Solutions, regular phase separation

Muthukumar, M., Hua, J., and Kundagrami, A., 2010. Charge regularization in phase separating polyelectrolyte solutions, J. Chem. Phys., 132,084901. 

The mixed cmc behavior of these (and many other) mixed surfactant systems can be adequately described by a nonideal mixed micelle model based on the psuedo-phase separation approach and a regular solution approximation with a single net interaction parameter B. However, the heats of micellar mixing measured by calorimetry show that the assumptions of the regular solution approximation do not hold for the systems investigated in this paper. This suggests that in these cases the net interaction parameter in the nonideal mixed micelle model should be interpreted as an excess free energy parameter. 

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 A-B binary system conforms to regular solution behaviour and the interaction parameter 2 is 17,400 J/mol. Find the critical temperature Tc below which phase separation occurs. Calculate the compositions of a and a in equilibrium at 900K. 

Theoretical calculations for llquld/llquid systems predict that the viscosity goes through a maximum at the spinodal. Depending on the type of system and its regularity, the increase may be quite large for example, Larson and Frederickson ( ) predicted that for block copolymers. These authors concluded that in the spinodal region a three-dimensional network is formed and that the system exhibits non-linear viscoelastic behavior. Experimentally, sharp Increases of n near the phase separation have been reported for low molar mass solutions as well as for oligomeric and polymeric mixtures (21). 

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