Richard A. MacPhail

The motional collapse of the methyl C–H stretching vibration bands

The asymmetric CH stretching bands of the methyl groups of a number of alkane systems have been examined as a function of temperature. At low temperatures, two bands are seen for a CH3 group. These bands collapse into one as the temperature is raised. Examination of crystals of alkanes with both odd and even numbers of carbon atoms, alkanes in urea clathrates, and deuterium substituted alkanes allows the separation of intramolecular and intermolecular contributions to the band splittings and widths. Model Hamiltonians that express the stretching energy levels as a function of both the methyl torsional coordinates and the external coordinates of the alkanes are set up. These are used in the Redfield equations to derive expressions for the splittings and widths in terms of parameters which give the coupling of the various types of motion. The splittings are found to be proportional to the average of cos 5ϑ, where ϑ is the torsional angle, and a contribution to the width is found to be due to fluctuations in...

Can the Bloch equations describe the vibrational spectra of a reacting molecule

The vibrational spectra of molecules that are rapidly interconverted among distinct species by very fast motions, for example, during ordinary chemical reactions or during the rotation of a molecule between different sites in a solid, are considered. The question of the title is addressed in a number of distinct stages. First, the spectra predicted by Bloch equations with the inclusion of exchange terms are derived. The results differ from those familiar from magnetic resonance spectroscopy, since the vibrational transition moment can have a different magnitude and orientation in each site. Next, the question of whether a reaction can be fast enough on the time scale required for the simple vibrational Bloch equations to be valid is addressed, and it is concluded that this is unlikely. The observed spectrum may be fit with the result of the Bloch equation analysis (as has been done often in the past), but we conclude that the rate of the reaction cannot be simply extracted from the parameters used in this...

Ultraslow nonequilibrium dynamics in supercooled glycerol by stimulated Brillouin gain spectroscopy

We have used high resolution stimulated Brillouin gain spectroscopy to monitor the nonequilibrium relaxation dynamics of supercooled glycerol near its glass transition temperature. After a temperature quench from 192.4 to 179.8 K, the Brillouin frequency shift increased over a period of 17 d from 16.877±0.005 GHz to 17.195±0.005 GHz, the equilibrium value expected for the final temperature. The relaxation of the shift appears to proceed in three distinct stages. The first and most rapid stage tracks the time dependence of the temperature. This is followed by a slower relaxation process which is well characterized by a stretched exponential function exp[−(t/τ)β]. The values determined for τ (12±2 ks) and β (0.61±0.09) are consistent with values predicted from recent dielectric and enthalpy relaxation studies of glycerol in the same temperature range, as long as allowances are made for the nonlinear nature of the nonequilibrium experiment. The third and final stage in the relaxation is approximately exponen...

Generalized hydrodynamic theory of viscoelasticity

A generalized hydrodynamic treatment of the dynamic behavior of transverse phenomena in a fluid is presented. An attempt is made to describe such phenomena (VH depolarized light scattering, flow birefringence, transverse sound or shear waves and viscous flow) in a consistent manner over a range of temperatures for which the fluid ranges from a low viscosity liquid to an amorphous solid or glass.

cw stimulated Brillouin gain spectroscopy of liquids

Abstract We demonstrate the use of cw stimulated Brillouin gain (SBG) spectroscopy to measure high resolution Brillouin spectra of liquids. Results are reported for thirteen liquids at room temperature, all obtained in a polarized (VV) configuration with a scattering angle of 178°. The observed Brillouin frequencies compare favorably with those predicted on the basis of previous spontaneous Brillouin light scattering measurements. The narrow Brillouin bands of carbon disulfide (70 MHz half-width at half-maximum) are easily resolved in the SBG experiment, and the sensitivity is sufficient to detect the Mountain mode in the SBG spectrum of carbon tetrachloride.

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

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...

High resolution stimulated Brillouin gain spectrometer

We describe a stimulated Brillouin gain (SBG) spectrometer based on low power continuous‐wave frequency‐stabilized lasers. The high resolution and broad tuning range of this spectrometer are demonstrated through a SBG spectrum of glycerol in the glassy state (T=146 K). The narrow Brillouin linewidth (17 MHz half‐width at half‐maximum) and large Brillouin shift (17.31 GHz) in this spectrum illustrate the extremely high equivalent ‘‘finesse’’ of the instrument, a finesse that would be difficult to achieve through interferometric techniques. The accuracy and precision with which the Brillouin shift can be measured are demonstrated using SBG spectra of liquid methylene chloride as an example. Our Brillouin shift values obtained over the temperature range 178–300 K are in excellent agreement with values measured previously by others using spontaneous and stimulated Brillouin scattering.

Dynamics in supercooled glycerol by high resolution stimulated Brillouin gain spectroscopy

We have used high resolution stimulated Brillouin gain spectroscopy to probe the dynamics of glycerol over the temperature ranges 146 to 305 K and 401 to 534 K, which include both the supercooled liquid and glass regimes. The high resolution and large spectral range of the technique have allowed us to resolve Brillouin peaks at low temperatures (146 K) with widths as narrow as 13 MHz and shifts as large as 17.3 GHz. A comparison of the observed Brillouin shifts and linewidths with predictions based on previous work at lower frequencies indicates that the main dispersion in our data arises from the primary (α) structural relaxation processes. However, this comparison also reveals that additional relaxation processes, perhaps associated with the secondary (β) processes, contribute to the Brillouin linewidths both above and below the glass transition. Our results also show a distinct kink in the temperature dependence of the speed of sound at 187 K, the glass transition temperature.

SOLVENT-SOLUTE INTERACTIONS AND THE RAMAN CH STRETCHING SPECTRUM OF CYCLOHEXANE-D11. I: SOLVENT-DEPENDENCE

We examine the gas‐to‐liquid frequency shifts and isotropic Raman linewidths for the axial and equatorial CH stretching vibrations of cyclohexane‐d11 in 13 different solvents. The ‘‘perturbed hard‐fluid model’’ of Ben‐Amotz and Herschbach provides a consistent description of the observed shifts in terms of average repulsive and attractive solute–solvent interactions. The attractive part of the shift is dominated by dispersive interactions, with a small contribution from inductive forces. This analysis also reproduces the observed ratio of equatorial to axial attractive shift components if certain details of the cyclohexane‐d11 geometry are accounted for when the repulsive part of the shift is calculated. The ratio of equatorial to axial peak linewidths is nearly the same for all solvents and is consistent with inhomogeneous broadening by attractive force fluctuations. A version of the Schweizer–Chandler theory of attractive force broadening, modified to incorporate interactions between the solute vibratio...

Torsional damping and solvent friction in liquid n‐butane: Experimental estimates from Raman spectroscopy

The isotropic Raman linewidths of the in‐phase CCC bending modes of liquid n‐butane are analyzed in terms of dephasing by torsional oscillations. A simple, effective Hamiltonian is developed to calculate the coupling between this bending mode and the torsion. For the gauche conformer the coupling is linear in the torsional coordinate and quite strong, but for the trans conformer the coupling is weak. This coupling is used to relate the linewidths of the bending modes to the torsional dynamics, which are modeled by a damped, harmonic oscillator. The damping constant and a related torsional correlation time are then extracted from the experimental linewidths. The resulting correlation times are compared with those calculated assuming either hydrodynamic or collisional (Enskog) friction on the torsional coordinate. Both theoretical models give values that lie below the experimental upper bound, but the Enskog friction compares somewhat better with our best experimental estimates of the torsional damping.