Guinier approximation

The radius of gyration of block copolymer micelles in dilute solution can be obtained from SAXS and SANS using the Guinier approximation (Guinier 1939, 1963) ... 

The most straightforward application of SAXS is in the determination of the radius of gyration, Rg, of the molecule of interest. This may be estimated from Guinier analysis of the low q data and is a model-free result obtained from the Guinier approximation, valid at low q ... 

At small values of Q, the Debye formula reduces to the Guinier approximation,... 

The porosity (1 — < ) is calculated from eq. 4 by using Ip and the value at the plateau of the scattering curve as the cross section for q —> 0. In addition, for small scattering vectors qR < 2 the Guinier approximation S qR < 2) = exp(—[7] was fitted, assuming homogeneous spheres with radius R . This was done in order to check whether this simple approximation is useful for an estimate of the mean micropore radii without assuming a pore size distribution. With the third fit parameter Xp/rn and eq. 2 the mean specific number density Np/rn of micropores with radius Rp is known as well as from... 

The function p(r) represents the frequency of vector length r connecting small volume elements within the volume of the scattering particle, that is, the protein molecule, with maximum dimension Dmax- As the use of the Guinier approximation for the determination of the radius of gyration, Rg, might lead to errors caused by concentration or aggregation effects, we used the normalized second moment of the pair distance distribution function for calculation of R, ... 

The simplest interpretation of the scattering curves for globular particles is based on the Guinier approximation At very low angles, the scattering curve can be described by the following equation ... 

In the case of low concentration and low q expansion, equation IB 1,9,1421 can be expressed by replacing (q) with the Guinier approximation (B1.9.130I... 

RPV steels will contain a range of cluster/precipitate sizes and so the Guinier approximation is inadequate. Analysis must take into consideration the size distribution of the clusters. Different researchers have adopted different approaches. The most frequently used methods are ... 

For sufficiently dilute solutions of biomolecules in which interparticle interactions can be neglected, the properties that can be easily extracted from SAXS profiles are first the radius of gyration Rg and then the scattering intensity /(O). These parameters can be obtained from the Guinier approximation... 

In the scattering curve we can loosely define some regions that contain information on different aspects of the scattering entities. Close to the direct beam one can obtain information about the particle size by the so called Guinier approximation... 

For most commonly occurring particle shapes the scattered intensity due to this shape is available in an analytical expression for the form factor. Quite often the fitting of the data with respect to a form factor function can generate more accurate particle parameters than by using for instance the Guinier approximation. 

The radius of gyration of the cross section, Rc, can be calculated from the Guinier approximation [21]. 

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