||At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the|
charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles,
effective charges Z* is therefore invoked in the models based on Debye-Hückel approximation, such
as the DLVO potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to
obtain various thermodynamic properties ω in a spherical Wigner-Seitz cell. The effect of dielectric
discontinuity is examined. We show that at the same particle volume fraction, counterions around
a highly charged spheres with Z may display the same value of ω as those around a weakly charged
sphere with Z*, i.e., ω(Z) = ω(Z*). There exists a maximally attainable value of ω at which
Z = Z*. Defining Z* as the effective charge, we find that the effective charge passes through a
maximum and declines again due to ion-ion correlation as the number of counterions is increased.
The effective charge is even smaller if one adopts the Debye-Hückel expression ωDH. Our results
suggest that charge renormalization can be performed by chemical potential, which may be observed
in osmotic pressure measurements.
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