Time-Resolved Small-Angle X-Ray Scattering

Johan E. ten Elshof, Rogier Besselink, Tomasz M. Stawski, and Hessel L Castricum 

The small-angle X-ray scattering (SAXS) technique is widely used to probe the microstructure, interactions, and transformations in sol-gel and related colloidal systems, in both precursor-hydrolyzed and condensed forms, as well as during crystallization. 

The scattering contrast of X-rays originates from local spatial fluctuations of the electron density, either continuous or particulate in nature, within a medium. Local electron densities depend mainly on the atomic number of the 

The Sol-Gel Handbook Synthesis, Characterization, and Applications, First Edition. 

and EXAFS and ex situ methodologies such as electron microscopy (SEM and TEM) are also powerful and important tools in the investigation of the mechanisms by which materials form. Combination of experimental approaches not only facilitates their interpretation but also enables cross-correlation between experimental phenomena. This is especially important because SAXS provides information on reciprocal space. The estimation of the structure of a scatterer from its scattering profiles is called the inverse scattering problem, and this problem cannot be solved uniquely [1]. Scattering profiles are complicated further when polydispersity effects are operative, which is usually to some extent the case for sol-gel systems. In practice, the interpretation of SAXS patterns therefore depends heavily on the development of hypothetical structural models and on comparison of the simulated scattering profile, which can be calculated from a given structure, with the experimental profile. Hence, additional independent structural or chemical information may aid in the interpretation of SAXS profiles. 

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Fig. 16. Time-resolved small-angle X-ray scattering patterns from polyethylene sheet recorded during stretch (12 mm/min, 32% stretch/min) in the horizontal direction. An exposure time for each pattern was 1 s. Intervals between exposures were 70 s. An X-ray wavelength was 0.155 nm...

Fig. 18. Time-resolved small-angle X-ray scattering patterns from polypropylene sheet under quick stretch in the horizontal direction. A speed of stretch was 233 mm/min (367 % stietch/min). An exposure time for each pattern was 0.1 s. Intervals between exposures were 0.2 s. An X-ray wavelength was 0.155 nm. A slight deformation of the symmetric SAXS pattern was already observed in the second patterns, suggesting some degree of orientation was brought about in quite an early stage. The SAXS patterns changed abruptly and drastically in the sixth pattern just when the sample began to yield (when the tension began to decrease).

Mesostructured aluminophosphate / surfactant composite materials were prepared from aqueous and alcoholic systems. Syntheses in ethanol or methanol, respectively, lead to mixtures of two nanostructured phases. One of these consists of hexagonally arranged rod-like assemblies of the surfactant molecules with the head groups located in the centres, encapsulating the inorganic aluminophosphate the other is lamellar. The syntheses were monitored by in-situ temperature- and time-resolved small angle X-ray scattering (SAXS). 

Hashimoto, T. (1985). Time resolved small-angle X-ray scattering studies on kinetics and molecular dynamics of order-disorder transition of block polymers. In Physical optics of dynamic phenomena and processes in macromolecular systems, (ed. B. Sedlacek), p. 106. Walter de Gruyter, Berlin. 

Lamb, J., Kwok, L., Qiu, X. Y., Andresen, K., Park, H. Y., and Pollack, L. (2008). Reconstructing three-dimensional shape envelopes from time-resolved small-angle X-ray scattering data.J. Appl. Crystallogr. 41, 1046—1052. 

Segel, D. J., Bachmann, A., Hofrichter, J., Hodgson, K. O., Doniach, S., and Kiefhaber, T. (1999). Characterization of transient intermediates in lysozyme folding with time-resolved small-angle X-ray scattering. J. Mol. Biol. 288, 489—499. 

Coimolly S, Fullam S, Korgel B, Fitzmaurice D (1998) Time-resolved small-angle X-ray scattering studies of nanocrystal superlattice self-assembly. J Am Chem Soc 120 2969-2970 deGroot F (2001) High-resolution X-ray emission and X-ray absorption spectroscopy. Chem Rev 101 1779-1808... 

This article is intended to give a survey of the application of synchrotron radiation (S.R.) in polymer science. Although several experimental techniques exist in the field of polymer physics and chemistry which could exploit the advantages of S.R., the main effort lies on the various X-ray scattering methods. Especially numerous time resolved small-angle X-ray scattering measurements facilitated by S.R. for the first time and many questions that have been answered by these experiments. 

Lee B, Shin TJ, Lee SW, Yoon J, Kim K, Ree M (2004) Secondary crystallization behavior of poly (ethylene isophthalate-co-terephthalate) time-resolved small-angle X-ray scattering and calorimetry studies. Macromolecules 37 4174 184... 

Schmolzer S, Grabner D, Gradzielski M, Narayanan T. MiUisecond-range time-resolved small-angle x-ray scattering studies of micellar transformations. Phys Rev Lett 2002 88 258301. 

Time-Resolved Small-Angle X-Ray Scattering Electron density Probability density... 

Ogasawara, T., Izawa, K., Hattori, R, Okabayashi, H., and O Connor, C.J. (2000) Growth process for fractal polymer aggregates formed by perfluorooctyltrimethoxysilane time-resolved small-angle X-ray scattering study. Colloid Polym. Set, 278,... 

Krakovsky, I., Urakawa, H., Kajiwara, K., and Kohjiya, S. (1998) Time resolved small angle X-ray scattering of inorganic-organic gel formation kinetics. /. Non-Cryst. Solids, 231, 31-40. 

Figure 11.15 Time-resolved small-angle X-ray scattering data for isothermal crystallization of a poly(ethylene-Z -(ethylene-fl/Cpropylene)) diblock copolymer. Each trace represents the intensity integrated over 6 seconds and is corrected, where q = (4 r/A) sinO, X is the radiation wavelength, and 20 is the scattering angle. Reprinted with permission from Reference [115]. Copyright 1995 American Chemical Society.

Sari MG, Stribeck N, Moradian S, inolebadi A, Bastani S, Botta S (2013) Correlation of nanostructural parameters and macromechanical behaviour of hyperbranched-modified polypropylene using time-resolved small-angle X-ray scattering measurements. Polym Int 62 1101-1111... 

Figure 4. Time-resolved small angle X-ray scattering observed from the ET-PTMO/TEOS mixtures during the sol-gel process...

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