Solute-solvent interaction in nonpolar supercritical fluid: A clustering model and size distribution

Solubility and solvatochromic shift of 4-(dimethylamino)benzonitrile (DMABN) in supercritical ethane were measured. The bathochromic shifts observed at various densities were much larger than expected from Onsager's reaction field theory. The discrepancy can be attributed to the solvent aggregation around DMABN even in nonpolar ethane. At low densities, the solvatochromic shift was found to be directly proportional to the fugacity of the solvent fluid. This relation was well rationalized by considering the size distribution of the cluster on a statistical mechanical basis using a grand canonical ensemble. With the help of intermolecular potential between ethane and DMABN, the cluster size distribution in low-density supercritical ethane was derived and the bathochromic shift per one solvent molecule was estimated.