ELECTROSTATIC MODELING OF SURFACTANT LIQUID-CRYSTALLINE AGGREGATES - THE MODIFIED POISSON-BOLTZMANN EQUATION

A model of liquid-crystalline aggregates is developed to calculate are as per surfactant head group in high-concentration cylindrical and pla nar geometries. Two free energy contributions, electrostatic and inter facial, are summed to generate the total cell free energy for a range of head-group areas. The modified Poisson-Boltzmann equation (MPBE) in cluding dielectric saturation and hydration energies is used to calcul ated the electrostatic free energy. A Stern layer is used to prevent c ounterions at the charged interface, the thickness of which is decreas ed for large head-group areas to simulate the intercalation of counter ions between head groups. The hydration constant was decreased at high surfactant concentration to account for reduced ion hydration as wate r is depleted. The calculation is performed for a one-dimensional vari ation of physical properties. Solutions to the MPBE were achieved for higher surface charge densities than previously reported, using a fini te difference to estimate the derivatives and solving the resulting no nlinear algebraic equations. The optimized head-group areas for lamell ar phase samples are compared to published X-ray data to estimate the extent of ion binding.