X-ray and neutron scattering data

The importance of the pore size in Prussian blue analogues is supported by differential pair distribution function analysis of X-ray and neutron scattering data of hydrogen- and deuterium-loaded Mn3[Co(CN)6]2 [119]. This shows that no evidence for adsorption interactions with unsaturated metal sites exists and that the hydrogen molecules are disordered about the center of the pores defined by the cubic framework. In conclusion, experimental results indicate that optimum pore dimensions in Prussian blue analogues are predominantly responsible for the heat of adsorption at low loadings rather than the polarizing effect of open metal sites. 

This point of interest is brought forward by the RISM approach to the structure of molecular liquids, and a RISM model with HNC closure supports a similar result for the excess chemical potential in terms of atom-atom correlations (Singer and Chandler, 1985 Hirata, 1998). RISM - reference interaction site model - is an acronym that refers to a class of theories for the joint two-atom distributions in molecular liquids. The most basic decision of RISM models is that theories of molecular liquids should focus first on the atom-atom distributions extracted from X-ray and neutron scattering data rather than more complex possibilities this highly practical point was not so obvious in an earlier epoch when models of molecular liquids were scarcely realistic on an atomic scale. That basic decision was encapsulated by invention of a site-site (or atom-atom) Ornstein-Zernike (SSOZ) (Cummings and Stell, 1982) equation that involved intramolecular atom-atom correlations. The original suggestions (Chandler and Andersen, 1972) were sufficiently successful as to support subsequent flamboyant developments, and to be substantially impervious to more fundamental improvements (Chandler et al, 1982). For these reasons a full discussion of the RISM models wouldn t fit here. Fortunately, a devoted exposition of current RISM work is already available (Hirata, 1998). 

T. P. Russell, J. S. Lin, S. Spooner, andG. D. Wignall, Intercalibration of small-angle x-ray and neutron scattering data,/.24pp/. Crystlh 629(1988). 

The presence of p r -bonded phenylene rings in the main-chain construction increases the complexity of the intrachain structure. Extended n conjugation is best achieved if the polymer chains adopt a fully planar conformation. However, the steric repulsion between, in the case of PPV, adjacent vinylene and phenylene ring hydrogen atoms favors a nonplanar construction. In PPP these effects become even more pronounced. To further quantify the degree of nonplanarity, structure factor refinements of X-ray and neutron scattering data have been used. In PPV [43] and PPP [ 10] the room temperature mean ring deviation from planarity, defined by H in Fig. 25.5, is found to be approximately 5° and 10°, respectively. 

Flory and his co-workers have developed a theoretical procedure for the RIS interpretation of small and intermediate angle X-ray and neutron scattering data. The scattering function P(s) for a system of independent molecules oriented at random is generally given by... 

For surface scattering the derivation of a D-W factor has been considered by a number of researchers (see, e.g., refs. [67, 68, 69]). Previously the theory had been primarily developed for including the effect of inelastic motion in the interpretation of X-ray and neutron scattering data [70]. 

Kumar, S. and Pineri, M. (1986) Interpretation of small angle X-ray and neutron scattering data for perfluorosulfonated ionomer membranes, J. Polym. Sci. Polym. Phys. Ed., 24, 1767-1782. 

For the pair styrene/isoprene, various other dependences of x or temperature have been reported in the literature, which give values of x that at 100°C differ by almost a factor of two, from 0.06 to around 0.14 (see Fig. 13-3) (Lin et al. 1994 Han et al. 1995). These estimates of x ot obtained by direct calorimetric measurements (the energetic effects are too minute to measure), but by fitting the predictions of thermodynamic theories (such as that of Leibler or Fredrickson and Helfand see below) to x-ray or neutron scattering data for diblock copolymers or blends. The values of / thereby obtained are only as accurate as the theories to which the data are fitted. 

AlCl3-A-butylpyridinium chloride, AlCl3-l-ethyl-3-methylimidazolium chloride, HCl-l-ethyl-3-methylimidazolium chloride, and AlCl3-LiSCN mixtures have been studied using X-ray and neutron scattering [164-167]. These studies have provided information about the specific interactions between anions and cations within the ILs. Unfortunately, little additional information could be extracted from the data. In particular, no information about the structure of the respective ILs beyond the first coordination sphere could be obtained. Importantly, however, the authors show that in AlCl3-LiSCN, the N and not the S atom of the SCN ion coordinates to the Al ion. This was explained with a hard base/hard acid interaction which can be expected for a Lewis acid compound like A1C13. 

Except for the fullerenes, carbon nanotubes, nanohoms, and schwarzites, porous carbons are usually disordered materials, and cannot at present be completely characterized experimentally. Methods such as X-ray and neutron scattering and high-resolution transmission electron microscopy (HRTEM) give partial structural information, but are not yet able to provide a complete description of the atomic structure. Nevertheless, atomistic models of carbons are needed in order to interpret experimental characterization data (adsorption isotherms, heats of adsorption, etc.). They are also a necessary ingredient of any theory or molecular simulation for the prediction of the behavior of adsorbed phases within carbons - including diffusion, adsorption, heat effects, phase transitions, and chemical reactivity. 

X-ray and neutron scattering has been applied to a number of neutral and polyanionic polysaccharides, namely starch granules [215,216], heparin [217-220], amylose [221], hyaluronic acid [213], and chondroitin sulphate [213]. Neutron matchpoints were reported for starch (50% H20), hyaluronate (51% H20) and chondroitin sulphate (60 5% H20). Both types of polysaccharides are usually analysed in terms of extended worm-like chain structures in solution. Data are commonly represented as cross-sectional R s values (typically around 1 nm) and... 

Fig. 1.30 The radial distribution function for water obtained from X-rays and neutron scattering [based on data from Narten and Levy (1971) and Soper (2000)].

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