SummaryTransmission electron microscopy is used to study the microdispersion of silica fillers within the polymer matrix of rubber. The resulting grey-value images are interpreted as realizations of random fields and are characterized by means of variograms. The so-called Cauchy class is a suitable model for this purpose. Statistical analysis shows that different filler dispersion properties are reflected in different variogram parameters. As a case study, the random field approach is demonstrated for four exemplary rubber compounds.
SummaryThe specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.
IntroductionTopological characteristics have become increasingly important in modern spatial statistics, in particular in investigations related to physics and materials science. The physical properties of materials, such as fracture behaviour or conductivity of heat, electricity and water, are often strongly correlated with the topology of their microstructure see Pothuaud et al., 2002b. This applies in particular to porous media, in which properties related to percolation are also studied.A valuable topological characteristic describing connectivity properties is the Euler-Poincaré characteristic χ . Its definition can be found for instance in Stoyan et al. (1995), Ohser & Mücklich (2000) and Mecke (2000). For a three-dimensional body, χ is equal to the number of components plus the number of (isolated) holes minus the number of tunnels. The mean Euler-Poincaré characteristic per unit volume is called specific Euler-Poincaré characteristic , or briefly specific Euler number or specific connectivity number . In this paper the specific Euler number is denoted by N V , while other characters used in the literature are χ V and e .There are efficient numerical algorithms for the estimation of N V from three-dimensional samples of porous media given as voxel data -see Mecke (1996), Vogel (1997, Nagel et al. (2000) and Ohser & Mücklich (2000). The quality of these algorithms is discussed in Ohser et al. (2002).An alternative way to study the topology of a porous medium is its approximation by a network and the analysis of its topological properties. With regard to the specific Euler number it is important to know that in the three-dimensional case it does not matter whether the pore phase or the solid phase is modelled because in this case the specific Euler number is the same for both phases.A network as used here consists of a set of points called vertices and a set of connections between them (see Fig. 1 developed in order to extract the pore network of threedimensional porous media given as voxel data -see for instance Tsao & Fu (1981), Lohmann (1998), Pothuaud et al. (2000) and Sok et al. (2002).Both voxel and network methods use approximations of the given spatial structure, which may produce considerable errors; see the discussion in Ohser et al. (2002) for the voxel case. The determination of N V is much easier for a network than for a voxel structure. S...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.