Pressure of correlated layer-charge and counterion fluctuations in charged thin films

Abstract

We predict the fluctuation contribution to the interaction between two surfaces with both mobile layer charges and delocalized counterions. The correlation (coupling) between the layer-charge fluctuations and the counterion fluctuations (around a piecewise homogeneous mean-field density profile) is taken into account in the Gaussian approximation. We find that this correlation significantly increases the magnitude of the interlayer fluctuation attraction. The counterion fluctuation pressure is calculated as a function of the intersurface distance and we show how the large and small distance limits correspond to three-dimensional (3D) and 2D fluctuations, respectively. In addition, we predict the charge density-density correlation functions. Experimental implications of the model are discussed.

Electrostatic interactions in strongly coupled soft matter

“…These correlations are systematically neglected on the mean-field level but become enhanced in strong-coupling conditions mentioned above. Recent theoretical attempts to incorporate ionic correlations include integral-equation methods [25,43], perturbative improvement of the mean-field theory including Gaussian-fluctuations theories [44,45,46,47,48,49,50,51,52,53,54,55,56,57], and local density functional theory [59,60], which compare well with numerical simulations and all exhibit attraction. These methods are mostly applicable for large separations between macroions or in the regime of low coupling strengths (the so-called high-temperature regime), and can not characterize the closely-packed bound state between like-charged macroions.…”

“…The main scenarios which are put forward to explain the phenomenon of like-charge attraction have gone beyond the mean-field level by demonstrating that this phenomenon can be reproduced quantitatively by inclusion of electrostatic correlations [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,…”

“…Counterions form electrostatically-bound clouds in the proximity of macroions and in many cases, predominantly determine the electric properties of charged solutions [3]. In particular, counterions can alter the effective interaction between like-charged macroions, and may generate a dominant electrostatic attraction between them in certain physical conditions [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,…”

Symmetry breaking and electrostatic attraction between two identical surfaces

“…It has been rigorously shown that, for two identical spheres with constant potential [6] the inter-particle interaction is necessarily repulsive according to the classical Poisson-Boltzmann (PB) mean-field theory [6]. For this reason, theories for like-charge attraction phenomena have sought mechanisms beyond the classical meanfield description to include spatial correlation of charge fluctuations [7,8,9,10].…”

“…More specifically, theories for correlated layers charges between two parallel plates separated by a distance 2h much larger than the Debye length λ, give rises to an effective "long-range" dipolar attractive pressure, p ∼ 1/(2h) 3 [15], an almost dipolar one p ∼ ln[2h/λ]/(2h) 3 [7,9], or a modified exponential attraction p ∼ exp −4h/λ /2h [16,17]-also found in colloids interactions [18]whereas the classical DLVO theory only predicts a repulsive exponential behaviour p ∼ exp −2h/λ .…”