Small-angle neutron scattering data

Small-angle neutron scattering (SANS) of labelled (deuterated) amorphous samples and rubber samples detects the size of the coiled molecules and the response of individual molecules to macroscopic deformation and swelling. It has been shown that uncrosslinked bulk amorphous polymers consist of molecules with dimensions similar to those of theta solvents in accordance with the Flory theorem (Chapter 2). Fernandez et al (1984) showed that chemical crosslinking does not appreciably change the dimensions of the molecules. Data on various deformed network polymers indicate that the individual chain segments deform much less than the affine network model predicts and that most of the data are in accordance with the phantom network model. However, defmite SANS data that will tell which of the affine network model and the phantom network model is correct are still not available. 

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Fig. 53. Small-angle neutron scattering data from the 12-arm polystyrene star PS120A (Mw = 1.49 x 105) where the 11 deuterated arms were matched by the solvent THF. In order to demonstrate the asymptotic Q behavior, the data are plotted in a generalized Kratky representation (Iq01 vs. Q with a = 1.5 and 5/3). The solid line marks the high Q-plateau. (Reprinted with permission from [149]. Copyright 1989 American Chemical Society, Washington)...

In Table III, results from this work and small angle neutron scattering data (SANS) of mixtures of d-PS in PPE and d-PPE in PS are given. Since X23 (=vi/v2 X23 ) is... 

The Debye function describes the q dependence of scattering data from dilute solutions of ideal chains. Such dilute solutions can either be obtained in a (9-solvent or by having a dilute solution of ordinary chains in a melt of perdeuterated chains. Small-angle neutron scattering data for four dilute concentrations of poly(methyl methacrylate) (PMMA with 2.50 000 g/mol ) in perdeuterated PMMA are shown to be fit by the Debye... 

Small-angle neutron scattering data lit to the Debye function multiplied by a zero wavevector scattering. Data are for 0.31% (circles), 0.63% (squares), 0.93% (triangles), and 1.19% (upside down triangles) PMMA with... 

Small-angle neutron scattering data for a semidilute solution of polystyrene (M = 1 100000 gmol ) in CS2 with i" = 0.025g/mr 2.5c. The curve is... 

This finding is quite important in the study of chain-folding mode in the lamella. The D and H chain stems are statistically randomly distributed in the lamella as clarified by the quantitative interpretation of the infrared band profile. The thermal data and the wide-angle and small-angle neutron scattering data also support this concept. Lrom all these data, we concluded that the PE chains show almost perfectly random reentry mode when crystallized from the melt, as far as a pair of DHDPE and LLDPE(2) is concerned. 

G. D. Wignall and F. S. Bates, Absolute calibration of small-angle neutron scattering data,-/. Appl Crystallogr. 20 28(1987). 

Such definitive forecasts do not result from the theories of Leibler or Hong and Noolandi. However, the latter theory describes in detail the phase diagram for copolymer — homopolymer mixtures and is therefore pertinent to the X-ray work of Roe Similarly, Leibler s theory provides a detailed description of a microphase separation mechanism and thus is of value in the interpretation of experiments investigating this phenomenon. Small angle neutron scattering data reported to date has been maitily concerned with pure styrene-diene block copolymers which are fully microphase separated and thus examined D, dj, and interfadal layer thickness as a function of molecular weight and composition and therefore comparison has usually been made with the MIA theory of Helfand. 

Fig. 15. Small angle neutron scattering data for SB,3 (O), SB7 (A) and a mixture of the two ( ) where the interference function scattering has been contrast matched out. Ref.

Values for the extension ratios, estimated by Kramer and colleagues [36, 42] and also by Ward and co-workers [18, 22] from analysis of optical interference patterns, compare reasonably well with estimates of the network extensibility from small-angle neutron scattering data [36] or stress-optical measurements [43]. It was therefore proposed that the criterion for craze failure, and hence crack propagation via a craze, is to assume that the entangled strands crossing the section of the craze at the crack tip break due to the development of the critical stress at the crack tip cTfaii,... 

Figure 3 Small-angle neutron scattering data of protonated PS dissolved In deuterated PS plotted as Zimm plot. Squares c=0.5% circles c=5%. The data were taken from WIgnall, G. D. Ballard, D. G. H. Schelten, J. J. Macromol. Sci. Phys. 1976, B12, 75. ...

The small-angle neutron scattering data for condensed amorphous polymers can be further analyzed by discussing the ratio For unperturbed chain dimension... 

Digital reconstruction of silica gels based on small angle neutron scattering data. 

Figure 7.7 Small-angle neutron scattering data r 0) versus 7 identifying the spinodal and the binodal temperatures, (a) / (O) versus 7 schematically (b) An experimental example of a polymer blend of polystyrene (PS) and...

MD simulations have also been performed for other polyolefin blends. Good agreement was found with small angle neutron scattering data of Krishnamoorti et al. [123, 124] on blends of poly(isobutylene) (PIB) with head-to-tail and head-to-head polypropylene (hhPP) [125]. In addition, MD simulations have been performed on all of the binary blends of PIB, iPP, sPP, hhPP, and PE [125]. 

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