Asymmetric electrostatic properties of an electric double layer: a generalized Poisson-Boltzmann approach taking into account non-uniform size effects and water polarization
We theoretically study electrostatic properties of electric double layer using a generalized Poisson-Boltzmann approach taking into account the orientational ordering of water dipoles and the excluded volume effect of water molecules as well as those of positive and negative ions with different sizes in electrolyte solution. Our approach enables one to predict that the number densities of water molecules, counterions and coions and the permittivity of electrolyte solution close to a charged surface, asymmetrically vary depending on both of sign and magnitude of the surface charge density and the volume of counterion. We treat several phenomena in more detail. Firstly, an increase in the volume of counterions and an increase in the surface charge density can cause the position of the minimum number density of water molecules to be farther from the charged surface. Secondly, width of the range of voltage in which the properties at the charged surface symmetrically vary decreases with increasing bulk salt concentration. In addition, we show that the excluded volume effect of water molecules and the orientational ordering of water dipoles can lead to early onset and lowering of the maximum of electric capacitance according to surface voltage. Our approach and results can be applied to describing electrostatic properties of biological membranes and electric double layer capacitor for which excluded volume effects of water molecules and ions with different sizes may be important.