Strong coupling electrostatics for randomly charged surfaces: antifragility and effective interactions

Abstract

We study the effective interaction mediated by strongly coupled Coulomb fluids between dielectric surfaces carrying quenched, random monopolar charges with equal mean and variance, both when the Coulomb fluid consists only of mobile multivalent counterions and when it consists of an asymmetric ionic mixture containing multivalent and monovalent (salt) ions in equilibrium with an aqueous bulk reservoir. We analyze the consequences that follow from the interplay between surface charge disorder, dielectric and salt image effects, and the strong electrostatic coupling that results from multivalent counterions on the distribution of these ions and the effective interaction pressure they mediate between the surfaces. In a dielectrically homogeneous system, we show that the multivalent counterions are attracted towards the surfaces with a singular, disorder-induced potential that diverges logarithmically on approach to the surfaces, creating a singular but integrable counterion density profile that exhibits an algebraic divergence at the surfaces with an exponent that depends on the surface charge (disorder) variance. This effect drives the system towards a state of lower thermal 'disorder', one that can be described by a renormalized temperature, exhibiting thus a remarkable antifragility. In the presence of an interfacial dielectric discontinuity, the singular behavior of counterion density at the surfaces is removed but multivalent counterions are still accumulated much more strongly close to randomly charged surfaces as compared with uniformly charged ones. The interaction pressure acting on the surfaces displays in general a highly non-monotonic behavior as a function of the inter-surface separation with a prominent regime of attraction at small to intermediate separations. This attraction is caused directly by the combined effects from charge disorder and strong coupling electrostatics of multivalent counterions, which dominate the surface-surface repulsion due to the (equal) mean charges on the two surfaces and the osmotic pressure of monovalent ions residing between them. These effects can be quite significant even with a small degree of surface charge disorder relative to the mean surface charge. The strong coupling, disorder-induced attraction is typically much stronger than the van der Waals interaction between the surfaces, especially within a range of several nanometers for the inter-surface separation, where such effects are predicted to be most pronounced.

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.…”

Charged nanorods at heterogeneously charged surfaces

“…(50), and C 0 (χ, 0) = 2 −1+χ √ π Γ (1 − χ/2) /Γ (3/2 − χ/2), reproducing the previously obtained result for pointlike counterions in Refs. [86,91]. Figure 2(b) also shows that, although the surface accumulation (or, midplane depletion) of counterion is highly enhanced by the monopolar term alone, the combined effects due to the cooperation between the surface charge disorder and the quadrupolar moment of counterions, entering through the termsũ qt andũ tt in Eq.…”

Ion-mediated interactions between net-neutral slabs: Weak and strong disorder effects

“…Our analysis in this paper is focused on yet another facet of the disorder-induced effects by assuming, in a system of two plane-parallel dielectric slabs, that the randomly charged surfaces of the slabs bear no net charge. This eliminates the direct strong coupling between multivalent ions and the mean surface charge and, thereby, also the ensuing strong-coupling interactions, considered in our previous papers [83,84], that would otherwise completely mask the vdW and image-induced, ion-depletion interactions between the slabs in an asymmetric Coulomb fluid. This allows us to address the question of how the presence of surface charge disorder affects the standard picture for the interaction of neutral bodies based on the vdW and ion-depletion effects.…”

“…[7,81,[99][100][101][102][103][104]). In disordered charged systems, such strong-coupling phenomena have been considered only in a few cases so far [62,74,83,84] by assuming that bounding surfaces carry a finite mean surface charge density, to which multivalent counterions can couple strongly, in the same sense as considered in the context of uniformly charged surfaces as noted above. Yet, the presence of charge randomness on bounding surfaces was shown to give rise to novel phenomena such as strong surface attraction of multivalent counterions, characterized by a density profile that diverges at the surface, in clear violation of the contact-value theorem established for uniformly charged surfaces.…”

“…The net effect due to the interplay between disorder, mono-and multivalent-ion contributions yields a qualitatively different behavior for the effective surface-surface interactions, depending on the strength of disorder as quantified by the disorder coupling (or strength) parameter [62,74,83,84]. This feature bears some conceptual resemblance to the strong-weak coupling dichotomy that exists for net-charged surfaces, dependent on the electrostatic coupling parameter in that case [106][107][108].…”