We report a quantitative analysis of the detailed equilibrium atomic structure of molten linear polyethylene, obtained using directed bridging Monte Carlo computer simulation techniques. The polydisperse sample has an average chain length of 6000 backbone carbon atoms, or approximately 84000 g mol −1 . This molecular weight greatly exceeds that used in previous atomistic simulation studies, and is typical of commercial grades that are widely used for injection moulded articles. This large-scale simulation allows direct measurement of such properties as the chain entanglement length, the characteristic ratio, and the extended-range intermolecular packing density fluctuations which give rise to the first sharp diffraction peak.
A new class of Monte Carlo algorithms for atomistic simulation of genuine high polymer systems is proposed. Derivations of two of these algorithms, dubbed "directed internal bridging" (DIB) and "directed end bridging" (DEB), are presented. Their performance is analyzed in detail, using linear united-atom polyethylene of mean chain length C 1000 as an archetypal entangled polymer melt. It is shown in particular that the DEB algorithm is substantially faster than previous alternatives in equilibrating such melts on all length scales. Used in a suitable protocol of mixed Monte Carlo moves, it thus provides the most powerful means available to date for quantitative molecular simulation of such materials, and makes atomic level characterization of realistic high polymer melts a feasible proposition.
Eleven different epoxy/diamine systems, including tetraglycidyl‐4,4′‐diaminodiphenylmethane (TGDDM), triglycidyl p‐aminophenol (TGAP), and diglycidyl ether of bisphenol A (DGEBA) with 4,4′‐diaminodiphenylsulfone (DDS), diethyltoluenediamine (DETDA), dimethylthiotoluenediamine (DMTDA), and meta‐phenylenediamine (m‐PDA), were studied with near‐infrared spectroscopy at different temperatures. The reactivities of the epoxies were determined and found to be in the following order when reacted with the same amine: DGEBA > TGAP > TGDDM. When the primary amine was reacted with the same epoxy, the order was DETDA > DDS > DMTDA; for the secondary amine, the order was DETDA > DMTDA > DDS. The relative reaction rates of the secondary amine to the primary amine were compared and discussed in terms of the structural differences and the corresponding substitution effect. It was concluded that the increase in the secondary amine reactivity of DETDA and DMTDA was caused by the deconjugation of the benzene‐ring π electrons from the lone pair on the N atom. The overall order of the secondary amine relative reactivity was DMTDA > DETDA > DDS for the same epoxy and TGDDM > TGAP > DGEBA for the same amine. The m‐PDA systems had no significant positive or negative substitution effects. Molecular orbital calculations were performed, and the results showed the most significant deconjugation effect in the secondary amine of DETDA. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3143–3156, 2004
The challenge of controlled sampling of the conformations of internal sections of chain molecules, subject to constrained interatomic bond lengths and angles, is central to many areas of macromolecular science. A new method for overcoming this challenge via an internal configuration bias (ICB) Monte Carlo algorithm is described. It is demonstrated that the algorithm obeys the detail balance (microscopic reversibility) criterion necessary for performing rigorous molecular simulations in equilibrium ensembles. The algorithm is applied to a study of the molecular conformations of cyclic alkane molecules in a vacuum, where it is shown to be up to ∼2 orders of magnitude more efficient than standard molecular dynamics simulation techniques. Qualitative transitions between constrained ring and flexible chain behavior are observed between 16 and 30 backbone atoms for local structure (torsion angle distribution) and between 30 and 50 backbone atoms for global ring dimensions.
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