] is the activity of the i-th particle of species α in a spatially-varying field φ α (r) and with a chemical potential µ α , with the asterisk distinguishing between activity and charge valency. The Boltzmann factor associated with the pair potential between a pair of particles i and j of species α and γ is given as e α,γ (i, j) = exp [-βu α,γ (r i , r j )]. Finally, we note that the integral over the water degrees of freedom can be taken out of the integrals, because the solvent remains non-interacting in this model. There is thus a factor (z * W V ) n W /n W ! before the integrals over the polymer and salt degrees of freedom. We will otherwise ignore this term, as it merely serves to establish the water species contribution to the ideal mixing entropy.