https://doi.org/10.1351/goldbook.DT07364

Equation describing the contraction (\(\Delta V_{\text{el}}\)) taking place in a dielectric medium of relative static @P04507@ \(\varepsilon_{\text{r}}\) (formerly called @D01697@) upon introduction of an ion of @C00993@ \(z\) and radius \(r\): \[\Delta V_{\text{el}} = -\frac{\left ( z\,e \right )^{2}}{2\,r\,\varepsilon_{\text{r}}}\frac{\partial\left ( \text{ln}\varepsilon_{\text{r}}\right)}{\partial\,p}\] with \(e\) the @E02032@.

Inasmuch as the derivative of \(\text{ln}\varepsilon_{\text{r}}\) with respect to pressure, \(\frac{\partial (\text{ln}\varepsilon _{\text{r}})}{\partial p}\), is not known for all media, there are approximations to evaluate this term as a function of \(\varepsilon_{\text{r}}\) and of the isothermal compressibility of the medium, \(\kappa_{T}\).

**Note:**

Inasmuch as the derivative of \(\text{ln}\varepsilon_{\text{r}}\) with respect to pressure, \(\frac{\partial (\text{ln}\varepsilon _{\text{r}})}{\partial p}\), is not known for all media, there are approximations to evaluate this term as a function of \(\varepsilon_{\text{r}}\) and of the isothermal compressibility of the medium, \(\kappa_{T}\).