Salt-Induced Collapse and Reexpansion of Highly Charged Flexible Polyelectrolytes

We study the salt-dependent conformations of dilute flexible polyelectrolytes in solution via computer simulations. Low concentrations of multivalent salt induce the known conformational collapse of individual polyelectrolyte chains, but as the salt concentration is increased further this is followed by a reexpansion. We explicitly demonstrate that multivalent counterions can overcompensate the bare charge of the chain in the reexpansion regime. Both the degree of reexpansion and the occurrence of overcharging sensitively depend on ion size. Our findings are relevant for a wide range of salt-induced complexation phenomena.

Figure 1

Squared radius of gyration $R_g^2$ of a polyelectrolyte of length $N=64$ as a function of salt concentration $C_s$. Curves corresponds to added salt with counterion valency from 1 to 4. The curve $3:1^{*}$ refers to a system with ions that have a twice smaller diameter (see text for details). The dashed line corresponds to a reference system without any electrostatic interactions. Error bars are smaller than the symbol size.

Figure 2

Scaling dimension $\nu$ of the radius of gyration for a polyelectrolyte in a tetravalent salt solution. At low salt concentration $C_s$, $\nu$ exceeds the self-avoiding random-walk value 0.588, owing to the electrostatic repulsions between monomers. For the concentration $C_{Z=4}$ corresponding to the minimum in Fig. 1, the exponent reaches the value for a compact globule. The subsequent reexpansion of the chain at higher salt concentrations is reflected in an increase in $\nu$.

Figure 3

Net charge $Q(r)$ within a tube of radius $r$ around a chain ($N=64$) at various salt concentrations $C_s$ of trivalent salt. (a) For ion diameter $\sigma$ (case $3:1$ in Fig. 1) an overcharging peak appears at short $r$. (b) For smaller ions (case $3:1^{*}$) the overcharging peak is absent.

Figure 4

Drift velocity $V_{\mathrm{drift}}$ (in units of $\sigma /\tau$) of the center of mass of a polyelectrolyte ($N=16$) as a function of salt concentration $C_s$, in the direction of the electric field. The sign reversal in the electrophoretic mobility provides direct evidence for charge reversal by multivalent counterions.