Dynamics of collapse of flexible polyelectrolytes in poor solvents

The collapse kinetics of strongly charged polyelectrolytes in poor solvents is investigated by Langevin simulations and scaling arguments. We investigate the role of valence z of counterions, solvent quality, and shape of counterions on the dynamics of collapse. On the basis of the simulations, a number of results are obtained. (1) The rate of collapse, which is measured using the time dependence of the radius of gyration of the chain, increases sharply as z increases from 1 to 4. The collapse is particularly slow for the monovalent case and is observed only when the solvent quality is sufficiently poor. (2) Although the routes to collapse depend on 2 and the solvent quality a general collapse mechanism emerges. Upon quenching to low temperatures, counterions condense rapidly on a diffusion-limited time scale. At intermediate times metastable pearl-necklace structures form. The clusters merge at longer times with the largest one growing at the expense of smaller ones which is reminiscent of the Lifshitz-Slyozov growth mechanism. (3) The structure of the globule is controlled by z and the solvent quality. The combined system of the collapsed chain and the condensed counterions forms a Wigner crystal when the solvent quality is not too poor provided E 1 2. For very poor solvents the morphology of the collapsed structure resembles a Wigner glass. These results are used to obtain a valence dependent diagram of states for strongly charged polyelectrolytes in poor solvents. (4) For a fixed z and quality of the solvent, the efficiency of collapse decreases dramatically as the size of the counterion increases. The shape of the counterions also affects the collapse dynamics. Spherical counterions are more efficient condensing agents than an isovalent cigar-shaped counterions.