Statistics versus dynamics: two methods for calculating the effective charge of colloidal particles

Two methods for calculating the effective charge of colloidal particles inside a salt free suspension are presented and analysed using Monte Carlo simulations. The rst method is based on the Alexander prescription, in which the exact electrostatic potential is matched asymptomatically to the solution of the linearized PoissonBoltzmann equation. The second method relies on a dynamical criterion, which denes the condensed counterions through a bound on their total energy. Although the two methods appear to be quite different, they lead to identical values of the effective colloidal charge, even for suspensions with multivalent counterions for which the PoissonBoltzmann equation fails. 1