Localized relaxation in a glass and the minimum in its orientational polarization contribution

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 τ_β( T, P)/τ_α( T, P) is invariant to variations of P and T, whereas τ_α( 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 τ_α( T, P) than the Debye relaxation time τ_D( T, P) is given.

Microscopic dynamics perspective on the relationship between Poisson's ratio and ductility of metallic glasses

In metallic glasses a clear correlation had been established between plasticity or ductility with the Poisson's ratio νPoisson and alternatively the ratio of the elastic bulk modulus to the shear modulus, K/G. Such a correlation between these two macroscopic mechanical properties is intriguing and is challenging to explain from the dynamics on a microscopic level. A recent experimental study has found a connection of ductility to the secondary β-relaxation in metallic glasses. The strain rate and temperature dependencies of the ductile-brittle transition are similar to the reciprocal of the secondary β-relaxation time, τβ. Moreover, metallic glass is more ductile if the relaxation strength of the β-relaxation is larger and τβ is shorter. The findings indicate the β-relaxation is related to and instrumental for ductility. On the other hand, K/G or νPoisson is related to the effective Debye-Waller factor (i.e., the non-ergodicity parameter), f0, characterizing the dynamics of a structural unit inside a cage formed by other units, and manifested as the nearly constant loss shown in the frequency dependent susceptibility. We make the connection of f0 to the non-exponentiality parameter n in the Kohlrausch stretched exponential correlation function of the structural α-relaxation function, ϕ(t)=exp[-(t/τα)(1-n)]. This connection follows from the fact that both f0 and n are determined by the inter-particle potential, and 1/f0 or (1 - f0) and n both increase with anharmonicity of the potential. A well tested result from the Coupling Model is used to show that τβ is completely determined by τα and n. From the string of relations, (i) K/G or νPoisson with 1/f0 or (1 - f0), (ii) 1/f0 or (1 - f0) with n, and (iii) τα and n with τβ, we arrive at the desired relation between K/G or νPoisson and τβ. On combining this relation with that between ductility and τβ, we have finally an explanation of the empirical correlation between ductility and the Poisson's ratio νPoisson or K/G based on microscopic dynamical properties.

Aging of the secondary relaxation to probe structural relaxation in the glassy state

The importance of glass formation and the glass transition is linked to their universality, embracing many classes of materials: metallic, inorganic, and organic. There is no agreement on what drives this phenomenon; moreover, experiments are challenging due to the nonequilibrium nature of the glassy state. We present a new approach that provides information about the very slow structural relaxation in the glassy state and reveals the important role of the secondary relaxation. Structural (alpha) relaxation times for glassy polyvinylethylene were determined from changes in the properties of the secondary process during physical aging. These alpha-relaxation times exceed 3 years, making them inaccessible via direct measurement.

Molecular mobility, thermodynamics and stability of griseofulvin's ultraviscous and glassy states from dynamic heat capacity

PURPOSE

To determine the calorimetric relaxation time needed for modeling griseofulvin's stability against crystallization during storage.

METHODS

Both temperature-modulated and unmodulated scanning calorimetry have been used to determine the heat capacity of griseofulvin in the glassy and melt state.

RESULTS

The calorimetric relaxation time, tau cal, of its melt varies with the temperature T according to the relation, tau cal [s] = 10(-13.3) exp [2, 292 /(T[K] - 289.5)] , and the distribution of relaxation times parameter is 0.67. The unrelaxed heat capacity of the griseofulvin melt is equal to its vibrational heat capacity.

CONCLUSIONS

Griseofulvin neither crystallizes on heating to 373 K at 1 K/h rate, nor on cooling. Molecular mobility and vibrational heat capacity measured here are more reliable for modeling a pharmaceutical's stability against crystallization than the currently used kinetics-thermodynamics relations, and molecular mobility in the (fixed structure) glassy state is much greater than the usual extrapolation from the melt state yields. Molecular relaxation time of the glassy state of griseofulvin is about 2 months at 298 K, and longer at lower temperatures. It would spontaneously increase with time. If the long-range motions alone were needed for crystallization, griseofulvin would become more stable against crystallization during storage.

New experimental evidence about secondary processes in phenylphthalein-dimethylether and 1,1'-bis(p-methoxyphenyl)cyclohexane

The slow secondary (beta) process of 1,1'-bis (4-methoxyphenyl) cyclohexane and phenolphthalein dimethylether has been investigated by dielectric spectroscopy. New experimental results about the pressure dependence of the two processes are reported, as well as new data about the dependence of the characteristic relaxation frequency on the cooling rate used to vitrify the system in isobaric conditions. Previous investigations on these systems suggested that the first one is not a true Johari-Goldstein relaxation and both processes should originate from the flip flop motion of the phenyl ring. The results herein reported evidence that the characteristic frequency of the beta process of phenolphthalein dimethylether is more sensitive to pressure variation and to the vitrification procedure than that of 1,1'-bis (4-methoxyphenyl) cyclohexane. Such results suggest an intermolecular origin for the secondary process in phenolphthalein dimethylether and an intramolecular origin for the other one, which do not completely agree with the previous interpretation. We evidence that the microscopic mechanism at the basis of these two processes is still an open question, which should be debated on the basis of new experimental investigations.

Additive property of secondary relaxation processes in di-n-octyl and di-isooctyl phthalates: Signature of non-Johari-Goldstein relaxation

Broadband dielectric spectroscopy was used to study relaxation dynamics of supercooled di-n-octyl phthalate, di-isooctyl phthalate, and their mixtures. Additionally, low temperature measurements were performed to investigate the nature of the secondary relaxation processes in both glass formers. The authors found that the secondary relaxation observed in the mixture is the additive sum of the secondary relaxations of the two components. This experimental evidence indicates that these secondary relaxation processes are intramolecular in origin, and they are non-Johari-Goldstein secondary relaxations.

Dielectric Relaxation and Crystallization of Ultraviscous Melt and Glassy States of Aspirin, Ibuprofen, Progesterone, and Quinidine

Molecular relaxation in ultraviscous melt and glassy states of aspirin, ibuprofen, progesterone, and quinidine has been studied by dielectric spectroscopy. The asymmetric relaxation spectra is characterized by the Kohlrausch distribution parameter of 0.46 +/- 0.02 for aspirin to 0.67 +/- 0.02 for progesterone. The dielectric relaxation time varies with the temperature, T, according to the Vogel-Fulcher-Tammann Equation, log(10)(tau(0)) = A(VFT) + [B(VFT)/(T - T(0))], where A(VFT), B(VFT), and T(0) are empirical constants. The extrapolated tau(0) at calorimetric glass-softening temperature is close to the value expected. The equilibrium permittivity, epsilon(0), is lowest for ibuprofen which indicates an antiparallel orientation of dipoles in its liquid's hydrogen-bonded structure. A decrease in epsilon(0) with time shows that ultraviscous aspirin, progesterone, and quinidine begin to cold-crystallize at a relatively lower temperature than ibuprofen. epsilon(0) of the cold-crystallized phases are, 4.7 for aspirin at 290 K, 2.55 for ibuprofen at 287 K, 2.6 for progesterone at 320 K, and 3.2 for quinidine at 375 K. It is argued that hydrogen-bonding, the Kohlrausch parameter, extent of localized motions and the long-range diffusion times all determine the physical and chemical stability of an amorphous pharmaceutical during storage.

Relaxations and nano-phase-separation in ultraviscous heptanol-alkyl halide mixture

To gain insight into the effects of liquid-liquid phase separation on molecular relaxation behavior we have studied an apparently homogeneous mixture of 5-methyl-2-hexanol and isoamylbromide by dielectric spectroscopy over a broad temperature range. It shows two relaxation regions, widely separated in frequency and temperature, with the low-frequency relaxation due to the alcohol and the high-frequency relaxation due to the halide. In the mixture, the equilibrium dielectric permittivity epsilon(s) of the alcohol is 41% of the pure state at 155.7 K and epsilon(s) of isoamylbromide is approximately 86% of the pure state at 128.7 K. The difference decreases for the alcohol component with decreasing temperature and increases for the isoamylbromide component. The relaxation time tau of 5-methyl-2-hexanol in the mixture at 155.7 K is over five orders of magnitude less than in the pure state, and this difference increases with decreasing temperature, but tau of isoamylbromide in the mixture is marginally higher than in the pure liquid. This shows that the mixture would have two T(g)'s corresponding to its tau of 10(3) s, with values of approximately 121 K for its 5-methyl-2-hexanol component and approximately 108 K for its isoamylbromide component. It is concluded that the mixture phase separates in submicron or nanometer-size aggregates of the alcohol in isoamylbromide, without affecting the latter's relaxation kinetics, while its own epsilon(s) and tau decrease markedly.

Aging of the Johari-Goldstein relaxation in the glass-forming liquids sorbitol and xylitol

Employing frequency-dependent dielectric susceptibility we characterize the aging in two supercooled liquids, sorbitol and xylitol, below their calorimetric glass transition temperatures. In addition to the alpha relaxation that tracks the structural dynamics, the susceptibility of both liquids possesses a secondary Johari-Goldstein relaxation at higher frequencies. Following a quench through the glass transition, the susceptibility slowly approaches the equilibrium behavior. For both liquids, the magnitude of the Johari-Goldstein relaxation displays a dependence on the time since the quench, or aging time, that is quantitatively very similar to the age dependence of the alpha peak frequency. The Johari-Goldstein relaxation time remains constant during aging for sorbitol while it decreases slightly with age for xylitol. Hence, one cannot sensibly assign a fictive temperature to the Johari-Goldstein relaxation. This behavior contrasts with that of liquids lacking distinct Johari-Goldstein peaks for which the excess wing of the alpha peak tracks the main part of the peak during aging, enabling the assignment of a single fictive temperature to the entire spectrum. The aging behavior of the Johari-Goldstein relaxation time further calls into question the possibility that the relaxation time possesses stronger temperature dependence in equilibrium than is observed in the out-of-equilibrium state below the glass transition.

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.

Orientation polarization from faster motions in the ultraviscous and glassy diethyl phthalate and its entropy

Dielectric spectra of the beta relaxation in glassy and ultraviscous liquid diethyl phthalate show that its relaxation strength Delta epsilon(beta), the distribution of times, and the relaxation rate are more sensitive to temperature T in the ultraviscous liquid than in the glassy state. The Delta epsilon(beta) against temperature plot has an elbow-shaped break near T(g) of approximately 181 K, which is remarkably similar to that observed in the entropy, enthalpy, and volume against temperature plots, and in the plot of Delta epsilon(beta) against the liquid's entropy minus its 0 K value. The ratio of Delta epsilon(beta) to diethyl phthalate's entropy, after subtracting the 0 K value, is 1.08 x 10(-3) mol K/J in the glassy state at 120.4 K, which decreases slowly to 0.81 x 10(-3) mol K/J at 176 K near T(g) and thereafter rapidly increases to 1.57 x 10(-3) mol K/J at 190 K. Variation in Delta epsilon(beta) parallels the variation of the entropy. A change in the activation energy of the beta process at T>T(g) indicates that its rate is also determined by the structure of the ultraviscous liquid. Features of beta relaxation are consistent with localized motions of molecules and may not involve small-angle motions of all molecules.

Glassy aging dynamics

We present time-dependent dielectric loss data for various glass formers below the glass temperature. The observed aging dynamics is described using a modified Kohlrausch-Williams-Watts law taking into account the variation of the relaxation time during aging. It leads to values for the aging relaxation time and stretching exponent, fully consistent with the results from equilibrium measurements performed at higher temperatures. Irrespective of the dynamic process prevailing in the investigated frequency region, the aging dynamics is always determined by the structural relaxation process.

Relation between the α-Relaxation and Johari−Goldstein β-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.

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.

Minimal model for Beta relaxation in viscous liquids

Contrasts between beta relaxation in equilibrium viscous liquids and glasses are rationalized in terms of a double-well potential model with structure-dependent asymmetry, assuming structure is described by a single order parameter. The model is tested for tripropylene glycol where it accounts for the hysteresis of the dielectric beta loss peak frequency and magnitude during cooling and reheating through the glass transition.