Vibrational relaxation in supercritical fluids near the critical point

Abstract

We present a theory for the temperature and density dependence of the vibrational lifetime T1 and the vibrational line position ν of a solute in a supercritical solvent, both close to and far from the critical point. The theory is based on the relation between a classical force correlation function and T1 and ν. The force correlation function is determined from density functional theory, and can be expressed in terms of the solvent structure factor and the solute–solvent direct correlation function, thereby allowing physical properties in the region of large critical fluctuations to be described by various phenomenological scaling laws. The theory has been used to investigate recent experiments on the density dependence of the lifetimes and frequencies of the asymmetric CO stretching mode of W(CO)6 in supercritical ethane. Near the critical point, the experimental data are essentially independent of the density over a fairly broad range of densities. This behavior is ascribed to the existence of long-range correlations in the fluid mixture near the critical point. Such correlations, manifested in the divergence or vanishing of thermodynamic quantities, are shown to essentially eliminate the density dependence in the static and dynamic correlation functions that enter the theory. Because it is the anomalous thermodynamics near the critical point that ultimately governs changes in T1 and ν, the results are not dependent on specific intermolecular interactions. The lack of a theoretical dependence on specific intermolecular interactions is supported by experiments that display the same behavior for various solute/solvent systems.