Angle fluctuations

Polycarbonate (PC) serves as a convenient example for both, the direct determination of the distribution of correlation times and the close connection of localized motions and mechanical properties. This material shows a pronounced P-relaxation in the glassy state, but the nature of the corresponding motional mechanism was not clear 76 80> before the advent of advanced NMR techniques. Meanwhile it has been shown both from 2H NMR 17) and later from 13C NMRSI) that only the phenyl groups exhibit major mobility, consisting in 180° flips augmented by substantial small angle fluctuations about the same axis, reaching an rms amplitude of 35° at 380 K, for details see Ref. 17). 

Miller and Flory (43) calculated of a-helices by taking bond-angle fluctuations into account. This approach gives the molecular rod a flexibility similar to that of wormlike chains but retains the a-helical conformation of the chain. Thus, in a sense, it may be regarded as a refinement of the treatment of Moha et al. The calculated results gave a nonlinear chain-length dependence of experimental results shown in Fig. 21. 

With the above-mentioned calculated results alone, it is impossible to distinguish which of the two mechanisms, interrupted helical structure or bond angle fluctuation, is mainly responsible for the observed nonlinear chain-length... 

Binary PF mixtures manifest several levels of structural hierarchy. The torsion angle between the monomer units represents the first level of this hierarchy. Wu et al. [28] studied PDMOF in THF and found a structure wherein each monomer unit adopted, at random, four rotational states. These were right- and left-handed torsional rotations of approximately 35 and 144° (consistent with either a 5/1 or 5/2 helices) and modest bond angle fluctuating (c.f., Fig. 4). At much larger distances, Rahman et al. [31] identified, in PF8, extended domain networks. The average distance between these aggregate domains is of the order of 60 nm (c.f., Fig. 5). 

Six homo- and heteronuclear Karplus relationships of vicinal couplings related to the

torsional angle have been analysed with MD/DFT calculations and model peptides by Case et It appeared that the average torsion angle fluctuation amplitudes of 24° had to be taken into account for ubiquitin in order to fit the calculated coupling values to the experimental ones. In addition, the authors have suggested that the / related Vnn coupling does not obey the usual Karplus type relationship. 

Photinos, D. J., Samulski, E. T., and Terzis, A. F, Conformations of n-hexane from proton dipolar couplings the role of torsion angle fluctuations, J. Phys. Chem., 96, 6979-6981... 

According to Fig. 8.23 in Section 8.5.1, a fluctuation component of the layer displacement u = u along the x-direction (within the smectic layer) is described by u x) = ucosq x. Since the director angle 9/ Sm/Sx = q xw. the free energy density in Eq. (8.49) can be rewritten in terms of the 9y-angle fluctuations ... 

The exit and scattering/recoil angle fluctuates due to extended beam spot and detector size... 

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