Quantifying the interaction between two polyelectrolyte chains using constraint self-consistent field theory

Polyelectrolytes (PEs) are polymers with charged repeating units which have broad applications in surfactants, absorbers, battery electrolytes, and stimuli-responsive functional materials, and are widely used as model systems to study biomolecules such as DNA, RNA, and proteins. The interaction between PE chains essentially governs a wealth of structure and dynamic properties. While interactions between rigid colloidal particles are well characterized by DLVO theory, a systematic description of the interactions between polyelectrolyte globules is still lacking as they are soft, deformable, and can overlap with each other. Here we developed a constraint self-consistent field theory that enables us to quantify the potential of mean force as a function of center-of-mass separation. The theory systematically captures the coupling between the position-dependent of interaction and chain conformation. The potential of mean force shows a long-range repulsion due to the electrostatic force and short-range attraction as the fusion of two polymer chains. Furthermore, we show multiple kinetic pathways for the association of two PEs because of different equilibrium structures of the final associates. This study elucidates that the two-body interaction between soft particles is essentially different from that of rigid particles. The potential of mean force obtained from our work is an important ingredient in the coarse-grained molecular simulations which can be used to study the aggregation and dynamics of charged macromolecules.