Debye-Bueche analysis

In some cases, a Debye-Bueche analysis was attempted. In such an analysis, the spatial correlation function is given by ... 

The Debye-Bueche analysis (5,6) was employed to obtain the correlation length, and the mean-square refractive index fluctuation, of the gels from... 

There are a number of works on rubber-based blends which exploited a SAXS data analysis based on approximations such as the Guinier, Porod or Debye-Bueche. These approaches are very interesting because they offer valuable information on the size of dispersed domains within the matrix of a blend, without the need of intensive calculation and without having to develop complex theoretical models for the fitting of SAXS patterns. 

The application of the Porod equation or of the Debye-Bueche approach are particularly attractive because they offer the possibility to evaluate the interfacial area between the phases of the blend, and they are probably the only way to quantify such feature in polymer blends and composites. In fact, when the two polymers are mixed together in a blend, traditional methods based on the adsorption of small molecules, i.e. the BET approach, are inapplicable. Image analysis of TEM micrographs can in principle be an option, but it is extremely time consuming and it suffers from a number of limitations, such as dependence on sample preparation, on projection effects, and on image defocus. The validity of SAXS for the study of interpenetrating networks has been shown for several systems. ... 

The success of such data analysis approach is necessarily linked to the reliability of the model chosen to describe the system. This limited the use of this method of interpretation in the study of blends, in favour of more model-independent methods, like the Porod and Debye-Bueche described above. However, some examples of the use of Equation (21.13) may be found in the literature. Micellar systems of block copolymers dispersed in a polyisoprene matrix were modelled by Pavlopoulos et al7 with the form factor of a homogeneous sphere, multiplied by a function accounting for the poly-dispersity in the micelles. In this case, the structure factor was neglected, due to the extreme dilution of the system. 

The approaches of colloidal optics are required for analysis of light scattering on heterogeneous gels. In particular, Rayleigh-Debye s approximation with the correlation function formedism finds application (see subsection 2.1.2) (Gallacher and Betterheim, 1962 Bueche, 1970 Pokrovski et al., 1976 Volkova et al., 1987). 

Calculate the root-mean-square end-to-end distance for a polystyrene with molecular weight 2 x 10 in benzene with an intrinsic viscosity of 107 mL/g. According to Debye and Bueche s analysis, the shielding ratio is in the vicinity of 0.836 with a = 3.92 (Debye and Bueche, 1948). 

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