Strong-Coupling Electrostatics in the Presence of Dielectric Inhomogeneities

We study the strong-coupling (SC) interaction between two like-charged membranes of finite thickness embedded in a medium of higher dielectric constant. A generalized SC theory is applied along with extensive Monte Carlo simulations to study the image charge effects induced by multiple dielectric discontinuities in this system. These effects lead to strong counterion crowding in the central region of the intersurface space upon increasing the solvent-membrane dielectric mismatch and change the membrane interactions from attractive to repulsive at small separations. These features agree quantitatively with the SC theory at elevated couplings or dielectric mismatch where the correlation hole around counterions is larger than the thickness of the central counterion layer.

Figure 1

Schematic view of two charged membranes and counterions in between. Here $2a$ is the closest-approach distance (leaving out the counterion diameter from the actual distance) and counterion excluded-volume repulsions are neglected.

Figure 2

(a) Rescaled counterion density profile between two like-charged dielectric membranes for $\Xi =100$, $b/\mu =100$, $a/\mu =1$ and as the dielectric mismatch $\Delta$ is increased (from bottom to top at $z=0$). (b) Rescaled intermembrane pressure as a function of $\Delta$ for $b/\mu =100$, $a/\mu =1$ and as $\Xi$ is increased (bottom to top); inset shows the details in the logarithmic scale. (c) The midplane ($z=0$) counterion density, $\tilde{\rho }(0)$, as a function of the coupling parameter $\Xi$ for $a/\mu =7$, $b/\mu =100$ and as $\Delta$ is increased (bottom to top). In (a)–(c) lines are the SC predictions (see the text) and symbols are simulation data.

Figure 3

(a) Same as Fig. 2b but for $a/\mu =7$. Inset shows the details for small pressures. (b) Simulated equilibrium half-distance, $a_{*}$, as a function of $\Xi$ for $b/\mu =2$ and as $\Delta$ is increased. Lines are SC predictions [from minimization of Eq. (3)]. (c) Simulation results for $a_{*}$ as a function of $b$ with all images (circles) and the first-order images only (squares) for $\Xi =50$ and $\Delta =0.95$ (the latter shows a very weak increase with $b$); here lines are guides to the eye. The surfaces attract for $a>a_{*}$ and repel for $a<a_{*}$.