Wayne L. Mattice

Bridging the gap between atomistic and coarse-grained models of polymers : Status and perspectives

Recent developments that increase the time and distance scales accessible in the simulations of specific polymers are reviewed. Several different techniques are similar in that they replace a model expressed in fully atomistic detail with a coarse-grained model of the same polymer, atomistic → coarse-grained (and beyond!), thereby increasing the time and distance scales accessible within the expenditure of reasonable computational resources. The bridge represented by the right-pointing arrow can be constructed via different procedures, which are reviewed here. The review also considers the status of methods which reverse this arrow, atomistic ← coarse-grained. This “reverse-mapping” recovers a model expressed in fully atomistic detail from an arbitrarily chosen replica generated during the simulation of the coarse-grained system. Taken in conjunction with the efficiency of the simulation when the system is in its coarse-grained representation, the overall process Open image in new window permits a much more complete equilibration of the system (larger effective size of Δt) when that equilibration is performed with the coarse-grained replicas (II → III) than if it were attempted with the fully atomistic replicas (I → IV).

Diffusion of liquid n-alkanes: Free-volume and density effects

In support of our numerical simulations of self-diffusion D of chain molecules in the melt, we have used the pulsed-gradient spin-echo NMR method to make detailed D measurements in 15 liquid n-paraffins (8–60 carbons; molecular weight M=114–844) at eight temperatures T from 30 to 170 °C. We find that D∼Mβ, with β changing approximately linearly from −2.72 to −1.85 as T increases. Thus the apparent activation energies also rises linearly with log M. In the absence of molecular entanglements, Rouse kinetics predicts β=−1, but Cohen–Turnbull–Bueche free-volume effects due to molecular chain ends add a further nonpower-law term, enhancing D increasingly at low M. The combined D vs M theory does, however, closely mimic a power law with the exponents observed at all our measurement temperatures. To obtain this result it is necessary to include in the free-volume term the dependence of the liquid’s density on M and T, analytically modeled based on the incomplete literature data. The fitted density model itself i...

Structure and energy of thin films of poly-(1,4-cis-butadiene): A new atomistic approach

SummaryIn this work we study the formation of a thin film in vacuum by collapsing a random parent chain under two-dimensional boundary conditions. The initial random parent chain is obtained from atomistic simulation of bulk amorphous poly-(1,4-cis-butadiene). Films with a thickness of ∼25 Å are obtained for parent chains with 100 monomers. The density drops off sigmoidally over a distance of ∼5 Å near the free surfaces, while in the interior bulk density is obtained. The backbone bonds are randomly oriented in the interior and sharply oriented along the film plane near the free surfaces; the onset of order corresponds roughly with the drop in the mass density from its bulk value. The trans state of the CH2 -CH2 bond is also enriched compared to the bulk, in order for the chain to track the plane of the film more effectively. The difference in the energy of a chain in the amorphous bulk (3D periodic) and in the thin film (2D periodic) allows us to calculate the internal energy contribution to the surface energy; the agreement with the experimental value is reasonable.

Circular dichroism and absorption study of the structure of methionine-enkephalin in solution.

Abstract The circular dichroism and absorption spectra of methionine-enkephalin have been measured in aqueous solution, as functions of temperature and pH, and in 2,2,2-trifluoroethanol. Ranges covered were: 190–330 nm; 5–50°C; pH = 1–12. Absorption data provide no evidence for a strong intramolecular hydrogen bond involving the hydroxyl proton of the tyrosine residue. All data can be interpreted without assuming methionine-enkephalin preferentially occupies a single conformation when in dilute solution. The biologically important conformation is presumably one of many which are present to significant extent.

LOCAL CHAIN DYNAMICS OF BULK AMORPHOUS POLYBUTADIENES : A MOLECULAR DYNAMICS STUDY

The local motions of bulk amorphous polybutadienes (PBDs) have been studied by a molecular dynamics simulation. Fully atomistic models of PBDs have been obtained at a realistic bulk density under periodic boundary conditions. Local chain motions are examined for poly(cis‐1,4‐butadiene) (cis‐PBD) and poly(trans‐1,4‐butadiene) (trans‐PBD) well above the glass transition temperature, where the only structural difference is imposed by the different conformational states at the double bond. The local motions are found to be strikingly different in the two polymers. Intramolecular cooperative conformational transitions occur at second‐neighbor bond pairs of CH–CH2 in both PBDs. In trans‐PBD, both CH2–CH2 and CH=CH triplets undergo cooperative counterrotations. In cis‐PBD, CH2–CH2 triplets undergo counterrotations while CH=CH triplets undergo corotations. Intermolecular cooperativity, probed by the local free volume, has little influence on local relaxation processes. The effect of libration on the shape of autocorrelation functions (ACFs) is significant over the entire time range. A universality is found in the time evolution of the Kohlrausch–Williams–Watts exponent regardless of the type and order of the ACF. On the other hand, the single exponential decay regarded as common at short times is only due to the discreteness of conformational states.

Rotational isomeric state chains on a high coordination lattice: Dynamic Monte Carlo algorithm details

A high coordination lattice model for simulating coarse-grained rotational isomeric state (RIS) chains has been under development recently. Initially, the model was developed for chains with symmetric torsional potential energy functions, E(φ)=−E(φ). A single-bead move Monte Carlo algorithm was used and found to be effective in simulating polyethylene chains. A modification was subsequently developed to allow for the simulation of chains with an asymmetric torsional potential, E(φ)≠−E(φ). The single-bead move Monte Carlo (MC) algorithm employed previously was found to be ineffective following this modification. Similar kinetic effects have been seen previously with single-bead MC moves on the cubic lattice, which lead to the Hilhorst–Deutch modification (two-bead crankshaft MC move) of the Verdier–Stockmayer (single-bead move MC) algorithm. A reptation MC move applied to this model appears problematic. A multiple-bead MC move is developed using the pivot algorithm formalism in order to avoid the lattice m...

New high-coordination lattice model for rotational isomeric state polymer chains

New methods for coarse graining polymer chains onto lattice systems have been investigated. The mapping should take place in a rather local and exact manner to retain the specific properties of the considered polymer system. First a short overview is given of the types of lattice representations of polymer chains currently available. Secondly a method based on high-coordination lattices that has proven to be successful for mapping proteins is examined and shown to be unsuitable for interdependent bond directions. Thirdly, a new high-coordination lattice model is introduced and results of single-chain simulations are shown. These results of random walk chains, non-reversal walk chains and self-avoiding walk chains agree well with the expected theoretical values.

Detection of the rate of exchange of chains between micelles formed by diblock copolymers in aqueous solution

SummaryA fluorescence method is described for the measurement of the rate of exchange of chains between micelles formed by diblock copolymers in aqueous solution. The method requires two samples of the diblock copolymer. One sample is labelled with a Förster donor, the other sample is labelled with a Förster acceptor. Successful application of the method is demonstrated with diblock copolymers composed of polystyrene and poly(ethylene oxide). The donor and acceptor are naphthalene and pyrene, respectively. The label is covalently attached to the copolymers at the junction points between the two blocks. Solutions with micelles are formed independently by the two labelled samples. At the time of mixing of the two solutions, no micelle contains both a donor and an acceptor. Micelles containing both types of labels may be formed at later times as a consequence of the exchange of labelled chains. The efficiency of nonradiative singlet energy transfer from naphthalene to pyrene is measured as a function of time after mixing of the two solutions. At 60° C the rate constant deduced from the time dependence of the fluorescence is on the order 10-5 s-1. At ambient temperature, however, no exchange can be detected, presumably because of the difficulty in extraction of a polystyrene block from the glassy core.

Intramolecular excimer formation in model compounds for polyesters prepared from 2,6-naphthalene dicarboxylic acid and eight different glycols

Abstract Fluorescence has been measured in dilute solutions of model compounds for polymers of 2,6-naphthalene dicarboxylic acid and eight different glycols. The glycols are HO-(CH 2 ) i -OH, i = 2–6, and H-(OCH 2 CH 2 ) j -OH, j = 1–4. The ratio of excimer to monomer emission depends on the glycol used. Studies as functions of temperature and solvent show that, in contrast with the analogous polyesters in which the naphthalene moiety is replaced with a benzene ring, there can be a substantial dynamic component to the excimer emission. Extrapolation to media of infinite viscosity shows that in the absence of rotational isomerism during the lifetime of the singlet excited state, there is an odd-even effect in the series in which the flexible spacers differ in the number of methylene units, but not in the series in which the flexible spacers differ in the number of oxyethylene units.

Atomistic modeling of the diffusion of small penetrant molecules in the bulk amorphous polyimide of 3,3′,4,4′-benzophenonetetracarboxylic dianhydride and 2,2-dimethyl-1,3-(4-aminophenoxy) propane

Abstract Diffusion of two small penetrant molecules, O 2 and N 2 , in the bulk amorphous polyimide of 3,3′,4,4′-benzophenonetetracarboxylic dianhydride and 2,2-dimethyl-1,3-(4-aminophenoxy) propane is studied with molecular dynamics simulations. This polyimide is abbreviated as PI-2. The temperature of the simulation is chosen to be slightly below the experimental glass transition temperature of PI-2 (230°C, or 503 K). The ratio of the diffusion coefficients of O 2 and N 2 in PI-2 from the simulation compares favorably with experimental results of the same ratio in structurally similar glassy polyimides. Detailed analysis is performed for the diffusion of O 2 in PI-2. Throughout the molecular dynamics trajectory, O 2 for most of the time is trapped in certain locations (voids) of the polymer matrix. The residence time is on the order of 100 ps. Occasionally, an O 2 goes into a fast motion and translates rapidly to a neighboring void. Some voids are visited by different O 2 at different times, indicating that although the thermal fluctuations of the polymer matrix play an important part in the diffusion process, conformational relaxation of the polymer chains may not be important for estimating the diffusion coefficient. The chemical and geometric environment of O 2 is studied via the pair correlation functions of the diffusant molecules and the atoms in the polymer. For some of the atoms in PI-2, the peaks in the pair correlation functions do not correspond exactly to the sum of the van der Waals radii of the atom in the diffusant molecule and the atom in the polymer chain. This finding indicates that the local packing of the amorphous polymer tends to shield some of the atoms from close contact with the diffusant molecules in the diffusion process. The atomic grouping in PI-2 that have the greatest exposure to O 2 are identified.