Phase Behaviors of a Binary Blend of Oppositely Charged Polyelectrolytes: A Weak Segregation Approach

Abstract

In our quest for a better understanding of phase behaviors regarding polyelectrolyte systems, we develop a Landau free energy for a stoichiometric blend of weakly charged polyanions and polycations. Its free energy functional is first formulated as that for Gaussian chains subject to effective interaction fields. The local interaction part, which necessitates excluded volume and charged chain connectivity, is given by a locally equilibrated excess equation of state for the charged hard-sphere chain blend with mean-field dispersion interactions. The long-ranged part of Coulomb interactions is included through an electric potential field generated inside. The resultant functional is then expanded as a series in two proper order parameters to yield the desired Landau free energy. Unfavorable energetics makes the blend phase segregated but only on a nanoscopic scale due to global electroneutrality. The interplay of self- and mutual dispersion interactions produces a variety of phase behaviors ranging from conventional order–disorder-type transitions to complicated ordering transitions in carefully selected blends. Critical compositions are revealed to depend on asymmetry in chain sizes and disparity in self-dispersion interactions between the constituents. Furthermore, it is argued that nanostructured materials with drastically different responses to pressure can be designed by blending polyelectrolytes.