Scattering curve corrected

If the structural entities are lamellae, Eq. (8.80) describes an ensemble of perfectly oriented but uncorrelated layers. Inversion of the Lorentz correction yields the scattering curve of the isotropic material I (5) = I (s) / (2ns2). On the other hand, a scattering pattern of highly oriented lamellae or cylinders is readily converted into the ID scattering intensity /, (53) by ID projection onto the fiber direction (p. 136, Eq. (8.56)). The model for the ID intensity, Eq. (8.80), has three parameters Ap, dc, and <7C. For the nonlinear regression it is important to transform to a parameter set with little parameter-parameter correlation Ap, dc, and oc/dc. When applied to raw scattering data, additionally the deviation of the real from the ideal two-phase system must be considered in an extended model function (cf. p. 124). 

It is always easy to calculate idealized scattering curves for perfect networks. The experimental systems vary from the ideal to a greater or lesser degree. Accordingly, any estimate of the correctness of a theoretical analysis which is based on an interpretation of experiment must be put forth with caution since defects in the network may play a role in the physical properties being measured. This caveat applies to the SANS measurement of chain dimensions as well as to the more common determinations of stress-strain and swelling behavior. 

Each scattering curve was measured six times. After the results were averaged and corrected for the day-to-day fluctuations in the incident intensity, the curves were corrected for the background scattering from the scattering system and the 0.001 inch Mylar plastic windows of the sample cell. Corrections were also made for the length and width of the collimating slits. 

Figure 2. Scattering curves for PSOC 93 lignite (circles) and PSOC 248 subbituminous coal (squares). The points show the corrected scattering data, and the curves were obtained from least-square fits of Equation 3 with n=l.

Corrected scattering curves for PSOC coals 93 and 248 are shown... 

Figure 3. The corrected scattering curve for PSOC 86 lignite (squares) and the fit of Equation 6 (line).

Figure 4. Collimation-corrected scattering curves of coal samples (abscissa, 20" x 10 ).

The raw scattering curve I raw ( ) is recorded and reduced to Ired (5) by (1) normalizing to the flux of the primary beam, (2) dividing by the thickness of the sample (cuvette) (assuming that the slits will not be changed after this calibration measurement), (3) carrying out the absorption correction. Then the scattering power is computed... 

Experimental studies of micellar systems were carried out using scattering methods [Selb et al., 1983 Rigby and Roe, 1984, 1986 Kinning et al., 1990, 1991]. Theoretical simulations of the scattering curves have been based on the assumptions that either an infinitely sharp boundary thickness or a diffuse interfacial thickness is equal to Al. In spite of these seemingly diverse principles the simulations were reasonably correct. 

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