On the Repulsive Interaction Between Strongly Overlapping Double Layers of Charge-regulated Surfaces

Abstract

A B S T R A C TThe Donnan equilibrium is employed to evaluate the entropic repulsion between two charged plates that feature charge regulation and are in equilibrium with a reservoir solution of monovalent salt. This approach represents the zero-field limit of the Poisson-Boltzmann equation, valid for strongly overlapping electrical double layers. We show that this scenario features an intrinsic length scale, which serves as the unscreened pendant of the Debye length for strongly overlapping double layers. In general, the scaling of the disjoining pressure with interplate distance is dependent on the boundary conditions (constant charge, constant potential, or charge regulation). Surprisingly, here we find for sufficiently low potentials the same inverse-square decay as for constant charge surfaces. We test the validity of the zero-field limit by comparison with self-consistent field lattice computations that invoke the full Poisson equation for finitely sized ions between two charge-regulated plates.The electrical double-layer repulsion between two charged surfaces in equilibrium with a salt reservoir is conventionally [1-10] evaluated under the assumption that surfaces are sufficiently far apart such that their double-layers only weakly interact. This so-called 'weak-overlap approximation' [4] implies that the electrical potential in the mid-plane between the two surfaces is small (though surface potentials, nevertheless, may be high). Within this weak-overlap approximation, the Poisson-Boltzmann (PB) equation eventually yields osmotic disjoining pressures that decay exponentially; the typical decay length being the Debye screening length κ −1 which measures the thickness of a diffuse electrical double-layer in solution. Together with Van der Waals attractions, one arrives at the exponentially screened, classical DLVO potential [1][2][3][4], which is applicable to dilute colloidal fluids in which the average colloid-colloid distance is (much) larger than κ −1 .When distances between charged surfaces are comparable to or less than κ −1 such that double-layers strongly overlap and the weak-overlap approximation breaks down, one must resort to more complicated solutions containing elliptic functions [11] or to numerical solutions. For low surface potentials with plates in close proximity and in presence of background salt, analytical approximations exist featuring a peculiar inverse square decay of the disjoining pressure with the inter-plate separation [11]. To the best of our knowledge, however, these approximations are only known for the boundary condition of constant surface charge [11-13], but not for surfaces featuring charge regulation, even though these boundary conditions in general do not lead to the same scaling behavior of the disjoining pressure [14]. It should be mentioned that an inverse square decay is also known for the salt-free (counter-ion only) limit at large separations, even in case of charge regulation [11,15]. Here we demonstrate a relatively straightforward and analytical treatment of th...

Experimental Evidence for Algebraic Double-Layer Forces

“…The accuracy of the 1/h 2 dependence, Eq. (12), is good at κλ ≤ 1, as discussed earlier [10], therefore one needs to go to high salt concentrations and low pH for it to become applicable. Furthermore for pH 3 solutions the ideal-gas equation is not accurate since the surfaces strongly regulate and the ideal-gas equation is derived for constant charge surfaces.…”

“…These results are consistent with the range of validity for both models. While the zero-field approximation is valid for weakly charged surfaces, the Langmuir equation is applicable for highly charged surfaces [10,12,18]. Another important experimental case where algebraic interactions are important is the multivalent coion case.…”

Derivation of a pH Dependent Solid-Liquid Interfacial Tension and Theoretical Interpretation of the Physicochemistry of Dewetting in the CO2-Brine-Silica System

“…For instance, receding contact angles of methyl methacrylate (MMA) copolymers containing hydrophilic or charged units were decreased (Hogt, et al, 1985) with surface charge increase. Also, the importance of double layer repulsion, which draws largely on increased surface charge density (Philipsea et al, 2017) and its contribution to disjoining pressure stabilization of the prewetting film has been reported (Joud et al, 2013). Simply put, increase in surface charge density or surface potential has been the major factor for wettability enhancement (Park et al, 2011;Guo et al, 2016).…”

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

“…The study of the interaction between two like‐charged surfaces suspended in an electrolyte is a key topic for understanding colloidal stability against flocculation. Vital contributions to the field were initiated by Derjaguin, Landau, Verwey, and Overbeek , who evaluated these exponentially screened repulsions using the Poisson‐Boltzmann (PB) equation under Debye‐Hückel (DH) linearization for weak electric double layer (EDL) overlaps. They appended the Van der Waals forces to develop the Derjaguin‐Landau‐Verwey‐Overbeek (DLVO) potential , which predicts a net attraction between the surfaces at very small as well as large separations, as opposed to a net repulsion for an intermediate range of separations.…”

“…For instance, κ −1 as large as 1 µm was observed in charged colloids of silica in ethanol and deionized water. Although a closed‐form analytical solution of the PB equation in such situations has been deemed infeasible , several approximate analytical solutions of the PB equation or its modified variants have been undertaken for conditions exhibiting the interaction or merging of Debye layers . Philipse et al.…”