Johari-Goldstein Β-relaxation Research Articles

Unifying the temperature dependent dynamics of glass formers.

Strong changes in bulk properties, such as modulus and viscosity, are observed near the glass transition temperature, Tg, of amorphous materials. For more than a century, intense efforts have been made to define a microscopic origin for these macroscopic changes in properties. Using transition state theory (TST), we delve into the atomic/molecular level picture of how microscopic localized unit relaxations, or "cage rattles," evolve to macroscopic structural relaxations above Tg. Unit motion is broken down into two populations: (1) simultaneous rearrangement occurs among a critical number of units, nα, which ranges from 1 to 4, allowing a systematic classification of glass formers, GFs, that is compared to fragility; and (2) near Tg, adjacent units provide additional free volume for rearrangement, not simultaneously, but within the "primitive" lifetime, τ1, of one unit rattling in its cage. Relaxation maps illustrate how Johari-Goldstein β-relaxations stem from the rattle of nα units. We analyzed a wide variety of glassy materials and materials with a glassy response using literature data. Our four-parameter equation fits "strong" and "weak" GFs over the entire range of temperatures and also extends to other glassy systems, such as ion-transporting polymers and ferroelectric relaxors. The role of activation entropy in boosting preexponential factors to high "unphysical" apparent frequencies is discussed. Enthalpy-entropy compensation is clearly illustrated using the TST approach.

Characterization of the secondary relaxations in glass-forming liquids. The contribution of the Starkweather line and of the Coupling Model to the rationalization of TSDC results

This work addresses the study by thermostimulated depolarization currents (TSDC) of Johari-Goldstein (JG) β-relaxations in glass forming systems. Here we analyze the differences between the β-relaxation and the fast secondary (γ, δ, ε, …) relaxations on the one hand, and the α-relaxation on the other.It is shown that TSDC is able to characterize JG although this mobility is often close to, or even partially overlapped with, the α-relaxation.It is also shown that the Starkweather line or zero entropy line (ZEL) can be used as a reference element to identify the secondary relaxations: non-compliance with the ZEL is an indicator of cooperativity.We finally showed that the non-cooperativeness of the Johari-Goldstein relaxation is highlighted by the joint consideration of the Coupling Model and the Starkweather line.

Reconsidering the relation of the JG β-relaxation to the α-relaxation and surface diffusion in ethylcyclohexane

According to the Coupling Model (CM), secondary relaxation belonging to a special class has strong connection to the α-relaxation. These Johari-Goldstein (JG) β-relaxations are predicted to be ubiquitous, and its relaxation time is approximately equal to the primitive relaxation time and the surface diffusion time. These predictions cannot be tested directly in ethylcyclohexane (ECH) because the JG β-relaxation is unresolved and overlapping the α-relaxation to modify its dispersion. To capture the actual dispersion of the α-relaxation we considered surface diffusion data, adiabatic calorimetry data of the JG β-relaxation, and dielectric data of cyanocyclohexane (CNCH). We demonstrated the dispersion of the α-relaxation is actually narrower than known before. The primitive relaxation times calculated are now in agreement with τ JG ( T ) and with τ surface ( T ), and in accord with the CM predictions.

Microscopic understanding of the Johari-Goldstein β relaxation gained from nuclear γ-resonance time-domain-interferometry experiments.

Traditionally the study of dynamics of glass-forming materials has been focused on the structural α relaxation. However, in recent years experimental evidence has revealed that a secondary β relaxation belonging to a special class, called the Johari-Goldstein (JG) β relaxation, has properties strongly linked to the primary α relaxation. By invoking the principle of causality, the relation implies the JG β relaxation is fundamental and indispensable for generating the α relaxation, and the properties of the latter are inherited from the former. The JG β relaxation is observed together with the α relaxation mostly by dielectric spectroscopy. The macroscopic nature of the data allows the use of arbitrary or unproven procedures to analyze the data. Thus the results characterizing the JG β relaxation and the relation of its relaxation time τ_{β} to the α-relaxation time τ_{α} obtained can be equivocal and controversial. Coming to the rescue is the nuclear resonance time-domain-interferometry (TDI) technique covering a wide time range (10^{-9}-10^{-5}s) and a scattering vector q range (9.6-40nm^{-1}). TDI experiments have been carried out on four glass formers, ortho-terphenyl [M. Saito etal., Phys. Rev. Lett. 109, 115705 (2012)10.1103/PhysRevLett.109.115705], polybutadiene [T. Kanaya etal., J. Chem. Phys. 140, 144906 (2014)10.1063/1.4869541], 5-methyl-2-hexanol [F. Caporaletti etal., Sci. Rep. 9, 14319 (2019)10.1038/s41598-019-50824-7], and 1-propanol [F. Caporaletti etal., Nat. Commun. 12, 1867 (2021)10.1038/s41467-021-22154-8]. In this paper the TDI data are reexamined in conjunction with dielectric and neutron scattering data. The results show the JG β relaxation observed by dielectric spectroscopy is heterogeneous and comprises processes with different length scales. A process with a longer length scale has a longer relaxation time. TDI data also prove the primitive relaxation time τ_{0} of the coupling model falls within the distribution of the TDI q-dependent JG β-relaxation times. This important finding explains why the experimental dielectric JG β-relaxation times τ_{β}(T,P) is approximately equal to τ_{0}(T,P) as found in many glass formers at various temperature T and pressure P. The result, τ_{β}(T,P)≈τ_{0}(T,P), in turn explains why the ratio τ_{α}(T,P)/τ_{β}(T,P) is invariant to changes of T and pressure P at constant τ_{α}(T,P), the α-relaxation time.

Tuning the Johari-Goldstein β-Relaxation and Its Separation from α-Relaxation of Poly(n-alkyl methacrylate)s by Small Molecule-bridged Hydrogen Bonds

Introducing small molecule-bridged hydrogen bonds (HBs) between polymer chains has been reported to effectively reduce the inter-chain cooperativity despite of strengthening the intermolecular interaction. Here, a systematic investigation on tuning the Johari–Goldstein β (βJG) relaxation by adding various low-molecular-weight phenols in poly(n-alkyl methacrylate)s is carried out to further clarify the anomalous dynamics. Given these small molecules capable of coupling the motion with pendent groups of host polymers due to forming at least two HBs per molecule, poly(n-alkyl methacrylate) mixtures exhibit rich dynamic changes in the βJG-properties and α, βJG separations. An increased loading of phenols with a small size and strong inter-HB strength (Δυi) clearly benefits for significant retardation and suppression of the βJG-relaxation, narrows the α, βJG separation and converges the βJG-peak with the α-peak, which demonstrates the alleviation of inter-chain topological constraints. However, small molecules with a relatively big size and weak Δυi are found to amplify the magnitude of the α, βJG separation of poly(butyl methacrylate), even though experimental results of changes in α-dispersion and dynamic fragility confirm a reduction of the coupling factor n in all of these hybrids. The counterintuitive phenomenon suggests that the crossover time tc in the Coupling Model is no longer a universal quantity if the inter-chain of polymers is strengthened by HBs. These compelling findings shed vital insights into the HB-induced anomalous dynamics, and provide essential guidance for tailoring the βJG behavior and designing glassy polymeric materials.

Polarity Matters: Dielectric Relaxation in All-cis-Multifluorinated Cycloalkanes.

The polarity of all-cis-multifluorinated cyclohexanes can be fine-tuned by the number and relative orientation of fluoro substituents, giving rise to a series of compounds with strong dipole moments. Simulations provided the energetics, the dipole moments, and the respective molecular polarizabilities, while dielectric spectroscopy gave information on the dielectric permittivities and the molecular dynamics. In special cases, dipole moments in excess of 6 D and dielectric permittivities of over 300 were obtained by simulation and experiment. Melting temperatures within a given family of multifluorinated cyclohexanes were found to scale with the molecular volume. The less-symmetric all-cis-octafluorotetrahydronaphthalene did not readily crystallize, permitting an investigation of the molecular dynamics in an energetically unfavorable yet rigid and facially polarized isomer. The resulting dynamics above the glass temperature conform to the structural α-relaxation and to the celebrated Johari-Goldstein β-relaxation.

Fast dynamics in a model metallic glass-forming material.

We investigate the fast β- and Johari-Goldstein (JG) β-relaxation processes, along with the elastic scattering response of glass-forming (GF) liquids and the boson peak, in a simulated Al-Sm GF material exhibiting a fragile-strong (FS) transition. These dynamical processes are universal in "ordinary" GF fluids and collectively describe their "fast dynamics," and we find these relaxation processes also arise in a GF liquid exhibiting a FS transition. String-like particle motion, having both an irreversible and a reversible nature (stringlets) component, occurs in the fast-dynamics regime, corresponding to a ps timescale. String-like collective motion associated with localized unstable modes facilitates irreversible and intermittent particle "jumping" events at long times associated with the JG β-relaxation process, while stringlets associated with localized stable modes and corresponding perfectly reversible atomic motion give rise to the boson peak. To further clarify the origin of the boson peak, we calculate the density of states for both the stringlet particles and the "normal" particles and find that the stringlet particles give rise to a boson peak, while the normal atoms do not. The growth of stringlets upon heating ultimately also leads to the "softening" of these excitations, and the boson peak frequency and shear modulus drop in concert with this softening. The growth of string-like collective motion upon heating in the fast-dynamics regime is further shown to be responsible for the growth in the intensity of the fast relaxation process. Relaxation in cooled liquids clearly involves a hierarchy of relaxation processes acting on rather different timescales and spatial scales.

Molecular dynamics in the supercooled liquid and glassy states of bezafibrate and binary mixture of fenofibrate

Two solubility limited pharmaceuticals bezafibrate and fenofibrate, belonging to BCS class II drugs, were compared, by investigating molecular dynamics of the former and compared with the neat and as a probe in an apolar host polystyrene of mole. wt. 800 (PS800) of the latter by broadband dielectric spectroscopy (BDS), other supporting thermal and spectroscopic experimental means and density functional theory (DFT) calculations. The BDS experiments from frozen glassy state to vibrant molten state of the title drugs were done to explore the role of parameters describing their complex molecular dynamics and the stabiliy of amorphous phase, such as glass transition temperature (Tg), temperature dependence of α-relaxation times (τα), width of structural dispersion and its role on the occurrence of Johari-Goldstein (JG) β-relaxation, fragility index (m) and apparent activation energy of secondary processes. Realizing that most of the pharmaceuticals have narrow α-dispersion which limits the visibility of JG β-relaxation as a separate process in the dielectric window, to resolve the conundrum, we have further explored the amorphous dynamics of fenofibrate as a probein an apolar host polystyrene of molecular weight 800 (PS800) having higher Tg than the polar probe. The Tg of bezafibrate and PS800-fenofibrate mixture were determined to be 298 K and 275 K respectively, whereas the fractional exponent of Kohlrausch–Williams–Watts function βKWW of bezafibrate was determined to be 0.68 which is closer to that of fenofibrate, whereas that of PS800-fenofibrate mixture was found to be much broader with a value of 0.39, all in the vicinity of Tg. Even though βKWW decreased in binary mixture of fenofibrate when compared to its pure form due to concentration fluctuations and other aspects, but cold crystallization tendency was absent and Tg is elevated than that of fenofibrate. Due to higher Tg than that of fenofibrate, amorphous bezafibrate is more stable than fenofibrate. Finally, using quantum computational calculations using DFT, the relevant flexible parts of the two drug molecules, whose motions manifests the secondary γ-relaxation was identified by calculating potential energy barriers and dipole moments on relaxed dihedral angle scans, as no experimental technique is available for this purpose.

Clarifying the nature of the Johari-Goldstein β-relaxation and emphasising its fundamental importance

ABSTRACT Since 1998 the primitive relaxation time τ 0(T,P) of the Coupling Model (CM) and the Johari-Goldstein (JG) β-relaxation time τJG (T,P) are shown approximately equal in many glass-formers. The CM relation between τ 0(T,P) and τα (T,P) at any T and P is exact. Additionally from the CM relation τα (T,P)/τ 0(T,P) is exactly invariant to variations of T and P while τα (T,P) is kept constant, and τ 0 is exactly a function of ρ γ/T like τα . However, since τJG (T,P) ≈ τ 0(T,P), the exact invariance of τα (T,P)/τ 0(T,P) leads to approximate invariance of τα (T,P)/τJG (T,P), and τJG is approximately a function of ρ γ/T. Notwithstanding, the CM prediction of the approximate relations between τβ and τα were mistaken as exact relations by some researchers. In this paper, we remove this misunderstanding by demonstrating via simulations and experiments that the JG β-relaxation is comprised of processes with different length-scales and degrees of cooperativity, and the process is heterogeneous. The distribution of processes makes τJG (T,P) equivocal, because it is just a single relaxation time used to represent the different processes within the distribution, which may change on varying T and P, at constant τα (T,P). The problem is compounded if the β-relaxation is not resolved, and fitting procedure used to extract τJG (T,P) and τα (T,P). Despite the relations of τJG (T,P) to τα (T,P) are approximate, we show these properties of τJG (T,P) are truly remarkable, fundamental, general, and important.

Breakdown of the isochronal structural (α) and secondary (JG β) exact superpositioning in probucol - A low molecular weight pharmaceutical

In this paper, Broadband Dielectric Spectroscopy (BDS) has been applied to study the molecular dynamics of the two active pharmaceutical ingredients (APIs), probucol (PRO) and droperidol (DRO), above and below the glass transition temperature, at varying thermodynamic conditions. We found that the structural (α)-relaxation process in both compounds is sensitive to compression. It was reflected in the high pressure coefficients of the glass transition temperature, dTg/dp = 227 K/GPa and dTg/dp = 427 K/GPa for DRO and PRO, respectively. In this context, it is worthwhile to emphasize that dTg/dp calculated for the latter API is the highest reported to date for the low molecular weight glass formers. Furthermore, the data collected upon squeezing samples revealed that the pressure dependence of the relaxation times of the Johari Goldstein (JG) β-process in PRO is weaker with respect to that of structural relaxation. Thus, a breakdown of exact superposition of both modes has been noted. A slightly different scenario was observed in DRO, where relaxation times of the secondary non-JG γ-process, obtained at different T and p, plotted versus Tg/T, collapsed forming a single curve. A breakdown of exact isochronal superpositioning of α- and JG β-relaxation times at varying thermodynamic conditions in PRO, that is weakly H-bonded low molecular weight glass former, is in accordance with the data reported for the strongly associating compounds (e.g., sorbitol). Moreover, recently a similar scenario has been observed for some polymers, i.e., 1,4-polybutadiene (PBD) (Ransom et al., 2018), poly(methyl methacrylate) (PMMA) (Casalini and Roland, 2013) and polyisoprene (PI) (Kołodziej et al., 2018). This phenomenon, which is consistent with the approximate invariance of the ratio of these two relaxation times to change of thermodynamics conditions (as predicted by the Coupling Model), was assigned to the increasing torsional rigidity of the macromolecule backbone or alternatively to the non-uniform responses to variations of temperature and pressure of the distributed modes composing the JG β-process, resulting in changes of the spectral shape and different fβ(p,T) obtained from the fitting procedure. One can suppose that due to the variation in the population of weak H-bonds at elevated pressure in PRO, the latter effect might be enhanced, contributing to the observed experimental finding. Finally, the data reported herein emphasize the impact of molecular aspects related to specific interactions on the correlation between α- and JG β-relaxation at varying T and p conditions.

Glassy Dynamics and Translational-Rotational Coupling of an Ionically Conducting Pharmaceutical Salt-Sodium Ibuprofen.

In this work, we study the structural dipolar relaxation and ionic conductivity relaxation in an ionized derived from a nonionized glass former. The latter is the salt form of a well-studied active pharmaceutical ingredient, sodium ibuprofen, and the former is ibuprofen. Quantum mechanical calculations were employed to study the variation in its molecular electrostatic potentials, and its spatial extent on its salt formation with Na+ ions. Measurements have been made using differential scanning calorimetry and broadband dielectric spectroscopy, and the characterization is assisted by density functional theory. The dielectric data contain information on both ionic and dipolar molecular mobility of NaIb and were extracted by representation in terms of the electric modulus and permittivity. A secondary β-conductivity relaxation coexists with the primary α-conductivity relaxation. By use of the coupling model, we show that the β-conductivity relaxation is connected to the α-conductivity relaxation and is the analogue of the relation of the Johari-Goldstein β-relaxation to the structural α-relaxation, shown valid also in ibuprofen. This remarkable result has an impact on the fundamental understanding of the dynamics of ionic conductivity. By representing the data as permittivity, a dipolar β-relaxation was found to have practically the same relaxation times as the β-conductivity relaxation in the glassy state and translational-rotational coupling is valid at a more local secondary relaxation level. However, the α-conductivity relaxation decouples from structural α-relaxation because the structural glass transition temperature is lower than the conductivity counterpart by 29 K. These are novel findings. The study elucidates the effects on the dynamics by the change in the nature of bonding and in size on introducing sodium ions to ibuprofen in the glassy and supercooled liquid states.

The JG β-relaxation in water and impact on the dynamics of aqueous mixtures and hydrated biomolecules.

Although by now the glass transition temperature of uncrystallized bulk water is generally accepted to manifest at temperature Tg near 136 K, not much known are the spectral dispersion of the structural α-relaxation and the temperature dependence of its relaxation time τα,bulk(T). Whether bulk water has the supposedly ubiquitous Johari-Goldstein (JG) β-relaxation is a question that has not been answered. By studying the structural α-relaxation over a wide range of temperatures in several aqueous mixtures without crystallization and with glass transition temperatures Tg close to 136 K, we deduce the properties of the α-relaxation and the temperature dependence of τα,bulk(T) of bulk water. The frequency dispersion of the α-relaxation is narrow, indicating that it is weakly cooperative. A single Vogel-Fulcher-Tammann (VFT) temperature dependence can describe the data of τα,bulk(T) at low temperatures as well as at high temperatures from neutron scattering and GHz-THz dielectric relaxation, and hence, there is no fragile to strong transition. The Tg-scaled VFT temperature dependence of τα,bulk(T) has a small fragility index m less than 44, indicating that water is a "strong" glass-former. The existence of the JG β-relaxation in bulk water is supported by its equivalent relaxation observed in water confined in spaces with lengths of nanometer scale and having Arrhenius T-dependence of its relaxation times τconf(T). The equivalence is justified by the drastic reduction of cooperativity of the α-relaxation in nanoconfinement and rendering it to become the JG β-relaxation. Thus, the τconf(T) from experiments can be taken as τβ,bulk(T), the JG β-relaxation time of bulk water. The ratio τα,bulk(Tg)/τβ,bulk(Tg) is smaller than most glass-formers, and it corresponds to the Kohlrausch α-correlation function, exp[-(t/τα,bulk)1-n], having (1-n) = 0.90. The dielectric data of many aqueous mixtures and hydrated biomolecules with Tg higher than that of water show the presence of a secondary ν-relaxation from the water component. The ν-relaxation is strongly connected to the α-relaxation in properties, and hence, it belongs to the special class of secondary relaxations in glass-forming systems. Typically, its relaxation time τν(T) is longer than τβ,bulk(T), but τν(T) becomes about the same as τβ,bulk(T) at sufficiently high water content. However, τν(T) does not become shorter than τβ,bulk(T). Thus, τβ,bulk(T) is the lower bound of τν(T) for all aqueous mixtures and hydrated biomolecules. Moreover, it is τβ,bulk(T) but not τα(T) that is responsible for the dynamic transition of hydrated globular proteins.

Study of Increasing Pressure and Nanopore Confinement Effect on the Segmental, Chain, and Secondary Dynamics of Poly(methylphenylsiloxane)

The effect of increasing pressure and two-dimensional (2D) confinement on the dynamics of glass-forming polymer poly(methylphenylsiloxane) (PMPS) was investigated with the use of dielectric spectroscopy. We demonstrate that the glass-forming polymer confined to nanoporous alumina might obey the density scaling relation similar to that in the bulk and that the same value of the scaling exponent is used to superimpose the α-relaxation time measured under different thermodynamic conditions. Our comprehensive analysis of the relaxation processes detected in the dielectric loss spectra of PMPS allows us to identify the Johari–Goldstein β-relaxation which for a bulk polymer shows up as a well-resolved peak while under 2D nanoconfinement only as an excess wing. In contrast to previous studies, we provide dielectric evidence of an additional α′-relaxation, slower than the segmental (α-) dynamics, which is related to the chain dynamics of PMPS.

Uncovering a novel transition in the dynamics of proteins in the dry state

The research of dynamics of protein is predominantly focused on the hydrated or solvated state, which is close to the physiological condition of biological relevance. Eclipsed by the hydrated and solvated counterparts, the dynamics of dry proteins are seldom studied in earnest. Studied occasionally, the data of dry proteins were not addressed, possibly due to the preconceived notion that dry proteins are bio inactive, and thus are uninteresting and unimportant. Actually lyophilized dry proteins are important for the pharmaceutical industry as the therapeutic proteins are often stored in lyophilized conditions to achieve long-term stability, which is of direct connection to the dynamics of protein in dry state. In order to uncover the intrinsic dynamics of dry proteins that previous studies overlooked or ignored, we analysed quasielastic neutron scattering, Mössbauer, and Brillouin light scattering data of various dry proteins. We demonstrate the existence of a novel transition of the dry protein dynamics at temperatures around 200 K, with the exact value dependent on the kind of protein. The transition temperature of dry proteins is found here independent of the time/frequency of the measurement, in stark contrast to the well-documented dynamical transition observed in hydrated proteins, the temperature of which is strongly depending on the time window probed experimentally. In addition we point out that this transition in dry proteins is analogous to those observed before in the glassy state of various glass-forming materials, the origin of which is the change of the caged molecule dynamics in response to the change of the temperature dependence of density when crossing the secondary glass transition temperature Tgβ for the Johari-Goldstein β-relaxation. We show that the transition of various dry proteins also occurs around Tgβ, thus suggesting that the underlying microscopic mechanism is the same as the one identified and explained before for many glass-formers of different types. The presence of the transition is independent of the trace amount of water in supposedly dry proteins, although the value of Tgβ can vary somewhat. The novel transition in dry proteins has impact on bio-pharmaceutical research and applications because of the connection to the Johari-Goldstein β-relaxation, which can affect long-term stability of lyophilized dry proteins.

Relations between the Structural α-Relaxation and the Johari-Goldstein β-Relaxation in Two Monohydroxyl Alcohols: 1-Propanol and 5-Methyl-2-hexanol.

The hydrogen-bonded monohydroxyl alcohols form a large class of glass formers studied more than one hundred years, and still the structure and dynamics have continued to be a research problem. Recent advance suggests a hydrogen-bonded transient supramolecular structure, which is the origin of the Debye relaxation dominating the dielectric loss spectra of many monohydroxyl alcohols. Obscured by the slower Debye relaxation, the structural α-relaxation is either not resolved or showing up as a shoulder and the supposedly universal Johari-Goldstein (JG) β-relaxation is not always observed. Thus, properties of the α-relaxation and the JG β-relaxation as well as the strong connection between the two relaxations generally observed in other classes of glass formers are not commonly known in the monohydroxyl alcohols. Notwithstanding, extremely broadband dielectric relaxation and high-precision light scattering experiments published recently have resolved the α-relaxation and a secondary relaxation in two archetypal monohydroxyl alcohols, 1-propanol and 5-methyl-2-hexanol (5M2H) by Gabriel et al. We analyzed their experimental data and applied the Coupling Model to show that the secondary relaxations in 1-propanol and 5M2H are JG β-relaxations with strong connection to the α-relaxation. The result is novel because it is not known before whether the secondary relaxations of these two monohydroxyl alcohols are JG β-relaxation involving the entire molecule or are intramolecular relaxations. On the basis of this conclusion, we predict that the secondary relaxation is pressure-dependent and the ratio τβ( T, P)/τα( T, P) is invariant to variations of P and T, whereas τα( T, P) is maintained constant and provided that the frequency dispersion of the α-relaxation is also constant. The prediction is compared with the dielectric data of 5M2H at elevated pressures. On the basis of the identification of monohydroxyl alcohols as short-chain polymeric liquids by others, an explanation of the stronger T and P dependences of τα( T, P) than the Debye relaxation time τD( T, P) is given.

Contrasting two different interpretations of the dynamics in binary glass forming mixtures.

In a series of papers on binary glass-forming mixtures of tripropyl phosphate (TPP) with polystyrene (PS), Kahlau et al. [J. Chem. Phys. 140, 044509 (2014)] and Bock et al. [J. Chem. Phys. 139, 064508 (2013); J. Chem. Phys. 140, 094505 (2014); and J. Non-Cryst. Solids 407, 88-97 (2015)] presented the data on the dynamics of the two components studied over the entire composition range by several experimental methods. From these sets of data, obtained by multiple experimental techniques on mixtures with a large difference ΔTg ≈ 200 K between the glass transition temperatures of two starting glass formers, they obtained two α-relaxations, α1 and α2. The temperature dependence of the slower α1 is Vogel-Fulcher like, but the faster α2 is Arrhenius. We have re-examined their data and show that their α2-relaxation is the Johari-Goldstein (JG) β-relaxation with Arrhenius T-dependence admixed with a true α2-relaxation having a stronger temperature dependence. In support of our interpretation of their data, we made dielectric measurements at elevated pressures P to show that the ratio of the α1 and α2 relaxation times, τα1(T,P)/τα2(T,P), is invariant to variations of T and P, while τα1(T,P) is kept constant. This property proves unequivocally that the α2-relaxation is the JG β-relaxation, the precursor of the α1-relaxation. Subsequently, the true but unresolved α2-relaxation is recovered, and its relaxation times with much stronger temperature dependence are deduced, as expected for the α-relaxation of the TPP component. The results are fully compatible with those found in another binary mixture of methyltetrahydrofuran with tristyrene and PS with ΔTg ≈ 283 K, even larger than ΔTg ≈ 200 K of the mixture of TPP with PS, and in several polymer blends. The contrast between the two very different interpretations brought out in this paper is deemed beneficial for further progress in this research area.

Why is the change of the Johari-Goldstein β-relaxation time by densification in ultrastable glass minor?

Ultrastable glasses (USG) formed by vapor deposition are considerably denser. The onset temperature of devitrification, Ton, is significantly higher than Ton or Tg of ordinary glass (OG) formed by cooling, which implies an increase of the structural α-relaxation time by many orders of magnitude in USG compared to that in OG at the same temperature. However, for a special type of secondary relaxation having properties strongly connected to those of the α-relaxation, called the Johari-Goldstein β-relaxation, its relaxation time in USG is about an order of magnitude slower than that in OG and it has nearly the same activation energy, Eβ. The much smaller change in τβ and practically no change in Eβ by densification in USG are in stark contrast to the behavior of the α-relaxation. This cannot be explained by asserting that the Johari-Goldstein (JG) β-relaxation is insensitive to densification in USG, since the JG β-relaxation strength is significantly reduced in USG to such a level that it would require several thousands of years of aging for an OG to reach the same state, and therefore the JG β-relaxation does respond to densification in USG like the α-relaxation. Here, we provide an explanation based on two general properties established from the studies of glasses and liquids at elevated pressures and applied to USG. The increase in density of the glasses formed under high pressure can be even larger than that in USG. One property is the approximate invariance of the ratio τα(Ton)/τβ(Ton) to density change at constant τα(Ton), and the other is the same ργ/T-dependence of τβ in USG and OG where ρ is the density and γ is a material constant. These two properties are derived using the Coupling Model, giving a theoretical explanation of the phenomena. The explanation is also relevant for a full understanding of the experimental result that approximately the same surface diffusion coefficient is found in USG and OG with and without physical aging, and ultrathin films of a molecular glass-former.

Quasielastic neutron scattering evidence of coupling of caged molecule dynamics to JG β-relaxation

In several publications we studied the fast caged dynamics of many glass-formers observed in the glassy state at high frequencies above circa 1GHz by various techniques, including neutron scattering, Brillouin scattering, 2H NMR spin-lattice relaxation, and THz dielectric spectroscopy. On increasing temperature, the intensity of the caged dynamics exhibit two step increases in intensity at two temperatures, first at THF below the glass transition temperature Tgα and subsequently at Tgα. THF is nearly coincident with the Johari-Goldstein (JG) β-glass transition temperature Tgβ. The phenomenon is general and found in polyalcohols, pharmaceuticals, many amorphous polymers, and two small molecular van der Waals glass-formers. It is remarkable since THF is determined from measurements of fast caged dynamics at short time scales typically in the ns to ps range, while Tgβ characterizes the JG β-glass transition at which the JG β-relaxation time τβ reaches a long time ~103s. The phenomenon was explained by coupling of the caged dynamics to the JG β-relaxation. In this paper we analyze exceptionally high quality quasielastic neutron scattering data of two molecular van der Waals glass-formers, cumene (isopropylbenzene) and cis-decalin (cis-decahydro-naphthalene) to demonstrate the generality of the phenomenon and validity of its theoretical explanation.

Effect of the strain rate on the intermediate temperature brittleness in Zr-based bulk metallic glasses

In this work, the effect of strain rate on the ductility, intermediate temperature brittleness and fracture surface of Zr-based BMG over a wide range of temperatures from 0.1 Tg to near Tg, has been systematically investigated. The results showed two remarkable ductile to brittle transition at low cryogenic and intermediate temperatures. At low temperatures, below 0.4 Tg, the activation of diffusion mediated phenomena is negligible and the combined effects of strain rate and temperature contribute to the plasticity of material by changing the STZ volume, hence the possibility of forming multiple shear bands. At the temperature range from 0.4 Tg to the temperature at which the intermediate brittleness happens, the activation of fewer STZs takes place during inelastic shuffling of caged atoms by nearly constant loss (NCL). At higher temperatures, with the onset of Johari-Goldstein β-relaxation, which is accompanied by the NCL caged dynamics termination, more atoms can leave the cages and cooperate together, thus facilitate the activation of STZs. Furthermore, increase of strain rate shifts the intermediate temperatures brittleness to higher temperatures. Moreover, an intriguing correlation between the shear offset and the width of stable crack region with ductility is reported by studying the fracture surface topography.

Relating Ultrastable Glass Formation to Enhanced Surface Diffusion via the Johari-Goldstein β-Relaxation in Molecular Glasses.

Glasses are materials essential for modern technology; they are usually prepared by cooling liquids. Recently, novel ultrastable glasses (SGs) with extraordinary thermodynamic and kinetic stability have been created by vapor deposition at appropriate substrate temperatures. However, the underlying mechanism for the formation of SGs is still not established. For most of the molecular SGs created so far, we demonstrate that the formation of SGs is closely related to the Johari-Goldstein β-relaxation from the fact that the lowest substrate temperatures possible for the formation of SGs match the secondary glass-transition temperatures, where the β-relaxation time reaches 103 s. Theoretically the β-relaxation time via the primitive relaxation time of the coupling model has proven capable of accounting for the enhancement of molecular mobility at the surface. Thus our findings provide evidence to support that the immense enhancement of molecular diffusion at the surface is critical for the formation of SGs. The result has implications in the design and fabrication of SGs.