Regular solution theory, treatment

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

It was recently ascertained that the behavior of the adsorbed film of two surfactants in equilibrium with their micelle can be explained by assuming both the surface region and the micelle particle to be mixtures of the surfactants (1 - ) - Further, the application of the regular solution theory to the mixtures was shown to be useful to describe the nonideal behavior of ionic surfactants ( - ) However, the above treatments are incomplete from the thermodynamic viewpoint, because they do not consider the dissociation of surfactants and ignore the presence of solvent (T). In addition, it is impossible to suppose that the regular solution theory is applicable to both the adsorbed film and the micelle of ionic surfactants accompanied by the electrical double layer ( ). 

Within the frames of the regular solution approach adopted in [4,19,23-29] the dipole-dipole interactions are treated similarly with the short-range ones and for this reason in many cases no distinction between these interactions is made. The dipole-dipole interactions arise from the electric field which is established due to the dipoles of the adsorbed particles. This feature is taken into account here to develop an alternative approach to treat these interactions. The treatment concerns adsorbed layers on energetically homogeneous surfaces. This is a necessary step in formulating an adsorption theory for heterogeneous surfaces, which is presented in section 5. 

Thus the theory of regular solutions turns out to be a useful tool to describe mixed micelle formation. However, some of the assumptions of this theory are inconsistent with a strict thermodynamic treatment. Scamehorn [43] and later Nishikido [34] presented experimental evidences of its inapplicability. Their arguments can be summarised as follows ... 

Ideal and regular solutions that can be described by electrostatic theories do not feature in the treatment. A number of other publications deal with these and with the theories elaborated for them. Only passing reference is made to these simple systems in this work, which is concerned primarily with the methods of studying specific solvent effects and their results. 

Before presenting examples, we should remark that the subject of solubility of nonelectrolytes has been treated in detail by Hildebrand and Scott (921). They discuss (in their Chapter XI) the various chemicaT and physical theories of the interactions, such as H bonding, that are responsible for extreme deviations from regular behavior. Both approaches can provide equations to fit experimental data. The first does so by relating equilibrium constants and activity coefficients for assumed reactions, and the second by the use of varying values of the energy of interaction and empirical factors for the effective volume of solute and solvent molecules. They conclude with the observation, still valid, that no satisfactory theoretical treatment is available. 

In the phenomenological characterization of small deviations from SI solutions, the concepts of regular and athermal solutions were introduced. Normally, the theoretical treatment of these two cases was discussed within the lattice theories of solutions. Here, we discuss only the very general conditions for these two deviations to occur. First, when Pt ab does not depend on temperature, we can differentiate (6.19) with respect to T to obtain... 

Hildebrand and Rotariu [14] have considered differences in heat content, entro])v and activity and classified solutions as ideal, regular, athermal, associated and solvated. Despite much fundamental work the theory of binary liquid mixtures is still e.ssentiaUy unsatisfactory as can be seen from the. systematic treatment of binar> mi.Ktures by Mauser-Kortiim [15]. The thermodynamics of mixtures is presented most instructively in the books of Mannchen [16] and Schuberth [17]. Bittrich et al. [17a] give an account of model calculations concerning thermophysical properties of juire and mixed fluids. 

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