Slow Tumbling

In a macroscopically disordered system such as a microcrystalline powder or a glassy frozen solution, all possible orientations p occur with weighting factors sin p. The EPR spectrum of such a disordered system depends on whether reorientation by rotational diffusion is very slow, moderate, or very fast on the EPR timescale. In the following we assume isotropic Brownian rotational diffusion with an isotropic value Riso of the diffusion tensor and a transverse relaxation time of 150 ns. 

The rotational correlation time is then given by 1/(6 Riso). Rotational diffusion is very slow (rigid limit) for TiRiso L In this regime, the spectrum 

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In microphase-separated systems, ESR spectra may consist of a superposition of two contributions, from nitroxides in both fast and slow-tumbling regimes. Such spectra provide evidence for the presence of two types of domains with different dynamics and transition temperatures. This case was detected for a HAS-derived nitroxide radical in heterophasic polyfacrylonitrile-butadiene-styrene) (ABS) as shown in Figure 5, the fast and slow components in the ESR spectrum measured represent nitroxide radicals located in butadiene-rich (B-rich) and styrene/acrylonitrile-rich (SAN-rich) domains, respectively [40]. These two components were determined by deconvoluting the ESR spectrum of HAS-NO measured at 300 K. 

In the slow tumbling limit in the absence of radio frequency pulses only terms with /(to = 0) = need to be retained. The contribution of the DD coupling is... 

Thus, in the fast tumbling limit Raoss = — ( —— ] rc and in the slow tumbling limit... 

PBLG/toluene samples, toluene was added by weight via a 0.05im filter (Millipore type VM). The samples were then flame-sealed and homogenized by slow tumbling at room temperature (DMF) or 100 C (toluene). 

Lee et al. evolved a comprehensive analytical-theoretical treatment, based on the solution of the reorientational isotropic diffusion equation, for an ensemble of high-spin systems under motion. These authors developed an analytical expression for the slow-tumbling motional region that relates the orientational-motion correlation time t (in s), or the corresponding tumbling rate t, with the step separation bB, of the ESR fine structure of a quartet by Eq. 8,... 

Figure 8 Solution spectrum of V0(H20)5 showing eight lines (/ = 7/2). Line intensity variation arises from slow tumbling of the ion resulting in coupled g-factor and hyperfine splitting anisotropy effects...

The expansion (3.11) can be employed to compute ESR lineshapes for slow-tumbling paramagnetic molecules in the presence of weak static magnetic fields. In such cases the computation of the nitroxide radical ESR spectrum is only a little more time-consuming. 

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