Electrostatic interactions of asymmetrically charged membranes

We predict the nature (attractive or repulsive) and range (exponentially screened or long-range power law) of the electrostatic interactions of oppositely charged, planar plates as a function of the salt concentration and surface charge densities (whose absolute magnitudes are not necessarily equal). An analytical expression for the crossover between attractive and repulsive pressure is obtained as a function of the salt concentration. This condition reduces to the high-salt limit of Parsegian and Gingell where the interaction is exponentially screened and to the zero salt limit of Lau and Pincus in which the important length scales are the inter-plate separation and the Gouy-Chapman length. In the regime of low salt and high surface charges we predict —for any ratio of the charges on the surfaces— that the attractive pressure is long-ranged as a function of the spacing. The attractive pressure is related to the decrease in counter-ion concentration as the inter-plate distance is decreased. Our theory predicts several scaling regimes with different scaling expressions for the pressure as a function of salinity and surface charge densities. The pressure predictions can be related to surface force experiments of oppositely charged surfaces that are prepared by coating one of the mica surfaces with an oppositely charged polyelectrolyte. Copyright c © EPLA, 2007 Introduction. – The interactions between oppositely charged surfaces are important in both biological and materials science contexts. Proteins contain both cationic and anionic regions and in some cases, interactions between proteins are due to unlike charge attraction, mediated by the intervening counterions and salt. The delivery of cationic vesicles to cells —of interest in gene therapy applications— involves counterion and salt-mediated electrostatic interactions of two oppositely charged membranes [1–3]. Similar considerations may also be important in understanding adhesion and fusion in systems of oppositely charged bilayers, as well as peptide binding to oppositely charged lipid membranes [4,5]. Recent experiments on hydrophobically prepared mica surfaces have indicated that such surfaces have domains with different charges and the observed long-range attractions (in the nanometer regime) may again be related to unlike charge attractions mediated by counterions and salt [6,7]. In this paper we predict the interactions between two homogeneously charged surfaces with opposite charge. The surfaces are in aqueous solution that contains the counterions and added salt. The interactions can be attractive or repulsive, short-ranged (exponentially decaying) or long-ranged (power law) depending on the ratio of the distance between the surfaces to the important length scales of the problem: i) The Gouy-Chapman length, λGC = 1/(2πlBσ) that is inversely proportional to the surface charge density σ; ii) the Bjerrum length lB = e/εkBT equal to about 7 Å in water (ε! 80) at room temperature; and, iii) the Debye-Hückel (DH) length, λD = 1/ √ 8πlBcb where cb is the bulk 1 : 1 salt concentration. Since there are several length scales there are several regimes that characterize the interactions. In order to model interactions between charged surfaces, membranes or particles, one typically considers two planar surfaces separated by a distance, d. Previous studies considered the symmetric case where the two surfaces have fixed and equal surface charge densities. Within Poisson-Boltzmann (PB) theory [8–11], it can be shown that the interaction between two surfaces with the same charge is always repulsive due to the counter-ion entropy. Other refinements include corrections to the PB theory especially in the limit of strong surface charges and multi-valent counterions. The theory of the interactions between two surfaces with opposite charges has received