https://doi.org/10.1351/goldbook.T06343
The length characterizing the decrease with distance of the potential in the double layer = characteristic Debye length in the corresponding electrolyte solution = \(\kappa^{-1}\):
where \(\varepsilon\) = static permittivity = \(\varepsilon_{\rm{r}}\varepsilon_{0}\), \(\varepsilon_{\rm{r}}\) = relative static permittivity of solution; \(\varepsilon_{0}\) = permittivity of vacuum, \(R\) = gas constant, \(T\) = thermodynamic temperature, \(F\) = Faraday constant, \(z_{\rm{i}}\) = concentration of species \(i\), \(z_{\rm{i}}\) = ionic charge on species \(i\).
| \[\frac{1}{\kappa } = \sqrt{\frac{\varepsilon_{\rm{r}}\varepsilon_{0}RT}{F^{2}\sum _{i}c_{i}z_{i}^{2} }}\] | \[\frac{1}{\kappa } = \sqrt{\frac{\varepsilon_{\rm{r}}RT}{4\pi F^{2}\sum _{i}c_{i}z_{i}^{2} }}\] | |
| (rationalized four-quantity system) | (three-quantity electrostatic system) |
where \(\varepsilon\) = static permittivity = \(\varepsilon_{\rm{r}}\varepsilon_{0}\), \(\varepsilon_{\rm{r}}\) = relative static permittivity of solution; \(\varepsilon_{0}\) = permittivity of vacuum, \(R\) = gas constant, \(T\) = thermodynamic temperature, \(F\) = Faraday constant, \(z_{\rm{i}}\) = concentration of species \(i\), \(z_{\rm{i}}\) = ionic charge on species \(i\).