A predictive multiscale computational framework for viscoelastic properties of linear polymers Ying Li a , Shan Tang a , Brendan C. Abberton b , Martin Kröger c , Craig Burkhart d , Bing Jiang d , George J. Papakonstantopoulos d , Mike Poldneff e , Wing Kam Liu a, * a Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA b Theoretical & Applied Mechanics, Northwestern University, Evanston, IL 60208, USA c Department of Materials, Polymer Physics, ETH Zurich, CH-8093 Zurich, Switzerland d Global Materials Science Division, The Goodyear Tire & Rubber Company, 142 Goodyear Blvd., Akron, OH 44305, USA e External Science & Technology Program Division, The Goodyear Tire & Rubber Company, 200 Innovation Way, Akron, OH 44309, USA article info Article history: Received 1 August 2012 Received in revised form 22 September 2012 Accepted 29 September 2012 Available online 9 October 2012 Keywords: Viscoelasticity Multiscale modeling Microstructure abstract A predictive multiscale computational framework has been proposed to study the viscoelastic properties of polymeric materials. Using the Inverse Boltzmann Method, both the static structures and dynamic behavior of all-atomistic models of polymers can be reproduced by a simple coarse-grained model, which bridges the scale from nano to meso. On this coarse-grained level, the entangled network of polymer chains is described via a primitive path analysis (Z1 code). This description allows extraction of the tube diameter and primitive chain length, quantities required to bridge the scale from meso to micro. Furthermore, by making the affine-deformation assumption, a continuum constitutive law for polymeric materials has been developed from the tube model of primitive paths, which bridges the scale from micro to macro. In this way, the different scales are crossed by using different bridging laws, which enable us to directly predict the viscoelastic properties of polymeric materials using a bottom-up approach. Our predicted dynamic moduli, zero-rate shear viscosities, and relaxation moduli of poly- isoprene and polyethylene polymers are found to be in excellent agreement with experimental results. The proposed multiscale computational framework can also be naturally extended to the finite- deformation regime. Both the tube diameter a and primitive chain length L are found to increase with deformation, which enhances the viscous energy dissipation of polymers under extremely large defor- mations. To the authors’ knowledge, this is the first work in which a multiscale computational framework has been proposed to predict the viscoelastic properties of entangled polymeric materials from the molecular level. Not only can the method put forth in this research be used to predict the viscoelastic properties of polymeric materials in a bottom-up fashion, it can also be applied to design the polymeric materials with targeted functions, within a top-down approach. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction As performance requirements become increasingly strict in many advanced technological applications, it is of great interest in material design to predict key physical and chemical properties of polymers from the molecular level. Consequently, it is extremely important to develop a predictive computational framework to determine the properties of polymers and assess their suitability to such applications. As a result, computer simulations are becoming increasingly relevant both in fundamental research and industrial applications of polymers, enhanced by the great development of computer power in recent years. Viscoelasticity, the mechanical property of materials that exhibits both viscous and elastic behavior when undergoing deformation, is one of the most important mechanical characteristics of polymeric materials. Therefore, the main goal of this paper is to develop a predictive multiscale computational framework to evaluate the viscoelastic properties of linear polymers based on their atomistic constituents. In this approach, all parameters have physical meanings and can be directly obtained through molecular-level simulations, i.e. coarse- grained molecular dynamics (CGMD) simulations, that are them- selves developed from atomistic models. These parameters are passed into our continuum mechanics model to predict the visco- elastic properties of linear polymers over a broad range of frequency or time, by using analytical models or finite element * Corresponding author. Tel.: þ1 847 491 7094; fax: þ1 847 491 3915. E-mail address: w-liu@northwestern.edu (W.K. Liu). Contents lists available at SciVerse ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer 0032-3861/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.polymer.2012.09.055 Polymer 53 (2012) 5935e5952 For your personal use only. Not for redistribution related contributions available from the author(s) at www.complexfluids.ethz.ch