Various methods were used for evaluation of homogeneity of polypropylene (PP) matrix composites with octakis([n‐octyl]dimethylsiloxy)octasilsesquioxane, octakis([n‐octadecyl]dimethylsiloxy)octasilsesquioxane, and silica (SiO2) fillers. The filler dispersion was determined on the basis of the results from the wide‐angle X‐ray scattering (WAXS) analysis, from the tests of selected mechanical properties, from scanning electron microscopy (SEM) with energy dispersive X‐ray spectroscopy and from the decomposable entropic descriptor method. The use of different methods allowed to evaluate homogeneity of PP composites on various levels and with different precisions. The dispersion degree was found to be mostly depended on the kind and amount of the filler used. The presence of long n‐alkyl chain substituents in POSS molecules greatly improved the level of filler dispersion in the polymer matrix in comparison to silica which was visually assessed by SEM. The WAXS method revealed the formation of filler aggregates in the PP matrix which influenced the structural characteristic of PP composites and changed the mechanical properties of those materials. However, the decomposable entropic descriptor method provided the possibility of quantitative and the most objective estimation of homogeneity of the obtained composite materials. POLYM. COMPOS., 40:1354–1364, 2019. © 2018 Society of Plastics Engineers

 We explore the multi-scale percolation behaviour in a few lattice models.  A change in the size of the basic cluster alters the value of the percolation threshold.  In the extended three-phase model, double-threshold routes appear on the conductivity surface. A B S T R A C TMacroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size k  k. We also explore its modified form. The focus is on the percolation behaviour of the effective conductivity of random twoand three-phase systems. We consider only the influence of geometrical features of local configurations at different length scales k. At scales accessible numerically, we find that an increase in the size of the basic cluster leads to characteristic displacements of the percolation threshold. We argue that the behaviour is typical of materials, whose conductivity is dominated by a few linear, percolation-like, conducting paths. Such a system can be effectively treated as one-dimensional medium. We also develop a simplified model that permits of an analysis at any scale. It is worth mentioning that the latter approach keeps the same thresholds predicted by the former one. We also briefly discuss a three-phase system, where the double-thresholds paths appear on model surfaces.

To quantify degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable 'phase splitting' of the adapted descriptor. As a result, each of the phase descriptors (PDs) describes the spatial inhomogeneity attributed to each phase-component. Obviously, their sum equals to the value of the overall spatial inhomogeneity. We apply this approach to three-phase synthetic patterns. The black and grey components are aggregated or clustered while the white phase is the background one. The examples show how the valuable microstuctural information related separately to each of the phases can be obtained at any integer length scale. Even dissimilar hidden statistical periodicities can be easily detected for chosen phases built-up of compact regular clusters.Comment: version clarified, 1 reference added, 19 pages, 9 figure

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