Charge renormalization of charged spheres based on thermodynamic properties.

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 charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega 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 sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega 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-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.

Surface tension increment due to solute addition.

Addition of solute into solvent may lead to an increase in surface tension, such as salt in water and water in alcohol, due to solute depletion at the interface. The repulsion of the solute from the interface may originate from electrostatic forces or solute-solvent attraction. On the basis of the square-well model for the interface-solute interaction, we derive the surface tension increment Deltagamma by both canonical and grand-canonical routes (Gibbs adsorption isotherm) for a spherical droplet. The surface tension is increased linearly with the bulk concentration of the solute c(b) and the interaction range lambda. The theoretical results are consistent with those obtained by experiments and Monte Carlo simulations up to a few molarity. For weak repulsion, the increment is internal energy driven. When the repulsion is large enough, the surface tension increment is entropy driven and approaches the asymptotic limit, Deltagamma approximately c(b)k(B)Tlambda, due to the nearly complete depletion of the solute at the interface. Our result may shed some light on the surface tension increment for electrolyte solutions with concentration above 0.2M.