Chunggi Baig

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.

Rheological and structural studies of liquid decane, hexadecane, and tetracosane under planar elongational flow using nonequilibrium molecular-dynamics simulations

We report for the first time rheological and structural properties of liquid decane, hexadecane, and tetracosane using nonequilibrium molecular-dynamics (NEMD) simulations under planar elongational flow (PEF). The underlying NEMD algorithm employed is the so-called p-SLLOD algorithm [C. Baig, B. J. Edwards, D. J. Keffer, and H. D. Cochran, J. Chem. Phys. 122, 114103 (2005)]. Two elongational viscosities are measured, and they are shown not to be equal to each other, indicating two independent viscometric functions in PEF. With an appropriate definition, it is observed that the two elongational viscosities converge to each other at very low elongation rates, i.e., in the Newtonian regime. For all three alkanes, tension-thinning behavior is observed. At high elongation rates, chains appear to be fully stretched. This is supported by the result of the mean-square end-to-end distance of chains (R(ete2)) and the mean-square radius of gyration of chains (R(g2)), and further supported by the result of the intramolecular Lennard-Jones (LJ) potential energy. It is also observed that (R(ete2)) and (R(g2)) show a different trend as a function of strain rate from those in shear flow: after reaching a plateau value, (R(ete2)) and (R(g2)) are found to increase further as elongation rate increases. A minimum in the hydrostatic pressure is observed for hexadecane and tetracosane at about epsilon(msigma2/epsilon)1/2=0.02. This phenomenon is shown to be associated with the intermolecular LJ potential energy. The bond-bending and torsional energies display similar trends, but a different behavior is observed for the bond-stretching energy. An important observation common in these three bonded-intramolecular interactions is that all three modes are suppressed to a small value at high elongation rates. We conjecture that a liquid-crystal-like, nematic structure is present in these systems at high elongation rates, which is characterized by a strong chain alignment with a fully stretched conformation.

A proper approach for nonequilibrium molecular dynamics simulations of planar elongational flow

We present nonequilibrium molecular dynamics simulations of planar elongational flow (PEF) by an algorithm proposed by Tuckerman et al. [J. Chem. Phys. 106, 5615 (1997)] and theoretically elaborated by Edwards and Dressler [J. Non-Newtonian, Fluid Mech. 96, 163 (2001)], which we shall call the proper-SLLOD algorithm, or p-SLLOD for short. [For background on names of algorithms see W. G. Hoover, D. J. Evans, R. B. Hickman, A. J. C. Ladd, W. T. Ashurst, and B. Moran, Phys. Rev. A 22, 1690 (1980) and D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984).] We show that there are two sources for the exponential growth in PEF of the total linear momentum of the system in the contracting direction, which has been previously observed using the so-called SLLOD algorithm. The first comes from the SLLOD algorithm itself, and the second from the implementation of the Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] boundary conditions. Using the p-SLLOD algorithm (to eliminate the first source) implemented with our simulation strategy (to eliminate the second) in PEF simulations, we no longer observe the exponential growth. By analyzing the equations of motion, we also demonstrate that both the SLLOD and the DOLLS algorithms are intrinsically unsuitable for representing a nonequilibrium system with elongational flow. However, the p-SLLOD algorithm has a rigorously canonical structure in laboratory phase space, and thus can represent a nonequilibrium system not only for elongational flow but also for a general flow.

Rheological and structural studies of linear polyethylene melts under planar elongational flow using nonequilibrium molecular dynamics simulations

We present various rheological and structural properties of three polyethylene liquids, C50H102, C78H158, and C128H258, using nonequilibrium molecular dynamics simulations of planar elongational flow. All three melts display tension-thinning behavior of both elongational viscosities, eta1 and eta2. This tension thinning appears to follow the power law with respect to the elongation rate, i.e., eta approximately epsilon(b), where the exponent b is shown to be approximately -0.4 for eta1 and eta2. More specifically, b of eta1 is shown to be slightly larger than that of eta2 and to increase in magnitude with the chain length, while b of eta2 appeared to be independent of the chain length. We also investigated separately the contribution of each mode to the two elongational viscosities. For all three liquids, the intermolecular Lennard-Jones (LJ), intramolecular LJ, and bond-stretching modes make positive contributions to both eta1 and eta2, while the bond-torsional and bond-bending modes make negative contributions to both eta1 and eta2. The contribution of each of the five modes decreases in magnitude with increasing elongation rate. The hydrostatic pressure shows a clear minimum at a certain elongation rate for each liquid, and the elongation rate at which the minimum occurs appears to increase with the chain length. The behavior of the hydrostatic pressure with respect to the elongation rate is shown to correlate with the intermolecular LJ energy from a microscopic viewpoint. On the other hand, R(ete)2 and R(g)2 appear to be correlated with the intramolecular LJ energy. The study of the effect of the elongational field on the conformation tensor c shows that the degree of increase of tr(c)-3 with the elongation rate becomes stronger as the chain length increases. Also, the well-known linear reaction between sigma and c does not seem to be satisfactory. It seems that a simple relation between sigma and c would not be valid, in general, for arbitrary flows.

A validation of the p-SLLOD equations of motion for homogeneous steady-state flows

A validation of the p-SLLOD equations of motion for nonequilibrium molecular dynamics simulation under homogeneous steady-state flow is presented. We demonstrate that these equations generate the correct center-of-mass trajectory of the system, are completely compatible with (and derivable from) Hamiltonian dynamics, satisfy an appropriate energy balance, and require no fictitious external force to generate the required homogeneous flow. It is also shown that no rigorous derivation of the SLLOD equations exists to date.

An Examination of the Validity of Nonequilibrium Molecular-dynamics Simulation Algorithms for Arbitrary Steady-state Flows

Nonlinear-response theory of nonequilibrium molecular-dynamics simulation algorithms is considered under the imposition of an arbitrary steady-state flow field. It is demonstrated that the SLLOD and DOLLS algorithms cannot be used for general flows, although the SLLOD algorithm is rigorous for planar Couette flow. Following the same procedure used to establish SLLOD as the valid algorithm for planar Couette flow [D. J. Evans and E. P. Morriss, Phys. Rev. A 30, 1528 (1984)], it is demonstrated that the p-SLLOD algorithm is valid for arbitrary flows and produces the correct nonlinear response of the viscous pressure tensor.

Projection of atomistic simulation data for the dynamics of entangled polymers onto the tube theory: calculation of the segment survival probability function and comparison with modern tube models

State-of-the-art tube models for the dynamics of entangled polymer melts are usually validated on the basis of the agreement of their predictions for the linear viscoelastic properties (LVE data) of the system against experimentally measured data. We present here a more direct and fundamental test of these models based on their comparison against molecular dynamics (MD) simulation data for the dynamics of primitive paths (PPs) in the system under study. More precisely, we show how one can take advantage of a recently developed computational methodology (P. S. Stephanou, C. Baig, G. Tsolou, V. G. Mavrantzas and M. Kroger, J. Chem. Phys., 2010, 132, 124904) for calculating the most important function of all tube models, the segment survival probability ψ(s,t) and its average Ψ(t) (the overall tube survival probability), by projecting MD data of atomistically detailed samples onto the level of the primitive paths, to directly probe mechanisms proposed for chain relaxation, such as contour length fluctuation (CLF) and constraint release (CR). The simulation data for ψ(s,t) and Ψ(t) can be used next to evaluate refinements of the original Doi–Edwards reptation theory based on a modified diffusion equation for ψ(s,t) incorporating the terms proposed to account directly or indirectly for these effects (CLF and CR). The functions ψ(s,t) and Ψ(t) determined directly from the atomistic MD simulation data account automatically for all these relaxation mechanisms, as well as for any other mechanism present in the real melt. We present and discuss results from such an approach referring to model, strictly monodisperse cis- and trans-1,4-polybutadiene and polyethylene melts containing on average up to 6 entanglements per chain, simulated in full atomistic detail for times up to a few microseconds (that is, comparable to the chain disentanglement time τd). From the same simulations we also present results for two other measures of the PP dynamics in the framework of the reptation theory, the time auto-correlation function of the PP contour length L and the time auto-correlation function of the chain end-to-end vector R. Our methodology, which serves as a bridge between molecular simulations and analytical tube theories, helps quantify chain dynamics in entangled polymers and understand how it is influenced by factors like melt polydispersity and chain molecular architecture, or the presence of interfaces. It can also be straightforwardly extended to polymeric liquids under non-equilibrium conditions (e.g., subjected to a flow field) to understand the interplay between flow and entanglements.

A generalized differential constitutive equation for polymer melts based on principles of nonequilibrium thermodynamics

Based on principles of nonequilibrium thermodynamics, we derive a generalized differential constitutive equation for polymer melts which incorporates terms that account for anisotropic hydrodynamic drag in the form suggested by Giesekus, finite chain extensibility with nonlinear molecular stretching, nonaffine deformation, and variation of the longest chain relaxation time with chain conformation. In the new equation, the expression for the Helmholtz free energy of deformation is defined such that the entropy remains bounded even at high deformation rates, as it should from a physical point of view. Key elements in the new constitutive model are the functions describing the dependence of the nonequilibrum free energy and the relaxation matrix on the conformation tensor. With suitable choices of these two functions, the new equation reduces to a number of well-known viscoelastic models. However, it is more general in the sense that it permits incorporating into a single constitutive differential equation m...

A comparison of simple rheological models and simulation data of n-hexadecane under shear and elongational flows

The microscopic origins of five rheological models are investigated by comparing their predictions for the conformation tensor and stress tensor with the same tensors obtained via nonequilibrium molecular dynamics simulations for n-hexadecane. Steady-state simulations were performed under both planar Couette and planar elongational flows, and the results of each are compared with rheological model predictions in the same flows, without any fitting parameters where possible. The use of the conformation tensor for comparisons between theory and experiment/simulation, rather than just the stress tensor, allows additional information to be obtained regarding the physical basis of each model examined herein. The character of the relationship between stress and conformation is examined using model predictions and simulation data.

A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition

We present a powerful kinetic Monte Carlo (KMC) algorithm that allows one to simulate the growth of nanocrystalline silicon by plasma enhanced chemical vapor deposition (PECVD) for film thicknesses as large as several hundreds of monolayers. Our method combines a standard n-fold KMC algorithm with an efficient Markovian random walk scheme accounting for the surface diffusive processes of the species involved in PECVD. These processes are extremely fast compared to chemical reactions, thus in a brute application of the KMC method more than 99% of the computational time is spent in monitoring them. Our method decouples the treatment of these events from the rest of the reactions in a systematic way, thereby dramatically increasing the efficiency of the corresponding KMC algorithm. It is also making use of a very rich kinetic model which includes 5 species (H, SiH3, SiH2, SiH, and Si2H5) that participate in 29 reactions. We have applied the new method in simulations of silicon growth under several conditions (in particular, silane fraction in the gas mixture), including those usually realized in actual PECVD technologies. This has allowed us to directly compare against available experimental data for the growth rate, the mesoscale morphology, and the chemical composition of the deposited film as a function of dilution ratio.