Critical Exponents for Solvent Extraction Resolved Using SAXS

The solvent extraction of an ionizable solute (H3PO4) from water into a water-in-oil microemulsion, and subsequent organic phase splitting (known as third phase formation), has been recast as a critical phenomenon by linking system structure to solute concentration via a critical exponent. The transuranic extraction (TRUEX) system was investigated by extracting increasing concentrations of H3PO4 into a microemulsion consisting of two extractant amphiphiles (CMPO and TBP) and water in n-dodecane and taking small-angle X-ray scattering (SAXS) measurements from the resulting solutions. The H3PO4 concentration at which phase splitting occurred was defined as the critical concentration (X-C), and this was related to the precritical concentrations (X) by the reduced parameter epsilon = (X-C - X)/X-C. The scattering intensity at the zero angle I(0), relating to the interaction between reverse micellar aggregates, conformed to the relation I(0) = I-0 epsilon(-gamma), with critical exponent gamma = 2.20. To check gamma, SAXS measurements were taken from the organic phase in situ with variable temperature through the point at which third phase formation initiates (the critical temperature), giving I(0) = I(0)t(-gamma), where t = (T - T-C)/T-C and T-C and T are the critical and precritical temperatures, with critical exponent gamma = 2.55. These gamma values suggest third phase formation is a universal phenomenon manifest from a critical double point. Thus, solvent extraction is reduced to its fundamental physical roots where the system is not defined by detailed analysis of metrical properties but by linking the fundamental order to thermodynamic parameters via an exponent, working toward a more predictive understanding of third phase formation.