Volume terms for charged colloids: a grand-canonical treatment

We present a study of thermodynamic properties of suspensions of charged colloids on the basis of linear Poisson-Boltzmann theory. We calculate the effective Hamiltonian of the colloids by integrating out the ionic degrees of freedom grand-canonically. This procedure not only yields the well-known pairwise screened-Coulomb interaction between the colloids, but also additional volume terms which affect the phase behavior and the thermodynamic properties such as the osmotic pressure. These calculations are greatly facilitated by the grand-canonical character of our treatment of the ions, and allow for relatively fast computations compared to earlier studies in the canonical ensemble. Moreover, the present derivation of the volume terms are relatively simple, make a direct connection with Donnan equilibrium, yield an explicit expression for the effective screening constant, and allow for extensions to include, for instance, nonlinear effects.