Ionic contribution to the electric current in an electrolytic cell submitted to an external voltage

The ionic contribution to the electrical current in an electrolytic cell submitted to an external voltage linearly increasing with the time is evaluated. The investigation is performed in the limit of small and large electric field, in which the density of ions depends on the actual electric field in the sample. In the analysis, it is assumed that the ionic separation induced by an external field can be described by a surface density of charge. We show that the ions are responsible for a peak in the current, followed by a delay in the application of the external voltage. From the analysis of the peak and its delay, it is possible to obtain information on the density of ions in thermodynamical equilibrium, and on the mobility of the ions in the considered liquid.

Figure 1

Cell of thickness $d$ filled with an isotropic fluid of dielectric coefficient ${\epsilon }_B$. The electrodes are covered with a film of thickness $L$, having a dielectric coefficient ${\epsilon }_S$.

Figure 2

Dimensionless surface charge density $s=\sigma ∕{\sigma }_M$ vs $t$.

Figure 3

Current in the external circuit vs $t$. The area under the curve is $n_{0}qd$, given in Eq. (12). The curve was depicted for $K=1\mathrm{V}∕\mathrm{s}$. The dotted line indicates the limiting value given by Eq. (11), $I_{\lim }\simeq 0.24\mathrm{nA}$.

Figure 4

Current in the external circuit vs $t$. Solid line corresponds to the reference value ${\mu }_1=3.28\times {10}^{-10}{\mathrm{m}}^2∕\mathrm{V}\mathrm{s}$, dotted line to $\mu =2{\mu }_1$, and dashed line to $\mu =0.5{\mu }_1$.

Figure 5

$t^{*}$ is the instant corresponding to the maximum in the current. ${\mu }_1$ is the reference mobility given in Fig. 4.

Figure 6

Surface charge density obtained from Eq. (15) vs $t$. Solid line refers to the case $p\ne 0$ (Onsager effect) and dashed line $p=0$.

Figure 7

Electrical current obtained with Eqs. (9, 15) vs $t$. Solid line refers to the case $p\ne 0$ (Onsager effect) and dashed line $p=0$. The dotted line indicates the limiting value given by Eq. (18), $I_{\lim }(p=0)\simeq 24\mathrm{nA}$, and $I_{\lim }(p\ne 0)\simeq 176\mathrm{nA}$. The curves were depicted for $K=100\mathrm{V}∕\mathrm{s}$.