Polyelectrolyte Condensation Induced by Linear Cations

We examine the role of the condensing agent in the formation of polyelectrolyte bundles, via grand-canonical Monte Carlo simulations. Following recent experiments we use linear, rigid divalent cations of various lengths to induce condensation. Our results clarify and explain the experimental results for short cations. For longer cations we observe novel condensation behavior owing to the alignment of the cations. We also study the role of the polyelectrolyte surface-charge density, and find a nonmonotonic variation in bundle stability. This nonmonotonicity captures two trends that have been observed in separate experiments.

Figure 1

Net osmotic pressure as a function of rod-rod separation $L$, for bulk diamine concentrations of 5, 30, and 60 mM, at a polyelectrolyte surface-charge density $\sigma =0.633e/{\mathrm{nm}}^2$. The diamine charge separation is (a) $\delta =2.5\AA$, and (b) $\delta =3.75\AA$. Error bars are comparable to the symbol size.

Figure 2

Effect of diamine charge separation on bundle stability for polyelectrolytes with $\sigma =0.633e/{\mathrm{nm}}^2$. (a) Stable rod-rod separation at fixed 60 mM diamine concentration. (b) Bulk diamine concentration $C^{*}$ at which bundling first occurs. (c) Separate contributions to the net osmotic pressure, for $L=80$, 85, and 90 Å, at fixed 60 mM diamine concentration. The dashed curves give the negative of the electrostatic contribution (i.e., electrostatic attraction), and the solid curves give the short-range contribution to the pressure.

Figure 3

Fluid structure within stable bundles, projected onto a plane perpendicular to the bundle axis, for three different diamine lengths (top to bottom: $\delta =2.5$, 7.5, and 20 Å). Left: diamine concentration; right: diamine orientation with respect to polyelectrolyte axis. For discussion see the text.

Figure 4

Stable rod separation $L^{*}$ as a function of polyelectrolyte surface-charge density $\sigma$, for $\delta =10\AA$ at 60 mM bulk diamine concentration. The curve demonstrates that increasing $\sigma$ can either increase or decrease bundle stability.