A semi-empirical equation modeling long-range contributions to the activity coefficients of individual ions at high ionic strengths

Abstract

Molecular thermodynamics is well developed with models like UNIQUAC, UNIFAC and SAFT. These models include robust codes and extensive databases for chemical and petroleum industries through ASPEN, DORTMUND, and others. However, important systems in the pharmaceutical and biotech industries now exist where these codes and their databases are not always sufficient. Cell culture media used to grow mammalian cells are multicomponent aqueous solutions with 50, 100, or more compounds including amino acids, salts, acids or bases, as well as sugars, fatty acids, etc. These components can exhibit both complexation and incomplete dissociation. The thermodynamics of these systems have proven challenging to model, as current solubility descriptions frequently assume complete dissociation in solutions containing a single solute in water at relatively low concentrations. However, not all compounds that are generally considered to be strong electrolytes are completely dissociated even at low concentrations. Further, mixtures of such components can show dramatic changes in dissociation and complexation with concentration, pH, and temperature. In this paper, we present a semi-empirical model for individual ions in aqueous solutions. We use data from 317 compounds to isolate the ionic contribution to a compound’s activity coefficient in aqueous systems from confounding short-range effects. We compare eight robust regression M−estimators with a least-squares estimate and provide a two-parameter equation relating ionic strength, valence, and the activity coefficient not requiring arduous characterization of the solute of interest. We demonstrate that the Fair M−estimator generates an accurate model that can serve as an appropriate reference state for use with a model based on perturbation theory up to 29 molal.