Segmental dynamics in polyethylene melts through atomistic molecular dynamics simulations (original) (raw)
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7 Segmental dynamics in polyethylene melts through atomistic molecular dynamics simulations
We have studied issues related to segmental mobility and dynamics in linear polyethylene (PE) melts, using a method that relies on the execution of rather long (up to 0.5µs) atomistic molecular dynamics (MD) simulations and analytical expressions from well-established mesoscopic theories providing a link between simulation data and experimental observables. The simulations have been carried out with linear PE model systems ranging in molecular length from C 78 to
Atomistic Molecular Dynamics Simulation of Polydisperse Linear Polyethylene Melts
Well-relaxed atomistic configurations of polydisperse, linear polyethylene (PE) melts, obtained with the end-bridging Monte Carlo algorithm, have been subjected to detailed molecular dynamics simulations in both the canonical (NVE) and microcanonical (NVT) ensembles. Three different systems have been investigated, characterized by mean molecular lengths C 24, C78, and C156, and by the same polydispersity index I of about 1.09. Results are presented for the static and (mainly) dynamic properties of these melts at P ) 1 atm and T ) 450 K. The diffusion coefficient D, determined for various chain lengths, N, is in very good agreement with experimentally measured values. The friction coefficient D is extracted from D by invoking the Rouse model; it is seen to increase from a relatively small value characteristic of short alkanes to a chain-length-independent plateau, reached in a region of N ) 60-80. The friction coefficient τ is also obtained by analyzing the decay of the time autocorrelation function for the normal modes Xp at various chain lengths; the values thus extracted are consistent with those obtained from D for N above 40. Although the decay of the autocorrelation function of the end-to-end vector is very well described by the Rouse model, individual Rouse modes show some deviation from theoretical predictions. Even for chains sufficiently long to be in the asymptotic regime, only the first two normal modes fully conform to Rouse theory in terms of their squared amplitudes and correlation times. Zeroshear viscosities computed from D values by means of the Rouse model are in excellent agreement with available experimental data for N ) 90.
Atomistic simulation of crystallization of a polyethylene melt in steady uniaxial extension
Journal of Non-Newtonian Fluid Mechanics, 2010
We present simulation results of flow-induced crystallization of a dense polymeric liquid subjected to a strong uniaxial elongational flow using a rigorous nonequilibrium Monte Carlo method. A distinct transition between the liquid and the crystalline phases occurred at critical values of flow strength, with an abrupt, discontinuous transition of the overall chain conformation. The flow-induced crystalline phase matched quantitatively the experimental X-ray diffraction data of the real crystals remarkably well, including the sharp Bragg peaks at small wavenumbers, k < 1.5 Å −1 , indicating the existence of a global long-range ordering. We also found that the enthalpy change ( H = 225 J/g) during the phase transition was quantitatively very similar to the experimental heat of fusion (276 J/g) of polyethylene crystals under quiescent conditions. Furthermore, a detailed analysis of the configuration-based temperature provided a sound microscopic physical origin for the effective enhancement of the crystallization (or melting) temperature that has been observed in experiments. Simulation results also allow for the deduction of potential nonequilibrium expressions for thermodynamic quantities, such as temperature and heat capacity.
Simulation of melting in crystalline polyethylene
The Journal of Chemical Physics, 2012
We carry out a molecular dynamics simulation of the first stages of constrained melting in crystalline polyethylene (PE). When heated, the crystal undergoes two structural phase transitions: from the orthorhombic (O) phase to the monoclinic (M) phase, and then to the columnar (C), quasi-hexagonal, phase. The M phase represents the tendency to the parallel packing of planes of PE zigzags, and the C phase proves to be some kind of oriented melt. We follow both the transitions O→M and M→C in real time and establish that, at their beginning, the crystal tries (and fails) to pass into the partially ordered phases similar to the RI and RII phases of linear alkanes, correspondingly. We discuss the molecular mechanisms and driving forces of the observed transitions, as well as the reasons why the M and C phases in PE crystals substitute for the rotator phases in linear alkanes.
Macromolecules, 1998
A method is developed for predicting the elasticity of a polymer melt through detailed atomistic simulations. The Helmholtz energy of a melt oriented by flow is postulated to be of the form A(T,F,c), where T is the temperature, F is the mass density, and c , the conformation tensor, is defined as the end-to-end tensor reduced by one-third the mean squared unperturbed end-to-end distance and averaged over all chains. The conjugate thermodynamic variable to c, r, is a tensorial orienting field intimately related to the strain rate in a flow situation. Assuming affine deformation of chain ends, the stress tensor τ can be expressed in terms of c and r. We have mapped out c, A, and τ for melts subjected to elongational flow by conducting Monte Carlo (MC) simulations at various values of R xx, all other components of r being zero. Two linear polyethylene melts, of mean chain lengths C24 and C78 and polydispersity index 1.09, have been studied. Efficient sampling of oriented melt configurations has been made possible through the use of the end-bridging MC algorithm. Comparison of the melt response to that of isolated chains subjected to the same orienting field shows that, while at low fields the two responses are similar, at high fields more anisotropy develops in the melt due to favorable lateral interactions between the oriented chains. Comparison against simple models used in flow calculations shows that FENE dumbbells and freely-jointed chains are more representative of the actual melt response than Hookean dumbbells, because they account for the finite extensibility of the polymer. Partitioning A into its energetic and entropic components shows that the melt response is purely entropic for long chains and low orienting fields, which leave the intrinsic shape of chains (averaged in the coordinate frame of their principal axes) practically unaltered. A significant energetic contribution develops for small chains and high orienting fields, where the chain intrinsic shape becomes more elongated and attractive lateral interchain interactions are intensified. Values of τ calculated from c and r are consistent with virial theorem predictions.
Macromolecules, 2010
Atomistic configurations of model unentangled ring polyethylene (PE) melts ranging in chain length from C 24 up to C 400 have been subjected to detailed molecular dynamics (MD) simulations in the isothermal-isobaric statistical ensemble at temperature T = 450 K and P = 1 atm. Strictly monodisperse samples were employed in all cases. We present and discuss in detail simulation results for a variety of structural, thermodynamic, conformational and dynamic properties of these systems, and their variation with chain length. Among others, these include the mean chain radius of gyration, the pair correlation function, the intrinsic molecular shape, the local dynamics, the segmental mean square displacement (msd), the chain center-of-mass self-diffusion coefficient D G , the chain terminal relaxation time τ d , the characteristic spectrum of the Rouse relaxation times τ p , and the dynamic structure factor S(q,t). In all cases, the results are compared against the corresponding data from simulations with linear PE melts of the same chain length (the linear analogues) and the predictions of the Rouse theory for polymer rings which we derive here in its entirety. The Rouse theory is found to provide a satisfactory description of the simulation findings, especially for rings with chain length between C 50 and C 170 . An important finding of our work (from the observed dependence of D G , τ p , ζ, and η 0 on chain length N) is that PE ring melts follow approximately Rouse-like dynamics even when their chain length is as long as C 400 ; this is more than twice the characteristic crossover chain length (∼C 156 ) marking the passage from Rouse to reptation dynamics for the corresponding linear PE melts. In a second step, and by mapping the simulation data onto the Rouse model, we have managed to extract the friction coefficient ζ and the zero-shear rate viscosity η 0 of the simulated ring melts. Overall, and in agreement with previous theoretical and experimental studies, our simulation results support that the structure of ring polymers in the melt is more compact than that of their linear analogues due to their nonconcatenated configurations. Additional results for the intermolecular mer-mer and center-of-mass pair correlation functions confirm that the effective correlation hole effect is more pronounced in melts of rings than in melts of linear chains.
Polymers
Atomistic simulations of the linear, entangled polyethylene C1000H2002 melt undergoing steady-state and startup conditions of uniaxial elongational flow (UEF) over a wide range of flow strength were performed using a united-atom model for the atomic interactions between the methylene groups constituting the polymer macromolecules. Rheological, topological, and microstructural properties of these nonequilibrium viscoelastic materials were computed as functions of strain rate, focusing on regions of flow strength where flow-induced phase separation and flow-induced crystallization were evident. Results of the UEF simulations were compared with those of prior simulations of planar elongational flow, which revealed that uniaxial and planar flows exhibited essentially a universal behavior, although over strain rate ranges that were not completely equivalent. At intermediate flow strength, a purely configurational microphase separation was evident that manifested as a bicontinuous phase c...
Macromolecules, 2017
Atomistic simulations have been very useful for predicting the viscoelastic properties of polymers but face great difficulties in accessing the dynamics of dense, well entangled longchain melts with relaxation times longer than μs due to the high computational cost required. A plethora of coarse-grained models have been developed to address longer time scales. In this article we present a multiscale simulation strategy that bridges detailed molecular dynamics (MD) simulations to slip-spring based Brownian dynamics/kinetic Monte Carlo (BD/kMC) simulations of long-chain polymer melts. The BD/kMC simulations are based on a mesoscopic Helmholtz energy function incorporating bonded, slip-spring, and nonbonded interaction contributions (Macromolecules 2017, 50, 3004). Bonded contributions are expressed as sums of stretching and bending potentials of mean force derived from detailed MD simulations of shorter-chain melts, while nonbonded interaction contributions in the absence of slipsprings are derived from an equation of state that is consistent with thermodynamic properties predicted by detailed MD and measured experimentally. Monodisperse linear polyethylene melts of chain lengths C 260 to C 2080 are used as a test case. Estimates of the chain self-diffusivity, the longest relaxation time, the stress relaxation modulus, and the zero-shear viscosity from ms-long equilibrium BD/kMC simulations are in excellent agreement with MD results for the shorter-chain melts and with experiment. The BD/kMC scheme is extended to simulate Couette flow using Lees−Edwards periodic boundary conditions over a range of Weissenberg numbers (Wi) from 10 −2 to 10 5. Predictions for the shear viscosity as a function of shear rate, the first and second normal stress difference coefficients, the startup shear stress, as well as for changes in chain conformation and entangled structure with increasing Wi are in favorable agreement with experimental and atomistic simulation evidence.
Macromolecules, 2018
A mesoscopic simulation approach is developed for liquid−gas interfaces of weakly and strongly entangled polymer melts and implemented for linear polyethylene at 450 K. A combined particle and field-theoretic treatment is adopted based on aggressive coarse-graining, each polymer bead representing ∼50 carbon atoms, with effective bonded interactions extracted from atomistic simulations. Nonbonded interactions in the mesoscopic model are dictated by an equation of state (here the Sanchez−Lacombe) in conjunction with a variant of gradient theorythe discrete square gradient theory. The dynamics of free films is examined in the presence and in the absence of topological constraints (modeled by slip-springs) to unveil the impact of the latter on chain self-diffusion, to assess their contribution to the interfacial free energy, and to explore how this contribution can be removed by invoking a compensating potential. The molar mass dependence of surface tension which arises from bonded contributions among beads in the mesoscopic chainsis extracted over a broad range of molar masses (10 3 −10 6 g/mol), in excellent agreement with experiment. Two approaches for computing the surface tension are adopted, based on stress profiles and based on changes in free energy with interfacial area, leading to consistent results. The predicted density profiles, conformations, and orientational tendencies of the mesoscopic chains are retrieved from the simulations and shown to reproduce very well the corresponding results from atomistic simulations. An annealing scheme is developed with the purpose of accelerating transitions of metastable states into more stable biphasic states such as spherical and cylindrical droplets, free films, and spherical and cylindrical bubbles, which minimize the free energy of the periodic model system. Results for the phase diagram as a function of polymer volume fraction conform to the predictions of atomistic simulations of simpler systems.