Monte-Carlo simulations for 3D modelling of rubber reinforcement

Full three-dimensional structural characterisation is crucial when the mechanical, electrical or chemical properties of the material under study may be highly dependent on the morphology. TEM tomography is an efficient tool to achieve three-dimensional morphological data. Besides obtaining qualitative information of the analysed structure, also quantitative data as volume or surface area can be determined by this technique. However, sometimes a more detailed understanding of the internal morphology of the structure is required, which may not be exposed by TEM tomography. This is the case, for example, for carbon black aggregates inside rubber: the carbon black basic units, which are spherical, chemically bond to form aggregated structures in the elastomeric matrix. In turn, the morphological characteristics of these aggregates are, among other factors, responsible for the ultimate properties of the material. The determination of the position and size of the spherical carbon units within the aggregates would be very useful information in order to develop predictive models and/or FEA calculations. Generating realistic 3D models of the aggregates, including the position and size of the carbon black basic spheres within the model, would be a way to extend the information provided by TEM tomography. In this work, we present a Monte Carlo simulation based method for modelling carbon black in 3D, as an alternative to a previously published method. For the development of the present method both made up and actual aggregates were used, the former for obtaining a suitable procedure for the simulations and the later for demonstrating its applicability to real-object tomographic models. Moreover, the modelization has been extended to larger volumes, containing several aggregates, in an attempt to broaden the length-scale of the analyzed volume, and to obtain results that are correlated to the macro-scale properties.