The phase behavior of charge-stabilized colloidal suspensions is modeled by a
combination of response theory for electrostatic interparticle interactions and
variational theory for free energies. Integrating out degrees of freedom of the
microions (counterions, salt ions), the macroion-microion mixture is mapped
onto a one-component system governed by effective macroion interactions. Linear
response of microions to the electrostatic potential of the macroions results
in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume
energy, while nonlinear response modifies the effective interactions [A. R.
Denton, \PR E {\bf 70}, 031404 (2004)]. The volume energy and effective pair
potential are taken as input to a variational free energy, based on
thermodynamic perturbation theory. For both linear and first-order nonlinear
effective interactions, a coexistence analysis applied to aqueous suspensions
of highly charged macroions and monovalent microions yields bulk separation of
macroion-rich and macroion-poor phases below a critical salt concentration, in
qualitative agreement with predictions of related linearized theories [R. van
Roij, M. Dijkstra, and J.-P. Hansen, \PR E {\bf 59}, 2010 (1999); P. B. Warren,
\JCP {\bf 112}, 4683 (2000)]. It is concluded that nonlinear screening can
modify phase behavior but does not necessarily suppress bulk phase separation
of deionized suspensions.Comment: 14 pages of text + 9 figure