Comparison of Simulation Methods for Charged Systems of Slab Geometry

Abstract

Using the specific model of a system of like charged ions confined between two planar like charged surfaces, we compare the predictions for the energy and density profile of four simulation methods available to treat the long range Coulomb interactions in systems periodic in two directions but bound in the third one. Monte Carlo simulations demonstrate unambiguously complete agreement between the results obtained with these methods where the potential between charges is solution of Poisson's equation in the simulation cell with adequate boundary conditions. The practical advantages of the different methods are assessed.

Lekner summations and Ewald summations for quasi-two-dimensional systems

“…Despite its obvious inaccuracy, for slab-like systems, as the system studied in ref. [25], the results found with the Hautman-Klein method are in very good agreement with results obtained with a purely electrostatic model and results obtained with the methods of refs. [18,20].…”

“…For n c = 50 and n K = 4, the separation occurs only after 60 MC-cycles and after the trajectories stay very close. For both cases, (n c , n K ) = (25,3) and (n c , n K ) = (50, 4) one may hope to obtain the same statistical averages than in the Ewald quasi-2D method. Of course a dramatic separation, as for (n c , n K ) = (10, 3), may still happen for both (n c , n K ) = (25, 3) and (n c , n K ) = (50, 3) after more MC-cycles, this had not happened for the first 10000 MC-cycles examined.…”

“…[24] and another study done in ref. [25] where we have compared the methods of references [16,18,20] on a system having a slab geometry. One of the aims of the present work is also to present explicitly a procedure to implement with accuracy (but not always with efficiency) the Lekner summations technique in Monte-Carlo simulations using the Metropolis algorithms.…”

Long ranged interactions in computer simulations and for quasi-2D systems

“…In the study done Ref. [106] where four different methods for quasi-2D methods are compared, two charged walls are used as a background for the systems, in this work all contributions due to background charges and background-background interactions are given for all the four methods considered in the work. The same background is used for bilayer systems [160].…”

“…Several systems confined in slab geometries as electrolytes models [103][104][105][106] or ferrofluid colloidal models with dipolar interactions [107][108][109][110][111][112][113] have been studied; the properties of water confined in a slab [114] have also been the subject of a lot of numerical studies (for a recent review the reader will refer to the work by Zangi [115]). The properties of membranes bilayers and biological membranes are very sensitive to long ranged interactions; a large number of numerical simulations using molecular dynamics is devoted to these studies [51].…”