Solution properties of charged quasi-random copolymers: Integral equation theory

Using the polymer integral equation method, we study the solution properties of charged quasi-random two-letter $(HP)$ copolymers with two different types of distribution of monomer units along a copolymer chain: proteinlike copolymers and random-block copolymers. The copolymers consist of monomer units of two types: associating electroneutral hydrophobic (H) units and charged (P) units. Small mobile counterions are treated explicitly. We explore the influence of the primary structure of $HP$-polyelectrolyte chains on their structural behavior and aggregation in a solution, which is poor for H units and good for P units. Analysis of the static structure factors shows that there is an evident tendency to the aggregation of the hydrophobic groups belonging to different macromolecules into spatially correlated clusters. The spinodal lines and various structure diagrams are calculated for both copolymers. The characteristic temperature of counterion condensation is also estimated. The main finding is that charged proteinlike copolymers are more prone to self-organization in a poor solvent than their random-block counterparts. In particular, the apparent spinodal temperatures for proteinlike copolymers are several fold larger than for random-block copolymers with the same average block length and $HP$ composition. The influence of the primary structure is more pronounced in the processes dominated by short-range hydrophobic interaction than in the processes mostly governed by long-range electrostatic interactions.