Purdue University Purdue e-Pubs Birck and NCN Publications Birck Nanotechnology Center 4-2014 Material property prediction of thermoset polymers by molecular dynamics simulations Chunyu Li Purdue University, Birck Nanotechnology Center, [email protected] Eric Coons Purdue University, Birck Nanotechnology Center, [email protected] Alejandro Strachan Purdue University, Birck Nanotechnology Center, [email protected] Follow this and additional works at: http://docs.lib.purdue.edu/nanopub Part of the Nanoscience and Nanotechnology Commons Li, Chunyu; Coons, Eric; and Strachan, Alejandro, "Material property prediction of thermoset polymers by molecular dynamics simulations" (2014). Birck and NCN Publications. Paper 1586. http://dx.doi.org/10.1007/s00707-013-1064-2 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Acta Mech 225, 1187–1196 (2014) DOI 10.1007/s00707-013-1064-2 Chunyu Li · Eric Coons · Alejandro Strachan Material property prediction of thermoset polymers by molecular dynamics simulations Received: 22 August 2013 / Revised: 22 October 2013 / Published online: 18 February 2014 © Springer-Verlag Wien 2014 Abstract Molecular dynamics simulations are conducted to predict thermal and mechanical properties of a family of thermoset polymers. We focus on the effect of cross-linkers on density, glass transition temperature, elastic constants, and strength. The polymers are composed of the epoxy resin DGEBA (EPON825) and a series of cross-linkers with different number of active sites and rigidity 33DDS, 44DDS, APB133, TREN, and TAPA. Our simulations quantify effects of cross-linkers on thermal and mechanical properties. 1 Introduction With the fast increase in computer power and advances in physics-based models and efficient algorithms, com- putational simulation has become one of three pillars in modern science and engineering. Simulation-Based Engineering Science (SBES) has been classified as a discipline indispensable in science and engineering [1]. Recognizing that predictive computational simulations in materials science and engineering have significant room to grow compared with the huge success of computational simulations in other field such as struc- tural engineering and mechanical engineering, Integrated Computational Materials Engineering (ICME) was recently identified as a transformational discipline for improved competitiveness and national security in a report issued by the US National Academy of Engineering [2]. More recently, the US government unveiled Materials Genome Initiative for Global Competitiveness (MGI) [3]. The goal is to significantly shorten the time elapsed from discovery to deployment of new materials. Reaching this objective will require significant effort in developing advanced computational tools for predictive modeling, simulation, design, and explora- tion of materials. The ability to simulate materials processing and fabrication as well as their performance on computers can bring in deep understanding of fundamental processes, such as chemical reactions and material failure mechanisms. In addition, such simulations can provide design guidelines and thus significantly reduce the number of experiments required for optimization of material formulation and manufacturing conditions. Aligned with these general objectives, our group has devoted significant efforts to predictive simulations of polymers, especially thermoset polymers, in the last few years [4–11]. Thermoset polymers are the matrix of choice for fiber-reinforced composites used in a wide variety of applications, especially in aerospace industry. Compared to thermoplastic polymers, the advantages of ther- moset polymers are in their better material properties, such as higher stiffness, higher strength as well as creep and thermal resistance. These properties depend on various factors, including the chemistry and molecular structures of resin and cross-linker, polymerization (conversion) degree, as well as thermal history. Detailed knowledge of the effect of these factors is of great interest to the applications of thermoset polymers. In honor of Professor George Weng, the 2013 Prager Medalist. C. Li (B) · E. Coons · A. Strachan School of Materials Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47906, USA E-mail: [email protected] 1188 C. Li et al. There have been extensive experimental studies to characterize the effect of conversion degree on mate- rial properties of thermoset polymers. Among the properties studied, glass transition temperature is the most extensively characterized one. A general trend of all these experimental studies is that Tg increases with increasing conversion in a nonlinear fashion with an increasing dependency for higher conversion degree. Atomistic simulations [5,8,12,13] have also confirmed the general trends observed experimentally. The role of the conversion degree for the elastic properties of thermoset polymers is not as deeply understood, and contradictory results are still in debate. For example, the studies of Theriault et al. [14] showed an increase in the Young’s modulus with increasing conversion degree. Li and Strachan further reported an almost linear increase in tensile modulus with conversion degree [5]. But Morel et al. [15] concluded that the effects of cross-linking density and glass transition temperature on the elastic properties of the polymers in the glassy state are insignificant. Marks and Snelgrove [16] even reported a uniform trend of decreasing tensile modulus with increasing conversion for various amine-cured epoxy thermosets. The material properties of thermoset polymers are also strongly dependent on the detailed molecular struc- tures of the constituent resin monomers and cross-linker molecules. Experiments have shown that the Tg of an epoxy network can be shifted by more than 140 K by just using different cross-linkers [17]. Atomistic simulations have also found that Tg values decrease with increasing chain length of the cross-linkers [18]. The studies of Marks and Snelgrove [16] indicated that the fracture toughness of epoxy thermosets often exhibit a maximum value for conversion degrees between 65 and 95 %, depending on the rigidity of the cross-linker. However, the understanding of the effect of the cross-linker is much less developed than that of the effect of the conversion degree. The objective of this paper was to systematically investigate the effect of cross-linkers on thermal and mechanical properties of epoxy thermosets. We use a procedure developed in our previous research to build network structures of thermoset polymers and characterize the thermomechanical response of the resulting structures using molecular dynamics (MD). In particular, we focus on the effect of cross-linker length and chemical functionality. 2 Molecular dynamics simulations Since molecular dynamics (MD) was first proposed in 1959 [19] for studying hard-sphere systems followed by soft-sphere systems [20], there have been numerous MD simulations conducted in various fields such as computational physics, computational chemistry, materials science, pharmaceuticals, and biochemistry. There are three basic stages in a classical MD simulation: building a molecular model with atomistic detail to be used as initial conditions, solving classical equations of motion to obtain the time evolution of the atomic positions and velocities subject to appropriate boundary conditions, and finally collecting desired properties from the trajectories following basic rules of statistical mechanics. MD simulations for polymers dates back to the 1970s with most studies focused on thermoplastics [21,22] and significantly less work on thermosets. The first fully atomistic MD simulation on 3D polymer networks was carried out by Hamerton et al. [23] for a 200-atom system, and the elastic modulus and glass transition temperatures were predicted in reasonable agreement with experimental data. Doherty et al. [24] first performed MD simulations that allow progressive polymerization reactions. Yarovsky and Evans [25] developed a computational procedure for constructing molecular models of cross-linked polymer networks and applied it to low molecular weight water-soluble epoxy resins cured with different cross-linking agents. Heine et al. [26] simulated the structure and elastic moduli of end-cross- linked poly(dimethylsiloxane) networks using a united atom force field. Wu and Xu [27] developed a method to construct polymer networks for epoxy resin system based on DGEBA (diglycidyl ether bisphenol A) and IPD (isophorone diamine). Komarov et al. [28] reported a computational method where the polymer network is polymerized at a coarse-grained level and then mapped into a fully atomistic model. Varshney et al. [29] studied molecular modeling of thermosetting polymers with special emphasis on cross-linking procedure. Lin and Khare [30] presented a single-step polymerization method for the creation of atomistic model structures of cross-linked polymers. Bermejo and Ugarte [12] introduced a method for building fully atomistic models of chemically cross-linked poly(vinyl alcohol). A more comprehensive review on MD simulations of thermoset polymers can be seen in the Journal of Applied Polymer Science [31]. The core of a MD simulation is the second stage in which a large number of atoms in the simulation system are allowed to interact with each other based on a well-defined molecular mechanics