Equations Guinier

Figure 4.14 shows the SAXS plots for the ACFs prepared by C02 and steam activation. All the scattering curves have the same trend, and the main difference between them is that the intensity increases with the burn-off degree due to the development of porosity. In order to estimate the mean pore size from the SAXS data, the general approach based on Guinier equation has been used (see Equation 4.50). Table 4.3 presents the Guinier radii for the ACF and the original fiber. These values are quite similar to those obtained in a previous study done with ACF [87], Table 4.3 also contains the pore width calculated for spherical particles (see Equation 4.51). 

Figure 2. Intensity of SAXS for a series of CeO /TiOz-doped glasses with different CeOz/TiOz molar ratios 1 -0.3/1 2-0.3/3 3-0.3/5 4-0.3/6.5 5-0.3/10. Inset Igl-s plots for derivation of particle sizes using the Guinier equation.

Application of the Guinier equation or of Porod-like power laws ... 

This is the Guinier equation (1939). The plot of In 7 versus (20) is called the Guinier plot. Note 20 is the scattering angle. In the small-angle region, h 20.)... 

Analysis of Data Depending on the way it is plotted, the Guinier equation can provide information about the size of macromolecules in various shapes ... 

Guinier s equation [19] was originally derived for a material with randomly positioned identical pores embedded in an uniform background. The intensity of small angle scattering, I(k), from pores with volume V, is... 

Juggling with projections and slices results in the Guinier-DuMond equation [64] (Hosemann [5], p. 605-607 Guinier Fournet [65], p. 116-117)... 

Figure 28a shows the result of SAXS on sample BrlOOO. We used Guinier s formula (see eq. 6) for the small angle scattering intensity, I(k), from randomly located voids with radius of gyration, Rg. Although Guinier s equation assumes a random distribution of pores with a homogeneous pore size, it fits our experimental data well. The slope of the solid line in Fig. 28b gives R - 5.5 A and this value has been used for the calculated curve in Fig. 28a. This suggests a relatively narrow pore-size distribution with an equivalent spherical pore diameter of about 14A. Similar results were found for the other heated resin samples, except that the mean pore diameter changed from about 12 A for samples made at 700°C to about 15 A for samples made at 1100°C.

Guinier function which describes the scattering from sphere-like objects (equation (3b)), and the Sphere function which gives the exact scattering from a perfect sphere, where R = (5/3) iRg (equation (3c)). 

Figure 2 shows the results of the non-linear fitting procedure on a part of the equator, first and second layer lines of TMV. The diffraction pattern used was taken by Dr. S. Warren and Dr. G. Stubbs at the Max-Plank-Institut in Heidelberg, Germany. This pattern was taken on a Guinier camera and the arcsdue to disorientation are not circular. The natural coordinate system (3)of the camera (rather than polar coordi-nates)was used in the deconvolution procedure. The standard... 

---