Modeling the Effective Conductive Properties of Polymer Nanocomposites with a Random Arrangement of Graphene Oxide Particles

Сomposite materials are widely used in various industrial sectors, for example, in the aviation, marine and automotive industries, civil engineering and others. Methods based on measuring the electrical conductivity of a composite material have been actively developed to detect internal damage in polymer composite materials, such as matrix cracking, delamination, and other types of defects, which make it possible to monitor a composite’s state during its entire service life. Polymers are often used as matrices in composite materials. However, almost always pure polymers are dielectrics. The addition of nanofillers, such as graphene and its derivatives, has been successfully used to create conductive composites based on insulating polymers. The final properties of nanomodified composites can be influenced by many factors, including the type and intrinsic properties of nanoscale objects, their dispersion in the polymer matrix, and interphase interactions. The work deals with modeling of effective electric conductive properties of the representative volume elements of nanoscale composites based on a polymer matrix with graphene oxide particles distributed in it. In particular, methods for evaluating effective, electrically conductive properties have been studied, finite element modelling of representative volumes of polymer matrices with graphene oxide particles have been performed, and the influence of the tunneling effect and the orientation of inclusions on the conductive properties of materials have been investigated. The possibility of using models of resistive strain gauges operating on the principle of the tunneling effect is studied. Based on the finite-element modeling and graph theory tools, we created approaches for estimating changes in the conductive properties of the representative volume elements of a nanomodified matrix subjected to mechanical loading.

From Brownian Motion to Bending Beams

This chapter argues that the hydrodynamic, correlation function methodology discussed in “fluid” contexts is really the same methodology employed in materials science to determine effective values for quantities like conductivity, elasticity, stiffness. Thus, Einstein’s arguments discussed in the previous chapter have a bearing on what prima facie appear to be completely different problems. The mesoscale approach using representative volume elements and correlation functions to describe the important features of those representative volume elements is presented in some detail.

Introduction

This chapter introduces a conception of the relative autonomy of upper-scale, continuum theories from lower-scale more fundamental molecular and atomic theories. It contrasts a notion of foundational philosophical problems with an understanding of autonomy and fundamentality. It lays out the key ingredients required to argue for a middle-out, mesoscale approach to many-body systems, including hydrodynamic descriptions, representative volume elements, and fluctuation and dissipation.

Brownian Motion

This chapter discusses the phenomenon of Brownian motion and Einstein’s pioneering arguments that explained various aspects of it. It shows how Einstein presented two arguments that relate directly to the themes of this book. The first is the upscaling or homogenization to effective continuum parameters from correlational structures in representative volume elements at mesoscales. Einstein’s argument is shown to answer the question about autonomy raised in Chapter 2. The second relates to the Fluctuation-Dissipation theorem. This theorem justifies the mesoscale hydrodynamic description of many-body systems and Einstein provided the first statement of the theorem.