SAXS Theories

It is well known in SAXS theory that isolated nuclei give a significant scattering intensity at a small scattering vector (q). The range of q between c/i and q2 will be simply denoted as c/n> i.e.,... 

SAXS has proved to be a very powerful tool for a quantitative analysis of the craze microstructure. This is not surprising since characteristic craze parameters such as the fibril diameters and the interfibrillar spacings frequently fall into the range of 1-5 X 10 nm covered by SAXS. The general theory of SAXS has extensively been treated in the literature (see e.g. Some basic elements of the SAXS theory,... 

Literature at a glance. Static investigations of strained polymer materials are, in fact, the earliest demonstrations of the SAXS method [7-9]. Tb this day, fibers and other nanocomposite materials are subjected to mechanical tests and investigated by X-ray scattering. Results of such experiments have fostered important developments in the field of SAXS theory. As an example, the fundamental work of Porod [10,11], Bonart [12-14] and Vonk [15] shall be mentioned. 

The most commonly investigated classes of sol-gel materials are silica, organically modified silica, template-directed mesostructured silica, titania and titania-based materials, zirconia and zirconia-based materials, and few others. After a brief overview of SAXS theory and some experimental details, each of these classes is discussed separately. 

Chapter2 briefly reviews the SAXS theories. The experimental works are explained in Chap. 3. Chapter4 is dedicated to the description of data evaluation methods. The results and discussions are covered in three separate Chaps. 5- 7 according to the studied materials. Finally, Chap. 8 summarizes the results and gives suggestions for future works. 

Scattering and Disorder. For structure close to random disorder the SAXS frequently exhibits a broad shoulder that is alternatively called liquid scattering ([206] [86], p. 50) or long-period peak . Let us consider disordered, concentrated systems. A poor theory like the one of Porod [18] is not consistent with respect to disorder, as it divides the volume into equal lots before starting to model the process. He concludes that statistical population (of the lots) does not lead to correlation. Better is the theory of Hosemann [158,211], His distorted structure does not pre-define any lots, and consequently it is able to describe (discrete) liquid scattering. The problems of liquid scattering have been studied since the early days of statistical physics. To-date several approximations and some analytical solutions are known. Most frequently applied [201,212-216] is the Percus-Yevick [217] approximation of the Ornstein-Zernike integral equation. The approximation offers a simple descrip-... 

The purpose of this section is to present direct evidence of nucleation during the induction period by means of synchrotron small angle X-ray scattering (SAXS). In the classical nucleation theory (CNT), the number density distribution function of nuclei of size N at time t, f(N, t), is expected to increase with an increase of t during the induction period and saturates to a steady f(N, t),fst(N) in the steady period. The change off(N, t) should correspond to that of the scattering intensity of SAXS. 

Fig. 12 Morphology diagram of PEP-6-PLA. ODTs determined by rheology A, , 0, x ordered microstrue lures directly observed by SAXS A S C 0 G x L. Solid lines ordered range of xN as determined by rheological measurements dashed lines approximate phase-transition boundaries using experimental data and mean-field theory predictions. From [63]. Copyright 2002 Wiley...

Crystallization in poly(ethy ene)-poly(ethylethylene) (PE-PEE) semicrystalline diblock copolymers has been investigated using SAXS and WAXS on oriented specimens. Microphase separation was found to precede crystallization for all samples, with 37-90wt% PE (Douzinas and Cohen 1992). The scaling of the lamellar domain spacing in the crystalline phase for the same samples was determined from measurements of the principal SAXS peak position (Douzinas et al. 1991). It was found that the domain spacing scales in agreement with the predictions of the theory of Whitmore and Noolandi (1988) (Section 5.3.5), i.e. 

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