Showing papers by "Jack H. Freed published in 1972"

An ESR Study of Anisotropic Rotational Reorientation and Slow Tumbling in Liquid and Frozen Media

Abstract: A careful study is described of the ESR lineshapes for the peroxylamine disulfonate (PADS) radical dissolved in 85% glycerol solution and in frozen water and D2O. In the frozen media, spectra characteristic of rotational correlation times τR ranging from 1.0 × 10−11sec to > 10−6sec are obtained, while the range in glycerol is from 1 × 10−10sec to >10−6sec. The very rapid rotational motion in frozen water is taken to imply that PADS is rotating in a clathrate cage. The activation energies in ice and 85% glycerol are 14.7 ± 0.1 and 11.3 ± 0.1 kcal/mole, respectively, (from motional‐narrowing data). The value for ice is very similar to that obtained for other rate processes in ice. The lineshapes for τR ≲ 10−9sec are analyzed in terms of the familiar spin‐relaxation theories valid in the motionally narrowed region. These results are well fitted by the model of axially symmetric rotational diffusion with the symmetry axis in the plane of the N, O, and S atoms and parallel to a line passing through the two S a...

Estimating slow-motional rotational correlation times for nitroxides by electron spin resonance

Abstract: A simple method of estimating slow-motional rotational correlation times rR for nitroxides by esr, which is based on the rigorous theory of Freed, Bruno, and Polnaszek, is discussed. The results can be fit to the expression r3 = a(1 S)b , where S is the ratio of the separation of the outer hyperfine extrema to that for t,he rigid limit value. The parameters a and b depend upon intrinsic line width, rotational model, and hyperfine parameters, and appropriate results are given.

ESR Study of Heisenberg Spin Exchange in a Binary Liquid Solution near the Critical Point

Abstract: A careful study of the Heisenberg spin‐exchange contribution ωHE to the ESR linewidths of the di‐t‐butyl nitroxide (DTBN) radical dissolved in mixtures of 2,2,4‐trimethylpentane and n‐perfluoroheptane was performed. The study includes samples of different radical concentration dissolved in the critical composition of the two solvents. This critical solvent system is known to exhibit an anomaly in the macroscopic kinematic viscosity ν near Tc. It is found that in the critical region, ωHE is not linear in T/ν. However, it was observed that ωHE is linear in T/ν′ both for noncritical compositions and critical compositions above Tc. Here ν′ is the macroscopically measured viscosity, but with the ``anomalous portion'' subtracted out. Deviations from ideal behavior of ωHE with respect to T/ν were observed and discussed. The experiments near the critical region required temperature stability and control to within ±0.01°C at the ESR sample, and a description is given of the experimental design.

ESR Lineshapes and Saturation in the Slow Motional Region—The Stochastic Liouville Approach

Abstract: Let us define an orientation-dependent spin-density matrix, σ(Ω, t) by: $$\sigma \left( {\Omega ,{\rm{ t}}} \right) = {{\rm{e}}^{ - \left( {{\rm{i}}{H^ \times } + {\Gamma _\Omega }} \right){\rm{t}}}}\sigma \left( 0 \right)$$ (1) such that 〈P0|σ(Ω, t)|G0〉 = σ(t) as given by eq. VIII-119. Then it obeys the stochastic Liouville equation of motion:1,2,3 $${\partial \over {\partial {\rm{ t}}}}\sigma \left( {\Omega ,{\rm{ t}}} \right) = - \left[ {{\rm{i}}H{{\left( \Omega \right)}^ \times } + {\Gamma _\Omega }} \right]\sigma \left( {\Omega ,{\rm{ t}}} \right).$$ (2)

ESR Saturation and Double Resonance in Liquids

Abstract: The well-known result from the steady-state (s.s.) solution of the Bloch Equations is that the absorption is given by the y-component of magnetization \({{\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over M} }}_{\rm{y}}}\) in the rotating frame: $${{\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over M} }}_{\rm{y}}} = {{{\rm{\gamma }}{{\rm{H}}_1}{{\rm{T}}_2}} \over {1 + {{\left( {{{\rm{T}}_2}\Delta {\rm{\omega }}} \right)}^2} + {{\rm{\gamma }}^2}{\rm{H}}_1^2{{\rm{T}}_1}{{\rm{T}}_2}}}{{\rm{M}}_{\rm{0}}}$$ (1) with M0 the equilibrium magnetization. When we switch to a quantum mechanical description, we can calculate: $${{\rm{M}}_ \pm } = {{\rm{M}}_{\rm{X}}} \pm {\rm{i}}{{\rm{M}}_{\rm{y}}} = \left( {{{{\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over M} }}}_{\rm{x}}}{\rm{i}}{{{\rm{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}}\over M} }}}_{\rm{y}}}} \right){{\rm{e}}^{ \pm {\rm{i\omega t}}}}$$ (2) statistically from its associated quantum mechanical operator $${{\rm{m}}_ \pm } = \Re {\rm{ }}{{\rm{Y}}_{\rm{e}}}{\rm{S}}{{\rm{ }}_ \pm }$$ (3) where ℜ is the concentration of electron spins, by taking a trace of the spin density matrix σ(t) with the spin operator S±: $${{\rm{M}}_ \pm }\left( {\rm{t}} \right) = \Re {{\rm{Y}}_{\rm{e}}}{\rm{ Tr}}\left[ {{\rm{\sigma }}\left( {\rm{t}} \right){{\rm{S}}_ \pm }} \right]$$ (4) The trace is invariant to a choice of zero-order basis states. The equation of motion for σ(t) is taken to be the relaxation matrix form given by Eq. VIII-20, and we shall neglect effects of higher order than R(2).

ESR Relaxation and Lineshapes from the Generalized Cumulant and Relaxation Matrix Viewpoint

Abstract: We start with the time rate of change of the spin density matrix for a single spin system: $$\dot \sigma \left( {\rm{t}} \right) = - {\rm{i}}\left[ {H,\sigma } \right] \equiv - {\rm{i}}{H^ \times }\sigma $$ (1) where H = H 0 + H 1 (t), and we use the Kubo2,3 notation for super-operators: A×, such that A×B = [A, B] We define an interaction representation by: $${\sigma ^\ddag }\left( {\rm{t}} \right) = {{\rm{e}}^{{\rm{i}}H_0^ \times {\rm{t}}}}\sigma = {{\rm{e}}^{{\rm{i}}{H_0}{\rm{t}}}}\sigma {{\rm{e}}^{ - {\rm{i}}{H_0}{\rm{t}}}}$$ (3) and $$H_1^\ddag \left( {\rm{t}} \right) = {{\rm{e}}^{{\rm{i}}H_0^ \times {{\rm{t}}_{{H_1}}}}}\left( {\rm{t}} \right) = {{\rm{e}}^{{\rm{i}}{H_0}{{\rm{t}}_{{H_1}}}}}\left( {\rm{t}} \right){{\rm{e}}^{ - {\rm{i}}{H_0}{\rm{t}}}}$$ (4)

Spin Relaxation via Quantum Molecular Systems

Abstract: Very often one has to consider the quantum nature of the molecular systems whose modulation induces spin relaxation. We first consider a "gas-like" model wherein strong collisions randomize the molecular degrees of freedom, more specifically the rotational states. Then we generalize the results to cover more general descriptions of the way that the molecular degrees of freedom relax through thermal contact.