Rotational Friction Kernel in Water from the Femtosecond Time-Resolved Optical Kerr Effect of Acetonitrile/Water Mixtures

Depolarized Rayleigh scattering (DRS) of acetonitrile/water mixtures is examined with the time-resolved, heterodyne-detected optical Kerr effect (OHD-OKE). For neat water, the rise of electronic response gives a symmetric apparatus function and an asymmetric correction is constructed with the help of high-frequency Raman data. For the mixtures at 21 °C, depolarized Raman spectra up to 1600 cm-1 are obtained with high signal/noise ratio. The DRS spectra for acetonitrile mole fraction 0.05 ≤ x ACN ≤ 1 are decomposed into the spectra of water and of neat acetonitrile and a “composite” spectrum with associated weight functions. The spectral density at infinite dilution in water is obtained by extrapolation and transformed into the second-rank orientational correlation function of single acetonitrile solutes. The Einstein frequency of 31.11 cm-1 is higher than the value of 27.11 cm-1 for the potential-free stochastic rotor and an oscillation is observed in the corresponding velocity correlation function, both indicating librational motion in a solvent cage. The rotational correlation time τ2 = 1.49 ± 0.015 ps may be used to rescale τ2 values from 14N nuclear quadrupole relaxation in water; the comparison provides an improved value 4.54 ± 0.03 MHz for the coupling constant. The correlation function is inverted to give the kernel for rotational friction. The latter consists of a fast biexponential decay with a 33-fs correlation time followed by exponential decay with a 0.779-ps time constant. An oscillatory residue around 0.3 ps indicates coupling between acetonitrile libration and the water frictional modes.