Collapse and expansion kinetics of a single polyelectrolyte chain with hydrodynamic interactions

We investigate the collapse and expansion dynamics of a linear polyelectrolyte (PE) with hydrodynamic interactions. Using dissipative particle dynamics with a bead-spring PE model, long-range electrostatics and explicit ions we examine how the timescales of collapse $t_\text{col}$ and expansion $t_\text{exp}$ depend on the chain length $N$, and obtain scaling relationships $t_\text{col}\sim N^\alpha$ and $t_\text{exp}\sim N^\beta$. For neutral polymers, we derive values of $\alpha=0.94\pm0.01$ and $\beta=1.97\pm0.10$. Interestingly, the introduction of electrostatic interaction markedly shifts $\alpha$ to $\alpha\approx1.4\pm0.1$ for salt concentrations within $c=10^{-4}$ M to $10^{-2}$ M. A reduction in ion-to-monomer size ratio noticeably reduces $\alpha$. On the other hand, the expansion scaling remains approximately constant, $\beta \approx 2$, regardless of salt concentration or ion size considered. We find $\beta > \alpha$ for all conditions considered, implying that expansion is always slower than collapse in the limit of long polymers. This asymmetry is explained by distinct kinetic pathways of collapse and expansion processes.