Symmetry breaking and electrostatic attraction between two identical surfaces

Franck Plouraboué (1) , Hsueh-Chia Chang (2, 3)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 Center for Microfluidics and Medical Diagnostics (Notre Dame, USA)
3 Department of Chemical and Biomolecular Engineering (Notre Dame, USA)

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 counterions 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 condition and previously derived modified mean-field formulations associated with correlated fluctuations theory. For a sufficiently potential-sensitive isotherm, antisymmetric 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.

Mots clés: Stern layers; Double layer; Poisson-Boltzmann

Domaines: Mécanique des fluides [physics.class-ph]

Franck Plouraboué, Hsueh-Chia Chang. Symmetry breaking and electrostatic attraction between two identical surfaces. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2009, 79 (4), pp.041404(1)-041404(9). ⟨10.1103/PhysRevE.79.041404⟩. ⟨hal-03563433⟩