Showing papers by "Jack H. Freed published in 1975"

Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids

Abstract: It is shown how the equilibrium pair correlation function between spin‐bearing molecules in liquids may be incorporated as an effective force in the relative diffusion expressions, and how one may solve for the resulting time correlation functions and spectral densities needed for studies of spin relaxation by translational diffusion. The use of finite difference methods permits the solution no matter how complex the form of the pair correlation function (pcf) utilized. In particular, a Percus–Yevick pcf as well as one corrected from computer dynamics, both for hard spheres, are utilized. Good agreement with the experiments of Harmon and Muller on dipolar relaxation in liquid ethane is obtained from this analysis. Effects of ionic interactions in electrolyte solutions upon dipolar relaxation are also obtained in terms of Debye–Huckel theory for the pcf. Analytic solutions are given which are appropriate for the proper boundary‐value problem for the relative diffusion of molecules (i.e., a distance of mini...

Electron spin resonance studies of anisotropic rotational reorientation and slow tumbling in liquid and frozen media. III. Perdeuterated 2,2,6,6-tetramethyl-4-piperidone N-oxide and an analysis of fluctuating torques

Abstract: A detailed analysis of line shapes and relaxation is made for the perdeuterated 2,2,6,6-tetramethyl-4-piperidone N-oxide (PD-Tempone) nitroxide radical covering the whole range from fast motional narrowing ( TR - 10-12 sec) to the rigid limit (TR - 10-6 sec) in several deuterated solvents. The slow tumbling results show particularly good agreement with the slow tumbling theory of Freed, et al., for a reorientational model of moderate jumps (ca. 50° rrns), and essentially isotropic reorientation. It is shown that while such a model may not be readily distinguished, purely from its slow tumbling spectral predictions, from a free diffusion model including inertial effects, the latter model is incompatible with most other considerations. However, a simple analysis explicitly including the fluctuating (or random) torques indicates that more fundamental analysis of the dynamics may explain the slow tumbling results without necessarily involving substantial jumps. The spectral analysis is considerably enhanced by the increased resolution obtained from the use of the perdeuterated spin probe and deuterated solvents. Careful analysis of results at X-band and 35 GHz has shown that the nonsecular spectral densities exhibit significant deviations from a Debyelike spectral density yielding results very similar to those recently reported for the peroxylaminedisulfonate (PADS) radical. Related observations are discussed of apparent non-Debye-like spectral densities in the incipient slow tumbling spectra. These anomalies are also found to be amenable to a unified explanation in terms of the fluctuating torques. The analysis of much of the results in terms of a simple model yields an rms value for the fluctuating torques of ca. AT and TM - TR where TM is the relaxation time of the torques. The high-temperature electron-spin flip processes are consistent with a Hubbard-type spinrotational mechanism, but the low-temperature results may be due to spin-rotational relaxation from intramolecular motions. The simple analysis of spin-rotational relaxation in terms of relaxation of the fluctuating torques is found to yield equivalent predictions to conventional treatments when the estimated values of rms torque and TM are used.

A comparison of generalized cumulant and projection operator methods in spin‐relaxation theory

Abstract: The general spin‐relaxation theories of Albers and Deutch and of Argyres and Kelley based on different projection operator methods, and the theory of Freed based on generalized cumulant expansions are compared. It is shown that the first two yield equivalent expressions for the time evolution of the spin density matrix. They are also found to be equivalent to a cumulant expansion based on total ordering of the cumulant operators (TTOC), which is different from the partial time ordering method (PTOC) used by Freed. The TTOC method is found to be the more convenient for the frequency domain (i.e., for calculating spectra), while the PTOC method is for time domain analyses. Examples of the use of the TTOC method are given. Useful expressions are given for the case where the lattice may be treated in terms of classical Markov processes, but, in general, it is found that for such cases the stochastic Liouville method is the more useful for computations.

Generalized Einstein relations for rotational and translational diffusion of molecules including spin

Abstract: In this work the validity of generalized Einstein relations, D (ω) = kT/Iβ (ω), where D (ω) and β (ω) are frequency‐dependent diffusion and damping coefficients, is examined from a general point of view. It is shown that generalized Smoluchowski (S) equations for both translational and rotational diffusion involving the D (ω), which are defined in terms of simple correlation functions of the fluctuating forces and torques, follow from the appropriate generalized Fokker–Planck (FP) expressions when the translational and angular momenta are taken as rapidly relaxing and a coarse graining in time is introduced. It is found useful in this context to distinguish between those forces and torques fluctuating at rates faster than the diffusive‐type motions of the B particle versus those fluctuating more slowly. The appropriate FP equation for rotational diffusion is also derived. Generalized FP and S equations are also derived for the semiclassical case where the molecule(s) examined contains spin degrees of free...

Theory of chemically induced dynamic electron polarization. III. Initial triplet polarizations

Abstract: An analysis of dynamical aspects of the CIDEP mechanism proposed by Wong et al. is given. This mechanism is based upon the formation of an excited triplet by intersystem crossing that populates the three triplet levels unequally. The subsequent rotational averaging of the initial population distribution coupled with the orientational effects of the zero field splitting is carefully treated in this work utilizing the stochastic Liouville equation in a manner closely analogous to that recently given for ESR line shapes and relaxation of slow−tumbling triplets. It is shown that the predicted CIDEP polarizations can indeed be very substantial, in agreement with Wong et al., but they will depend in general on the relative magnitudes of not only the zero field (D and E) and Zeeman terms (ω0) but also the relevant reaction rates and the rotational tumbling times (τR). A useful perturbation expression valid for D2 ≲ (1/2)[ω02 + τR−2] is obtained which shows these details. Typical complete solutions, obtained nume...

An ESR and ENDOR study of spin relaxation of semiquinones in liquid solution

Abstract: A quantitative test of the ENDOR theory for free radicals in solution has been developed experimentally using the semiquinone (SQ) radical anions of parabenzo‐ (PBSQ), duro‐ (DSQ), and 2,5‐dimethyl‐para‐benzo‐ (2,5‐DPMBSQ) dissolved in ethyl alcohol (EtOH) and dimethoxyethane (DME) solvents. It is shown that, in general, an ENDOR signal arising from a molecule containing four or less equivalent nuclei, such as PBSQ, can be analyzed rigorously whereas a molecule containing more than four equivalent nuclei, such as DSQ, which, in principle, could be analyzed rigorously, practically is best analyzed using approximate forms of the ENDOR theory. It is shown that 2,5‐DMPBSQ may be analyzed using a combination of both the rigorous and approximate forms of the ENDOR theory. The analysis involves calculation of the ENDOR relaxation parameters, T2n, Ωn, and Ωe,n, from the experimental ENDOR percent enhancement and linewidth studies. A comparison was made by performing the ESR linewidth and saturation studies to obt...

A hydrodynamic effect on chemically induced dynamic spin polarization

Abstract: Deutch has recently suggested that the effect of the hydrodynamic interaction represented by Oseen’s tensor, on the relative diffusion of radical pairs, should have consequences for CIDNP and CIDEP signals. Detailed solutions to this problem have now been obtained by the finite difference approach of Pedersen and Freed to the stochastic−Liouville equation for the radical−pair mechanism. These solutions show that the hydrodynamic interaction typically leads to polarizations enhanced by factors of the order of 0.9−3 for CIDEP and reduced by factors of (3/4) −2(1/2) for the appropriate CIDNP parameter, and these factors are a function of the nature and magnitudes of the various interactions.