Ion condensation on solid particles: Theory and simulations

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Abstract
For polyelectrolytes the Manning theory predicts an effective charge density, which increases with the bare charge density up to the point where the thermal energy of an ion balances the reversible work necessary to remove the ion from the polymer. From that point on, the effective charge remains constant, as no more ions will desorb. For spherical colloidal particles, a similar maximum effective charge can be expected, which indeed is predicted by the Poisson–Boltzmann theory. To check these predictions quantitatively, Monte Carlo simulations have been performed on the ionic distribution of a salt-free colloid at a volume fraction of 36%, both in the spherical cell model and in a periodic system of cubic symmetry. In the latter system the interactions were evaluated using the Ewald summation method. These simulations show that the effective charge of a colloid at this volume fraction does not reach a plateau value for large bare charges, but instead the effective charge passes through a maximum, and decreases again as the number of ions present increases. To extrapolate the simulation results to large particles, a weighted density-functional theory was developed that not only reproduces this maximum, but even predicts the simulation results within approximately 1%. According to this theory, the maximum is always present, and for large particles it appears at a given surface charge density which is nearly independent of the colloid volume fraction.