4 August 2000 | D.J. Myers, Motoyuki Shigeiwa, C. Stromberg, M.D. Fayer, Binny J. Cherayil
The temperature dependence of solute vibrational relaxation in supercritical fluids is studied experimentally and theoretically. The vibrational lifetime (T₁) of the asymmetric CO stretching mode of W(CO)₆ in supercritical ethane and CO₂ is measured as a function of temperature at fixed densities. The results are compared with a recently developed extended hydrodynamic theory of vibrational relaxation. The theory successfully reproduces the experimental data without free parameters.
In ethane at the critical density, T₁ initially increases with temperature, reaching a maximum ~70 K above the critical temperature, then decreases. In contrast, in CO₂ and at high densities in ethane, T₁ decreases with increasing temperature. The theory accounts for these behaviors by incorporating the solvent's hydrodynamic and thermodynamic properties. The theory uses a hard sphere model for the solute-solvent direct correlation function and the dynamic structure factor of the solvent. The dynamic structure factor is expressed as a product of the equilibrium static structure factor and a time-dependent term, which includes contributions from diffusive motion and propagating waves.
The quantum correction factor, Q, is derived from the Egelstaff form and significantly affects the temperature dependence of the calculated T₁. The theory is sensitive to the choice of ω, the frequency of the energy deposited into the solvent. The calculations show that ω is not a single frequency but can be a distribution of frequencies. The theory is able to reproduce the experimental data for T₁ in ethane and CO₂ without free parameters, capturing the essential features of the data, including the inverted temperature dependence observed in ethane at the critical density.
The theory also predicts the absence of inverted temperature dependence in high density ethane and CO₂. The results indicate that the extended hydrodynamic theory captures the essential features of vibrational energy relaxation in supercritical fluids, without requiring solute-solvent clustering. The theory incorporates detailed solvent parameters and accounts for critical phenomena, providing a comprehensive description of vibrational relaxation in supercritical fluids.The temperature dependence of solute vibrational relaxation in supercritical fluids is studied experimentally and theoretically. The vibrational lifetime (T₁) of the asymmetric CO stretching mode of W(CO)₆ in supercritical ethane and CO₂ is measured as a function of temperature at fixed densities. The results are compared with a recently developed extended hydrodynamic theory of vibrational relaxation. The theory successfully reproduces the experimental data without free parameters.
In ethane at the critical density, T₁ initially increases with temperature, reaching a maximum ~70 K above the critical temperature, then decreases. In contrast, in CO₂ and at high densities in ethane, T₁ decreases with increasing temperature. The theory accounts for these behaviors by incorporating the solvent's hydrodynamic and thermodynamic properties. The theory uses a hard sphere model for the solute-solvent direct correlation function and the dynamic structure factor of the solvent. The dynamic structure factor is expressed as a product of the equilibrium static structure factor and a time-dependent term, which includes contributions from diffusive motion and propagating waves.
The quantum correction factor, Q, is derived from the Egelstaff form and significantly affects the temperature dependence of the calculated T₁. The theory is sensitive to the choice of ω, the frequency of the energy deposited into the solvent. The calculations show that ω is not a single frequency but can be a distribution of frequencies. The theory is able to reproduce the experimental data for T₁ in ethane and CO₂ without free parameters, capturing the essential features of the data, including the inverted temperature dependence observed in ethane at the critical density.
The theory also predicts the absence of inverted temperature dependence in high density ethane and CO₂. The results indicate that the extended hydrodynamic theory captures the essential features of vibrational energy relaxation in supercritical fluids, without requiring solute-solvent clustering. The theory incorporates detailed solvent parameters and accounts for critical phenomena, providing a comprehensive description of vibrational relaxation in supercritical fluids.