Solvent–solute interactions and the Raman CH stretching spectrum of cyclohexane-d11. II. Density dependence in supercritical carbon dioxide

Abstract

We have measured the isotropic Raman CH stretching spectrum of cyclohexane-d11 in supercritical CO2 at 49.7 °C and in liquid CO2 at room temperature over a range of densities from 0.2ρc to 2ρc, where the critical number density ρc for CO2 is 6.4 nm−3. The axial and equatorial CH stretching bands in the spectrum shift to lower frequencies and broaden with increasing density. As was the case in an earlier study of cyclohexane-d11 in liquid solvents [G. J. Remar and R. A. MacPhail, J. Chem. Phys. 103, 4381 (1995)], the “perturbed hard-fluid model” of Ben-Amotz and Herschbach provides a satisfyingly consistent description of the observed shifts in terms of competing contributions from repulsive and attractive solute–solvent forces along the CH bond. In particular, when the repulsive contribution to the shift is calculated according to the prescription developed in the liquid solution study, the attractive contribution is found to scale linearly with the density and with the polarizability derivative of the CH bond, as predicted by the model. The ratio of the equatorial to axial linewidths has a density-independent value of 1.2, nearly the same value found for the liquid solutions and numerically equivalent to the ratio of polarizability derivatives for the CH bonds. This equivalence is consistent with Schweizer and Chandler’s theoretical result for the width of a band that is inhomogeneously broadened by attractive force fluctuations, but the density dependence is not; their result would predict a nonlinear density dependence with a maximum near ρc, whereas the observed linewidths show a nearly linear dependence on density. Neither the frequency shifts nor the linewidths show any clear evidence for a “local solvent density enhancement” that would be predicted for this mixture near the critical point. In the accompanying paper, Frankland and Maroncelli describe molecular-dynamics simulations of cyclohexane in supercritical CO2 that reproduce the observed linewidths nearly quantitatively. They show convincing evidence that the linewidths are dominated by binary, collisional interactions between the hydrogen and the solvent, and they discuss the apparent absence of a density enhancement.

Molecular-dynamics simulations of solvent effects on the C–H stretching Raman bands of cyclohexane-d11 in supercritical CO2 and liquid solvents

“…The linear dependence of the Raman linewidths on density observed in experiment suggested little or no local density augmentation in the cyclohexane-CO 2 system. 38, 39 The simulations are consistent with this interpretation. The simulated local densities are in excess of those expected based on the high-density behavior, but only by a modest amount, 10%-40%, depending on the region of the fluid examined.…”

“…MacPhail 38, 39 and co-workers reported the following changes to the C-H stretching spectrum over the density range between 0.2 c and 2 c ( c is the critical density͒. From the gas-phase limit to the highest CO 2 density the bands undergo only a small red-shift of about 2 cm Ϫ1 .…”

“…Theoretical explanations for this behavior in terms of critical slowing down of density fluctuations was also provided by several groups. [34][35][36] Of more direct relevance to the present work are several recent vibrational studies on dilute solutes in supercritical a͒ Electronic mail: mpm@chem.psu.edu solvents, [37][38][39][40][41][42][43][44][45][46] described in more detail below.…”

“…44 Convincing evidence for their interpretation was provided by the ability to predict the behavior of a 1:1 mixture of ethane and xenon using the same models applied to the pure fluids. 45 Finally, in two related studies, MacPhail and co-workers [37][38][39] reported on solvent effects on the Raman spectra of isolated CH stretches in cyclopentaned 9 and cyclohexane-d 11 in supercritical CO 2 (1.06T c ). In the cyclopentane work 37,38 a band shape analysis of the isotropic Raman spectrum was used to deduce the friction on the pseudorotation coordinate.…”

“…38 The second study, by Pan, McDonald, and MacPhail, on cyclohexane-d 11 in supercritical CO 2 , provided the impetus for the present simulations. The experiments are described in detail in the companion paper, 39 which immediately precedes this one ͑see also Ref. 38͒.…”