Distribution of counterions near discretely charged planes and rods

Abstract

Abstract. -Realistic charged macromolecules are characterized by discrete (rather than homogeneous) charge distributions. We investigate the effects of surface charge discretization on the counterion distribution at the level of mean-field theory using a two-state model. Both planar and cylindrical geometries are considered; for the latter case, we compare our results to numerical solutions of the full Poisson-Boltzmann equation. We find that the discretization of the surface charge can cause enhanced localization of the counterions near the surface; for charged cylinders, counterion condensation can exceed Oosawa-Manning condensation.Introduction. -The interaction between charged macromolecules and counterions is a crucial component of the physics of charged systems [1]. Although realistic macromolecules are often composed of discrete charges, theoretical models typically assume a homogeneous surface charge distribution. In the case of cylindrical polyelectrolytes (PEs), this assumption leads to Oosawa-Manning (OM) condensation [2,3], in which counterions become closely associated with the macromolecule, effectively lowering its overall charge. A similar effect also occurs for spherical macromolecules [4]. Theoretically, the effects of surface charge inhomogeneities on the counterion distribution has been studied for planar [5,6], cylindrical [7][8][9][10], and spherical [11,12] geometries. In particular, both Moreira et al. [5] and Lukatsky et al. [6] have shown analytically that the heterogeneity of a planar charge distribution leads to an enhanced localization of the counterions near the macromolecular surface. Thus, theoretical models that assume homogeneous surface charge distributions -including OM condensation theory -must be modified for realistic charge distributions.In this letter, we explore the effects of surface charge discretization on the counterion distribution in the absence of added salt. For small charge modulation, it is appropriate to use a perturbative expansion of the Poisson-Boltzmann (PB) equation to describe the meanfield behavior of the counterion distribution. It has already been shown that such an expansion

Scaling and universality in the counterion-condensation transition at charged cylinders

“…This trend is also observed in previous simulations [24,64,65,66] and in experiments with multivalent counterions [73], and will be analyzed in more detail in the following sections. However, in contrast to previous conclusions (obtained based on small values of ∆) [24,40], the aforementioned behavior for large Ξ does not imply a larger condensed fraction as defined within the inflection-point criterion.…”

“…Surprisingly, the mean-field theory is found to be exact in 2D in the whole range of Manning parameters (or temperatures) when N → ∞. In 3D, however, correlation effects in the condensation phase (ξ > ξ c ) lead to strong deviations from meanfield theory and support the strong-coupling predictions characterized by an excessive accumulation of counterions near the cylinder surface in agreement with previous numerical studies [24,40,64,65,66] and experiments [73]. An important result is that the large-distance form of the density profile remains unaffected by these correlations and thereby a universal condensed fraction is obtained when the inflection-point criterion is applied.…”

“…This indicates that making a distinction between two layers of condensed and decondensed counterions, in the sense of two-fluid models frequently used in literature [1,2,3,4,5,6,7,8,29,31,32,33,34,35,40,41], requires a criterion.…”

“…Since its discovery, the CCT has been at the focus of numerical [23,24,25,26] and analytical [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44] studies. Under particular dispute has been the connection between CCT and the celebrated Kosterlitz-Thouless transition of logarithmically interacting particles in two dimensions [31,45,46,47].…”

Electrostatic correlations at the Stern layer: Physics or chemistry?

“…This has been a recurrent topic in the statistical mechanics of interfaces. Already in the 1970s, Nelson [29][30][31][32] have revisited the problem, finding that discrete charges add to relatively minor corrections to an approximation where the interface is treated as a smooth background. The crucial aspect between the interaction of interfacial charges and ions is that it describes a strong correlation 20 ͑see also Ref.…”