Symmetry breaking and electrostatic attraction between two identical surfaces

Abstract

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, 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.

Membrane Potential Generated by Ion Adsorption

“…Ling and Cheng, almost no researchers have proposed the evaluation of membrane potential by employing such theories—Langmuir isotherm and Poisson-Boltzmann equation—instead of using GHK equation [ 1 , 2 , 9 , 10 , 11 , 12 , 13 ]. However, the basically same idea—potential evaluation by employing Langmuir isotherm and Poisson-Boltzmann equation—has been often used in the research fields outside the membrane potential research field for quantitatively estimating the potential behavior in electrolytic solution around charged surface [ 17 , 18 , 19 , 20 ]. Moreover, the quantitative potential evaluation around the charged surface in aqueous solution primarily using the Poisson-Boltzmann equation has been very common research for more than several decades [ 17 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ].…”

Membrane potential generation without ion transport

“…20. K + is adsorbed to -SO 3 − of membrane of Selemion CMV at the interface between the KCl solution and membrane by obeying the Langmuir isotherm, and all the ions distribute according to the Boltzmann distribution [1,2,6,[9][10][11][12][13][14][18][19][20][21][22][23][24][25][26].…”

Energy Conversion Efficiency of Nanofluidic Batteries: Hydrodynamic Slip and Access Resistance

“…Moreover, an interacting double layer in a nanopore can lead to counterion condensation and even charge inversion. 41 At low ionic strength, protonation and deprotonation at the surface become more prevalent. 10,42,43 The constant surface charge assumption may no longer be valid.…”

“…However, since this current, represented by the pore resistance R p in Figure b, drains useful current to the load, we shall minimize its effect by choosing materials with sufficiently low electron tunneling or ion hopping currents within the Helmholtz–Stern layer. Moreover, an interacting double layer in a nanopore can lead to counterion condensation and even charge inversion . At low ionic strength, protonation and deprotonation at the surface become more prevalent. ,, The constant surface charge assumption may no longer be valid.…”