Quenched charge disorder and Coulomb interactions (original) (raw)
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The Journal of Chemical Physics, 2014
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 a charged surface.
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.
Sample-to-sample fluctuations of electrostatic forces generated by quenched charge disorder
Physical Review E, 2011
It has been recently shown that randomly charged surfaces can exhibit long range electrostatic interactions even when they are net neutral. These forces depend on the specific realization of charge disorder and thus exhibit sample to sample fluctuations about their mean value. We analyze the fluctuations of these forces in the parallel slab configuration and also in the sphere-plane geometry via the proximity force approximation. The fluctuations of the normal forces, that have a finite mean value, are computed exactly. Surprisingly, we also show that lateral forces are present, despite the fact that they have a zero mean, and that their fluctuations have the same scaling behavior as the normal force fluctuations. The measurement of these lateral force fluctuations could help to characterize the effects of charge disorder in experimental systems, leading to estimates of their magnitudes that are complementary to those given by normal force measurements.
Electrostatic interactions mediated by polarizable counterions: Weak and strong coupling limits
The Journal of Chemical Physics, 2012
We investigate the statistical mechanics of an inhomogeneous Coulomb fluid composed of charged particles with static polarizability. We derive the weak-and the strong-coupling approximations and evaluate the partition function in a planar dielectric slab geometry with charged boundaries. We investigate the density profiles and the disjoining pressure for both approximations. Comparison to the case of non-polarizable counterions shows that polarizability brings important differences in the counterion density distribution as well as the counterion mediated electrostatic interactions between charged dielectric interfaces.
Electrostatic disorder-induced interactions in inhomogeneous dielectrics
Europhysics Letters (EPL), 2006
We investigate the effect of quenched surface charge disorder on electrostatic interactions between two charged surfaces in the presence of dielectric inhomogeneities and added salt. We show that in the linear weak-coupling regime (i.e., when mean-field and Gaussianfluctuations contributions are included), the image-charge effects lead to a non-zero disorderinduced interaction free energy between two surfaces of equal mean charge that can be repulsive or attractive depending on the dielectric mismatch across the bounding surfaces and the exact location of the disordered charge distribution.
Nonmonotoic fluctuation-induced interactions between dielectric slabs carrying charge disorder
The Journal of Chemical Physics, 2010
We investigate the effect of monopolar charge disorder on the classical fluctuation-induced interactions between randomly charged net-neutral dielectric slabs and discuss various generalizations of recent results (A. Naji et al., Phys. Rev. Lett. 104, 060601 (2010)) to highly inhomogeneous dielectric systems with and without statistical disorder correlations. We shall focus on the specific case of two generally dissimilar plane-parallel slabs, which interact across vacuum or an arbitrary intervening dielectric medium. Monopolar charge disorder is considered to be present on the bounding surfaces and/or in the bulk of the slabs, may be in general quenched or annealed and may possess a finite lateral correlation length reflecting possible 'patchiness' of the random charge distribution. In the case of quenched disorder, the bulk disorder is shown to give rise to an additive long-range contribution to the total force, which decays as the inverse distance between the slabs and may be attractive or repulsive depending on the dielectric constants of the slabs. By contrast, the force induced by annealed disorder in general combines with the underlying van der Waals forces in a non-additive fashion and the net force decays as an inverse cube law at large separations. We show however that in the case of two dissimilar slabs the net effect due to the interplay between the disorder-induced and the pure van der Waals interactions can lead to a variety of unusual non-monotonic interaction profiles between the dielectric slabs. In particular, when the intervening medium has a larger dielectric constant than the two slabs, we find that the net interaction can become repulsive and exhibit a potential barrier, while the underlying van der Waals force is attractive. On the contrary, when the intervening medium has a dielectric constant in between that of the two slabs, the net interaction can become attractive and exhibit a free energy minimum, while the pure van der Waals force is repulsive. Therefore, the charge disorder, if present, can drastically alter the effective interaction between net-neutral objects.
Long-ranged attraction between disordered heterogeneous surfaces
2011
Graham some 150 years ago, hinges on the balance between attractive and repulsive surface forces(1). In aqueous media the electrostatic double-layer repulsion between likecharged surfaces plays the dominant role in the stabilization, keeping particles from aggregating under van der Waals attraction(1-3). Such forces have been studied for decades(3-6): but while nearly all understanding of the interactions relate to uniformlycharged surfaces, most real surfaces are in fact heterogeneous and disordered. Here we demonstrate that two surfaces covered with random charge patches experience a longranged attraction across water that is orders of magnitude stronger than van der Waals forces, and which persists, remarkably, even in the complete absence of any correlations between opposing positive and negative domains (so-called 'quenched disorder'). The origin of this attraction is, as we show, in the counter-intuitive observation that two oppositely-charged surfaces attract each other across water (or other ion-containing liquids) much more strongly than equally-charged surfaces repel, for identical surface separations and charge densities. This striking asymmetry may result in strong, longranged attraction between randomly charged surfaces even when they are overall-
Symmetry breaking and electrostatic attraction between two identical surfaces
Physical Review E, 2009
By allowing the surface charge of one surface to affect the adsorption equilibrium of the other, we establish the existence of a long-range attractive interaction between two identical surfaces in an electrolyte containing polyvalent counter ions with a mean-field Poisson-Boltzmann approach. A Stern electrostatic condition from linearization of the mass-action adsorption isotherm is used to capture how polyvalent ion condensation affects and reverses the surface charge. We furthermore establish a direct mapping between this Stern layer conditions and previously derived modified Mean-field formulations associated with correlated fluctuations theory. For a sufficiently potential-sensitive isotherm, anti-symmetric charge inversion can occur to produce an attractive force that increases with decreasing ionic strengths. Analyses of a mass-action isotherm produce force-separation relations, including an exponential far-field force decay distinct but consistent with previously proposed correlated fluctuation theories, and in quantitative agreement with experimental data.
Perspective: Coulomb fluids—Weak coupling, strong coupling, in between and beyond
The Journal of Chemical Physics, 2013
We present a personal view on the current state of statistical mechanics of Coulomb fluids with special emphasis on the interactions between macromolecular surfaces, concentrating on the weak and the strong coupling limits. Both are introduced for a (primitive) counterion-only system in the presence of macroscopic, uniformly charged boundaries, where they can be derived systematically. Later we show how this formalism can be generalized to the cases with additional characteristic length scales that introduce new coupling parameters into the problem. These cases most notably include asymmetric ionic mixtures with mono-and multivalent ions that couple differently to charged surfaces, ions with internal charge (multipolar) structure and finite static polarizability, where weak and strong coupling limits can be constructed by analogy with the counterion-only case and lead to important new insights into their properties that cannot be derived by any other means. © 2013 AIP Publishing LLC. [http://dx.