Моделювання перколяційної поведінки властивостей полімерних нанокомпозитів, наповнених вуглецевими нанотрубками

Abstract

The paper considers the application of the scaling approach of the percola-tion theory to describe the step-like change in electrical and thermal conductivi-ty of polymer nanocomposites containing carbon nanotubes. In connection with the use of nano-sized fillers for the creation of polymer composite materials, the problem of mathematical description of the behavior of the properties of such systems at critical filling has arisen. The increasing difficulty of describing a sudden change in properties is due to the fact that the described phenomena, due to the fluctuating processes of aggregation of nanotubes and the formation of an infinite cluster that permeates the entire volume of the material, are essen-tially critical, and therefore cannot be described by traditional mathematical models. In order to solve the problem considered in the publication, it is pro-posed to use universal scaling equations. In this case, an analogy is used be-tween the behavior of a ferromagnet in an external electric field and the behav-ior of the properties of a polymer nanocomposite with non-zero conductivity when it is critically filled with nanotubes. According to the above analogy, a number of equations are written to describe the percolation behavior of both electrical conductivity and thermal conductivity of polymer-filler systems. The results of simulation of real data for systems of this type are given and it is shown that the proposed equations allow to describe the step-like behavior of electrical and thermal conductivity of polymer-nanotube systems with high ac-curacy. The critical exponents of the scaling equations were determined and the behavior of the properties when these indices were varied was modeled. When describing the section of the graph before the percolation threshold, the increase in critical exponents leads to an increase in conductivity, while in the section after the percolation threshold, the increase in critical exponents leads to a de-crease in conductivity