Self-motion and the alpha relaxation in a simulated glass-forming polymer: crossover from Gaussian to non-Gaussian dynamic behavior

Position-Dependent Segmental Relaxation in Bottlebrush Polymers

Segmental dynamics of specifically labeled poly(propylene oxide), PPO, based bottlebrush polymers, PNB-g-PPO, were studied using quasi-elastic neutron scattering. The focus was set to different parts of the side chains to investigate the hypothetical gradual relaxation behavior within the side chains of a bottlebrush polymer. Different sections of the side chains were highlighted for QENS via sequential polymerization of protonated and deuterated monomers to allow the study of the relaxation behavior of the inner and outer parts of the side chain separately. A comparison of these two parts reveals a slowdown due to the grafting process happening across the different regions. This is seen for the segmental relaxation time as well as on the time-dependent mean-square displacement. Additionally, the non-Gaussian parameter, α, shows a decreasing difference from Gaussian behavior with the distance to the backbone. Altogether, this leads to the conclusion that gradual relaxation behavior exists.

Nature of Subdiffusion Crossover in Molecular and Polymeric Glassformers

A crossover from a non-Gaussian to Gaussian subdiffusion has been observed ubiquitously in various polymeric and molecular glassformers. We have developed a framework that generalizes the fractional Brownian motion model to incorporate non-Gaussian features by introducing a jump kernel. We illustrate that the non-Gaussian fractional Brownian motion model accurately characterizes the subdiffusion crossover. From the solutions of the non-Gaussian fractional Brownian motion model, we gain insights into the nature of van Hove self-correlation in non-Gaussian subdiffusive regime, which is found to exhibit exponential tails, providing first such experimental evidence in molecular glassformers. The validity of the model is supported by comparison with incoherent quasielastic neutron scattering data obtained from several molecular and polymeric glassformers.

Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra

Modern 4-wave mixing spectroscopies are expensive to obtain experimentally and computationally. In certain cases, the unfavorable scaling of quantum dynamics problems can be improved using a generalized quantum master equation (GQME) approach. However, the inclusion of multiple (light-matter) interactions complicates the equation of motion and leads to seemingly unavoidable cubic scaling in time. In this paper, we present a formulation that greatly simplifies and reduces the computational cost of previous work that extended the GQME framework to treat arbitrary numbers of quantum measurements. Specifically, we remove the time derivatives of quantum correlation functions from the modified Mori-Nakajima-Zwanzig framework by switching to a discrete-convolution implementation inspired by the transfer tensor approach. We then demonstrate the method's capabilities by simulating 2D electronic spectra for the excitation-energy-transfer dimer model. In our method, the resolution of data can be arbitrarily coarsened, especially along the t2 axis, which mirrors how the data are obtained experimentally. Even in a modest case, this demands O(103) fewer data points. We are further able to decompose the spectra into one-, two-, and three-time correlations, showing how and when the system enters a Markovian regime where further measurements are unnecessary to predict future spectra and the scaling becomes quadratic. This offers the ability to generate long-time spectra using only short-time data, enabling access to timescales previously beyond the reach of standard methodologies.

The effect of chemical constitution on polyisoprene dynamics

Polyisoprene (PI) melts have been studied, with most reports focusing on systems with high 1,4-cis content. In contrast, 1,4-trans PI homopolymers or random copolymers have seldom been examined, despite a handful of investigations suggesting a distinct dynamic behavior. Herein, we employ all-atom simulations to investigate the effect of chemical architecture on the dynamics of cis and trans-PI homopolymers, as well as copolymers. We examine the thermodynamic, conformational, and structural properties of the polymers and validate the performance of the models. We probe chain dynamics, revealing that cis-PI presents accelerated translation and reorientation modes relative to trans as recorded by the mean square displacement of the chain center-of-mass as well as by the characteristic times of the lower modes in a Rouse analysis. Interestingly, progressing to higher modes, we observe a reversal with trans units exhibiting faster dynamics. This was further confirmed by calculations of local carbon-hydrogen vector reorientation dynamics, which offer a microscopic view of segmental mobility. To obtain insight into the simulation trajectories, we evaluate the intermediate incoherent scattering function that supports a temperature-dependent crossover in relative mobility that extends over separations beyond the Kuhn-length level. Finally, we analyzed the role of non-Gaussian displacements, which demonstrate that cis-PI exhibits increased heterogeneity in dynamics over short-timescales in contrast to trans-PI, where deviations persist over times extending to terminal dynamics. Our all-atom simulations provide a fundamental understanding of PI dynamics and the impact of microstructure while providing important data for the design and optimization of PI-based materials.

Microscopic versus Macroscopic Glass Transitions and Relevant Length Scales in Mixtures of Industrial Interest

We have combined X-ray diffraction, neutron diffraction with polarization analysis, small-angle neutron scattering (SANS), neutron elastic fixed window scans (EFWS), and differential scanning calorimetry (DSC) to investigate polymeric blends of industrial interest composed by isotopically labeled styrene-butadiene rubber (SBR) and polystyrene (PS) oligomers of size smaller than the Kuhn length. The EFWS are sensitive to the onset of liquid-like motions across the calorimetric glass transition, allowing the selective determination of the "microscopic" effective glass transitions of the components. These are compared with the "macroscopic" counterparts disentangled by the analysis of the DSC results in terms of a model based on the effects of thermally driven concentration fluctuations and self-concentration. At the microscopic level, the mixtures are dynamically heterogeneous for blends with intermediate concentrations or rich in PS, while the sample with highest content of the fast SBR component looks as dynamically homogeneous. Moreover, the combination of SANS and DSC has allowed determining the relevant length scale for the α-relaxation through its loss of equilibrium to be ≈30 Å. This is compared with the different characteristic length scales that can be identified in these complex mixtures from structural, thermodynamical, and dynamical points of view because of the combined approach followed. We also discuss the sources of the non-Gaussian effects observed for the atomic displacements and the applicability of a Lindemann-like criterion in these materials.

Side Chain Dynamics of Poly(norbornene)-g-Poly(propylene oxide) Bottlebrush Polymers

The segmental dynamics of the side chains of poly(norbornene)-g-poly(propylene oxide) (PNB-g-PPO) bottlebrush polymer in comparison to PPO is studied by quasi-elastic neutron scattering. Having experimental time and length scale information simultaneously allows to extract spatial information in addition to relaxation time. Tethering one end of the PPO side chain onto a stiff PNB backbone slows down the segmental relaxation, over the length and time scales investigated. The power law dependence of the relaxation time on the momentum transfer, Q, indicates a more heterogeneous relaxation pattern for the bottlebrush polymer, whereas the linear PPO has less deviations from a homogenous relaxation. Similar conclusions can be drawn from the time dependent mean square displacement, 〈r² (t)〉, and the non-Gaussian parameter, α₂ (t). Herein, the bottlebrush polymer shows a more restricted dynamics, whereas the linear PPO reaches 〈r² (t)〉∝t^0.5 at the highest temperature. The deviations from Gaussian behavior are evident at the α₂ (t). Both samples show a decaying α₂ (t). The non-Gaussian parameter supports the results from the power law dependence of the relaxation times, with lower α₂ (t) values for PPO compared to those for PNB-g-PPO, pointing to less deviations from Gaussian behavior.

Fractional Coupling of Primary and Johari-Goldstein Relaxations in a Model Polymer

A polymer model exhibiting heterogeneous Johari−Goldstein (JG) secondary relaxation is studied by extensive molecular-dynamics simulations of states with different temperature and pressure. Time−temperature−pressure superposition of the primary (segmental) relaxation is evidenced. The time scales of the primary and the JG relaxations are found to be highly correlated according to a power law. The finding agrees with key predictions of the Coupling Model (CM) accounting for the decay in a correlation function due to the relaxation and diffusion of interacting systems. Nonetheless, the exponent of the power law, even if it is found in the range predicted by CM (0<ξ<1), deviates from the expected one. It is suggested that the deviation could depend on the particular relaxation process involved in the correlation function and the heterogeneity of the JG process.

Application of Nano-SiO2 Reinforced Urea-Formaldehyde Resin and Molecular Dynamics Simulation Study

Nano-SiO₂ is a typical modifier used for urea-formaldehyde (UF) resins to balance the reduced formaldehyde content and maintain bond strength. However, the microstructure of UF resin and the interaction between UF resin and nano-SiO₂ are microscopic phenomena; it is difficult to observe and study its intrinsic mechanism in traditional experimental tests. In this work, the enhancement mechanism was explored by molecular dynamics simulations combined with an experiment of the effect of nano-SiO₂ additions on UF resin. The results showed that the best performance enhancement of UF resin was achieved when the addition of nano-SiO₂ was 3 wt%. The effects caused by different additions of nano-SiO₂ were compared and analyzed by molecular dynamics simulations in terms of free volume fraction, the radius of gyration, and mechanical properties, and the results were in agreement with the experimental values. Meanwhile, the changes in hydrogen bonding and radial distribution functions in these systems were counted to explore the interaction between nano-SiO₂ and UF resin. The properties of the UF resin were enhanced mainly through the large number of different forms of hydrogen bonds with nano-SiO₂, with the strongest hydrogen bond occurring between H_(SiO2)… O = _(PHMU).

Decoding polymer self-dynamics using a two-step approach

The self-correlation function and corresponding self-intermediate scattering function in Fourier space are important quantities for describing the molecular motions of liquids. This work draws attention to a largely overlooked issue concerning the analysis of these space-time density-density correlation functions of polymers. We show that the interpretation of non-Gaussian behavior of polymers is generally complicated by intrachain averaging of distinct self-dynamics of different segments. By the very nature of the mathematics involved, the averaging process not only conceals critical dynamical information, but also contributes to the observed non-Gaussian dynamics. To fully expose this issue and provide a thorough benchmark of polymer self-dynamics, we perform analyses of coarse-grained molecular dynamics simulations of linear and ring polymer melts as well as several theoretical models using a "two-step" approach, where interchain and intrachain averagings of segmental self-dynamics are separated. While past investigations primarily focused on the average behavior, our results indicate that a more nuanced approach to polymer self-dynamics is clearly required.

Glass transition of ion-containing polymer melts in bulk and thin films

Ion-containing polymers often are good glass formers, and the glass transition temperature is an important parameter to consider for practical applications, which prescribes the working temperature range for different mechanical and dynamic properties. In this work, we present a systematic molecular dynamics simulation study on the coupling of ionic correlations with the glass transition, based on a generic coarse-grained model of ionic polymers. The variation of the glass transition temperature is examined concerning the influence of the electrostatic interaction strength, charge fraction, and charge sequence. The interplay with the film thickness effect is also discussed. Our results reveal a few typical features about the glass transition process that are in qualitative agreement with previous studies, further highlighting the effects of counterion entropy at weak ionic correlations and physical crosslinking of ionic aggregates at strong ionic correlations. Detailed parametric dependencies are displayed, which demonstrate that introducing strong ionic correlations promotes vitrification while adopting a precise charge sequence and applying strong confinement with weak surface affinity reduce the glass transition temperature. Overall, our investigation provides an improved picture towards a comprehensive understanding of the glass transition in ion-containing polymeric systems from a molecular simulation perspective.

Insight into the Structure and Dynamics of Polymers by Neutron Scattering Combined with Atomistic Molecular Dynamics Simulations

Combining neutron scattering and fully atomistic molecular dynamics simulations allows unraveling structural and dynamical features of polymer melts at different length scales, mainly in the intermolecular and monomeric range. Here we present the methodology developed by us and the results of its application during the last years in a variety of polymers. This methodology is based on two pillars: (i) both techniques cover approximately the same length and time scales and (ii) the classical van Hove formalism allows easily calculating the magnitudes measured by neutron scattering from the simulated atomic trajectories. By direct comparison with experimental results, the simulated cell is validated. Thereafter, the information of the simulations can be exploited, calculating magnitudes that are experimentally inaccessible or extending the parameters range beyond the experimental capabilities. We show how detailed microscopic insight on structural features and dynamical processes of various kinds has been gained in polymeric systems with different degrees of complexity, and how intriguing questions as the collective behavior at intermediate length scales have been faced.

Surface Modification Design for Improving the Strength and Water Vapor Permeability of Waterborne Polymer/SiO2 Composites: Molecular Simulation and Experimental Analyses

Polymer-based nanocomposites properties are greatly affected by interfacial interaction. Polyacrylate nanocomposites have been widely studied, but few studies have been conducted on their interface mechanism. Therefore, there was an urgent demand for providing a thorough understanding of the polymethyl acrylate/SiO₂ (PMA/SiO₂) nanocomposites to obtain the desired macro-performance. In this paper, a methodology, which combined molecular dynamics simulation with experimental researches, was established to expound the effect of the surface structure of SiO₂ particles which were treated with KH550, KH560 or KH570 (KH550-SiO₂, KH560-SiO₂ and KH570-SiO₂) on the mechanical characteristic and water vapor permeability of polymethyl acrylate/SiO₂ nanocomposites. The polymethyl acrylate/SiO₂ nanocomposites were analyzed in binding energy and mean square displacement. The results indicate that PMA/KH570-SiO₂ had the highest tensile strength, while PMA/KH550-SiO₂ had the highest elongation at break at the same filler content; KH550-SiO₂ spheres can significantly improve water vapor permeability of polyacrylate film.

Heterogeneous dynamics of unentangled chains in polymer nanocomposites

We present a systematic investigation on the effect of adding nanoparticles on the dynamics of polymer chains by using coarse-grained molecular dynamics simulation. The dynamics is characterized by three aspects: molecular motion, relaxation at different length scales, and dynamical heterogeneity. It is found that the motion of polymer chains slows down and the deviation from Gaussian distribution becomes more pronounced with increasing nanoparticle volume fractions. For polymer nanocomposites with R ≤ R_g, the relaxation at the wave vector q = 7.0 displays multistep decay, consistent with the previous reports in strongly interacting polymer nanocomposites. Moreover, a qualitatively universal law is established that dynamic heterogeneity at whole chain's scale follows a nonmonotonic increase with increasing nanoparticle loadings, where the volume fraction of the maximum dynamic heterogeneity corresponds to the particle loading when the average distance between nanoparticles is equal to the Kuhn length of polymer chains. We show that the decoupling between whole chain's dynamics and segment dynamics is responsible for the nonmonotonic behavior of dynamic heterogeneity of whole chains.

Universal localization transition accompanying glass formation: insights from efficient molecular dynamics simulations of diverse supercooled liquids

The origin of the precipitous dynamic arrest known as the glass transition is a grand open question of soft condensed matter physics. It has long been suspected that this transition is driven by an onset of particle localization and associated emergence of a glassy modulus. However, progress towards an accepted understanding of glass formation has been impeded by an inability to obtain data sufficient in chemical diversity, relaxation timescales, and spatial and temporal resolution to validate or falsify proposed theories for its physics. Here we first describe a strategy enabling facile high-throughput simulation of glass-forming liquids to nearly unprecedented relaxation times. We then perform simulations of 51 glass-forming liquids, spanning polymers, small organic molecules, inorganics, and metallic glass-formers, with longest relaxation times exceeding one microsecond. Results identify a universal particle-localization transition accompanying glass formation across all classes of glass-forming liquid. The onset temperature of non-Arrhenius dynamics is found to serve as a normalizing condition leading to a master collapse of localization data. This transition exhibits a non-universal relationship with dynamic arrest, suggesting that the nonuniversality of supercooled liquid dynamics enters via the dependence of relaxation times on local cage scale. These results suggest that a universal particle-localization transition may underpin the glass transition, and they emphasize the potential for recent theoretical developments connecting relaxation to localization and emergent elasticity to finally explain the origin of this phenomenon. More broadly, the capacity for high-throughput prediction of glass formation behavior may open the door to computational inverse design of glass-forming materials.

Dynamics of the lignin glass transition

Despite lignin being a heterogenous polyphenolic, its glass transition obeys well-established polymer theory concepts.

Surface Mechanical and Rheological Behaviors of Biocompatible Poly((D,L-lactic acid-ran-glycolic acid)-block-ethylene glycol) (PLGA-PEG) and Poly((D,L-lactic acid-ran-glycolic acid-ran-ε-caprolactone)-block-ethylene glycol) (PLGACL-PEG) Block Copolymers at the Air-Water Interface

Air-water interfacial monolayers of poly((D,L-lactic acid-ran-glycolic acid)-block-ethylene glycol) (PLGA-PEG) exhibit an exponential increase in surface pressure under high monolayer compression. In order to understand the molecular origin of this behavior, a combined experimental and theoretical investigation (including surface pressure-area isotherm, X-ray reflectivity (XR) and interfacial rheological measurements, and a self-consistent field (SCF) theoretical analysis) was performed on air-water monolayers formed by a PLGA-PEG diblock copolymer and also by a nonglassy analogue of this diblock copolymer, poly((D,L-lactic acid-ran-glycolic acid-ran-caprolactone)-block-ethylene glycol) (PLGACL-PEG). The combined results of this study show that the two mechanisms, i.e., the glass transition of the collapsed PLGA film and the lateral repulsion of the PEG brush chains that occur simultaneously under lateral compression of the monolayer, are both responsible for the observed PLGA-PEG isotherm behavior. Upon cessation of compression, the high surface pressure of the PLGA-PEG monolayer typically relaxes over time with a stretched exponential decay, suggesting that in this diblock copolymer situation, the hydrophobic domain formed by the PLGA blocks undergoes glass transition in the high lateral compression state, analogously to the PLGA homopolymer monolayer. In the high PEG grafting density regime, the contribution of the PEG brush chains to the high monolayer surface pressure is significantly lower than what is predicted by the SCF model because of the many-body attraction among PEG segments (referred to in the literature as the "n-cluster" effects). The end-grafted PEG chains were found to be protein resistant even under the influence of the "n-cluster" effects.

Parametrization and Validation of Intramolecular Force Fields Derived from DFT Calculations

The energy and its first and second geometrical derivatives obtained by DFT calculations for a number of conformations of a single molecule are used to parametrize intramolecular force fields, suitable for computer simulations. A systematic procedure is proposed to adequately treat either fully atomistic or more simplified force fields, as within the united atom approach or other coarse grained models. The proposed method is tested and validated by performing molecular dynamics simulations on several different molecules, comparing the results with literature force fields and relevant experimental data. Particular emphasis is given to the united atom approach for flexible molecules characterized by "soft" torsional potentials which are known to retain a high degree of chemical specificity.

Dynamics of a rigid rod in a disordered medium with long-range spatial correlation

We investigate the diffusion of a rigid rodlike object in a two-dimensional disordered host medium, which consists of static pointlike sources of force. The points are distributed with long-range spatial correlation and interact with the rod via a repulsive potential. The time dependence of the rod's center-of-mass mean-squared displacement and its rotational mean-squared displacement are obtained for various degrees of long-range spatial correlation and rod's lengths. These transport characteristics are compared to those obtained in previous studies for the case of homogeneous distribution of force points. It is shown that existence of long-range correlation among force points makes the center of mass diffusion anomalous.

Structural, dynamic and photophysical properties of a fluorescent dye incorporated in an amorphous hydrophobic polymer bundle

The properties of a low molecular weight organic dye, namely 4-naphthyloxy-1-methoxy-2,2,6,6-tetramethylpiperidine, covalently bound to an apolar polyolefin were investigated by means of a multi-level approach, combining classical molecular dynamics simulations, based on purposely parameterized force fields, and quantum mechanical calculations based on density functional theory (DFT) and its time-dependent extension (TD-DFT). The structure and dynamics of the dye in its embedding medium were analyzed and discussed taking the entangling effect of the surrounding polymer into account, and also by comparing the results to those obtained for a different environment, i.e. toluene solution. Finally, the influence was investigated of long lived cages found in the polymeric embedding on photophysical properties, in terms of the slow and fast dye's internal dynamics, by comparing computed IR and UV spectra with their experimental counterparts.

Effect of acrylonitrile content on compatibility and damping properties of hindered phenol AO-60/nitrile-butadiene rubber composites: molecular dynamics simulation

By combining molecular dynamics simulations with experiment, the effect of acrylonitrile content on the compatibility and damping properties were investigated in the AO-60/nitrile-butadiene rubber composites.

Applicability of mode-coupling theory to polyisobutylene: a molecular dynamics simulation study

The applicability of Mode Coupling Theory (MCT) to the glass-forming polymer polyisobutylene (PIB) has been explored by using fully atomistic molecular dynamics simulations. MCT predictions for the so-called asymptotic regime have been successfully tested on the dynamic structure factor and the self-correlation function of PIB main-chain carbons calculated from the simulated cell. The factorization theorem and the time-temperature superposition principle are satisfied. A consistent fitting procedure of the simulation data to the MCT asymptotic power-laws predicted for the α-relaxation regime has delivered the dynamic exponents of the theory-in particular, the exponent parameter λ-the critical non-ergodicity parameters, and the critical temperature T(c). The obtained values of λ and T(c) agree, within the uncertainties involved in both studies, with those deduced from depolarized light scattering experiments [A. Kisliuk et al., J. Polym. Sci. Part B: Polym. Phys. 38, 2785 (2000)]. Both, λ and T(c)/T(g) values found for PIB are unusually large with respect to those commonly obtained in low molecular weight systems. Moreover, the high T(c)/T(g) value is compatible with a certain correlation of this parameter with the fragility in Angell's classification. Conversely, the value of λ is close to that reported for real polymers, simulated "realistic" polymers and simple polymer models with intramolecular barriers. In the framework of the MCT, such finding should be the signature of two different mechanisms for the glass-transition in real polymers: intermolecular packing and intramolecular barriers combined with chain connectivity.

The non-Gaussian dynamics of glycerol

We have combined incoherent quasielastic neutron scattering experiments and atomistic molecular simulations to investigate the microscopic dynamics of glycerol moving away from the hydrodynamic limit. We relate changes in the momentum transfer (Q) dependence of the relaxation time to distinct changes of the single-particle dynamics. Going from small to large values of Q, a first crossover at about 0.5 Å(-1) is related to the coupling of the translational diffusion dynamics to the non-Debye structural relaxation, while the second crossover at a Q-value near the main diffraction peak is associated with the Gaussian to non-Gaussian crossover of the short-time molecular dynamics, related to the decaging processes. We offer an unprecedented extension of previous studies on polymeric systems towards the case of the typical low-molecular-weight glass-forming system glycerol.

Quasielastic neutron scattering study of hydrogen motions in an aqueous poly(vinyl methyl ether) solution

We present a quasielastic neutron scattering (QENS) investigation of the component dynamics in an aqueous Poly(vinyl methyl ether) (PVME) solution (30% water content in weight). In the glassy state, an important shift in the Boson peak of PVME is found upon hydration. At higher temperatures, the diffusive-like motions of the components take place with very different characteristic times, revealing a strong dynamic asymmetry that increases with decreasing T. For both components, we observe stretching of the scattering functions with respect to those in the bulk and non-Gaussian behavior in the whole momentum transfer range investigated. To explain these observations we invoke a distribution of mobilities for both components, probably originated from structural heterogeneities. The diffusive-like motion of PVME in solution takes place faster and apparently in a more continuous way than in bulk. We find that the T-dependence of the characteristic relaxation time of water changes at T ≲ 225 K, near the temperature where a crossover from a low temperature Arrhenius to a high temperature cooperative behavior has been observed by broadband dielectric spectroscopy (BDS) [S. Cerveny, J. Colmenero and A. Alegría, Macromolecules, 38, 7056 (2005)]. This observation might be a signature of the onset of confined dynamics of water due to the freezing of the PVME dynamics, that has been selectively followed by these QENS experiments. On the other hand, revisiting the BDS results on this system we could identify an additional "fast" process that can be attributed to water motions coupled with PVME local relaxations that could strongly affect the QENS results. Both kinds of interpretations, confinement effects due to the increasing dynamic asymmetry and influence of localized motions, could provide alternative scenarios to the invoked "strong-to-fragile" transition.

Relaxation properties in a diffusive model of k-mers with constrained movements on a triangular lattice

We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are k-mers that can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean-square displacement, the self-part of the van Hove correlation function, and the self-intermediate scattering function. We observe a considerable slowing of diffusion on a long-time scale when suppressing the rotational motion of k-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self-intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale τ(q(n)) is found to decrease with the wave vector q(n) according to a simple power law. Furthermore, the slowing of the dynamics with density ρ(0) is consistent with the scaling law 1/τ(q(n);ρ(0))∝(ρ(c)-ρ(0))(ϰ), with the same exponent ϰ=3.34±0.12 for all wave vectors q(n). The density ρ(c) is approximately equal to the closest packing limit, θ(CPL)≲1, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient D(s) scales with the same power-law exponent and critical density.

Dynamical heterogeneity in a highly supercooled liquid: consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length ξ(4), intensity χ(4), and lifetime τ(hetero). We evaluated all three quantities consistently from a single order parameter. In a previous study [H. Mizuno and R. Yamamoto, Phys. Rev. E 82, 030501(R) (2010)], we examined the lifetime τ(hetero)(t) in two time intervals t = τ(α) and τ(ngp), where τ(α) is the α-relaxation time and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime τ(hetero)(t), we evaluated the correlation length ξ(4)(t) and the intensity χ({4)(t) from the same order parameter used for the lifetime τ(hetero)(t). We found that as the temperature decreases, the lifetime τ(hetero)(t) grows dramatically, whereas the correlation length ξ(4)(t) and the intensity χ(4)(t) increase slowly compared to τ(hetero)(t) or plateaus. Furthermore, we investigated the lifetime τ(hetero)(t) in more detail. We examined the time-interval dependence of the lifetime τ(hetero)(t) and found that as the time interval t increases, τ(hetero)(t) monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which τ(hetero)(t) plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.

The free volume of poly(vinyl methylether) as computed in a wide temperature range and at length scales up to the nanoregion

In the present work, we focus on the free volume evaluations from different points of view, including the aspect of probe sizes, temperature, and cavity threshold. The free volume structure is analyzed on structures of poly(vinyl methylether) prepared by fully atomistic molecular dynamics. At first, the temperature behavior of an overall free volume and a free volume separated into individual cavities is shown. The origin of large free volume cavities is explained. A complex view on the cavity number is provided, while a complicated behavior previously observed is now explained. The number of large cavities remained almost constant with the temperature. Oppositely, the number of small cavities related to the atomic packing changes with temperature in a distinct way for glassy and supercooled regions. The cavity number maxima determine a percolation threshold according to percolation theory. The change in polymer properties with temperature can be related to a percolation of the free volume according to the free volume theory, when proper probe radii ∼0.8 Å are used for its observation. A construction of probabilistic distribution of free volume sizes is suggested. The free volume distributions reported here are bimodal. The bimodal character is explained by two different packings--atomic and segmental--forming a prepeak and a main peak on the distribution. Further attention is dedicated to comparisons of the computed free volume sizes and the ortho-positronium (o-Ps) lifetimes. The prepeak of the free volume distribution is probably unseen by o-Ps because of a cavity threshold limit. The effect of the shape factor on the computed o-Ps lifetimes is tested. The quasicavities obtained by redistributing the free volume maintain the ratio of the main dimensions with temperature. Finally, novel data on the cavity environment are provided, while it is suggested how these can be useful with the recent developments in the positron annihilation methods. The coordination number of large cavities with the polymer segments is around 1, as predicted in the free volume theory. Similarly to the percolation and the cavity number, the coordination number exhibits a change when explored by a suitable probe radius ∼0.8 Å. The insightful visualizations showed properties of interest investigated within the actual work.

Characterization of the "simple-liquid" state in a polymeric system: coherent and incoherent scattering functions

By means of time-of-flight neutron scattering, we have characterized the dynamic structure factor and the hydrogen motions of polyethylene above its melting point. As signatures of simple-liquid dynamics, we observe that (i) in the explored dynamic window, the intermediate scattering functions display a single-step decay, without reminiscence of cage effects, and (ii) the structural relaxation as observed at the intermolecular structure factor peak shows a weak temperature dependence, indicating a low degree of interchain cooperativity. However, stretched functional forms are observed for all length scales and temperatures investigated. An apparent direct crossover from the microscopic regime to Rouse-like dynamics suggests an essential role of connectivity in the observed stretching. Finally, while at momentum-transfer values above the structure factor peak the relation between coherent and incoherent characteristic times is reasonably described by the de Gennes narrowing, at larger length scales it is not reproduced by any existing approach.

Cooperative dynamics in homopolymer melts: a comparison of theoretical predictions with neutron spin echo experiments

We present a comparison between theoretical predictions of the generalized Langevin equation for cooperative dynamics (CDGLE) and neutron spin echo data of dynamic structure factors for polyethylene melts. Experiments cover an extended range of length and time scales, providing a compelling test for the theoretical approach. Samples investigated include chains with increasing molecular weights undergoing dynamics across the unentangled to entangled transition. Measured center-of-mass (com) mean-square displacements display a crossover from subdiffusive to diffusive dynamics. The generalized Langevin equation for cooperative dynamics relates this anomalous diffusion to the presence of the interpolymer potential, which correlates the dynamics of a group of slowly diffusing molecules in a dynamically heterogeneous liquid. Theoretical predictions of the subdiffusive behavior, of its crossover to free diffusion, and of the number of macromolecules undergoing cooperative motion are in quantitative agreement with experiments.