ID Interface Distribution Functions IDF

Opportunities and Limits. If we intend to obtain a clearer look on nanostructure than the one the CLD is able to offer, we can try to get rid of the orientation smearing - either by considering materials with a special topology (layer stacks), or by studying anisotropic materials. 

If the scattering entities in our material are stacks of layers with infinite lateral extension, Eq. (8.47) is applicable. This means that we can continue to investigate isotropic materials, and nevertheless unwrap the ID intensity of the layer stack. To this function Ruland applies the edge-enhancement principle of Merino and Tchoubar (cf. Sect. 8.5.3) and receives the interface distribution function (IDF), gi (x). Ruland discusses isotropic [66] and anisotropic [67] lamellar topologies. 

For a layer-stack material like polyethylene or other semicrystalline polymers the IDF presents clear hints on the shape of the layer thickness distributions, the range of order, and the complexity of the stacking topology. Based on these findings inappropriate models for the arrangement of the layers can be excluded. Finally the remaining suitable models can be formulated and tested by trying to fit the experimental data. 

As pointed out by Stribeck [139,171] gi (x) is, as well, suitable for the study of oriented microfibrillar structures and, generally, for the study of ID slices in deliberately chosen directions of the correlation function. This follows from the Fourier-slice theorem and its impact on structure determination in anisotropic materials, as discussed in a fundamental paper by Bonart [16]. 

In practical application to common isotropic polymer materials the IDF frequently exhibits very broad distributions of domain thicknesses. At the same time fits of the IDF curve to the well-known models for the arrangement of domains (cf. Sect. 8.7) are not satisfactory, indicating that the existing nanostructure is more complex. In this case one may either fit a more complex model on the expense of significance, or one may switch to the study of anisotropic materials and display their nanostructure in a multidimensional representation, the multidimensional CDF. Complex domain topology is more clearly displayed in the CDF than in the IDF. The CDF method is presented in Sect. 8.5.5. 

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