Guinier regime

The region of crossover between the functionalities of Equations 14.25a and b is called the Guinier regime and for p 0 is described by... 

In summary, return to Figure 14.10, which schematically illustrates all the quantitative aspects of the structure factor. In htting data from a real system it is best to analyze the Guinier regime hrst. Equation I4.47a implies that the inverse normalized (to q = 0) scattered intensity is a linear function of q, i.e.. 

A similar expansion can be obtained for scattering intensity S q,C) oc 1/(1 + q R +...). For very low q, in the Guinier regime qR<, this expansion is the basis for the so-called Zimm plots that are commonly used to determine the radius of a chain and the second virial coefficient of a solution. 

Hence, the dominant multipoles for the Guinier regime are So and S2 and the effective diffusion coefficient can be approximated by ... 

Considering the general solution for static structure factor in the Guinier regime (1 and approximately assuming proportionality between and the... 

It is useful to consider the low-4 nd the high-4 asymptotic regimes. In the low-4 regime (the Guinier regime, cjRg < 1) the exponential function in eqn [25] can be expanded as... 

The small t /T data — inclusing data of earlier work — give elliptic shapes. They are characterized by their axis ratio, which can be compared to the affine value In the q, t range where both the parallel and perpendicular S(q) are close to the affine value, the axis ratio has the affine value (even in the intermediate regime for the parallel or in the Guinier regime for the perpendicular). As soon as the affine variation is abandoned in one direction, the axis ratio decreases with time and with q, but curves remain elliptic ,23,24) pjg second set of data, obtained re-... 

Above the Guinier regime at very low q values, we enter the Porod domain. For sihca aerogels this domain corresponds to 5 > 0.1 A When the material does not show a fractal geometry and exhibits a smooth interface, the scattered intensity varies as (Porod, 1951) ... 

Beaucage and Schafer [47] proposed a general form for the cross-section of a fractal object combining both the Guinier regime where da/dQ... 

Figure 54 presents the temperature-dependent scattering profiles from the same polymer-wax combination under wax contrast. The data displays a very pronounced Q" behavior up to high Q, leading to the conclusion that the wax platelets need to be very thin since no two-dimensional Guinier regime is visible. The extended Q" pattern is compatible with plates from a single layer of stretched C24 molecules (deff = 32 A) and excludes formation of stacks of... 

Guinier regime The condition q > R(m) can be satisfied, in this case, with light scattering. The observation scale is larger than the clusters size (Guinier regime). The intensity scattered per monomer is ... 

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