Molecular dynamics simulation study of the alpha- and beta-relaxation processes in a realistic model polymer

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.

Role of torsional potential in chain conformation, thermodynamics, and glass formation of simulated polybutadiene melts

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis-trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature T_g. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ_T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature (T) dependence of ρ and κ_T. We also find that our data obey the linear relation between 1/k_BTρκ_T and 1/T (with the Boltzmann constant k_B) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine T_g from the density-temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ(T) is vanishingly small in the equilibrium liquid, the effect of the torsions on T_g is large. We find that T_g decreases by about 150 K when going from the CRC to the FRC model.

Mutual Information in Molecular and Macromolecular Systems

The relaxation properties of viscous liquids close to their glass transition (GT) have been widely characterised by the statistical tool of time correlation functions. However, the strong influence of ubiquitous non-linearities calls for new, alternative tools of analysis. In this respect, information theory-based observables and, more specifically, mutual information (MI) are gaining increasing interest. Here, we report on novel, deeper insight provided by MI-based analysis of molecular dynamics simulations of molecular and macromolecular glass-formers on two distinct aspects of transport and relaxation close to GT, namely dynamical heterogeneity (DH) and secondary Johari–Goldstein (JG) relaxation processes. In a model molecular liquid with significant DH, MI reveals two populations of particles organised in clusters having either filamentous or compact globular structures that exhibit different mobility and relaxation properties. In a model polymer melt, MI provides clearer evidence of JG secondary relaxation and sharper insight into its DH. It is found that both DH and MI between the orientation and the displacement of the bonds reach (local) maxima at the time scales of the primary and JG secondary relaxation. This suggests that, in (macro)molecular systems, the mechanistic explanation of both DH and relaxation must involve rotation/translation coupling.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein β -relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG)β -relaxation process in a model metallic glass-forming (GF) material (Al 90 Sm 10 ), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JGβ -relaxation timeτ J G and the lifetime of the mobile particle clustersτ M , defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between theα -relaxation timeτ α and the lifetime of immobile particle clustersτ I M . Moreover, we find that the average diffusion coefficient D nearly coincides withD A l of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides withτ J G to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JGβ -relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JGβ -relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find thatAl 90 Sm 10 exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

Coincident Correlation between Vibrational Dynamics and Primary Relaxation of Polymers with Strong or Weak Johari-Goldstein Relaxation

The correlation between the vibrational dynamics, as sensed by the Debye-Waller factor, and the primary relaxation in the presence of secondary Johari-Goldstein (JG) relaxation, has been investigated through molecular dynamics simulations. Two melts of polymer chains with different bond length, resulting in rather different strength of the JG relaxation are studied. We focus on the bond-orientation correlation function, exhibiting higher JG sensitivity with respect to alternatives provided by torsional autocorrelation function and intermediate scattering function. We find that, even if changing the bond length alters both the strength and the relaxation time of the JG relaxation, it leaves unaffected the correlation between the vibrational dynamics and the primary relaxation. The finding is in harmony with previous studies reporting that numerical models not showing secondary relaxations exhibit striking agreement with experimental data of polymers also where the presence of JG relaxation is known.

Relaxation processes and glass transition of confined polymer melts: A molecular dynamics simulation of 1,4-polybutadiene between graphite walls

Molecular dynamics simulations of a chemically realistic model for 1,4-polybutadiene in a thin film geometry confined by two graphite walls are presented. Previous work on melts in the bulk has shown that the model faithfully reproduces static and dynamic properties of the real material over a wide temperature range. The present work studies how these properties change due to nano-confinement. The focus is on orientational correlations observable in nuclear magnetic resonance experiments and on the local intermediate incoherent neutron scattering function, F_s(q_z, z, t), for distances z from the graphite walls in the range of a few nanometers. Temperatures from about 2T_g down to about 1.15T_g, where T_g is the glass transition temperature in the bulk, are studied. It is shown that weakly attractive forces between the wall atoms and the monomers suffice to effectively bind a polymer coil that is near the wall. For a wide regime of temperatures, the Arrhenius-like adsorption/desorption kinetics of the monomers is the slowest process, while very close to T_g the Vogel-Fulcher-Tammann-like α-relaxation takes over. The α-process is modified only for z≤1.2 nm due to the density changes near the walls, less than expected from studies of coarse-grained (bead-spring-type) models. The weakness of the surface effects on the glass transition in this case is attributed to the interplay of density changes near the wall with the torsional potential. A brief discussion of pertinent experiments is given.

Effects of atomic interaction stiffness on low-temperature relaxation of amorphous solids

While low-temperature relaxations show significant differences among metallic glasses with different compositions, the underlying mechanism remains mysterious. Using molecular dynamics simulation, low-temperature relaxation of amorphous solids is investigated in model systems with different atomic interaction stiffness. It was found that as the interaction stiffness increases, the low-temperature relaxation is enhanced. The fraction of mobile atoms increases with increasing interaction stiffness, while the length scale of dynamical heterogeneity does not change. The enhanced relaxation may be due to increased dynamical heterogeneity. These findings provide a physical picture for better understanding the origin of low-temperature relaxation dynamics in amorphous solids, and the experimentally observed different β-relaxation behaviors in various metallic glasses.

Dielectric α-relaxation of 1,4-polybutadiene confined between graphite walls : Molecular dynamics investigations through numerical simulations of polymer molecules relaxation

We present results of Molecular Dynamics (MD) simulations of a chemically realistic model of 1,4-polybutadiene confined by crystalline graphite walls. The simulations cover a large range of temperatures from T ≈ 2T g to T ≈ 1.15T g, where relevant time scales are accessible using such computational methods. We investigate the dielectric relaxation close to the walls in comparison to the one in the center of the film, and study the latter as a function of the film thickness from the walls. The segmental dynamics in the film is slowed down close to the walls, in comparison to the bulk. In addition to the α-process, the relaxation exhibits an additional long time decay, the so-called wall desorption process. We focus here on the α-process and find no significant shift of the dielectric T g as a function of layer thickness, in agreement with recent dielectric experiments. These findings can be correlated with the importance of the dihedral dynamics for all relaxation processes in polymers, which is unaltered except for the first nanometer next to the walls.

Rotational dynamics of simple asymmetric molecules

Molecular dynamic simulations were carried out on rigid diatomic molecules, which exhibit both α (structural) and β (secondary) dynamics. The relaxation scenarios range from onset behavior, in which a distinct α process emerges on cooling, to merging behavior, associated with two relaxation peaks that converge at higher temperature. These properties, as well as the manifestation of the β peak as an excess wing, depend not only on thermodynamic conditions, but also on both the symmetry of the molecule and the correlation function (odd or even) used to analyze its dynamics. These observations help to reconcile divergent results obtained from different experiments. For example, the β process is more intense and the α-relaxation peak is narrower in dielectric relaxation spectra than in dynamic light scattering or NMR measurements. In the simulations herein, this follows from the weaker contribution of the secondary relaxation to even-order correlation functions, related to the magnitude of the relevant angular jumps.

Characteristics of the Johari-Goldstein process in rigid asymmetric molecules

Molecular dynamics simulations were carried out on a Lennard-Jones binary mixture of rigid (fixed bond length) diatomic molecules. The translational and rotational correlation functions, and the corresponding susceptibilities, exhibit two relaxation processes: the slow structural relaxation (α dynamics) and a higher frequency secondary relaxation. The latter is a Johari-Goldstein (JG) process, by its definition of involving all parts of the molecule. It shows several properties characteristic of the JG relaxation: (1) merging with the α relaxation at high temperature; (2) a change in temperature dependence of its relaxation strength on vitrification; (3) a separation in frequency from the α peak that correlates with the breadth of the α dispersion; and (4) sensitivity to volume, pressure, and physical aging. These properties can be used to determine whether a secondary relaxation in a real material is an authentic JG process, rather than more trivial motion involving intramolecular degrees of freedom. The latter has no connection to the glass transition, whereas the JG relaxation is closely related to structural relaxation, and thus can provide new insights into the phenomenon.

Molecular dynamics simulation of the Johari-Goldstein relaxation in a molecular liquid

Molecular dynamics simulations were carried out to investigate the reorientational motion of a rigid (fixed bond length), asymmetric diatomic molecule in the liquid and glassy states. In the latter the molecule reorients via large-angle jumps, which we identify with the Johari-Goldstein (JG) dynamics. This relaxation process has a broad distribution of relaxation times, and at least deeply in the glassy state, the mobility of a given molecule remains fixed over time; that is, there is no dynamic exchange among molecules. Interestingly, the JG relaxation time for a molecule does not depend on the local density, although the nonergodicity factor is weakly correlated with the packing efficiency of neighboring molecules. In the liquid state the intensity of the JG process increases significantly, eventually subsuming the slower α relaxation. This evolution of the JG motion into structural relaxation underlies the correlation of many properties of the JG and α dynamics.

Why are coarse-grained force fields too fast? A look at dynamics of four coarse-grained polymers

Coarse-grained models decrease the number of force sites and thus reduce computational requirements for molecular simulation. While these models are successful in describing structural properties, dynamic evolution is faster than the corresponding atomistic simulations or experiments. We consider coarse-grained models for four polymers and one polymer mixture, where accurate dynamics are obtained by scaling to match the mean-squared displacements of the corresponding atomistic descriptions. We show that the required scaling is dictated by local friction and that this scaling is only valid after the onset of continuous motion.

Glass transition in 1,4-polybutadiene: Mode-coupling theory analysis of molecular dynamics simulations using a chemically realistic model

We present molecular dynamics simulations of the glass transition in a chemically realistic model of 1,4-polybutadiene (PBD). Around 40 K above the calorimetric glass transition of this polymer the simulations reveal a well-developed two-stage relaxation of all correlation functions. We have analyzed the time-scale separation between vibrational degrees of freedom (subpicosecond dynamics) and the alpha relaxation behavior (nanosecond to microsecond dynamics) using the predictions of mode-coupling theory (MCT). Our value for the mode-coupling critical temperature Tc agrees perfectly with prior experimental estimates for PBD. The predictions of MCT for the scaling behavior of the so-called beta relaxation, the plateau regime separating vibrational dynamics and the alpha relaxation, are well fulfilled. Furthermore, we are able to derive a consistent set of MCT exponents, completely characterizing the scaling behavior of relaxation processes in the vicinity of Tc. For the temperature dependence of the alpha relaxation we find deviations from MCT predictions which we trace to the influence of torsional barriers on the atomic motions.