Tumbling regime

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. 

Tumbling regime At very low shear rates, the birefringence axis (or the director) of the nematic solution tumbles continuously up to a reduced shear rate T < 9.5. While the time for complete rotation stays approximately equal to that calculated from Eq. (85), the scalar order parameter S,dy) oscillates around its equilibrium value S. Maximum positive departures of S(dy) from S occur at 0 n/4 and — 3n/4, and maximum negative departures at 0 x — k/4 and — 5it/4, while the amplitude of oscillation increases with increasing T. 

Doi [23] had already noted that his theory was restricted to a monodomain or textureless sample. The extension by Marucci and Maffettone [68] retains that restriction. This issue was addressed by Larson and Doi [72], who proposed a model for the rheology of textured lyotropic solutions in the tumbling regime. In the linear Larson-Doi polydomain model the response of the material is expressed in terms of a variable / proportional to the defect density. The defect density is proportional to the shear rate, so that texture refinement is a feature of this model. The steady state predictions for the order parameter S are independent of shear rate. 

The dynamics of spin probes in polymers is often characterized by Tsog, the temperature for which the extreme separation is 50 G, corresponding to AArei = 0.5 and Tc 3.5 ns. Below Tsog the nitroxide is in the slow tumbling regime and... 

The middle panels of Figs. 5 and 6 show typical patterns in the slow tumbling regime if A = 0 and A yl 0 as in nitroxides, respectively. Note that in the latter case the resulting three lines, corresponding to the three possible transitions induced by the microwave field (see Fig. 2, bottom), overlap resulting in a complex pattern. 

Figure 6.3 Orientation dependence of the EPR spectrum of a planar copper(II) complex and lineshapes in the slow tumbling regime (simulations), (a) Geometry of the complex, molecular coordinate frame, and orientations of the magnetic field vector Bo corresponding to the spectra in (b). (b) EPR spectra at four selected orientations simulated with EasySpin 1.3 (http //www.esr.ethz.ch). (c) Slow tumbling spectra assuming isotropic Brownian diffusion with rotational correlation time Tr = 1 /(6 2 ) simulated with the Schneider-Freed suite of programs [32].

Figure 9.17 Plots of a versus Dj.f, describing the motion of the director in the tumbling regime,...

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