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formation of ionic surfactants in aqueous solution. The cell model combines classical electrostatics with surface free energy and hydrophobic driving force contributions. A detailed exposition of these results will be presented elsewhere. The morning session concluded with a presentation by Judith Herzfeld (Brandeis University) describing a theory of liquid-crystalline phases in micellar systems. The theory combines a phenomenological description of the thermodynamics of micelle assembly with a statistical calculation of excluded volume interactions between micelles. The afternoon session, chaired by Kenneth Cox (Shell Development Company), included four papers discussing primarily recent experimental developments in a variety of self-assembling systems. The composition of the session vividly reflected the remarkable heterogeneity of self-assembling systems, ranging from surfactants in the presence of salts, through microemulsions and block copolymers, to surfactants in supercritical fluids. The afternoon session began with a presentation by Michael Fisch (John Carroll University) describing recent experimental efforta to detect an isotropic-to-nematic phase transition in micellar solutions composed of grown flexible rod-like micelles. Measurements of the persistence length, a measure of micellar flexibility, were presented, and various theoretical approaches to describe the isotropic-to-nematic phase transition were discussed. Marcia Middleton (University of Texas at Austin) then presented measurements of the dielectric permittivities of anionic and nonionic oil continuous microemulsions with varying water content, temperature, alkane carbon number, and electrolyte concentration. The results confirmed the belief that the underlying morphology and associated phase behavior have a profound effect on the dielectric properties of microemulsions. Zhen-Gang Wang (Exxon Research and Engineering Company) then reviewed results of experimental and the-
oretical studies of the dilute solution properties of selfassembling polymers, with particular emphasis on the micellization phenomenon and the nature of the resulting micellar size distribution. The afternoon session concluded with a presentation by John Ritter (University of Delaware) describing studies of the equilibrium multiphase behavior of two ternary mixtures consisting of carbon dioxide, water, and a nonionic surfactant of the polyethylene glycol monoether family at temperatures and pressures near the critical point of carbon dioxide. A rich variety of four-phase equilibria and multiple regions of three-phase equilibria exhibiting critical end points and tricritical points were presented. In the course of the symposium, there were many useful and illuminating discussions between the participants, which highlighted the extraordinary interdisciplinary nature of the symposium topic. I would like to thank the authors and other participants for their valuable contributions to the success of the symposium and the editors of Langmuir for offering the opportunity to share the contents of the symposium with the Colloid and Surface Science community. I am particularly indebted to Robert Rowell, Associate Editor of Langmuir, for his continued guidance,assistance, and support in putting together the symposium papers presented in this issue of Lungmuir. Last, but not least, I would like to express my sincere gratitude to my co-organizer, Kenneth Cox, for his invaluable advice, continued assistance, and organizationalskills, which culminated in a very successful and stimulating symposium.
Molecular-ThermodynamicApproach To Predict Micellization, Phase Behavior, and Phase Separation of Micellar Solutionst
tion and growth. These factors include (i) hydrophobic interactions between surfactant hydrocarbon chains and water, (ii) conformational effects associated with hydrocarbon chain packing in the micellar core, (iii) curvaturedependent interfacial effects at the micellar core-water interface, and (iv) steric and electrostatic interactions between surfactant hydrophilic moieties. The free energy of micellization, gmic, was computed for various micellar shapes, Sh, and micellar core minor radii, 1,. The “optimum” equilibrium values, IC*, Sh*, and gmic*, were obtained by minimizing gmic with respect to 1, and Sh. The deduced “optimum” micellar shape, Sh*, determines whether the micelles exhibit twodimensional, one-dimensional, or no growth. These results were then utilized in the thermodynamic theory to predict a broad spectrum of micellar solution equilibrium properties as a function of surfactant concentration and temperature. These properties include (1) the critical micellar concentration, (2) the micellar size distribution, (3) the critical surfactant concentration for the onset of phase separation, and (4)other ther-
Sudhakar Puwada and Daniel Blankschtein’ Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received December 11, 1989 A molecular-thermodynamic approach which consists of blending a molecular model of micellization with a thermodynamic theory of phase behavior and phase separation of isotropic (surfactant-water) micellar solutions has been developed.1 The molecular model incorporates the effects of solvent properties and surfactant molecular architecture on physical factors which control micelle forma+ Extended Abstract presented at the symposium entitled ‘Thermodynamics of Micellar Solutions”, American Institute of Chemical Engineers Spring National Meeting, Houston, TX, April 2-7, 1989.
0743-7463/90/2406-0894$02.50/0
Daniel Blankschtein Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139
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modynamic properties such as the osmotic compressibility. The proposed molecular-thermodynamic approach provides an excellent description of a wide range of experimental findings in aqueous solutions of nonionic surfactants belonging to the polyethylene glycol monoether and glucoside families. We are currently extending our theoretical framework to describe micellar solutions of ionic and zwitterionic surfactants, as well as micellar solutions of mixed surfactants. We believe that beyond its fundamental value the proposed molecular-thermodynamic approach could become a valuable computational tool for the surfactant technologist. Indeed, using this approach, the surfactant technologist could identify, select, and possibly even tailor surfactants for a particular application without the need of performing routine measurements of a large number of equilibrium properties, thus making his work more efficient and productive. In a related study, we have examined2 the peculiari-
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ties of osmotic pressure measurements of self-assembling micellar solutions. We have shown that under certain conditions these measurements c-an yield the weightaverage micellar molecular weight, M,, contrary to the generally accepted notion that they yield the numberaverage micellar molecular weight, M,. In view of this surprising new result, we have reevaluated osmotic pressure measurements of aqueous micellar solutions of the nonionic surfactant n-dodecyl hexaoxyethylene glycol monoether (C12Ee). We have found that, contrary to previous interpretations indicating the presence of monodisperse micelles, the measurements are consistent with the presence of polydisperse micelles which grow with increasing surfactant concentration and temperature. Registry No.
C12E8,3055-96-7.
(1) Puwada, S.; Blankschtein, D. J. Chem. Phys., in press. (2) Puwada, S.; Blankschtein, D. J. Phys. Chem. 1989, 93, 77537755.
Model Calculations on the Transitions between Surfactant Aggregates of Different Shapes? Jan Christer Eriksson* and Stig Ljunggren Department of Physical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden Received May 19, 1989. In Final Form: November 1, 1989
In a series of papers published earlier, we presented theories about the formation of surfactant micelles which include detailed treatments of the mechanics, surface thermodynamics, and small system thermodynamics of spherical, rod-shaped, and disk-shaped aggregates. In the present paper, we develop a calculation scheme which yields the volume fractions of the various kinds of sodium dodecyl sulfate (SDS)micelles and also of SDS vesicles, at different solution states. The familiar hierarchy of surfactant aggregates of different shapes is generated automatically upon raising the salt concentration, i.e., without introducing any extraneous packing or geometrical constraints, and is due to the more rapid decrease of the electrostatic free energy for the less curved aggregate surfaces. Moreover, we find that when spherical and rod-shaped micelles coexist, the weight-average aggregation number as a function of the total surfactant concentration shows positive deviations from a linear relationship at high salt concentrations and negative deviations at low salt concentrations, in broad agreement with the available experimental evidence on the sphere-to-rod transition.
Introduction It has often been assumed in the past that large, rodshaped surfactant micelles are formed from small, spherical micelles by means of a straightforward elongation/ growth process. Accordingly, there would be a single peak in the size distribution function which would shift toward larger average sizes and, at the same time, broaden upon + Presented a t the symposium entitled 'Thermodynamics of Micellar Solutions", American Institute of Chemical Engineers Spring National Meeting, Houston, April 2-7, 1989.
changing the solution conditions so as to favor the formation of elongated, rod-shaped micelles. The models employed by Mukerjee,l Israelachvili et a1.,2 Nagarajan,3 and Missel et al.*v5 are essentially of this nature. (1) Mukerjee, P. J. Phys. Chem. 1972, 76, 565. (2) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. SOC., Faraday Trans. 2 1976, 72,1525. (3) Nagarajan, R. J. Colloid Interface Sci. 1982, 90,477. (4) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J. Phys. Chem. 1980,84,1044. (5) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Carey, M. C. J. Phys. Chem. 1983,87, 1264.
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