Surfactants nonideal mixed monolayer model

A generalized nonideal mixed monolayer model based on the pseudo-phase separation approach is presented. This extends the model developed earlier for mixed micelles (J. Phys. Chem. 1983 87, 1984) to the treatment of nonideal surfactant mixtures at interfaces. The approach explicity takes surface pressures and molecular areas into account and results in a nonideal analog of Butler s equation applicable to micellar solutions. Measured values of the surface tension of nonideal mixed micellar solutions are also reported and compared with those predicted by the model. 

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... 

Holland, R, Nonideal mixed monolayer model, in Phenomena in Mixed Surfactant Systems, Scamehorn, J.F., Ed., ACS Symposinm Series 311, American Chemical Society, Washington, D.C., 1986, chap. 8. 

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 pseudo-phase separation approach has been successfully applied in developing a generalized nonideal multicomponent mixed micelle model (see I4) and it is Interesting to consider whether this same approach can be used to develop a generalized treatment for adsorbed nonideal mixed surfactant monolayers. The preferred form for suoh a model is that it be suitable (at least in principle) for treating multiple components and be extendable to other interfaoes and properties of interest suoh as oontaot angles. Earlier models (5, 18, 27) based on the pseudo-phase separation approach and... 

One interesting feature of the functional form derived here is the direct relationship of the activity coefficients and composition between the micellar and surface psuedo-phases. This allows a comparison of nonideal interactions in the micelle and monolayer as modeled by their respective net interaction parameters. In principle, this form may also allow extension to more complicated situations such as the treatment of contact angles in nonideal mixed surfactant systems. Here, the functional form derived above depends on differences in surface pressures and these may be directly obtained from experimentally measured parameters under the proper conditions (30). 

Adopting this viewpoint, the net interaction parameter for surface mixing in the present model may be seen as a useful way to account for changes in the surface free energy in nonideal mixed surfactant monolayers. Here, the parameter must not only account for the effects due to counterions, but for changes in molar surface... 

Using this approach, a model can be developed by considering the chemical potentials of the individual surfactant components. Here, we consider only the region where the adsorbed monolayer is "saturated" with surfactant (for example, at or above the cmc) and where no "bulk-like" water is present at the interface. Under these conditions the sum of the surface mole fractions of surfactant is assumed to equal unity. This approach diverges from standard treatments of adsorption at interfaces (see ref 28) in that the solvent is not explicitly Included in the treatment. While the "residual" solvent at the interface can clearly effect the surface free energy of the system, we now consider these effects to be accounted for in the standard chemical potentials at the surface and in the nonideal net interaction parameter in the mixed pseudo-phase. 

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