Vlasis G. Mavrantzas

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...

On the compatibility between various macroscopic formalisms for the concentration and flow of dilute polymer solutions

A detailed comparison is made of three different formulations of the macroscopic equations governing the concentration changes and the rheology in flows of dilute polymer solutions. More specifically, the governing equations obtained using an inhomogeneous kinetic theory, a continuum two‐fluid Hamiltonian model, and a body‐tensor continuum formalism are compared on a term by term basis. To allow the comparison, an improved kinetic theory‐based model for inhomogeneous polymer solutions is developed in which all terms up to and including second‐order derivatives in space are consistent retained in the Taylor expansions. The analysis is carried out both for the elastic Hookean dumbbell and the bead‐spring Rouse chain models. With both mechanical models, it is seen that the new approach leads to the same equation for the polymer chain number density, which is also identical to that derived by the two continuum models. Regarding the stress evolution equation all formulations are found to lead to identical expressions, provided that second‐ and higher‐order terms (with respect to the deformation gradient) are neglected.

Quantifying chain reptation in entangled polymer melts: Topological and dynamical mapping of atomistic simulation results onto the tube model

The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static (statistical) properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics (MD) trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability psi(s,t) that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed psi(s,t) curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained psi(s,t) curves for three different polymer melts (polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene) are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories (accumulated through long MD simulations) of other model polymers or polymeric systems (e.g., bidisperse, branched, grafted, etc.); it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.

Detailed molecular dynamics simulation of the self-diffusion of n-alkane and cis-1,4 polyisoprene oligomer melts

Results are presented for the self-diffusion properties of monodisperse n-alkanes and cis-1,4 polyisoprene (PI) oligomer melts, as obtained through detailed atomistic molecular dynamics (MD) simulations. The simulations have been conducted in the NVT statistical ensemble on model systems thoroughly pre-equilibrated through an efficient Monte Carlo (MC) algorithm. Results for the self-diffusion coefficient D as a function of molecular weight M support a scaling law of the form D∼Mb, with b strongly depending on temperature T, for both the n-alkanes and the cis-1,4 PI melts. The simulation results have been fitted to an expression for D involving elements of Rouse dynamics and Cohen–Turnbull–Bueche chain-end (excess free volume) effects, proposed recently by von Meerwall et al. [J. Chem. Phys. 108, 4299 (1998)]. Using a geometric analysis involving tessellation of space in Delaunay tetrahedra developed by Greenfield and Theodorou [Macromolecules 26, 5461 (1993)], we have also calculated the excess chain-end...

Structure and dynamics of polymer rings by neutron scattering: breakdown of the Rouse model

We present a static and quasi-elastic neutron scattering study on both the structure and dynamics of a ring polymer in a ring and linear polymer melt, respectively. In the first case, the ring structure proved to be significantly more compact compared to the linear chain with the same molecular weight. In the mixture, the ring molecules swell as was confirmed by small angle neutron scattering (SANS) in accordance with both theory and simulation work. The dynamical behavior of both systems, which for the first time has been explored by neutron spin echo spectroscopy (NSE), shows a surprisingly fast center of mass diffusion as compared to the linear polymer. These results agree qualitatively with the presented atomistic MD simulations. The fast diffusion turned out to be an explicit violation of the Rouse model.

Theoretical study of wall effects on the rheology of dilute polymer solutions

The recently developed generalized bracket formulation of transport phenomena (a Helmholtz free energy‐based approach) is used to predict the rheological behavior of high molecular weight, dilute polymer solutions near planar, smooth, noninteracting solid surfaces. A boundary‐value problem (passage to a stochastic differential equation) is set up in order to estimate the entropy reduction caused by the presence of the solid barrier. Under flow, in addition to diffusional effects, such an entropy reduction results in different conformations of the macromolecules next to the wall, which in turn causes a different than the bulk rheological behavior. The resulting continuum equations account for wall effects under arbitrary flow conditions provided the confining flow boundary is smooth. For the steady‐state simple shear flow, two limiting cases, corresponding to a uniform and a nonuniform (fully developed) concentration profile, have been examined. In both cases, calculated apparent slip velocities are found ...

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...

Atomistic molecular dynamics simulation of diffusion in binary liquid n-alkane mixtures

Well relaxed atomistic configurations of binary liquid mixtures of n-alkanes, obtained via a new Monte Carlo simulation algorithm [Zervopoulou et al., J. Chem. Phys. 115, 2860 (2001)], have been subjected to detailed molecular dynamics simulations in the canonical ensemble. Four different binary systems have been simulated (C5–C78 at T=474 K, C10–C78 at T=458 K, and C12–C60 at T=403.5 and 473.5 K). Results are presented for the diffusion properties of these mixtures over a range of concentrations of the solvent (lighter component). The self-diffusion coefficients of the n-alkanes, calculated directly from the simulations, are reported and compared with the predictions of two theories: the detailed free volume theory proposed by Vrentas and Duda based on the availability of free volume in the blends, and a combined Rouse diffusant and chain-end free volume theory proposed by Bueche and von Meerwall et al. A direct comparison with recently obtained experimental data [von Meerwall et al., J. Chem. Phys. 111,...

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.

Stress gradient-induced migration effects in the Taylor–Couette flow of a dilute polymer solution

Abstract We present an investigation of the phenomenon of stress-induced polymer migration for dilute polymer solutions in the Taylor–Couette device, consisting of two infinitely long, concentric cylinders rotating at constant angular velocities. The underlying physical model is represented by the dilute limit of a two-fluid Hamiltonian system involving two components: one (the polymer) is viscoelastic and obeys the Oldroyd-B constitutive equation, and the other (the solvent) is viscous Newtonian. The two components are considered to be in thermal, but not mechanical equilibrium, interacting with each other through an isotropic drag coefficient tensor. This allows for stress-induced diffusion of polymer chains. The governing equations consist of the continuity and the momentum equations for the bulk velocity, the constitutive model for the polymer chain conformation tensor and the diffusion equation for the polymer concentration. The diffusion equation contains an extra source term, which is proportional to gradients in the polymer stress, so that polymer concentration gradients can develop even in the absence of externally imposed fluxes in the presence of stress inhomogeneities. The solution to the steady-state purely azimuthal flow is obtained first using a spectral collocation method and an adaptive mesh formulation to track the steep changes of the concentration in the flow domain. The calculations show the development of strong polymer migration towards the inner cylinder with increasing Deborah number (De) in agreement with experimental observations. The migration is enhanced for increasing values of the gap thickness resulting in concentration changes by several orders of magnitude in the area between the inner and outer cylinder walls. The extent of the migration also depends strongly on the ratio of the solvent to the polymer viscosity. In addition to a strongly inhomogeneous polymer concentration, significant deviations from the homogenous flow are also observed in the velocity profile. Next, results are reported from a linear stability analysis around the steady-state solution against axisymmetric disturbances corresponding to various wavenumbers in the axial direction. The calculations show that the steady-state solution remains stable up to moderate values of the Deborah number, explaining why some of the predicted stress-induced migration effects should be experimentally observable. The role of the Peclet number (Pe) on the stability of the system is elucidated.