Relaxation Time Τα Research Articles

Charge transport in highly acidic glass-forming protic ionic liquids tailored by zwitterionic precursors.

Highly acidic protic ionic liquids (PILs) are promising materials for potential electrochemical applications due to their high proton conductivity and excellent thermal stability. Still, little is known about the correlation between charge transport and structural dynamics as well as the proton transport mechanism despite the large body of literature on this topic. Here, we have examined the charge transport and structural dynamics by employing broadband dielectric spectroscopy in two highly acidic PILs in their supercooled liquid and glassy states, which included the same anion [TfO]- and different cations, [Tau]+ vs [Ahs]+. Unlike many other ionic liquids, the conductivity relaxation time τe of two studied PILs is substantially faster than the structural relaxation time τα. The decoupling behavior between charge transport and structural dynamics of two materials, which is manifested by a decoupling index Rτ, varies between 0.3 and 2.3 over the temperature range above Tg. Moreover, "Walden" plots of the molar conductivity vs the viscosity qualify both compounds as "Super ILs." All findings support the physical picture of large, polar, and orientationally correlated ion clusters, where the slow α-relaxation can be identified as structural relaxation associated with cooperative reorientations of the cluster macrodipole. In contrast, the shortest timescale for diffusive charge transport, τe, is 1-2 decades shorter than τα, implying that proton hopping is triggered by "single particle" (ions or ion pair) rotations and jumps on a sub-length scale of the cluster size, a dynamics being present even in the glassy state as indicated by a strong β-relaxation. These results demonstrate the practicality of employing highly acidic PILs in electrochemical fields.

Real-Time Determination of the Glass Transition Temperature during Reversible Network Formation Based on Furan–Maleimide Diels–Alder Cycloadditions Using Dielectric Spectroscopy

The molecular dynamics of the reversible network 4F230-2M230 were studied systematically by dielectric relaxation spectroscopy (DRS) at frequencies between 10–1 and 107 Hz under both isothermal and non-isothermal conditions, focusing on the cooperative segmental dynamics as sensed by the dielectric α-relaxation. This reversible network is based on the furan–maleimide Diels–Alder reaction of a 4-functional furan-functionalized Jeffamine coupled with a 2-functional maleimide. Different strategies for extracting a “dielectric” glass transition temperature (Tg) were employed and compared. First, relaxation times τα were derived by conventional Havriliak–Negami fits of dielectric spectra and then fitted to the Vogel–Fulcher–Tammann (VFT) equation, which yields the dynamic Tg of partially cured samples (approach I). Alternatively, the thermal glass transition temperature was derived from the dielectric spectra ε′(f, T) using a fine structure analysis by bivariate differential sampling. Both the dynamic and thermal Tgs revealed an excellent agreement, confirming the stability of the VFT fits as well as the equivalence of both quantities as usually expected for bulk glass-forming materials. Two attempts were made to find a unique set of VFT parameters based on a global fit considering DRS spectra from partially cured samples during heating from −120 to 100 °C. Via a first procedure (approach II), a unique set of VFT parameters EV and τ∞ was obtained that well describes the relaxation times during non-isothermal cure at temperatures where the effects of ongoing cure kinetics can be neglected. To overcome this restriction, a refined approach III was developed that includes the earlier reported kinetic model for the DA reaction and allows accurate predictions for the relaxation time evolution during both isothermal and non-isothermal cure experiments. Based on this unique description, a new technique for continuous cure monitoring was proposed and tested. This technique allows us to compute in real-time dynamic Tg from the relaxation time τα at any stage of the isothermal or non-isothermal cure process using two unique VFT parameters from the global fit procedure. This approach might stimulate new applications of DRS-based cure monitoring.

Molecular Dynamics Investigation of the Pressure Dependence of Glass Formation in a Charged Polymer Melt

Most commodity polymers are derived from petroleum raw materials, and correspondingly, these materials are normally uncharged and nonpolar, attributes that make this class of material relatively insoluble in water and relatively slow to breakdown in the environment. Natural and synthetic charged polymer materials often do not exhibit these drawbacks, thereby offering the potential for being more sustainable. As with all polymer materials, properties related to glass formation play a central role in the design and characterization of materials. Here, we investigate the influence of a crucial processing variable, the pressure P, on the glass formation of a coarse-grained charged polymer melt using molecular dynamics simulation. We find that the temperature (T) dependence of the thermodynamics and segmental dynamics under variable P conditions largely resemble the trends observed before for uncharged polymer liquids. In particular, we are able to organize all our segmental relaxation data as functions of both T and P in terms of the conventional phenomenology for uncharged polymer melts, namely, the Vogel–Fulcher–Tammannn temperature dependence of the structural relaxation time τα and a pressure analog of this equation, etc. Moreover, we can quantitatively describe all our simulation data for both charged and uncharged polymer melts with the string model of glass formation. Importantly, our results indicate that the main effect of charge on the dynamics of polymeric glass-forming liquids is to “renormalize” the cohesive interaction strength. This opens the possibility of applying theories of neutral polymer melts to describe the glass formation of synthetic and natural charged polymer melts, ionic fluids, and possibly even polar polymer melts, once an accounting is made for how charge modifies the effective cohesive interaction strength.

Breakdown of isochronal superpositioning of [formula omitted]- and [formula omitted]-relaxation times in the van der Waals system – Loratadine

In this paper, high-pressure (HP) dielectric studies on the van der Waals active pharmaceutical ingredient (API) - loratadine (LOR) were carried out. It was found that, surprisingly, the secondary (β) relaxation, which, according to the Coupling Model (CM) predictions, was classified as a Johari-Goldstein (JG) process, separates from the structural (α)-mode with compression (although the shape of the α-peak is invariant to the thermodynamic conditions at constant τα). Consequently, there is a breakdown of the isochronal superpositioning of α- and β- relaxation times (τα and τβ) in this system, which is a typical behavior for the secondary process with intermolecular character. Based on these findings, two possibilities concerning the origin of the β-relaxation in LOR have been proposed: 1) it is a non-JG process (probably originating from fluctuations within cyclic rings of the API molecule), which, however, satisfies the CM predictions; or 2) it is a JG-process, which similarly to a few earlier examined H-bonded compounds (e.g., probucol and sorbitol) is characterized by a different sensitivity to compression when compared to the α-process. Moreover, it was found that the activation entropy for the β-process takes negative values, irrespective of the pressure conditions. That may be interpreted as a result of conformational variation or the loss of translational and rotational degrees of freedom, leading to increased order in API due to densification. The results presented herein give a new insight into the relationship between the structural and secondary relaxations in the close vicinity of the glass transition temperature. Furthermore, they show that HP studies are crucial in elucidating the correlation between these processes.

Microscopic Dynamics in the Strain Hardening Regime of Glassy Polymers

We study by dielectric spectroscopy the molecular dynamics of relaxation processes during plastic flow of glassy polymers up to the strain hardening regime for three different protocols of deformation. The measured dielectric spectra cover 4 decades in frequencies and allow us to measure the evolution as a function of the applied strain of the dominant relaxation time τα and of the width wτ of the distribution of relaxation times. The first protocol is performed at constant strain rate λ̇. We confirm that for increasing strain both τα and wτ first decrease, reaching a minimum in the stress softening regime before increasing in the strain hardening regime. In the second protocol we stop the deformation at some point λw in the strain hardening regime, and we let the sample age for a waiting time tw, during which the applied stress remains high. Upon resuming the deformation at constant λ̇, stress–strain displays a yield stress and a stress softening regime comparable in magnitude to that of the reference protocol before rejoining the reference curve. In contrast, the dielectric spectrum measured during the second protocol recovers the one measured during the reference curve much later than strain–stress. In the third protocol the stress is canceled during tw. In this case, after recovering the constant λ̇ the dielectric spectrum and the stress–strain curve rejoin almost immediately the reference curve. We interpret these different behaviors as the consequence of changes in the free energy barriers for α-relaxation induced by the stress applied to the sample. These changes are the sum of two contributions: (a) The first one, which allows for plastic flow, is due to the applied stress σ and, according to a recently published theory, scales as −σ2. (b) The second contribution κ(λ), which is a function of the chain orientation at the monomer level, is positive and is responsible for the stress hardening regime. The first one evolves immediately upon varying the stress, whereas the second relaxes very slowly upon cessation of the applied stress. Our interpretation for the results of the third protocol is that aging dynamics is frozen when the stress is removed, as it is known for polycarbonate at room temperature. Our experiments set precise conditions for a theory of strain hardening.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets.

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (Tg). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with Tg, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τα becomes almost a universal function of reduced temperature, (T - Tg)/Tg, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - Tg)/Tg. Evidently, Tg dominates both τα and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Inhibition of celecoxib crystallization by mesoporous silica – Molecular dynamics studies leading to the discovery of the stabilization origin

In this article, the effect of mesoporous silica (MS) on the physical stability and molecular dynamics of the amorphous form of Celecoxib (CEL) is investigated. It has been proven that the recrystallization process of CEL slows down with increasing the MS content. Beside the elongation of stabilization time with the increase silica content leads to an increase in the amorphous drug fraction remaining after the finished crystallization. The conducted analyses show that the observed inhibition of CEL's recrystallization is associated with the formation of a monomolecular drug layer on the silica's surface. The performed non-isothermal dielectric studies of CEL + MS systems having both fully and partially amorphous CEL shows that the biggest impact of the drug's the temperature dependences of structural relaxation time τα(T) has a crystalline fraction of the API. Silica, even in high concentration, does not modify the temperature dependence of structural relaxation of CEL.

Crystallization Propensity of Amorphous Pharmaceuticals: Kinetics and Thermodynamics.

Four model compounds, nifedipine, indomethacin, felodipine, and ketoconazole, all with nearly identical glass transition temperatures, were chosen to study the effects of thermodynamics and molecular mobility on their crystallization propensities. The time and temperature dependence of the crystallization induction time of each compound was determined by differential scanning calorimetry (DSC) and enabled the generation of their time-temperature-transformation (TTT) diagrams. The relaxation times (τα) were measured by dielectric spectroscopy, and the Gibbs free energy (ΔG) and entropy (ΔS) difference between the crystalline and amorphous states were obtained by DSC. The temperature dependence of the crystallization induction time (τ0(T)) is a function of the thermodynamic activation barrier and the frequency of "attempted jumps" (1/τα(T)) to overcome the barrier. Even though the four model compounds exhibited very similar molecular mobility (relaxation time) over a wide range of temperatures, their crystallization propensities were very different. The observed difference in crystallization propensity was explained in terms of the difference in the thermodynamic barrier, and it is correlated to the empirical relation (TΔS3)/ΔG2.

Isochronal superpositioning of the caged dynamics, the α, and the Johari-Goldstein β relaxations in metallic glasses.

The superposition of the frequency dispersions of the structural α relaxation determined at different combinations of temperature T and pressure P while maintaining its relaxation time τα(T, P) constant (i.e., isochronal superpositioning) has been well established in molecular and polymeric glass-formers. Not known is whether the frequency dispersion or time dependence of the faster processes including the caged molecule dynamics and the Johari-Goldstein (JG) β relaxation possesses the same property. Experimental investigation of this issue is hindered by the lack of an instrument that can cover all three processes. Herein, we report the results from the study of the problem utilizing molecular dynamics simulations of two different glass-forming metallic alloys. The mean square displacement 〈Δr2t〉, the non-Gaussian parameter α2t, and the self-intermediate scattering function Fsq,t at various combinations of T and P were obtained over broad time range covering the three processes. Isochronal superpositioning of 〈Δr2t〉, α2t, and Fsq,t was observed over the entire time range, verifying that the property holds not only for the α relaxation but also for the caged dynamics and the JG β relaxation. Moreover, we successfully performed density ρ scaling of the time τα2,maxT,P at the peak of α2t and the diffusion coefficient D(T, P) to show both are functions of ργ/T with the same γ. It follows that the JG β relaxation time τβ(T, P) is also a function of ργ/T since τα2,maxT,P corresponds to τβ(T, P).

Structure and Dynamics of Star Polymer Films from Coarse-Grained Molecular Simulations

We simulate the structure and dynamics of star polymer films of varying arm mass Ma and number of star arms f on a supporting solid substrate with an attractive interaction and compare to the corresponding properties of thin films of linear polymers. While the spatial variation of segmental density profile is only weakly dependent on star polymer topology, the polymer topology significantly affects both the average rate of relaxation and the spatial variation of the average segmental relaxation time τα as a function of depth from the film substrate, z. In particular, we observe a general slowing down in the rate of relaxation of the entire film with an increasing functionality f, a general trend attributed mainly to an alteration of the effective cohesive interaction strength when f is increased. The mobility gradients in the film, quantified by the relaxation time obtained from the intermediate scattering function on a layer-by-layer basis, are also significantly altered by f. In particular, the width of the substrate interfacial layer grows with increasing f, saturating in value around f = 12, while the width of the interfacial zone near the “free” boundary, where the polymer dynamics is greatly accelerated compared to the film interior, is less influenced by changes in polymer topology. These observations are qualitatively consistent with the interpretation of recent X-ray photon correlation spectroscopy on supported star polymer films.

Dehydration induced dynamical heterogeneity and ordering mechanism of lipid bilayers.

Understanding the influence of dehydration on the membrane structure is crucial to control membrane functionality related to domain formation and cell fusion under anhydrobiosis conditions. To this end, we perform all-atom molecular dynamic simulations of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dimyristoylphosphatidylcholine lipid membranes at different hydration levels at 308 K. As dehydration increases, the lipid area per head group decreases with an increase in bilayer thickness and lipid order parameters indicating bilayer ordering. Concurrently, translational and rotational dynamics of interfacial water (IW) molecules near membranes slow down. On the onset of bilayer ordering, the IW molecules exhibit prominent features of dynamical heterogeneity evident from non-Gaussian parameters and one-dimensional van Hove correlation functions. At a fully hydrated state, diffusion constants (D) of the IW follow a scaling relation, D∼τα -1, where the α relaxation time (τα) is obtained from self-intermediate scattering functions. However, upon dehydration, the relation breaks and the D of the IW follows a power law behavior as D∼τα -0.57, showing the signature of glass dynamics. τα and hydrogen bond lifetime calculated from intermittent hydrogen bond auto-correlation functions undergo a similar crossover in association with bilayer ordering on dehydration. The bilayer ordering is accompanied with an increase in fraction of caged lipids spanned over the bilayer surface and a decrease in fraction of mobile lipids due to the non-diffusive dynamics. Our analyses reveal that the microscopic mechanism of lipid ordering by dehydration is governed by dynamical heterogeneity. The fundamental understanding from this study can be applied to complex bio-membranes to trap functionally relevant gel-like domains at room temperature.

Identification of time scales of the violation of the Stokes–Einstein relation in Yukawa liquids

We investigate the origin of the violation of the Stokes–Einstein (SE) relation in two-dimensional Yukawa liquids. Using comprehensive molecular dynamics simulations, we identify the time scales supporting the violation of the SE relation D∝(η/T)−1, where D is the self-diffusion coefficient and η is the shear viscosity. We first compute the self-intermediate scattering function Fs(k,t), the non-Gaussian parameter α2, and the autocorrelation function of the shear stress Cη(t). The time scales obtained from these functions include the structural relaxation time τα, the peak time of the non-Gaussian parameter τα2, and the shear stress relaxation time τη. We find that τη is coupled with D for all temperatures indicating the SE preservation; however, τα and τα2 are decoupled with D at low temperatures indicating the SE violation. Surprisingly, we find that the origins of this violation are related to the non-exponential behavior of the autocorrelation function of the shear stress and non-Gaussian behavior of the distribution function of particle displacements. These results confirm dynamic heterogeneity that occurs in two-dimensional Yukawa liquids that reflect the presence of regions in which dust particles move faster than the rest when the liquid cools to below the phase transition temperature.

Diffusion-controlled and `diffusionless' crystal growth: relation between liquid dynamics and growth kinetics of griseofulvin

Understanding how liquid dynamics govern crystallization is critical for maintaining the physical stability of amorphous pharmaceutical formulations. In the present study, griseofulvin (GSF), a classic antifungal drug, was used as the model system to investigate the correlations between crystal growth kinetics and liquid dynamics. The temperature dependence of the kinetic part of the bulk crystal growth in a supercooled liquid of GSF was weaker than that of the structural relaxation time τα and scaled as τα −0.69. In the glassy state, GSF exhibited the glass-to-crystal (GC) growth behavior, whose growth rate was too fast to be under the control of the α-relaxation process. Moreover, from the perspective of τα, the GC growth of GSF also satisfied the general condition for GC growth to exist: D/u < 7 pm, where D is the diffusion coefficient and u the speed of crystal growth. Also compared were the fast surface crystal growth rates u s and surface relaxation times τsurface predicted by the random first-order transition theory. Here, the surface crystal growth rate u s of GSF exhibited a power-law dependence upon the surface structural relaxation time: u s ∝ τsurface −0.71, which was similar to that of the bulk growth rate and τα. These findings are important for understanding and predicting the crystallization of amorphous pharmaceutical solids both in the bulk and at the surface.

Molecular Mobility and Crystal Growth in Amorphous Binary Drug Delivery Systems: Effects of Low-Concentration Poly(Ethylene Oxide).

Polymer additives have been widely reported to affect the crystallization of amorphous drugs, while the underlying mechanism is poorly understood. The present study aims to investigate the relationship between the crystal growth and the molecular mobility of amorphous nifedipine (NIF) in the presence and absence of low-concentration poly(ethylene oxide) (PEO). The addition of 3% w/w PEO yields approximately a 5-fold increase in the crystal growth rate of NIF in the glassy matrix and a 10-fold increase in the supercooled liquid. Broadband dielectric spectroscopy is performed to investigate the molecular mobility of amorphous pure NIF system and NIF doped with low-concentration PEO. With 3% w/w PEO, the structural relaxation time τα of amorphous NIF significantly decreases, indicating an increase in the global molecular mobility. However, the increase of the molecular mobility is insufficient to explain the 5- to 10-fold increase of the crystal growth rate at the same τα scale. Moreover, we compare the accelerating effect of PEO in NIF-PEO systems to other PEO-doped systems. The accelerating effect of low-concentration PEO on the crystal growth of amorphous drugs is found to be independent of the Flory-Huggins interaction, Tg of the drug, or the increase of the global molecular mobility. These findings suggest that an in-depth understanding regarding the effects of polymer additives on the crystallization of drugs should consider the localized mobility of the host molecules near the crystal-liquid interface.

Localization model description of the interfacial dynamics of crystalline Cu and Cu64Zr36 metallic glass films.

Recent studies of structural relaxation in Cu-Zr metallic glass materials having a range of compositions and over a wide range of temperatures and in crystalline UO2 under superionic conditions have indicated that the localization model (LM) can predict the structural relaxation time τα of these materials from the intermediate scattering function without any free parameters from the particle mean square displacement ⟨r2⟩ at a caging time on the order of ps, i.e., the "Debye-Waller factor" (DWF). In the present work, we test whether this remarkable relation between the "fast" picosecond dynamics and the rate of structural relaxation τα in these model amorphous and crystalline materials can be extended to the prediction of the local interfacial dynamics of model amorphous and crystalline films. Specifically, we simulate the free-standing amorphous Cu64Zr36 and crystalline Cu films and find that the LM provides an excellent parameter-free prediction for τα of the interfacial region. We also show that the Tammann temperature, defining the initial formation of a mobile interfacial layer, can be estimated precisely for both crystalline and glass-forming solid materials from the condition that the DWFs of the interfacial region and the material interior coincide.

Enhancement of the Physical Stability of Amorphous Sildenafil in a Binary Mixture, with either a Plasticizing or Antiplasticizing Compound.

The main purpose of this paper was to evaluate the impact of both high- and low-Tg polymer additives on the physical stability of an amorphous drug, sildenafil (SIL). The molecular mobility of neat amorphous SIL was strongly affected by the polymeric excipients used (Kollidon VA64 (KVA) and poly(vinylacetate) (PVAc)). The addition of KVA slowed down the molecular dynamics of amorphous SIL (antiplasticizing effect), however, the addition of PVAc accelerated the molecular motions of the neat drug (plasticizing effect). Therefore, in order to properly assess the effect of the polymer on the physical stability of SIL, the amorphous samples at both: isothermal (at constant temperature—353 K) and isochronal (at constant relaxation time—τα = 1.5 ms) conditions were compared. Our studies showed that KVA suppressed the recrystallization of amorphous SIL more efficiently than PVAc. KVA improved the physical stability of the amorphous drug, regardless of the chosen concentration. On the other hand, in the case of PVAc, a low polymer content (i.e., 25 wt.%) destabilized amorphous SIL, when stored at 353 K. Nevertheless, at high concentrations of this excipient (i.e., 75 wt.%), its effect on the amorphous pharmaceutical seemed to be the opposite. Therefore, above a certain concentration, the PVAc presence no longer accelerates the SIL recrystallization process, but inhibits it.

Reconciling computational and experimental trends in the temperature dependence of the interfacial mobility of polymer films.

Many measurements have indicated that thin polymer films in their glass state exhibit a mobile interfacial layer that grows in thickness upon heating, while some measurements indicate the opposite trend. Moreover, simulations and limited measurements on glass-forming liquids at temperatures above the glass transition temperature Tg exhibit a growing interfacial mobility scale ξ upon cooling. To better understand these seemingly contradictory trends, we perform molecular dynamics simulations over a temperature regime for which our simulated polymer film enters a non-equilibrium glassy state and find that the relaxation time τα within the film interior, relative to the polymer-air interfacial layer, exhibits a maximum near the computational Tg. Correspondingly, we also observe that the interfacial mobility length scale exhibits a maximum near Tg, explaining the apparent reversal in the temperature dependence of this scale between the glass and liquid states. We show that the non-monotonic variation of ξ and the relative interfacial mobility to the film interior arise qualitatively from a non-monotonic variation of the gradient of the effective activation free energy of the film; we then obtain a quantitative description of this phenomenon by introducing a phenomenological model that describes the relaxation time layer-by-layer in the film for a temperature range both above and below Tg of the film as a whole. This analysis reveals that the non-monotonic trend in the relative interfacial mobility and ξ both arise primarily from the distinctive temperature dependence of relaxation in the interfacial layer, which apparently remains in local equilibrium over the whole temperature range investigated.

Predicting the α-relaxation time of glycerol confined in 1.16 nm pores of zeolitic imidazolate frameworks.

Uhl et al. [J. Chem. Phys., 2019, 150, 024504] studied the molecular dynamics of glycerol confined in a microporous zeolitic imidazolate framework (ZIF-8) with well-defined pore diameters of 1.16 nm by broadband dielectric spectroscopy. Of interest is a fast process in the central part of the pores identified as the α-relaxation of the confined supercooled glycerol with relaxation times τα,conf(T) reduced from τα,bulk(T) of bulk glycerol and having a temperature dependence different from the super-Arrhenius temperature of the latter. The focus of Uhl et al. was relating the confined molecular dynamics to the cooperativity length scales Lcorr(T) of molecular motion above the glass transition, and deducing the limiting high-temperature value of the correlation length of about 1.22 nm. Not yet considered by anyone are the observed values of τα,conf(T) and temperature dependence. Since the cooperativity length scales Lcorr(T) were found to be larger than the pore size of ZIF-8 over the temperature range studied and the density of the glycerol in the pore is possibly lower than the bulk, the cooperativity of the α-relaxation of glycerol confined in ZIF-8 is drastically reduced. Thus, within the framework of the Coupling Model (CM), τα,conf(T) should be nearly the same as the primitive relaxation time τ0(T) for glycerol when devoid of intermolecular coupling and cooperativity. Consistent with the absence of cooperativity of the glycerol confined in ZIF-8, we find the calculated τα,conf(T) are either the same or slightly longer than the calculated values of τ0(T). The quantitative prediction of the CM is verified. At this time we know of no other theory that can make such a quantitative prediction.

What does the instantaneous normal mode spectrum tell us about dynamical heterogeneity in glass-forming fluids?

We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum [unstable localized (UL) modes] and find that the particles making the dominant contribution to the participation ratio form clusters that grow upon cooling in a fashion similar to the dynamical heterogeneity in glass-forming fluids, i.e., highly mobile (or immobile) particles form clusters that grow upon cooling; however, a comparison of the UL mode clusters to the mobile and immobile particle clusters indicates that they are distinct entities. We also show that the cluster size provides an alternate method to distinguish localized and delocalized modes, offering a significant practical advantage over the finite-size scaling approach. We examine the trajectories of particles contributing most to the UL modes and find that they have a slightly enhanced mobility compared to the average, and we determine a characteristic time quantifying the persistence time of this excess mobility. This time scale is proportional to the structural relaxation time τα of the fluid, consistent with a prediction by Zwanzig [Phys. Rev. 156, 190 (1967)] for the lifetime of collective excitations in cooled liquids. Evidently, these collective excitations serve to facilitate relaxation but do not actually participate in the motion associated with barrier crossing events governing activated transport. They also serve as a possible concrete realization of the "facilitation" clusters postulated in previous modeling of glass-forming liquids.

Localization model description of diffusion and structural relaxation in superionic crystalline UO2.

We test the Localization Model (LM) prediction of a parameter-free relationship between the α-structural relaxation time τα and the oxygen ion diffusion coefficient DO with the Debye-Waller factor ⟨u2⟩ for crystalline UO2 under superionic conditions where large anharmonic interactions lead to non-Arrhenius relaxation and high ion mobility. As in a previous study of structural relaxation in Cu-Zr metallic glass materials having a range of compositions, we find that the LM relationship between the picosecond atomic dynamics ("fast" beta relaxation) and the long-time structural relaxation time and oxygen ion diffusion coefficient holds to an excellent approximation without any free parameters over the full range of temperatures and pressures investigated in our simulations.