The Guinier-Plot

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... 

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. 

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. 

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. 

From Equation (5), it is seen that the radius of gyration may be calculated from the slope of a plot of In I h) versus this is the so-called Guinier plot or curve. In a system in which all the scattering particles are of equal size, the Guinier plot will be a straight line. 

No Unear dependence is found in the Guinier plot of 5 peaks... 

Since 1(0) is proportional to M, the presence of aggregates is again seen to be serious. Scattering curve intensities in the Guinier plot are no longer linear in the In I(Q)v plot but curve upwards as Q decreases. 

The temperatures were chosen so that they are between the transition temperatures. Blends that had been annealed at 70°C and 120°C showed no reflex so that the BPDF could not be calculated. However, the Guinier plot showed two scattering radii and r 2-... 

In Table II, a number of asphalt dispersions in a variety of solvents are listed. In general, our results indicate that the radii of gyration as evaluated from the Guinier plot is around 4 nm and the morphological diameter is ca. 10 nm. This value does not vary with polarity of the solvent or concentration. 

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.)... 

Table 1 The estimated values of Rg from the Guinier plots for dC(6)PC micelles in the presence of 2 M sorbitol at 25°C.

In order to determine the aggregation number n and the volume Pin, we performed a contrast-variation experiment at constant dC(6)PC concentration (50 mM). The contrast, = ( m/Kn) — Ps> was changed by various D2O/H2O mixtures. Figure 4 presents the Guinier plots for dC(6)PC micelles in the presence of 2 M sorbitol with various contrasts. Equation (1) also indicates that and n can be determined from the position of the zero intensity and the slope of the plot of 7(0) as a function of contrasts, respectively. Figure 5 is a plot of the square root of 7(0) vs. the volume fraction of H20.7(0) vanishes in a solvent containing 16.1 vol% D2O. This corresponds to = 6.93 X 10 A . From this value and the slope of the straight line in Fig. 5, we found n = 32 and Fm = 640 A. In this calculation, the value of the micellar concentration estimated from the above measurement was also taken into consideration. 

The linearity of the Guinier plot was not so good as those for the other three concoitrations... 

The salt effect on the structure of the solution was also studied [60, 69]. The scattering spectra are dramatically affected - the interference peak disappears and the intensity scattered at low Q increases - when a simple salt is added to a concentrated solution. At low polymer concentration, the Guinier plot remains unchanged except for an increase of the scattered intensity at very low Q values (Fig. 19.10). These effects were attributed to a decrease of the order associated to the beginning of aggregation without any change in the shape and the size of the particles. The quantity of salt necessary to affect the interference peak in concentrated solutions is related to the dielectric constant of the solvent. The same effect occurs respectively with 10 , 10" and 10 mol/1 of added salt in ethanol, water and N-methylformamide solutions [69]. 

When nano-nuclei are isolated and dispersed uniformly, Ix q, t) is given by a summation of the scattering intensities from the isolated nuclei. According to the Guinier plot, Ix q, t) is approximated by... 

On account of the absence of a linear range in the Guinier plot (suggesting a broad distribution in pores size) and a deviation from Porod law, at the large angle, for all the samples, we have not been able to compute the conventional Fourier transformation requiring two extrapolations of each curve. 

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