Neutron scattering quasi-elastic

The first and the second diffusion coefficients, Ddif and Diep are defined by relations (5.11) and (5.20), respectively. The two competing mechanisms have a different length dependence of the self-diffusion coefficient 

One can see from the comparison of equations (5.10) and (5.19) that the reptation motion of the macromolecules is revealed at the condition 

This relation determines a molecular weight M at which the mechanism of diffusion changes. To determine the dynamic transition point M, which separates the strongly entangled (M M ) and weekly entangled (M M ) systems, one considers the parameter B to be dependent on x and, taking equations (3.17) and (3.25) into account, finds a solution of the equation 

It is not difficult to solve this equation, taking empirical value S = 2.4 into account, and estimate the number value of the transition point between weakly and strongly entangled systems as 

This is the point, above which the reptation mechanism of diffusion predominates. 

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The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

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)]. 

Quantum-chemical cluster models, 34 131-202 computer programs, 34 134 methods, 34 135-138 for chemisorption, 34 135 the local approach, 34 132 molecular orbital methods, 34 135 for surface structures, 34 135 valence bond method, 34 135 Quantum chemistry, heat of chemisorption determination, 37 151-154 Quantum conversion, in chloroplasts, 14 1 Quantum mechanical simulations bond activation, 42 2, 84—107 Quasi-elastic neutron scattering benzene... 

To date, incoherent quasi-elastic neutron scattering experiments on the a-relaxation regime of glass-forming polymers have revealed the following main features for the self-motion of hydrogens ... 

The application of neutron spin-echo spectroscopy to the analysis of the slow dynamics of biomolecules is still in its infancy, but developing fast. The few published investigations either pertain to the diffusion of globular proteins in solution [332-334] or focus on the internal subnanosecond dynamics on the length scale, <10 A as measured on wet powders [335,336]. The latter regime overlaps with other quasi-elastic neutron scattering methods as backscattering and TOE spectrometry [337-339]. 

A primary hydration number of 6 for Fe + in aqueous (or D2O) solution has been indicated by neutron diffraction with isotopic substitution (NDIS), XRD, 16,1017 EXAFS, and for Fe " " by NDIS and EXAFS. Fe—O bond distances in aqueous solution have been determined, since 1984, for Fe(H20)/+ by EXAFS and neutron diffraction, for ternary Fe " "-aqua-anion species by XRD (in sulfate and in chloride media, and in bromide media ), for Fe(H20)g by neutron diffraction, and for ternary Fe -aqua-anion species. The NDIS studies hint at the second solvation shell in D2O solution high energy-resolution incoherent quasi-elastic neutron scattering (IQENS) can give some idea of the half-lives of water-protons in the secondary hydration shell of ions such as Fe aq. This is believed to be less than 5 X I0 s, whereas t>5x10 s for the binding time of protons in the primary hydration shell. X-Ray absorption spectroscopy (XAS—EXAFS and XANES) has been used... 

H-n.m.r. [71], quasi-elastic neutron scattering [72], frequency response [73] and piezometric sorption uptake [34]. On the other hand, theself-consistency of data reported in [4,39,66,67] suggests further analysis of phenomena, probably interfered with bothithe samples and the experimental techniques used. 

Estimates of the rotational diffusivity may be made from MD calculations by fitting an exponential function to Legendre polynomials that express the decorrelation of a unit vector that is fixed in the methane coordinate frame (11). The rotational diffusivity was found to increase with concentration (as a result of sorbate-sorbate collisions which act to decorrelate the molecular orientation). The values are of the same order as those for liquid methane and are 2 orders of magnitude larger than those found by Jobic et al. (73) from a quasi-elastic neutron scattering study of methane in NaZSM-5. 

In this section we shall show that the joint use of RMT and AEP succeed in explaining the strong deviation from Pick s law observed in quasi-elastic neutron scattering experiments, that is, the appearance of super-Bumett coefficients. ... 

To compare the calculated values of the linewidth of the principal Lorentzian Xg(A ) with those obtained by quaa-elastic neutron scattering, we have carri out the calculation using the same k values as in these experiments. The calculated Xo(A ) values and the experimental linewidth A (k ) of the corrected quasi-elastic neutron-scattering line are shown in Fig. 12. The calculated deviation from Pick s law appears to be higher than... 

Furthermore, in the picture of this chapter also, the appearance of more than one Lorentzian curve in the spectrum of the quasi-elastic neutron scattering (a result which has been recendy confirmed by Teixeira et al. ) is related to the H-bond dynamics, whereas Teixeira et al. ascribe this effect to the orientational part of the intermediate scattering function. We believe that both physical causes can contribute to this effect. 

In the present study, we have made X-ray diffraction, neutron diffraction with isotopic substitution, and quasi-elastic neutron scattering measurements on highly concentrated aqueous solutions of lithium halides in a wide temperature range from room temperature to below glass transition temperature, from which the microscopic behaviors of the static structure and dynamic properties of the solutions are revealed with lowering temperature. The results obtained are discussed in connection with ice nucleation, anisotropic motion of water, crystallization, and the partial recovery of hydrogen bonds. 

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