We aim to develop statistical thermodynamic theory for head group interactions in bilayer membranes, micelles, and other surfactant aggregates. We have recently developed two treatments for equations of state of surfactant molecules at low density at the heptane/water interface: (i) containing ionic head groups as a function of added salt, and (ii) containing zwitterionic head groups, particularly phosphatidyl cholines and phosphatidyl ethanolamines, as a function of temperature. Predictions are well-supported by experimental pressure/area isotherms and the temperature dependences of second virial coefficients. Here we aim to extend and develop statistical thermodynamic theory for head group interactions at higher density, and where curvature is important, in colloidal aggregates such as bilayers and micelles. One application is in the prediction of passive transport rates of hydrophobic ions through bilayers, and of the equilibrium separations of bilayers relevant to fusion and flocculation processes. The second application, and a principal long-term goal toward which we plan to begin here, is the development of statistical thermodynamic theory of colloidal stability. This will require coupling this electrostatics treatment with recent efforts of ours and others on chain conformations in interfacial systems, in a relevant aggregation theory framework. We plan to use Hill's adaptation of McMillan-Mayer solution theory for the latter purpose, to go beyond current ideal solution thermodynamics treatments of surfactant aggregation. The work has major bearing on biomedical science inasmuch as it aims to develop a more microscopic understanding of the fundamental physical chemistry of colloidal aggregates, including structures and stabilities of biomembranes and micelles, partitioning and passive transport of charged solutes through them, and ultimately other dynamic and higher concentration colloidal properties.
