Asymmetric Coulomb fluids at randomly charged dielectric interfaces: Anti-fragility, overcharging and charge inversion

Abstract

We study the distribution of multivalent counterions next to a dielectric slab, bearing a quenched, random distribution of charges on one of its solution interfaces, with a given mean and variance, both in the absence and in the presence of a bathing monovalent salt solution. We use the previously derived approach based on the dressed multivalent-ion theory that combines aspects of the strong and weak coupling of multivalent and monovalent ions in a single framework. The presence of quenched charge disorder on the charged surface of the dielectric slab is shown to substantially increase the density of multivalent counterions in its vicinity. In the counterion-only model (with no monovalent salt ions), the surface disorder generates an additional logarithmic attraction potential and thus an algebraically singular counterion density profile at the surface. This behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact-value theorem, reflecting the anti-fragility effects of the disorder that drive the system towards a more "ordered" state. In the presence of an interfacial dielectric discontinuity, depleting the counterion layer at the surface, the charge disorder still generates a much enhanced counterion density further away from the surface. Likewise, the charge inversion and/or overcharging of the surface occur more strongly and at smaller bulk concentrations of multivalent counterions when the surface carries quenched charge disorder. Overall, the presence of quenched surface charge disorder leads to sizable effects in the distribution of multivalent counterions in a wide range of realistic parameters and typically within a distance of a few nanometers from the charged surface.

A Novel Antifragility Measure Based on Satisfaction and Its Application to Random and Biological Boolean Networks

“…The concept of antifragility has been actively applied in numerous areas such as risk analysis [2,3], physics [4], molecular biology [5,6], transportation planning [7,8], engineering [9,10,11], aerospace and computer science [12][13][14][15]. However, a practical measure of antifragility has not been developed yet.…”

Electrolyte solutions at heterogeneously charged substrates

“…In recent years considerable theoretical interest has emerged in the effective interaction between two heterogeneously charged walls (which typically are the surfaces * Electronic address: mussotter@is.mpg.de † Electronic address: bier@is.mpg.de of colloidal particles) mediated by an electrolyte solution [16][17][18][19][20][21][22][23][24][25][26]. In contrast to uniform substrates, this effective interaction can lead to lateral forces, in addition to the common ones in normal direction.…”

“…Due to the linear relationship between the wall nonuniformities and the corresponding number density deviations from the bulk values, the latter are given by linear combinations of elementary response features, which are discussed first. Next, two main cases are studied: wall heterogeneities, which are laterally isotropic around a certain center and wall heterogeneities, which possess the symmetry of a two-dimensional lattice; the study of randomly distributed nonuniformities [16,[18][19][20][21] is left to future research. For both cases various length scale regimes are discussed, which are provided by the bulk correlation length of the pure solvent, the Debye length, and a characteristic length scale associated with the wall nonuniformities.…”

An analysis of the fluctuation potential in the modified Poisson-Boltzmann theory for restricted primitive model electrolytes

“…where the quantity C contains the valencies Z + , Z − , and has spatial dependence through g(1, 3) and g(2, 3). Thus, although C is not a constant per se, it can be assumed to be approximately constant for the purposes of solution to equation (42). An approximate analytic form of Φ(1, 2; 3) in region I, whose value is not necessarily zero, would then be available.…”