Crossover behavior in crystal growth rate from n‐alkane to polyethylene

A crystal growth rate equation, parameterized from molecular dynamics simulations of n‐alkanes, is compared to recent experiments on growth rates for polyethylene at high undercooling. The analysis reveals that the growth rate of alkanes and polyethylene can both be described by the same relationship. The appropriate relaxation time is used to describe the kinetic barrier to crystallization. For chains shorter than the entanglement length, this is the Rouse time. For chains longer than the entanglement molecular weight, kinetic limitations are modeled by the local relaxation of an entangled segment at the interface. This model supports a different mechanism for fast crystal growth at high undercooling than that usually inferred from slow growth data near the melting temperature. Use of the crystal growth rate model is illustrated for polyethylene crystallizing under conditions of slow cooling and fast cooling. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2468–2473, 2005     

Monte Carlo simulations of stress relaxation of entanglement-free Fraenkel chains. I. Linear polymer viscoelasticity

Shear stress relaxation modulus GS(t) curves of entanglement-free Fraenkel chains have been calculated using Monte Carlo simulations based on the Langevin equation, carrying out both in the equilibrium state and following the application of a step shear deformation. While the fluctuation-dissipation theorem is perfectly demonstrated in the Rouse-chain model, a quasiversion of the fluctuation-dissipation theorem is observed in the Fraenkel-chain model. In both types of simulations on the Fraenkel-chain model, two distinct modes of dynamics emerge in GS(t), giving a line shape similar to that typically observed experimentally. Analyses show that the fast mode arises from the segment-tension fluctuations or reflects the relaxation of the segment tension created by segments being stretched by the applied step strain-an energetic-interactions-driven process-while the slow mode arises from the fluctuations in segmental orientation or represents the randomization of the segmental-orientation anisotropy induced by the step deformation-an entropy-driven process. Furthermore, it is demonstrated that the slow mode is well described by the Rouse theory in all aspects: the magnitude of modulus, the line shape of the relaxation curve, and the number-of-beads (N) dependence of the relaxation times. In other words, one Fraenkel segment substituting for one Rouse segment, it has been shown that the entropic-force constant on each segment is not a required element to give rise to the Rouse modes of motion, which describe the relaxation modulus of an entanglement-free polymer over the long-time region very well. This conclusion provides an explanation resolving a long-standing fundamental paradox in the success of Rouse-segment-based molecular theories for polymer viscoelasticity-namely, the paradox between the Rouse segment size being of the same order of magnitude as that of the Kuhn segment (each Fraenkel segment with a large force constant HF can be regarded as basically equivalent to a Kuhn segment) and the meaning of the Rouse segment as defined in the Rouse-chain model. The general agreement observed in the comparison of the simulation and experimental results indicates that the Fraenkel-chain model, while being still relatively simple, has captured the key element in energetic interactions--the rigidity on the segment--in a polymer system.     

Dynamics of free chains in polymer nanocomposites

The dynamics of entangled polymeric chains in a polymer filled with nanoparticles is studied by means of molecular dynamics simulations of a model system. The primary objective is to study to what extent the reptation of polymers not in direct contact with fillers is modified with respect to the neat material. To this end, two systems are considered: A regular filled material in which the filler-polymer affinity is controlled, and a system in which the beads in contact with the filler at the beginning of the production phase of the simulation are tethered to the filler surface. This second system represents the limit case of long polymer-filler attachment time. In this case attention is focused on the free chains of the melt. The dynamics in the two models is different. In the filled system uniform slowing down for all Rouse modes is observed. The effect varies monotonically with the filler-polymer affinity. Up to saturation, this behavior may be captured by usual models with an effective, affinity-dependent, friction coefficient. In the system with grafted chains, the free chain Rouse dynamics is identical to that in the neat material, except for the longest modes which are significantly slowed down. More interestingly, the dynamics of the free chains depends in a nonmonotonic way on the polymer-filler affinity, although the free chains do not come in direct contact with the filler. This effect is due to small changes in the structure of the polydisperse brush upon modification of the affinity. Specifically, the density of the brush and the amount of interpenetration of free and grafted chains depend on the filler-polymer affinity. The use of a reptation model with modified tube diameter to capture this behavior is discussed.     

Combined Molecular Dynamics Simulation and Rouse Model Analysis of Static and Dynamic Properties of Unentangled Polymer Melts with Different Chain Architectures

Chain architecture effect on static and dynamic properties of unentangled polymers is explored by molecular dynamics simulation and Rouse mode analysis based on graph theory. For open chains, although they generally obey ideal scaling in chain dimensions, local structure exhibits nonideal behavior due to the incomplete excluded volume(EV) screening, the reduced mean square internal distance(MSID) can be well described by Wittmer' theory for linear chains and the resulting chain swelling is architecture dependent, i.e., the more branches a bit stronger swelling. For rings, unlike open chains they are compact in term of global sizes. Due to EV effect and nonconcatenated constraints their local structure exhibits a quite different non-Gaussian behavior from open chains, i.e., reduced MSID curves do not collapse to a single master curve and fail to converge to a chain-length-independent constant, which makes the direct application of Wittmer's theory to rings quite questionable.Deviation from ideality is further evidenced by limited applicability of Rouse prediction to mode amplitude and relaxation time at high modes as well as the non-constant and mode-dependent scaled Rouse mode amplitudes, while the latter is architecture-dependent and even molecular weight dependent for rings. The chain relaxation time is architecture-dependent, but the same scaling dependence on chain dimensions does hold for all studied architectures. Despite mode orthogonality at static state, the role of cross-correlation in orientation relaxation increases with time and the time-dependent coupling parameter rises faster for rings than open chains even at short time scales it is lower for rings.     

Relaxation of flexible chains in dilute and non‐dilute systems. Dynamic Monte Carlo results for linear and star chains

A dynamic Monte Carlo algorithm is employed to investigate the dynamics of flexible linear and star chains on a cubic lattice at different concentrations. Some results for similar systems are also obtained with an off‐lattice algorithm. Diffusion coefficient, relaxation times and mean size data are combined into friction‐independent ratios in good agreement with the theoretical predictions from the Rouse theory. The relaxation times and amplitudes corresponding to the Rouse normal modes are analyzed in terms of their variation with the mode order. The end‐to‐end vector correlation times obtained from the simulations for linear chains are compared with the theoretical expression obtained from the Rouse theory. Deviations from this theory are observed for the contribution of the different modes in the non‐dilute systems. Finally, the time correlation function corresponding to a subchain's end‐to‐end vector is investigated. The results also show deviations from the Rouse theory, which are in qualitative agreement with the features observed in data from dielectric relaxation experiments of block copolymers.     

Segmental versus chain dynamics of linear polymers

Segmental dynamics of relatively short linear polymers are discussed in terms of two distinct contributions, one related to the local segmental motion (alpha relaxation) and the other to polymer-specific effects that reflect Brownian dynamics of the polymer under chain connectivity constraints (Rouse relaxation modes). These two aspects of polymer dynamics are reflected, though differently, in relaxation spectra of different experimental techniques. Two contrasting cases of the (collective) dipolar response (dielectric techniques) versus the individual segmental response (e.g., NMR spin-lattice relaxation spectroscopy) are considered. The second-rank orientational correlation function of an elementary (Kuhn) segment, directly related to NMR observables, is derived in terms of Rouse normal modes. The effect of alpha dynamics is estimated under the assumption of a separation of time scales which, as it is argued, is a necessary precondition of the Rouse approach. The relative magnitude of the polymer-related dynamics is expressed through the number of elementary Rouse units in the chain and the number of Kuhn segments in a Rouse unit. The results are discussed in the context of recent literature.     

Monte Carlo study of the coil-to-globule transition of a model polymeric system

Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment–segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20–10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0–0.45k_BT, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and underwent a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties (“volume approximation”) is only valid for extraordinarily long chains [molecular weight of O(10⁹)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3651–3666, 2006     

Finite system size effects in the interfacial dynamics of binary liquid films

We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.     

Interchain coupled chain dynamics of poly(ethylene oxide) in blends with poly(methyl methacrylate): coupling model analysis

Quasielastic neutron scattering and molecular dynamics simulation data from poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA) blends found that for short times the self-dynamics of PEO chain follows the Rouse model, but at longer times past t(c) = 1-2 ns it becomes slower and departs from the Rouse model in dependences on time, momentum transfer, and temperature. To explain the anomalies, others had proposed the random Rouse model (RRM) in which each monomer has different mobility taken from a broad log-normal distribution. Despite the success of the RRM, Diddens et al. [Eur. Phys. Lett. 95, 56003 (2011)] extracted the distribution of friction coefficients from the MD simulations of a PEO/PMMA blend and found that the distribution is much narrower than expected from the RRM. We propose a simpler alternative explanation of the data by utilizing alone the observed crossover of PEO chain dynamics at t(c). The present problem is just a special case of a general property of relaxation in interacting systems, which is the crossover from independent relaxation to coupled many-body relaxation at some t(c) determined by the interaction potential and intermolecular coupling/constraints. The generality is brought out vividly by pointing out that the crossover also had been observed by neutron scattering from entangled chains relaxation in monodisperse homopolymers, and from the segmental α-relaxation of PEO in blends with PMMA. The properties of all the relaxation processes in connection with the crossover are similar, despite the length scales of the relaxation in these systems are widely different.     

Interdiffusion of polymers across interfaces

Neutron Reflection (NR) and Dynamic Secondary Ion Mass Spectroscopy (DSIMS) experiments were conducted on symmetrically deuterated polystyrene triblock bilayers (HDH/DHD) which directly probed the interdiffusion dynamics of the chains during welding. The HDH chains had their centers deuterated 50%, the DHD chains had their ends deuterated (25% at each end) such that each chain contained approximately 50% D. During welding, anisotropic motion of the chains produces a time-dependent oscillation (ripple) in the H and D concentration at the interface, which bears the characteristic signature of the polymer dynamics. These oscillations were compared with those predicted by Rouse, polymer mode coupling (PMC), and reptation dynamics. The following conclusions can be made from this study. (a) During the interdiffusion of high molecular weight HDH/DHD pairs, higher mobility of the chain ends caused a concentration oscillation which increased to a maximum amplitude, and eventually vanished at times, t > τ_D. The amplitude, or excess enrichment found, was appreciably more than that predicted by Rouse and PMC simulations, and was only slightly less than that predicted from reptation simulations. (b) The oscillations were completely missing in the 30 and 50K HDH/DHD polymers, which are only weakly entangled. The lack of oscillations for the 30 and 50K pairs may be due to a combination of surface roughness and fluctuations of order 30 Å. (c) It was found that the position of the maximum in this ripple stayed at the interface during its growth. This is also consistent with reptation and has not been explained by other theories. (d) All dynamics models for linear polymers produce ripples, many of which are qualitatively similar to that predicted for reptation. However, each ripple bears the fingerprint of the dynamics in terms of its time-dependent shape, position, and magnitude, and the models are clearly distinguishable. Our results, in summary, support reptation as a candidate mechanism of interdiffusion at polymer(SINGLEBOND) polymer interfaces and its uniqueness is being further pursued. © 1996 John Wiley & Sons, Inc.     

Dynamics of polyethylene melts studied by Monte Carlo simulations on a high coordination lattice

A detailed comparison is made between the experiment, prior simulations by other groups, and our simulation based on a newly designed dynamic Monte Carlo algorithm, on the dynamics of polyethylene (PE) melts. The new algorithm, namely, noncross random two-bead move has been developed on a high coordination lattice (the 2nnd lattice) for studying the dynamics of realistic polymers. The chain length (molecular weight) in our simulation ranges from C40 (562 Da) to C324 (4538 Da). The effects of finite chain length have been confirmed and significant non-Gaussian statistics evidently results in nonstandard static and dynamic properties of short PE chains. The diffusion coefficients scale with molecular weight (M) to the −1.7 power for short chains and −2.2 for longer chains, which coincides very well with experimental results. No pure Rouse scaling in diffusion has been observed. The transitional molecular weight to the entanglement regime is around 1500 Da. The detailed mean square displacements of middle bead (g1) are presented for several chain lengths. The reptation-like slowdown can be clearly observed only above M ∼ 2400 Da. The slope 0.25 predicted by the theory for the intermediate regime is missing; instead a slope close to 0.4 appears, indicating that additional relaxation mechanism exists in this transitional region. The relaxation times extracted by fitting the autocorrelation function of end-to-end vectors with reptation model scale with M to 2.5 for long chains, which seemingly conflicts with the scaling of diffusion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2556–2571, 2006     

Hierarchical Modeling of Entangled Polymers

Summary : We demonstrate that it is possible to link multi-chain molecular dynamics simulations with the tube model using a single chain slip-links model as a bridge. This hierarchical approach allows significant speed up of simulations, permitting us to span the time scales relevant for a comparison with the tube theory. Fitting the mean-square displacement of individual monomers in molecular dynamics simulations with the slip-spring model, we show that it is possible to predict the stress relaxation. Then, we analyze the stress relaxation from slip-spring simulations in the framework of the tube theory. In the absence of constraint release, we establish that the relaxation modulus can be decomposed as the sum of contributions from fast and longitudinal Rouse modes, and tube survival. Finally, we discuss some open questions regarding possible future directions that could be profitable in rendering the tube model quantitative, even for mildly entangled polymers.     

Phase behavior and local dynamics of concentrated triblock copolymer micelles

We report a neutron-scattering study to characterize the ordering and local dynamics of spherical micelles formed by the triblock copolymer polyethylene oxide (PEO)--polypropylene oxide (PPO)--polyethylene oxide (Pluronic) in aqueous solution. The study focuses on two Pluronic species, F68 and F108, that have the same weight fraction of PEO but that differ in chain length by approximately a factor of 2. At sufficiently high concentration, both species undergo a sequence of phase changes with increasing temperature from dissolved chains to micelles with liquid-like order to a cubic crystal phase and finally back to a micelle liquid phase. A comparison of the phase diagrams constructed from small-angle neutron scattering indicates that crystallization is suppressed for shorter chain micelles due to fluctuation effects. The intermediate scattering function I(Q,t)I(Q,0) determined by neutron spin echo displays a line shape with two distinct relaxations. Comparisons between I(Q,t)I(Q,0) for fully hydrogenated F68 chains in D2O and for F68 with deuterated PEO blocks reveal that the slower relaxation corresponds to Rouse modes of the PPO segments in the concentrated micelle cores. The faster relaxation is identified with longitudinal diffusive modes in the PEO corona characteristic of a polymer brush.     

Molecular dynamics study of the thermal and the density effects on the local and the large-scale motion of polymer melts: scaling properties and dielectric relaxation

Results from a molecular dynamics simulation of a melt of unentangled polymers are presented. The translational motion, the large-scale and the local reorientation processes of the chains, as well as their relations with the so-called "normal" and "segmental" dielectric relaxation modes are thoroughly investigated in wide temperature and pressure ranges. The thermodynamic states are well fitted by the phenomenological Tait equation of state. A global time-temperature-pressure superposition principle of both the translational and the rotational dynamics is evidenced. The scaling is more robust than the usual Rouse model. The latter provides insight but accurate comparison with the simulation calls for modifications to account for both the local chain stiffness and the nonexponential relaxation. The study addresses the issue whether the temperature or the density is a dominant control parameter of the dynamics or the two quantities give rise to comparable effects. By examining the ratio /alphatau//alphaP between the isochronic and isobaric expansivities, one finds that the temperature is dominant when the dynamics is fast. If the relaxation slows down, the fluctuations of the free volume increase their role and become comparable to those of the thermal energy. Detectable cross-correlation between the "normal-mode" and the "segmental" dielectric relaxations is found and contrasted with the usual assumption of independent modes.     

Polymer Dynamics in a Polymer-Solid Interphase: Molecular Dynamics Simulations of 1,4-Polybutadiene At a Graphite Surface

A chemically realistic model of 1,4-polybutadiene confined by graphite walls in a thin film geometry was studied by molecular dynamics simulations. The chemically realistic approach allows for a quantitative determination of a variety of experimentally accessible relaxation functions (e.g., dielectric, NMR, or neutron scattering responses). The simulations yield these experimental observables. Additionally, the simulations can be resolved as a function of distance to the solid interface on a much finer scale than experimentally possible, providing a detailed mechanistic picture of the segmental and large scale motions of polymers in the interfacial region between bulk polymer melts and solid walls. Extending the study of 1,4-polybutadiene on graphite to temperatures close to the glass transition temperature, we also address the question to what extent growing length scales associated with the glass transition influence the melt dynamics in the interphase. It was found that there is an interplay of this intrinsic slowing down with the adsorption/desorption kinetics of the chains close to the wall. It is argued that the monomer density changes near the wall can overcome the effect of rotational barriers only in a region of about 2 nm next to the wall.     

Dynamics of polymer melts confined by smooth walls: crossover from nonentangled region to entangled region

The authors present the results of molecular dynamics simulations of polymer films confined by smooth walls. Simulations were performed for a wide range of chain lengths covering both nonentangled and entangled regions, as well as film thicknesses ranging from the order of unperturbed chain size to the bulk state. The simulation results for the chain size dependence on the film thickness are compared with the prediction of the scaling model. By measuring the correlation function of the end-to-end vectors, we have determined the relaxation time of confined polymer chains in different entangled states. It is shown that there is a minimum in the relaxation time of long chains when decreasing the film thickness, which is partially due to the confinement-induced disentanglement effect.     

Monte Carlo study of defect fluctuations and reptation in polymer melts

Defect fluctuations in highly distorted polymer chains were simulated by Monte Carlo calculation. The NMR autocorrelation function was derived and described by the superposition of three exponential functions with time constants spread over two orders of magnitude. As a consequence of defect diffusion, longitudinal chain diffusion (reptation) can be expected in polymer melts. By simulating the mean-square displacement of a segment, it was found that after sufficiently long times, compared with defect density correlation times, a linear relationship holds fairly well. As a rule of thumb, it can be stated that the linear Einstein equation is valid for times much greater than 10³ mean step times in practical cases (chain length: several thousand segments, defect concentration: 10–20%), or, in other words, for mean-square displacements greater than a few diffusion step lengths. A long-time chain-diffusion coefficient depending on the molecular weight and on the defect concentration could be derived. Effects on the low-field NMR relaxation behavior are derived and discussed.     

Mechanical Spectral Hole Burning in polymer solutions

Mechanical Spectral Hole Burning (MSHB) was previously developed to investigate dynamic heterogeneity for polymeric materials, which exhibit relatively weak dielectric responses. In our previous work, MSHB was applied to a densely entangled block copolymer and successfully distinguishes the heterogeneous from the homogeneous states. Here, a series of polystyrene (PS) solutions was chosen to further investigate the effect of different types of heterogeneity on mechanical spectral hole burning. The three types of heterogeneity of interest include the entanglement spacing, the entanglement density (or number of entanglements per chain), and chain end density. The heterogeneity was varied by changing either solution concentration or molecular weight of the PS. Different types of dynamics from close to the Rouse regime into the terminal region were also examined. Our results are consistent with a heterogeneous dynamics over the time scales from close to Rouse regime into the rubbery plateau regime and the rubbery plateau‐to‐terminal flow transition regime. Terminal relaxation dynamics, on the other hand, were found to be homogeneous for the PS/diethyl phthalate solutions investigated. The results also indicate the hole properties are dominated by the type of dynamics rather than the length scale of heterogeneity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2047–2062, 2009     

Rouse's dynamics of networks with pendant chains

A model to describe the dynamics of networks with linear pendant chains has been formulated based on the properties of ensembles of micronetworks, using the Rouse model. This development indicates that the terminal relaxation time of pendant chains with relatively large molecular weight scales with the square of the molecular weight of those chains. On the other hand, when the molecular weight of pendant and elastically active chains are comparable, a nearly exponential growth of the terminal relaxation time with the molecular weight is predicted. The main predictions of the model are compared with experimental results of model poly(dimethyl siloxane) (PDMS) networks, with controlled amounts of linear pendant chains of known molecular weight. The terminal relaxation time of these networks was estimated from the values of the loss modulus G″(ω) measured experimentally. An exponential dependence on the molecular weight of pendant chains was derived for the terminal relaxation time. This behavior is in good agreement with the predictions of our model for micronetworks, provided that the friction coefficient scales linearly with the number of entanglements. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1121–1130, 1999