No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Equilibration and Deformation of Amorphous Polystyrene: Scale‐jumping Simulational Approach
Abstract
A polymer sample-preparation method (extended-chain condensation, ECC) based solely on molecular-dynamics simulations has been compared to a connectivity-altering Monte Carlo method (coarse-grained end-bridging, CGEB). Since the characteristic ratio for the CGEB samples is closer to the experimental value, ECC results in polymer structures that are too compact. The stress-strain relations are different in the strain-hardening regime. For CGEB samples, a stronger strain hardening is observed and the strain-hardening modulus is more realistic; for the CGEB polystyrene (PS) sample G(R) = 9 +/- 1 MPa is found versus G(R) = 4 +/- 2 MPa for the ECC samples. These differences have to be attributed to a steeper increase in the contributions to the total stress from bond- and dihedral angles for CGEB than for ECC samples.
... In order to validate the assumption of the isotropic behavior of the PNC, we present in Appendix the nine engineering constants for an orthotropic material, namely E x x , E yy , E zz , G x y , G x z , G yz , ν x y , ν x z and ν yz , which are determined from MD simulations after applying 6 strain rates as boundary conditions on the unit box, namelyε x x ,ε yy ,ε zz ,ε x y ,ε x z andε yz . The simulated stress-strain behavior in Fig. 5 at a strain rate ofε x x = 3 × 10 −6 fs −1 exhibits the same trends as those observed in numerical modeling and experimental testing for amorphous polymers [10,69,78]. This is because we consider temperatures T ≪ T g , so that the effect of the strain rate is not expected to be important. ...
The mechanical properties of glassy polymer nanocomposites (PNCs) are investigated via a new hierarchical computational methodology, which combines atomistic molecular dynamics (MD) simulations and homogenization approaches. The homogenization methodology is based on a systematic nano/micro/macro coupling between detailed atomistic MD simulations and a variational approach through the Hill–Mandel lemma. The proposed methodology is applied in model glassy polybutadiene/silica nanocomposites for different nanoparticle (NP) volume fractions. Initially, using MD simulations, the polymer/NP interphase in PNCs is directly examined by probing the density distribution and the stress profile at equilibrium. By using a continuum mechanics based approach, we can compute effective deformation gradients for each atom, allowing us to probe the distribution of the (local) stress and strain fields in the atomistic model. With this new approach, the effective Young modulus and the Poisson ratio of the polymer/NP interphases are directly calculated, exhibiting a higher rigidity compared to the polymer matrix. In the last part of the proposed approach, the mechanical properties at the interphases and the polymer are used together with the homogenization approach to develop a continuum model for predicting the mechanical properties of the PNCs, which are found to be in very good agreement with the effective mechanical properties calculated through atomistic MD simulations.
... The mapping scheme shown in Figure 4c was developed by Qian et al. [353] which yields potentials capable of reproducing the isothermal compressibility as well as structural properties of the PS melts from 400 to 500 K. Finally, in order to include the tacticity effects on the structural and dynamic properties of PS, Harmandaris et al. [354,355] and Fritz et al. [356] used the CG models shown in Figure 4d. This model has been applied to study both the mechanical properties of PS glasses [357,358] and the dynamic properties of PS melts [359,360]. These works manifest the influence of the definition of super atoms on the final outcome of the simulations. ...
Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.
... Interestingly, the time scale factors are not identical for these models [42]. Moreover, the model can be applied to study both the mechanical properties of PS glasses [202,203] and the dynamic properties of PS melts [204,205]. From these studies, it is important to know that although there are different ways to define the super atom in deriving a coarse-grained model, the static, dynamic or thermodynamic properties of the coarse-grained model should be tested and validated before it is further applied [42]. ...
The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale modeling of polymeric materials and how these methods can help us to optimize and design new polymeric materials.
We have investigated thermal and mechanical properties of bio-based furan polyamides and petroleum-based nylons with atomistic simulations. Glass transition temperatures estimated from a series of simulations at different temperatures were in good agreement with experimental measurements. Stress–strain relationships under uniaxial deformation conditions were also obtained and analyzed. Overall, polymers with smaller repeat units exhibited slightly higher glass transition temperatures and elastic moduli, which were attributed to higher cohesive energy densities. Furan polyamides displayed higher van der Waals cohesive energy densities and maintained more rigid planar structures near furan rings compared to nylons. As a result, bio-based furan polyamides showed higher glass transition temperatures and comparable mechanical properties despite having overall weaker hydrogen bonding than nylons.
The mechanisms underlying the increase in stress for large mechanical strains of a polymer
glass, quantified by the strain-hardening modulus, are still poorly understood. In the present paper we aim to
elucidate this matter and present new mechanisms. Molecular-dynamics simulations of two polymers with
very different strain-hardening moduli (polycarbonate and polystyrene) have been carried out. Nonaffine
displacements occur because of steric hindrances and connectivity constraints. We argue that it is not
necessary to introduce the concept of entanglements to understand strain hardening, but that hardening is
rather coupled with the increase in the rate of nonaffine particle displacements. This rate increases faster for
polycarbonate, which has the higher strain-hardening modulus. Also more nonaffine chain stretching is
present for polycarbonate. It is shown that the inner distances of such a nonaffinely deformed chain can be
well described by the inner distances of the worm-like chain, but with an effective stiffness length (equal to the
Kuhn length for an infinite worm-like chain) that increases during deformation. It originates from the finite
extensibility of the chain. In this way the increase in nonaffine particle displacement can be understood as
resulting from an increase in the effective stiffness length of the perturbed chain during deformation, so that at
larger strains a higher rate of plastic events in terms of nonaffine displacement is necessary, causing in turn the
observed strain hardening in polymer glasses.
Simulation of the deformation of polymers below their glass transition through molecular dynamics provides an useful route to correlate their molecular architecture to deformation behavior. However, present computational capabilities severely restrict the time and length scales that can be simulated when detailed models of these macromolecules are used. Coarse-graining techniques for macromolecular structures intend to make bigger and longer simulations possible by grouping atoms into superatoms and devising ways of determining reasonable force fields for the superatoms in a manner that retains essential macromolecular features relevant to the process under study but jettisons unnecessary details. In this work we systematically develop a coarse-graining scheme aimed at simulating uniaxial stress-strain behavior of polymers below their glass transition. The scheme involves a two step process of obtaining the coarse grained force field parameters above glass transition. This seems to be enough to obtain "faithful" stress-strain responses after quenching to below the glass transition temperature. We apply the scheme developed to a commercially important polymer polystyrene, derive its complete force field parameters and thus demonstrate the effectiveness of the technique.
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together (up to five backbone carbon atoms) and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together (more than ten backbone carbon atoms), leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and action must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
Well-equilibrated atactic-polystyrene (aPS) samples are obtained through the end-bridging Monte Carlo (EBMC) algorithm. A coarse-grained (CG) description of aPS is used; monomers are represented by two CG beads. The algorithm produces correct polymer conformations on all length scales, beyond the size of the CG beads. The code is very efficient, even though the acceptance of 0.001–0.005% is approximately 10–100 times lower than in the original EB code for PE. Systems of aPS of the order of 5000 monomers (50 chains of 100 monomers on average) can be equilibrated on all length scales within a week, in a single-processor run. The computer code is also adequate for simulations of other polymers that have the same regularity in their sequence of chemical groups and that are modeled at the same or at a coarser level of description.
A method is presented to obtain well-equilibrated atactic polystyrene (aPS) samples for molecular simulations. The method starts with equilibrating the polymer in the melt at length scales beyond the Kuhn length lK, using end-bridging Monte Carlo techniques; at this level a (2:1)-coarse-grained description of aPS is being employed. Subsequently atomistic detail is reintroduced, and the sample is equilibrated at the smallest length scales as well. At length scales beyond lK the simulated polymer chain conformations fulfill the random-coil hypothesis of Flory, and C∞ = 8.7 ± 0.1 at 463 K. Eventually various glassy samples are created by subjecting the melt sample to different cooling rates. Pair correlations are in agreement with existing X-ray data, and the amount of dihedral angles in the trans (t) state agrees with NMR data. On the level of dyads, the conformations of racemic dyads agree well with existing NMR results. At the same time, meso dyads conformations do not agree: 65% of meso dyads is in the gt/tg state (NMR: 80%); 25% is in tt state (NMR: <10%). An attempt has been made to relate the observation in simulations, namely that an increase in cooling time causes an increase in yield stress, to effects of the cooling rate on the polymer structure.
A quantitative understanding and prediction of the dynamics of entangled polymer melts is a long-standing problem. In this work we present results about the dynamical and rheological properties of atactic polystyrene melts, obtained from a hierarchical approach that combines atomistic and coarse-grained dynamic simulations of unentangled and entangled systems. By comparing short chain atomistic and coarse-grained simulations, the time mapping constant is determined. Self-diffusion coefficients, after correcting for the chain end free volume effect, show a transition from Rouse to reptation-like behavior. In addition, the entanglement molecular weight is calculated through a primitive path analysis. All properties are compared to experimental data.
The full-atomic computer simulation of bulk plastic polyimides based on dianhydride 1,3-bis(3′,4-dicarboxyphenoxy)benzene and two types of diamines, 4,4′-bis(4″-aminophenoxy)diphenyl sulfone and 4,4′-bis(aminophenoxy)diphenyl oxide, is performed on the microsecond scale via the moleculardynamics method. For the investigated molecules, which consist of eight repeating units, the limiting values of the characteristic sizes of individual polymer chains are established. The limiting sizes obtained via computer simulation are in good agreement with theoretical values calculated in terms of virtual-bond formalism. It is found that the time of sample equilibration for the full-atomic computer simulation of bulk plastic polyimides is ∼1 μs, which agrees in order of magnitude with the displacement time of the center of mass of an individual molecule by a distance equal to its own size.
Polyimide-based composite materials with a single-walled carbon nanotube as filler were studied by means of extensive fully-atomistic molecular-dynamics simulations. Polyimides (PI) were considered based on 1,3-bis-(3 0 ,4-dicarboxyphenoxy)-benzene (dianhydride R) and various types of diamines: 4,4 0 -bis-(4 00 -aminophenoxy)-diphenylsulfone (diamine BAPS) and 4,4 0 -bis-(4 00 -aminophenoxy)-diphenyl (diamine BAPB). The influence of the chemical structure of the polyimides on the microstructure of the composite matrix near the filler surface and away from it was investigated. The formation of subsurface layers close to the nanotube surface was found for all composites considered. In the case of R–BAPB-based composites, the formation of an organized structure was shown that could be the initial stage of the matrix crystallization process observed experimentally. Similar structural features were not observed in the R–BAPS composites. Carbon nanotubes induce the elongation of R–BAPB chains in composites whereas R–BAPS chains become more compact similar to what is observed for EXTEM™ polyimide. It was shown that electrostatic interactions do not influence the microstructure of composites but slow down significantly the dynamics of PI chains in composites.
The ability of atomistic and coarse-grained models to discern between two polymers of very similar architecture is examined. To this end, polyether ether ketone (PEEK) and polyether ketone ketone (PEKK) are chosen. The difference in glass transition temperature and the similarity in compressive responses of the two polymers are captured by all-atom models. A coarse-graining scheme, with 6 beads per monomer and 3 types of beads, leads to a good approximation of the structure and packing of chains of PEEK and PEKK. The CG model reproduces differences in weakly rate-dependent properties such as $${T}_{\mathrm{g}}$$ T g . Comparison between strongly rate-dependent uniaxial stress–strain responses of these two polymers requires a knowledge of the scaling between physical strain rate in one to the effective rate in the other. The scaling can be approximately determined by comparing the variation of yield strength with strain rate, obtained from small-sized simulations.
Graphic abstract
Ferrogels and magnetic elastomers differentiate themselves from other
materials by their unique capability of reversibly changing shape and
mechanical properties under the influence of an external magnetic field. A
crucial issue in the study of these outstanding materials is the interaction
between the mesoscopic magnetic particles and the polymer matrix in which they
are embedded. Here we analyze interactions between two such particles connected
by a polymer chain, a situation representative for particle-crosslinked
magnetic gels. To make a first step towards a scale-bridging description of the
materials, effective potentials for mesoscopic configurational changes are
specified using microscopic input obtained from simulations. Furthermore, the
impact of the presence of magnetic interactions on the probability
distributions and thermodynamic quantities of the system is considered. The
resulting mesoscopic model potentials can be used to economically model the
system on the particle length scales. This first coarse-graining step is
important to realize simplified but realistic scale-bridging models for these
promising materials.
A comprehensive modeling and simulation approach using molecular dynamics (MD) is presented in this paper. The influence of aspect ratio of carbon nanotubes (CNTs) in thermosetting epoxy is studied using MD. The thermo-mechanical properties of epoxy models reinforced by CNTs with various aspect ratios are extracted. CNTs with the higher aspect ratio increase stiffness of the epoxy resin with facilitating premature yield in tension while a noticeable degradation in thermal properties is evidenced. The evolution of internal energy during straining shows that CNTs prolong the constant transition rate of dihedral and van der Waals energy in the elastic region. This might delay conformational changes of epoxy molecules to the lower energy level. Free volume and pair distribution function studies of the molecular models with CNTs compared with the neat epoxy model provide the plausible conclusion that the steric hindrance of CNTs in the three-dimensional epoxy molecular domain may result in the less dense structure of the epoxy.
In recent years, polymer/carbon nanotube composites have attracted increased attention because the polymer properties have significantly improved. In this paper, a single walled carbon nanotube (SWCNT) is used to reinforce polystyrene matrix. Molecular dynamics (MD) simulations are used to study two periodic systems -a long CNT-reinforced polystyrene composite and amorphous polystyrene matrix itself. The axial and transverse elastic moduli of the amorphous polystyrene matrix and nanocomposites are evaluated using constant-strain energy minimization method. The results from MD simulations are compared with corresponding rule-ofmixture predictions. The simulation results show that CNTs significantly improve the stiffness of polystyrene/ CNT composite, especially in the longitudinal direction of the nanotube. Polystyrene posses a strong attractive interaction with the surface of the SWCNT and therefore play an important role in providing effective adhesion. The conventional rule-of-mixture predicts a smaller value than MD simulation where there are strong interfacial interactions. Here the authors report a study on the interfacial characteristics of a CNT-PS composite system through MD simulations and continuum mechanics.
A literature review is presented on a multiscale approach to the simulation of nanocomposites based on thermoplastic polymers that includes calculations using quantum-chemical methods and molecular dynamics simulations with the use of full-atomic and mesoscopic models. Common problems arising during the multiscale simulation of thermoplastic nanocomposites and the ways to solve them are discussed. The results of studies of the structural, thermal, and mechanical properties of thermoplastic nanocomposites obtained via the simulation with consideration for the detailed chemical structures of components are given.
In recent years, polymer/carbon nanotube composites have attracted increased attention because the polymer properties have significantly improved. In this paper, a single walled carbon nanotube (SWCNT) is used to reinforce polystyrene matrix. Molecular dynamics (MD) simulations are used to study two periodic systems - a long CNT-reinforced polystyrene composite and amorphous polystyrene matrix itself. The axial and transverse elastic moduli of the amorphous polystyrene matrix and nanocomposites are evaluated using constant-strain energy minimization method. The results from MD simulations are compared with corresponding rule-of-mixture predictions. The simulation results show that CNTs significantly improve the stiffness of polystyrene/CNT composite, especially in the longitudinal direction of the nanotube. Polystyrene posses a strong attractive interaction with the surface of the SWCNT and therefore play an important role in providing effective adhesion. The conventional rule-of-mixture predicts a smaller value than MD simulation where there are strong interfacial interactions. Here the authors report a study on the interfacial characteristics of a CNT-PS composite system through MD simulations and continuum mechanics.
The method of re-introducing atomistic detail into a coarse-grained polymer structure, so-called backmapping, is extended to a nonequilibrium situation. Problems in backmapping coarse-grained polymer models, on which a nonequilibrium shear flow has been imposed, are discussed. A backmapping protocol, where the globally deformed conformations are maintained during backmapping by applying position restraints, is proposed. The local optimization of the atomistic structure is performed in the presence of these restraints. The artifact of segment isolation introduced by position restraints is minimized by applying different restraint patterns iteratively. The procedure is demonstrated on the test case of atactic polystyrene under a steady shear flow.
Molecular-dynamics (MD) simulations have been performed for two
amorphous polymers with extremely different mechanical properties,
atactic polystyrene (PS) and bisphenol A polycarbonate (PC), in
the isotropic state and under load. The glass transition
temperatures, Young moduli, yield stresses and strain-hardening
moduli are calculated and compared to the experimental data. Both
chemistry-specific and mode-coupling aspects of the segmental
mobility in the isotropic case and under the uniaxial deformation
have been identified. The mobility of the PS segments in the
deformation direction is increased drastically beyond the yield
point. A weaker increase is observed for PC.
Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the simulation cell and introduces the excluded volume rapidly, leads to deformation on short length scales. This deformation is strongest for long chains and relaxes only after the chains have moved their own size. Two methods are shown to overcome this local deformation of the chains. One method is to first pre-pack the Gaussian chains, which reduces the density fluctuations in the system, followed by a gradual introduction of the excluded volume. The second method is a double-pivot algorithm in which new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. We demonstrate the effectiveness of these methods for a linear bead spring polymer model with both zero and nonzero bending stiffness, however the methods are applicable to more complex architectures such as branched and star polymer. Comment: 12 pages, 9 figures
This thoroughly revised and updated third edition is written by seven
well-known authorities in the polymer science community. Each author
contributes a chapter which reflects his own interests and expertise in
the physical states and associated properties of polymers. Second
Edition published by the American Chemical Society Hb (1993):
0-841-22505-2
The post-yield behaviour of glassy polymers is governed by intrinsic strain softening followed by strain hardening. Intrinsic softening is the dominant factor in the initiation of plastic localisation phenomena like necking, shear band formation or crazing. Removal, or a significant reduction, of intrinsic softening can be achieved by mechanical or thermal pre-conditioning, and is known to suppress necking in tough amorphous polymers like polycarbonate and polyvinylchloride. Here, the effect of mechanical pre-conditioning on the macroscopic deformation of a brittle polymer, notably polystyrene, is studied. As a result of mechanical pre-conditioning, a 30% thickness reduction by rolling, the yield stress is decreased and the intrinsic softening drastically reduced, resulting in a more stable deformation behaviour yielding an increase in the macroscopic strain to break to approx. 20% as compared to 2% in the untreated samples. The effect observed is of a temporary nature, as, due to progressive ageing, the yield stress increases and intrinsic softening is restored on a time-scale of minutes. This indicates that the toughening is indeed caused by the removal of intrinsic softening, and not due to enhanced strain hardening related to molecular orientation induced by the rolling treatment. q 2000 Elsevier Science Ltd. All rights reserved.
Molecular dynamics simulations are employed to study the phenyl-ring flip in polystyrene, thought to be the molecular origin of the γ-relaxation. The results show that upon cooling the system toward the glass transition the motion of the phenyl ring becomes more heterogeneous, which seems to result from a distribution of local energy barriers in combination with slower transitions between states with these local energy barriers. The growing of the heterogeneity affects the determination of the effective energy barrier. In particular, the “static” energy barrier (as determined from the distribution of the orientation of the phenyl ring with respect to the backbone) is found to be different from the “dynamic” energy barrier, as determined from the temperature dependence of some relaxation time (i.e., the activation energy). However, below the glass transition temperature it appears that the two methods render the same value for the height of the energy barrier, although the time scales differ approximately by a constant factor. It is shown that another relaxation time can be determined to characterize the ring-flip process, which seems not to be affected by the growth of heterogeneity and which closely follows the “static” energy barrier. The effective barrier as determined in this way by the simulations is in fair agreement with experimental values for the γ-relaxation.
We present a hierarchical approach that combines atomistic and mesoscopic simulations that can generally be applied to vinyl polymers. As a test case, the approach is applied to atactic polystyrene (PS). First, a specific model for atactic PS is chosen. The bonded parameters in the coarse-grained force field, based on data obtained from atomistic simulations of isolated PS dimers, are chosen in a way which allows to differentiate between meso and racemic dyads. This approach in principle allows to study isotactic and syndiotactic melts as well. Nonbonded interactions between coarse-grained beads were chosen as purely repulsive. The proposed mesoscopic model reproduces both the local structure and the chain dimensions properly. An explicit time mapping is performed, based on the atomistic and CG mean-square displacements of short chains, demonstrating an effective speed up of about 3 orders of magnitude compared to brute force atomistic simulations. Finally the equilibrated coarse-grained chains are back mapped onto the atomistic systems. This opens new routes for obtaining well equilibrated high molecular weight polymeric systems and also providing very long dynamic trajectories at the atomistic level for these polymers.
Molecular dynamics (MD) simulations of bulk atactic polystyrene have been performed for chains up to 320 monomer units in a temperature range from 100 to 600 K and in a broad pressure range from 0.1 to 1000 MPa. The MD-determined specific volume vs temperature curves are in a good agreement with experimental PVT data at different values of applied pressure, but the measured glass-transition temperature, Tg, is displaced to somewhat higher temperature than the longer time experimental value. Local translational mobility has been investigated by measuring the mean-square translational displacements of monomers as a function of time. The long-time asymptotic slope of these dependencies is close to 0.6 at T > Tg, showing diffusive behavior. The cage effect, when local translational motions are essentially frozen in the glassy state, has been studied. The characteristic time of cage release does not depend on molecular weight, but the duration of the crossover to the diffusive regime increases almost linearly with increasing chain molecular weight, for both the backbone monomers and phenyl side groups.
We have performed a systematic study of the relationship between polymer structure and the phenomenon of strain hardening by employing controlled stress molecular dynamics computer simulation in conjunction with a simple polyethylene-like model. We find that varying the sample preparation history produces materials which, while being chemically identical, differ profoundly in their response to an applied stress.
Wide-angle X-ray diffraction measurements were performed on polymer melts of isotactic and syndiotactic polypropylene (IPP and SPP), poly(ethylenepropylene) (PEP), polystyrene (PS), polyisobutylene (PIB), and polyethylene (PE), to study the dependence of the short-range structure of polymer liquids on chain architecture. Total structure functions, which comprise intra- and intermolecular contributions, were derived from the scattering data. The trivial Fourier components of the intramolecular structure (C(SINGLE BOND)>C ≃ 1.54 Å and C(SINGLE BOND)C(SINGLE BOND)C ≃ 2.55 Å) were subtracted from the total structure functions. The remaining functions contain only those intramolecular contributions dependent on the chain's conformational degrees of freedom, plus the intramolecular contributions. The structural differences between the polymers in momentum space are discerned only when the trivial components are subtracted. This subtraction also reduces the effects of truncation errors on Fourier transformation to real space. The short-range structure of PIB appears very different compared to all the others, which correlates with anomalies in a number of physical properties for this polymer. © 1996 John Wiley & Sons, Inc.
In order to have better insight into the polymer specifics of the dynamic glass transition molecular dynamics (MD) computer simulations of three glass-formers have been carried out: low-molecular-weight isopropylbenzene (iPB), brittle atactic polystyrene (PS) and tough bisphenol A polycarbonate (PC). Simulation of the uniaxial deformation of these mechanically different types of amorphous polymers shows that the mechanical experimental data could be realistically reproduced. Now the objective is to study the local orientational mobility in the non-deformed isotropic state and to find the possible connection of the segmental dynamics with the different bulk mechanical properties. Local orientational mobility has been studied via Legendre polynomials of the second order and CONTIN analysis. Insight into local orientational dynamics on a range of length- and time scales is acquired. The fast transient ballistic process describing the very initial part of the relaxation has been observed for all temperatures. For all three simulated materials the slowing down of cage escape (α-relaxation) follows mode-coupling theory above Tg, with non-universal, material-specific exponents. Below Tg universal activated segmental motion has been found. At high temperature the α process is merged with the β process. The β process which corresponds to the motions within cage continues below Tg and can be described by an activation law.
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
This article describes the collisional dynamics (CD) method adapted for molecules with geometrical constraints within a description using Cartesian coordinates for the atoms. In the CD method, stochastic collisions with virtual particles are included in usual molecular dynamics simulations to couple the considered polymer molecule to a solvent. The actual presence of the solvent is not explicitly included in the simulation. The results-of CD simulations of a polymer chain immersed in the time-dependent elongational flow field are presented. The influence of nonbonded interactions on the coil-stretch transition of the chain occurring in the flow is discussed. © 1996 John Wiley & Sons, Inc.
Thesis (doctoral)--Technische Universiteit Eindhoven, 2002.
Thesis--Technische Hogeschool Delft. Vita. An authorized xerographic copy (N78-71340) reproduced by the National Technical Information Service of the U.S. Dept. of Commerce for the National Aeronautics and Space Administration. Includes bibliographical references and indexes.
The conformational statistics of atactic polystyrene have been investigated by solid-state NMR, on a sample labeled with 25% 13CH2 groups. Double-quantum pulse sequences are used to select statistically formed 13C-13C spin pairs. An experiment correlating the 13C-13C internuclear vector with the 13C chemical-shift anisotropy determines the conformational statistics of a single backbone torsion angle. Double-quantum experiments correlating the 13CH2 chemical-shift anisotropies of two adjacent segments provide information on two consecutive torsion angles. The analysis of the spectra yields a trans content of 68% (+/-10%). This represents the first direct experimental estimate of the trans/gauche ratio in atactic polystyrene. The trans content found here agrees well with rotational-isomeric-state models but is inconsistent with results from more elaborate atomistic models that take packing effects into account.
Molecular dynamics simulation is used to reveal the origin of increased molecular mobility that accompanies plastic deformation of a glassy amorphous polymer under an applied stress. Significant increases in torsional transition rates are observed during active deformation prior to and just beyond the yield point. The transition rate drops when active deformation ceases. Increased transition rates are not contingent upon dilation. These simulations verify recent experimental observations of increased mobility during active deformation.
We present theoretical arguments and numerical results to demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers, which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion u(s) approximately s/rho R3(s) approximately c(e)/sqrt[s] when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c(e) approximately 1/rho b(e)3 the "swelling coefficient," b(e) the effective bond length, and rho the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to u(s). The analysis of different moments of this distribution allows for a precise determination of the effective bond length b(e) and the swelling coefficient c(e) of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by s monomers along the chain is found to decay algebraically as 1/s(3/2). Effects of finite chain length are briefly considered.
Molecular-dynamics simulation is used to explore the influence of thermal and mechanical history of typical glassy polymers on their deformation. Polymer stress-strain and energy-strain developments have been followed for different deformation velocities, also in closed extension-recompression loops. The latter simulate for the first time the experimentally observed mechanical rejuvenation and overaging of polymers, and energy partitioning reveals essential differences between mechanical and thermal rejuvenation. All results can be qualitatively interpreted by considering the ratios of the relevant time scales: for cooling down, for deformation, and for segmental relaxation.
- R Auhl
- R Everaers
- G S Grest
- K Kremer
- S J Plimpton
R. Auhl, R. Everaers, G. S. Grest, K. Kremer, S. J. Plimpton,
J. Chem. Phys. 2003, 119, 12718.
- J P Wittmer
- P Beckrich
- H Meyer
- A Cavallo
- A Johner
- J Baschnagel
J. P. Wittmer, P. Beckrich, H. Meyer, A. Cavallo, A. Johner,
J. Baschnagel, Phys. Rev. E 2007, 76, 011803.
[18] H. G. H. Melick, Deformation and Failure of Polymer Glasses,
Ph.D. Thesis, 2002, Eindhoven University of Technology, Eindhoven, The Netherlands.
- A V Lyulin
- J Li
- T Mulder
- B Vorselaars
- M A J Michels
A. V. Lyulin, J. Li, T. Mulder, B. Vorselaars, M. A. J. Michels,
Macromol. Symp. 2006, 237, 108.
- A S Lemak
- N K Balabaev
A. S. Lemak, N. K. Balabaev, J. Comput. Chem. 1996, 17,
1685.
- J D Londono
- A Habenschuss
- J G Curro
- J J Rajasekaran
J. D. Londono, A. Habenschuss, J. G. Curro, J. J. Rajasekaran,
J. Polym. Sci. B 1996, 34, 3055.
- M G Dunbar
- B M Novak
- K Schmidt-Rohr
M. G. Dunbar, B. M. Novak, K. Schmidt-Rohr, Solid State Nucl.
Magn. Reson. 1998, 12, 119.
Standard Pressure-Volume-Temperature Data for Polymers
- P Zoller
- D J Walsh
P. Zoller, D. J. Walsh, Standard Pressure-Volume-Temperature
Data for Polymers, Technomic Publishing Co., Inc., Lancaster,
Basel 1995.