Rheology and Microscopic Topology of Entangled Polymeric Liquids

Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly

We present a new adaptive resolution technique for efficient particle-based multiscale molecular-dynamics simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially localized domains whereas a lower mesoscopic level of detail is sufficient for the rest of the system. Our method allows an on-the-fly interchange between a given molecule's atomic and coarse-grained levels of description, enabling us to reach large length and time scales while spatially retaining atomistic details of the system. The new approach is tested on a model system of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, and the other containing only one-particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The hybrid and the atomistically resolved systems have the same statistical properties at the same physical conditions.

Topological study of pseudo-cubic hydrogen-bond networks in a binary system composed of primary ammonium carboxylates: an analogue of an ice cube

Hierarchical classification and single-crystal X-ray analysis of unique pseudo-cubic hydrogen-bond networks composed of primary ammonium carboxylates were carried out. The networks consist of four carboxylate anions and four primary ammonium cations at the corners of the cube, and twelve charge-assisted N--H...O hydrogen bonds on the sides of the cube. The configuration of the carboxylate anions generates topological diversity in the network. The results of this hierarchical classification showed that pseudo-cubic hydrogen-bond networks composed of primary ammonium carboxylates can form nine topologically different networks. These pseudo-cubic networks are a subset of the networks formed by octameric water in the form of an "ice cube". The classification system can be applied to other pseudo-cubic networks in a similar way. A survey of crystal structures based on combinations of triphenylacetic acid with various alkylamines (carbon numbers up to eight) and examination of the CSD (Cambridge Structural Database) showed eight salts that form such networks in their crystal structures. These structures are classified into six topologically different networks. Similar networks composed of other salts are also discussed from a topological point of view.

Molecular-dynamics simulation study of the glass transition in amorphous polymers with controlled chain stiffness

We report computation results obtained from extensive coarse-grained molecular-dynamics simulations of amorphous ensembles of polymer chains at constant density. In our polymer model, we use bending and torsion potentials acting along the polymer backbone to control the chain stiffness. The static and dynamic properties of the polymer bulk have been analyzed over a large temperature interval in search for the onset of the glass transition. The glass transition temperatures Tg, for different types of chain stiffness, have been determined from the dependence of the self-diffusion coefficient D on the temperature T as the limiting value where the diffusion vanishes. Increasing the chain stiffness induces an increase of the glass transition temperature. The Tg values estimated from diffusion are confirmed by analyzing the relaxation times of the autocorrelation functions for the torsion angle and for the end-to-end vector. The dependence of the diffusion coefficient D on the chain length N is strongly affected by temperature for chains with bending and torsion stiffness. For systems with relatively short chains (N<or=50), the exponent nu from D proportional to N(-nu) increases from the value nu approximately 1 expected in the Rouse regime to nu approximately 2 as the temperature is lowered towards Tg.

Intramolecular long-range correlations in polymer melts: the segmental size distribution and its moments

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.

Reptational dynamics in dissipative particle dynamics simulations of polymer melts

Understanding the fundamental properties of polymeric liquids remains a challenge in materials science and soft matter physics. Here, we present a simple and computationally efficient criterion for topological constraints, i.e., uncrossability of chains, in polymeric liquids using the dissipative particle dynamics (DPD) method. No new length scales or forces are added. To demonstrate that this approach really prevents chain crossings, we study a melt of linear homopolymers. We show that for short chains the model correctly reproduces Rouse-like dynamics whereas for longer chains the dynamics becomes reptational as the chain length is increased--something that is not attainable using standard DPD or other coarse-grained soft potential methods.

Dynamic evolution in coarse-grained molecular dynamics simulations of polyethylene melts

We test a coarse-grained model assigned based on united atom simulations of C50 polyethylene to seven chain lengths ranging from C76 to C300. The prior model accurately reproduced static and dynamic properties. For the dynamics, the coarse-grained time evolution was scaled by a constant value [t=alphatCG] predictable based on the difference in intermolecular interactions. In this contribution, we show that both static and dynamic observables have continued accuracy when using the C50 coarse-grained force field for chains representing up to 300 united atoms. Pair distribution functions for the longer chain systems are unaltered, and the chain dimensions present the expected N0.5 scaling. To assess dynamic properties, we compare diffusion coefficients to experimental values and united atom simulations, assign the entanglement length using various methods, examine the applicability of the Rouse model as a function of N, and compare tube diameters extracted using a primitive path analysis to experimental values. These results show that the coarse-grained model accurately reproduces dynamic properties over a range of chain lengths, including systems that are entangled.

Computational tool to model the packing of polycyclic chains: Structural analysis of amorphous polythiophene

A very efficient computational procedure, which was previously developed to generate and relax atomistic models of linear and comb-like amorphous polymers, has been adapted to model the amorphous phase of polycyclic systems. The strategy, which is a based in a generation algorithm that eliminates the torsion strain and a simple Monte Carlo Metropolis method to relax the generated structures, has been used to predict the density of amorphous polythiophene by combining NVT and NPT simulations. The theoretical value is in the excellent agreement with the experimental one, the former being overestimated by only 3-5%. Next, the molecular conformation and the packing of the rings were studied in detail. Interestingly, the amorphous phase of polythiophene can be described as a packing of elongated molecular chains more or less aligned in the same direction, in which the thiophene rings close in the space but belonging to different chains tend to adopt approximate parallel or antiparallel displaced pi-stacked arrangements.

Morphology of multi-component polymer systems: single chain in mean field simulation studies

Recent work exploring phase separation and self-assembly in multicomponent polymer fluids using a particle-based self-consistent field simulation method is reviewed. The computational method is placed in the context of classical molecular dynamics and Monte Carlo simulations as well as field-theoretic approaches. Its potential is illustrated by applications ranging from spinodal decomposition in symmetric polymer blends and the ordering of diblock copolymers in the bulk to more complex phenomena such as solvent evaporation from thin polymer films and the fabrication of three-dimensional bicontinuous diblock copolymer morphologies reconstruction on patterned substrates.

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.

Long time atomistic polymer trajectories from coarse grained simulations: bisphenol-A polycarbonate

Based on coarse grained simulations of a specially adapted model for bisphenol-A polycarbonate (BPA-PC) we generate by inverse mapping, the reintroduction of chemical details, well equilibrated all-atom conformations and time trajectories of dense polymeric melts for up to 7.8 µs. This is several orders of magnitude more than any direct all-atom simulations have reached so far. These polymer melts contain up to 68600 atoms in = 100 chains of molecular weight = 5217. By comparison with short all-atom simulations we show that these trajectories are physically meaningful, providing us with a powerful tool to compare long time simulations to experiments, which probe specific local dynamics on long time scales, such as NMR relaxation.

The role of temperature and density on the glass-transition dynamics of glass formers

A correlation between the monomeric volume and the dynamic quantity E*(V)/H*, used to provide a quantitative measure of the role of temperature and density on the dynamics, is demonstrated for a series of polymers and glass-forming liquids. We show that monomeric volume and local packing play a key role in controlling the value of this ratio and thus the dynamics associated with the glass temperature.

Effect of equilibration on primitive path analyses of entangled polymers

We use recently developed primitive path analysis (PPA) methods to study the effect of equilibration on entanglement density in model polymeric systems. Values of Ne for two commonly used equilibration methods differ by a factor of 2-4 even though the methods produce similar large-scale chain statistics. We find that local chain stretching in poorly equilibrated samples increases entanglement density. The evolution of Ne with time shows that many entanglements are lost through fast processes such as chain retraction as the local stretching relaxes. Quenching a melt state into a glass has little effect on Ne. Equilibration-dependent differences in short-scale structure affect the craze extension ratio much less than expected from the differences in PPA values of Ne.

Utilization of a Combination of Weak Hydrogen-Bonding Interactions and Phase Segregation to Yield Highly Thermosensitive Supramolecular Polymers

Supramolecular polymerization, i.e., the self-assembly of polymer-like materials through the utilization of the noncovalent bond, is a developing area of research. In this paper, we report the synthesis and investigation of nucleobase-terminated (N6-anisoyl-adenine and N4-(4-tert-butylbenzoyl)cytosine) low molecular weight poly(THF) macromonomers (<2000 g mol(-1)). Even though the degree of interaction between the nucleobase derivatives is very low (<5 M(-1)) these macromonomers self-assemble in the solid state to yield materials with film and fiber-forming capability. While the mechanical properties of films of both materials show extreme temperature sensitivity, resulting in the formation of very low viscosity melts, they do behave differently, which is attributed to the nature of the self-assembly controlled by the nucleobase. A combination of FT-IR, WAXD, and rheological experiments was carried out to further investigate the nature of the self-assembly in these systems. The studies demonstrate that a combination of phase segregation between the hard nucleobase chain ends and the soft poly(THF) core combined with aromatic amide hydrogen bonding is utilized to yield the highly thermosensitive supramolecular polymeric materials. In addition, analysis of the data suggests that the rheological properties of these supramolecular materials is controlled by the disengagement rate of the nucleobase chain ends from the "hard" phase, which, if shown to be general, provides a design criteria in the development of more thermally responsive materials.

Segmental order in end-linked polymer networks: a Monte Carlo study

Segmental order in end-linked monomodal and bimodal polymer networks is investigated by means of bond-fluctuation Monte Carlo simulations. The tensor order parameter, which is a central observable in NMR experiments, is not uniquely related to simple vectorial order. The relaxation of NMR-detected tensorial interactions towards their finite long-time limit is best described by a power law and occurs over much longer time scales than the relaxation of vectorial order. The well-known prediction for the segmental order of Gaussian chains as a simple function of the segment number between constraints is not straightforwardly obeyed, neither in dry nor in swollen networks. Excluded-volume interactions tend to significantly reduce the tensorial order, as is clearly observed in single-chain simulations. A distribution extends along the chain, where order is increased in a region of 30-40 bonds around the cross-links in networks. The dominating contribution to the order parameter distribution arises from the frozen-in distribution of end-to-end separations. We find strong deviations from the Gamma distribution, which has so far been implicitly used in most NMR works, as it is a straightforward consequence of a Gaussian distribution of end separations. Specifically, we find narrower distributions, as small values of the tensor order parameter are strongly suppressed, most probably as a result of trapped entanglements. The markedly subaffine behavior of the average order parameter and the changes in its distribution on swelling are assigned to orientation processes of strands which compensate for the non-affine local deformation. Our central observations and interpretations are well supported by our previous experimental and theoretical work.

Effect of bending and torsion rigidity on self-diffusion in polymer melts: A molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for N<Ne (Rouse regime) and with nu=2 for N>Ne (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for N<Ne and nu=2.2 for N>Ne. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.

Ultrasonic wave spectroscopy study of sugar oligomers and polysaccharides in aqueous solutions: The hydration length concept

The determination of apparent persistence length and radius of gyration of maltodextrins in water is achievable through high-resolution ultrasonic spectroscopy measurements. Classical hydration number for those carbohydrates is characteristic of an apparent persistence degree of polymerisation of the polymer. A force-field based molecular modeling of a 10DP malto-oligomer allows measurement of the corresponding length for the lowest energetic conformation in solution. A good agreement between the apparent radii of gyration determined by this technique and the freely rotating polymer chain model is found with radii of gyration calculated from the intrinsic viscosity.

Nonequilibrium Monte Carlo simulation of lattice block copolymer chains subject to oscillatory shear flow

This paper has extended nonequilibrium Monte Carlo (MC) approach to simulate oscillatory shear flow in a lattice block copolymer system. Phase transition and associated rheological behaviors of multiple self-avoiding chains have been investigated. Stress tensor has been obtained based upon sampled configuration distribution functions. At low temperatures, micellar structures have been observed and the underlying frequency-dependent rheological properties exhibit different initial slopes. The simulation outputs are consistent with the experimental observations in literature. Chain deformation during oscillatory shear flow has also been revealed. Although MC simulation cannot account for hydrodynamic interaction, the highlight of our simulation approach is that it can, at small computing cost, investigate polymer chains simultaneously at different spatial scales, i.e., macroscopic rheological behaviors, mesoscopic self-assembled structures, and microscopic chain configurations.

Chain retraction potential in a fixed entanglement network

When a chain, tethered at one end, is immersed in a fixed entanglement network, the mobile tip of the chain encounters an entropic potential barrier that penalizes deep fluctuations needed to bring the tip close to the tethering point. Using the tube model, Doi and Kuzuu [J. Polym. Sci., Polym. Lett. Ed. 18, 775 (1980)] estimated that this potential, which is crucial to describe the rheology of branched polymers in fixed networks and melts, has a quadratic form with a prefactor nu = 1.5. Later calculations based on regular lattices indicated that the potential is nonquadratic, and its steepness depends on the lattice coordination number. In this Letter, we analyze the primitive paths obtained using the bond-fluctuation model for chains with up to 12.5 entanglements. Our simulations confirm a quadratic form for the potential with a prefactor close to the Doi-Kuzuu value, nu approximately 1.5.

Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks

We use molecular dynamics simulations to investigate the microscopic and macroscopic response of model polymer networks to uniaxial elongations. By studying networks with strand lengths ranging from N(s)=20 to 200 we cover the full crossover from cross-link to entanglement dominated behavior. Our results support a recent version of the tube model which accounts for the different strain dependence of chain localization due to chemical cross-links and entanglements.

Entanglements in quiescent and sheared polymer melts

We visualize entanglements in polymer melts using molecular dynamics simulation. A bead at an entanglement interacts persistently for long times with the nonbonded beads (those excluding the adjacent ones in the same chain). The interaction energy of each bead with the nonbonded beads is averaged over a time interval tau much longer than microscopic times but shorter than the onset time of tube constraints tau e. Entanglements can then be detected as hot spots consisting of several beads with relatively large values of the time-averaged interaction energy. We next apply a shear flow with rate much faster than the disengagement motion of entangled chains. With increasing strain the chains take zigzag shapes and one-half of the hot spots become bent. The chains are first stretched as a network but, as the bends approach the chain ends, disentanglements subsequently occur, leading to stress overshoot observed experimentally.