NSE measurements

This paper reviews NSE measurements on polymer melts, networks and solutions, published since the first successful NSE study on polymers [16] was performed in 1978. The experimental observations are discussed in the framework of related microscopic models, scaling predictions or other theoretical approaches. 

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... 

The reduced characteristic frequencies Q(Q)/Q3, as obtained from NSE measurements, are plotted vs. Q for both systems in Fig. 54. The minimum, which occurs for the full stars, does not occur in the system, where the... 

NSE measurements at zero average contrast conditions on a symmetric diblock copolymer of H-PS and D-PS dissolved in an appropriate mixture of proto-nated and deuterated benzene are reported [171,172]. The measurements were performed at different concentrations c > c. For comparison, the interdiffusion of a corresponding blend of H-PS and D-PS homopolymers dissolved in deuterated benzene was studied, too [171]. Owing to the relatively low molecular masses, only the regime Q1/2 < 1 was accessible, and the internal modes could not be probed. 

In addition, NSE measurements have allowed confirmation of the relation between non-Debye behaviour and Q-dispersion of r eif (Eq. 4.11) proposed from the early BS studies of Sseif(Q,t) [148]. Figure 4.14b displays for PIB the characteristic times determined from the NSE experiments. The law pro-... 

The only currently existing theory for the glass transition is the mode coupling theory (MCT) (see, e.g. [95, 96, 106]). MCT is an approach based on a rather microscopic description of the dynamics of density fluctuations and correlations among them. Although the theory was only formulated originally for simple (monatomic) fluids, it is believed to be of much wider applicability. In this review we will only briefly summarize the main basis and predictions of this theory, focusing on those that can be directly checked by NSE measurements. 

Fig. 5.7 Relaxation rate F divided by for PDMS in toluene solution vs. the reduced variable T/ri. Results correspond to NSE measurements =0.1 (filled circle) and DLS for =0.1 (filled triangle), (p=0.07 (empty triangle) and =0.02 (empty diamond). Solid line shows a linear regression fit of the (p=0,l NSE and DLS data. (Reprinted with permission from [186]. Copyright 2001 American Chemical Society)...

Up to date the only published work on the dynamic structure factor of a glass forming system at intermediate length scales is a study on PIB [147]. The NSE measurements explored the Q-range 0.20[Pg.136]

As shown in Fig. 12, a monotonous decrease in the self-diffusion coefficient was measured by PPG NMR for a series of n-alkanes in Na-X [50]. A similar trend was observed in ZSM-5 by QENS. From the NSE experiments performed in 5A, one finds that Dt drops to a minimum at Cs and has a clear maximiun at Ci2. A similar variation is obtained for Do after correcting from the thermodynamic correction factor (the number of carbon atoms per cavity is the same). Recent PEG NMR results indicate also a small minimum for Ds at Cg and a small maximum at Cm [51]. The NSE data obtained for longer n-alkanes in 5A are in contradiction with simulations which predict increasing diffusivities from C12 to Ci7 [52] whereas a decreasing trend is observed (Fig. 12). Finally, the activation energies derived from the NSE measurements show a minimum for C12, in agreement with the explanation in terms of the window effect. These results are related to similar concepts such as resonant diffusion [53] or the levitation effect, which corresponds to a maximum in self-diffusivity when the size of the diffusant is comparable to the diameter of the void [54]. 

This concept was introduced in 1948 by Sondheimer and Kertesz who nsed pH values of 2 and 3.4 for analyses of strawberry jams. Since then, the nse of other pH values has been proposed. Fnleki and Francis (1968) used pH 1 and 4.5 bnffers to measure anthocyanin content in cranberries, and modifications of this techniqne have been applied to a wide range of commodities. The absorbance of anthocy-anins at two different pH levels (1 and 4.5) is measured at Kis-max and at 700 mn, which corrects for haze in the sample (Table 6.3.1). The total monomeric anthocy-... 

Optical Methods Reflectance and ellipsometry snffer from lack of a theory at the molecnlar level. The same is true for SERS and SHG. The main advances will be in the nse of far-IR spectroscopy and SFG. SFG measurements performed with femtosecond lasers open np new possibilities for time-resolved adsorbate stndies. 

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]. 

This is done in Fig. 15 where the viscosity is shown as a function of molecular mass. The open circles represent the predictions of the NSE result, whereas the filled circles represent the viscosity measurement. Both data sets are in excellent agreement and demonstrate the consistency of evaluation. 

Fig. 26. NSE spectra in polyethyleneo melts at 509 K in a Rouse scaling plot (o Q = 0.078 A-1 Q = 0.116 A-1 A Q = 0.155 A-1. Above Spectra in comparison to a fit of the generalized Rouse model [49]. Below comparison of the data with the predictions of the local reptation model [53] omitting the measurement points which correspond to the initial Rouse relaxation. The arrows indicate Q2/2V/Wxe. (Reprinted with permission from [39]. Copyright 1992 American Chemical Society, Washington)...

Obviously, in the case of PS these discrepancies are more and more reduced if the probed dimensions, characterized by 2ti/Q, are enlarged from microscopic to macroscopic scales. Using extremely high molecular masses the internal modes can also be studied by photon correlation spectroscopy [111,112], Corresponding measurements show that - at two orders of magnitude smaller Q-values than those tested with NSE - the line shape of the spectra is also well described by the dynamic structure factor of the Zimm model (see Table 1). The characteristic frequencies QZ(Q) also vary with Q3. Flowever, their absolute values are only 10-15% below the prediction. 

The crossover from 0- to good solvent conditions in the internal relaxation of dilute solutions was investigated by NSE on PS/d-cyclohexane (0 = 311 K) [115] and on PDMS/d-bromobenzene(0 = 357K) [110]. In Fig. 45 the characteristic frequencies Qred(Q,x) (113) are shown as a function of t = (T — 0)/0. The QZ(Q, t) were determined by fitting the theoretical dynamic structure factor S(Q, t)/S(Q,0) of the Zimm model (see Table 1) to the experimental data. This procedure is justified since the line shape of the calculated coherent dynamic structure factor provides a good description of the measured NSE-spectra under 0- as well as under good solvent conditions. 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

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