Orientational fluctuations

In the absence of significant molecular motion the spectra can be calculated simply as a powder-like super-imposition of the individual molecular static lines of Lorentzian shape from all over the sample. These lines are then positioned into the spectrum according to Eq. (5) as in Ref. [6j. To include also dynamic effects, such as fluctuations of molecular long axes (defining the scalar order parameter S and the director n) and translational molecular diffusion, it is convenient to use a semi-classical approach with the time-dependent deuteron spin Hamiltonian [25] where the H NMR line shape I cj) is calculated as the Fourier transform of 

Here ljz denotes the Zeeman frequency, while the brackets. ..)i stand for the ensemble average over all molecules in the sample. The instantaneous resonance frequency of the ith molecule with coordinates rj is given by ( z + where = a Q[ (ui B/H) - i]. It 

In order to estimate how dynamic processes influence the spectra, it is necessary to compare their typical time scales to the characteristic NMR 

In addition to fluctuations of the long molecular axes we would now like to include also translational molecular diffusion into the analysis. Let us consider, for simplicity, the case in which the diffusion is characterized by a single motional constant (the diffusion tensor is isotropic), i.e., the probability for a molecular diffusion does not depend on the local orientation of the director. In a bulk unconstrained nematic phase the diffusion anisotropy can be typically up to 2, with D  

Isotropic translational diffusion has been simulated by a simple random walk process in which each spin — representing one or more nematic molecules — jumps to one of its nearest neighbor sites with equal probability [11]. After the diffusion jump has been performed, the spin acquires the orientation of the local director at the new coordinates. Calculating G t) we have, like in the diffusion-less case, updated from the MC data the spin configuration inside the droplet 8 times per NMR cycle. Now additional diffusion steps have been added in between these structural updates, with their number A ranging from 1 to 32. In this last case the spectra are completely motionally averaged due to dififiision effects since for A = 32 each of the spins exhibits a total of 256 jumps within the duration of one NMR cycle. This already corresponds to the fast diffusion limit with C to- 

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Additional neutron scattering studies on different polymer systems could prove very important. Strobl [31,32,47,103] provides evidence that, for some polymers, lamellar crystallization is preceded by pre-ordering of the melt followed by formation of planar arrays of blocks. Investigating crystallization from the melt, Kaji and coworkers [25] find pre-ordering phenomena relating to orientational fluctuations of stiff polymer segments which, under appropriate conditions, determine phase separation prior to crystallization. 

Microphase separation due to orientational fluctuations (spinodal decomposition type) ... 

Fig. 10 Schematic diagram for the explanation of spinodal decomposition due to the orientation fluctuation of stiff segments occurring in the induction period prior to crystallization [19]. On the basis of Doi s kinetic theory [24,25] Vexcl> excluded volume b, nearly equal to the diameter d of the rod or stiff segment L, rod length (9, angle between neighboring rods v, critical stiff segment concentration...

Fig. 12 Normalized invariant /orient of DPLS intensity for PET as a function of annealing time at 80 °C [11]. The invariant giving orientation fluctuations is normalized to that for a sufficiently annealed sample which was taken to be unity. Arrow indicates the initiation of crystallization...

The dry nematic solution exhibits a smooth texture after being annealed, with a field of disclinations at any glass-solution interface. A nematic phase produced by cooling the isotropic phase will exhibit a complex, mottled texture that slowly anneals to the smooth texture. The ratio Rvv(q)/ Hv(q) (for e = 20 deg.) for either morphology indicates appreciable orientational averaging of the orientation fluctuation. Photon correlation scattering on the... 

There are other types of fluctuations. For example, if sugar is dissolved in water, after thorough stirring the sugar concentration will be statistically homogeneous, but concentration fluctuations will give rise to scattering. If the molecules are nonspherical, there will be orientation fluctuations. 

The processes observed in the depolarized Rayleigh spectrum correspond to internal modes of motion. Thus, they may have relaxation times which substantially exceed those obtained from the longitudinal or bulk relaxation alone. Nevertheless they are a part of the a relaxation process as it is normally observed in the creep compliance. All processes with the same shift factors make up the full a relaxation. In liquids with substantial depolarized Rayleigh scattering the slowly relaxing part of the W scattering is also dominated by the orientation fluctuations associated with the internal modes of motion. Each internal mode contributes some intensity, but it is believed that fairly short wavelength modes dominate the scattered intensity. 

The electronic wave function of a solvated electron, spread over several solvent molecules, should be very sensitive to orientation fluctuations of these molecules, unlike that of an ordinary reactant. 

Because of (1) the mean kinetic energy of the solvated electron changes appreciably during the orientation fluctuations required for the system to reach the intersection hypersurface. Such changes are included in Figure 1, which represents a plot of the total electronic energy of the system as a function of the atomic coordinates. 

Imai, M., Kaji, K. and Kanaya, T. (1993) Orientation fluctuations of polyethylene tereph-thalate) during the induction period of crystallization, Phys. Rev. Lett. 71(25), 4162-4165... 

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