The nonlinear Poisson-Boltzmann equation is solved variationally to obtain the electrostatic potential profile in a spherical cavity containing an aqueous electrolyte solution. The variational solution is based on the linear solution to the Poisson-Boltzmann equation. It is found that a three-parameter trial function provides sufficient accuracy to make the variational potential profile indistinguishable from exact numerical results. The variational solution is valid over the concentration, size, and surface potential ranges typical of phospholipid vesicles. It is anticipated that this solution will be useful in determining the stability of membraneous vesicles and reverse micelles.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Surfaces, Coatings and Films
- Colloid and Surface Chemistry