Fitting ambiguities mask deficiencies of the Debye–Hückel theory: revealing inconsistencies of the Poisson–Boltzmann framework and permittivity†

Abstract

The more than 100-year-old Debye–Hückel theory displays the most widely used approach for modeling ionic activities in electrolytes. The Debye–Hückel theory finds widespread application, such as in equations of state and Onsager's theory for conductivities. Here, a theoretical inconsistency of the Debye–Hückel theory is discussed, which originates from the employed Poisson–Boltzmann framework that violates the statistical independence of states presumed for the Boltzmann statistics. Furthermore, the static permittivity of electrolytic solutions is discussed as not directly measurable, while common methods for its extraction from experimental data are assessed as erroneous. A sensitivity analysis of modeled activity coefficients with respect to the permittivity and ionic radii as input parameters is conducted, showing that their influences overshadow physicochemical differences of common variations of Debye–Hückel models. Eventually, this study points out that the justification of the traditional and still often used Debye–Hückel models by experimental validation is affected by fitting ambiguities that eventually impede its predictive capabilities.