Thermo-viscoelastic response of nanocomposite melts A.D. Drozdov a, * , E.A. Jensen b , J. de C. Christiansen b a Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel b Department of Production, Aalborg University, Fibigerstraede 16, Aalborg DK-9220, Denmark Received 4 September 2007; received in revised form 13 September 2007; accepted 17 September 2007 Available online 29 October 2007 Abstract Observations are reported in shear oscillatory tests with small strains (the frequency-sweep mode) on a hybrid nano- composite melt [thermoplastic elastomer (ethylene–octene copolymer) reinforced with various concentrations of montmo- rillonite nanoclay] at temperatures ranging from 150 to 210 °C. A constitutive model is developed for the viscoelastic behavior of a nanocomposite melt at arbitrary three-dimensional deformations with small strains. The melt is treated as an inhomogeneous, permanent polymer network with sliding junctions (entanglements and physical cross-links at the surfaces of nanofiller). It is assumed that macro-deformation induces sliding (plastic flow) of junctions between strands with respect to their reference positions, and the strain energy of the network depends on strain tensors for elastic and plastic deformations. Stress–strain relations are derived by using the laws of thermodynamics. These equations involve four adjustable parameters that are found by fitting the observations. It is demonstrated that (i) the governing equations correctly reproduce the experimental data and (ii) the material parameters change consistently with temperature and con- centration of filler. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Thermoplastic elastomer; Hybrid nanocomposite melt; Shear oscillations; Thermo-viscoelasticity; Constitutive equations 1. Introduction This paper deals with experimental investigation and constitutive modeling of the linear viscoelastic response of hybrid nanocomposite melts (polymer melts reinforced with nanoclay platelets and their stacks). Experimental and theoretical analysis of the rheological behavior of nanocomposite melts has been a focus of attention in the past decade. This may be explained by two reasons: (i) rheological tests provide a convenient and reliable tool to characterize polymer/clay nanocomposites and (ii) observations in these tests are exqui- sitely sensitive to concentration, size, and distribution of particles, as well as to structural changes in morphol- ogy of the host matrix driven by the presence of nanofiller [1–4]. Observations on the linear viscoelastic response of polymer/organically modified silicate melts have been reported in a number of studies, see, for 0020-7225/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijengsci.2007.09.004 * Corresponding author. Tel.: +972 8 647 21 46; fax: +972 8 647 29 16. E-mail address: aleksey@bgumail.bgu.ac.il (A.D. Drozdov). Available online at www.sciencedirect.com International Journal of Engineering Science 46 (2008) 87–104 www.elsevier.com/locate/ijengsci