Glass Transition Event Research Articles

Miscibility of Itraconazole-Hydroxypropyl Methylcellulose Blends: Insights with High Resolution Analytical Methodologies.

Drug-polymer miscibility is considered to be a prerequisite to achieve an optimally performing amorphous solid dispersion (ASD). Unfortunately, it can be challenging to evaluate drug-polymer miscibility experimentally. The aim of this study was to investigate the miscibility of ASDs of itraconazole (ITZ) and hydroxypropyl methylcellulose (HPMC) using a variety of analytical approaches. The phase behavior of ITZ-HPMC films prepared by solvent evaporation was studied before and after heating. Conventional methodology for miscibility determination, that is, differential scanning calorimetry (DSC), was used in conjunction with emerging analytical techniques, such as fluorescence spectroscopy, fluorescence imaging, and atomic force microscopy coupled with nanoscale infrared spectroscopy and nanothermal analysis (AFM-nanoIR-nanoTA). DSC results showed a single glass transition event for systems with 10% to 50% drug loading, suggesting that the ASDs were miscible, whereas phase separation was observed for all of the films based on the other techniques. The AFM-coupled techniques indicated that the phase separation occurred at the submicron scale. When the films were heated, it was observed that the ASD components underwent mixing. The results provide new insights into the phase behavior of itraconazole-HPMC dispersions and suggest that the emerging analytical techniques discussed herein are promising for the characterization of miscibility and microstructure in drug-polymer systems. The observed differences in the phase behavior in films prepared by solvent evaporation before and after heating also have implications for processing routes and suggest that spray drying/solvent evaporation and hot melt extrusion/melt mixing can result in ASDs with varying extent of miscibility between the drug and the polymer.

The glass transition of trinitrotoluene (TNT) by flash DSC

Flash differential scanning calorimetry has been used to determine the glass transition response of the rapidly crystallizing energetic material, TNT. After heating at 600K/s, it was found that for cooling rates from 1000K/s to 10K/s the glass transition changes from 247.5K to 239.3K. The dynamic fragility index was determined to be m=62±6 and the activation energy determined from the range of cooling rates in which vitrification occurred was found to be 290±16kJ/mol. Crystallization was found to occur during cooling at rates below 0.3K/s, whereas cold crystallization was found on subsequent heating after cooling between 10K/s and 30K/s. At cooling rates of 100K/s and above, and for the same heating rate of 600K/s investigated, the glass transition event was observed, but cold crystallization during heating did not occur. Hence, the crystallization behavior of the fully amorphous TNT upon heating depends on the cooling rate and vitrification path.

Nonisothermal crystallization kinetics, fragility and thermodynamics of Ti20Zr20Cu20Ni20Be20 high entropy bulk metallic glass

Abstract

Simultaneous improvement of solubility and permeability by fabricating binary glassy materials of Talinolol with Naringin: Solid state characterization, in-vivo in-situ evaluation

The aim of the current study was to prepare binary amorphous forms of Talinolol (TLN) by using Naringin (NRG) as a stabilizing agent. The secondary objective of this study was to study the effect of P-gp inhibitor NRG on the P-gp probe drug TLN. The binary amorphous samples were prepared by quench cooling technique in the molar ratios TLN:NRG (1:1), TLN:NRG (1:2), TLN:NRG (2:1). The prepared samples were characterized by DSC, FTIR and XRD. Amorphicity of the prepared binary amorphous samples was confirmed by spotting diffuse halo in the diffractograms and further corroborated by detecting glass transition event (Tg) in the thermograms of the respective samples. The Tgs for all prepared systems were found above room temperature, the highest being 45.43°C. The systems were found physically stable at 25°C and 40°C at dry conditions for 60days. The temperature stability of prepared amorphous forms may be attributed to strong intermolecular hydrogen bond interaction between TLN and NRG, which was confirmed by Gordon–Taylor calculations and FTIR data. The solubility of TLN in amorphous form was increased by approximately 9-fold as compared to its crystalline counterpart. The in-vivo bioavailability study conducted on wistar rats demonstrated 5.4-fold increase in the AUC0-t value for TLN as compared to its crystalline counterpart. Further to learn the contribution of P-gp inhibition by NRG on the permeability of TLN, In-vitro single pass perfusion studies were conducted on the ileum of wistar rats. The permeability of TLN in rat ileum in the presence of NRG was significantly increased to 3.16×10−5cm/s as compare to control value 2.48×10−5cm/s. The current study demonstrated the ability of binary amorphous technology to simultaneously overcome both the BCS barriers i.e. solubility and permeability.

Crystallization Kinetics of Indomethacin/Polyethylene Glycol Dispersions Containing High Drug Loadings.

The reproducibility and consistency of physicochemical properties and pharmaceutical performance are major concerns during preparation of solid dispersions. The crystallization kinetics of drug/polyethylene glycol solid dispersions, an important factor that is governed by the properties of both drug and polymer has not been adequately explored, especially in systems containing high drug loadings. In this paper, by using standard and modulated differential scanning calorimetry and X-ray powder diffraction, we describe the influence of drug loading on crystallization behavior of dispersions made up of indomethacin and polyethylene glycol 6000. Higher drug loading increases the amorphicity of the polymer and inhibits the crystallization of PEG. At 52% drug loading, polyethylene glycol was completely transformed to the amorphous state. To the best of our knowledge, this is the first detailed investigation of the solubilization effect of a low molecular weight drug on a semicrystalline polymer in their dispersions. In mixtures containing up to 55% indomethacin, the dispersions exhibited distinct glass transition events resulting from amorphous-amorphous phase separation which generates polymer-rich and drug-rich domains upon the solidification of supercooled polyethylene glycol, whereas samples containing at least 60% drug showed a single amorphous phase during the period in which crystallization normally occurs. The current study demonstrates a wide range in physicochemical properties of drug/polyethylene glycol solid dispersions as a result of the complex nature in crystallization of this system, which should be taken into account during preparation and storage.

Solution-State Polymer Assemblies Influence BCS Class II Drug Dissolution and Supersaturation Maintenance

Spray dried dispersions (SDDs), solid dispersions of polymer excipients and active pharmaceuticals, are important to the field of oral drug delivery for improving active stability, bioavailability, and efficacy. Herein, we examine the influence of solution-state polymer assemblies on amorphous spray-dried dispersion (SDD) performance with two BCS II model drugs, phenytoin and probucol. These drugs were spray dried with 4 model polymer excipients consisting of poly(ethylene-alt-propylene) (PEP), N,N,-dimethylacrylamide (DMA), or 2-methacrylamido glucopyranose (MAG): amphiphilic diblock ter- and copolymers, PEP-P(DMA-grad-MAG) and PEP-PDMA, and their respective hydrophilic analogues, P(DMA-grad-MAG) and PDMA. Selective and nonselective solvents for the hydrophilic block of the diblock ter- and copolymers were used to induce or repress solution-state assemblies prior to spray drying. Prespray dried solution-state assemblies of these four polymers were probed with dynamic light scattering (DLS) and showed differences in solution assembly size and structure (free polymer versus aggregates versus micelles). Solid-state structures of spray dried dispersions (SDDs) showed a single glass transition event implying a homogeneous mixture of drug/polymer. Crystallization temperatures and enthalpies indicated that the drugs interact mostly with the DMA-containing portions of the polymers. Scanning electron microscopy was used to determine SDD particle size and morphology for the various polymer-drug pairings. In vitro dissolution tests showed excellent performance for one system, spray-dried PEP-PDMA micelles with probucol. Dissolution structures were investigated through DLS to determine drug-polymer aggregates that lead to enhanced SDD performance. Forced aggregation of the polymer into regular micelle structures was found to be a critical factor to increase the dissolution rate and supersaturation maintenance of SDDs, and may be an attractive platform to exploit in excipient design for oral drug delivery.

Characterization, quantification and stability of differently prepared amorphous forms of some oral hypoglycaemic agents

The study deals with the investigation of possible differences induced in the physicochemical properties within the amorphous forms prepared by different methods. Enthalpy of solution measured by solution calorimetry was utilized to highlight the differences prevailing within the amorphous forms and to determine the percentage of amorphous content. Emphasis is laid on the quantification and physical stability of these forms. Amorphization was induced in poorly water-soluble oral hypoglycaemic agents (repaglinide, gliclazide and glipizide), by quench cooling, vaporization under reduced pressure and lyophilization. The amorphous nature was evident from a halo pattern in powder X-ray diffraction. A glass transition event is evident in differential scanning calorimetry thermograms of the amorphous forms of the three drugs. As expected, the amorphous forms show improvement in solubility and dissolution profiles. On subjecting these amorphous forms to different relative humidities at 25°C for three months and subsequent analysis showed that amorphous form of repaglinide prepared by quench cooling is most stable and has the potential to be formulated without any additive while amorphous form of gliclazide tends to devitrify pointing towards its unstable nature.

Molecular Weight Effects on the Miscibility Behavior of Dextran and Maltodextrin with Poly(vinylpyrrolidone)

To characterize and interpret the miscibility of dextran and maltodextrin with poly(vinylpyrrolidone) (DEX-PVP) as a function of polymer molecular weights. Blend miscibility was studied using 4 different molecular weight (MW) grades of DEX combined with 5 MW grades of PVP, over a broad compositional range. Miscibility was evaluated by inspection of glass transition events measured by differential scanning calorimetry (DSC). Fourier transform mid-infrared spectroscopy (FTIR), combined with curve fitting, was performed to characterize the extent of hydrogen bonding. The observed miscibility behavior was further interpreted in terms of mixing thermodynamics. Miscibility of the blends ranged from fully miscible to completely immiscible with multiple partially miscible systems observed. Increasing polymer molecular weight decreased miscibility. For the lowest DEX grade, hydrogen bonding was independent of PVP MW, as expected since all systems were completely miscible. Higher molecular weights of DEX resulted in reduced intermolecular hydrogen bonding and decreased miscibility, increasingly so for higher MW PVP grades. Evaluation of the mixing thermodynamics supported these findings. With higher combined molecular weights of DEX-PVP blends, phase behavior evolves from completely miscible to virtually immiscible. Concurrently, DEX-PVP hydrogen bonding decreases. From a thermodynamic perspective, the combinatorial mixing entropy was observed to decrease as the molecular weight of the polymers increased, providing a reduced counterbalance to the unfavorable mixing enthalpy thought to accompany this polymer combination.

Topological instability and glass forming ability of Al–Ni–Sm alloys

The thermal crystallization of Al-based metallic glasses can be described in association with the topological instability λ criterion. In the present work, we report on the crystallization behavior and glass forming ability of Al-rich, Al–Ni–Sm alloys, designed with compositions corresponding to the same topological instability condition of λ ≈ 0.1. Amorphous melt-spun alloys were prepared with the following compositions, varying the ratio of Ni and Sm elements: Al 87.5Ni 4Sm 8.5, Al 83.5Ni 10Sm 6.5, Al 80.5Ni 14.5Sm 5 and Al 76.5Ni 20.5Sm 3. The glass forming ability of each alloy composition was evaluated based on the thermal parameters obtained from DSC runs and on X-ray diffraction patterns. Better glass forming ability was observed in compositions whose Sm content was increased and Ni content reduced. Thermal crystallization of the alloys with low Sm content showed only one crystallization peak and no glass transition event. In alloys with higher rare-earth content, a glass transition event was clearly detected before the crystallization event. The results are interpreted considering the different types and proportions of Sm–Al and Ni–Al clusters that can be formed in the alloys along the λ ≈ 0.1 line. They also emphasize the relevance of these different types of clusters in the amorphous phase in defining the stability of the glass and the types of thermal crystallization.

Use of dynamic mechanical analysis (DMA) to determine critical transition temperatures in frozen biomaterials intended for lyophilization

Dynamic mechanical analysis is widely used to determine glass transitions in solid state materials. However, here we demonstrate the application of DMA for the determination of glass transitions (Tg ’) in the frozen liquid state by means of a steel sample pocket. The use of the pocket allows frozen material to be analysed and glass transition events demonstrated. In addition, it allows weak glass transitions to be detected clearly in some complex formulations where they can be obscured by eutectic and other strong thermal events when other methods such as DSC or DTA are used. Classical excipients (trehalose, lactose, dextran) were analysed and shown to give reproducible Tg ’ values, though with values slightly higher than those obtained by DSC. Finally, several complex real biological materials, typical of those encountered when freeze drying biological and biopharmaceutical materials, were analysed and the potential value of DMA demonstrated to determine the relevant glass transition temperatures for use in cryobiology and freeze drying.

Thermal stability and magnetocaloric effect of the Gd65Fe20Al15−xBx (x=–7) glassy ribbons

The thermal stability, magnetocaloric effect, and refrigeration capacity (RC) of Gd-based Gd65Fe20Al15−xBx (x=0–7) glassy ribbons have been investigated. A relatively wide supercooled liquid region ΔTx(ΔTx=Tx−Tg) (50–80 K) and large reduced glass transition temperature Trg(Trg=Tg/Tm) (>0.63) are found in Gd65Fe20Al15−xBx glassy ribbons. The distinctive glass transition and sharp crystalline events as well as large values of ΔTx and Trg confirm the excellent glass forming ability of these alloys. The maximal magnetic entropy changes, −ΔSMmax, and RC values of the specimens are about 4.80–5.21 J/kg K and 700–800 J/kg under 50 kOe, respectively. These −ΔSMmax values are comparable to or even higher than that of some reported bulk metallic glasses. Moreover, the larger RC values are due to the broad ΔSM peak (∼200 K), which is caused by the glassy structure. The large ΔSM and RC values make the Gd-based Gd65Fe20Al15−xBx glassy ribbons attractive candidates for magnetic refrigeration materials.

Kinetics of thermally-induced conformational transitions in soybean protein films

Abstract The thermally-induced conformational transitions of soybean protein films were studied as the films were heated under isothermal conditions in the range 40–100 °C. By comparing the kinetics of protein–water interactions as a function of temperature using time-resolved Fourier transform infrared (FTIR) spectroscopy, thermogravimetric analysis (TGA), and dynamic mechanical thermal analysis (DTMA) measurements on soybean protein films, we have shown that simply evaporating water from the film (TGA) is insufficient to explain the rate of conformational changes (FTIR and DMTA). We suggest that an elastic instability condition of denaturation or glass transition events in water-amide interactions is the governing mechanism for conformational changes that allows the evolution of disordered structures into more ordered secondary structures, thereby controlling the changes in physical properties such as stiffness and water sensitivity.

Investigation of molecular reorientation in poly(butylene terephthalate)/decylamine/fullerene nanocomposites

The relaxation processes as well as the properties of new polymer nanocomposites poly(butylene terephthalate)/decylamine/fullerene have been studied by the 1H nuclear magnetic resonance methods. The correlation times and the activation energies of molecular motions in the nanocomposites were determined. The thermal transitions (glass transition, crystallization and melting events) of these nanocomposites have been investigated by the differential scanning calorimetry (DSC).

Soft shape memory in main-chain liquid crystalline elastomers

The field of shape memory polymers (SMPs) has been dominated by polymeric network systems whose fixing mechanism is based on crystallization or vitrification of the constituent chains, rendering such systems stiff in comparison to elastomers, gels, and living tissues. In this report, we describe the synthesis and characterization of liquid crystalline elastomers that exhibit both bulk and surface shape memory effects with compositionally dependent transition temperatures that determine the shape fixing and shape recovery critical temperatures. Main-chain, segmented liquid crystalline elastomers were synthesized using hydrosilylation linking of poly(dimethylsiloxane) oligomers with mesogenic dienes of two compositions and a tetrafunctional crosslinker. Calorimetric and dynamic mechanical analyses revealed two composition-determined thermal transitions for the LCEs, including a glass transition event at low temperatures (33 °C < Tg < 48 °C) and a first-order isotropization transition at higher temperatures (57 °C < Ti < 71 °C), each increasing with an increase in the concentration of the more slender, unsubstituted mesogenic diene, 5H. Despite the existence of a glass transition event, the materials remain soft at low temperature, a finding explained by vitrification of only the mesogen-rich layers within the smectic phase. Shape memory behavior was evaluated quantitatively and revealed excellent shape fixing and shape recovery values, generally in excess of 98%, with the recovery temperature depending on composition in a manner determined by the LCE phase behavior, particularly Tg. The temperature-dependent kinetics of shape memory were analyzed for a selected LCE composition, revealing exponential time dependence with rate constants that depended on temperature in an Arrhenius manner. Finally, the softness of the LCE SMPs was exploited to fix an embossed, micron-scale pattern on the surface and then recover the equilibrium flat state quite completely. We envision application of this surface shape memory phenomenon in the areas of soft lithography, especially microcontact printing and microfluidics.

Characterisation of the thermal properties of ethylcellulose using differential scanning and quasi-isothermal calorimetric approaches

The thermal behaviour of the ethylcellulose (EC), a polymer that is widely used in pharmaceutical dosage forms, has been investigated with a view to study the glass transition and higher temperature thermal events as well as to develop new approaches to characterise this complex polymer system. Samples of EC powder were studied using conventional and modulated temperature differential scanning calorimetry (MTDSC), quasi-isothermal (Qi-)MTDSC and hot stage microscopy (HSM) with simultaneous transmitted light intensity measurements. The T g was noted at circa 128–130 °C, with an accompanying baseline drift associated with a temperature dependent heat capacity change. A higher temperature combined endo/exothermic event was noted at 170–190 °C. TGA studies indicated that the exotherm was associated with oxidative degradation, with the accompanying DSC data being highly dependent on the sample encapsulation method used. The endotherm was found to be kinetically hindered, as demonstrated using Qi-MTDSC; the technique also indicated that there was little evidence for reversing processes through this transition. HSM studies indicated birefringence for the sample at low temperatures which disappeared as the material temperature approached T g but reappeared on further heating, again disappearing at circa 180 °C. Light intensity scans produced a profile similar to that seen for the DSC studies. It is proposed that the sample contains microcrystals composed of unsubstituted segments of the cellulose backbone. The implications of these findings for the understanding of the pharmaceutical behaviour and thermal characterisation of ethylcellulose are discussed.

Phase Behavior of Poly(vinylpyrrolidone) Containing Amorphous Solid Dispersions in the Presence of Moisture

The objective of this study was to investigate the phase behavior of amorphous solid dispersions composed of a hydrophobic drug and a hydrophilic polymer following exposure to elevated relative humidity. Infrared (IR) spectroscopy, differential scanning calorimetry (DSC) and moisture sorption analysis were performed on five model systems (nifedipine-poly(vinylpyrrolidone) (PVP), indomethacin-PVP, ketoprofen-PVP, droperidol-PVP, and pimozide-PVP) immediately after production of the amorphous solid dispersions and following storage at room temperature and elevated relative humidity. Complete miscibility between the drug and the polymer immediately after solid dispersion formation was confirmed by the presence of specific drug-polymer interactions and a single glass transition (T(g)) event. Following storage at elevated relative humidity (75-94% RH), nifedipine-PVP, droperidol-PVP, and pimozide-PVP dispersions formed drug-rich and polymer-rich amorphous phases prior to crystallization of the drug, while indomethacin-PVP and ketoprofen-PVP dispersions did not. Drug crystallization in systems exhibiting amorphous-amorphous phase separation initiated earlier (<6 days at 94% RH) when compared to systems that remained miscible (>or=46 days at 94% RH). Evidence of moisture-induced amorphous-amorphous phase separation was observed following storage at as low as 54% RH for the pimozide-PVP system. It was concluded that, when an amorphous molecular level solid dispersion containing a hydrophobic drug and hydrophilic polymer is subjected to moisture, drug crystallization can occur via one of two routes: crystallization from the plasticized one-phase solid dispersion, or crystallization from a plasticized drug-rich amorphous phase in a two-phase solid dispersion. In the former case, the polymer is still present in the same phase as the drug, and can inhibit crystallization to a greater extent than the latter scenario, where the polymer concentration in the drug phase is reduced as a result of the amorphous-amorphous phase separation. The strength of drug-polymer interactions appears to be important in influencing the phase behavior.

A brief discussion: Thermodynamic and dynamic fragilities, non-divergent dynamics and the Prigogine–Defay ratio

Abstract This article brings together some of the work performed by the present author and collaborators that is related to the glass transition event and to some of its entropy aspects. The purpose of the work and discussion was motivated by a view that some of the frameworks in which we currently look at glassy behavior, while potentially useful, may also have limitations that we often do not fully consider. Discussion focuses on isochoric glass formation paths, thermodynamic and dynamic fragilities and how dynamic fragility in many systems (especially polymers, metals, ionic liquids and hydrogen bonding systems) seems to vary primarily with the glass transition temperature itself. This leads to the conclusion that such systems have an apparent activation energy that varies as the square of the glass temperature. The work then discusses evidence for a non-diverging relaxation time or viscosity as the glass temperature is approached and ends with a discussion of the Prigogine–Defay ratio.

Toward understanding the evolution of griseofulvin crystal structure to a mesophase after cryogenic milling

The purpose of this research is to investigate the response of crystalline griseofulvin to mechanically induced stress through cryogenic milling. Crystalline griseofulvin was subjected to cryogenic milling for two different lengths of time. Following cryo-milling, the samples were immediately analyzed by differential scanning calorimetry (DSC) and X-ray powder diffraction (XRPD). The DSC thermograms of cryo-milled griseofulvin showed a complex exothermic event at around 65 °C for the 30 min cryo-milled sample and around 75 °C for the 60 min cryo-milled sample. A glass transition event was not observed for the cryo-milled samples. This is in direct contrast to the X-ray amorphous griseofulvin sample prepared through the quench melt method The XRPD patterns of cryo-milled griseofulvin show a loss of the crystalline Bragg peaks and a corresponding increase in diffuse scattering (halos). The disordered griseofulvin material produced through cryo-milling appears X-ray amorphous, yet different from the amorphous phase produced using the quench melt method. Both X-ray amorphous materials have distinctive DSC thermograms and X-ray powder patterns. These findings suggest that the evolution of the griseofulvin crystal structure during cryo-milling is not simply a crystal-to-amorphous transition but a transition to an intermediate mesophase.

Laser deposition of a Cu-based metallic glass powder on a Zr-based glass substrate

Laser Engineered Net Shaping (LENS™) is a laser-assisted manufacturing process that offers the possibility of producing metallic coatings and components with highly nonequilibrium microstructures. In this work, the microstructure developed by LENS deposition of Cu47Ti33Zr11Ni8Si1 powder on a bulk metallic glass substrate, with nominal composition Zr58.5Nb2.8Cu15.6Ni12.8Al10.3, is investigated. Single-layer deposition results in the formation of an inhomogeneous but partially amorphous layer above a crystalline heat-affected zone. Elemental analysis of the deposited layer indicates incomplete mixing of the powder with the melt pool. The as-deposited alloy exhibits a single glass transition event and its primary crystallization event is consistent with the first crystallization temperature of the Cu-based powder. Subsequent remelting of this layer results in a still partially amorphous deposit with a uniform composition of (Zr + Nb)51.8Cu24.7Ti3.4Ni16.4Al3.7. The remelted layer exhibits a structural rearrangement immediately prior to the primary crystallization event, possibly associated with the formation of a quasicrystalline phase.

Development of fcc-Al nanocrystals in Al–Ni–Gd metallic glasses during continuous heating DSC scan

This paper examines the early crystallization stages in Al–Ni–Gd glass-forming alloys, especially in Al 87Ni 7Gd 6, Al 85Ni 7Gd 8 and Al 90Ni 5Gd 5, to more thoroughly quantify the mechanisms responsible for two-step fcc-Al nanocrystal formation phenomenon observed in certain amorphous Al alloys. Alloys were systematically studied using differential scanning calorimetry (DSC), X-ray diffraction (XRD), transmission electron microscopy (TEM), and high-resolution TEM techniques. It was found that a confined range of chemistries for Al–Ni–Gd alloys partially devitrified into fcc-Al nanocrystals during both the first and second stages. The morphology of fcc-Al nanocrystals evolves gradually from spherical to irregular as the bulk Al content is decreased, consistent with an earlier report [M.C. Gao, G.J. Shiflet, Scripta Mater. 53 (2005) 1129–1134]. The current study reveals a close relationship among crystallization behavior during continuous heating DSC, isothermal annealing and plastic deformation, especially on the compositional dependence. For alloys of high Al contents such as Al 87Ni 7Gd 6 whose first crystallization peak during a DSC scan spans a wide temperature range with a long decaying tail, the presence of medium-range Al clustering in the amorphous solid is responsible for exclusive formation of fcc-Al nanocrystals when annealed at low temperatures or when plastically deformed at room temperature and the absence of an apparent glass transition event. The morphology of the initially spherical nanocrystals evolves into irregular shapes after passing the first stage peak temperature. The fact that both particle number density and volume fraction keeps rising throughout both stages suggests continuous nucleation and crystal growth. For alloys of low Al contents such as Al 85Ni 7Gd 8, there is no sign of medium range Al clustering in the as-quenched state, and they exhibit a well-defined glass transition and a supercooled liquid regime. It is noted that the particle number density drops while the volume fraction rises during the second stage.