Anomalous temperature dependence of differential capacity at an uncharged interface with Debye-Hückel electrolyte: Field theoretical approach

Using a field theoretical approach we study the effect of the charge fluctuations in an ionic solution for the simple case of planar geometry and uncharged interface. To obtain the correction to the differential capacity beyond the Gouy-Chapman result we calculate the charge-charge correlation function at the one loop approximation. We consider the capacity temperature dependence due to this correction in relation to experimental and simulation results. At low temperatures we find an increase of the differential capacity with temperature in contrast to the Gouy-Chapman formula predicting a monotonous decrease. We discuss a simple estimation of the inversion temperature found to be in a fair agreement with simulation results.