Clustering in dilute, binary supercritical mixtures: A fluctuation analysis

Abstract

Solute-solvent concentration fluctuation correlations at infinite dilution are a statistical measure of the excess number of solvent molecules surrounding a given solute molecule, with respect to a uniform distribution at the prevailing density. This leads to the concept of a cluster which, in dilute supercritical mixtures (trace solute(s) in the vicinity of a solvent's critical point) acquires mechanistic and not merely statistical significance. Experimental measurements of solute partial molar volumes at infinite dilution in such systems are shown to be equivalent, when analyzed in the light of fluctuation theory, to a cluster size determination. This quantity can be either positive or negative. Calculations based on experimental measurements of infinite dilution partial molar volumes of organic solids in supercritical fluids indicate the existence of clusters of ca 100 solvent molecules per solute molecule. The fluctuation approach cannot be used arbitrarily close to the solvent's critical point, since it is based on the assumption of a finite solvent compressibility. Asymptotic laws for the behavior of solute fluctuations in dilute mixtures within differently defined regions of space (constant volume; constant solvent mass) are derived. Finally, it is shown that there is a univocal relationship between cluster formation and the experimentally observed solubility enhancement in dilute mixtures of non-volatile solutes in supercritical solvents.