle formation in nonpolar solvents such as hydrocarbons i a markedly affected by the kind of polar parts of surfactants (4). For example, ionic surfactants make larger micelle than nonionic ones, anionic sulfates making larger micelle than cationic ammonium salts(4). On the other hand, the effect of hydrocarbon parts of surfactants on micelle formation is not so much remarkable than the effect in aqueous media. However, the considerable effect of hydrocarbon parts on micelle formation in nonpolar systems has been recognized. Thus the aggregation number of micelle decreased with increase of the carbon number of hydro carbon part of quarternary ammonium halides or sodium di-(n-alkyl) sulfosuccinates(4). This trend was also shown by metal soaps in toluene(5). In order to consider a theory of micelle formation in nonpolar media, the interaction was divided into two parts, that i s , the interaction among polar parts of surfactants and that of hydrocarbon parts themselves and hydrocarbon parts and solvent molecules. The former can be estimated by ionic force for ionic surfactants or hydrgen bonding for nonionic surfactantsQ3,6,7_ ). As for the effect of hydrocarbon parts, Singleterry and Fowkes suggested the steric hinderanceQê). However, no quantitative explanation about the latter has yet been proposed. In this paper, the idea of the entropie and enthalpic para meters for the interaction of hydrocarbon parts with solvent molcules at micelle formation w i l l be introduced. The idea has been proposed by Flory for dissolution of polymers(8). This idea can be essentially u t i l i z e d for low molecular weight substance. The idea has been used for elucidation of the protective effect on colloidal dispersion, that i s , by F i s c h e r ^ ) , Meier (10), Napper(11) and Bagchi and Void(12) for polymer dispersants and by Ottewill and Walker(13) for surfactant dispersants. 225


226


BEHAVIOR

Theory The model as shown i n Figure I was assumed to make a theory for micelle formation of a surfactant in nonpolar media. It was assumed that the monomer solution of an oil-soluble surfactant is ideal and micelle formed becomes nonideal i n the area which hydrocarbon parts exist. Excess chemical potential of the solvent resulting from nonideality can be expressed as follows(8,13): 2

μ

2

2

- μ°= -δΤ(ψ - κ )ν =-ΕΤ(ψ - κ )c /D ι ι 1 1 2 ι ι

(1)

where ψι and Κ ι are entropie and enthalpic paramters of mixing Proposed by Flory and vz being volume fraction of hydrocarbon part of the surfactant i reduced to c/D(c is the concentratio the area,kg 1~ and D the density of hydrocarbon). Equation (1) was alternatively deduced by Fischer with use of second v i r i a l coefficient Β as Equation ( l ) : 1

- -

μ

2 f

- μ° = -RTBVc (l ) ι ι where V i s the p a r t i a l molar volume of the solvent. On the other hand, the excess osmotic pressure π can be related to excess chemical potential by the following equation thermodynamically: β χ

μ

ι

- μ° = -π V ι ex

(2)

v

Equation (3) can be obtained from Equation (1) and (2): 2

IT =ΕΤ(ψ - κ ) c / V D ex ι i

2

(3)

Hence the free energy change of hydrocarbon parts, AG, resulting from micelle formation can be expressed by Equation ( 4 ) . ? ?

2

2

AG, =/TT dV = {ΕΤ(ψ -κ )c /VD }/dV η ex ι 1

(4)

where fdV shows the volume of the area which hydrocarbon parts exist. We concider ionic surfactants i n this paper. Interaction among polar parts can be expressed by electrostatic force i n ionic parts. It can be written in micelle as follows: 2

AG.=-Xe / 2 · 4 π ε ° d 1 et

(5)

where λ is the aggregating number of micelle, e the elementary c h a r g e , £ the effective permittivity and d interionic distance i n the interior of micelle. The numeral 2 is the factor for pair counting. ε

β


15.

KiTAHARA

227

Micelle Formation

AND KON-NO

Total free energy change following micelle formation ^G is the sum of Equations (4) and (5). That i s , AG=AG.

+ A G

h

. JMiz£i)£i =

1

/ d V

-

X e

VD*

*

(6)

8ve° d f

Furthermore, c can be rewitten as follows:

e

(7)

c=Np X//dV 0

where Ν and ρ are the number and the mass of CH group in the hydrocarbon part of the surfactant. Then Equation (6) is reduced to Equation (8) with use of Equation (7), 2

L c

_ RTÇih-KQNWX

2

Xe^

(

g

)

V Numerical Calculations A few assumptions were made i n order to calculate numerically: 1) We assumed that micelle is a concentric sphere as shown in Figure 2 in which the polar ionic part makes an inner sphere having radius R and the hydrocarbon area makes an outer sphere having thickness r . For a surfactant having longer hydrocarbon, thickness of the hydrocarbon area is thicker than the ionic part, so that r » R was assumed as an extreme case. Then we can obtain the following equation: 3

JdV= 4 π τ / 3

(9)

Contrary, for a surfactant of shorter hydrocarbon, r « R can be assumed as another extreme case. Then Equation (10) can be obtained: 2

/dV= 4TCRr

(10)

2) Next, we assumed two limiting cases for r . model was taken for longer hydrocarbon, that i s , r= ( 2 N 1 )

1/2

A polymer

(11)

where 1 is the carbon-carbon distance. On the other hand, we took a rod-shaped model for shorter hydrocarbon, that i s , r= N l

f

(12)

f

where l is the length proportional to 1. For a real surfactant, r would have the value between Equations (11) and (12), that i s , Equation (13) would be true:



Monomer solution (Ideal solution)

BEHAVIOR

Micelle /Hydrocarbon part: \ \Nonideal s o l u t i o n /

Figure 1. Model of micelle formation in nonaqueous media

Figure 2. Model of micelle depicted in Figure 1


15.

KiTAHARA AND KON-NO

229

Micelle Formation

η

r = *Ν 1

1/2 < n< 1

(13)

where k is a constant. For a longer hydrocarbon surfactant, AG is rephrased as Equation (T4) from Equations (9) and (11). AG = AG +AG h

2

KX ifa

i=

-

2

Xe /8ire° d 2

where

Κ = 3ΕΤ(ψ -κ )ρ§/4/2πνΊ) 1 1

(14)

f

3

(15)

1

The equilibrium aggregation number λ 8(AG)/3X=0, that i s ,

0

can be obtained from

λ„ = We took a benzene system tentatively. values are as follows:

Here numerical

23

6

3

1

Ψι-Κ!=0.1*, po=0.014/6.02xl0 kg, V=97.5xl0" m mol"" , D=700 kg m" , 1=1.54x10" m, T=300 K. 3

10

22

Then K=1.3xl0~ was obtained. In order to compare the theory with the experiment on the benzene solution of dialkyl dimethyl ammonium bromide, the following value of d was assumed: d = r

Br-

+ r

(CH ) NH 3

2

= 5

-

3 x l 0

"

1 0 m

'

Hence Equation (16) is reduced to the following equation with use of above values: λ

0

= 840/e vfa

(17)

e£

where ε ~ is effective d i e l e c t r i c constant. An experimental point of the Reference 4 ( λ = 6 . 2 at N=20) was u t i l i z e d to determine the value of ε - with use of Equation (17). The value of 30 obtained as ε ~ i f reasonable from view of polar property i n micelle. Then Equation (17) is reduced to Equation (18): e

0

λ

0

= 28/*4*

(18)

The theoretical curve following Equation (18) was drawn as a f u l l line in Figure 3 i n which open circles indicate experimental results in the Reference 4. For shorter hydrocarbon surfactants, we took another limiting case to which Equations (10) and (12) are applied. *

We referred to the value of Napper (11) as$i-Ki.


230


Here Equation (8) can be expressed as follows: f

2

2

AG = K λ Ν - Xe /8-ne° d

(19)

ef

K= RTî-K )p§/4WD R l f

where

2

2

l

(20)

l

Similar to the way of obtaining Equation (16), the following equilibrium aggregation number XQ can be obtained: λ

2

0

f

= e /167TK Ne° d

(21)

£

Now no direct estimation of K* was done, because values of R and 1 · are d i f f i c u l t to be estimated. With use of the ε value obtained above and the λ value at lower Ν(for example, λ = 8 . 8 at N=16),_the value of K K =2.6xl0" . Hence Equatio equation: f

0

f

0

23

λ

0

= 140/N

(22)

This theoretical curve was depicted as a dotted line in Figure 3. The real theoretical curve should be between Equations (17) and (21), because both equations express two limiting cases. Equation (14) or (19) indicates that the longer hydrocarbon surfactant has lower equilibrium aggregation number. We can graphically elucidate the theoretical result by Figure 4. This corresponds with the experimental results that increase of carbon number of surfactant hydrocarbon decreases the aggregation number (4,5). Since AG. is considerably negative for ionic interaction, minima appear in total AG and the equilibrium aggregation numbers λο are present as shown in Figure 4. However, i f polar interact ion i s small, that i s , AG is low, total AG is always positive and no aggregates are presint. This can be seen in benzene solution of nonionic surfactants (-4, 14). Literature Cited 1. Singleterry, C . R . , J . Am. O i l Chem. Soc.,(1955),32, 446. 2. Fowkes, F . M . , in "Solvint Properties of Surfactants" K. Shinoda, Ed. P.65, Marcel Dekker, New York, 1967. 3. Kitahara, Α., in "Cationic Surfactants" Jungermann, Ed. p.287 Marcel Dekker, New York, 1970. 4. Kon-no, K. and Kitahara, Α., J. Colloid Interface Sci.,(1971), 35, 636. 5. Nelson, S.M. and Pink, R . C . , J. Chem. S o c .,

(1952), 1744.


KITAHARA

AND KON-NO

16

Micelle Formation

20

2A

28

32

Carbon Number: N

Figure 3. Region of aggregation number and carbon number of RR'N(CH ) Br in benzene. Q: experimental; , : theoretical. 3

2

>N*.low

Figure 4. Qualitative explanation of equilibrium aggregation number (λ ) 0



232

6. Fowkes, F . M . , J. Phys. Chem., (1962), 66, 1843. 7. Debye, P. and C o l l , H . , J. Colloid S c i . , (1962), 17, 220. 8. F l o r y , P . J . , "Principles of Polymer Chemistry" Ch.12, Cornell Univ. Press, Ithaca New York, 1953. 9. Fischer,E.W., K o l l o i d - Z . , (1958), 160, 120. 10.Meier,D.J., J. phys. Chem., (1967), 71, 1861. 11.Napper,D.H., Trans. Faraday S o c ., (1968), 64, 1701; J. Colloid Interface Sci., (1970), 32, 106. 12.Bagchi,P. and Vold,R.D. 38, 652; (1970), 33, 405. 13.Ottewill,R.H. 108.

and Walker,T., Kolloid-Z. Z. Polym. (1968), 227,

14.Sirianni,A.F. and Coleman,R.D., Can. J. Chem., (1964), 42, 682.


16 Thermodynamics of Micelle Formation K. S. BIRDI Fysisk-Kemisk Institut, Technical University of Denmark, Lyngby, Denmark 2800

Introduction The understanding of the thermodynamics of micelle form ation i s of much theoretical and p r a c t i c a l importance.Even though a great many studies on the thermodynamics of micelle formation have been reported i n the l i t e r a t u r e (1-14), the data available are not completely consistent. The purpose of this study i s to report on the current theories and to comment on the data reported i n the l i t e r a t u r e on the thermodynamics of micelle formation. The variation of c r i t i c a l micelle con centration (CMC) and the aggregation number (N) of a nonionic surfactant (Triton-X-100) with temperature were measured,since these data are essential i n order to discuss the current theories reported on the micelle formation i n the l i t e r a t u r e . Experimental Triton X-100 (OPE1o) was used as supplied by Rohm and Haas Co. The sample i s reported to be polydisperse with respect to the ethyleneoxide adducts. C r i t i c a l micelle concentration (CMC) of OPE1 o i n water and 0.025 M-KBr was determined at three different temperatures,viz.,25,35 and 45°C by the U.V. difference spectrophotometric method,as reported i n litera ture (10). The values of CMC i n water and i n 0.025 M-KBr were i d e n t i c a l , i . e . within the experimental accuracy. Furthermore, these results agreed with the data reported by other investig ators i n water at these temperatures (1 θ ) . The micellar molecular weights (number average,M ) of OPE^ were determined i n 0.025 M-KBr aqueous solutions by using membrane osmometry, as reported by us elsewhere i n d e t a i l ( 1 5 . 1 6 ) . The micelle molecule weights,and subsequently the aggregation numbers,N,were determined at various temperatures r

Ψ

e.g.,5,10,15,25,30,35*40

a

n

d

e

*5 C

233


234


BEHAVIOR

Results and Discussion It i s of interest to describe the micellar system of a nonionic surfactant, before discussing the data on the var i a t i o n of aggregation number of micelles,N, and the CMC with temperature. The process of micellization involves the rever s i b l e aggregation of Ν molecules of the amphiphile to form a micelle ( 2 » 1 7 . 1 6 , 1 9 ) as given below: N-m

f

- M

(1)

The equilibrium constant of this reaction i s given by:

where A and A^ are th respectively. At low surfactant c o n c e n t r â t i o n , h o w e v e r , i t i s reasonable to replace the a c t i v i t i e s of monomer and micelles by t h e i r respective concentrations (12.) :

where C and C., are the concentrations of monomer and micelle ,m M respectively. Assuming i d e a l i t y , the chemical potential of micelles is given by: μ

- μ°

Μ

+

RT In C

(4)

M

and for monomer: = μ° m m

U

+ RT In C m

(5)

At equilibrium we have : N

\

- M,,

From these relations the standard free energy of m i c e l l i z a t i o n , AG°,per monomer is found to be given by (19)s 0

AG » RT In C - RT / Ν In C RT In Cm + RT / Ν In Ν - RT / Ν In CM M

M

(7) (θ)

where Ο. = Ν. Ο. . It i s generally assumed that i f Ν i s large, then at CMC , tKe Equation (8) reduces to (2,19)? 0

AG %zRT In C « RT In CMC


(9)

16.

BIRDI

235

Micelle Formation

Many investigators have further assumed that i f the variation of Ν with temperature is negligible 0 . 2 6 - 1 0 , 1 £ ) , t h e enthalpy of micelle formation,AH°,can be obtained by using a Clausius-Clapeyron type of relationship: t

0

ΔΗ

= - T

2

(dâa°/T

/&T)

(10)

2

= - RT ('d In CMC / d T)

(.11) 0

A great number of investigations on the determination of ΔΗ by applying Equation ( 1 1 ) have been reported i n the l i t e r a t u r e for both the ionic and nonionic micellar systems ( 1 , 2 » 6 - 1 0 ) . These ΔΗ® values reported,however,do not a l l give a s t r i c t l y consistent description of the micellar formation. For instance, the heat of m i c e l l i z a t i o determined from Equatio (I) f while the calorimetric value is reported to be 2 6 0 0 cal/mole ( j j . Another t y p i c a l example i s that of the n-dodecylpyridinium bromide i n 2Μ urea solutions f the ΔΗ values by Equation ( 1 1 ) and by calorimetric method are reported to be - 7 9 8 cal/mole and - 3 4 9 6 cal/mole,respectively (lj.)» This indicates that the method of using the r e l a t i o n i n Equation (II) to obtain ΔΗ· i s imprecise,probably due to certain ass umptions used i n the derivation of this relation,as discussed further below. Further,in many investigations reported on the determination of ΔΗ by using Equation ( l l ) , t h e data obtained does not give a s t r i c t l y consistent description of the micelle formation ( 7 , 8 , 1 0 - 1 3 ) . T h i s analysis therefore c l e a r l y indicates that the usage of the relationship given i n Equation ( l l ) , i s not s t r i c t l y v a l i d for obtaining the heat of m i c e l l i z a t i o n , as also pointed out by other investigators (19)* It was therefore considered of interest to reconsider the assumptions made i n the derivations of Equations (9) and ( 1 1 ) . Since μ° is a function of T,p and Ν (12.), the v a r i a tion of CMC and Ν with temperature of a nonionic surfactant, OPE^ ,was determined. The values of CMC were found to agree with the values reported by other investigators ( 1 0 ) . The aggregation number,N,was determined by using membrane osmomet ry as described under experimental section. The relationship i n Equation ( β ) at the CMC,can then be r e written as Î 0

0

0

àG° = RT In CMC + RT / Ν In Ν

(12)

It i s thus seen that the r e l a t i o n given i n the above Equation ( 1 2 ) d i f f e r s from that given i n Equation ( 9 ) » i n that while former i s a function of both CMC and N, l a t t e r i s only a function of CMC. The results of CMC and Ν versus temperature of 0 ? are given i n Figure 1 . It is seen that the CMC decreases with E

1 O



BEHAVIOR

Temperature (°C) Figure 1.

Aggregation number (N) and CMC vs. temperature of OPE in 0.025M KBr 10


16.

BiRDi

237

Micelle Formation

temperature, and f i n a l l y around 40-45°C no change i n CMC with temperature i s observed,as also reported by other investigators ( 10 ).The aggregation number,N, on the other hand increases with temperature from 5 - 45°C. This i s t y p i c a l f o r the non ionic micelles,as reported i n l i t e r a t u r e , and discussed else where (jhSj.The results i n Figure 1 thus c l e a r l y show that the heat of micellization i s not zero around 40 - 45°^* as has been reported i n l i t e r a t u r e (lO)by using the Equation (11).The second term i n the Equation (12) relates to the transfer of material to and from already exsisting micelles. Since the Equations (12) and (9) d i f f e r by the term: HT / Ν In Ν

(13)

we find that the difference i n ΔΗ determined after making this correction f o r A G 5-45 C (from the data given i n Figure 1). The aggregation c

E

number , N , of C. Eg, i 2 6

, C

E

14 6

3 1 1 ( 1C

E

16 6

h

a

v

e

b

e

e

n

(5.)to change wixR temperature^" as expressed below:

r

e

P

Coin N/dT) » 0.109

o

r

t

e

d

(14)

p

This shows that the Ν increases with increasing temperature, and that the alkyl chain has no effect on this change. It i s also reported that the rate of change of Ν with temperature decreases as the number of ethyleneoxide adducts increases ( i f u ^ h u s i n Figure 1, the change of Ν f o r 0PE i s about four times lesser than that reported f o r the a l k y l chain with s i x ethyleneoxide adducts,as mentioned above (^).In other words,the AH values w i l l d i f f e r by about 600 cal/mole due to the term i n Equation (13) i n the case of these surfactants with s i x ethyleneoxide adducts. To summarize,we have shown that the aggregation number ,N,of nonionic micelles changes appreciably with temperature.Prelim inary results of another nonionic surfactant,nonylphenol with 10 ethyleneoxide units,also indicates that Ν changes with temperature quite appreciably,as determined by membrane osmometry. Since the r e l a t i o n given i n Equation (9) f o r AG does not seem to give consitent results f o r the heat of m i c e l l i z a t i o n , i t i s clear that at this stage the thermodynamics of micelle formation i s f a r from well understood. In the case of nonionic micelles,the determination of Ν as a function of temperature gives a more consistent description. It shows that this process has positive enthalpy over a large temperatu re range (from 5 - 45°C , f o r both OPE^ and nonylphenol with 10 ethyleneoxide adducts). 1

0



238 Acknowledgements

It is a pleasure to thank Prof. J^rgen Koefoed for many helpful suggestions. The excellent technical assistance of Mrs. H. Birch is acknowledged. Literature

Cited

1. Herman,K.W.,J.Phys. Chem.(1962)66, 295 2. Schinoda,K. and Hutchinson,E.,J.Phys.Chem.(1962)66 , 5 7 7 3. B a l a m b r a , R . R . , C l u n i e , J . S . , C o r k i l l , J . M . and Goodman,J.F., Trans. Faraday Soc. ( 1 9 6 2 ) 58, 1661 4. Benjamin,L.,J.Phys.Chem. ( 1 9 6 4 ) 6 8 , 3575 5. B a l a m b r a , R . R . , C l u n i e , J . S . , C o r k i l l , J . M . and Goodman,J.F., Trans. Faraday Soc. ( 1 9 6 4 ) 6 0 ,979 6. Adderson,J.E. and T a y l o r , H . , J . C o l l o i 7. Corkill,J.M.,Goodman,J.F. and Harrold,S.P.,Trans. Faraday Soc.(1964)60 ,202 8. Corkill,J.M.,Goodman,J.F.,Robson,P. and T a t e , J . R . , T r a n s . Faraday S o c . ( 1 9 6 6 ) 6 2 , 987 9. Corkill,J.M.,Goodman,J.F.,Harrold,S.P. and T a t e , J . R . , Trans. Faraday Soc. ( 1 9 6 7 ) 6 3 , 2 4 0 10.Ray,A. and Nemethy,G.,J.Phys. Chem.(1971)75, 809 1 1 .Elias,Hans-Georg,J.Macromol.Sci.(1973)A-7,(3)601 12.Piercy,J.,Jones,N.M. and Ibbotson,G.,J.Colloid Interface S c i . ( 1 9 7 1 ) 3 7 , 165 13.Jones,M.N.,Agg,G. and Pilcher,G.,J.Chem. Thermodynamics, ( 1 9 7 1 ) 3 , 801 14.Poland,D.C. and Scheraga,H.A.,J.Phys.Chem.(1965)69,2431 and 4 4 2 5 . 15.B i r d i , K . S . and Kyllingsbæk,H.,J.Pharm. Pharmacol.(1971) 23, 900 16.B i r d i , K . S . , K o l l o i d - Z . Z. Polym. (1972) 250, 731 17.Murray,R.C. and Hartley,G.S.,Trans.Faraday S o c . ( 1 9 3 5 ) 3 1 , 183 18.V o l d , M . J . , J . C o l l o i d S c i . ( 1 9 5 5 ) 5 1 , 561 1 9 .H a l l , D . G . and P e t h i c a , B . A . , i n "Nonionic Surfactants", M . J . S c h i c k , E d . , p p . 5 1 6 - 5 5 7 , M a r c e l Dekker,Inc.,New York, 1967.


17 Anomalies of Partially Fluorinated Surfactant Micelles* PASUPATI MUKERJEE School of Pharmacy, University of Wisconsin, Madison, Wis. 53706 KAROL J. MYSELS 8327 La Jolla Scenic Drive, La Jolla, Calif. 92037

Introduction The behavior of amphipathic compounds such as ordinary sur factants having a hydrophobic hydrocarbon moiety and a hydro philic polar one or of the perfluoro surfactants in which a l l the hydrogens of the hydrophobic moiety are replaced by fluorines is now reasonably well understood. Partially fluorinated sur factants, in which the hydrophobic moiety contains both hydrogens and fluorines, present, however, anomalies to which we wish to call attention. Our main point is that these anomalies can be readily understood once it is realized that the partially fluorocarbon parts, though both hydrophobic, are not mutually philic but phobic and tend to exclude each other. The lipo philic hydrocarbon part is fluorophobic and the fluorocarbon part is lipophobic. The anomalies of the partially fluorinated surfactants involve both macroscopic phenomena such as their critical micellisation concentrations (c.m.c.) and microscopic ones as revealed by fluorine-NMR results. Both are in accord however with the bulk behavior of fluoro- and hydrocarbons and with the mixed micelle formation of ordinary and perfluorosurfactants. The Mutual Phobicity of Hydrocarbons and Fluorocarbons Though often neglected, this has been known and well docu mented since the early days of fluorocarbon development. In 1950 Simons and Dunlap (V) reported that n-pentane and nperfluoropentane were completely miscible only above 265.5 Κ *The main conclusion of this paper was presented at the Fall 1970 ACS meeting in Chicago in connection with a paper by Mukerjee, P. and Cardinal, J . R. (unpublished work). The principal arguments were submitted in a paper received July 19, 1971, but not accepted by the Journal of Physical Chemistry. This material has been re organized and amplified for presentation at the Voids symposium. 239


240


whereas regular solution theory would predict 62°K for their consolute temperature. The corresponding carbon compounds form two phases up to 40°C (2). Hildebrand, Prausnitz, and Scott devote several pages of their book (3) to this tendency of perfluorocarbons and hydrocarbons to unmix. Even though completely miscible at room temperature, the C* compounds form extremely non-ideal solutions, the activity coeffi cient of the perfluorobutane reaching the value of 10 at infinite dilution (4). In other words, the tendency of an isolated per fluorobutane molecule to escape from η-butane is ten times greater than when i t is surrounded by its own kind. For η-butane the activity coefficient reaches 5 (4). Thus clearly hydrocarbons and fluorocarbons, though they will mix i f the temperature is high enough, show a considerable reluc tance to do so and a considerabl Mixed Micelle Formation Between Ordinary and Perfluoro Surfactants Klevens and Raison (5_) had published about 20 years ago what seems to be the only study thus far of the micellization of such a mixed system, namely sodium dodecyl sulfate (SDS) and perfluorooctanoic acid (F0A). Figure 1 shows their results for surface tension measurements on the pure systems (though the SDS itself contains minor impurities as shown by the minimum) and at four intermediate mole fractions, plotted as a function of total sur factant concentration. They noted the peculiar character of their results but an interpretation had to wait t i l l a better under standing of solubilization and mixed micelle formation of ordinary surfactants had been gained. Details of such an interpretation will be given elsewhere (6) and only the feature pertinent to the present discussion will be brought out here. It may be noted that ordinary surfactants generally form mi celles which are mutually completely miscible. Thus commercial non-ionic surfactants which are generally mixtures of many homo logues behave very much as their average, and the phase diagram of sodium decyl and dodecyl sulfates (7) (Figure 2) shows only minor deviations from ideality. If the results of Klevens and Raison for systems containing 1.0, 0.75 and 0.20 mole fraction F0A are plotted against the con centration of the F0A as shown in Figure 3, several points become apparent. All three systems reach substantially the same low and constant surface tension after a sharp change of slope which indi cates the formation of F0A micelles after a definite c.m.c. for them. For the 1.0 and 0.75 mole fraction systems, the values of the c.m.c. are indistinguishable at about 8.5 mM showing that the solubility of the SDS in these micelles is sufficiently small to be undetectable. In the 0.2 mole fraction system these micelles do not form until the F0A concentration reaches 30 mM, i.e. 21.5 mM higher than in the other two. This system also shows a change of slope and perhaps a small minimum around 2 mM F0A where


MUKERJEE AND MYSELS

Partially Fluorinated Surfactant Micelles

SURFACTANT, mM

Figure 1. Surface tensions of sodium dodecyl sulfate, perfluoro octanoic acid and their mixtures as a function of the total surfactant concentration. This is Figure 4 of reference (5) replotted from the data given in that reference.

mole % NaDS


Figure 2. The equilibrium compositions of micelles and monomers in the sodium decyl and dodecyl sulfate system. Solid lines represent the behavior of ideal solutions of both monomers and micelles. X = experimental c.m.c!s. = the composition of mixed micelles as deduced from conduc tivity data (7).


242


BEHAVIOR

the concentration of SDS is about 8 mM. Hence this is where SDS micelles must begin to form. Thus i t appears that between these concentrations some of the FOA is solubilized by the SDS micelles but the rest continues to increase its monomer activity t i l l its c.m.c. is reached. The 21.5 mM FOA difference indicates upon closer analysis that the SDS micelle dissolves about 15 moles% of FOA. The resulting phase diagram is shown schematically in Fig ure 4. The contrast with Figure 2 is striking and clearly can only be ascribed to the mutual phobicity of hydro- and perfluorocarbons. Thus this characteristic of macroscopic behavior is also found in the micellar realm. Following presentation of this paper an interesting confirma tion of this point was reported by Tiddy and Wheeler (8) who found that the solubilization of octanol by ammonium perfluorooctanoate was about 4 times less than that by sodium octanoate. C.m.c.'s of Perfluorinated Surfactants Perfluoro alkanes are more hydrophobic than the hydrocarbon ones. Though comparative solubility data are sparse, the effect is clear. CF4 is almost seven times {9) less soluble in water on a mole basis than CH* and water is also almost seven times (10) less soluble in perfluoroheptane than ordinary heptane on a weight basis and this becomes a factor over 25 on a mole basis. This greater hydrophobicity leads to a more pronounced amphipathic character of the perfluoro surfactants as shown by their well known greater surface activity both in terms of surface tension lowering at same concentration, and by the ultimate value attained which goes below 20 dyne/cm for many perfluoro surfactants. This is also reflected in their lower c.m.c.'s. Figure 5 shows the available comparisons (11 ). The best documented values are those for the potassium octanoates. Here the perfluorocompound has a 13-fold lower c.m.c. than the ordinary one. At lower chain!engths the difference seems to decrease as shown by the only three-fold lower values for the very poorly documented potassium hexanoate and for the better established butyric acids. In this last case the c.m.c.'s are of the order of 1 M so that the intermicellar liquid is no longer simply aqueous. Since in the following comparisons we will consider only compounds having 8 or more carbon atoms in the chain, we can conservatively take 13 as the ratio of c.m.c.'s in hydrocarbon and perfluorocarbon systems. C.m.c.'s of Partially Fluorinated Surfactants If partially fluorinated chains were to behave ideally, one would expect the c.m.c.'s of these compounds to l i e between those of the corresponding perfluoro and ordinary surfactants varying approximately linearly with the fraction of hydrogens replaced by fluorines as indicated by the solid line of Figure 6. As shown


17.

MUKERJEE AND MYSELS


243

Figure 3. Data for selected systems of Figure 1 as a function of the concentration of perftuorooctanoic acid present

tshSDS (MICELLES/

— •> .

C S0 Na n

4

.

.

1.

-C OOH 8

Figure 4. Schematic of the equilibrium compositions of micelles and monomers in the sodium dodecyl sulfate and perfluoro octanoic acid system. Note the presence of two types of micelles having limited mutual solubility. Based on Ref. (6).


244


BEHAVIOR

Figure 5. Critical micelle concentrations of perfluoro and corresponding ordinary surfac tants as a function of carbon atoms. Data from Ref. (11).

Figure 6. Relative critical micelle con centrations of ordinary, perfluoro, and partiallyfluorinatedsurfactants as func tion of the F/H ratio in the molecule. Based on Figures 5, 7, and 8. Solid line indicates ideal behavior.


17.

MUKERjEE A N D MYSELS


245

also on that figure, the real situation is quite different. The two groups of intermediate points of Figure 6 correspond to the ω-hydro perfluoro and the ω - t r i f l u o r o compounds. The com parison of c.m.c.'s on which these points are based are shown in Figures 7 and 8. It should be noted that the replacement of a single fluorine by a hydrogen increases the c.m.c. by a factor of about 3 or 5, i.e. brings i t within a factor of 3 or 4 of the ordinary surfactant. Replacement of three ω-hydrogens by fluor ines in the ω-trifluoro surfactants actually raises the c.m.c. instead of reducing i t as would be expected from the simple mix ture rule. These anomalous c.m.c.'s of the partially fluorinated surfac tants are readily understandable, however, in terms of the mutual phobicity of the hydrocarbon and fluorocarbon portions of their chains which counteracts the aggregating tendency due to the hy drophobic character of th hydrophobic character of the fluorocarbon part. Additional fac tors reinforcing the mutual phobicity at the water interface include the dipole moment of the partially fluorinated chains (12J and the possible tendency of the ω-hydrogen to form hydrogen bonds with water (13). Fluorine NMR Results The NMR line of an atom shifts generally with the solvent and thus can be used to investigate the surroundings of an atom within the micelle. Muller (14) developed the concept of the "degree of hydrocarbon-like character," Z, of the environment of such an atom. Ζ = ( a ~ £ ) / ( ô - ô ) where δ is the line shift and the sub scripts indicate m, tne micelle, h hydrocarbon, and w, water, respectively. This can be readily generalized to a "degree of organic character" by replacing 6u by δ for the shift in the appropriate organic solvent as Muller has effectively done later (15). m

h

h

0

Perfluoro Surfactants. There are data for two perfluorosurfactants, the C4 carboxylic acid reported by Bailey and Cady (16) and the Cg sodium carboxylate studied by Muller and Simsohn (loT. The former authors did not interpret their results in terms of environment effects but their data permit the calculation of Ζ factors using the anhydrous perfluorobutyric acid itself as the basis for the δ value and obtaining the 6 values by extrapola tion of the linear portion of their graph. Table I shows the Ζ values so obtained as well as those given by Muller and Simsohn. It is apparent from Table I that Ζ is higher, i.e. the en vironment is more organic for the ω-carbon than for the /8-carbon and this is higher than for the l N

- C

R

N- rnethyl-ocetcmide

CH

Νι-ί R

7

4:i X

CH -CH 2

3

3

N- methyl— pyrrolidone

Ν - methyl-coproloctorn

R . . . . C, , C R

0

\

II N-C

/

\

L

c=o

J

Figure 1.


BEHAVIOR

21.

ASSARSSON E T A L .

Mixing Mono-Amides and Poly-Peptides with Water

VISCOSITY AT 25°C PHASE DIAGRAM

ΔΗ MIX

DENSITY AT 25°C HEAT OF MIXING

80

Figure 3.

291

The a) (top) N-methylacetamide and the b) (bottom) water systems

i.OO

Ν,Ν-dimethylacetamide-


292



BEHAVIOR


ASSARSSON E T A L .

Ν - methyl - acetamide

.35

.90

65

.80

X,

ΙΗ,ΟΪ

Figure 6.

pp

CAL

Partial excess functions of wa ter in NMA at 30°C

e

/M0LE- C

(H 0) 2

Figure 7.

Heat capacities of amide-wa ter systems at25°C


294


see Figure 7. We interpret the many interesting features of the plots as follows: we make the assumption that the heat capacities of a mixture of molecules (partly due to the intramolecular degrees of freedom and partly to the vibrational and translational degrees of freedom of the molecules i n the mixtures as a whole) are additive unless the external degrees of freedom are changed by non-ideal grouping or pairing of the mixing molecules* The straight lines connecting the heat capacity values of the pure amides, on the l e f t side, with the heat capacity of pure water, on the right hand side, are drawn to represent such an ideality. In fact, N-Methyl acetamide, not shown here, exhibits such a linear relation up to 67 mole % of water. Strong devia tions and changes i n directions of the real heat capacity curves from this " i d e a l i t y " should, therefore, indicate non-average changes i n the arrangement and packing of the molecules i n the mixture. Positive deviation from a rise i n the number of molecules which are capable of i n creasing the numbers of their intermolecular degrees of freedom. In the mixtures under investigation we deduce that primarily the inter-molecular degrees of freedom of vibration and rotation, but not of translation, are increased, since we find that the densi ties of the mixtures rise less, while the viscosities r i s e more, than ideally. Specifically, we see on Figure 7 that the f i r s t introduction of water up to a molar ratio of 1:4 into the partly polar, partly hydrocarbon, moiety of the pure amides changes the liequid struc ture only to a minor degree. From this point, the number of the molecules per volume acquiring previously inactive degrees of freedom, i.e. amides as well as the introduced water, rises sub stantially up to a mole ratio of about 1:1. From there, the heat capacity s t i l l stays i n excess of additivity, though s l i g h t l y declining, u n t i l a mole ratio of 3 molecules of water to 2 amides i s reached. We interpret the deviations up to this 3:2 ratio as being the result f i r s t of a breakup of amide association by the water, followed by hydrogen bonding up to 1 molecule of water per amide. At s t i l l higher amounts of water and consequent Η-bonding, the excess heat capacity declines further, with a striking jump around the 20:1 ratio of water to amide. This signifies most l i k e l y the beginning of the formation of the regular water struc ture or, coming from the side of pure water, the completion of the breakdown of the water structure by the amide (7). In most studies of amide or peptide solutions i n water i n the literature i t i s this range of concentrations which has been covered. Mix tures near the 1:1 ratio have not been studied. Yet, i n some biological systems i n which we know that bound water i s an essential part of the native conformations, this may be the very range of importance. Another aspect which we would like to emphasize i s that the coincidence of breaks, or maxima, i n the mixing functions for a variety of substituted amides at 67% of


21.

ASSARSSON E T A L .


295

water, indicates a returning form of interaction between the amide group and water, somewhat modified by the substiuents on the nitrogen or on the alpha carbon, consisting of coupling 2 water molecules per substituted peptide bond. b Poly-Amides. In unsubstituted amino acids, and i n p a r t i cular i n polypeptides, the hydrogen of the amide group w i l l , of course, participate i n bonding to other peptide groups and to water. We have extended our studies, at f i r s t , to the three mentioned amino acids gly, pro, and hypro, and to some of their homo-oligomers and polymer and copolymers. N-substituted gly cines were also studied by means of viscosity, density, and freezing point measurements. While this work i s s t i l l i n pro gress, we want to report here on some heat of mixing data obtained by a calorimeter with a precision of better than 1/100 of a degree. In conjunction with the heat capacity of the instru ment, this amounts to a precision of about 0.2 c a l . Because of the rather low s o l u b i l i t y of some of the oligomers and polymers, low number average molecular weights from about 4,000 to 9,000 were used so that the polymers would dissolve i n a sufficiently short period of time commensurate with the heat insulation of the instrument, and i n sufficient amounts to yield data within the limits of our precision. The monomer concentrations up to about 4%, and of the polymers up to approximately 1% i n water were studied. Based on an average amino acid molecular weight, the solutions were therefore approximately 1/1000 molar i n amino acid residues. The polymer molecular weights were determined by osmometry and the composition of the copolymers by optical rota tion analysis. Among other basic d i f f i c u l t i e s encountered were the unknown degrees of c r y s t a l l i n i t y of the monomeric samples undergoing solution, (the polymers were found to be non-crystalline by x-ray and birefringence analysis), which caused endothermic solution enthalpies which varied with the state of c r y s t a l l i n i t y . We instituted therefore dilution studies i n which we extrapolate to zero water, a method which yields also the heats of fusion for which we can not find data i n the literature. At this moment we want to report qualitatively that the heats of mixing of the simple amino acids are less negative than those of the d i substituted amides, and that heat of fusion for the three amino acids gly, pro, hypro are of the order of 3,000-4,000 c a l . Figures 8 and 9 show the heats of mixing of two of the homopolymers, pro and hypro. The polymer of gly i s too insoluble to obtain data. The Figures show also curves of copolymers of pro line and glycine, of hydroxyproline and glycine, of proline and hydroxyproline, and a terpolymer of gly-pro-hypro at the approxi mate mole ratio of 3:4:5. The most important results are that a l l the heats of mixing are negative, substantially more so than those expected for the monomers once they w i l l be f u l l y evaluated. From data not here presented there i s l i t t l e effect




BEHAVIOR

21.

ASSARSSON E T A L .


297

of molecular weights i n our molecular weight range. The heats of mixing for these unsubstituted polypeptide groups are also substantially more negative than those for the N-substituted peptides. Discussion By and large, during the introduction of dry, unsubstituted, polypeptides into water three factors w i l l affect the heat of mixing: the disruption of the inter-peptide forces, the disrup tion of the water structure, and the rebuilding of a different water structure around the solute. In the light of our e a r l i e r solvation studies on peptides the exchange of bulk hydrogen bonding to heterogeneous Η-bonding, i . e . , from the Α-A to the A-B type, should not make a major difference. The increased negativity of the enthalpie restructuring of water i n the sense of iceberg formation which is well known to be the cause of the negative heats of mixing of the short chain alcohols (§)· The finding that the heat of mixing of polypro i s substan t i a l l y more negative than that of polyhypro i s surprising i n view of the hydrogen bonding to be expected between water and the hydroxy groups of the hypro. Again, one might explain this i n terms of the rough equivalence of exchanging Α-A by A-E hydrogen bond, and i n terms of the more extensive hydrophobic bonding and structuring of water around polyproline. Another p o s s i b i l i t y would be differences i n the polypeptide conformations (9,10). A more t r i v i a l factor may be that not a l l of the protective acetyl groups on hypro were removed. Looking at the copolymers between gly and pro, Figure 8, we see that the heats of mixing are a l l less negative than for polypro. The close likeness of the proportions of the monomer feed i n the reaction mixture to the monomer residue ratio i n the polymer indicates an approximately random distribution, or at least the formation of blocks or of periodicities of similar length. Thus, the decrease i n the negative heats of mixing for increasing gly proportions i n the glypro copolymer indicates less hydrophobic bonding to this polypeptide. In polyglycine, as stated, the absence of nonpolar groups together with high chain regularity leads to a high heat of fusion which prevents polymer solution. For the prohypro copolymers, Figure 9, the heats of mixing l i e approximately between the curves for the homopolymers, so that no new factors seem to enter i n the solvation behavior of these copolymers. Unexpectedly, though, the copolymer of glyhypro shows a more negative enthalpy than polyhypro, i n contrast to the effect of the gly-component i n the gly-pro copolymer.


298


BEHAVIOR

Summary Our data on the thermodynamics of mixing of N-substituted amides with water confirm our earlier conclusion (1) of a strong binding of two water molecules to di-N-substituted amides, with a third more l i g h t l y bonded. This indicates that the carbonyl group i s capable of holding two water molecules by H-bonding, the third presumably being attached to the nitrogen. Applying this conclusion to N-substituted amides or peptides, these should also be solvated by an inner shell of three water mole cules. In dilute solution, according to our heat capacity data, these simple amides affect approximately 15 water molecules i n an outer zone. Since, i n the competition between inter-peptide and peptide-water forces, the latter appear to be substantially favored, the water molecule ratio. For unsubstituted polymeric peptides, the regular array of hydrogen bonds along the polymeric molecules favors the interpep tide Η-bonding, as indicated by the low s o l u b i l i t i e s of many unsubstituted polypeptides. For the polypeptides of the pro-, hypro-, and gly- series here studied, we find great exothermicity and therefore more extensive hydrogen bonding and formation of water structures than those accompanying the solution of simpler peptides and amides. Literature Cited 1 Assarsson, P. and E i r i c h , F. R., i n "Molecular Association i n Biological and Related Systems", Adv. Chem. Ser. No.84, American Chemical Society, Washington, D. C., 1968. 2 Wood, F., Ramsden, D. Κ., and King, G., Nature, (1966) 212, (5062), 606 3 Needham, Τ. Ε., J r . , Diss. Abst. Inter. B., (1970) 31 (6) 3303 4 Klotz, J . and Franzen, J . , J. Am. Chem. Soc. (1960), 82, 5241 5 Pauling, L., Proc. Nat. Acad. S c i . U.S., (1932), 18, 293 6 Costain, C. C. and Dowling, J . Μ., J . Chem. Phys. (1960), 32, 158 7 Klotz, I. M. and Farnham, S. Β., Biochem., (1968) 7 (11) 3879 8 Franks, F., Ann. Ν. Y. Acad. S c i . , (1965), 125, 277 9 Forsythe, Κ. H. and Hopfinger, A. J . , Macromolecule, (1973), 6(3) 423 10 Segal, D. Μ., J . Mol. Biol., (1969), 43(3) 497


22 Equilibrium Dialysis and Viscometric Studies on the Interaction of Surfactants with Proteins W. U. MALIK and V. P. SAXENA Department of Chemistry, University of Roorkee, Roorkee, India

Introduction Ever since the discovery o f Kuhn and coworkers (1) i n 1940 that c e r t a i n c a t i o n i c soaps exert powerful d i s i n f e c t i n g a c t i o n on b a c t e r i a , presumably owing t o t h e i r combining c a p a c i t y with the cell p r o t e i n and that t h e i r a c t i o n i s p r o p o r t i o n a l to t h e i r s u r face activity, chemists have evinced keen i n t e r e s t i n studying the r o l e of synthetic detergents i n b i o l o g i c a l systems and p r o cesses. Recent studies have shown that the nonionic polysorbate 80 causes a d i s r u p t i o n o f the membrane s t r u c t u r e (2) and the non i o n i c T r i t o n X-100 exerts a s i m i l a r e f f e c t on lysosomes, m i t o c h o n d r i a , and erythrocytes ( 3 , 4 ) . The s o l u b i l i z i n g a c t i o n of detergents on c h o l e s t e r o l has been reported t o check the develop ment of atheroma (5). The formation o f bile salt-monoglyceride mixed m i c e l l e s has been shown t o be a s i g n i f i c a n t f a c t o r i n lipid absorption (6). In view of the important r o l e played by the syn t h e t i c detergents i n v a r i o u s metabolic processes and t h e i r ever -growing use i n the food and pharmaceutical i n d u s t r i e s , the need to develop a knowledge of t h e i r b i o l o g i c a l e f f e c t s acquires great s i g n i f i c a n c e p r o v i d i n g enough justification f o r c a r r y i n g out s y s tematic studies on the chemical i n t e r a c t i o n of detergents with b i o l o g i c a l e f f e c t s acquires great s i g n i f i c a n c e p r o v i d i n g enough justification f o r c a r r y i n g out systematic studies on the chemical i n t e r a c t i o n o f detergents with b i o l o g i c a l substances. In the present communication we have discussed the r e s u l t s of our in vestigations on some protein-detergent systems employing e q u i l ibrium dialysis and v i s c o m e t r i c techniques. Substituted pro t e i n s , viz., p-toluene sulphonylated g e l a t i n (hereafter c a l l e d TSG) and i o d i n a t e d casein (hereafter c a l l e d IC) were used f o r the e q u i l i b r i u m dialysis s t u d i e s which provided evidence f o r t h e i r statistical b i n d i n g with the a n i o n i c detergents: sodium dodecyl sulphate (hereafter c a l l e d SDS) and sodium o c t y l sulphate (hereafter c a l l e d (S0S). The v i s c o m e t r i c s t u d i e s were made with

299


300

COLLOIDAL DISPERSIONS AND MICELLAR

BEHAVIOR

ovalbumin (hereafter called OV), a globular protein, and trans fusion gelatin (hereafter called TG), a f i b r i l l a r protein with the anionic detergent sodium lauryl sulphate (hereafter called (SLS) and the cat ionic detergent cetylpyridinium bromide (here after called CPB) with a view to gain an insight into the nature of particle-particle interaction. Experimental Materials (a) Proteins, p-toluene sulphonylated gelatin was prepared by adding p-toluene sulphonyl chloride (lOg) in small lots to a solution of gelatin (30g) made alkaline (pH 11) with potassium hydroxide and maintaining the pH throughout at this value by the occasional addition of the a l k a l i . The re action mixture was stirred for 3 hours and then centrifuged. The centrifugate was acidifie was 3.5 when a white coagulum formed. This was separated and cut into small pieces which were subjected to prolonged washing with cold methyl alchol ( l l i t r e ) in a continous extractor for a week when a chloride free product was obtained. It was dried in vacuo and ground to a powder. Its sulphur content was found to be 1.985$. Iodinated casein was prepared by adding chloramine-T (6g) in small lots to a solution of cow s whole milk case in (20g) in water (800ml) containing dissolved sodium bicarbonate (6g) and potassium iodide (2.5g). The reaction mixture was stirred for an hour and the protein precipitated at pH 3.8 by the addition of hydrochloric acid. The curd was subjected several times to dissolution in dilute sodium hydroxide and precipitated with hydrochloric acid u n t i l the inorganic iodide was completely removed. The product was dried at 80°C. It was found to contain 1.13% of iodine. Ovalbumin was prepared from egg white according to the procedure of S^rensen and H^yrup (j) by extraction with a saturated ammonium sulphate solution and c r y s t a l l i z i n g at a pH of about h.6 brought down by adding 0.2N sulphuric acid. Trans fusion gelatin was obtained through the courtesy of the Director, National Chemical Laboratory, Poona, India in the form of 6% so lution. (b) Detergents. A l l the four detergents (SDS, SOS, SLS, and CPB) were B r i t i s h Drug House products. These were further p u r i fied by recrystallization from acetone. 1

Preparation of solutions. Solutions of TSG and IC were pre pared by soaking the protein in doubly d i s t i l l e d water for sev eral hours and then s t i r r i n g the mixture mechanically after add ing a known amount of 0.1 Μ KOH to bring the pH to 6 . 5 . Concen trations of these solutions were determined by drying a known aliquot to constant weight in an air oven at 105°C and applying the correction for potassium hydroxide to get the absolute weight of the protein. Ovalbumin solution was prepared by shaking i t with water at room temperature. The solutions of ovalbumin and


22.

M A L I K AND SAXENA

Interaction of Surfactants with Proteins

301

transfusion gelatin were purified "by dialysis and the concentra tions of the dialysed solutions determined "by drying a known v o l ume at 105-U0°C to constant weight in an air oven. Procedure for equilibrium d i a l y s i s . 20 ml aliquot s of the protein-detergent mixture in which the concentrations of SDS and SOS varied from 0.2X10"3M to 20.0x10"% at a fixed cone. (6x10 ~5g) of the protein were made "by mixing requisite volumes of 6% protein, 0.05M detergent, and d i s t i l l e d water, and "brought up to the desired pH. These were stored for two days at 2 5 ° C 5 ml por tion from each aliquot was then pipetted into dialysis bags made from 15cm long strips of Visking Nojax sausage casing (l.8cm in diameter), freed from sulphur by repeated boiling with d i s t i l l e d water, by tying a square knot on one end. Most of the a i r inside the bags was forced out b two overhead knots, one abov suspended in a test tube containing 5 ml of double d i s t i l l e d water brought up to the same pH, which was then stoppered. The tubes were placed in a stand supported inside a water thermostat and gently shaken for k8 hours by means of an e l e c t r i c a l shaker. The dialysis bags were then withdrawn fromthe test tubes and the amount of the detergent present in the dialysate was estimated spectrophotometrically using the cationic dye pararosaniline hydrochloride. To 1 ml solution of pararosaniline hydrochloride (1x10 M) was added an appropriate volume of the test solution (not exceeding k ml). The t o t a l volume was made up to 5 ml with d i s t i l l e d water. 5 ml of a mixed solvent (equal volumes of chloroform and ethyl acetate) were added and the solution shaken manually about 50 times. It was then centrifuged for about a minute at 5000 r . p . m . , for complete separation of the organic and aqueous phases, the former containing the coloured complex at the bottom. Its spectral absorption was measured on Klett Summersion Photo electric Colorimeter using green f i l t e r against a reference tube f i l l e d with the solvent. Procedure for viscometric studies. Three sets of proteindetergent aliquots of 20 ml each were prepared for viscosity measurements as given below: (i) In the f i r s t set, the protein concentration was fixed (0.5$) while the concentration of the detergent varied from 2-50 millimoles per l i t r e . The viscosities of the aliquots of this set were measured at pH 2 . 0 , 3 . 0 , 6.0 and 8.0 in the case of anionic detergent-protein system and at pH 2 . 0 , 3 . 0 , 8.0 and 9-0 in the case of cationic detergent-protein system. ( i i ) In the second set, the concentration of the protein was varied, from 0.8% to l.k% in the case of 0Y and from 0.6% to 1.2% in the case of TG using the same concentrations of detergent solutions. Viscosity measurements were made at pH 8.0 for the anionic detergent-protein system and at pH 3.0 for the cationic detergent-pirotein system, ( i i i ) The third set consisted of s o l -


302


BEHAVIOR

u t i o n s having d i f f e r e n t p r o t e i n - d e t e r g e n t r a t i o s . Viscositymeasurements were made at pH 8.0. The v i s c o s i t i e s were measured by Scarpa's method as modified by Prasad et a l . ( 8 ) . The v i s c o metric c o n s t a n t , k , was c a l c u l a t e d from the experimentally d e t e r mined values o f t^ and t 2 , the time o f r i s e and the time o f f a l l r e s p e c t i v e l y , f o r a given volume o f s o l u t i o n under constant p r e s sure (for double d i s t i l l e d w a t e r ) . The v i s c o s i t y , T| , o f the s o l u t i o n i s r e l a t e d to ti and t o under constant pressure as

The v i s c o s i t y o f the t e s t s o l u t i o n was determined by f i n d i n g t]_ and t2 f o r a known volume of s o l u t i o n (20ml). A l l measurements were c a r r i e d out at 30 + 0 . 1 ° C i n a thermostatic water b a t h . Calculations (i) E q u i l i b r i u m D i a l y s i s . The extent of b i n d i n g was c a l c u l a t e d by K l o t z s equation (9): 1

€

V s €

where a p p i s the molar e x t i n c t i o n molar e x t i n c t i o n t i o n o f the free of the detergent pression :

apparent molar e x t i n c t i o n c o e f f i c i e n t , *S the c o e f f i c i e n t o f the bound detergentthe c o e f f i c i e n t o f free detergent and oi i s the f r a c detergent. The v a l u e of Vm, the number of moles bound per mole o f p r o t e i n , i s given by the ex

V

m

= A

p

/ P

t

where Ap i s the number o f moles o f p r o t e i n bound detergent and Pt i s the t o t a l number of p r o t e i n molecules. ( i i ) V i s c o s i t y . The i n t r i n s i c v i s c o s i t y , [Ή] at d i f f e r e n t detergent c o n c e n t r a t i o n was obtained by p l o t t i n g 7J p/c vs c. ( 7? p i s the s p e c i f i c v i s c o s i t y and c the cone, o f the p r o t e i n i n *g/ml) and e x t r a p o l a t t i n g the curves t o zero c o n c e n t r a t i o n . The i n t e r a c t i o n index k , was c a l c u l a t e d u s i n g Kramer's equation which has been found t o be v a l i d f o r such systems over a wide range o f c o n c e n t r a t i o n s . The equation i s 9

S

S

In 7 j where

1

^rel

1

r e l

/c

= [17] - k [ T 7 ]

i s the r e l a t i v e

2 c

viscosity.


22.

MALIK AND SAXENA

Interaction of Surfactants with Proteins

303

Results and D i s c u s s i o n E q u i l i b r i u m d i a l y s i s s t u d i e s . T y p i c a l data f o r the b i n d i n g of SDS -with TSG and of SDS with IC are given i n Table I and I I . T y p i c a l curves f o r the p l o t s o f Vm vs l o g C and p l o t s of l/\ vs 1/C are given i n F i g u r e s 1, 2 and 3. Values o f V obtained from e x t r a p o l a t i o n are given i n Table I I I . The course o f b i n d i n g o f SDS and SOS with p-toluene sulphonylated g e l a t i n and i o d i n a t e d c a s e i n as the detergent i s added i n p r o g r e s s i v e l y i n c r e a s i n g con c e n t r a t i o n to a f i x e d amount o f the p r o t e i n at d e f i n i t e values o f pH (7.7 and 9.5) has been followed by p l o t t i n g the average number o f moles of the detergent bound per 10*g p r o t e i n , V , against the l o g of c o n c e n t r a t i o n o f the unbound detergent, l o g Op (Figure l ) . The general shape o f the curves obtained w i t h d i f f e r e n t detergent p r o t e i n combinations at d i f f e r e n amination of the p l o t s o the mode of b i n d i n g o f the surface a c t i v e molecules to the p r o t e i n v a r i e s i n three d i s t i n c t p a t t e r n s as the concentration o f the former i s g r a d u a l l y i n c r e a s e d . These p a t t e r n s o f b i n d i n g have been roughly demarcated by d i v i d i n g the p l o t s i n t o three regions A , B , and C , w i t h a view t o f a c i l i t a t i n g a b e t t e r a p p r e c i a t i o n of the mechanism of d e t e r g e n t - p r o t e i n i n t e r a c t i o n at v a r i o u s stages. In the r e g i o n A , which i s the r e g i o n o f r e l a t i v e l y high p r o p o r t i o n o f p r o t e i n to detergent, the p l o t o f V vs l o g Cp follows a l i n e a r course. T h i s i s i n d i c a t i v e of a more or l e s s s t a t i s t i c a l d i s t r i b u t i o n o f the detergent over the e n t i r e a v a i l a b l e p r o t e i n molecules i n t h i s r e g i o n . S i m i l a r observations have been r e ported by K l o t z et a l . (9) i n d y e - p r o t e i n i n t e r a c t i o n . The ap p l i c a b i l i t y o f the simple s t a t i s t i c a l theory i n the present studies may be e a s i l y t e s t e d by p l o t t i n g l / V against 1/Cp (Figure 2, 3) when a p l o t i s obtained which i s l i n e a r up t o a c e r t a i n l i m i t . The values o f the r e c i p r o c a l o f the i n t e r c e p t s on the o r d i n a t e obtained a f t e r e x t r a p o l a t i o n s o f the s t r a i g h t l i n e s w i t h v a r i o u s d e t e r g e n t - p r o t e i n combinations are given i n T a b l e l l l . These values represent the maximum number o f b i n d i n g s i t e s a v a i l a b l e , i . e . , t h e max.values o f V , i n t h i s r e g i o n . Beyond the r e g i o n A , t h e course o f the p l o t s o f V vs l o g Cp s h a r p l y deviates from the i n i t i a l l i n e a r course i n the d i r e c t i o n o f higher values o f V , r e f l e c t i n g a d i s t i n c t change i n the mode o f b i n d i n g which no l o n g e r appears to be wholly s t a t i s t i c a l . I t i s reasonable to assume that a f t e r combination with the number o f moles o f detergent as a maximum f o r s t a t i s t i c a l b i n d i n g (vide Table III) , a large number of ions get bound e s s e n t i a l l y as a u n i t . P o s s i b l y a f t e r occupying the r e a d i l y a c c e s s i b l e s i t e s (basic groups) on the surface o f the p r o t e i n molecule,the e x t r a detergent molecules penetrate the o r i g i n a l t i g h t l y f o l d e d p r o t e i n molecule causing i t to undergo a change i n p h y s i c a l o r g a n i z a t i o n i n which form i t o f f e r s h i t h e r t o f o r e i n a c c e s s i b l e s i t e s f o r combination and, t h e r e f o r e , e x h i b i t s greater b i n d i n g c a p a c i t y f o r the detergent. With the s t r u c t u r a l d i s o r d e r i n g o f the p r o t e i n molecule, the p o t e n t i a l p

m

m

m

m

m

m

m



20 30 1^0 60 80 100 120 200 300 i+oo 600 800 1000 1200 1600 2000

5

Cone, of SDS (C) xlO~ M

12 18 26 36 51.5 6k 75 116 150 175 26k 3k2 i+oo 1+50 520 590

F

Cone, of free SDS(C ) X10-5M 8 12 16 2k 28.5 36 1+5 8k 150 225 336 1+58 600 750 1080 11+10

Cone, of hound SDS(Cg) xlO^M

1.33 2.0 2.66 1+.0 k.75 6.0 7.5 ll+.O 25.0 37.5 56.0 78.0 100.0 125.0 180.0 235.0

¥.0792 1.2553 ΐ.3802 ΐ.5563 ΐ.7118 T. 8062 Ί+.8751 3.061+5 3.1761 3\2l*55 ΙΛ216 3.531+0 3.6021 3.6532 3.7160 3.7709

m

Moles SDS hound log Cp per lO^g TSG,V m

0.75 0.50 0.375 0.25 0.21 0.166 0.133 0.07 0.

Colloidal dispersions and micellar behavior: Papers from a symposium honoring Robert D. Vold and Marjorie J. Vold (ACS symposium series ; 9)

Adsorption at interfaces: Papers from a symposium honoring Robert D. Vold and Marjorie J. Vold sponsored by the Division of Colloid and Surface Chemistry ... 2-5, 1974 (ACS symposium series ; no. 8)

Adsorption at interfaces : papers from a symposium honoring Robert D. Vold and Marjorie J. Vold sponsored by the Division of Colloid and Surface Chemistry at the 167th meeting of the American Chemical Society, Los Angeles, Calif., April 2-5, 1974

Isotopes and chemical principles: A symposium (ACS symposium series ; 11)

Hemicelluloses: Science and Technology (Acs Symposium Series)

Chemical Sensors and Microinstrumentation (Acs Symposium Series)

Food and Packaging Interactions (Acs Symposium Series)

Carbohydrate Antigens (Acs Symposium Series)

Environmental Catalysis (Acs Symposium Series)

Fermentation Biotechnology (Acs Symposium Series)

Polyethers (ACS symposium series ; 6)

Clean Energy from Waste and Coal (Acs Symposium Series)

Polymers from Renewable Resources: Biopolyesters and Biocatalysis (Acs Symposium Series)

Fuels and Chemicals from Biomass (Acs Symposium Series)

Light-Activated Pesticides (ACS Symposium Series 339)

Ultraclean Transportation Fuels (Acs Symposium Series)

Dietary Supplements (ACS Symposium Series 987)

Light-Activated Pesticides (ACS Symposium Series 339)

Zeolite Synthesis (ACS Symposium Series 398)

Smart Coatings II (ACS Symposium Series 1002)

Drug Metabolism Concepts (ACS symposium series ; 44)

Clinical Chemistry (ACS symposium series ; 36)

Metal-DNA Chemistry (Acs Symposium Series)

Human Medicinal Agents from Plants (Acs Symposium Series)

Molybdenum Enzymes, Cofactors, and Model Systems (Acs Symposium Series)

Introduction to Microlithography: Theory, Materials, and Processing (Acs Symposium Series)

Bioregulators: Chemistry and Uses (ACS Symposium Series, Volume 257)

Expression Systems and Processes for rDNA Products (Acs Symposium Series)

Protein Folding: In Vivo and In Vitro (Acs Symposium Series)

Nuclear Energy and the Environment (ACS Symposium Series)

Deactivation and Testing of Hydrocarbon-Processing Catalysts (Acs Symposium Series,)

Colloidal dispersions and micellar behavior: Papers from a symposium honoring Robert D. Vold and Marjorie J. Vold (ACS symposium series ; 9)

Adsorption at interfaces: Papers from a symposium honoring Robert D. Vold and Marjorie J. Vold sponsored by the Division of Colloid and Surface Chemistry ... 2-5, 1974 (ACS symposium series ; no. 8)

Adsorption at interfaces : papers from a symposium honoring Robert D. Vold and Marjorie J. Vold sponsored by the Division of Colloid and Surface Chemistry at the 167th meeting of the American Chemical Society, Los Angeles, Calif., April 2-5, 1974

Isotopes and chemical principles: A symposium (ACS symposium series ; 11)

Hemicelluloses: Science and Technology (Acs Symposium Series)

Chemical Sensors and Microinstrumentation (Acs Symposium Series)

Food and Packaging Interactions (Acs Symposium Series)

Carbohydrate Antigens (Acs Symposium Series)

Environmental Catalysis (Acs Symposium Series)

Fermentation Biotechnology (Acs Symposium Series)

Polyethers (ACS symposium series ; 6)

Clean Energy from Waste and Coal (Acs Symposium Series)

Polymers from Renewable Resources: Biopolyesters and Biocatalysis (Acs Symposium Series)

Fuels and Chemicals from Biomass (Acs Symposium Series)

Light-Activated Pesticides (ACS Symposium Series 339)

Ultraclean Transportation Fuels (Acs Symposium Series)

Dietary Supplements (ACS Symposium Series 987)

Light-Activated Pesticides (ACS Symposium Series 339)

Zeolite Synthesis (ACS Symposium Series 398)

Smart Coatings II (ACS Symposium Series 1002)

Drug Metabolism Concepts (ACS symposium series ; 44)

Clinical Chemistry (ACS symposium series ; 36)

Metal-DNA Chemistry (Acs Symposium Series)

Human Medicinal Agents from Plants (Acs Symposium Series)

Molybdenum Enzymes, Cofactors, and Model Systems (Acs Symposium Series)

Introduction to Microlithography: Theory, Materials, and Processing (Acs Symposium Series)

Bioregulators: Chemistry and Uses (ACS Symposium Series, Volume 257)

Expression Systems and Processes for rDNA Products (Acs Symposium Series)

Protein Folding: In Vivo and In Vitro (Acs Symposium Series)

Nuclear Energy and the Environment (ACS Symposium Series)

Deactivation and Testing of Hydrocarbon-Processing Catalysts (Acs Symposium Series,)

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