Correlation between primary and secondary Johari-Goldstein relaxations in supercooled liquids: invariance to changes in thermodynamic conditions

The primary alpha and the secondary Johari-Goldstein (JG) beta relaxations of supercooled glass-forming neat epoxy resin and 2-picoline in mixture with tristyrene are monitored by broadband dielectric relaxation spectroscopy at ambient pressure and elevated pressures. For different combinations of pressure and temperature that maintain the alpha-relaxation time constant, the frequency dispersion of the alpha relaxation is unchanged, as previously found in other glass-formers, but remarkably the JG beta-relaxation time remains constant. This is more clear evidence of a strong connection between the alpha- and JG beta-relaxation times, a fact that should be taken into account in the construction of a viable theory of glass transition.     

Relation between the alpha-relaxation and Johari-Goldstein beta-relaxation of a component in binary miscible mixtures of glass-formers

The coupling model was applied to describe the alpha-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the alpha-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x --> 0 and x --> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau(alpha)/tau(JG), the ratio of the alpha-relaxation time, tau(alpha), to the Johari-Goldstein (JG) secondary relaxation time, tau(JG), of the same component A. This prediction enables us to obtain the coupling parameter, n(A), of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n(A) of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n(A) obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n(A) with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau(alpha)/tau(JG) of component A changes with composition, x. The data of tau(alpha) and tau(JG) of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.     

Two secondary modes in decahydroisoquinoline: which one is the true Johari Goldstein process?

Broadband dielectric measurements were carried out at isobaric and isothermal conditions up to 1.75 GPa for reconsidering the relaxation dynamics of decahydroisoquinoline, previously investigated by Richert et al. [R. Richert, K. Duvvuri, and L.-T. Duong, J. Chem. Phys. 118, 1828 (2003)] at atmospheric pressure. The relaxation time of the intense secondary relaxation tau(beta) seems to be insensitive to applied pressure, contrary to the alpha-relaxation times tau(alpha). Moreover, the separation of the alpha- and beta-relaxation times lacks correlation between shapes of the alpha-process and beta-relaxation times, predicted by the coupling model [see for example, K. L. Ngai, J. Phys.: Condens. Matter 15, S1107 (2003)], suggesting that the beta process is not a true Johari-Goldstein (JG) relaxation. From the other side, by performing measurements under favorable conditions, we are able to reveal a new secondary relaxation process, otherwise suppressed by the intense beta process, and to determine the temperature dependence of its relaxation times, which is in agreement with that of the JG relaxation.     

The protein "glass" transition and the role of the solvent

Hydrated proteins undergo a change in their dynamical properties in the neighborhood of a temperature. The change of dynamics has been likened to glass transition of glass-forming substances because similar properties were found. However, a complete understanding of the conformation fluctuations of hydrated proteins and their relation to the dynamics of the solvent is still not available, possibly due to the protein molecules being more complex than ordinary glass-formers. For this reason, we turn our attention to the experimental findings of the dynamics of mixtures of water with simpler glass-formers (small molecules and polymers). Two major relaxation processes have been observed in these aqueous mixtures. One is the structural alpha-relaxation of the hydrophilic glass-former hydrogen bonded to the water, which is responsible for glass transition. The other one is the local secondary beta-relaxation of water in the mixture. Remarkably, these two relaxation processes in aqueous mixtures have analogues in hydrated proteins with the same properties. The conformation fluctuations of the protein and the relaxation of the solvent in hydrated proteins behave like the alpha-relaxation of the hydrophilic glass-former hydrogen bonded to the water and the beta-relaxation of water in other aqueous mixtures, respectively. At low temperatures, the Arrhenius activation energy of the relaxation time of the solvent in a hydrated protein is almost the same as that of the beta-relaxation of water in the glassy states of aqueous mixtures. The Arrhenius T-dependence of the solvent relaxation times no longer holds at temperatures that exceed the "glass" transition temperature of the hydrated protein, defined as the temperature at which the conformation relaxation time is very long. This behavior of the solvent in hydrated proteins is similar to that found in the beta-relaxation of water in aqueous mixtures when crossing the glass transition temperature of the mixture (Capaccioli, S.; Ngai, K. L.; Shinyashiki, N. J. Phys. Chem. B 2007, 111, 8197). Furthermore, the same dynamics were found in mixtures of two van der Waals glass-formers, which are even simpler systems than aqueous mixtures because of the absence of hydrogen bonding. The experimental data of these ideal mixtures of van der Waals glass-formers have been given a satisfactory theoretical explanation. Since the properties of hydrated proteins, aqueous mixtures, and the mixtures of van der Waals liquids are similar, we transfer the theoretical understanding gained in the study of the last system sequentially to the two other increasingly more complex systems.     

Interdependence of primary and Johari-Goldstein secondary relaxations in glass-forming systems

We report evidence from broadband dielectric spectroscopy that the dynamics of the primary alpha- and secondary Johari-Goldstein (JG) beta-processes are strongly correlated in different glass-forming systems over a wide temperature T and pressure P range, in contrast with the widespread opinion of statistical independence of these processes. The alpha-beta mutual dependence is quantitatively confirmed by (a) the overall superposition of spectra measured at different T-P combinations but with an invariant alpha-relaxation time; (b) the contemporary scaling of the isothermal-pressure and isobaric-temperature dependences of the alpha-and beta-relaxation times as plotted versus the reduced variable Tg(P)/T where Tg is the glass transition temperature. These novel and model-independent evidences indicate the relevance of the JG relaxation phenomenon in glass transition, often overlooked by most current theories.     

Classification of secondary relaxation in glass-formers based on dynamic properties

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time taubeta and the primary relaxation time taualpha at any chosen taualpha; (3) whether taubeta is approximately equal to the independent (primitive) relaxation time tau0 of the coupling model; (4) whether both taubeta and tau0 have the same pressure and temperature dependences; (5) whether it is responsible for the "excess wing" of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Deltaepsilonbeta and taubeta across the glass transition temperature Tg; (8) the changes of Deltaepsilonbeta and taubeta with aging below Tg; (9) whether it arises in a glass-former composed of totally rigid molecules without any internal degree of freedom; (10) whether only a part of the molecule is involved; and (11) whether it tends to merge with the alpha-relaxation at temperatures above Tg. After the secondary relaxations in many glass-formers have been characterized and classified, we identify the class of secondary relaxations that bears a strong connection or correlation to the primary relaxation in all the dynamic properties. Secondary relaxations found in rigid molecular glass-formers belong to this class. The secondary relaxations in this class play the important role as a precursor or local step of the primary relaxation, and we propose that only they should be called the Johari-Goldstein beta-relaxation.     

Effects of T-tubules on dielectric spectra of skeletal muscle simulated by boundary element method with two-dimensional models

In order to investigate the origin of large intensity the alpha-relaxation in skeletal muscles observed in dielectric measurements with extracellular electrode methods, effects of the interfacial polarization in the T-tubules on dielectric spectra were evaluated with the boundary-element method using two-dimensional models in which the structure of the T-tubules were represented explicitly. Each model consisted of a circular inclusion surrounded by a thin shell corresponding to the sarcolemma. The T-tubules were represented by simplified two types of invagination of the shell: straight invagination along the radial directions, and branched one. Each of the models was subjected to two kinds of calculations relevant to experiments with the extracellular and the intracellular electrode methods. Electrical interactions between the cells were omitted in the calculations. Both calculations showed that the dielectric spectra of the models contained two relaxation terms. The low-frequency relaxation term assigned to the alpha-relaxation depended on the structure of the T-tubules. Values of the relaxation frequency of the alpha-relaxation obtained from the two types of calculations agreed with each other. At the low-frequency limit, the permittivity obtained from the extracellular-electrode-type calculations varied in proportion to the capacitance obtained from the intracellular-electrode-type ones. These results were consistent with conventional lumped and distributed circuit models for the T-tubules. This confirms that the interfacial polarization in the T-tubules in a single muscle cell is not sufficient to explain the experimental results in which the intensity of the alpha-relaxation in the extracellular-electrode-type experiments exceeded the intensity expected from the results of the intracellular-electrode-type experiments. The high-frequency relaxation term that was assigned to the beta-relaxation was also affected by the T-tubule structure in the calculations relevant to the extracellular-electrode-type experiments.     

Dielectric studies on mobility of the glycosidic linkage in seven disaccharides

Isobaric dielectric relaxation measurements were performed on seven chosen disaccharides. For five of them, i.e., sucrose, maltose, trehalose, lactulose, and leucrose, we were able to observe the temperature evolution of the structural relaxation process. In the case of the other disaccharides studied (lactose and cellobiose), it was impossible to obtain such information because of the large contribution of the dc conductivity and polarization of the capacitor plates to the imaginary and real part of the complex permittivity, respectively. On the other hand, in the glassy state, two secondary relaxations have been identified in the dielectric spectra of all investigated carbohydrates. The faster one (gamma) is a common characteristic feature of the entire sugar family (mono-, di-, oligo-, and polysaccharide). The molecular origin of this process is still not unambiguously identified but is expected to involve intramolecular degrees of freedom as inferred from insensitivity of its relaxation time to pressure found in some monosaccharides (fructose and ribose). The slower one (labeled beta) was recently identified to be intermolecular in origin (i.e., a Johari-Goldstein (JG) beta-relaxation), involving twisting motion of the monosugar rings around the glycosidic bond. The activation energies and dielectric strengths for the beta-relaxation determined herein provide us valuable information about the flexibility of the glycosidic bond and the mobility of this particular linkage in the disaccharides studied. In turn, this information is essential for the control of the diffusivity of drugs or water entrapped in the sugar matrix.     

Kinetics of spontaneous change in the localized motions of D-sorbitol glass

The dielectric relaxation spectra of D-sorbitol glass have been studied in real time during annealing at 221.1 K, which is 47 K below its T(g) of 268 K. As the glass structurally relaxes during annealing, features of the Johari-Goldstein (JG) relaxation change with time: (i) the relaxation strength decreases, (ii) the relaxation peak at 48 Hz shifts to a higher frequency, and (iii) the relaxation spectra become narrower. All seem to follow the relation p proportional, variant exp[-(kt)(n)], where p is the magnitude of a property, k the rate constant, and t the time. The parameter n may well be less than 1, but this could not be ascertained. It is proposed that shift of the relaxation peak to a higher frequency and narrowing of the relaxation spectra occur when local, loosely packed regions of molecules in the glass structure collapse nonuniformly and the relaxation time of some of the molecules in the collapsed state becomes too long to contribute to the JG-relaxation spectra. Consequently, the half width of the spectra decreases, and the relaxation peak shifts to a higher frequency. Molecules whose diffusion becomes too slow after the local regions' collapse would contribute to the alpha-relaxation spectra and thus the net relaxation strength would increase on structural relaxation. It is argued that these findings conflict with the NMR-based conclusions that motion of all molecules in the glass and supercooled liquid contributes to the faster relaxation process.     

The true Johari-Goldstein beta-relaxation of monosaccharides

Broadband isothermal dielectric relaxation measurements of anhydrous fructose, glucose, galactose, sorbose, and ribose were made at ambient pressure in their liquidus and glassy states. We found a new secondary relaxation in fructose and glucose that is slower than those seen before by others. This new secondary relaxation also appears in the dielectric spectra of galactose, sorbose, and ribose, and hence it is a general feature of the relaxation dynamics of the monosaccharides. Dielectric measurements at elevated pressure of fructose and ribose show that the new secondary relaxation shifts to lower frequencies with applied pressures, mimicking the behavior of the alpha-relaxation. In contrast, the faster secondary relaxation remains stationary on applying pressure. These results together with other inferences indicate that the slower secondary relaxation bears relations to the alpha-relaxation, and hence, it is the true Johari-Goldstein secondary relaxation of the monosaccharides.     

The nearly constant loss,Johari‐Goldstein β‐relaxation,and α‐relaxation of 1,4‐polybutadiene

From high‐resolution dielectric spectroscopy measurements on 1,4‐polybutadiene (1,4‐PB), we show that in addition to the structural α‐relaxation and higher frequency secondary relaxations in the spectra, a nearly constant loss (NCL) is observed at shorter times/lower temperatures. The properties of this NCL are compared to those of another chemically similar polymer, 1,4‐polyisoprene. The secondary relaxations in 1,4‐PB include the well‐known Johari‐Goldstein (JG) β‐relaxation and two other higher‐frequency peaks. One of these, referred to as the γ‐relaxation, falls between the JG‐relaxation and the NCL. Seen previously by others, this γ‐relaxation in 1,4‐PB is not the JG‐process and bears no relation to the glass transition. At very low temperatures (<15 K), we confirm the existence of a very fast secondary relaxation, having a weak dielectric strength and an almost temperature‐invariant relaxation time. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 342–348, 2007     

Identification of the molecular motions responsible for the slower secondary (beta) relaxation in sucrose

Broad-band isothermal dielectric relaxation measurements of anhydrous sucrose were made at ambient pressure in its liquid and glassy states. We found a new secondary relaxation that is slower than the one commonly observed in sugars. Additionally, we carried out the dielectric measurements of the equimolar mixture of D-glucose and D-fructose in wide ranges of temperature and frequency. Comparison of the behavior of these two systems allowed us to make suggestions on the origin of the slower beta-relaxation in sucrose. Computer simulations and coupling model calculations were performed to support our interpretation of the kind of molecular motions responsible for the slower secondary relaxation in the disaccharide considered.     

Anomalous narrowing of the structural relaxation dispersion of tris(dimethylsiloxy)phenylsilane at elevated pressures

Broadband dielectric relaxation measurements of tris(dimethylsiloxy)phenylsilane were made at ambient pressure and at elevated pressures. The data show an anomalous behavior not previously seen in any other glass-formers; namely, the structural alpha-relaxation loss peak narrows with increasing pressure and temperature at constant peak frequency. Interpreted by the coupling model, the effect is due to reduction of intermolecular coupling at elevated pressures. This interpretation has support from the observed decrease of the separation between the alpha-relaxation and the Johari-Goldstein secondary relaxation, as well as the smaller steepness or "fragility" index m of the data obtained at 1.7 GPa than at ambient pressure.     

Primary and secondary relaxations in bis-5-hydroxypentylphthalate revisited

The molecular structure of bis-5-hydroxypentylphthalate (BHPP) is like dihexyl phthalate but having appended to it two hydroxyl end groups, which contribute additional dipole moments and capacity for hydrogen-bond formation. In a previously published dielectric study of the primary and secondary relaxations of BHPP, it was found that all the dynamic properties are normal except for the anomalously large width of the primary relaxation loss peak. There are two secondary relaxations, the relaxation time of the slower one increases with increasing pressure, whereas that of the faster one is practically insensitive to pressure. Hence, the slower secondary relaxation is the "universal" Johari-Goldstein (JG) [J. Chem. Phys. 53, 2372 (1970); 55, 4245 (1971)] relaxation in BHPP. All is well except if the observed large width of the primary relaxation were an indication of a corresponding large coupling parameter n=0.45 in the coupling model. Then the predicted relations between the primary relaxation time tau(alpha) and the JG relaxation time tau(JG) found previously to hold in many glass formers would be violated. It was recognized that this singular behavior of BHPP is likely due to broadening of the primary loss peak by the overlapping contributions of two independent dipole moments present in BHPP, and the actual coupling parameter is smaller. However, at the time of publication of the previous work there were not enough data to support this explanation. By making broadband dielectric measurements of dibutyl phthalate (DBP) and dioctyl phthalate (DOP) that have chemical structures closely related to BHPP but with only one dipole moment, we show that all their dynamic properties are almost the same as BHPP but the widths of their primary relaxation loss peaks are significantly narrower corresponding to a smaller coupling parameter n=0.34. The new data presented here indicate that the coupling parameter of BHPP is about the same as DBP and DOP, and the predicted relations between tau(alpha) and tau(JG) of BHPP are brought back in agreement with the experimental data.     

Separable cooperative and localized translational motions of water confined by a chemically heterogeneous environment

We report quasi-elastic neutron scattering experiments at two resolutions that probe timescales of picoseconds to nanoseconds for the hydration dynamics of water, confined in a concentrated solution of N-acetyl-leucine-methylamide (NALMA) peptides in water over a temperature range of 248 K to 288 K. The two QENS resolutions used allow for a clean separation of two observable translational components, and ultimately two very different relaxation processes, that become evident when analyzed under a combination of the jump diffusion model and the relaxation cage model. The first translational motion is a localized beta-relaxation process of the bound surface water, and exhibits an Arrhenius temperature dependence and a large activation energy of approximately 8 kcal mol(-1). The second non-Arrhenius translational component is a dynamical signature of the alpha-relaxation of more fluid water, exhibiting a glass transition temperature of approximately 116 K when fit to the Volger Fulcher Tamman functional form. These peptide solutions provide a novel experimental system for examining confinement in order to understand the dynamical transition in bulk supercooled water by removing the unwanted interface of the confining material on water dynamics.     

A molecular dynamics simulation study of the alpha-relaxation in a 1,4-polybutadiene melt as probed by the coherent dynamic structure factor

The dynamic coherent structure factor Scoh(q,t) for a 1,4-polybutadiene (PBD) melt has been investigated using atomistic molecular dynamics simulations. The relaxation of Scoh(q,t) at q = 1.44 angstroms(-1) and q = 2.72 angstroms(-1), corresponding to the first and second peaks in the static structure factor for PBD, was studied in detail over a wide range of temperature. It was found that time-temperature superposition holds for the alpha-relaxation for both q values over a wide temperature range and that the alpha-relaxation can be well described by a stretched (Kohlrauch-William-Watts) exponential with temperature independent but q dependent amplitude and stretching exponent. The alpha-relaxation times for both q values were found to exhibit the same non-Arrhenius temperature dependence, indicating that the same physical processes are responsible for relaxation on both length scales. The alpha-relaxation time was found to depend strongly upon the dynamical range of data utilized in determining the relaxation time, accounting for qualitative discrepancies between alpha-relaxation times reported here and those extracted for PBD from experimentally measured Scoh(q,t).     

Emergence of the genuine Johari-Goldstein secondary relaxation in m-fluoroaniline after suppression of hydrogen-bond-induced clusters by elevating temperature and pressure

The dielectric spectra of the glass former, m-fluoroaniline (m-FA), at ambient pressure show the presence of a secondary relaxation, which was identified in the literature as the universal Johari-Goldstein (JG) beta relaxation. However, published elastic neutron scattering and simulation data [D. Morineau, C. Alba-Simionesco, M. C. Bellisent-Funel, and M. F. Lauthie, Europhys. Lett. 43, 195 (1998); D. Morineau and C. Alba-Simionesco, J. Chem. Phys. 109, 8494 (1998)] showed the presence of hydrogen-bond-induced clusters of limited size in m-FA at ambient pressure and temperature of the dielectric measurements. The observed secondary relaxation may originate from the hydrogen-bond-induced clusters. If so, it should not be identified with the JG beta relaxation that involves essentially all parts of the molecule and has certain characteristics [K. L. Ngai and M. Paluch, J. Chem. Phys. 120, 857 (2004)], but then arises the question of where is the supposedly universal JG beta relaxation in m-FA. To gain a better understanding and resolving the problem, we perform dielectric measurements at elevated pressures and temperatures to suppress the hydrogen-bond-induced clusters and find significant changes in the dielectric spectra. The secondary relaxation observed at ambient pressure in m-FA is suppressed, indicating that indeed it originates from the hydrogen-bond-induced clusters. The spectra of m-FA are transformed at high temperature and pressure to become similar to that of toluene. The new secondary relaxation that emerges in the spectra has properties of a genuine JG relaxation like in toluene.     

Secondary relaxation behavior in a strong glass

In the present paper we study the enthalpy relaxation behavior of the hyperquenched GeO(2) (HQGeO(2)) glass, one of the strongest glass systems. By applying the hyperquenching-annealing-calorimetry approach, we have found that unlike fragile glasses the strong HQGeO(2) glass relaxes in a manner that all the secondary relaxation units contribute to the primary relaxation. By analyzing dynamic properties of the secondary relaxation, we have identified two typical features of the Johari-Goldstein relaxation in the HQGeO(2) glass. First, the quantitative relationship observed here between E(beta) and T(g) agrees well with the empirical relation of the JG relaxation. Second, the characteristic relaxation time of the GeO(2) glass at T(g) is found to be about 10 s, larger than that of relatively fragile glasses. These results verify that the JG peak in strong glasses is hidden by the alpha peak in the dielectric loss curves.     

Johari-Goldstein relaxation and crystallization of sorbitol to ordered and disordered phases

The equilibrium permittivity epsilon(s) and the dielectric relaxation spectra of supercooled liquid D-sorbitol were measured during its crystallization to orientationally disordered or ordered phases depending on the sample preparation procedure at several fixed temperatures up to a period of 6 days. The epsilon(s) measurements showed that when the sample was contaminated by a minute amount of crystals, it crystallized to an ordered phase. When the liquid was not contaminated, the sample crystallized to an orientationally disordered phase. When supercooled D-sorbitol was kept close to its T(g), its dielectric spectra did not change over a period of 138.5 h. It was found that the Johari-Goldstein (JG) relaxation rate of the orientationally disordered crystalline phase is higher in comparison with that of the supercooled liquid, the spectrum broader, and the relaxation strength lower. Its glasslike transition temperature is higher than T(g) of the liquid. The results on crystallization showed that the structural changes occurring at a temperature where the alpha relaxation emerges from the JG relaxation affects the crystallization kinetics of the liquid.