Effective interactions and volume energies in charge-stabilized colloidal suspensions

Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudoparticles. Within this scheme, the utility of a linear response approximation for deriving effective interparticle interactions has been demonstrated (Grimson M J and Silbert M 1991 Mel. Phys. 74 397). Here the response approach is extended to suspensions of finite-sized macroions and used to derive explicit expressions for (1) an effective electrostatic pair interaction between pseudo-macroions and (2) an associated volume energy that contributes to the total free energy. The derivation recovers precisely the form of the DLVO (Dejaguin, Landau, Verwey, and Overbeek) screened Coulomb effective pair interaction for spherical macroions and makes manifest the important influence of the volume energy on thermodynamic properties of deionized suspensions. Excluded-volume corrections are implicitly incorporated through a natural modification of the inverse screening length. By including the nonlinear response of counterions to macroions, the theory may be generalized to systematically investigate effective many-body interactions.