Regular solution model general

The clay ion-exchange model assumes that the interactions of the various cations in any one clay type can be generalized and that the amount of exchange will be determined by the empirically determined cation-exchange capacity (CEC) of the clays in the injection zone. The aqueous-phase activity coefficients of the cations can be determined from a distribution-of-species code. The clay-phase activity coefficients are derived by assuming that the clay phase behaves as a regular solution and by applying conventional solution theory to the experimental equilibrium data in the literature.1 2 3... 

It is generally observed that as the temperature increases, real solutions tend to become more ideal and r can be interpreted as the temperature at which a regular solution becomes ideal. To give a physically meaningful representation of a system r should be a positive quantity and larger than the temperature of investigation. The activity coefficient of component A for various values of Q AB is shown as a function of temperature for t = 3000 K and xA = xB = 0.5 in Figure 9.3. The model approaches the ideal model as T - t. 

With Amix//m = 0 the ideal Temkin model for ionic solutions [13] is obtained. If deviations from ideality are observed, a regular solution expression for this mixture that contains two species on each of the two sub-lattices can be derived using the general procedures already discussed. The internal energy is again calculated... 

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. 

The Chao-Seader and the Grayson-Streed methods are very similar in that they both use the same mathematical models for each phase. For the vapor, the Redlich-Kwong equation of state is used. This two-parameter generalized pressure-volume-temperature (P-V-T) expression is very convenient because only the critical constants of the mixture components are required for applications. For the liquid phase, both methods used the regular solution theory of Scatchard and Hildebrand (26) for the activity coefficient plus an empirical relationship for the reference liquid fugacity coefficient. Chao-Seader and Grayson-Streed derived different constants for these two liquid equations, however. 

Regular solution theory, the solubility parameter, and the three-dimensional solubility parameters are commonly used in the paints and coatings industry to predict the miscibility of pigments and solvents in polymers. In some applications quantitative predictions have been obtained. Generally, however, the results are only qualitative since entropic effects are not considered, and it is clear that entropic effects are extremely important in polymer solutions. Because of their limited usefulness, a method using solubility parameters is not given in this Handbook. Nevertheless, this approach is still of some use since solubility parameters are reported for a number of groups that are not treated by the more sophisticated models. 

The interrelation between the effects of size, nucleation, phase transition, and depletion in first-order phase transitions has been studied elsewhere for the cases of ideal and regular solutions and paraboHc approximations [57, 59, 61]. To generalize these results, let us consider other thermodynamic models for the new and parent phases. We will consider the formation of a spherical nucleus of an intermediate phase inside a spherical particle of the supersaturated solid solution at an initial concentration Co, when the composition of a new phase is assumed fixed and known. 

Without loss of generality, let us choose the model of the new phase as a Hne (strictly stoichiometric) intermediate phase with composition C = Ci = 0.5, and exclude the elastic contributions to the Gibbs energy. The parent phase in the vicinity of the phase transition points will be described by the ideal solution law and will be also denoted as the a-phase. In fact, the model of regular solution would be more reasonable since the existence of intermediate phases usually correlates with negative mixing energy. Yet, for simpHcity, below we restrict ourselves to the... 

The VfT model has generally been used as the molecular model to study the solution thermodynamics of ternary and quaternary alloys in compound saniconductor alloys. Energy minimization techniques have been used to determine the interaction parameter in the regular solution theory and then, the binodal and spinodal curves have been calculated. Kim et al., have... 

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