Fluid Phase Equilibria 351 (2013) 61–68 Contents lists available at SciVerse ScienceDirect Fluid Phase Equilibria j ourna l ho me page: www.elsevier.com/locate/fluid Polymer equations of state derived from molecular simulation Amir Vahid, J. Richard Elliott * Chemical and Biomolecular Engineering Department, The University of Akron, Akron, OH 44325-3906, United States a r t i c l e i n f o Article history: Received 5 July 2012 Received in revised form 7 October 2012 Accepted 8 October 2012 Available online 17 October 2012 Keywords: Polymer Equation of state Molecular simulation Thermodynamic perturbation theory Discontinuous molecular dynamics Transferable potential models Characteristic ratio a b s t r a c t This work characterizes fluid equations of state for many common polymers from small oligomers to the infinite chain limit. The methodology applies the formalism of discontinuous molecular dynamics (DMD) and thermodynamic perturbation theory (TPT) previously developed for polyethylene [1,2]. Oligomers with each structure are simulated for a series of molecular weights varying from the monomer to roughly 1100 g/mol. Each oligomer is simulated at 21 densities to interpolate the reference and perturbation con- tributions to the equation of state. Plotting the perturbation term vs. density for a polymer series leads to an asymptotic inference in the long chain limit. Interpolation functions are then developed to char- acterize the polymer at any molecular weight. The polymers characterized include polyethyleneoxide, polylacticacid, polypropylene, polyisoprene, and polystyrene. The characterizations are compared to the result of Wertheim’s theory of polymerization to show how individual monomer structure lead distinctive behavior. Given these characterizations, it is straightfor- ward to predict phase behavior of polymer blends and solutions that can be tested by experiment and targeted molecular simulations at specific compositions. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Polymers and polymer solutions comprise a significant portion of global petrochemical output. Analysis of all polymer products, their monomers and precursors, plasticizers, and solvents shows that the volume in tons per year of these materials substantially exceeds all chemical applications except fuels [3]. Nevertheless, the thermodynamic pedagogy for polymers and polymer solutions is not as fully developed as it is for small molecules. To some extent, this may be excused because poly- mers simply exhibit solution behavior similar to smaller molecules. On the other hand, there are many behaviors that are peculiar to polymers in general and even to specific polymeric architectures. The large number of repeat units tends to amplify the impacts of molecular interactions such that small differences in solubility parameter, for example, lead to large differences in macroscopic behavior, like virtually complete immiscibility of most polymer blends. Similarly, arrangements of copolymers and block copoly- mers open the door to a myriad of materials and morphologies. Further study reveals that not only intermolecular interactions are involved, but conformational details have major impacts. The com- binations of homopolymers, copolymers, and conformations lead to a wide range of materials, each with its own peculiar properties and thermodynamic behavior. * Corresponding author. Tel.: +1 330 972 7253; fax: +1 330 972 5856. E-mail address: jelliott@uakron.edu (J.R. Elliott). The subject of polymer thermodynamics advanced significantly through the adaptation of Wertheim’s theory and the related SAFT methodology to provide a rigorous, off-lattice connection from spherical molecules to polymers. Wertheim’s theory describes how monomeric segments can assemble into tangent sphere chains. The theory can be extended to describe copolymers, but always within the context of tangent sphere chains of segments composed of multiple atoms. The identification of atoms comprising a spher- ical “segment” can be ambiguous, and peculiar to the polymer. Furthermore, conformational behavior is peculiar to each poly- mer and even to the polymer–solvent combination, whereas the behavior of tangent sphere chains represents a singular, idealized conformational characterization. A complete pedagogy of polymer thermodynamics must be capable of distinguishing polymers at the atomic level, including peculiar conformational effects. Molecular simulation offers the prospect of atomic scale res- olution of polymer structures and conformational effects but there are challenges related to the system sizes required to represent truly polymeric behavior. Polymer simulation can be approached by assuming atomic interactions developed through the characterization of small molecules and their solutions through the principle of transferability. Similarly, the descriptions of intramolecular interactions like bond angles and dihedral distribu- tions are straightforwardly extended to bonding between multiple monomers. A problem arises, however, in deciding how many monomers must be bonded together in the simulation in order to achieve a description of a polymer of virtually infinite molec- ular weight. Is it sufficient, for example, to simply characterize the 0378-3812/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fluid.2012.10.008