Thermodynamic factors for locally non-neutral, concentrated electrolytic fluids

Abstract

A constitutive framework is created to parameterize the composition-dependent parts of thermodynamic differentials that undergird the diffusion driving forces in non-neutral electrolytic fluids. The definition of a novel two-ion secondary reference state allows us to formulate a neutralizable composition basis, in which one natural composition variable is replaced by the molar excess charge. This basis is conjugate to a set of energy descriptors we call core potentials, among which Maxwell relations and Gibbs–Duhem constraints take simple forms that isolate charge effects. Core potentials derive from intensive measures of energy and composition, a refinement of Kokotov's twin-potential scheme that enables applications to materials wherein properties vary spatially. Matrix representations are constructed for the transformations that interconvert among Guggenheim (electrochemical), Smyrl–Newman (quasielectrostatic), and core potentials. These transformations reveal how the Guggenheim and Smyrl–Newman formalisms can be extended to handle charge-imbalanced microscopic equilibria. The core-potential framework is naturally parameterized in terms of conventional electroneutral thermodynamic factors, but also includes an independent set of new electrostatic colligative properties that can account for an additional equation of state governing molar charge. Consistent thermodynamic parameterizations are derived for electrolytes that obey the ideal-solution approximation and electrolytes that follow Poisson–Boltzmann theory. We explicitly develop constitutive equations for the species electrochemical-potential differentials within a chemically nonideal binary solution of a symmetrical-valence electrolyte that also satisfies the Poisson–Boltzmann charge–potential relation.