Atomistically Informed Continuum Model of Polymer-Based Nanocomposites
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Atomistically Informed Continuum Model of Polymer-Based Nanocomposites Catalin R. Picu, Alireza Sarvestani and Murat S. Ozmusul Department of Mechanical, Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute, Troy, NY 12180 ABSTRACT A model polymeric material filled with spherical nanoparticles is considered in this work. Monte Carlo simulations are performed to determine the polymer chain conformations in the vicinity of the curved interface with the filler. Several discrete models of increasing complexity are considered: the athermal system with excluded volume interactions only, the system in which entropic and energetic interactions take place while the filler is a purely repulsive sphere, and the system in which both filler-polymer and polymer-polymer energetic interactions are accounted for. The total density, chain end density, chain segment preferential orientation and chain size and shape variation with the distance from the filler wall are determined. The structure is graded, with the thickness of the transition region being dependent on the property and scale considered. Hence, the polymer in the vicinity of the filler is represented in the continuum sense by a material with graded properties whose elasticity is determined based on the local structure. Homogenization theory is the used to obtain the overall composite moduli. The filler size effect on the composite elasticity is evaluated. INTRODUCTION Polymer-based nanocomposites form a new class of reinforced polymers in which the fillers have at least one dimension less than 100 nm. These materials have macroscopic properties significantly different from those of conventional composites of same filler volume fraction [e.g.1,2]. For example, the dispersion of only 2% volume fraction of nanoparticles in thermoplastics almost doubles the yield stress and increases the Young's modulus. The mechanisms responsible for the enhanced properties are not fully understood and controlled. It appears that interesting properties are obtained when the filler size and/or the filler wall-to-wall distance become comparable with the chain radius of gyration. Two principal ideas have been promoted in this connection: the novel properties are either due to chains connecting several fillers (the double network theory), or to the special distribution and density of entanglements in the confined polymer matrix. In all situations, it is generally accepted that the structure of polymeric chains confined between fillers and their binding to the wall are the major elements controlling the properties of the composite. This work is part of an ongoing effort to relate the polymer structure to the macroscopic nanocomposite properties. We consider a model polymer filled with spherical impenetrable particles. The chain structure in the vicinity of fillers is determined by Monte Carlo simulations. The elasticity of the matrix is determined based on the local structure. The composite is homogenized for its overall elastic properties. We first review the main features o
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