Neutron Spin Echo Results

In Fig. 3.3 the corresponding NSE spectra are plotted against the scaling variable of the Rouse model. As predicted by Eq. 3.18 the results for the different momentum transfers follow a common straight line. 

Recently it also became possible to observe directly the incoherent cross section of a protonated chain. As eluded to in Sect. 2.2, incoherent scattering 

The data follow the scaling prediction with satisfying precision. The small deviations are related to the translational diffusion of the chains. This becomes evident from Fig. 3.7, where the obtained relaxation rates IXQ) are plotted versus Q in a double logarithmic fashion. The dashed line gives the Rouse prediction JoeWhile at larger momentum transfers the experimental results follow this prediction very well, towards lower Q a systematic relative increase of the relaxation rate is observed. Including translational diffusion, we have  

The solid lines in Fig. 3.7 represents the prediction of Eq. 3.27. Perfect agreement is obtained. 

The above expressions provide a universal description of the dynamics of a Gaussian chain and are valid for real linear polymer chains on intermediate length scales. The specific (chemical) properties of a polymer enter only in terms of two parameters N =Rl and The friction parameter is gov- 

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Neutron Spin Echo Results on Chain Confinement... 

Neutron Spin Echo Results in Polymer Blends... 

This section presents results of the space-time analysis of the above-mentioned motional processes as obtained by the neutron spin echo technique. First, the entropically determined relaxation processes, as described by the Rouse model, will be discussed. We will then examine how topological restrictions are noticed if the chain length is increased. Subsequently, we address the dynamics of highly entangled systems and, finally, we consider the origin of the entanglements. 

Fig. 4. Neutron spin echo spectra for the self-(above) and pair-(below) correlation functions obtained from PDMS melts at 100 °C. The data are scaled to the Rouse variable. The symbols refer to the same Q-values in both parts of the figure. The solid lines represent the results of a fit with the respective dynamic structure factors. (Reprinted with permission from [41]. Copyright 1989 The American Physical Society, Maryland)...

In this review we will present the outcome of NSE studies on polymer systems covering results beyond those reported in an earlier review in Advances in Polymer Science [5] eight years ago. Table 1.1 shows the chemical structure and information on the chain dimensions of the systems considered here. In Chap. 2 we will commence with a brief description of neutron scattering principles and a discussion of the two different ways neutron spin echo may be implemented - the traditional NSE approach with precession coils and the neu-... 

It thus appears that in real zeolite crystals diffusion over long distances reflects the influence of surface and internal barriers rather than the pore structure of the idealized framework. As a result the apparent intracrystalline diffusivities often show a strong dependence on the length scale of the measurement. Measurements by QENS and neutron spin-echo methods over distances corresponding to a few unit cells often approach the theoretical values derived by MD calculations for an ideal lattice. Similar values are often obtained by PEG NMR when the measurement is made over short distances. Measurements by most macroscopic methods are on the length scale of the crystals, and these tend to yield lower apparent diffusivities as a consequence of the intrusion of surface barriers and internal resistances due to structural defects. 

Abstract Neutron scattering was first used to derive the self-diffusivities of hydrocarbons in zeolites, but transport diffusivities of deuterated molecules and of molecules which do not contain hydrogen atoms can now be measured. The technique allows one to probe diffusion over space scales ranging from a few A to hundreds of A. The mechanism of diffusion can, thus, be followed from the elementary jumps between adsorption sites to Lickian diffusion. The neutron spin-echo technique pushes down the lower limit of diffusion coefficients, traditionally accessible by neutron methods, by two orders of magnitude. The neutron scattering results indicate that the corrected diffusivity is rarely constant and that it follows neither the Darken approximation nor the lattice gas model. The clear minimum and maximum in diffusivity observed by neutron spin-echo for n-alkanes in 5A zeolite is reminiscent of the controversial window effect . 

FIGURE 13.3 Comparison of results (data with error bars) for normalized dynamic structure factors near obtained from neutron spin echo experiments on deuterated samples with MD simulation data (open circles) at the same Q value [39]. Timescales for the experimental data were shifted-15 K in (see text). Source Narros et al. [39]. Reprinted with permission of AIP Publishing LLC. 

In the Introduction it was mentioned that most other techniques are imsuitable to study melts in the range T, Welding studies (t and selMifiFusion experiments (t > were reviewed by de Gennes together with results from other techniques for solutions and also for long times. Neutron Spin Echo suffers from an... 

Fig. 50. Spin relaxation in CuMn 5 atom% spin glass at various temperatures. Data points at times shorter than 10 s tvere directly measured by neutron-spin-echo technique at = 0.093 A" (Mezei and Murani 1979), those beyond 10 s were calculated from ac susceptibility results (Tholence 1980). The lines are guides to the eye only (from Mezei 1983).

Results from neutron spin-echo measurements on the insulating Eu Srj S compounds will be described briefly in sec. 8. 

This chapter has considered measurements of the dynamic structure factor S q, t) of polymer solutions. Here behaviors of the first cumulant, the polymer slow mode, and the high-frequency Rayleigh-Brillouin spectrum have been considered. Neutron spin-echo methods as supplements to light scattering spectroscopy were noted. Results on Ki and the Rayleigh-Brillouin spectrum are readily summarized. The discussion of the slow mode is considerably more extended, but leads to a comparison with modem models for glass formation. 

Hans launched the constmction of the first time-of-flight reflectometer at the ILL He performed the first magnetic reflectometry studies on a prototype reQ lometer. His research interest includes the development of reQ lometry usmg the zero-field neutron spin-echo method. His studies resulted in about 190 publications as author or coauthor. 

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... 

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