Atomistic Monte Carlo simulation of strictly monodisperse long polyethylene melts through a generalized chain bridging algorithm

Combined molecular algorithms for the generation, equilibration and topological analysis of entangled polymers: methodology and performance

We review the methodology, algorithmic implementation and performance characteristics of a hierarchical modeling scheme for the generation, equilibration and topological analysis of polymer systems at various levels of molecular description: from atomistic polyethylene samples to random packings of freely-jointed chains of tangent hard spheres of uniform size. Our analysis focuses on hitherto less discussed algorithmic details of the implementation of both, the Monte Carlo (MC) procedure for the system generation and equilibration, and a postprocessing step, where we identify the underlying topological structure of the simulated systems in the form of primitive paths. In order to demonstrate our arguments, we study how molecular length and packing density (volume fraction) affect the performance of the MC scheme built around chain-connectivity altering moves. In parallel, we quantify the effect of finite system size, of polydispersity, and of the definition of the number of entanglements (and related entanglement molecular weight) on the results about the primitive path network. Along these lines we approve main concepts which had been previously proposed in the literature.

Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

Contact network in nearly jammed disordered packings of hard-sphere chains

We present salient results of the analysis of the geometrical structure of a large fully equilibrated ensemble of nearly jammed packings of linear freely jointed chains of tangent hard spheres generated via extensive Monte Carlo simulations. In spite the expected differences due to chain connectivity, both the pair-correlation function and the contact network for chain packings are found to strongly resemble those in packings of monomeric hard spheres at the maximally random jammed (MRJ) state. A remarkable finding of the present work is the tendency of chains to form closed loops at the MRJ state as a consequence of chain collapse. Our simulations on disordered nearly jammed chain packings yield an average coordination number of 6, which fulfills the isostaticity condition and is in excellent agreement with the corresponding simulation [A. Donev, S. Torquato, and F. H. Stillinger, Phys. Rev. E 71, 011105 (2005)] and experimental [T. Aste, M. Saadatfar, and T. J. Senden, Phys. Rev. E 71, 061302 (2005)] findings for jammed packings of monatomic hard spheres. An exact correspondence between the statistical-mechanical ensembles of monomeric spheres and of hard-sphere chains offers insights regarding the structure and topology of the contact network of hard-sphere systems at the MRJ state.

Cooperative dynamics in homopolymer melts: a comparison of theoretical predictions with neutron spin echo experiments

We present a comparison between theoretical predictions of the generalized Langevin equation for cooperative dynamics (CDGLE) and neutron spin echo data of dynamic structure factors for polyethylene melts. Experiments cover an extended range of length and time scales, providing a compelling test for the theoretical approach. Samples investigated include chains with increasing molecular weights undergoing dynamics across the unentangled to entangled transition. Measured center-of-mass (com) mean-square displacements display a crossover from subdiffusive to diffusive dynamics. The generalized Langevin equation for cooperative dynamics relates this anomalous diffusion to the presence of the interpolymer potential, which correlates the dynamics of a group of slowly diffusing molecules in a dynamically heterogeneous liquid. Theoretical predictions of the subdiffusive behavior, of its crossover to free diffusion, and of the number of macromolecules undergoing cooperative motion are in quantitative agreement with experiments.

Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross-over predictions

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12-500 and at packing densities from dilute ones up to the maximally random jammed state.

Molecular simulation of the effect of temperature and architecture on polyethylene barrier properties

We present a multiscale approach for calculating the low-concentration solubility, diffusivity, and selectivity of small molecules through polymer matrixes. The proposed modeling scheme consists of two main stages; first, thoroughly equilibrated and representative poly(ethylene) (PE) atomistic melt configurations were obtained through the application of a Monte Carlo (MC) scheme based on advanced chain-connectivity altering moves (linear architectures) or the combination of localized MC moves followed by molecular dynamics. In the second phase, transition-state theory (TST), as proposed by Gusev and Suter [Gusev, A. A.; Suter, U. W. J. Chem. Phys. 1993, 99, 2228], was invoked in a coarser level of description to calculate the barrier properties of the studied macromolecules to small gas molecules at infinite dilution. The multiscale methodology was successfully applied on PE melts characterized by various molecular weights (MW) (from C78 up to C1000) and polydispersity indices at a wide range of temperature conditions. The effect of molecular architecture on the barrier properties was examined through the comparison between linear and short-chain branched structures bearing the same total number of carbon atoms. Simulation results were found to be in very good agreement with available experimental data. Additionally, the new scheme has been further validated by comparing the qualitative behavior of solubility, diffusivity, and selectivity with previously reported trends in the literature based on both experimental and simulation studies. The present study concludes that density plays a dominant role that determines the behavior of the polymer as a barrier material, especially in terms of diffusivity. Additionally, it is evidenced that short-chain branching has a small effect on the barrier properties of PE when the comparison is performed on purely amorphous samples. The hierarchical method presented here not only is faster when compared against conventional molecular dynamics simulations, but in some cases, like the vicinity of the glass transition temperature or for long polymer chain melts, it opens the way to the calculation of the barrier properties at realistic simulation times.

Min-map bias Monte Carlo for chain molecules: biased Monte Carlo sampling based on bijective minimum-to-minimum mapping

A novel Monte Carlo (MC) simulation scheme based on Theodorou's bijective mapping strategy [D. N. Theodorou, J. Chem. Phys. 124, 034109 (2006)] is introduced. This min-map bias Monte Carlo acts in combination with any other proper, bare MC. It carries over the bare MC move from the original configuration space Omega(0), where trial move acceptance may be low, to a different configuration space, Omega(1), where acceptance is higher. The bare MC move is then performed in Omega(1) and the resulting configuration is finally mapped back to Omega(0). Mappings between Omega(0) and Omega(1) entail weighted selection of trial configurations, the bias of which is subsequently removed in the overall acceptance criterion. The new method is applied, in conjunction with continuum configurational bias as bare MC scheme, to the simulation of explicit hydrogen linear alkanes in the canonical ensemble. Min-map bias MC is found to alleviate the pervasive problem of very low acceptance rates encountered when using an explicit molecular description.

Accelerating molecular simulations by reversible mapping between local minima

A new framework is presented for performing Monte Carlo simulations of condensed matter based on a recently developed bijective mapping between local energy minima. The framework is used to implement a range of new multiparticle Monte Carlo moves, which are investigated by simulating atomic Lennard-Jones fluids in the canonical and grand canonical ensembles. Important aspects of the simulation protocol and their effect on performance are analyzed in detail. Using the mapping accelerates the simulations by many orders of magnitude when compared to the equivalent moves without the mapping, and leads to particularly efficient configurational sampling at low temperatures and high densities. The method appears to be suitable for adapting to quantitative simulations of more complex molecular systems over long effective time scales.

Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments

We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion u(s) approximately s/rho R3(s) approximately c(e)/sqrt[s] when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c(e) approximately 1/rho b(e)3 the "swelling coefficient," b(e) the effective bond length, and rho the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to u(s). The analysis of different moments of this distribution allows for a precise determination of the effective bond length b(e) and the swelling coefficient c(e) of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by s monomers along the chain is found to decay algebraically as 1/s(3/2). Effects of finite chain length are briefly considered.

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.

Effect of equilibration on primitive path analyses of entangled polymers

We use recently developed primitive path analysis (PPA) methods to study the effect of equilibration on entanglement density in model polymeric systems. Values of Ne for two commonly used equilibration methods differ by a factor of 2-4 even though the methods produce similar large-scale chain statistics. We find that local chain stretching in poorly equilibrated samples increases entanglement density. The evolution of Ne with time shows that many entanglements are lost through fast processes such as chain retraction as the local stretching relaxes. Quenching a melt state into a glass has little effect on Ne. Equilibration-dependent differences in short-scale structure affect the craze extension ratio much less than expected from the differences in PPA values of Ne.

Computational Study of the Structure, Dynamics, and Photophysical Properties of Conjugated Polymers and Oligomers under Nanoscale Confinement

Computational simulations were used to investigate the dynamics and resulting structures of several para-phenylenevinylene (PPV) based polymers and oligomers (PPV, 2-methoxy-5-(2'-ethyl-hexyloxy)-p-phenylenevinylene --> MEH-PPV and 2,5,2',5'-tetrahexyloxy-7,8'-dicyano-p-phenylenevinylene --> CN-PPV). The results show how the morphology and structure are controlled to a large extent by the nature of the solute-solvent interactions in the initial solution-phase preparation. Secondary structural organization is induced by using the solution-phase structures to generate solvent-free single molecule nanoparticles. Isolation of these single molecule nanostructures from microdroplets of dilute solution results in the formation of electrostatically oriented nanostructures at a glass surface. Our structural modeling suggests that these oriented nanostructures consist of folded PPV conjugated segments with folds occurring at tetrahedral defects (sp3 C-C bonds) within the polymer chain. This picture is supported by detailed experimental fluorescence and scanning probe microscopy studies. We also present results from a fully quantum theoretical treatment of these systems which support the general conclusion of structure-mediated photophysical properties.

Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene

We present the derivation of coarse-grained force fields for two types of polymers, polyethylene (PE), and cis-polybutadiene (cis-PB), using the concept of potential of mean force. Coarse-grained force fields were obtained from microscopic simulations for several coarse-graining levels, i.e., different number of monomers lambda per mesoscopic unit called "bead." These force fields are then used in dissipative particle dynamics (DPD) simulations to study structural and dynamical properties of polymer melts of PE and cis-PB. The radial distribution functions g(R), the end-to-end distance R0, the end-to-end vector relaxation time tau, and the chain center of mass self-diffusion D(CM), are computed for different chain lengths at different coarse-graining factor lambda. Scaling laws typical of the Rouse regime are obtained for both polymers for chain lengths ranging from 6 to 50 beads. It is found that the end-to-end distance R0 obtained from DPD simulations agree well with values obtained from both microscopic simulations and experiments. The dependence of the friction coefficient used in DPD simulations versus the coarse-graining level is discussed in view of the overall scaling of the dynamical properties.