By Yves R?mond, Said Ahzi, Majid Baniassadi, Hamid Garmestani

ISBN-10: 1119307562

ISBN-13: 9781119307563

ISBN-10: 1119307570

ISBN-13: 9781119307570

ISBN-10: 1119307635

ISBN-13: 9781119307631

ISBN-10: 1848219016

ISBN-13: 9781848219014

Statistical correlation capabilities are a widely known type of statistical descriptors that may be used to explain the morphology and the microstructure-properties courting. A accomplished examine has been played for using those correlation features for the reconstruction and homogenization in nano-composite fabrics. Correlation capabilities are measured from various innovations reminiscent of microscopy (SEM or TEM), small perspective X-ray scattering (SAXS) and will be generated via Monte Carlo simulations. during this e-book, varied experimental strategies akin to SAXS and photograph processing are awarded, that are used to degree two-point correlation functionality correlation for multi-phase polymer composites.

Higher order correlation services needs to be calculated or measured to extend the precision of the statistical continuum strategy. to accomplish this goal, a brand new approximation technique is applied to procure N-point correlation features for multiphase heterogeneous fabrics. The two-point capabilities measured by means of varied concepts were exploited to reconstruct the microstructure of heterogeneous media.

Statistical continuum conception is used to foretell the potent thermal conductivity and elastic modulus of polymer composites. N-point likelihood capabilities as statistical descriptors of inclusions were exploited to resolve powerful distinction homogenization for potent thermal conductivity and elastic modulus houses of heterogeneous fabrics. Finally, reconstructed microstructure is used to calculate powerful houses and harm modeling of heterogeneous materials.

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**Sample text**

Case study for structural characterization using SAXS data Materials The polymer matrix of the studied nanocomposite, polystyrene (PS), was supplied by Scientific Polymer Products Inc. It has a molecular weight of about 120,000 g/mol. The zirconium oxide (ZrO2) nanofiller was provided by Sigma Aldrich under the reference #544760 (average particle size <100 nm according to the datasheet). 89 g/cm3, respectively [BAN 11b]. Preparation of the nanocomposites All nanocomposites were prepared by melt mixing.

19] where C2 ( r1α , r2α ) represents the two-point probability correlation function, which measures the spatial distribution of the heterogeneities (phase α ) in the matrix (phase β ). C2 ( r1α , r2α ) should verify the following conditions: C2 ( r1α , r2α ) = φ1 when r = r1 − r2 = 0, C2 ( r1α , r2α ) = ( φ1 ) when r = r1 − r2 → ∞. e. if the second condition is not verified then the distribution of the heterogeneities is not homogeneous in the matrix). 1. Case study for structural characterization using SAXS data Materials The polymer matrix of the studied nanocomposite, polystyrene (PS), was supplied by Scientific Polymer Products Inc.

Monte Carlo calculation of TPCF The one-point probability function of phase-1 is defined by the probability of occurrence of random points in this phase [TOR 02]. Therefore, the one-point correlation function for each phase indicates the volume fraction of this particular phase. 1). In the example of nanotube polymer composites, there exist exactly two states; phase-1 (polymer matrix) and phase-2 (nanotube particles). Therefore, four different configurations of two-point correlation functions are obtained.

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