Microcalorimetric Measurement of the Interactions Between Water Vapor and Amorphous Pharmaceutical Solids

Purpose. Use a microcalorimetric technique to measure the interactions between water vapor and amorphous pharmaceutical solids and describe the relationship between long-term physical stability and the storage relative humidity (RH) at constant temperature. Methods. A thermal activity monitor was used to characterize interactions of water vapor with spray-dried amorphous sucrose, lactose, raffinose, and sodium indomethacin. Differential scanning calorimetry was used to measure glass transition temperature, T _g. X-ray powder diffraction was used to confirm that the spray-dried samples were amorphous. Scanning electron microscopy was used to examine particle morphology. Specific surface area was determined by BET analysis of nitrogen and krypton adsorption isotherms. Results. The moisture-induced thermal activity traces (MITATs) of the materials in this study exhibit general behavior that helps explain the effect of moisture content on the physical stability of the glassy phase at a given storage temperature. At some RH threshold, RH _m, the MITAT exhibits a dramatic increase in the energy of interaction between water vapor and the glass that cannot be explained by a phase or morphology change. Calorimetric data indicate that water vapor-solid interactions are reversible below RH _m; above RH _m, energetic hysteresis is observed and water-water interactions predominate. In addition, the MITAT was deconvoluted into sorptive and nonsorptive components, making it possible to assign the observed heat flow to unique thermal events. Samples stored at a RH just below RH _m for more than 2 months show no evidence of morphology or phase change. In addition, the MITAT can be deconvoluted into sorptive and nonsorptive components by using a twin-calorimeter arrangement. This analysis provides specificity to the microcalorimetric analysis and helps explain the nature of the physical changes that occur during the hydration glassy phase. Conclusions. The MITAT is a useful tool to determine the onset of moisture-induced physical instability of glassy pharmaceuticals and may find a broad application to determine appropriate storage conditions to ensure long-term physical stability.     

Effect of Polymer Content and Molecular Weight on the Morphology and Heat- and Moisture-Induced Transformations of Spray-Dried Composite Particles of Amorphous Lactose and Poly(vinylpyrrolidone)

Purpose. The aim was to investigate the influence of polymer content and molecular weight on the morphology and heat- and moisture-induced transformations, as indicators of stability, of spray-dried composite particles of amorphous lactose and poly(vinylpyrrolidone) (PVP). Methods. Amorphous lactose and composite particles of amorphous lactose with different contents and molecular weights of PVP were prepared by spray drying. The nanostructure of the particles was analyzed by x-ray powder diffractometry, the morphology by light microscopy and SEM, the glass transition temperatures (T_g), crystallization temperatures (T_c), heats of crystallization and melting temperatures by differential scanning calorimetry, and moisture-induced crystallizations gravimetrically and by microcalorimetry. Results. All the types of particles prepared were amorphous. The T_g was unchanged or only marginally increased as a result of the inclusion of PVP. However, crystallization temperature, time to moisture-induced crystallization, and particle morphology were affected by both content and molecular weight of PVP. Conclusions. Increased content and molecular weight of PVP may have the potential to increase the physical stability of amorphous lactose. However, T_g seems not to be a relevant indicator for the stability of this type of amorphous composite materials.     

Dynamics of pharmaceutical amorphous solids: the study of enthalpy relaxation by isothermal microcalorimetry

The structural relaxation time is a measure of the molecular mobility involved in enthalpy relaxation, and thus, is a measure of the dynamics of amorphous (glassy) pharmaceutical solids that determines physicochemical properties and reactivity of drugs in amorphous formulations. In this article we describe a novel method for characterization of structural relaxation using isothermal microcalorimetry, which directly measures the rate of heat release during the relaxation processes. The structural relaxation time is then obtained from a fit of the power data to the derivative version of the Kohlrausch-Williams-Watts (KWW) equation. The relaxation times of quenched and lyophilized samples of saccharides were studied using an isothermal microcalorimeter, the Thermal Activity Monitor (TAM). In addition to the KWW derivative function, a derivative equation of the modified stretched exponential function (MSE) was employed to evaluate TAM data. The later (MSE) appeared to have numerical advantages over the KWW equation. The data demonstrate, as expected, that structural relaxation times of amorphous solids depend on a number of variables, including nature of material, temperature, moisture content, thermal history, etc. Isothermal microcalorimetry with the TAM provides a very fast and reliable way to characterize the dynamics of glassy materials, which in many respects is superior to the conventional DSC approach. To the extent stability and structural relaxation dynamics in the glass are correlated, structural relaxation parameters derived by isothermal microcalorimetry may provide data useful for rational development of stable peptide and protein formulations and for the control of their processing.     

Effect of Preparation Method on Physical Properties of Amorphous Trehalose

PURPOSE: To determine the effect of preparation method on the physical properties of amorphous trehalose. METHODS: Amorphous anhydrous trehalose was prepared by four different methods. viz., freeze-drying, spray-drying, dehydration, and melt quenching. The glass transition temperature (Tg), enthalpic relaxation behavior, and crystallization were studied by differential scanning calorimetry, whereas X-ray diffractometry was used for phase identification. The rate and extent of water uptake at different relative humidity values were also obtained. RESULTS: Though the enthalpic relaxation and crystallization behaviors were influenced by the method of preparation of amorphous trehalose, the Tg and fragility were not. The phase prepared by dehydration showed the highest enthalpic recovery at Tg, indicating that aging may have occurred during preparation. Among the four methods used, trehalose prepared by dehydration had the highest tendency to crystallize, whereas there was no crystallization in melt-quenched amorphous trehalose. The method of preparation influenced not only the rate and extent of water sorption but also the phase crystallized. Water vapor sorption removed the effects of structural history in the amorphous phase formed by dehydration. CONCLUSIONS: The method of preparation strongly influenced the pharmaceutically relevant properties of amorphous trehalose. The resistance to crystallization can be rank ordered as trehalose prepared by dehydration < freeze-dried approximately spray-dried < melt-quenched. The rate of water sorption can be rank ordered as trehalose prepared by dehydration < freeze-dried < spray-dried.     

Enthalpy Relaxation in Binary Amorphous Mixtures Containing Sucrose

Purpose. To compare the enthalpy relaxation of amorphous sucrose and co-lyophilized sucrose-additive mixtures near the calorimetric glass transition temperature, so as to measure the effects of additives on the molecular mobility of sucrose. Methods. Amorphous sucrose and sucrose-additive mixtures, containing poly(vinylpyrrolidone) (PVP), poly(vinylpyrrolidone-co-vinyl-acetate) (PVP/VA) dextran or trehalose, were prepared by lyophilization. Differential scanning calorimetry (DSC) was used to determine the area of the enthalpy recovery endotherm following aging times of up to 750 hours for the various systems. This technique was also used to compare the enthalpy relaxation of a physical mixture of amorphous sucrose and PVP. Results. Relative to sucrose alone, the enthalpy relaxation of co-lyophilized sucrose-additive mixtures was reduced when aged for the same length of time at a comparable degree of undercooling in the order: dextran PVP > PVP/VA > trehalose. Calculated estimates of the total enthalpy change required for sucrose and the mixtures to relax to an equilibrium supercooled liquid state (H) were essentially the same and were in agreement with enthalpy changes measured at longer aging times (750 hours). Conclusions. The observed decrease in the enthalpy relaxation of the mixtures relative to sucrose alone indicates that the mobility of sucrose is reduced by the presence of additives having a T_g that is greater than that of sucrose. Comparison with a physically mixed amorphous system revealed no such effects on sucrose. The formation of a molecular dispersion of sucrose with a second component, present at a level as low as 10%, thus reduces the mobility of sucrose below T_g, most likely due to the coupling of the molecular motions of sucrose to those of the additive through molecular interactions.     

Molecular Mobility of Amorphous Pharmaceutical Solids Below Their Glass Transition Temperatures

Purpose. To measure the molecular mobility of amorphous pharmaceutical solids below their glass transition temperatures (Tg), using indomethacin, poly (vinyl pyrrolidone) (PVP) and sucrose as model compounds. Methods. Differential scanning calorimetry (DSC) was used to measure enthalpic relaxation of the amorphous samples after storage at temperatures 16-47 K below Tg for various time periods. The measured enthalpy changes were used to calculate molecular relaxation time parameters. Analogous changes in specimen dimensions were measured for PVP films using thermomechanical analysis. Results. For all the model materials it was necessary to cool to at least 50 K below the experimental Tg before the molecular motions detected by DSC could be considered to be negligible over the lifetime of a typical pharmaceutical product. In each case the temperature dependence of the molecular motions below Tg was less than that typically reported above Tg and was rapidly changing. Conclusions. In the temperature range studied the model amorphous solids were in a transition zone between regions of very high molecular mobility above Tg and very low molecular mobility much further below Tg. In general glassy pharmaceutical solids should be expected to experience significant molecular mobility at temperatures up to fifty degrees below their glass transition temperature.     

Effect of Aging on the Physical Properties of Amorphous Trehalose

PURPOSE: The purpose of this investigation was i) to study the effect of physical aging on crystallization and water vapor sorption behavior of amorphous anhydrous trehalose prepared by freeze-drying, and ii) to determine the effects of water sorption on the relaxation state of the aged material. METHODS: Freeze-dried trehalose was aged at 100 dgrees C for varying time periods to obtain samples with different degrees of relaxation. The glass transition temperature (Tg) and enthalpic relaxation were determined by differential scanning calorimetry, and the rate and extent of water uptake at different relative humidity values were quantified using an automated vapor sorption balance. RESULTS: Annealing below the Tg caused nucleation in the amorphous trehalose samples, which decreased the crystallization onset temperature on subsequent heating. However, no crystallization was observed below the Tg even after prolonged annealing. Physical aging caused a decrease in the rate and extent of water vapor sorption at low relative humidity values. Moreover, the water sorption removed the effects of physical aging, thus effectively causing enthalpic recovery in the aged samples. This recovery occurred gradually in the glassy phase and was not associated with a glass to rubber transition. We believe this aging reversal to be due to volume expansion during water sorption in the amorphous structure. CONCLUSIONS: Thermal history of amorphous materials is a crucial determinant of their physical properties. Aging of amorphous trehalose led to nucleation below the Tg, and decrease in rate and extent of water sorption. Sorption of water resulted in irreversible changes in the relaxation state of the aged material.     

Direct Observation of the Enthalpy Relaxation and the Recovery Processes of Maltose-Based Amorphous Formulation by Isothermal Microcalorimetry

Purpose. The applicability of isothermal microcalorimetry (IMC) for evaluating enthalpy relaxation and recovery processes of amorphous material was assessed. Methods. A maltose-based formulation was prepared by freeze-dry method. Differential scanning calorimetry (DSC) was used to investigate its glass transition and relaxation behaviors. IMC was applied to quantitatively analyze the relaxation and the recovery processes. The IMC data were analyzed using a derivative of the Kohlrausch-Williams-Watts equation. Results. The glass transition temperature of the formulation and its fictive temperature stored at 15°C for 1 year were 62 and 32°C, respectively. DSC study showed that annealing below the fictive temperature increased the enthalpy recovery, but it was decreased by annealing at higher temperatures. IMC enabled direct observation of the heat flow during both the relaxation and the recovery processes. The decay constant for the recovery process (recovery time) was much smaller and less sensitive to the temperature than that for the relaxation process (relaxation time). Conclusions. IMC was successfully used to obtain quantitative information on both relaxation and recovery processes of amorphous material. The relaxation parameters obtained by this method could explain the thermodynamic behavior of the formulation.     

Moisture-induced surface crystallization of spray-dried amorphous lactose particles studied by atomic force microscopy

The aim of this study was to show that atomic force microscopy (AFM) can be used to obtain mechanistic and kinetic information about the process of moisture-induced surface crystallization of single particles of amorphous lactose. Completely amorphous lactose particles were prepared by spray-drying a solution of alpha-lactose monohydrate, and moisture-induced crystallization was monitored for a bed of particles by microcalorimetry and for single particles by AFM. From the AFM images it was found that crystallization of the surface of single particles can be described in terms of a sequence of three events: an initial smoothening of the surface, formation of crystalline nanostructures dispersed in amorphous material, and growth of these structures to a complete crystalline surface. The surface roughness parameter rugosity was used to estimate the fraction crystalline surface, and the growth kinetics were found to obey the JMAK equation. The fraction crystalline surface at different times could also be estimated by determining the growth rate of individual crystals. It was concluded that AFM offers a unique means of visualizing the process of moisture-induced surface crystallization of amorphous particles and enables mechanistic and kinetic information about the process to be extracted.     

The quantification of small degrees of disorder in lactose using solution calorimetry

There is a realisation that small quantities of amorphous material can have a significant impact on the properties of crystalline solids. Consequently there is a growing interest in quantifying the amount of amorphous material that is present in "crystalline powders". Success has been reported when using isothermal microcalorimetry and vapour sorption techniques, however, the use of solution calorimetry has largely been ignored. In this study the enthalpies of solution of mixtures of amorphous and crystalline lactose are reported concentrating on the range 0-10% w/w amorphous content. It was found that there was a possible error due to water vapour penetration into the ampoule, resulting in crystallisation of the amorphous content, however this was overcome by double sealing the ampoules with wax. Subsequently there was a good correlation between the enthalpy of solution and the amorphous content, which was not adversely affected by stirring rate used during the experiment. Over the range from 0 to 10% amorphous content, quantification of the amorphous content of an unknown would be good to +/-0.5%. The effects of residual moisture retained within a sample were also investigated. Storage at 33% or 43% RH resulted in a much reduced wetting (exothermic) response compared with that seen for completely dry samples, which in turn led to a higher net enthalpy of solution.     

Molecular Mobility as a Predictor of the Water Sorption by Annealed Amorphous Trehalose

Purpose

The work aims at investigating the correlation of water sorption potential with different measures of molecular mobility in an annealed amorphous model compound (trehalose).

Methods

Amorphous trehalose, prepared by freeze-drying, was annealed at 100°C (17°C < T _g) for up to 120 h. Global molecular mobility was studied using a broadband dielectric spectrometer in the frequency range of 10⁶–10^?2?Hz. Enthalpic recovery was measured by differential scanning calorimetry and water sorption profiles were obtained using an automated vapor sorption balance.

Results

As a function of annealing time, there was an increase, both in average α-relaxation time and enthalpic recovery and a decrease in the amount of sorbed water. A strong linear correlation was observed between the water sorption potential and the dielectric relaxation time, indicating a common underlying mechanism of the effect of annealing time on these properties. Enthalpic recovery, which is widely used as a measure of structural relaxation, did not correlate well with the extent of water sorption.

Conclusions

The α-relaxation time can be used as a predictor of the water sorption potential of amorphous trehalose. It will be of interest and value to develop such predictive models for other amorphous compounds of pharmaceutical interest.     

Coupling Between Chemical Reactivity and Structural Relaxation in Pharmaceutical Glasses

Purpose To test the hypothesis that the molecular motions associated with chemical degradation in glassy amorphous systems are governed by the molecular motions associated with structural relaxation. The extent to which a chemical process is linked to the motions associated with structural relaxation will depend on the nature of the chemical process and molecular motion requirements (e.g., translation of a complete molecule, rotational diffusion of a chemical functional group). In this study the chemical degradation and molecular mobility were measured in model systems to assess the degree of coupling between chemical reactivity and structural relaxation. The model systems included pure amorphous cephalosporin drugs, and amorphous molecular mixtures containing a chemically labile drug and an additive expected to moderate molecular mobility.Methods Amorphous drugs and mixtures with additives were prepared by lyophilization from aqueous solution. The physical properties of the model systems were characterized using optical microscopy and differential scanning calorimetry. The chemical degradation of the drugs alone and in mixtures with additives was measured using high-performance liquid chromatography (HPLC). Molecular mobility was measured using isothermal microcalorimetry to measure enthalpy changes associated with structural relaxation below T _g.Results A weak correlation between the rates of degradation and structural relaxation times in pure amorphous cephalosporins suggests that reactivity in these systems is coupled to molecular motions in the glassy state. However, when sucrose was added to one of the cephalosporin drugs stability improved even though this addition reduced T _g and the relaxation time constant, , suggesting that there was no correlation between reactivity and structural relaxation in the cephalosporin mixtures. In contrast, the rate of ethacrynate sodium dimer formation in mixtures was more strongly coupled to the relaxation time constant, .Conclusions These studies suggest that the extent to which chemical degradation is coupled to structural relaxation in glasses motions is determined by how closely the motions of the rate controlling step in chemical degradation are associated with structural relaxation. Moderate coupling between the rate of dimer formation for ethacrynate sodium in mixtures with sucrose, trehalose and PVP and structural relaxation constants suggests that chemical changes that require more significant molecular motion, and includes at least some translational diffusion, are more strongly coupled to the molecular motions associated with structural relaxation. The observation that sucrose stabilizes cefoxitin sodium even though it lowers T _g and reduces the relaxation time constant, is perhaps a result of the importance of other kinds of molecular motions in determining the chemical reactivity in glasses.     

Pharmaceutical micro-particles give amorphous sucrose higher physical stability

The aim of this study was to explore how pharmaceutical micro-sized filler particles affect the amorphous stability of sucrose in sucrose/filler particle composites produced by freeze-drying. Focus was put on the filler particles' properties crystallinity, hygroscopicity, hydrophobicity, and surface area, and their influence on physical stability of the amorphous phase. The micro-sized filler particles were examined with Blaine permeametry, gas adsorption, pycnometry, gravimetric vapour sorption, X-ray diffraction, and light microscopy before composites of sucrose and micro-sized filler particles were prepared by freeze-drying. The stability of the composites was examined with X-ray diffraction, differential scanning calorimetry (DSC), and microcalorimetry. All composites were amorphous and showed higher stability compared to pure amorphous sucrose, which was evident from a delay in heat and moisture-induced crystallization. However, calcium carbonate and oxazepam micro-sized filler particles lost their ability to stabilize the amorphous sucrose when exposed to humidity. The dry glass transition temperature (T(g)) was higher for the composites, indicating the stabilization was mediated by a reduced molecular mobility of the amorphous phase.     

Characterization and quantification of amorphous material in milled and spray-dried salbutamol sulfate: a comparison of thermal, spectroscopic, and water vapor sorption approaches

A study has been undertaken using a range of established and novel approaches to examine the effects of milling on the structure and crystallization behavior of salbutamol sulfate. A combination of modulated temperature differential scanning calorimetry, attenuated total reflectance Fourier-transform infrared spectroscopy, powder X-ray diffraction, and gravimetric vapor sorption analysis have been employed, with a particular view to examining the validity of using spray-dried material as a comparator. Although the expected increase in amorphization with milling time was observed, several unexpected observations were made including an apparently anomalous relationship between glass transition temperature and water content; this was used as the basis for the development of a novel method of quantifying amorphous content. Reasonable agreement was found between the data obtained from the spectroscopic and thermal methods, particularly those latter approaches that do not rely on recrystallization for quantification. The activation energy for the onset process was determined and found to be similar for all materials studied. The study has indicated that when using spray-dried material as a standard, the associated limitations must be appreciated, particularly in terms of the assumption of comparability of the recrystallization process between materials that is embedded in many quantification techniques.     

Enthalpy Relaxation Studies of Celecoxib Amorphous Mixtures

Purpose. The purpose of this study was to compare the structural relaxation and molecular mobility of amorphous celecoxib (CEL) with that of CEL amorphous mixtures consisting of various excipients and to study the effect of different excipients on the relaxation of high-energy amorphous systems. Methods. The measurement of glass transition temperatures (Tg) and enthalpy relaxation were performed using differential scanning calorimetry. The interactions between drug and excipients and the absence of crystalline forms were further confirmed by conducting Fourier transform infrared spectroscopic and X-ray powder diffraction studies on same samples. Results. All samples exhibited a single Tg value. Polymers had a prominent effect on the lowering of the relaxation rate in amorphous CEL. The lowering of the rate of relaxation was directly dependent on the concentration and type of polymer used. The total enthalpy required for relaxation was same, although additives affected the rate of relaxation. Conclusions. In absence of any specific interactions during Fourier transform infrared studies, it was concluded that the antiplasticizing activity of polymers is responsible for the stabilization of CEL amorphous systems. Glassy amorphous dispersions of CEL exhibited a complex type of relaxation pattern, which failed to fit in Kohlrausch-Williams-Watts equation with respect to calculation of relaxation time constants.     

Water sorption behavior of lyophilized protein–sugar systems and implications for solid-state interactions

This study examines the water sorption behavior of proteins co-lyophilized with sugar/polyol excipients. Gravimetric sorption analysis (GSA) was used to measure water sorption of the lyophilized mixtures and these data allowed for calculation of the water monolayer (M₀). Lyophilized protein–mannitol mixtures behaved as predicted from the data for the pure components. Mannitol was shown to crystallize upon lyophilization. For protein co-lyophilized with sucrose or trehalose, which remain amorphous upon lyophilization, M₀ tended to be lower than that expected based on contributions of the pure protein and sugar. This negative deviation supports the view that amorphous sugars and pharmaceutical proteins interact in the solid state in such a way as to reduce the availability of water-binding sites. At high relative humidities (rh), sucrose and trehalose were susceptible to moisture-induced crystallization. When co-lyophilized protein was present, the GSA data revealed that this crystallization required a higher rh, or did not occur. For the temperature-induced (non-isothermal) sucrose crystallization, which was studied by differential scanning calorimetry, it was found that the temperature of crystallization tended to increase with an increasing amount of protein. The tendency to crystallize rose in the presence of elevated moisture, whether or not protein was present, likely due to the ability of water to plasticize the solid phase.     

Molecular Mobility of Supercooled Amorphous Indomethacin,Determined by Dynamic Mechanical Analysis

Purpose. To determine the viscosity and the frequency-dependent shear modulus of supercooled indomethacin as a function of temperature near and above its glass transition temperature and from these data to obtain a quantitative measure of its molecular mobility in the amorphous state. Methods. Viscoelastic measurements were carried with a controlled strain rheometer in the frequency domain, at 9 temperatures from 44° to 90°C. Results. The viscosity of supercooled indomethacin shows a strong non-Arrhenius temperature dependence over the temperature range studied, indicative of a fragile amorphous material. Application of the viscosity data to the VTF equation indicates a viscosity of 4.5 × 10¹⁰ Pa.s at the calorimetric Tg of 41°C, and a T₀ of –17°C. From the complex shear modulus and the Cole-Davidson equation the shear relaxation behaviour is found to be non-exponential, and the shear relaxation time at Tg is found to be approximately 100 sec. Conclusions. Supercooled indomethacin near and above its Tg exhibits significant molecular mobility, with relaxation times similar to the timescales covered in the handling and storage of pharmaceutical products.     

Stability and Solubility of Celecoxib-PVP Amorphous Dispersions: A Molecular Perspective

PURPOSE: The purpose of the current study is to evaluate the solubility advantage offered by celecoxib (CEL) amorphous systems and to characterize and correlate the physical and thermodynamic properties of CEL and its amorphous molecular dispersions containing poly(vinylpyrrolidone) (PVP). METHODS: The measurement of crystalline content, glass transition temperatures, and enthalpy relaxation was performed using differential scanning calorimetry. Solubility and dissolutions studies were conducted at 37 degrees C to elucidate release mechanisms. Further, the amorphous systems were characterized by polarized light microscopy and X-ray powder diffraction studies. RESULTS: The PVP content has a prominent effect on the stability and solubility profiles of amorphous systems. A dispersion of 20% w/w PVP with CEL resulted in a maxima in terms of solubility enhancement and lowering of relaxation enthalpy. The release of drug from amorphous molecular dispersions was found to be drug-dependent and independent of the carrier. CONCLUSIONS: The solubility enhancement and enthalpy relaxation studies with respect to PVP concentration helped in a better prediction of role of carrier and optimization of concentration in the use of solid dispersions or amorphous systems. The drug release mechanism is drug-controlled rather than carrier-controlled.     

Prediction of the onset of crystallization of amorphous sucrose below the calorimetric glass transition temperature from correlations with mobility

The objective of the present work is to determine if crystallization onset observed for an amorphous solid correlate with relaxation time at temperatures above and below the calorimetric glass transition (T(g)). Crystallization onset of spray-dried and freeze-dried amorphous sucrose were measured calorimetrically. Relaxation times measured in two temperature ranges by different techniques (isothermal calorimetry, dielectric spectroscopy) followed the expected modified Vogel-Tammann-Fulcher (VTF) behavior when extrapolated to a temperature near T(g). However, the change in slope was more conspicuous for freeze-dried sucrose, indicating that amorphous materials generated using different techniques differ in their mobilities for temperatures below T(g). Dielectric relaxation time values obtained above T(g) were well correlated to onset of crystallization. The model predicted 21 days for crystallization onset for spray-dried samples stored 7 K below T(g), compared to the experimentally observed crystallization onset of 17 days. Onset times versus temperature for freeze-dried sucrose, however, show a change in slope on approaching T(g), with the onsets somewhat decoupling from measured mobility for temperatures below T(g). Molecular mobility in amorphous materials at temperatures both above and below T(g) can be correlated to macroscopic physical change such as crystallization, but prediction of crystallization onset from relaxation time is only qualitatively correct at temperatures well below T(g).