Decrease of permittivity of an electrolyte solution near a charged surface due to saturation and excluded volume effects

Excluded volume effect of counterions and water dipoles near a highly charged surface due to a rotationally averaged Boltzmann factor for water dipoles

“…It is generally accepted that negatively charged electrode is covered by a thin molecular layer of water with a net dipole orientation dependent on the respective electrode charge (Bergethon 1998). The adsorbed water molecules are partially displaced by counterions (cations) of EDL formed at the negatively charged electrode surface (Gongadze and Iglič 2012) and specific adsorption and/or chemisorption of coions (anions) (Bergethon 1998;Butt et al 2003).…”

“…Previously, also the mean-field Langevin-Bikerman model for finite size of molecules (Iglič et al 2010) was generalized by including the cavity field (Gongadze and Iglič 2012). It was shown that in the vicinity of a charged surface the number densities of counterions (+), coions (-) and water molecules (w) are stronly influenced by the charged surface (Gongadze and Iglič 2012).…”

“…Previously, also the mean-field Langevin-Bikerman model for finite size of molecules (Iglič et al 2010) was generalized by including the cavity field (Gongadze and Iglič 2012). It was shown that in the vicinity of a charged surface the number densities of counterions (+), coions (-) and water molecules (w) are stronly influenced by the charged surface (Gongadze and Iglič 2012). Within the lattice statistic approach the probabilities that a single lattice site in electrolyte solution is occupied by a particle of one of the three kinds is determined by the corresponding (average) Boltzmann factors (Gongadze and Iglič 2012):…”

“…Here n + (x) and n -(x) are the number densities of counterions and coions, respectively, n w (x) is the number density of water molecules, φ(x) is the electrostatic po- Gongadze and Iglič tential, E is the magnitude of the electric field strength, e 0 is the elementary charge, kT is the thermal energy, β = 1/kT, n 0 is the bulk number density of positively and negatively charged ions in electrolyte solution, n 0w is the bulk number density of water, n s being the number density of lattice sites: n s = n w (x) + n + (x) + n -(x) in bulk n s = n 0w + 2n 0 , p 0 stands for the magnitude of the water dipole moment and γ = 3(2 + n 2 )/6, where n = 1.33 is the optical refractive index of water (Gongadze and Iglič 2012). The axis x is perpendicular to the charged surface and points in the direction of the bulk solution.…”

“…Note that ω describes the angle between the water dipole vector and the vector in the direction of the x-axis, i.e. vector -E. The space dependence of electric potential can be determined by solving (Gongadze and Iglič 2012):…”