SAXS Experiments

In situ SAXS investigations of a variety of sol-gel-derived silicates are consistent with the above predictions. For example, silicate species formed by hydrolysis of TEOS at pH 11.5 and H20/Si = 12, conditions in which we expect monomers to be continually produced by dissolution, are dense, uniform particles with well defined interfaces as determined in SAXS experiments by the Porod slope of -4 (non-fractal) (Brinker, C. J., Hurd, A. J. and Ward, K. D., in press). By comparison, silicate polymers formed by hydrolysis at pH 2 and H20/Si = 5, conditions in which we expect reaction-limited cluster-cluster aggregation with an absence of monomer due to the hydrolytic stability of siloxane bonds, are fractal structures characterized by D - 1.9 (Porod slope — -1.9) (29-30). 

To further understand the structure of these samples, SAXS experiments were carried out and the resulting profiles are shown in Figure 4. The smeared intensity was plotted against the angular scattering variable, s, which is defined as ... 

Thus for an ideal two-phase system the total calibrated intensity that is scattered into the reciprocal space is the product of the square of the contrast between the phases and the product of the volume fractions of the phases, Vi (1 — Vi) = V1V2. V1V2 is the composition parameter66 of a two-phase system which is accessible in SAXS experiments. The total intensity of the photons scattered into space is thus independent from the arrangement and the shapes of the particles in the material (i.e., the topology). Moreover, Eq. (8.54) shows that in the raw data the intensity is as well proportional to the irradiated volume. From this fact a technical procedure to adjust the intensity that falls on the detector is readily established. If, for example, we do not receive a number of counts that is sufficient for good counting statistics, we may open the slits or increase the thickness of a thin sample. 

In many cases the broader distribution can be attributed to the amorphous (or soft) phase. Even higher significance of the assignment can be achieved if the material is studied in time-resolved SAXS experiments during processing (under thermal load, mechanical load). Thus it is not always necessary to resort to secondary methods112 in order to resolve the ambiguity inherent to Babinet s theorem. 

Isothermal crystallization was observed by means of SAXS and a polarizing optical microscope (POM, OLYMPUS, BX or BHS-751-P). The SAXS experiment was carried out using synchrotron radiation on the beam line BL40B2 of SPringS (SP8) at JASRI in Harima and at the BL-10C small angle installation of the Photon Factory (PF) at KEK in Tsukuba. 

These conclusions were later supported by time-resolved SAXS experiments by Stiihn et al. (1994) who studied the ordering of a PS-PI diblock with /PS = 0.44 following quenches from the disordered phase into the lamellar phase. They found that the relaxation times of the structure factor were wavevector dependent, and consistent with the Cahn-Hilliard from (Cahn and Hilliard 1958)... 

Results from SAXS experiments for PS-PB in heptane (Bluhm and Whitmore 1985) were consistent with this scaling. An exponent 0.5, close to the theoretical prediction (eqn 3.19), was observed using SAXS on PS-P1 diblocks in heptane, using copolymers with a wider range of M (Bluhm and Malhotra 1986). 

For a selective solvent, a scaling relation for the domain spacing in the ordered lamellar phase d (l/T)1 3 was obtained from SAXS experiments on a PS-PB... 

Seguela and Prud homme (1989) investigated a PE-PEP-PE triblock copolymer containing 27wt% poly(ethylene) cast from a neutral solvent close to the Tm of PE and well below it. The samples cast above Tm crystallized within the assumed hexagonal-packed cylinder microphase-separated structure. However, SAXS experiments performed on the samples cast at room temperature suggested that crystallization occurred without prior microphase separation in the melt. This path dependence is a general feature of crystallization in block copolymers. 

The precise structural nature of the CL/DNA complexes is elucidated in high resolution synchrotron small-angle X-ray scattering (SAXS) experiments carried out at the Stanford Synchrotron Radiation Laboratory (Raedler et al., 1997 Salditt et al., 1997, 1998 Koltover et al., 1999 Lin et al 2000). 

Nevertheless, small-angle scattering techniques are not very suitable for the study of lower dendrimer generations because such dendrimers yield only weak scattering signals and a high uncertainty factor therefore exists. SANS and SAXS experiments are not only costly, but also make substantial demands on time and require relatively large amounts of substances (several 100 mg). These methods are therefore out of the question for routine use, such as for the determination of the molar mass of dendrimers. 

Figure 12.1 A schematic representation of a SAXS experiment. The X-ray beam is incident from the left and scatters from die sample. A detector, located to the right of the sample, records the angular variation of intensity of scattered X-rays. The shape of this scattering profile contains information about die global structural features of the molecules in the sample. More details about the beamline components, as well as the process for converting CCD images into one dimensional curves of intensity versus angle, can be found elsewhere in this volume (Chapter 19).

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