Schematic illustration of the systems modeled in this work. Two parallel slabs with dielectric constant are immersed in a bulk medium with dielectric constant . The slabs have thickness and their proximal faces are separated by . Static surface charges are arranged on a square lattice lying immediately below the dielectric interface between each slab and the sandwiched water region. These charges are neutralized by counterions that are freely diffusing in the central water region. Periodic boundary conditions in the plane of the slabs are assumed. The various length scales used in the figure are defined in Table I. Note that interface B coincides with the plane .
Counterion density at midplane between the two dielectric slabs is plotted as a function of the width of dielectric slabs . More counterions are driven to the center for narrow slabs. The dashed line represents the expected density for an ideal gas, i.e., uniform distribution of all counterions within region 3. The case corresponds to a system without any dielectric contrast between the slabs and bulk solution. The geometry of the system and physical parameters for the simulation are as follows: , , , , , and .
Pressure between the two slabs as a function of the slab width. Physical parameters are identical to those in Fig. 2. The presented error bars in this figure and subsequent figures represent standard deviations over several Monte Carlo runs; i.e., these error bars reflect finite sampling of the thermal ensemble and do not indicate any inherent errors associated with the image charge methodology, which is, for all practical purposes, exact.
Counterion density at midplane between the two dielectric slabs as a function of the slab dielectric constant. Two different values are considered, as indicated. The remaining physical parameters are identical to those in Fig. 2, except that and .
Pressure between two slabs as a function of the slab dielectric constant. Physical parameters are identical to those in Fig. 4.
The density of counterions as a function of the position for three different dielectric constants of the slabs . Physical parameters are otherwise identical to those in Fig. 4.
Counterion density at midplane between the two dielectric slabs is plotted as a function of the interslab separation . Physical parameters are same as in Fig. 2, except that .
The density of counterions as a function of position for the system studied in Fig. 7, assuming the two values of indicated. The inset overlays the regions for both cases in the immediate vicinity of the interface and further compares to simple exponential decay.
Pressure between two slabs as a function of the interslab separation for the system in Fig. 7.
Notations used in the paper.
Article metrics loading...
Full text loading...