How to account for the concentration dependency of relative permittivity in the Debye–Hückel and Born equations

This work discusses the introduction of the concentration dependency of relative permittivity in the context of activity coefficient models at different stages of the derivation of the models. We evaluate an experimental correlation and the Michelsen–Mollerup–Breil model for the relative permittivity in order to assess the impact of using these models both in the Debye–Hückel and Born equations. Our results show that the effects of introducing the relative permittivity at different levels in the models derivation are significant and quantitative. Using the concentration dependency as early as before deriving the Helmholtz free energy has the best overall performance. We derive a general method to include any relative permittivity correlation for concentration-dependency before the charging process to calculate the Helmholtz free energy, with no clear advantage on using charge-dependent or independent models.