Neutron spin echo experiment

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. 

The basic quantity measured by inelastic scattering techniques, such as dynamic light scattering or neutron spin echo experiments, is the mutual diffusion... 

Coo/ and Ne, Me these scales are fixed. This procedure was used for the data of Table 4.1. A direct and simple test is to compare for the bond fluctuation simulation from Table 4.1 with Fig. 4.9. The agreement and thus the consistency of different simulations is excellent. From this mapping, one finds that the crossover time varies considerably from one polymer to another as one would expect. Some typical values for are 5.5 x 10 s for PS at 485 K compared to 3.2 x 10 s for PTHF at a comparable temperature, 500 K. For PDMS at 273 K, = 4.1 x 10 s while it decreases to 1.7 X 10 s at 373 K. This sheds some hght on the long-standing discussion about whether neutron spin-echo scattering could be used to observe the predicted plateaus in S q, t) or not. The first spin-echo experiments were for PDMS and PTHF. From the estimates of Ref. 54 of for the temperatures of the experiments it became clear that the neutron spin-echo experiments on PTHF should have seen a deviation from the Rouse model which they did. However for PDMS this was not the case, since the times were beyond the resolution of the experiment, which was around 10 seconds at the temperature used. In both cases the q-range was sufficient in spite of some early concerns. Later experiments on p p 124,135,191 pj 135 pg (pEB 2)i24,i35 well defined cross-... 

In addition to the above techniques, inverse gas chromatography, swelling experiments, tensile tests, mechanical analyses, and small-angle neutron scattering have been used to determine the cross-link density of cured networks (240—245). Si soHd-state nmr and chemical degradation methods have been used to characterize cured networks stmcturaHy (246). H- and H-nmr and spin echo experiments have been used to study the dynamics of cured sihcone networks (247—250). 

Other possible direct probes are optical experiments similar to studies [113] of vesicles but expanded towards shorter A (20-30 A). Alternatively neutron spin-echo studies of stacked bilayer arrays, which can probe the 10-30 A range [114], might possibly be applicable here. Finally, the x-ray grazing-incidence technique has been shown to be a powerful tool for studying short wavelength fluctuations at fluid interfaces [100]. The application of this technique to the investigation of membrane surface fluctuations can reasonably be expected in the near future [115,116]. 

Most of the experiments reported so far have been performed on linear homopolymer systems. In Chap. 6 we discuss what has been achieved so far beyond such simple materials. We begin with the discussion of neutron spin echo data on miscible polymer blends, where the main issue is the dynamic miscibility . There are two questions Firstly, on what length and time scales and to what extent does a heterogeneous material like a blend exhibit homogeneous dynamics Secondly, how does it relate to the corresponding homopolymer properties ... 

Firstly, the essential correctness of the tube picture has only recently been established in a remarkable series of experiments. The complex monomer diffusive self-correlation predicted has now been seen in field-gradient NMR. Reptative motion across an interface was the only successful explanation of time-resolved neutron reflectivity. Neutron Spin Echo (NSE) can now be extended in time sufficiently to identify the tube diameter directly. A series of massive many-chain numerical simulations have shown tube-like constraints with sizes identical to those obtained by rheology via the plateau modulus Go and NSE). 

Figure 2.13 Schematic elastic scattering curve of a spherical colloid (e.g. a microemulsion droplet) in solution. As a rule of thumb q 1 is an approximate measure for the spatial resolution of the used scattering experiment. At low values of q (i.e. in the Cuinier region of the scattering curve) the overall size and shape of the particles as well as correlations between different particles can be monitored (typically by static and dynamic light scattering). At high values q, the internal structure of the particles, i.e. the local structure of the interfacial film is resolved (e.g. by neutron or X-ray small angle scattering and neutron spin-echo spectroscopy (NSE)).

Neutron spin-echo is an experimental technique which allows for quasi-elastic neutron scattering experiments with an extremely high energy resolution (in the range of neV). This is achieved by exploiting the magnetic moment of the neutrons. In a neutron spin-echo... 

Fig. 2. Time (x) and scattering vector (Q) raqge for various scattering experiments on dynamics SANS ILL spectrometers Dll and DI7 relaxation after stepstrain, cyclic experiments, steady couette shear. Elastic neutron scattering ILL spectrometer D20, also real time experiment. Neutron Spin Echo (NSE) ILL spectrometer, inelastic measurement and classical quasielastic light scattering (QELS) (from Ref. )...

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... 

Shapiro et al. (1985) have performed neutron-spin-echo (NSE) experiments in EUj,Sri S with x = 0.40 and x = 0.54 in order to further study the double transition PM FM and FM SG in x = 0.54. They observe no depolarization of the neutron beam for the SG sample x = 0.40), but in the RSG sample (x = 0.54) the beam partly depolarizes near T. It becomes more depolarized on cooling further into the FM phase but less depolarized in the SG state. The incomplete depolarization of the scattered beam confirms the absence of true long-range FM order below T. Thus, there is sufficient neutron polarization of the incident beam to perform the experiment at all temperatures. 

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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