Effective interactions and volume energies in charged colloids: linear response theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out the degrees of freedom of all microions from the partition function, and assuming a linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the Derjaguin-Landau-Verwey-Overbeek screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy-a natural consequence of the one-component reduction-contributes to the total free energy, and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.