Guinier region

Discuss some of the limiting forms of the form factor. Explain what is meant by (a) the center-of-mass region, (b) the Guinier region, (c) the fractal region, and (d) the Porod region. 

Coupling this with SAXS measurements in the Guinier region gives a measure of the change in size of the system as the protein collapses to fold. 

For homopolymer blends consisting of deuterated (labeled) polymer molecules randomly dispersed or dissolved in a protonated polymer matrix, small-angle neutron scattering in the Guinier region arises from the contrast between the labeled (deuterated) and the protonated species. The scattering cross-section can be expressed... 

X-ray and neutron scattering curves measured beyond the Guinier region lead to further shape information in addition to values. Theoretical curves calculated from simple models of uniform density illustrate this (Fig. 7). Thus for a sphere, the scattering curve is given by [6] ... 

Fig. 28. The three basic scattering functions from the shape Iy(Q), the cross-term /vf(0 nd the fluctuations /p(2) fro contrast variation studies on the chromatin core particle [387]. I (Q) corresponds to the scattering from the shape as observed at infinite contrast where there is no influence from the internal structure Pp(r) from the DNA and protein components. Its Guinier region gives the Rq of the Stuhrmann plot. /p(2) is the internal structure function and should correspond to the scattering curve measured at the matchpoint of the core particle in 48% H20. The cross-term /vp(2) is the correlation of the shape and internal structures. The calculated curves from 3 models are shown in...

Guinier region, one can obtain particle size information, while the Porod or power law region, at wider angles, contains information on the shape of the particles. (Reproduced with permission from Ref [45].)... 

Schematic showing Guinier region in which slope is directly related to size of scattering features. 

Figure 3.8 Scattering intensity envelopes for small, medium, and large particles. The Guinier region contains both the small and medium ranges, but the medium range is far more useful for scattering experiments.

The different regimes of interest are illustrated in Figure 8 (drawn afla Ref. 30) for spherical particles. The cross-section has been normalized to its value at K=0. The oscillations only occur when the particle radius, a, is well-defined, and become damped as the radius takes on a spread of values(26). Figure 8a shows the Guinier region at low K. From equation 26, the intercept at K=0 is equal to C (ft,P - pn ) (Np fV). Thus, the initial portion cf the scattering curve gives information about the i cle size and volume fraction, provided die scatto ing contrast and instrumentation factors are known. 

This is the Guinier region. It provides information concerning polymer mass or radius, which is determined by the intercept and slope of a plot of log l(K) versus [124]. 

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