INTEGRATION OF THE NONLINEAR POISSON BOLTZMANN-EQUATION FOR CHARGED VESICLES IN ELECTROLYTIC SOLUTIONS

The Poisson-Boltzmann equation (PBE), with specific ion-surface interactions and a cell model, was used to calculate the electrostatic properties of aqueous solutions containing vesicles of ionic amphiphiles. Vesicles are assumed to be water- and ion-permeable hollow spheres and specific ion adsorption at the surfaces was calculated using a Volmer isotherm. We solved the PBE numerically for a range of amphiphile and salt concentrations (up to 0.1 M) and calculated co-ion and counterion distributions in the inside and outside of vesicles as well as the fields and electrical potentials. The calculations yield results that are consistent with measured values for vesicles of synthetic amphiphiles.

EXPLICIT SOLUTIONS FOR TRUNCATED COULOMB POTENTIAL OBTAINED FROM SUPERSYMMETRY

The Schrodinger equation with the truncated Coulomb potential is solved using the supersymmetric quantum mechanics formalism, with and without the cutoff in the angular momentum potential. We obtain some analytical eigenfunctions and eigenvalues for particular values of the cutoff parameter.