A comparison of single and multiple imaging approaches to the ionic adsorption isotherm

An ionic adsorption isotherm is deduced. The model used is the imaging in the metal only. Coulombic and dispersive lateral interaction energies for the adsorbed ions are calculated without approximation; Flory-Huggins' statistics are used. The capacitanee-charge curve is interpreted quantitatively with respect to the phenomenology of the capacitance hump and minimum. The failure of the water model for capacitance hump is rationalized. The method of Fourier-Bessel integral has been used to calculate electrostatic image energy in the solution (multiple imaging) and to examine the effect on this quantity of diffuseness of the dielectric barrier in the double layer. The present diffuse dielectric boundary model shows an imaging energy in solution some 40 times less than that for a sharp boundary. The multiple image energy across the real diffuse dielectric boundary is only l% more than that of the single imaging in the metal. The isotherm based on multiple imaging approximation using a sharp dielectric boundary does not predict a capacitance minimum (anodic) but predicts a capacitance hump which is in discrepance with experiment in respect to the ionic dependence and temperature.