Guinier-plot

In spite of its similarity to light scattering, small-angle x-ray scattering is not usually used to determine M and A2 as mentioned before it is used mainly in the determination of the size and shape. The versatility of the experiment for the measurement of size and shape lies in the interpretation of the designated 

In either expression, X is the wavelength. In the magnitude expressions the angle 0 is the scattering angle and h is almost identical to Q  

It is the structure factor (F (h)) that correlates the scattering intensity and the configuration of the molecule it is the center of the study of x-ray scattering. The structure factor can be expressed in the well-known Debye formula (1915) 

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  

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Figure 7. Guinier plot for a rod-like particle. Sample C40 in O.IM NaCl (6 10 g/L) with calcium (6 10 mol/L)...

Figure 8.1. Guinier plot. Applicability of Guinier s approximation to scattering data and determination of its parameters, I (0) and Rg., smin is the lowest scattering angle at which valid data are present. From, smax deviation between the data and the straight line is observed...

No linear dependence is found in file Guinier plot of 5 peaks... 

Step 3 Guinier Plot Separation of Size and Distortion Effects. The inner part of the correlation functions y0bs(h) (T) s readily expanded into a power series. For this purpose we resort to Eq. (8.14). Assuming that instrumental broadening is already eliminated we have... 

Figure 8.4 presents a sketch of the graphical procedure. According to Eq. (8.26) the intercepts in this Guinier plot are... 

The observed size of the nucleus (N0bs) is estimated by applying the Guinier plot [30] at c/n-... 

Figure 13 shows the Guinier plots of Ix d(q, t) at after quenching up to a little higher t than ri(SAXS). Linear lines are obtained and the slope does not change with an increase in time. From the slope, we estimated... 

Figure 11.8 Zimm and Guinier plots of G4 PAMAM dendrimer and G5 hyperbranched polyol. The dendrimer fits Guinier (spherical) and the hyperbranched fits Zimm (Gaussian)...

In most of the physical studies made to date there is little evidence of sufficient care being taken to assure sample quality. Especially pronounced is the effect this has on scattering results curvature of the Guinier plots (which provide the radius of gyration) due to polydispersity allows only an approximation of the radius of gyration at best. 

As for independent particles can be obtained from the slope of a Guinier plot In I vs. q. However, is emphatically not to be considered as a particle radius in the systems under consideration. Rather, it is a more generally defined parameter which characterizes the size of the optical inhomogeneities. 

Fig. 25. Guinier plot of the soft sphere model. The numbers denote the number of branching shells the filled and open circles are lightscattering results from polyvinyl acetate (PVAc) microgels in methanol at 20 °C at A0 = 546 nm and 436 nm, respectively. The dot-dash line corresponds to the Rayleigh-Gans behavior of hard spheres, i.e. no Mie scattering93)...

Sometimes a monodisperse system can be derived from a polydisperse one. For example, free sub-micelles (produced on disintegration of whole micelles) are quasi-monodisperse, and can be analyzed by Guinier plots and other techniques applicable to monodisperse systems. 

The radius of gyration is a useful parameter to quantitatively describe a monodisperse colloidal solution, since no assumptions are made as to particle shape. Polydisperse samples often show a flattening of the Guinier plot at higher Q. For such samples, the absolute value of Rg has less significance, but the relative values (before and after treatment or processing) can be significant. 

Figure 1. Guinier plot of SANS for casein sub-micelles in 0.07 M NaCl solution in D20. Protein concentration is 16.1 mg/ml. I is coherent neutron scattered intensity.

Stothart and Cebula (1982) and Stothart (1989) obtained linear Guinier plots of sub-micelles of whole casein, giving a radius of gyration of 64 A (Figure 1). On a uniform sphere model, this would indicate sphere radius of 84 A. This sphere size was input to a model fitting calculation (below). Thum et al (1987) found similar sizes for sub-micelles of kappa-casein. 

A Guinier plot of deuterated calmodulin-peptide complex (Heidorn et al,1989) showed a sharp change of behaviour at the match point for the peptide. The Guinier plot was effectively due to the calmodulin part of the complex, with little contribution from the peptide. 

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