VISCONANONET · Modelling the viscoelasticity of polymer-based nanocomposites guided byprinciples of non-equilibrium thermodynamics

Modelling the viscoelasticity of polymer-based nanocomposites guided by principles of non-equilibrium thermodynamics

Our objective was to set the framework for the development of the new family of constitutive equations for heterogeneous, polymer nanocomposites with near-spherical nanoparticles from a non-equilibrium thermodynamics perspective. We have employed the Generalized Bracket formalism [Beris, A. N. & Edwards, B. J. 1994 Thermodynamics of flowing systems with internal microstructure, Oxford University Press, London, UK] to describe systems consisting of a polymer matrix and a nanofiller phase. A thoroughly investigation of the relevant literature was undertaken in order to be able to set down the correct definition of the state of state variables, the Hamiltonian of the system and the Poisson and the Dissipation brackets. In the proposed approach, the nanofiller phase was consistently coupled to the polymer phase both hydrodynamically and thermodynamically. To the first approach, which is the one being reported here, we have produced a constitutive model by employing the experience we have gained in deriving our model for homopolymers and the available infrastructure of constitutive models for polymer nanocomposites in the literature. For the polymer system, we employed the general viscoelastic model for homopolymers melts we had developed recently [Stephanou, P. S., Baig, C. and Mavrantzas, V.G., J. Rheol. 53, 309-337 (2009)] accounting for several complex phenomena and interactions: anisotropic hydrodynamic drag, finite chain extensibility with non-linear molecular stretching, non-affine deformation, and variation of the longest chain relaxation time with chain conformation. It has proven to work remarkably well when compared against available rheological data for short polyethylene melts obtained through direct atomistic NEMD simulations in shear and planar elongation. Previous attempts to model nano-fibers [Rajabian M., Naderi G., Dubois C., and Lafleur P. G., Rheol. Acta 49, 105-118 (2010)] and nano-clays [Eslami H., Grmela M. and Bousmina, M., J. Rheol. 51, 1189-1222 (2007)] have considered an orientation tensor to describe nanoparticles. As such, we have also decided to consider in our vector of state variables, in addition to the ones we have used in our homopolymer constitutive polymer namely the momentum density and the polymer conformation tensor (for incompressible and isothermal systems), the orientation tensor. In a second stage the numerical values of the parameter involved were obtained by comparing the predictions of the model against the predictions of recent coarse-grained non-equilibrium molecular dynamics (NEMD) simulations typically treating polymer chains as bead-spring sequences [ Kairn, T., Daivis, P. J., Ivanov, I. and Bhattacharya, S. N., J. Chem. Phys. 123, 194905 (2005)]. This comparison shows that the new model is indeed able to predict the behavior of simulated polymer nanocomposites.

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