Ion distribution around a charged rod in one and two component solvents: preferential solvation and first order ionization phase transition.

In one and two component polar solvents, we calculate the counterion distribution around an ionizable rod treating the degree of ionization alpha as an annealed variable dependent on its local environment. In the two component case, we take into account the preferential solvation of the charged particles and the short-range interaction between the rod and the solvent. It follows a composition-dependent mass action law. The composition becomes heterogeneous around a charged rod on a mesoscopic scale, strongly affecting the counterion distribution. We predict a first order phase transition of weak-to-strong ionization for hydrophobic chains. This transition line starts from a point on the solvent coexistence curve and ends at an ionization critical point. The composition heterogeneity is long-ranged near the solvent critical point.