On the electrical double layer capacitance of the restricted primitive model: a link between the mesoscopic theory and the associative mean spherical approximation

Abstract

The results for the electrical double layer capacitance and the charge density of ``free ions'' obtained from the mesoscopic theory are compared with the corresponding results of the associative mean spherical approximation. While the first theory takes into account the fluctuations of the charge density, the second theory assumes that the free ions and ion pairs are in chemical equilibrium according to the mass action law. Our results demonstrate a fairly good agreement between the two theories at high densities and low temperatures.

Figures (2)

• Figure 1: The EDL capacitance $C$ of the RPM in units of the Helmholtz capacitance $C_{\mathrm{H}}=\epsilon/(4\pi a)$ obtained from the mesoscopic theory (solid line), MSA (dash-dotted line), AMSA with Ebeling's association constant (dashed line) for $T^*=0.5$ (left-hand panel) and $T^*=0.25$ (right-hand panel). The Debye capacitance, Eq. (\ref{['C_Debye']}), is shown by a dash-dot-dotted line. $\rho$ is the dimensionless density of ions, $T^*=1/l_B$ where $l_B$ is the Bjerrum length in $a$ units ($a$ is the ion diameter). The inset in the right-hand panel shows the magnified plot of the range $0.5<\rho<0.55$ where the capacitance obtained from the mesoscopic theory and from the AMSA takes almost the same values.
• Figure 2: Effective density of ions $\rho_R$ obtained from the mesoscopic theory, Eq. (\ref{['roR']}), (solid line) and the density of free ions $\rho_{{\rm free}}=\alpha\rho$ ($\alpha$ is the degree of dissociation) obtained from the AMSA with Ebeling's association constant (dashed line) for $T^*=0.5$ (left-hand panel) and $T^*=0.25$ (right-hand panel). $\rho$ is the dimensionless density of ions, $T^*=1/l_B$ where $l_B$ is the Bjerrum length in $a$ units ($a$ is the ion diameter).