Charge asymmetric electrolytes around a rigid cylindrical polyelectrolyte: A generalization of the capacitive compactness

Abstract

The surface mean electrostatic potential and capacitive compactness of the electrical double layer surrounding an infinite rigid cylindrical polyelectrolyte are analysed for equally-sized -1:z+ aqueous electrolytes. Monte Carlo simulations, the non-linear Poisson–Boltzman equation, the modified Poisson–Boltzmann theory, and the hypernetted chain/mean spherical approximation integral equation are used to examine the role of multivalent cations (coions) when the properties of monovalent anions (counterions) are fixed. A non-zero mean electrostatic potential in the neighbourhood of an uncharged polyelectrolyte is predicted by the simulations and the modified Poisson–Boltzmann theory in the presence of multivalent cations. The concept of capacitive compactness is generalised to overcome the divergence found in the classical definition, when a non-zero potential at the point of zero charge is present. With a highly electrified colloidal surface an inversion is observed, as a function of colloidal charge, in the precedence of the mean electrostatic potential near the polyelectrolyte’s surface and of the capacitive compactness between -1:+1 and -1:z+ electrolytes.