Dynamic correlations and heterogeneity in the primary and secondary relaxations of a model molecular liquid

Role of anisotropy in understanding the molecular grounds for density scaling in dynamics of glass-forming liquids

Molecular Dynamics (MD) simulations of glass-forming liquids play a pivotal role in uncovering the molecular nature of the liquid vitrification process. In particular, much focus was given to elucidating the interplay between the character of intermolecular potential and molecular dynamics behaviour. This has been tried to achieve by simulating the spherical particles interacting via isotropic potential. However, when simulation and experimental data are analysed in the same way by using the density scaling approaches, serious inconsistency is revealed between them. Similar scaling exponent values are determined by analysing the relaxation times and pVT data obtained from computer simulations. In contrast, these values differ significantly when the same analysis is carried out in the case of experimental data. As discussed thoroughly herein, the coherence between results of simulation and experiment can be achieved if anisotropy of intermolecular interactions is introduced to MD simulations. In practice, it has been realized in two different ways: (1) by using the anisotropic potential of the Gay-Berne type or (2) by replacing the spherical particles with quasi-real polyatomic anisotropic molecules interacting through isotropic Lenard-Jones potential. In particular, the last strategy has the potential to be used to explore the relationship between molecular architecture and molecular dynamics behaviour. Finally, we hope that the results presented in this review will also encourage others to explore how 'anisotropy' affects remaining aspects related to liquid-glass transition, like heterogeneity, glass transition temperature, glass forming ability, etc.

Johari-Goldstein β relaxation in glassy dynamics originates from two-scale energy landscape

Supercooled liquids undergo complicated structural relaxation processes, which have been a long-standing problem in both experimental and theoretical aspects of condensed matter physics. In particular, past experiments widely observed for many types of molecular liquids that relaxation dynamics separated into two distinct processes at low temperatures. One of the possible interpretations is that this separation originates from the two-scale hierarchical topography of the potential energy landscape; however, it has never been verified. Molecular dynamics simulations are a promising approach to tackle this issue, but we must overcome laborious difficulties. First, we must handle a model of molecular liquids that is computationally demanding compared to simple spherical models, which have been intensively studied but show only a slower process: α relaxation. Second, we must reach a sufficiently low-temperature regime where the two processes become well-separated. Here, we handle an asymmetric dimer system that exhibits a faster process: Johari-Goldstein β relaxation. Then, we employ the parallel tempering method to access the low-temperature regime. These laborious efforts enable us to investigate the potential energy landscape in detail and unveil the first direct evidence of the topographic hierarchy that induces the β relaxation. We also successfully characterize the microscopic motions of particles during each relaxation process. Finally, we study the correlation between low-frequency modes and two relaxation processes. Our results establish a fundamental and comprehensive understanding of experimentally observed relaxation dynamics in supercooled liquids.

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.

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.

Segmental and secondary dynamics of nanoparticle-grafted oligomers

The local segmental and secondary dynamics of tetramethylene oxide oligomer grafted to silica nanoparticles (NPs) were investigated as a function of grafting density and molecular weight. Grafting slows the segmental (α) dynamics, but gives rise to faster secondary (β) motions. Interestingly, the magnitude of these effects decreases with the extent of grafting (i.e., surface coverage), as well as with oligomer molecular weight. The disparity in dynamical effects reflects the decoupling of the segmental and more local β dynamics, the former is associated with stronger dynamic correlations that extend over a greater spatial range. This results in greater sensitivity to interactions, including tethering of the chains to the NP surface.

Non-polymeric asymmetric binary glass-formers. II. Secondary relaxation studied by dielectric, 2H NMR, and 31P NMR spectroscopy

We investigate the secondary (β-) relaxations of an asymmetric binary glass former consisting of a spirobichroman derivative (SBC; T_g = 356 K) as the high-T_g component and the low-T_g component tripropyl phosphate (TPP; T_g = 134 K). The main relaxations are studied in Paper I [B. Pötzschner et al., J. Chem. Phys. 146, 164503 (2017)]. A high T_g contrast of ΔT_g = 222 K is put into effect in a non-polymeric system. Component-selective studies are carried out by combining results from dielectric spectroscopy (DS) for mass concentrations c_TPP ≥ 60% and those from different methods of ²H and ³¹P NMR spectroscopy. In the case of NMR, the full concentration range (10% ≤ c_TPP ≤ 100%) is covered. The neat components exhibit a β-relaxation (β₁ (SBC) and β₂ (TPP)). The latter is rediscovered by DS in the mixtures for all concentrations with unchanged time constants. NMR spectroscopy identifies the β-relaxations as being alike to those in neat glasses. A spatially highly restricted motion with angular displacement below ±10° encompassing all molecules is involved. In the low temperature range, where TPP shows the typical ³¹P NMR echo spectra of the β₂-process, very similar spectral features are observed for the (deuterated) SBC component by ²H NMR, in addition to its "own" β₁-process observed at high temperatures. Apparently, the small TPP molecules enslave the large SBC molecules to perform a common hindered reorientation. The temperature dependence of the spin-lattice relaxation time of both components is the same and reveals an angular displacement of the SBC molecules somewhat smaller than that of TPP, though the time constants τ_β2 are the same. Furthermore, T₁(T) of TPP in the temperature region of the β₂-process is absolutely the same as in the mixture TPP/polystyrene investigated previously. It appears that the manifestations of the β-process introduced by one component are essentially independent of the second component. Finally, at c_TPP ≤ 20% one finds indications that the β₂-process starts to disintegrate. More and more TPP molecules get immobilized upon decreasing c_TPP. We conclude that the β-process is a cooperative process.

Direct Evidence of Relaxation Anisotropy Resolved by High Pressure in a Rigid and Planar Glass Former

Rigid molecular glass-formers with no internal degrees of freedom nonetheless have a single secondary β-relaxation. For a rigid and planar molecule, 1-methylindole (1MID), although a secondary relaxation is resolved at ambient pressure, its properties do not conform to the rules established for rigid molecules reported in early studies. By applying pressure to the dielectric spectra of 1MID, we find the single secondary relaxation splits into two. The slower one is pressure sensitive showing connections to the α-relaxation as observed in other rigid molecules, while the faster one is almost pressure insensitive and dominate the loss at ambient pressure. The two secondary relaxations, identified to associate with the out-of-plane and in-plane rotations of the rigid and planar 1MID, are resolved and observed for the first time by increasing density via elevating pressure.

A test for the existence of isomorphs in glass-forming materials

We describe a method to determine whether a material has isomorphs in its thermodynamic phase diagram. Isomorphs are state points for which various properties are invariant in reduced units. Such materials are commonly identified from strong correlation between thermal fluctuations of the potential energy, U, and the virial W, but this identification is not generally applicable to real materials. We show from molecular dynamic simulations of atomic, molecular, and polymeric materials that systems with strong U-W correlation cannot be pressure densified, that is, the density obtained on cooling to the glassy state and releasing the pressure is independent of the pressure applied during cooling.

Role of structure in the α and β dynamics of a simple glass-forming liquid

The elusive connection between dynamics and local structure in supercooled liquids is an important piece of the puzzle in the unsolved problem of the glass transition. The Johari-Goldstein β relaxation, ubiquitous in glass-forming liquids, exhibits mean properties that are strongly correlated to the long-time α dynamics. However, the former comprises simpler, more localized motion, and thus has perhaps a more straightforward connection to structure. Molecular dynamics simulations were carried out on a two-dimensional, rigid diatomic molecule (the simplest structure exhibiting a distinct β process) to assess the role of the local liquid structure on both the Johari-Goldstein β and the α relaxation. Although the average properties for these two relaxations are correlated, there is no connection between the β and α properties of a given (single) molecule. The propensity for motion at long times is independent of the rate or strength of a molecule's β relaxation. The mobility of a molecule averaged over many initial energies, a measure of the influence of structure, was found to be heterogeneous, with clustering at both the β and α time scales. This heterogeneity is less extended spatially for the β than for the α dynamics, as expected; however, the local structure is the more dominant control parameter for the β process. In the glassy state, the arrangement of neighboring molecules determines entirely the relaxation properties, with no discernible effect from the particle momenta.

Correlated and cooperative motions in segmental relaxation: Influence of constitutive unit weight and intermolecular interactions

This work clarifies the notion of correlated and cooperative motions appearing during the α-relaxation process through the role of the molecular weight of the constitutive units and of the interchain dipolar interactions. By studying amorphous copolymers of poly(ethylene-co-vinyl acetate) with different vinyl acetate contents, we show that the correlated motions are not sensitive to the interchain dipolar interactions, in contrast to the cooperative motions, which increase with a strengthening of the intermolecular interactions for this sample family. Concerning the influence of the molecular weight m_{0}, the notion of "correlated motions" seems to be equivalent to the notion of "cooperative motions" only for low m_{0} systems.

Influence of hydrogen bonds and temperature on dielectric properties

Dielectric properties are evaluated by means of molecular dynamics simulations on two model systems made up of dipolar molecules. One of them mimics methanol, whereas the other differs from the former only in the ability to form hydrogen bonds. Static dielectric properties such as the permittivity and the Kirkwood factor are evaluated, and results are analyzed by considering the distribution of relative orientations between molecular dipoles. Dipole moment-time correlation functions are also evaluated. The relevance of contributions associated with autocorrelations of molecular dipoles and with cross-correlations between dipoles belonging to different molecules has been investigated. For methanol, the Debye approximation for the overall dipole moment correlation function is not valid at room temperature. The model applies when hydrogen bonds are suppressed, but it fails upon cooling the nonassociated liquid. Important differences between relaxation times associated with dipole auto- versus cross-correlations as well as their relative relevance are at the root of the Debye model breakdown.

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.