Electrochemical properties of spherical polyelectrolytes: I. Impermeable sphere model

Abstract

The Poisson-Boltzmann equation was numerically solved to obtain the electrostatic potential in the vicinity of spherical polyelectrolyte particles at finite concentration and low ionic strength, using the cell model. The polyelectrolyte particles were treated as impermeable spheres having a uniform surface charge density. The electrostatic potential was studied as a function of surface charge density, concentration of added salt, and particle size. The osmotic coefficient, Δp K, and the local ion concentrations were computed from the electrostatic potential. The computational results were compared with experimental ionic activities and osmotic coefficients for micelles of ionic detergents. Excellent agreement was obtained between the experimental and computed osmotic coefficients for micelles of sodium dodecyl sulfate and potassium laurate, but not for the cationic detergents dodecylpyridinium chloride and dodecylammonium chloride. The reason for the disagreement is unknown. The present calculations at finite particle concentration are compared with the electrostatic potential tables of Loeb et al. (“The Electrical Double Layer around a Spherical Colloid Particle,” M.I.T. Press, Cambridge, Mass., 1961), which were computed for the special case of infinite dilution or high ionic strength in order to show the range of applicability of those tables. Detailed comparison requires the specification of all parameters; for the particular parameters used in this paper it was found that for particles having the radius of detergent micelles (∼18 Å), the presence of 0.1 M salt was required to give good agreement (within 1.5%) between the surface potential computed by the present method and the infinite-dilution method, whereas only 10 −4 M salt was needed to give similarly good agreement for particles having the radius of phospholipid vesicles (∼300 Å).