Micelles binary system modeled

Taking Simultaneous Micellizadon and Adsorption Phenomena into Consideration In the presence of an adsorbent in contact with the surfactant solution, monomers of each species will be adsorbed at the solid/ liquid interface until the dual monomer/micelle, monomer/adsorbed-phase equilibrium is reached. A simplified model for calculating these equilibria has been built for the pseudo-binary systems investigated, based on the RST theory and the following assumptions ... 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Recently, Rubingh ll) and Scamehorn et al. (9) have shown that the activity coefficients obtained by fitting the mixture CMC data can be correlated by assuming the mixed micelle to be a regular solution. This model proposed by Rubingh for binary mixtures has been extended to include multicomponent surfactant mixtures by Holland and Rubingh (10). Based on this concept Kamrath and Frances (11) have made extensive calculations for mixed micelle systems. 

Results for the various binary mixed surfactant systems are shown in figures 1-7. Here, experimental results for the surface tension at the cmc (points) for the mixtures are compared with calculated results from the nonideal mixed monolayer model (solid line) and results for the ideal model (dashed line). Calculations of the surface tension are based on equation 17 with unit activity coefficients for the ideal case and activity coefficients determined using the net interaction 3 (from the mixed micelle model) and (equations 12 and 13) in the nonideal case. In these calculations the area per mole at the surface for each pure component, tOj, is obtained directly from the slope of the linear region in experimental surface tension data below the cmc (via equation 5) and the maximum surface pressure, from the linear best fit of... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

In this study we restrict our consideration by a class of ionic liquids that can be properly described based on the classical multicomponent models of charged and neutral particles. The simplest nontrivial example is a binary mixture of positive and negative particles disposed in a medium with dielectric constant e that is widely used for the description of molten salts [4-6], More complicated cases can be related to ionic solutions being neutral multicomponent systems formed by a solute of positive and negative ions immersed in a neutral solvent. This kind of systems widely varies in complexity [7], ranging from electrolyte solutions where cations and anions have a comparable size and charge, to highly asymmetric macromolecular ionic liquids in which macroions (polymers, micelles, proteins, etc) and microscopic counterions coexist. Thus, the importance of this system in many theoretical and applied fields is out of any doubt. 

This chapter will focus on a simpler version of such a spatially coarse-grained model applied to micellization in binary (surfactant-solvent) systems and to phase behavior in three-component solutions containing an oil phase. The use of simulations for studying solubilization and phase separation in surfactant-oil-water systems is relatively recent, and only limited results are available in the literature. We consider a few major studies from among those available. Although the bulk of this chapter focuses on lattice Monte Carlo (MC) simulations, we begin with some observations based on molecular dynamics (MD) simulations of micellization. In the case of MC simulations, studies of both micellization and microemulsion phase behavior are presented. (Readers unfamiliar with details of Monte Carlo and molecular dynamics methods may consult standard references such as Refs. 5-8 for background.)... 

Micellization, which forms a major focus of this chapter, is the simplest class of phenomena accessible through simulations and, perhaps arguably, is the first step that needs to be examined before embarking on more complex problems. Both micellization [30,31] and micellar phase behavior [32] have been studied by Care and coworkers for a binary surfactant-solvent system using simple lattice models of the type we discuss here. The recent work of Talsania et al. [33] includes a preliminary examination of micellar solubilization, in addition to micellization in surfactant solutions. The latter is the first attempt to examine solubilization (i.e., encapsulation) at low solute (i.e., oil) concentration in a systematic manner. 

Recently, the phase diagrams in various ternary surfactant-solute-solvent systems [25] and micellization in binary surfactant-solvent systems [42] based on the model of Larson et al. have also been presented using different simulation methodologies (i.e., Gibbs ensemble simulations and configurational bias NVT ensemble simulations). We shall also comment on these briefly. 

Polystyrene (PS) and poly(methyl methacrylate) (PMMA) are frequently used as binary model systems to study phase separation dynamics in polymer thin films and in polymer-polymer and polymer-substrate interactions (Zhu et al. 1999 Winesett et al. 2000). Using scanning force microscopy (SIM), Zhu et al. showed that, after the PS/PMM A bilayer samples were annealed for seven days at 180°C and washed in cyclohexane to selectively dissolve the PS homopolymer, the phase of PS was differently organized on the PMMA layer surface due to the content of a 30% dPS-PMMA diblock copolymer, namely in undissolved nticelles (for a thickness of 100 nm for PS layer), coexisting micelles and microanulsion structures (for 80 nm), and in microemulsion (for 50 nm). 

The theoretical aspects of the kinetics of two-component micelles based on the stepwise association model were later extended to high surfactant concentrations. - This model applies to binary mixtures of nonionic surfactants as well as to one ionic surfactant, the surfactant ion and its counterion then being the two components of the system. 

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