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sahimi m heterogeneous materials i linear transport optical properties 2003

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Textbook in PDF format Disorder plays a fundamental role in many natural and man-made systems that are of industrial and scientific importance. Of all the disordered systems, heterogeneous materials are perhaps the most heavily utilized in all aspects of our daily lives, and hence have been studied for a long time. With the advent of new experimental techniques, it is now possible to study the morphology of disordered materials and gain a much deeper understanding of their properties. Novel techniques have also allowed us to design materials’ morphology with the properties that are suitable for intended applications. With the development of a class of powerful theoretical methods, we now have the ability for interpreting the experimental data and predicting many properties of disordered materials at many length scales. Included in this class are the renormalisation group theory, various versions of the effective-medium approximation, percolation theory, variational principles that lead to rigorous bounds to the effective properties, and Green function formulations and perturbation expansions. The theoretical developments have been accompanied by a tremendous increase in the computational power and the emergence of massively-parallel computational strategies. Hence, we are now able to model many materials at molecular scales and predict many of their properties based on first-principle computations. In this two-volume book we describe and discuss various theoretical and computational approaches for understanding and predicting the effective macroscopic properties of heterogeneous materials. Most of the book is devoted to comparing and contrasting the two main classes of, and approaches to, disordered materials, namely, the continuum models and the discrete models. Predicting the effective properties of composite materials based on the continuum models, which are based on solving the classical continuum equations of transport, has a long history and goes back to at least the middle of the nineteenth century. Even a glance at the literature on the subject of heterogeneous materials will reveal the tremendous amount of work that has been carried out in the area of the continuum modeling. Rarely, however, can such continuum models provide accurate predictions for the effective macroscopic properties of strongly disordered, multiphase materials. In particular, if the contrast between the properties of a material’s phases is large, and the phases form large clusters, most continuum models break down. At the same time, due to their very nature, the discrete lattice representation of a material’s morphology, have the ability of providing accurate predictions for the effective properties of heterogeneous materials, even when the heterogeneities are strong, while another class of discrete models which represents a material as a collection of its constituent atoms and molecules provides accurate predictions for the material’s properties at mesoscopic scales, and thus, in this sense, the discrete models are complementary to the continuum models. Last three decades of the twentieth century witnessed great advances in discrete modelling of materials and predicting their macroscopic properties, and one main goal of this book is to describe these advances and compare their predictions with those of the continuum models. In Volume I, we consider characterization and modelling of the morphology of disordered materials, and describe theoretical and computational approaches for predicting their linear transport and optical properties, while Volume II focusses on non-linear properties, and fracture and breakdown of disordered materials, in addition to describing their atomistic. Some of the theoretical and computational approaches are rather old, while others are very new, and therefore we attempt to take the reader through a journey to see the history of the development of the subjects that are discussed in this book. Most importantly, we alway compare the predictions with the relevant experimental data in order to gain a better understanding of the strengths and/or shortcomings of the two classes of models. Preface Introduction PART I: CHARACTERIZATION AND MODELLING OF THE MORPHOLOGY Characterization of Connectivity and Clustering Characterization and Modelling of the Morphology PART II: LINEAR TRANSPORT AND OPTICAL PROPERTIES Effective Conductivity, Dielectric Constant and Optical Properties: The Continuum Approach Effective Conductivity and Dielectric Constant: The Discrete Approach Frequency-Dependent Properties: The Discrete Approch Rigidity and Elastic Properties: The Continuum Approach Rigidity and Elastic Properties: The Discrete Approach Rigidity and Elastic Properties of Network Glasses, Polymers, and Composite Solids: The Discrete Approach

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sahimi m heterogeneous materials i linear transport optical properties 2003

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