Use of Reptation Dynamics in Modelling Molecular Interphase in Polymer Nano-Composite

Abstract

In polymer matrix composites, exhibiting heterogeneous structure at multiple length scales, the interphase phenomena at various length scales were shown to be of pivotal importance for the control of the performance and reliability of such structures. At the micro-scale, the interphase is modelled as a 3D continuum with some average properties most commonly resulting from data fitting procedures. Number of continuum mechanics models was derived over the last 50 years to describe the stress transfer between matrix and an individual fiber, considering the interphase with various chemical structure and thickness the third component of the model composite characterized by some average shear strength, τ_a, with realtively good success. The observed strong thickness dependence of the elastic modulus of the interphase with thickness smaller than 500 nm suggested presence of its underlying nano-scale molecular sub-structure. On the nano-scale, the discrete molecular structure of the polymer has to be considered. At this length scale, the continuum mechanics can only be used for materials with characteristic length scale greater than approximately 20 nm. Below 20 nm, continuum mechanics becomes not valid and gradient-strain elasticity along with molecular dynamics approach has to be used. The segmental immobilization seems to be the primary mechanism controlling the behavior of nano—scale “interphase”. Modified reptation model was used to describe the dynamics of chains near a solid nano-particles and to explain the peculiarities in the viscoleastic response of polymer nanocomposites. These results reflecting the discrete molecular nature of the nano-scale interphase can be used in gradient-strain elasticity models. Experimental results obtained for model nanocomposites were used to support theoretical predictions.