Nikos Ch. Karayiannis

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

This work is concerned with the atomistic simulation of the volumetric, conformational and structural properties of monodisperse polyethylene (PE) melts of molecular length ranging from C78 up to C1000. In the past, polydisperse models of these melts have been simulated in atomistic detail with the end-bridging Monte Carlo algorithm [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas et al., Macromolecules 32, 5072 (1999)]. In the present work, strictly monodisperse as well as polydisperse PE melts are simulated using the recently introduced double bridging and intramolecular double rebridging chain connectivity-altering Monte Carlo moves [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002)]. These algorithms constitute generalizations of the EB move, since they entail the construction of two trimer bridges between two properly chosen pairs of dimers along the backbones of two different chains or along the same chain. In the simulations, a new molecular model is employed which is a hybrid o...

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.

Structure, Dimensions, and Entanglement Statistics of Long Linear Polyethylene Chains

This work elucidates the effect of both temperature and molecular length on the conformational and structural properties as well as on the entanglement statistics of long amorphous, polydisperse, and molten linear polyethylene (PE). A large number of PE samples are modeled in atomistic detail, with average molecular lengths ranging from C24 up to C1,000 over a wide range of temperatures in the interval of 300 <or= T <or= 600 K under constant pressure (P ) 1 atm). By employing enhanced chain-connectivity-altering moves, full-scale equilibration is achieved within modest computational time even for the longest molecules at ambient conditions.At a second stage, direct geometrical analysis is applied on all equilibrated polymer configurations providing the corresponding primitive paths and intermolecular entanglements. Simulation findings on the characteristic ratio, density, and atomic packing are in excellent agreement with available experimental data. The same holds for the calculated plateau modulus; simulation predicts 1.8 ( 0.1 MPa. Regarding the primitive path statistics, the average contour length and the number of entanglements are found to exhibit a simple exponential type dependency on temperature. For the polydisperse samples studied here, a superposition of Poissonians(often represented by a negative binomial) describes best the distribution of entanglements of the primitive paths.

An advanced Monte Carlo method for the equilibration of model long-chain branched polymers with a well-defined molecular architecture: Detailed atomistic simulation of an H-shaped polyethylene melt

With few exceptions, atomistic simulation work on polymers has been limited to linear chain systems. The main reason for this is the inability of existing Monte Carlo (MC) methods to equilibrate the short- and long-length scale characteristics of nonlinear polymers without destroying their complex molecular architecture. We report here the first MC simulation of a well-defined model long-chain branched polymer, the H-shaped polyethylene melt, in full atomistic detail. The simulation has been executed with an advanced set of chain connectivity-altering moves based on the end-bridging [Pant and Theodorou, Macromolecules 28, 7224 (1995); Mavrantzas et al., Macromolecules 32, 5072 (1999)] and double-bridging [Karayiannis et al., Phys. Rev. Lett. 88, 105503 (2002); Karayiannis et al., J. Chem. Phys. 117, 5465 (2002)] algorithms. The new scheme provides excellent system equilibration at all length scales. The new method opens up the way toward the simulation of other nonlinear polymer systems where chain branch...

Diffusion of small molecules in disordered media: study of the effect of kinetic and spatial heterogeneities

The diffusion of small molecules in disordered media has been studied by employing kinetic Monte Carlo (KMC) simulations and the time-dependent effective medium approximation (EMA). The simulations were conducted in a cubic lattice, to the bonds of which were assigned rate constants governing the elementary jump events, according to a prescribed probability distribution function. Different distributions with a variance ranging from a very small value, representative of a homogeneous medium, to a very large value, representative of a highly disordered, heterogeneous medium, were studied. It was found that the variance of the distribution of rate constants has a profound effect on the diffusion process, giving rise to an anomalous, non-Fickian regime at short time scales. The higher the variance of the distribution, the longer the duration of the anomalous regime and the smaller the value of the diffusion coefficient in the long-time, Fickian regime. The EMA-based calculations are in excellent quantitative agreement with the simulation findings, particularly for distributions of not too high variance. Simulations were also performed on spatially correlated lattices, consisting of domains within each of which the rate constants assume similar values. Spatial correlations were found to strongly influence the diffusion process at short time scales, prolonging the duration of the anomalous regime; at long time scales, however, spatially correlated lattices are characterized by the same diffusivity as uncorrelated ones with the same rate constant distribution.

The structure of random packings of freely jointed chains of tangent hard spheres.

We analyze the structure of dense random packings of freely jointed chains of tangent hard spheres as a function of concentration (packing density) with particular emphasis placed on the behavior in the vicinity of their maximally random jammed (MRJ) state. Representative configurations over the whole density range are generated through extensive off-lattice Monte Carlo simulations on systems of average chain lengths ranging from N=12 to 1000 hard spheres. Several measures of order are used to quantitatively describe either local structure (sphere arrangements and bonded geometry) or global behavior (chain conformations and statistics). In addition, the employed measures are used to elucidate the effect of connectivity on structure, by comparing monatomic and chain assemblies of hard spheres at the MRJ state.

Evolution of fivefold local symmetry during crystal nucleation and growth in dense hard-sphere packings

Crystal nucleation and growth of monodisperse hard-spheres as a function of packing density is studied by collision-driven molecular dynamics simulations. Short-range order in the form of fivefold local symmetry is identified and its dynamical and structural evolution is tracked as the originally amorphous assembly transits to the stable ordered phase. A cluster-based approach shows that hard-sphere configurations having initially a similar average fraction of fivefold and ordered sites can crystallize in completely different patterns both in terms of dynamics and morphology. It is found that at high volume fractions crystallization is significantly delayed in assemblies where sites with fivefold symmetry are abundant. Eventually, once the crystal phase is reached, fivefold symmetry either diminishes or arranges in specific geometric patterns. Such defects are spatially strongly correlated with twinning planes at crystalline boundaries. A detailed analysis is provided on the structural characteristics of the established crystal morphologies.

The characteristic crystallographic element norm: A descriptor of local structure in atomistic and particulate systems

We introduce the characteristic crystallographic element (CCE) norm as a powerful descriptor of local structure in atomistic and particulate systems. The CCE-norm is sensitive both to radial and orientational deviations from perfect local order. Unlike other measures of local order, the CCE-norm decreases monotonically with increasing order, is zero for a perfectly ordered environment, and is strictly discriminating among different, competing crystal structures in imperfectly ordered systems. The CCE-norm descriptor can be used as a sensitive, quantitative measure to detect and track changes in local order in atomistic and general particulate systems. In a specific example we show the ability of the CCE-norm to monitor the onset and evolution of order in an initially amorphous, densely packed assembly of hard-sphere chains generated through extensive Monte Carlo simulations [Phys. Rev. Lett. 100, 050602 (2008)].

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.

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.