Neutron-spin-echo measurements

Fig. 3.11 Dynamic structure factor for a PB melt at 353 K (M =l,600) obtained from simulation (lines) and neutron spin echo measurements (symbols). The Q-values are given adjacent to the respective lines. (Reprinted with permission from [55]. Copyright 2000 Elsevier)...

In this subsection, the theoretical background for SANS and neutron spin-echo measurements carried out with o/w- and w/o-droplet microemulsions will be presented. According to Milner, Safran and others, shape fluctuations in droplet microemulsions can be described in terms of spherical harmonics [42-44]. This offers the possibility to calculate a dynamic structure factor S(q,w) or its Fourier transform, i.e. the intermediate scattering function I(q,t) for the problem, which can be used to analyse dynamical measurements by neutron spin-echo spectroscopy [45]. For the scattering from thin shells I(q,t) was calculated [43]... 

The bending modulus k is measured by techniques such as monitoring the thermal undulations of membranes [89-94], probing the low-tension stress-strain relation [95], X-ray scattering [96-99], neutron spin echo measurements [100-102] (note however the caveats raised by Watson and Brown [103]), or pulling thin... 

Fig.10. Intermediate scattering functions 7(Q,t)/7(Q,0) of polybutadiene (PB) obtained by neutron spin echo measurements, which are scaled to a master curve using a shift factor Uj evaluated from the viscosity. Inset shows the temperature dependence of the non-ergodic factor, which is a fraction of the a-process. (Reprinted with permission from [80], Copyright 1988 American Physical Society, New York)...

Richter et al. carried out neutron spin echo measurements at the minimum position of S(Q) on the same polymer (PB) as that described above [82]. The intermediate scattering functions were described by a stretched exponential function as well, but could not be scaled to a master curve using a shift factor a-j. The relaxation times extracted from the observed stretched exponential functions are plotted in the relaxation time map in Fig. 9, from which it is seen that they deviate from the relaxation time of the a-process and the temperature dependence of Tjg is well described by the Arrhenius formula. It was confirmed that the process observed in PB at the minimum position Q ,j in S(Q) is the JG process. The fact that the JG process is observed at Q jjj suggests that the process is not a cooperative motion but an isolated one. 

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

Via small angle neutron scattering in the melt. Measured by neutron-spin-echo. Measurement at 435 K... 

In this review we consider large-scale polymer motions which naturally occur on mesoscopic time scales. In order to access such times by neutron scattering a very high resolution technique is needed in order to obtain times of several tens of nanoseconds. Such a technique is neutron spin echo (NSE), which can directly measure energy changes in the neutron during scattering [32,33]. 

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]. 

In the neutron spin echo technique, the normalized intermediate dynamic structure factor I(q,t)/I(qfi) is measured directly. This method has been used to probe... 

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)).

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 . 

Higgins et al. measured f) for polytetrahydrofuran in CSj and in the melt. Measurements were taken on both the conventional back-scattering spectrometer, giving S(Q,w), and the new neutron spin echo spectrometer (NSE), which measures S Q,t) directly. The agreement between the two sets of data was good and it was found that in solution and Q J- - - in the melt, with the melt values... 

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. )...

Information about the elasticity can be obtained using a variety of scattering methods. Small-angle scattering is mainly used for systems with small interlamellar spacing [75,77-82], whereas light scattering can be applied for the study of swollen systems [76,83,84]. Neutron spin-echo spectroscopy has also been used to directly measure the bilayer dynamics in lamellar liquid crystalline phases [85-87]. 

Richter and coworkers [80] have measured normalized intermediate scattering functions I Q,t)/I(Q,0) from the a-process of PB using a neutron spin echo technique in a temperature range between 200 K and 280 K above the glass transition temperature (Tg=181 K). These measurements were performed at a first maximum position (=1.48 A ) of the structure factor S(Q). They found that... 

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).

---