Neutron Spin Echo Technique

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]. 

Unlike these conventional techniques, NSE measures the neutron velocities of the incident and scattered neutrons using the Larmor precession of the neutron spin in an external magnetic field, whereby, the neutron spin vector acts like the hand of an internal clock, which is linked to each neutron and stores the result of the velocity measurement at the neutron itself. The velocity measurement is thus performed individually for each neutron. For this reason, the 

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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. 

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... 

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 . 

Coherent and isotopic-incoherent scattering involve no spin-flip, whereas spin incoherent scattering (i.e., for hydrogenated molecules) inverts the neutron spin with a probability of 2/3. Since spin-polarized neutrons are used in the neutron spin-echo technique, the polarization of the neutron beam, after spin-incoherent scattering woifld be reversed and three times less intense. 

Similar to the PPG NMR method, neutron scattering techniques are successfully employed for the determination of diffusivities under equihbrium conditions. These techniques and their apphcation are discussed in Chapter 5 by H. Jobic. Particularly efficient is a novel combination of quasi-elastic neutron scattering (QENS) and a neutron spin-echo technique (NSE), which considerably expands the range of accessible diffusivities, viz. down to 10... 

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).

Fig. 92. Time correlation function, S(q,e)/S(q,0), for EUjSrj. S as measured for the SG compound (x = 0.40) and the RSG compound (x = 0.54) for q = 0.072 A at various temperatures by the neutron spin-echo technique (from Shapiro et al. 1985).

Neuutn scattering is often perftrmed as a function cf particle concentration to determine specific interactions between components. Blends cf metallocene synthesized polyolefins (32) and efi ds cf solvent on dendrima- size (33) have been studied using SANS. Interface widths between two polymer blend components in the melt have been studied by neuu-on reflectivity (34). Dynamic studies have been undertaken on bimodal melts (35) using neutron spin echo techniques. Some of these recent developments will be reported in ttie following chrqiters. 

The highest energy resolution is obtained by using the neutron spin echo technique. In this type of instrument, the velocities of neutrons incident on, and scattered from, a sample are coded as the number of Larmor precessions that the neutron spins undergo in a well-defined applied magnetic field. The method requires a beam of polarized neutrons with a distribution of velocities. As indicated in Figure 7, these neutrons enter the precession-field region with their spins perpendicular to the field. As a neutron... 

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]. 

Anticipating further discussions on micro-emulsions, planned for volume V, it is noted that k, or k, or the combination (2kj -i- k ) can also be obtained using scattering techniques or, preferably, combinations thereof. For instance, neutron spin echo spectroscopy (NSES) can be combined with small-angle neutron scattering (SANS) or with dynamic light scattering. Alternatively, 2k + k can be obtained from the polydispersity of the micro-emulsion and then a second type of... 

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... 

Hayter, J.B. (1981) Quasielastic neutron spin-echo spectroscopy. In S.-H. Chen, B. Chu and R. Nossal. (eds), Scattering Techniques Applied To Supramolecular and Nonequilibrium Systems. Plenum, New York, pp. 3-33. 

Among other topics that can now be studied are the distribution of polymer segments at an interface, the dynamics of water adsorbed in clays and lamellar liquid crystals, and, using the more recent technique of neutron spin echo , the diffusion of colloidal particles and its dependence on particle concentration. 

Quasi-elastic techniques can also be applied to other types of scattering. For example, as facilitated by the spin echo technique, the method may be may be applied to neutron scattering to look at mobility of smaller regions at larger wavelength light. Isotropic labeling permits studies of motions of selected parts of molecules. 

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... 

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