Polymer complexation: Partially ionizable asymmetric polyelectrolytes

Theories of bulk coacervation of oppositely charged polyelectrolytes (PE) obscure single molecule level thermodynamic details, considered significant for coacervate equilibrium, whereas simulations account for only pairwise Coulomb interaction. Also, studies of effects of asymmetry on PE complexation are rare compared to symmetric PEs. We develop a theoretical model, accounting for all entropic and enthalpic contributions at the molecular level, and the mutual segmental screened Coulomb and excluded volume interactions between two asymmetric PEs, by constructing a Hamiltonian following Edwards and Muthukumar. Assuming maximal ion-pairing in the complex, the system free energy comprising configurational entropy of the polyions and free-ion entropy of the small ions is minimized. The effective charge and size of the complex, larger than sub-Gaussian globules as for symmetric chains, increase with asymmetry in polyion length and charge density. The thermodynamic drive for complexation is found to increase with ionizability of symmetric polyions and with a decrease in asymmetry in length for equally ionizable polyions. The crossover Coulomb strength demarcating the ion-pair enthalpy-driven (low strength) and counterion release entropy-driven (high strength) is marginally dependent on the charge density, because so is the degree of counterion condensation, and strongly dependent on the dielectric environment and salt. The key results match the trends in simulations. The framework may provide a direct way to calculate thermodynamic dependencies of complexation on experimental parameters such as electrostatic strength and salt, thus to better analyze and predict observed phenomena for different sets of polymer pairs.