Charge renormalization of cylinders and spheres: Ion size effects

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Abstract
The effect of the counterion size on the degree of counterion condensation onto a cylindrical macroion and a spherical one in the absence of salt is studied theoretically within a modified Poisson–Boltzmann approach. We find that excluded volume interactions reduce the degree of condensation. Using a simple variational free energy we show that this reduction can be attributed to an effective increase in the macroion size due to the contribution of the condensed counterions. We also find that for a charged cylinder, the reduction in charge renormalization vanishes at infinite dilution because of the extended nature of the condensed layer. In contrast, excluded volume interactions can reduce the degree of charge renormalization of a sphere even at high dilutions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3598–3615, 2004