Some comments regarding the pressure tensor and contact theorem in a nonhomogeneous electrolyte

Abstract

A systematic Monte Carlo simulation study of the primitive model planar electrical double layer over an extended range of concentrations, electrode charges, cation diameters and valences

Inverse calculation of three-dimensional solvation structure on an arbitrary surface from a force distribution measured by liquid AFM

“…(1) derived by considering an infinitesimal movement of the probe in the system is an exact one in classical statistical mechanics of liquid. This equation is strictly consistent with the contact theorem [6][7][8][9]. (The contact theorem explains the pressure on a wall, the derivation of which is performed by an infinitesimal change of the system or solute volume.)…”

Monte Carlo simulation of an ion-dipole mixture as a model of an electrical double layer

“…͑14͒ in the work of Blum and Henderson 18 differs from that given by Carnie and Chan 37 as it is commented in Ref. 38. The difference comes from a different definition of the pressure tensor, and the agreement found here for lower surface charges gives additional support to the definition of Blum and Henderson.…”

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

“…But it also exhibits an algebraic dependence onz, which dominates at small separations from the surface and thus shows that, in the presence of surface charge disorder, the counterion density diverges in the immediate vicinity of the surface. The presence of disorder thus clearly violates the contact-value theorem which was derived for uniformly charged surfaces [93][94][95][96]; this theorem entails a contact value ofc(0) = 1 in the whole range of coupling parameters. Note that, nevertheless, the electroneutrality is exactly satisfied as ∞ 0 dzc(z) = 1.…”

“…In the case of counterions only, we show that a randomly charged surface generates a singular density profile for multivalent counterions with an algebraically diverging behavior at the surface; the latter is characterized by an exponent which is determined by the disorder strength (variance). Thus, multivalent counterions are predicted to accumulate strongly in the immediate vicinity of the randomly charged surface in a way that violates the contact-value theorem, which describes the behavior of counterions at uniformly charged surfaces and predicts a finite contact density [93][94][95]. This behavior stems from the interplay between the translational entropy of the solution ions and the (non-thermal) configurational entropy due to the averaging over different realizations of the quenched disorder.…”

“…In the particular example of the counterion-only model (with no monova-lent salt ions and no interfacial dielectric discontinuity), we show that multivalent counterions experience an additional logarithmic attraction towards the surface due to the presence of the surface charge disorder in a way that their density profile exhibits an algebraically singular behavior at the surface with an exponent that depends on the disorder strength (variance). This behavior persists also in the presence of a monovalent salt bath and results in significant violation of the contact-value theorem [93][94][95][96]. 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.…”