A study of the relation between translational and rotational diffusion through measurement of molecular recollision

Abstract

Translational and rotational diffusion rates of perdeuterated tempone (PDT) in ethanol are determined using electron paramagnetic resonance spectroscopy. The translational motion is measured on two scales: the macroscopic, as represented by the Heisenberg spin-exchange rate, and the microscopic, which entails recollisions between the same spin-exchange particle pair. The spin-exchange and recollision rates are used together to calculate the overall translational diffusion coefficient without recourse to assumptions concerning the value of the Stokes radius or collision distance. When observed as a function of solvent isothermal compressibility, the recollision time in ethanol is displaced from the common alkane curve at low temperatures but joins that curve at higher temperatures. Rotational correlation times in ethanol are obtained and show a decreasing rotation-translation coupling with increasing temperature, revealing a pattern that is qualitatively identical with respect to both collision and recollision. In comparison, an examination of PDT diffusion in toluene reveals an increasing rotation-translation coupling with increasing temperature. The contrasting behavior of the coupling in the two solvents is attributable to the degree of anisotropy in PDT rotation.

Determination of Very Rapid Molecular Rotation by Using the Central Electron Paramagnetic Resonance Line

“…The previous study in this series determined τ R for PDT in ethanol. 22 The τ R – κ T curve for ethanol generated from the data of that study lies significantly far from the alkane and aromatic curves of Figure 4, and is not shown here. It seems that the known tendency of PDT to form hydrogen bonds with ethanol 6 greatly affects the relationship between rotation and compressibility.…”

“…Previous studies 25,26 have already shown that PDT recollision forms common alkane and aromatic curves as a function of isothermal compressibility, with ethanol joining the alkanes at high temperature. 22 Figure 4 shows τ R as a function of κ T in all solvents (see Refs. 25 and 26 and references therein for details on how compressibilities were obtained).…”

“…31 has also been used to fit EPR spectra very well in many other studies. 16,22,25,26,32–37 After the Lorentzian and Gaussian components were extracted, the Lorentzian width of the middle line was taken to be A , while B and C were found in the standard way with the line-height ratios.…”

“…Therefore, assuming isotropy is not likely to affect the accuracy of rotational rates determined with A . Another study, 22 which determined the rotation of perdeuterated tempone (PDT) in ethanol by using B , found that varying N from 1/3 to 6 made at most a 3.7% difference in τ R . In the temperature range of that study, PDT had rotational correlation times between 3 and 8 ps.…”

Simulation of Rigid-Limit and Slow-Motion EPR Spectra for Extraction of Quantitative Dynamic and Orientational Information

“…However, even in this case, it is possible to distinguish the significantly different contributions of dipole-dipole interaction and spin exchange to broadening of the spectral lines by means of the method [12]. Recently it was supposed [20][21][22] that paramagnetic molecules in the solvent cage repeatedly collide and exchange their spin states. In such case the spin exchange does not reflect adequately the rate of translational diffusion of molecules in the medium.…”