Free energy single surfactant systems

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. 

Free Energy of Adsorption, a) System with only one surfactant. Experimentally, it is found that the adsorption of the single surfactants is well described by an equation of the form... 

In general, one must consider the chemical potential of a molecule at the interface and in the solution. The equality of the two chemical potentials is the criterion for equilibrium and hence determines the area per molecule on the interface. When the amount of interface is fixed, as in the case of a single water-oil interface, this equality fixes 27 (see the problems at the end of Chapter 2). However, when the amount of interface can vary to minimize the free energy, 27 is determined by minimizing the interfacial free energy per molecule the chemical potential then determines the number of interfaces that exist in the system as well as the (small) volume fraction of surfactant that is not incorporated in these interfaces the properties of each interface are determined to a first approximation by the minimization of the local free energy of the film. 

An essentially equivalent approach to that of small-systems thermodynamics has been formulated by Corkill and co-workers and applied to systems of nonionic surfactants [94,176]. As with the small-systems approach, this multiple-equilibrium model considers equilibria between all micellar species present in solution rather than a single micellar species, as was considered by the mass-action theory. The intrinsic properties of the individual micellar species are then removed from the relationships by a suitable averaging procedure. The standard free energy and enthalpy of micellization are given by equations of similar form to Equations 3.44 and 3.45 and are shown to approximate satisfactorily to the appropriate mass-action equations for systems in which the mean aggregation number exceeds 20. 

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