Dynamic incoherent

Kummrow A and Lau A 1996 Dynamics in condensed molecular systems studied by incoherent light Appi. Rhys. B 63 209-23... 

A procedure commonly used to extract dynamic data directly from experimental incoherent neutron scattering profiles is described in Ref. 17. It is assumed that the atomic position vectors can be decomposed into two contributions, one due to diffusive motion, fi /t), and the other from vibrations, Uijt), i.e.. 

Inelastic Incoherent Scattering Intensity. For a system executing harmonic dynamics, the transform in Eq. (4) can be performed analytically and the result expanded in a power series over the nonnal modes in the sample. The following expression is obtained [26] ... 

C. Incoherent Neutron Scattering Measurements of Lipid Dynamics... 

The amplitude of the elastic scattering, Ao(Q), is called the elastic incoherent structure factor (EISF) and is determined experimentally as the ratio of the elastic intensity to the total integrated intensity. The EISF provides information on the geometry of the motions, and the linewidths are related to the time scales (broader lines correspond to shorter times). The Q and ft) dependences of these spectral parameters are commonly fitted to dynamic models for which analytical expressions for Sf (Q, ft)) have been derived, affording diffusion constants, jump lengths, residence times, and so on that characterize the motion described by the models [62]. 

We finish this section by comparing our results with NMR and incoherent neutron scattering experiments on water dynamics. Self-diffusion constants on the millisecond time scale have been measured by NMR with the pulsed field gradient spin echo (PFGSE) method. Applying this technique to oriented egg phosphatidylcholine bilayers, Wassail [68] demonstrated that the water motion was highly anisotropic, with diffusion in the plane of the bilayers hundreds of times greater than out of the plane. The anisotropy of... 

This question is closely related to the coherent-incoherent transition problem absent from the standard situation in the gas phase namely, a true rate constant can be defined only when the tunneling dynamics is incoherent, i.e., once prepared in the initial state (reactant valley), the system... 

The prerequisite for an experimental test of a molecular model by quasi-elastic neutron scattering is the calculation of the dynamic structure factors resulting from it. As outlined in Section 2 two different correlation functions may be determined by means of neutron scattering. In the case of coherent scattering, all partial waves emanating from different scattering centers are capable of interference the Fourier transform of the pair-correlation function is measured Eq. (4a). In contrast, incoherent scattering, where the interferences from partial waves of different scatterers are destructive, measures the self-correlation function [Eq. (4b)]. 

The self-correlation function leads directly to the mean square displacement of the diffusing segments Ar2n(t) = <(rn(t) — rn(0))2>. Inserting Eq. (20) into the expression for Sinc(Q,t) [Eq. (4b)] the incoherent dynamic structure factor is obtained... 

As mentioned in Section 3.1, the incoherent dynamic structure is easily calculated by inserting the expression for the mean square displacements [Eqs. (42), (43)] into Eq. (4b). On the other hand, for reptational motion, calculation of the pair-correlation function is rather difficult. We must bear in mind the problem on the basis of Fig. 19, presenting a diagrammatic representation of the reptation process during various characteristic time intervals. 

As in the case of the Rouse dynamics (see Sect. 3.1.1), the intermediate incoherent scattering law for dominant hydrodynamic interaction (Zimm model) can be... 

Comparing Eqs. (83), (84) and Eqs. (21), (22) it follows immediately that Rouse and Zimm relaxation result in completely different incoherent quasielastic scattering. These differences are revealed in the line shape of the dynamic structure factor or in the (3-parameter if Eq. (23) is applied, as well as in the structure and Q-dependence of the characteristic frequency. In the case of dominant hydrodynamic interaction, Q(Q) depends on the viscosity of the pure solvent, but on no molecular parameters and varies with the third power of Q, whereas with failing hydrodynamic interaction it is determined by the inverse of the friction per mean square segment length and varies with the fourth power of Q. 

The long-time behavior (Q(Q)t) > 1 of the coherent dynamic structure factors for both relaxations shows the same time dependence as the corresponding incoherent ones... 

Dynamics Simulation of a Glassy Polymer Melt Incoherent Scattering Function. 

Ishizaki A, Fleming GR (2009) Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer reduced hierarchy equation approach. J Chem Phys 130 234111... 

Huber D. L. (1981) Dynamics of Incoherent Transfer, Top. Appl. Phys. 49, 83-111. 

Now, the decay rate of the incoherent dynamic structure factor is proportional to fc(i+2v)/v xherefore, the -dependence of the decay rate for salt-free solutions is independent of whether the hydrodynamic interaction is present or not. 

Fig. 4.1 a Typical time evolution of a given correlation function in a glass-forming system for different temperatures (T >T2>...>T ), b Molecular dynamics simulation results [105] for the time decay of different correlation functions in polyisoprene at 363 K normalized dynamic structure factor at the first static structure factor maximum solid thick line)y intermediate incoherent scattering function of the hydrogens solid thin line), dipole-dipole correlation function dashed line) and second order orientational correlation function of three different C-H bonds measurable by NMR dashed-dotted lines)... 

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