Bimolecular collisions between perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-l-oxyl molecules in three alkanes have been studied by measuring the electron paramagnetic resonance ͑EPR͒ spectral changes induced by spin exchange. We define an "encounter" to be a first-time collision followed by a series of re-encounters prior to the diffusing pair's escaping each other's presence. The present work stems from a recent proposal ͓B. L. Bales et al., J. Phys. Chem. A 107, 9086 ͑2003͔͒ that an unexpected linear dependence of the spin-exchange-induced EPR line shifts on spin-exchange frequency can be explained by re-encounters of the same probe pair during one encounter. By employing nonlinear least-squares fitting, full use of the information available from the spectral changes allows us to study encounters and re-encounters separately. The encounter rate constants appear to be dominated by hydrodynamic forces, forming a common curve for hexane, decane, and hexadecane when plotted against T / , where is the shear viscosity. Unexpectedly, encounters are not dependent on the ratio = a / a s , where a and a s are the van der Waals radii of the nitroxide probe and the solvent, respectively. It is argued that the near coincidence of the resulting encounter rate constant with the hydrodynamic prediction is likely due to a near cancellation of terms in the general diffusion coefficient. Thus, the semblance of hydrodynamic behavior is coincidental rather than intrinsic. In contrast, the mean times between re-encounters do depend on the relative sizes of probe and solvent. For hexane at lower temperatures, the Stokes-Einstein equation apparently describes re-encounters well; however, at higher temperatures and for decane and hexadecane, departures from the hydrodynamic prediction become larger as becomes smaller. This is in qualitative agreement with the theory of microscopic diffusion of Hynes et al. ͓J. Chem. Phys. 70, 1456 ͑1979͔͒. These departures are well correlated with the free volume available in the solvent; thus, the mean times between re-encounters form a common curve when plotted versus the free volume. Because free volume is manifested macroscopically by the isothermal compressibility, it is expected and observed that the re-encounter rate also forms a common curve across all three solvents when plotted with respect to compressibility. The existence of a common curve for alkanes raises the prospect of using EPR to determine the compressibility of substances such as fossil fuels and biological membranes.

Diffusion of perdeuterated tempone (PDT) in various nonpolar hydrocarbon solvents on both the large and microscopic scales is examined through electron paramagnetic resonance spectroscopy. Spectral line broadening and hyperfine spacing are measured in order to extract both the Heisenberg spin-exchange rate as well as the average recollision times between spin-probe pairs. Probe recollision is responsible for a linear component to the dependence of the line shift on spectral broadening which has been identified in recent years. The present study extends the work of a previous paper by Kurban et al. [J. Chem. Phys. 129, 064501 (2008)], in which it was reported that recollision rates for PDT formed a common curve across n-alkanes when plotted with respect to free volume and to isothermal compressibility. It is now found that such common curves occur within distinct chemical families, in particular, the alkane and aromatic groups. Within each chemical family, the spin probe recollision rate correlates with free volume and compressibility independently of the geometry of the particular solvent. All solvents show significantly enhanced recollisional diffusion over the Stokes-Einstein (SE) prediction at high temperatures. The spin-exchange rate forms a common curve with respect to T/eta for all alkanes except cyclohexane and another common curve in all three aromatic compounds. It is reasoned that although all spin-exchange rates are near to the SE prediction, the semblance of hydrodynamic behavior is superficial and arises incidentally from mathematical cancellation of terms in a generalized diffusion coefficient. As a collision pair coexists for a time within a solvation shell, the recollision time places a lower limit on the lifetime of the solvent cage. Although molecular dynamics simulations conducted thus far have yielded cage lifetimes lower than the measured recollision times, this is attributable to the fact that such simulations have mostly examined cage configurations too small to harbor a spin-exchange encounter, and is also likely due to restrictive mathematical definitions of cage lifetimes that are employed in such simulations.

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.

Picosecond rotational correlation times of perdeuterated tempone (PDT) are found in alkane and aromatic liquids by directly using the spectral width of the central electron paramagnetic resonance line. This is done by mathematically eliminating the non-secular spectral density from the spectral parameter equations, thereby removing the need to assume a particular form for it. This is preferable to fitting a constant correction factor to the spectral density, because such a factor does not fit well in the low picosecond range. The electron-nuclear spin dipolar interaction between the probe and solvent is shown to be negligible for the very rapid rotation of PDT in these liquids at the temperatures of the study. The rotational correlation times obtained with the proposed method generally agree to within experimental uncertainty with those determined by using the traditional parameters. Using the middle line width offers greater precision and smoother trends. Previous work with the central line width is discussed, and past discrepancies are explained as possibly resulting from residual inhomogeneous broadening. The rotational correlation time almost forms a common curve across all of the solvents when plotted with respect to isothermal compressibility, which shows the high dependence of rotation on liquid free volume.