Thermodynamic Description of Synergy in Solvent Extraction: I. Enthalpy of Mixing at the Origin of Synergistic Aggregation

Revisiting aggregation of extractant molecules into water-poor mixed reverse micelles, we propose in this paper to identify the thermodynamic origins of synergy in solvent extraction. Considering that synergistic extraction properties of a mixture of extractants is related to synergistic aggregation of this mixture, we identify here the elements at the origin of synergy by independently investigating the effect of water, acid, and extracted cations. Thermodynamic equations are proposed to describe synergistic aggregation in the peculiar case of synergistic solvent extraction by evaluating critical aggregation concentration (CAC) as well as specific interactions between extractants due to the presence of water, acid and cations. Distribution of two extractant molecules in the free extractants and in reverse micelles was assessed, leading to an estimation of the in-plane interaction parameter between extractants in the aggregates as introduced by Bergström and Eriksson (Bergström, M.; Eriksson, J. C. A Theoretical Analysis of Synergistic Effects in Mixed Surfactant Systems. Langmuir 2000, 16, 7173−7181). Based on this model, we study the <i>N</i>,<i>N</i>′-dimethyl-<i>N</i>,<i>N</i>′-dioctylhexylethoxymalonamide (DMDOHEMA) and di­(2-ethylexyl) phosphoric acid (HDEHP) mixture and show that adding nitric acid enhances synergistic aggregation at the equimolar ratio of the two extractants and that this configuration can be related to a favored enthalpy of mixing.