Generation of well relaxed all atom models of stereoregular polymers: a validation of hybrid particle-field molecular dynamics for polypropylene melts of different tacticities (original) (raw)
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Polymers, 2020
Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of va...
Macromolecules
A hierarchical (triple scale) simulation methodology is presented for the prediction of the dynamical and rheological properties of high molecular weight entangled polymer melts. The methodology consists of atomistic, moderately coarse-grained (mCG), and highly coarse-grained slip-spring (SLSP) simulations. At the mCG level, a few chemically bonded atoms are lumped into one coarse-grained bead. At this level, the chemical identity of the underlying atomistic system, and the interchain topological constraints (entanglements) are preserved. The mCG interaction potentials are derived by matching local structural distributions of the mCG model to those of the atomistic model through iterative Boltzmann inversion. For matching mCG and atomistic dynamics, the mCG time is scaled by a time scaling factor, which compensates for the lower monomeric friction coefficient of the mCG model than that of the atomistic one. At the SLSP level, multiple Kuhn segments of a polymer chain are represented by one coarse-grained bead. The very soft nonbonded interactions between beads do not prevent chain crossing and, hence, can not capture entanglements. The topological constraints are represented by slip-springs, restricting the lateral motion of polymer chains. A compensating pair potential is used in the SLSP model, to keep the static macromolecular properties unaltered upon the introduction of slip-springs. The static and kinetic parameters of the SLSP model are determined based on the lower level simulation models. Particularly, matching the orientational autocorrelation of the end-to-end vector, we determine the number of slip-springs and calibrate the timescale of the SLSP model. As the test case, the hierarchical methodology is applied to cis-1,4-polybutadiene (cPB) at 413 K. Dynamical single-chain and linear viscoelastic properties of cPB melts are calculated for a broad range of molecular weights, ranging from unentangled to well-entangled chains. The calculations are compared, and found in good agreement, with experimental data from the literature.
Macromolecules, 2002
The dynamics of atactic polypropylene has been explored with quasielastic neutron scattering (QENS) measurements in the temperature range 4-460 K and momentum transfer range q ) 0.2-2.25 Å -1 . In parallel, molecular dynamics simulations of the same polymer have been conducted in the temperature range 260-600 K, using both a fully atomistic model and a model with united-atom methyl groups. In conjunction with the second model, a computational procedure for introducing the motion of methyl hydrogens a posteriori is proposed and tested against the fully atomistic simulation results. Simulated intermediate incoherent scattering functions I(q,t) reveal an initial exponentially decaying regime of duration ca. 1 ps, which is dominated by bond angle bending vibrations and torsional oscillations, as well as features attributable to torsional transitions of the methyl groups and to correlated conformational transitions of the backbone bonds at longer times. The time decay of I(q,t) beyond 1 ps is well-described by stretched exponential functions, the stretching exponent being around 0.5 at 600 K and decreasing with decreasing temperature. Analysis of the atomistic simulation trajectories yields distributions of relaxation times with a distinct log-Gaussian peak characteristic of methyl motion, from which a Gaussian distribution of activation energies for methyl torsional transitions with mean around 15 kJ/mol and standard deviation around 3 kJ/mol is extracted, in excellent agreement with QENS estimates. Torsional transitions of different methyls occur essentially independently of each other. QENS experiments reveal a nondecaying elastic contribution to the scattering over the time window of the measurement, which is not seen in the simulations. Apart from this, computed I(q,t) and incoherent dynamic structure factor S(q,ω) curves are in very favorable agreement with the measured QENS spectra and with earlier NMR data on atactic polypropylene. σ 2π exp [ -(E A -E o ) 2 2σ 2 ] (3) 7112 Ahumada et al.
A comparison of neutron scattering studies and computer simulations of polymer melts
Chemical Physics, 2000
Neutron scattering and computer simulations are powerful tools for studying structural and dynamical properties of condensed matter systems in general and of polymer melts in particular. When neutron scattering studies and quantitative atomistic molecular dynamics simulations of the same material are combined, synergy between the methods can result in exciting new insights into polymer melts not obtainable from either method separately. We present here an overview of our recent eorts to combine neutron scattering and atomistic simulations in the study of melt dynamics of polyethylene and polybutadiene. Looking at polymer segmental motion on a picosecond time scale, we show how atomistic simulations can be used to identify molecular motions giving rise to relaxation processes observed in experimental dynamic susceptibility spectra. Examining larger length and longer time scale polymer dynamics involving chain self-diusion and overall conformational relaxation, we show how simulation results can motivate experiment and how combined results of scattering and simulation can be used to critically test theories that attempt to describe melt dynamics of short polymer chains.
Macromolecules, 2001
Simulations have been performed at 473 K for one-component melts of polyethylene (PE) and head-to-head, tail-to-tail polypropylene (hhPP) as well as a mixture of the two species. The densities are 0.760, 0.753, and 0.756 g/cm 3 for these three NVT simulations, respectively. The Monte Carlo simulation uses coarse-grained representations of the chains on a sparsely occupied high coordination lattice. The short-range intramolecular interactions are controlled by rotational isomeric state models for the two types of chains, and the intermolecular interactions are represented by a discretized version of Lennard-Jones potential energy functions. Equilibrated coarse-grained replicas are reverse-mapped to atomistically detailed models in continuous space. The pair correlation functions clearly demonstrate the onset of demixing for the two-component melt, which is qualitatively consistent with the conclusion from small-angle neutron scattering reported by Jeon et al. [Macromolecules 1998, 31, 3340]. Analysis of the components of the energy in the simulations shows that the positive energy change on mixing is completely dominated by the intermolecular Lennard-Jones contributions, with negligible contributions from the short-range intramolecular interactions in the rotational isomeric state models. Quantitative comparison with experiment shows that the deduced from the simulations is larger than the deduced from the experiments. Several factors in the experiments and in the simulations may contribute to the quantitative difference.
Atomistic Molecular Dynamics Simulations of Polymer/Graphene Nanostructured Systems
Materials Today: Proceedings
A) Structural Properties B) Self-Diffusion C) Dynamic Structure Factor D) Friction Factor-Zero-Shear Rate Viscosity 5.4. Conclusions 6. DYNAMICS OF N-ALKANES-THE FREE VOLUME THEORY 6.1. Free Volume Theory 6.2. Molecular model, Methodology and Systems Studies 6.3. Density of Liquid n-alkanes 6.4. Geometrical Analysis of Free volume 6.5. Diffusion of Liquid n-alkanes 6.6. Conclusions 7. DIFFUSION OF BINARY LIQUID N-ALKANE MIXTURES iv 7.1. Molecular model, Methodology and Systems Studies 7.2. Free Volume Theory of Vrentas and Duda 7.3. Chain-End Free Volume Theory Proposed by Bueche and von Meerwall 7.4. Structure of Binary Blends 7.5. Terminal Relaxation-Diffusion of Binary Blends 7.6. Conclusions 8. ATOMISTIC MODELLING OF STRESS RELAXATION EXPERIMENT UPON CESSATION OF STEADY-STATE UNIAXIAL ELONGATIONAL FLOW 8.1. Introduction 8.2. A Hierarchical Methodology 8.2.1. Stage I: Generation of oriented configurations 8.2.2. Stage II: From field-on EBMC simulations to field-off MD simulations 8.2.3. Stage III: Mapping to a coarse-grained model of dynamics 8.3. Calculations by the Rouse model 8.3.1. Relaxation of the stress component σ xx 8.3.2. The relaxation of the conformation tensor component c xx 8.4. Calculation of the stress 8.5. Results A) Equilibrium conformational properties B) Relaxation of the chain end-to-end vector C) Relaxation of the conformation tensor components D) Relaxation of the stress tensor components E) Comparison to the Rouse model predictions F) The shear stress relaxation modulus G(t) 8.6. Conclusions 9. CONCLUSIONS AND RECOMMENDATIONS 9.1. Main results 9.2. Recommendations for future work v APPENDIX A. Time Correlation Functions B. The Fixman potential C. Finite Rouse Model D. Dynamic Structure factor S(q,t) according to Rouse model E. MD Simulations in the NTL x σ yy σ zz Statistical Ensemble BIBLIOGRAPHY CHAPTER 1 INTRODUCTION The ability to predict the key physical and chemical properties of polymers from their molecular structure is of great value in the design of polymers. Performance criteria, which must be satisfied for the technological applications of polymers, have become increasingly more stringent with the recent advances in many areas of technology. Consequently, the development of predictive computational schemes to evaluate candidates for specific applications has gained urgency. To this direction, with the huge development of computers nowadays, computer simulation techniques have become valuable tools of fundamental and basic research in polymer science. Brownian dynamics, molecular dynamics and non-equilibrium dynamics are the main methods that are employed for the study of dynamic and viscoelastic properties of polymer liquids [1]. Polymers, however, are macromolecular systems characterized by a complex internal microstructure that gives rise to an enormous spectrum of length scales in their structure and a very wide spectrum of time scales in their molecular motion. Consequently the dynamic behavior of polymers is substantially different than those of a simple Newtonian liquid, exhibiting both liquidlike and solidlike characteristics [2],[3]. Even a single chain exhibits a much more complicated structure, than the simple atomic liquids, as it is shown in Fig. 1.1 [1]; from the scale of a single chemical bond (~ 1 Å) to the persistence statistical length (~ 10 Å) to the coil radius of the chain (~ 100 Å). Intramolecular correlations and local packing of chains in the bulk exhibit features on the length scale of bond lengths and atomic radiii. The statistical, Kuhn, segment length of a typical synthetic randomly coiled polymer is on the order of 10 Å and can be considerable larger for very stiff polymers. The radius of gyration of entire chains in the amorphous bulk scales as N 1/2 with the chain length N and is on the order of 100 Å for common molecular weights. On the other hand the smallest dimension of microphases times for volume and enthalpy relaxation in a glassy polymer just a few degrees below the glass transition temperature are on the order of years. Molecular simulations, on the other hand, particularly those of atomistic nature typically tracks, the evolution of model systems of length scale of about 100 Å for times up to a few tens of ns. Thus a straightforward application of the molecular dynamics (MD) simulations, for example, in order to extract the dynamic properties of polymers is at least problematic since it would require enormous computer time and would also MD simulations and a thorough mapping of the MD simulation data onto proper theoretical coarse-grained models. Key in our hierarchical approach is the combination of both MC and MD atomistic simulations. First the simulated systems are equilibrated through a very powerful MC algorithm, the end-bridging Monte Carlo method. With this algorithm very long polymer melts have been fully equilibrated at all length scales. Then detailed atomistic MD simulations, incorporating the multiple time step algorithm, have been conducted to track the evolution of the simulated systems for very long times, up to a few hundreds of ns. simulations of short polyethylene (PE) melts in the unentangled regime are presented. In the next chapter, i.e. chapter 5, the hierarchical methodology introduced in chapter 4, is extended to longer polymer melts in the crossover regime from unentangled (Rouse behavior) to entangled regime. The short n-alkanes like regime, is studied in chapter 6 through atomistic MD simulations. In this regime extra free volume phenomena due to chain ends are very
…, 2003
Results are presented from 300 ns long atomistic molecular dynamics (MD) simulations of polyethylene (PE) melts, ranging in molecular length from C 78 to C250. Above C156, the self-diffusion coefficient D is seen to exhibit a clear change in its power-law dependence on the molecular weight (M), significantly deviating from a Rouse (where D ∼ M-1) toward a reptation-like (where D ∼ M-2.4) behavior. The mean-square displacement (msd) of chain segments and the dynamic structure factor is also calculated and the crossover from the Rouse to entangled behavior is again observed above C156. A novel strategy is also developed for projecting atomistic chain configurations to their primitive paths and thereby mapping simulation trajectories onto the reptation model. Results for the friction factor , the zero-shear rate viscosity η0 and the self-diffusion coefficient D are found to be internally consistent and in agreement with experimental rheological data.
2011
We have carried out a quantitative analysis of the chain packing in polymeric melts using molecular dynamics simulations. The analysis involves constructing Voronoi tessellations in the equilibrated configurations of the polymeric melts. In this work, we focus on the effects of temperature and polymer backbone rigidity on the packing. We found that the Voronoi polyhedra near the chain ends are of higher volumes than those constructed around the other sites along the backbone. Furthermore, we demonstrated that the backbone rigidity (tuned by fixing the bond angles) affect the Voronoi cell distribution in a significant manner, especially at lower temperatures. For the melts consisting of chains with fixed bond angles, the Voronoi cell distribution was found to be wider than that for the freely jointed chains without any angular restrictions. As the temperature is increased, the effect of backbone rigidity on the Voronoi cell distributions diminishes and becomes similar to that of the freely jointed chains. Demonstrated dependencies of the distribution of the Voronoi cell volumes on the nature of the polymers are argued to be important for efficiently designing the polymeric materials for various energy applications.
Molecular Dynamics of a 1,4-Polybutadiene Melt. Comparison of Experiment and Simulation
Macromolecules, 1999
We have made detailed comparison of the local and chain dynamics of a melt of 1,4-polybutadiene (PBD) as determined from experiment and molecular dynamics simulation at 353 K. The PBD was found to have a random microstructure consisting of 40% cis, 50% trans and 10% 1,2-vinyl units with a number average degree of polymerization = 25.4. Local (conformational) dynamics were studied via measurements of the 13 C NMR spin-lattice relaxation time T 1 and the nuclear Overhauser enhancement (NOE) at a proton resonance of 300 MHz for 12 distinguishable nuclei. Chain dynamics were studied on time scales up to 22 ns via neutronspin echo (NSE) spectroscopy with momentum transfers ranging from q = 0.05 Å -1 to 0.30 Å -1 . Molecular dynamics simulations of a 100 carbon (X n = 25) PBD random copolymer of 50% trans and 50% cis units employing a quantum chemistry based united atom potential function were performed at 353 K. The T 1 and NOE values obtained from simulation, as well as the center of mass diffusion coefficient and dynamic structure factor, were found to be in qualitative agreement with experiment. However, comparison of T 1 and NOE values for the various distinguishable resonances revealed that the local dynamics of the simulated chains were systematically too fast, while comparison of the center of mass diffusion coefficient revealed a similar trend in the chain dynamics. In order to improve agreement with experiment (1) the chain length was increased to match the experimental M z , (2) vinyl units groups were included in the chain microstructure, and (3) rotational energy barriers were increased by 0.4 kcal/mol in order to reduce the rate of conformational transitions. With these changes dynamic properties from simulation were found to differ 20-30% or less from experiment, comparable to the agreement seen in previous simulations of polyethylene using a quantum chemistry based united atom potential.
Macromolecules, 2005
Thoroughly equilibrated atomistic configurations of H-shaped polyethylene (PE) melts, obtained through a novel implementation of the double-bridging Monte Carlo algorithm [Karayiannis et al. J. Chem. Phys. 2003, 118, 2451, have been subjected to equilibrium NPT molecular dynamics (MD) simulations at T ) 450 K and P ) 1 atm, for times up to 4 µs. The simulated model H-shaped systems consist of PE chains possessing a main backbone (a "crossbar") trapped between two branch points each of which is linked to two dangling arms. In our simulations, the average number of carbon atoms in the backbone ranged from 48 up to 300 corresponding to both unentangled and entangled crossbars, while the average arm length was kept relatively small (it ranged from 24 up to 50) corresponding always to unentangled arms. Our long MD simulation studies reveal the different relaxation mechanisms exhibited by an H-polymer: the rapid relaxation due to arm breathing (on the order of a few nanoseconds for the short, unentangled arms considered here, up to C 50) and the slow branch point diffusion (on the order of a few microseconds for the size of the entangled backbones considered here, up to C300), which, in turn, governs the sluggish diffusive motion of the entire H-molecule. Analysis of the curves describing the time decay of the autocorrelation functions for the unit vectors directed from the branch point to the free end of the arm and from one branch point to the other reveals a number of relaxation modes, indicative of the strong cooperativity between arm and backbone relaxations in H-shaped structures. It is further observed that once Fickian diffusion is established, the mean-square displacement (msd) of the chain center-of-mass follows remarkably faithfully that of branch points. This validates from first principles the assumption of the pom-pom model [Bishko et al. Phys. Rev. Lett. 1997, 79, 2352 that all friction in an H-polymer is concentrated at the two branch points. Values of the branch point friction coefficient, b, a significant parameter entering the pom-pom model, have also been calculated. For the longest H-polymers studied, logarithmic plots of the msd of the inner crossbar segments against time are seen to exhibit the four different regimes predicted by the reptation theory of Doi-Edwards for entangled linear polymer melts, with corresponding exponents remarkably close to those of the theory. This allowed us to extract the characteristic relaxation times τ e, τR, and τd of the theory for all simulated systems and the value of the effective diameter, a, of the underlying tube model.