Theory of Spin–Lattice Relaxation

Review of electron spin relaxation times for organic radicals and transition metal ions in magnetically dilute samples. Emphasis is placed on studies that have been performed as a function of temperature and that provide insight into the relaxation processes.

Relaxation Times of Organic Radicals and Transition Metal Ions

Electron spin lattice relaxation rates were measured for 12 nitroxyls with molecular weights between 144 and 438, and for galvinoxyl, 1,3-bisdiphenylene-2-phenylallyl (BDPA), and 2,2-diphenyl-1-picrylhydrazyl (DPPH) in glassy sucrose octaacetate. Relaxation rates for polar nitroxyls also were measured in glassy sorbitol. Dependence on T where V eff is effective molecular volume and γ is a material-specific parameter, was used to compare processes. Values of V eff were determined based on molecular libration in glassy sucrose octaacetate (γ = 3.5), tumbling in viscous decalin at 233 K (γ = 4.7), or tumbling in heavy mineral oil (γ = 6.0). For nitroxyl relaxation there is a master curve: log(1/T 1) vs log( T) (γ = 0.89). The similarity of the values of γ for the Raman process and for the additional process that contributes at higher temperatures, and the absence of frequency dependence between X- and Q-band, support assignment of this additional process as a local mode. For these radicals the contributions ...

Impact of molecular size on electron spin relaxation rates of nitroxyl radicals in glassy solvents between 100 and 300 K

The role of extensively delocalized π-electrons in electrical conductivity, non-linear optical properties and physical properties of polymers

Site-directed spin labeling (SDSL) and electron paramagnetic resonance (EPR) spectroscopy offer accurate, sensitive tools for the characterization of structure and function of macromolecules and their assemblies. A new rigid spin label, spirocyclohexyl nitroxide α-amino acid and its N-(9-fluorenylmethoxycarbonyl) (Fmoc) derivative, has been synthesized that exhibit slow enough spin echo dephasing to permit accurate distance measurements by pulse EPR at temperatures up to 125 K in 1:1 water:glycerol and at higher temperatures in matrices with higher glass transition temperatures. Distance measurements in the liquid nitrogen temperature range are less expensive than those that require liquid helium, which will greatly facilitate applications of pulsed EPR to the study of structure and conformation for peptides and proteins.

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A spirocyclohexyl nitroxide amino acid spin label for pulsed EPR spectroscopy distance measurements.

In the usual treatment of the temperature dependence of spin-lattice relaxation of impurity ions, the vibrational properties of the paramagnetic ion are assumed to be those of a normal host ion. For impurities that do not affect the vibrational properties of the lattice, this is expected to be a resonable approximation. However, if a paramagnetic impurity is associated with a gross defect in a crystal, it should be expected that the temperature dependence of the spin-lattice relaxation time will be dominated by the vibrational properties of the defect. An ion could be trapped at a site about which the potential is highly anharmonic and such that the vibrational amplitude is very large and effectively independent of the state of excitation. Under these circumstances lattice vibrations whose amplitudes have the usual temperature dependence could beat with the vibrations of the defect, producing a difference frequency resulting in a spin transition. In the high-temperature limit one would expect a spin transition rate that is proportional to $T$ rather than to ${T}^{2}$ because only the lattice-vibration part of the interaction is temperature-dependent and at high temperatures this dependence is linear. In this paper two simple defect models are discussed. In the first, a paramagnetic ion tunnels between two stable positions, and in the second, the ion is trapped in a one-dimensional square well. In the tunneling model, the form of the temperature dependence is independent of the details of the spin-lattice interaction, whereas the square-well results are sensitive to these details. In the latter case, the effect of electric and magnetic interactions is discussed. Recent measurements by Feldman, Castle, and Wagner of the spin-lattice relaxation time of hydrogen centers in fused quartz exhibit the behavior described by either of these models, but their data can be fitted better by the square-well model.

J. Murphy

Papers

Spin-Lattice Relaxation Due to Local Vibrations with Temperature-Independent Amplitudes