Guinier s law

Guinier s law states that for any scattering pattern, /(s), of a diluted system the initial intensity decay is approximated by a Gaussian... 

Guinier s law should never be considered. Crosses show a deviation that may be explained by the influence of the direct primary beam to the measured data. The value of, v2max gives some hint on the confidence of the approximation. After determination of R2 the relation 0.1 < ax < 0.4 should hold. 

Guinier s law exhibits two parameters, I (0) and R2, which describe structural aspects of the sample. The experimentalist should consider their determination, if the recorded SAXS data show a monotonous decay that is indicative for the scattering from uncorrelated1 particles. Particularly useful is the evaluation of Guinier s law, if almost identical particles like proteins or latices are studied in dilute solution (cf. Pilz in [101], Chap. 8). The absolute value of 1(0) is only accessible, if the scattering intensity is calibrated in absolute units (Sect. 7.10.2). 

Notice the change of variables Guinier s law is applied to the Fourier transform of the peak as a function of the order (h) of the peak at fixed positions r. 

For small scattering angles the scattering intensity of an isolated particle (Eq. 4) may be expanded to yield Guinier s law [32,33] ... 

If the particles are small, this condition may never be met. It is still possible, however, to determine a fractal dimension for such particles in a scattering experiment. This method makes use of Guinier s law, which ap-... 

Assuming that no correlation among particles is present, the meanings of the structure related parameters of Guinier s law are readily established by application of the mathematical tools of scattering (cf. Chap. 2). Further assumptions state that each particle k is considered to be immersed in a matrix of constant electron density and that its correlation function is monotonously decaying. Thus, the particle is discriminated from the matrix by its number nik of electrons that it has more (respectively, less) than the homogeneous matrix, nik is called the number of excess electrons of the particle k. 

Contrast variation low-angle part ofl(q). Series expansion of Eq.(2) leads to Guinier s law [Ij ... 

Slit-smeared SAXS patterns for sample l.OOA (as-cast) and LOOT (thermolyzed) are shown in Figure 4. As in the PAN-I-Co case, the change in the SAXS pattern after thermolysis reflects Co particle formation. The net scattering (above the background) for samples LOOT and 1.50T was well-described by Guinier s Law (27), as shown in Figure 5 ... 

There are three regimes cf interest in the scattering curve, which determine various parameters cf ttje particles. At low values of K (K->0) Guinier s Law (4) gives the scattering cross-section as ... 

Small-Angle Scattering by a Set of Uncorrelated Nano-Objects. Guinier s Law... 

A dilute and isotropic system composed of a set of nano-objects with a distribution of radii of gyration defined by 7 /( Rg) yields a total scattering intensity I q), at small q, given by the sum of the individual contributions of each object. In this case, Guinier s law also holds at very small q but the relevant parameters are in this case average values. For a two electron density system consisting of a isotropic set of uncorrelated nano-objects, equation (8-15) becomes... 

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