Density dependence of vibrational energy relaxation rates in supercritical solution: A hydrodynamic model

An approximate expression describing the density dependence of vibrational energy relaxation rates in fluids in terms of thermodynamic and transport parameters of the fluid is developed on the basis of a classical statistical mechanical theory of vibrational energy relaxation of highly excited molecules in polyatomic solvents. The energy relaxation rate is expressed via the friction coefficient, which describes the interaction between solute oscillator and solvent molecules. The corresponding force-force time correlation function is expressed in terms of the dynamic structure factor of the solvent and the force of interaction between solute and solvent molecules. Approximating the dynamic structure factor appropriately leads to expressions for the density dependence of vibrational relaxation rates in terms of thermophysical solvent parameters. Using these expressions the density dependence of vibrational relaxation rates in supercritical ethane and propane both in the vicinity of the critical point and far from it are evaluated and compared with measured relaxation rates obtained under the same physical conditions.