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

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

Disentangling Self-Atomic Motions in Polyisobutylene by Molecular Dynamics Simulations

We present fully atomistic molecular dynamics simulations on polyisobutylene (PIB) in a wide temperature range above the glass transition. The cell is validated by direct comparison of magnitudes computed from the simulation and measured by neutron scattering on protonated samples reported in previous works. Once the reliability of the simulation is assured, we exploit the information in the atomic trajectories to characterize the dynamics of the different kinds of atoms in PIB. All of them, including main-chain carbons, show a crossover from Gaussian to non-Gaussian behavior in the intermediate scattering function that can be described in terms of the anomalous jump diffusion model. The full characterization of the methyl-group hydrogen motions requires accounting for rotational motions. We show that the usually assumed statistically independence of rotational and segmental motions fails in this case. We apply the rotational rate distribution model to correlation functions calculated for the relative positions of methyl-group hydrogens with respect to the carbon atom at which they are linked. The contributions to the vibrational density of states are also discussed. We conclude that methyl-group rotations are coupled with the main-chain dynamics. Finally, we revise in the light of the simulations the hypothesis and conclusions made in previously reported neutron scattering investigations on protonated samples trying to address the origin of the dielectric β-process.

Glassy dynamics of a binary Voronoi fluid: a mode-coupling analysis

The binary Voronoi mixture is a fluid model whose interactions are derived from the Voronoi-Laguerre tessellation of the configurations of the system. The resulting interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the structural relaxation of this mixture in the supercooled-liquid regime. From the simulations we determine the time- and temperature-dependent coherent and incoherent scattering functions for a large range of wave vectors, as well as the mean-square displacements of both particle species. We perform a detailed analysis of the dynamics by comparing the MD results with the first-principles-based idealized mode-coupling theory (MCT). To this end, we employ two approaches: fits to the asymptotic predictions of the theory, and fit-parameter-free binary MCT calculations based on static-structure-factor input from the simulations. We find that many-body interactions of the Voronoi mixture do not lead to strong qualitative differences relative to similar analyses carried out for simple liquids with pair-wise interactions. For instance, the fits give an exponent parameter λ ≈ 0.746 comparable to typical values found for simple liquids, the wavevector dependence of the Kohlrausch relaxation time is in good qualitative agreement with literature results for polydisperse hard spheres, and the MCT calculations based on static input overestimate the critical temperature, albeit only by a factor of about 1.2. This overestimation appears to be weak relative to other well-studied supercooled-liquid models such as the binary Kob-Andersen Lennard-Jones mixture. Overall, the agreement between MCT and simulation suggests that it is possible to predict several microscopic dynamic properties with qualitative, and in some cases near-quantitative, accuracy based solely on static two-point structural correlations, even though the system itself is inherently governed by many-body interactions.

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.

Continuous-time random-walk approach to supercooled liquids: Self-part of the van Hove function and related quantities

From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature [Formula: see text] of mode-coupling theory: the mean-square displacement g₀(t), the non-Gaussian parameter [Formula: see text] and the self-part of the van Hove function [Formula: see text] which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near [Formula: see text]. In the time window of the early [Formula: see text] relaxation [Formula: see text] is large and [Formula: see text] is broad, reflecting the coexistence of monomer displacements that are much smaller ("slow particles") and much larger ("fast particles") than the average at time t, i.e. than [Formula: see text]. For large r the tail of [Formula: see text] is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of [Formula: see text] at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early [Formula: see text] regime we also analyze the MD results for [Formula: see text] via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below [Formula: see text] , deviations occur for larger r comprising the tail of [Formula: see text]. The CTRW analysis suggests that single-particle "hops" are a contributing factor for these deviations.

Are polymers standard glass-forming systems? The role of intramolecular barriers on the glass-transition phenomena of glass-forming polymers

Traditionally, polymer melts have been considered archetypal glass-formers. This has been mainly due to the fact that these systems can easily be obtained as glasses by cooling from the melt, even at low cooling rates. However, the macromolecules, i.e. the structural units of polymer systems in general, are rather different from the standard molecules. They are long objects ('chains') made by repetition of a given chemical motif (monomer) and have intra-macromolecular barriers that limit their flexibility. The influence of these properties on, for instance, the glass-transition temperature of polymers, is a topic that has been widely studied by the polymer community almost from the early times of polymer science. However, in the framework of the glass-community, the relevant influence of intra-macromolecular barriers and chain connectivity on glass-transition phenomena of polymers has started to be recognized only recently. The aim of this review is to give an overview and to critically revise the results reported on this topic over the last years. From these results, it seems to be evident that there are two different mechanisms involved in the dynamic arrest in glass-forming polymers: (i) the intermolecular packing effects, which dominate the dynamic arrest of low molecular weight glass-forming systems; and (ii) the effect of intra-macromolecular barriers combined with chain connectivity. It has also been shown that the mode coupling theory (MCT) is a suitable theoretical framework to discuss these questions. The values found for polymers for the central MCT parameter--the so-called λ-exponent--are of the order of 0.9, clearly higher than the standard values (λ ≈ 0.7) found in systems where the dynamic arrest is mainly driven by packing effects ('standard' glass-formers). Within the MCT, this is a signature of the presence of two competing mechanisms of dynamic arrest, as it has been observed in short-ranged attractive colloids or two component mixtures with dynamic asymmetry. Moreover, recent MD-simulations of a 'bead-spring' polymer model, but including intra-macromolecular potential of different strengths, confirm that the high λ-values found in polymers are due to the effect of intra-macromolecular barriers. Although there are still open questions, these results allow to conclude that there is a fundamental difference between the nature of the glass transition in polymers and in simple (standard) glass-formers.

Simulated glass-forming polymer melts: dynamic scattering functions, chain length effects, and mode-coupling theory analysis

We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c (∞) . This increase can be described by T c (∞) - T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c (-1/4), where ρ c is the monomer density at T c. In addition, we also estimate T c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.