David T. Wu, PhD , Colorado School of Mines
In the first year, a new graduate student was trained in both the underlying theory and simulation methodologies. In particular, he built a software platform for rapidly developing and testing analytical liquid-state (statistical mechanical) theories for the conformations and pair-distribution functions of ion/polymer molecule mixtures. In addition, atomistic MD simulations were also being developed to compare with the analytical theory. A liquid-state theory approach was adopted because of the possibility of accounting for the local molecular conformations around a complexed ion. The complexation typically involves 12 -20 backbone atoms, for instance 4-6 oxygen atoms in polyethylene-oxide. While the overall polymer might be described as a random walk on a coarse-grained level, the theory is expected to be able to predict atomic pair-correlation functions for molecules of this smaller size.
We tested the ability of the theory to capture atomic-level structure by considering a model system of a melt of cyclic polymers with 20 atoms along the backbone, accounting for steric effects. These cyclic polymers are small enough that the coarse-grained theories invoking a random walk conformation do not apply. Using a Wall-PRISM (Polymer Reference Interaction Site Model) theory, we calculated the ordering of the cyclic polymers at an interface, assuming a non-overlapping freely jointed chain model for the intramolecular conformations. In addition, we carried out molecular dynamics simulations of these molecules to obtain more realistic intramolecular distribution functions. We compared with neutron reflectivity experiments on blends of linear and cyclic polymers that produced composition profiles at the interface. Our theory showed that the linear polymers were enriched at the surface compared to their bulk composition, in agreement with experiment. We were able to determine that in fact both linear and cyclic polymers are attracted to the interface, but that the linear molecules are attracted more strongly.
With the liquid-state theory code developed and tested, we have merged this code with code to carry out Monte Carlo sampling of polymer conformations to provide more accurate intramolecular pair-correlation functions needed as inputs into the PRISM part of the theory. We are currently carrying out calculations on small linear and cyclic chains together with lithium ions to study the complexation geometry and binding energy, and are planning to extend our studies to more computationally intensive calculations involving long-chain polymers mixed with lithium ions.
This Petroleum Research Fund grant has been of significant benefit to the principal investigator in allowing for continuity in his long-term theoretical research on atomistic effects in polymer structure and interactions, and allows him to build on and extend from this expertise to attack fundamental problems relevant to battery technology. Moreover, this support has also allowed the training of a motivated and bright graduate student, coming from a non-theoretical background, to be able to learn the significant core knowledge and skills, including the statistical mechanics of atomistically realistic molecules as well as coarse-grained polymers, numerical analysis and programming, and large-scale simulation, needed to attack the complex theoretical problems associated with ionic transport in polymer electrolytes.