Localized relaxation’s strength and its mimicry of glass-softening thermodynamics

Dynamic Heterogeneity in the Monoclinic Phase of CCl4

Carbon tetrachloride (CCl4) is one of the simplest compounds having a translationally stable monoclinic phase while exhibiting a rich rotational dynamics below 226 K. Recent nuclear quadrupolar resonance experiments revealed that the dynamics of CCl4 is similar to that of the other members of the isostructural series CBrnCl4-n, suggesting that the universal relaxation features of canonical glasses such as α and β relaxation are also present in nonglass formers. Using molecular dynamics simulations we studied the rotational dynamics in the monoclinic phase of CCl4. The molecules undergo C3-type jump-like rotations around each one of the four C-Cl bonds. The rotational dynamics is very well described with a master equation using as the only input the rotational rates measured from the simulated trajectories. It is found that the heterogeneous dynamics emerges from faster and slower modes associated with different rotational axes, which have fixed orientations relative to the crystal and are distributed among the four nonequivalent molecules of the unit cell.

Many-Body Nature of Relaxation Processes in Glass-Forming Systems

Most glass-forming systems are composed of basic units interacting with each other with a nontrivial anharmonic potential. Naturally, relaxation and diffusion in glass formers is a many-body problem. Results from recent experimental studies are presented to show the effects of many-body relaxation and diffusion manifested on the dynamic properties of glass formers. Considering that the effects are general and critical, the problem of glass transition will not be solved until the many-body nature of the relaxation process has been incorporated fundamentally into any theory.

Dielectric study of equimolar acetaminophen-aspirin, acetaminophen-quinidine, and benzoic acid-progesterone molecular alloys in the glass and ultraviscous states and their relevance to solubility and stability

Equimolar mixtures of acetaminophen-aspirin, acetaminophen-quinidine, and benzoic acid-progesterone have been vitrified and dielectric properties of their glassy and ultraviscous alloys have been studied. For 20 K/min heating rate, their T(g)s are 266, 330, and 263 K, respectively. The relaxation has an asymmetric distribution of times, and the distribution parameter increases with increase in temperature. The dielectric relaxation time varies with 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 equilibrium permittivity is highest for the aspirin-acetaminophen and lowest for the benzoic acid-progesterone alloy, indicating a substantial interpharmaceutical hydrogen bonding that makes the alloy more stable against crystallization than the pure components. The benzoic acid-progesterone alloy is thermodynamically the most nonideal. It showed cold crystallization on heating, which is attributed to its relatively greater magnitude of the JG relaxation in relation to its alpha-relaxation. It is argued that the difference between the free energy of an alloy and the pure components would have an effect on the solubility. Studies of solution thermodynamics of a glassy molecular alloy may be useful for optimizing choice of components and composition to form molecular alloys and to impact drug delivery.

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.

The Johari-Goldstein beta-relaxation of water

There is a plethora of experimental data on the dynamics of water in mixtures with glycerol, ethylene glycol, ethylene glycol oligomers, poly(ethylene glycol) 400 and 600, propanol, poly(vinyl pyrrolidone), poly(vinyl methylether), and other substances. In spite of the differences in the water contents, the chemical compositions, and the glass transition temperatures Tg of these aqueous mixtures, a faster relaxation originating from the water (called the nu-process) is omnipresent, sharing the following common properties. The relaxation time tau(nu) has Arrhenius temperature dependence at temperatures below Tg of the mixture. The activation energies of tau(nu) all fall within a neighborhood of 50 kJ/mol. At the same temperature where mixtures are all in their glassy states, the values of tau(nu) of several mixtures are comparable. The Arrhenius temperature dependence of tau(nu) does not continue to higher temperatures and instead it crosses over to a stronger temperature dependence at temperatures above Tg. The dielectric relaxation strength of the nu-process, Deltaepsilon(nu)(T), has a stronger temperature dependence above Tg than below, mimicking the change of enthalpy, entropy, and volume when crossing Tg. These general property of the nu-process (except for the magnitude of the activation energy) had been found before in the secondary relaxation of the faster component in several binary nonaqueous mixtures. Other properties of the secondary relaxation in these nonaqueous mixtures have helped to identify it as the Johari-Goldstein (JG) secondary relaxation of the faster component. The similarities in properties lead us to conclude that the nu-processes in water mixtures are the JG secondary relaxations of water. The conclusion is reinforced by the processes behaving similarly to the nu-process found in 6 A thick water layer (two molecular layers) in fully hydrated Na-vermiculite clay, and in water confined in molecular sieves, silica hydrogels, and poly(2-hydroxyethyl methacrylate) hydrogels.

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.

Effect of Pressure on Molecular and Ionic Motions in Ultraviscous Acetaminophen–Aspirin Mixture

Effect of pressure and temperature on molecular motions and dc conductivity in ultraviscous, 50 wt% acetaminophen-aspirin melt has been studied by dielectric relaxation spectroscopy. The spectra obtained over the pressure range, 5-300 MPa and temperature range, 295-320 K show a distribution of relaxation times greater than found in pure acetaminophen. The equilibrium dielectric permittivity and relaxation time, tau, of the melt increase with increase in pressure and decrease in temperature and the dc conductivity, sigma(dc), decreases. The pressure and temperature variation of the limiting high frequency permittivity shows significant contribution from infrared polarization. The volumes of activation for sigma(dc) and tau vary with both the pressure and temperature, indicating that there is also a structural effect that determine sigma(dc). This effect would add a non-linear term to the Debye-Stokes-Einstein equation for variation of sigma(dc) with tau. The ultraviscous liquid remains stable with time, and with change in temperature and pressure, suggesting that a more stable glassy state of a pharmaceutical may be obtained by mixing a second component.

Dynamic Heat Capacity and Relaxation Time of Ultraviscous Melt and Glassy Acetaminophen

The real and imaginary components, C'(p) and C''(p), of the complex heat capacity, C*(p)=C'(p)-iC"(p) of supercooled, ultraviscous melt of acetaminophen have been measured at different temperatures during cooling through its vitrification range and during heating through its glass-softening range by using a modulation frequency of 3.3 mHz. From these data, the distribution of relaxation time parameter, beta, and a characteristic (calorimetric or configurational) relaxation time, tau(cal), have been determined. A constant value of 0.65 for beta fits the data, and tau(cal) varies with the temperature according to the Vogel-Fulcher-Tammann equation, tau(cal) = 10(-12.95) exp[1813/(T - 240.5)]. This relation differs significantly from the one deduced by others in which the configurational entropy theory was used to deduce tau(cal). The C'(p) and C''(p) values measured during the cooling of its ultraviscous melt and during the heating of its glassy state show a small hysteresis only at low temperatures. These investigations also provide a comparison of calorimetric and dielectric relaxation times in ultraviscous acetaminophen and highlight the role of faster modes of relaxation at low temperatures in organic, molecular glasses that can help in a better understanding of the crystal nucleation process in glasses at T below their T(g).

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.

Dielectric Studies of Molecular Motions in Amorphous Solid and Ultraviscous Acetaminophen

The dielectric permittivity and loss spectra of glassy and ultraviscous states of acetaminophen have been measured over the frequency range 10 Hz-0.4 MHz. The relaxation spectra show an asymmetric distribution of times expressed in terms of the Kohlrausch exponent, beta, which remains constant at 0.79+/-0.02 over the 305-341 K range. The dielectric relaxation time increases on cooling according to the Vogel-Fulcher-Tammann equation. However, the values of the parameters are considerably different from the values deduced from earlier work by other researchers using the heat capacity of ultraviscous acetaminophen and relating it to its molecular mobility. The calorimetric glass softening temperature of 296 K obtained from differential scanning calorimetry is close to the value measured from dielectric relaxation. The equilibrium permittivity of ultraviscous acetaminophen decreases on heating like that of a normal dipolar liquid, as anticipated from the Curie law. But, its value decreases rapidly with time when it begins to crystallize. The equilibrium permittivity of this crystal phase is approximately 3.1 at 300 K and increases with temperature, which indicates a partial, orientational-disordering of its structure. The results show limitations of the procedures used in the modeling of the kinetics of molecular motions, that is, estimating physical stability, using thermodynamic considerations based on thermal analyses of the amorphous solid phase of acetaminophen.

Dielectric relaxation time of bulk water at 136–140K, background loss and crystallization effects

Dielectric relaxation time, tau, of ultraviscous bulk water has been determined by analyzing its loss tangent, tan delta, data, which had been measured on heating the vapor-deposited amorphous solid water and hyperquenched glassy water in our earlier studies. [Johari, Hallbrucker, and Mayer, J. Chem. Phys. 95, 2955 (1991); 97, 5851 (1992)]. As for glasses and liquids generally, the measured tan delta of water is the sum of a frequency-independent background loss and a frequency-dependent relaxational loss. A two-frequency method is provided for determining the background loss and used for obtaining the relaxational part of tan delta. After considering the structural relaxation and crystal-nuclei growth effects, tau for water has been determined. At 136+/-1 K, it is 2.5+/-0.6 s when a single relaxation time is (untenably) assumed, and 42+/-14 s when a distribution of relaxation times, a characteristic of viscous liquids, is assumed, with Davidson-Cole distribution parameter of 0.75. Structural relaxation time of approximately 70 s for water at 136 K, which was originally estimated from the DSC endotherm [Johari, Hallbrucker, and Mayer, Nature (London) 330, 552 (1987)], has been revised to approximately 33 s. Temperature dependence of tau could not be determined because ultraviscous water crystallizes too rapidly to cubic ice containing stacking faults and intergranular water. The study demonstrates that water is a liquid over the 136-155 K range, thus removing the basis for a recent contention on its state.

Sub-Tg relaxations due to dipolar solutes in nonpolar glass-forming solvents

It is well known that rigid dipolar solutes (in smaller quantity) dispersed in a nonpolar glassy matrix exhibit a sub-T(g) (or beta(s)) relaxation due to the solute often designated as Johari-Goldstein (JG) relaxation, which is intermolecular in nature. In this article, we report the results of our study of such a sub-T(g) process in a wide variety of dipolar solutes in different glassy systems using dielectric spectroscopy over a frequency range of 20-10(6) Hz down to a temperature of 77 K. The T(g) of these solutions are determined using differential scanning calorimetry. The solvents used in this study are o-terphenyl (OTP), isopropylbenzene (IPB), and methylcyclohexane. In the case of rigid molecular solutes, like mono-halogen benzenes, the activation energy (DeltaE(beta)) of the beta(s) process is found to increase with decreasing T(g) of the solvent, with a corresponding decrease in the magnitude of the beta(s) process. In the case of more symmetrical molecular solute, for example, tert-butylchloride, the change in DeltaE(beta) is not very appreciable. These results emphasize the importance of the size of the cage of the host matrix in the relaxation of the solute molecules. We have also studied the sub-T(g) relaxation(s) due to some flexible molecular solutes, viz., 1butylbromide, 1hexylbromide, 1butylacetate, and benzylacetate. These solutes in IPB matrix exhibit only one relaxation, whereas in OTP matrix they exhibit an additional sub-T(g) process, which may be identified with a JG type of relaxation. These observations lead us to the conclusion that the beta process observed in the glassy states of these pure solutes is predominantly intramolecular in nature.

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.

Dynamics of supercooled and glassy dipropyleneglycol dibenzoate as functions of temperature and aging: Interpretation within the coupling model framework

Dielectric relaxation measurements of a typical small molecular glassformer, dipropyleneglycol dibenzoate show the presence of two secondary relaxations. Their dynamic properties differ in the equilibrium liquid and glassy states, as well as the changes during structural recovery after rapid quenching the liquid to form a glass. These differences enable us to identify the slower secondary relaxation as the genuine Johari-Goldstein (JG) beta-relaxation, acting as the precursor of the primary alpha-relaxation. Agreement between the JG beta-relaxation time and the independent relaxation time of the coupling model leads to predicted quantitative relations between the JG beta-relaxation and the alpha-relaxation that are supported by the experimental data.

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.

The effects of changes of intermolecular coupling on glass transition dynamics in polymer thin films and glass-formers confined in nanometer pores

Intermolecular coupling plays an important role in determining the dynamics and the mobility of polymeric and non-polymeric glass-formers. The breadth of the dispersion is an indicator of the intermolecular coupling strength. The coupling model relates intermolecular coupling through the breadth of the dispersion to the dynamics of bulk glass-formers. When a glass-former is confined in nanometer pores or in thin films and if there is absence of chemical and physical interactions with the wall, intermolecular coupling is reduced, resulting in an increase of mobility. The coupling model is used to account for such changes of relaxation time of 1) ortho-terphenyl and poly(dimethyl siloxane) confined in nanometer pores, 2) polymer thin film confined between two impenetrable walls from Monte Carlo simulation, and 3) polymer film confined by perfectly smooth and purely repulsive potential acting on the repeat units from molecular-dynamics simulation. The model continues to explain the opposite effects observed when there is an increase of intermolecular coupling due to the presence of chemical or physical interaction with the walls.