Micelle thermodynamic approach

In this paper, a molecular thermodynamic approach is developed to predict the structural and compositional characteristics of microemulsions. The theory can be applied not only to oil-in-water and water-in-cil droplet-type microemulsions but also to bicontinuous microemulsions. This treatment constitutes an extension of our earlier approaches to micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in the oil phase and the excluded-volume interactions among the droplets. Illustrative results are presented for an anionic surfactant (SDS) pentanol cyclohexane water NaCl system. Microstructur al features including the droplet radius, the thickness of the surfactant layer at the interface, the number of molecules of various species in a droplet, the size and composition dispersions of the droplets, and the distribution of the surfactant, oil, alcohol, and water molecules in the various microdomains are calculated. Further, the model allows the identification of the transition from a two-phase droplet-type microemulsion system to a three-phase microemulsion system involving a bicontinuous microemulsion. The persistence length of the bicontinuous microemulsion is also predicted by the model. Finally, the model permits the calculation of the interfacial tension between a microemulsion and the coexisting phase. 

In this paper, a predictive molecular thermodynamic approach is developed to calculate the structural and compositional characteristics of microemulsions. The theory applies not only to oil-in-water and water-in-oil droplet-type microemulsions but also to bicontinuous microemulsions. The treatment is an extension of our earlier theories for micelles, mixed micelles, and solubilization but also takes into account the self-association of alcohol in oil and the volume-excluded interactions among... 

Adsorption of nonionic surfactants on porous solids has been studied by Huinink et al. in a series of p ers [ 149,150]. They elaborated a thermodynamic approach that accounts for the major features of experimental adsorption isotherms. It is a very well known fact that during the adsorption of nonionic surfactants there is a sharp step in the isotherm. This step is interpreted as a change from monomer adsorption to a regime where micelle adsorption takes place. Different surfactants produce the step in a different concentration range. The step is more or less vertical depending on the adsorbate. The thermodynamic analysis made by Huinink et al. is based on the assumption that the step could be treated as a pseudo first order transition. Their final equation is a Kelvin-like one, which shows that the change in chemical potential of the phase transition is proportional to the curvature constant (Helmholtz curvature energy of the surface). 

Nagarajan, R. and Ruckenstein, E., Critical micelle concentration A transition point for micellar size distribution A statistical thermodynamical approach, J. Colloid Interface Sci., 60, 221, 1977. 

Bautista F, Soltero JFA, Macias ER, Puig JE, Manero O (2002) Irreversible thermodynamics approach and modeling of shear-banding flow of wormlike micelles. J Phys Chem B... 

F. Micromechanical/Surface-Thermodynamic Approach to Treating Surfactant Micelles... 

In the literature on micelle formation, two primaiy models have gained general acceptance as useful (although not necessarily accurate) for understanding the energetic basis of the process. The two approaches are the mass action model, in which the micelles and monomeric species are considered to be in a kind of chemical equilibrium, and the phase separation model, in which the micelles are considered to constitute a new phase formed in the system at and above the critical micelle concentration. In each case, classical thermodynamic approaches are used to describe the overall process of micellization. 

Most of the studies on thermodynamics of mixed micellar systems are based on the variation of the critical micellar concentration (CMC) with the relative concentration of both components of the mixed micelles (1-4). Through this approach It Is possible to obtain the free energies of formation of mixed micelles. However, at best, the sign and magnitude of the enthalpies and entropies can be obtained from the temperature dependences of the CMC. An Investigation of the thermodynamic properties of transfer of one surfactant from water to a solution of another surfactant offers a promising alternative approach ( ), and, recently, mathematical models have been developed to Interpret such properties (6-9). 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

To this point, only models based on the pseudo—phase separation model have been discussed. Mixed micelle models utilizing the mass action model may be necessary for micelles with small aggregation numbers, as demonstrated by Kamrath and Franses ( ). However, even for large micelles, the fundamental basis for the pseudophase separation model needs to be examined. In micelles, how much solvent or how many counterions (bound or in the electrical double layer) should be included in the micellar pseudo-phase is unclear. The difficulty is normally surmounted by assuming that the pseudo—phase consists of only the surfactant components i.e., solvent or counterions are ignored. The validity of treating the micelle on a surfactant—oniy basis has not been verified. Funasaki and Hada (22) have questioned the thermodynamic consistency of such an approach. 

Following this, the thermodynamic arguments needed for determining CMC are discussed (Section 8.5). Here, we describe two approaches, namely, the mass action model (based on treating micellization as a chemical reaction ) and the phase equilibrium model (which treats micellization as a phase separation phenomenon). The entropy change due to micellization and the concept of hydrophobic effect are also described, along with the definition of thermodynamic standard states. 

In summary, whether a reaction equilibrium or a phase equilibrium approach is adopted depends on the size of the micelles formed. In aqueous systems the phase equilibrium model is generally used. In Section 8.5 we see that thermodynamic analyses based on either model merge as n increases. Since a degree of approximation is introduced by using the phase equilibrium model to describe micellization, micelles are sometimes called pseudophases. 

In this section we consider the thermodynamics of micellization from two points of view the law of mass action and phase equilibrium. This will reveal the equivalency of the two approaches and the conditions under which this equivalence applies. In addition, we define the thermodynamic standard state, which must be understood if derived parameters are to be meaningful. 

Among other approaches, a theory for intermolecular interactions in dilute block copolymer solutions was presented by Kimura and Kurata (1981). They considered the association of diblock and triblock copolymers in solvents of varying quality. The second and third virial coefficients were determined using a mean field potential based on the segmental distribution function for a polymer chain in solution. A model for micellization of block copolymers in solution, based on the thermodynamics of associating multicomponent mixtures, was presented by Gao and Eisenberg (1993). The polydispersity of the block copolymer and its influence on micellization was a particular focus of this work. For block copolymers below the cmc, a collapsed spherical conformation was assumed. Interactions of the collapsed spheres were then described by the Hamaker equation, with an interaction energy proportional to the radius of the spheres. 

The micellization of surfactants has been described as a single kinetic equilibrium (10) or as a phase separation (11). A general statistical mechanical treatment (12) showed the similarities of the two approaches. Multiple kinetic equilibria (13) or the small system thermodynamics by Hill (14) have been frequently applied in the thermodynamics of micellization (15, 16, 17). Even the experimental determination of the factors governing the aggregation conditions of micellization in water is still a matter of considerable interest (18, 19) and dispute (20). 

The Mass Action Model The mass action model represents a very different approach to the interpretation of the thermodynamic properties of a surfactant solution than does the pseudo-phase model presented in the previous section. A chemical equilibrium is assumed to exist between the monomer and the micelle. For this reaction an equilibrium constant can be written to relate the activity (concentrations) of monomer and micelle present. The most comprehensive treatment of this process is due to Burchfield and Woolley.22 We will now describe the procedure followed, although we will not attempt to fill in all the steps of the derivation. The aggregation of an anionic surfactant MA is approximated by a simple equilibrium in which the monomeric anion and cation combine to form one aggregate species (micelle) having an aggregation number n, with a fraction of bound counterions, f3. The reaction isdd... 

There are several approaches to derive the Gibbs free energy of micellization. We only discuss one of them which is called the phase separation model. Even this approach only leads to approximate expressions for nonionic surfactants. More detailed discussions of the thermodynamics of micellization can be found in Refs. [3,528,529],... 

However, these experimental approaches appeared to be relevant enough to form the basis of the first thermodynamic treatment of the solubilization of protein in reversed micelles developed by Caselli et. (58). The micellar phase before solubilization forms the reference state of thermodynamic calculations. According to the structural model of spherical monodisperse droplets, the knowledge of the micelle radius and density completely characterizes the system. The uptake of protein is made... 

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