The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.

We investigate the unfolding of single polyelectrolyte (PE) chains collapsed by trivalent salt under the action of alternating-current (AC) electric fields through computer simulations and theoretical scaling. The results show that a collapsed chain can be unfolded by an AC field when the field strength exceeds the direct-current (DC) threshold and the frequency is below a critical value, corresponding to the inverse charge relaxation/dissociation time of condensed trivalent counterions at the interface of the collapsed electrolyte. This relaxation time is also shown to be identical to the DC chain fluctuation time, suggesting that the dissociation of condensed polyvalent counterion on the collapsed PE interface controls the polyelectrolyte dipole formation and unfolding dynamics under an AC electric field.

Langevin dynamics simulations are performed to investigate ejection dynamics of spherically confined flexible polymers through a pore. By varying the chain length $N$ and the initial volume fraction ${\varphi }_0$ of the monomers, two scaling behaviors for the ejection velocity $v$ on the monomer number $m$ in the cavity are obtained: $v\sim m^{1.25}{\varphi }_0^{1.25}/N^{1.6}$ for large $m$ and $v\sim m^{-1.4}$ as $m$ is small. A robust scaling theory is developed by dividing the process into the confined and the nonconfined stages, and the dynamical equation is derived via the study of energy dissipation. After trimming the prior stage related to the escape of the head monomer across the pore, the evolution of $m$ is shown to be well described by the scaling theory. The ejection time exhibits two proper scaling behaviors: $N^{(2/3\nu )+y_1}{\varphi }_0^{-(2/3\nu )}$ and $N^{2+y_2}$ under the large and small ${\varphi }_0$ or $N$ conditions, respectively, where $y_1=1/3$, $y_2=1-\nu$, and $\nu$ is the Flory exponent.

Langevin dynamics simulations are performed to study polyelectrolytes driven through a nanopore in monovalent and divalent salt solutions. The driving electric field E is applied inside the pore, and the strength is varied to cover the four characteristic force regimes depicted by a rederived scaling theory, namely the unbiased (UB) regime, the weakly-driven (WD) regime, the strongly-driven trumpet (SD(T)) regime and the strongly-driven isoflux (SD(I)) regime. By changing the chain length N, the mean translocation time is studied under the scaling form $⟨\tau ⟩\sim N^{\alpha }{E}^{-\delta }$ . The exponents $\alpha$ and $\delta$ are calculated in each force regime for the two studied salt cases. Both of them are found to vary with E and N and, hence, are not universal in the parameter’s space. We further investigate the diffusion behavior of translocation. The subdiffusion exponent ${\gamma }_{\mathrm{p}}$ is extracted. The three essential exponents ${\nu }_{\mathrm{s}}$ , q, $z_{\mathrm{p}}$ are then obtained from the simulations. Together with ${\gamma }_{\mathrm{p}}$ , the validness of the scaling theory is verified. Through a comparison with experiments, the location of a usual experimental condition on the scaling plot is pinpointed.