  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.
