Conformation of a single polyelectrolyte in poor solvents

Understanding the conformation of a polyelectrolyte (PE) is not only a fundamental challenge in polymer science but also critical for understanding the folding and aggregation of proteins. Here, we develop a theory by systematically including the electrostatic interactions into the self-consistent field theory for polymers to study the conformational behaviors of a single PE in poor solvents. As the backbone charge fraction of the PE increases, our theory predicts that the spherical globule (Sph) can either be elongated to a series of pearl-necklace (PN) structures or be flattened to two novel structures that have not been reported before: biconcave red cell and toroid. While the PN structures are stable conformations, the two fattened structures are metastable. We find that the cylindrical globule, the stability of which is under debate, is an unstable structure. The signature of the PN structures obtained by our calculation is less pronounced than that reported by other theoretical works due to the continuous change in the curvature from the pearl to the necklace, which, however, is in good agreement with the results from molecular simulations and neutron scattering experiments. In addition, our theory reveals different characteristics of the globule to PN transition: the transition from the Sph to the PN with double pearls is discontinuous, whereas those from adjacent PN structures are continuous at finite salt concentrations. Furthermore, we observe different scaling behaviors: the string width is not a constant as a thermal blob but decays as the backbone charge fraction increases.