Analytic Gradients for the Effective Fragment Molecular Orbital Method

The analytic gradient for the Coulomb, polarization, exchange-repulsion, and dispersion terms of the fully integrated effective fragment molecular orbital (EFMO) method is derived and the implementation is discussed. The derivation of the EFMO analytic gradient is more complicated than that for the effective fragment potential (EFP) gradient, because the geometry of each EFP fragment is flexible (not rigid) in the EFMO approach. The accuracy of the gradient is demonstrated by comparing the EFMO analytic gradient with the numeric gradient for several systems, and by assessing the energy conservation during an EFMO NVE ensemble molecular dynamics simulation of water molecules. In addition to facilitating accurate EFMO geometry optimizations, this allows calculations with flexible EFP fragments to be performed

Mechanisms Underlying Ion Transport in Lamellar Block Copolymer Membranes

Recent experiments have reported intriguing trends for the molecular weight (MW) dependence of the conductivity of block copolymer lamellae that contrast with the behavior of homopolymer matrices. By using coarse-grained simulations of the sorption and transport of penetrant cations, we probe the possible mechanisms underlying such behavior. Our results indicate that the MW dependence of conductivity of homopolymeric and block copolymeric matrices arise from different mechanisms. On the one hand, the solvation energies of cations, and, in turn, the charge carrier concentrations, themselves, exhibit a MW dependence in block copolymer matrices. Such trends are shown to arise from variations in the thickness of the conducting phase relative to that of the interfacial zones. Moreover, distinct mechanisms are shown to be responsible for the diffusivities of ions in homopolymer and block copolymer matrices. In the former, diffusivity effects associated with the free ends of the polymers play an important role. In contrast, in block copolymer lamellae, the interfacial zone between the blocks presents a zone of hindered diffusivity for ions and manifests as a molecular weight dependence of the ionic diffusivity. Together, the preceding mechanisms are shown to provide a plausible explanation for the experimentally observed trends for the conductivity of block copolymer matrices