Spatial distribution of polyelectrolyte and counterions in nanocapsules: A computer simulation study

We study a spatial distribution of polyelectrolyte chains and counterions inside nanometer-size capsules by means of molecular dynamics simulation on the level of a colloidal model in which polyelectrolyte coils are modeled as soft charged spheres. The capsule shell is treated as a semipermeable membrane, impermeable for the polyelectrolyte chains, but allowing free diffusion of solvent molecules and counterions. As a result, counterions leak out from the capsule immersed into a fluid of low ionic strength. This counterion leakage leads to a formation of characteristic polyelectrolyte density profiles with the central plateau and large peaks at the wall. We show that a nonuniform distribution of the inner polyelectrolyte depends on the capsule radius, surface charge, concentration of encapsulated polyelectrolyte, and the volume fraction of capsules.

Figure 1

(Color online) Pair distribution function for the centers of mass of polymer chains in the bulk as obtained from the MD simulation of the bead-spring model and the same distribution obtained from MD simulation of the “colloidal” model. The vertical dashed line shows the half of the simulation box.

Figure 2

(Color online) Snapshots from an MD simulation of polyelectrolyte molecules in the bulk (a) and corresponding “colloidal” system (b).

Figure 3

(Color online) Effective surface charge density of the capsule, $Q^{\mathit{cap}}∕4\pi R^2$, as a function of the capsule volume fraction, $\Phi$ for different concentrations of encapsulated polyelectrolyte, $C$ (capsule radius $R=300{\sigma }_{\mathit{cc}}$).

Figure 4

(Color online) Effective surface charge density, $Q^{\mathit{cap}}∕4\pi R^2$ as a function of capsule radius, $R$, for different concentrations of encapsulated polyelectrolyte, $C$, and capsule volume fraction, $\Phi$.

Figure 5

(Color online) Typical density profiles of counterions across the spherical WS cell at (a) various capsule volume fractions at $R=300{\sigma }_{\mathit{cc}}$, $C=2.65\times {10}^{-6}$; (b) various capsule radii ($R=250$, 300, and $350{\sigma }_{\mathit{cc}}$) polyelectrolyte concentration $C=2.65\times {10}^{-6}$, $\Phi \sim 0.05$ is nearly the same; (c) various polyelectrolyte concentrations $C=1.77\times {10}^{-6}$, $2.65\times {10}^{-6}$, and $3.54\times {10}^{-6}$ ($R=300{\sigma }_{\mathit{cc}}$, $\Phi =0.064$). The thin lines show the corresponding density profiles for the case $\Phi =1$.

Figure 6

(Color online) Typical ratios of mean polyelectrolyte density in the surface layer $\left(25{\sigma }_{\mathit{cc}}\right)$ to the mean polyelectrolyte density in the capsule bulk as a function of capsule volume fraction $\Phi$ (capsule radius $R=300{\sigma }_{\mathit{cc}}$) for different concentrations of encapsulated polyelectrolyte, $C$.

Figure 7

(Color online) Typical density profiles of encapsulated polyelectrolyte across the capsule at (a) various capsule volume fractions at $R=300{\sigma }_{\mathit{cc}}$, $C=2.65\times {10}^{-6}$; (b) various capsule radii ($R=250$, 300, and $350{\sigma }_{\mathit{cc}}$) polyelectrolyte concentration $C=2.65\times {10}^{-6}$, $\Phi \sim 0.05$ is nearly the same; (c) various polyelectrolyte concentrations $C=1.77\times {10}^{-6}$, $2.65\times {10}^{-6}$, and $3.54\times {10}^{-6}$ ($R=300{\sigma }_{\mathit{cc}}$, $\Phi =0.064$). Thin lines show corresponding density profiles for the case $\Phi =1$.