Isothermal Crystallization and Time-Temperature Transformation of Amorphous Nifedipine: A Case of Polymorphism Formation and Conversion.

Crystallization of active pharmaceutical ingredients (APIs) from the supercooled liquid state is an important issue in determining the stability of amorphous pharmaceutical dispersions. In the present study, the isothermal crystallization from the supercooled liquid state of the pharmaceutical compound nifedipine was investigated by both rheological and differential scanning calorimetry (DSC) measurements, and the crystallization kinetics was fitted to the Johnson-Mehl-Avrami (JMA) equation. Both the crystallization induction time and completion time from the two methods were used to construct the time-temperature-transformation (TTT) diagram for nifedipine. A model based on a modification of classical homogeneous nucleation and crystal growth theory was employed to fit the induction and completion time curves. Both DSC and rheological methods give similar results for the crystallization kinetics of the nifedipine. From the crystallization kinetics modeling, the solid-liquid interfacial surface tension σSL of nifedipine was estimated and the value was found to be consistent with prior results obtained from melting point depression measurements as a function of crystal size. Evidence is shown that for temperatures below 110 °C, at the early stage of nucleation, NIF first nucleates into the metastable ß'-form and later converts into the stable α-form during the isothermal crystallization. We are also able to report the heat of fusion of the γ'-NIF based on the calorimetric experiments.

Isothermal Crystallization Monitoring and Time-Temperature-Transformation of Amorphous GDC-0276: Differential Scanning Calorimetric and Rheological Measurements.

Cold crystallization of amorphous pharmaceuticals is an important aspect in the search to stabilize amorphous or glassy compounds used as amorphous pharmaceutical ingredients (APIs). In the present work, we report results for the isothermal crystallization of the compound GDC-0276 based on differential scanning calorimetric and rheometric measurements. The kinetics of isothermal crystallization from the induction time to the completion of crystallization can be described by the classic Johnson-Mehl-Avrami (JMA) equation. The time-temperature-transformation (TTT) diagrams were constructed for two time points-that of induction and that of completion of crystallization. The results show that the rheological measurement for GDC-0276 has a better overall sensitivity in detection of the early stage nucleation and, consequently, detects the onset of crystallization sooner than does the differential scanning calorimetry. Rheological measurements were also used to obtain the temperature dependence of the viscosity of GDC-0276 and the relevant parameters were used in a modified form of the JMA model to describe the temperature dependence of the crystal induction and completion times, that is, the TTT diagram for the material. In the modification, we assumed that the kinetics followed the viscosity to the 0.75 power as suggested by the recent work of Huang et al. (Huang, C., et al., J. Chem. Phys.2018,149, 054503). The relationship and the possible impact on crystallization kinetics of the break-down of the Stokes-Einstein relation in glass-forming liquids are discussed. From the crystallization kinetics modeling, the solid-liquid interfacial surface tension σSL was obtained for GDC-0276 and was compared with that obtained from the melting point depression measurements of the material confined in nanoporous glasses. The differences between the values from the two methods are discussed.

Prediction of the Synergistic Glass Transition Temperature of Coamorphous Molecular Glasses Using Activity Coefficient Models.

The glass transition temperature (Tg) of a binary miscible mixture of molecular glasses, termed a coamorphous glass, is often synergistically increased over that expected for an athermal mixture due to the strong interactions between the two components. This synergistic interaction is particularly important for the formulation of coamorphous pharmaceuticals since the molecular interactions and resulting Tg strongly impact stability against crystallization, dissolution kinetics, and bioavailability. Current models that describe the composition dependence of Tg for binary systems, including the Gordon-Taylor, Fox, Kwei, and Braun-Kovacs equations, fail to describe the behavior of coamorphous pharmaceuticals using parameters consistent with experimental ΔCP and Δα. Here, we develop a robust thermodynamic approach extending the Couchman and Karasz method through the use of activity coefficient models, including the two-parameter Margules, non-random-two-liquid (NRTL), and three-suffix Redlich-Kister models. We find that the models, using experimental values of ΔCP and fitting parameters related to the binary interactions, successfully describe observed synergistic elevations and inflections in the Tg versus composition response of coamorphous pharmaceuticals. Moreover, the predictions from the NRTL model are improved when the association-NRTL version of that model is used. Results are reported and discussed for four different coamorphous systems: indomethacin-glibenclamide, indomethacin-arginine, acetaminophen-indomethacin, and fenretinide-cholic acid.

Mechanical spectral hole burning in glassy polymers-Investigation of polycarbonate, a material with weak ß-relaxation.

Mechanical spectral hole burning (MSHB) has been used to investigate the nonlinear dynamics in polymers, ranging from melts, solutions, block co-polymers, and glasses. MSHB was developed as an analog to the dielectric spectral hole burning method, which is not readily applicable in polymers due to weak dielectric response. While similar holes were observed in both mechanical and dielectric hole burning, the interpretations were different. In the latter case, it has been argued that the holes are related to dynamic heterogeneity as related to an increase in the local temperature of molecular sub-ensembles (spatial heterogeneity), while in the former case, the holes have been related to the type of dynamics (rubbery, Rouse, etc.). Recent work from our laboratories used MSHB to investigate glassy poly(methyl methacrylate) and showed evidence of hole burning and supported the hypothesis that the origin of holes was related to dynamic heterogeneity as evidenced by the holes being developed near the strong ß-relaxation in PMMA. In this work, MSHB is used to study polycarbonate, which has a weak ß-relaxation, and the results are compared with those observed in PMMA. We observe that the polycarbonate exhibits weak holes and the nature of the holes with a change in pump amplitude and frequency is different than observed in PMMA. These results support the hypothesis that the hole burning observed in amorphous polymers below the glass transition temperature is related to the strength of the ß-transition, which, in turn, is related to molecular level heterogeneity in the material dynamics.

The Laplace approach in microrheology.

When coupled with the generalized Stokes-Einstein (GSE) equation, it is often reported that micro-rheology probes the dynamic properties differently than do macroscopic rheological measurements, especially in relatively condensed systems. In the present work, we empirically examine the GSE in its widely used form: following an analytical continuation, the Fourier transformed particle mean-square displacement (MSD) is used to determine the dynamic moduli [G'(ω) and G''(ω)] and we compare the results with those obtained by direct inverse Laplace transform calculation of the relevant viscoelastic functions (either relaxation modulus or creep compliance) from the MSD. The results show that the inverse Laplace approaches can differ from the Fourier approach and give better agreement with macroscopic rheological measurements when this is the case. Some instances of agreement between the Fourier approach and the direct Laplace transform approaches are also shown. It is recommended that micro-rheology MSD data be interpreted using one of the direct Laplace transform based approaches.

"Dense diffusion" in colloidal glasses: short-ranged long-time self-diffusion as a mechanistic model for relaxation dynamics.

Despite decades of exploration of the colloidal glass transition, mechanistic explanation of glassy relaxation processes has remained murky. State-of-the-art theoretical models of the colloidal glass transition such as random first order transition theory, active barrier hopping theory, and non-equilibrium self-consistent generalized Langevin theory assert that relaxation reported at volume fractions above the ideal mode coupling theory prediction φg,MCT requires some sort of activated process, and that cooperative motion plays a central role. However, discrepancies between predicted and measured values of φg and ambiguity in the role of cooperative dynamics persist. Underlying both issues is the challenge of conducting deep concentration quenches without flow and the difficulty in accessing particle-scale dynamics. These two challenges have led to widespread use of fitting methods to identify divergence, but most a priori assume divergent behavior; and without access to detailed particle dynamics, it is challenging to produce evidence of collective dynamics. We address these limitations by conducting dynamic simulations accompanied by experiments to quench a colloidal liquid into the putative glass by triggering an increase in particle size, and thus volume fraction, at constant particle number density. Quenches are performed from the liquid to final volume fractions 0.56 ≤ φ ≤ 0.63. The glass is allowed to age for long times, and relaxation dynamics are monitored throughout the simulation. Overall, correlated motion acts to release dynamics from the glassy plateau - but only over length scales much smaller than a particle size - allowing self-diffusion to re-emerge; self-diffusion then relaxes the glass into an intransient diffusive state, which persists for φ < 0.60. We observe similar relaxation dynamics up to φ = 0.63 before achieving the intransient state. We find that this long-time self-diffusion is short-ranged: analysis of mean-square displacement reveals a glassy cage size a fraction of a particle size that shrinks with quench depth, i.e. increasing volume fraction. Thus the equivalence between cage size and particle size found in the liquid breaks down in the glass, which we confirm by examining the self-intermediate scattering function over a range of wave numbers. The colloidal glass transition can hence be viewed mechanistically as a shift in the long-time self-diffusion from long-ranged to short-ranged exploration of configurations. This shift takes place without diverging dynamics: there is a smooth transition as particle mobility decreases dramatically with concomitant emergence of a dense local configuration space that permits sampling of many configurations via local particle motion.

Mechanical hole-burning spectroscopy of PMMA deep in the glassy state.

Nonlinear mechanics of soft materials such as polymer melts or polymer solutions are frequently investigated by Large Amplitude Oscillatory Shear (LAOS) spectroscopy tests. Less work has been reported on the characterization of the nonlinear viscoelastic properties of glassy polymers within a similar framework. In the present work, we use an extension of LAOS, i.e., mechanical spectral hole burning (MSHB), to investigate the nonlinear dynamics of an amorphous polymer in the deep glassy state. MSHB was developed as an analog to non-resonant spectral hole burning developed by Schiener et al. [Science 274(5288), 752-754 (1996)], who attributed the presence of holes to dynamic heterogeneity. On the other hand, Qin et al. [J. Polym. Sci., Part B: Polym. Phys. 47(20), 2047-2062 (2009)] in work on polymer solutions of tailored heterogeneity have attributed the presence of holes to the type of dynamics (Rouse, rubbery, etc.) rather than to a specific spatial heterogeneity. Here, we have performed MSHB experiments on poly(methyl methacrylate) in the deep glassy state (at ambient temperature, which is near to the ß-relaxation) to investigate the presence and origin of holes, if any. The effects of pump frequency and pump amplitude were investigated, and we find that vertical holes could be burned successfully for frequencies from 0.0098 Hz to 0.0728 Hz and for pump amplitudes from 2% to 9% strain. On the other hand, horizontal holes were incomplete at high pump amplitude and low frequency, where higher spectral modification is observed. The results are interpreted as being related to the dynamic heterogeneity corresponding to the ß-relaxation rather than to the hysteresis energy absorbed in the large deformation pump.

Nanoconfinement Effects on the Glass Transition and Crystallization Behaviors of Nifedipine.

The impact of nanoconfinement on the crystallization and glass transition behaviors of nifedipine (NIF) has been investigated using differential scanning calorimetry. Nanoconfinement was provided by imbibing the NIF into a porous medium (controlled pore glass, CPG), and results were compared with the unconfined bulk material. Consistent with previous results from the literature, both glass transition temperature Tg and melting temperature Tm decrease with decreasing pore size. The melting temperature was found to decrease with the reciprocal of pore diameter and could be analyzed with the Gibbs-Thomson equation. In addition, for confinement sizes of 7.5 and 12 nm, it was found that no cold-crystallization occurs upon heating from the glassy state to above the expected melting transition. Finally, at intermediate confinements we find evidence of a possible new, confinement-induced polymorph of NIF.

Physical aging and compressed exponential behaviors in a model soft colloidal system.

Diffusing wave spectroscopy (DWS)-based micro-rheology has been used in different optical geometries (backscattering and transmission) as well as different sample thicknesses in order to probe system dynamics at different length scales [D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer. J. Phys., 1990, 51(18), 2101-2127]. Previous study from this lab [Q. Li, X. Peng, G. B. McKenna. Soft Matter, 2017, 13(7), 1396-1404] indicates the DWS-based micro-rheology observes the system non-equilibrium behaviors differently from macro-rheology. The object of the present work was to further explore the non-equilibrium dynamics and to address the range of utility of DWS as a micro-rheological method. A thermo-sensitive core-shell colloidal system was investigated both during aging and subsequent to aging into a metastable equilibrium state using temperature-jump induced volume fraction-jump experiments. We find that in the non-equilibrium state, significant differences in the measured dynamics are observed for the different geometries and length scales. Compressed exponential relaxations for the autocorrelation function g2(t) were observed for large length scales. However, upon converting the g2(t) data to the mean square displacement (MSD), such differences with length scale diminished and the long-time MSD behavior was consistent with diffusive behavior. These observations in the non-equilibrium behaviors for different length scales leads to questioning of some interpretations in the current field of light scattering-based micro-rheology and provides a possibility to interrogate the aging mechanisms in colloidal glasses from a broader perspective than normally considered in measurements of g2(t) using DWS-based micro-rheology.

Soft matter: rubber and networks.

Rubber networks are important and form the basis for materials with properties ranging from rubber tires to super absorbents and contact lenses. The development of the entropy ideas of rubber deformation thermodynamics provides a powerful framework from which to understand and to use these materials. In addition, swelling of the rubber in the presence of small molecule liquids or solvents leads to materials that are very soft and 'gel' like in nature. The review covers the thermodynamics of polymer networks and gels from the perspective of the thermodynamics and mechanics of the strain energy density function. Important relationships are presented and experimental results show that the continuum ideas contained in the phenomenological thermodynamics are valid, but that the molecular bases for some of them remain to be fully elucidated. This is particularly so in the case of the entropic gels or swollen networks. The review is concluded with some perspectives on other networks, ranging from entropic polymer networks such as thermoplastic elastomers to physical gels in which cross-link points are formed by glassy or crystalline domains. A discussion is provided for other physical gels in which the network forms a spinodal-like decomposition, both in thermoplastic polymers that form a glassy network upon phase separation and for colloidal gels that seem to have a similar behavior.

Long-term aging behaviors in a model soft colloidal system.

Colloidal and molecular systems share similar behaviors near to the glass transition volume fraction or temperature. Here, aging behaviors after volume fraction up-jump (induced by performing temperature down-jumps) conditions for a PS-PNIPAM/AA soft colloidal system were investigated using light scattering (diffusing wave spectroscopy, DWS). Both aging responses and equilibrium dynamics were investigated. For the aging responses, long-term experiments (100 000 s) were performed, and both equilibrium and non-equilibrium behaviors of the system were obtained. In the equilibrium state, as effective volume fraction increases (or temperature decreases), the colloidal dispersion displays a transition from the liquid to a glassy state. The equilibrium α-relaxation dynamics strongly depend on both the effective volume fraction and the initial mass concentration for the studied colloidal systems. Compared with prior results from our lab [X. Di, X. Peng and G. B. McKenna, J. Chem. Phys., 2014, 140, 054903], the effective volume fractions investigated spanned a wider range, to deeper into the glassy domain. The results show that the α-relaxation time τα of the samples aged into equilibrium deviate from the classical Vogel-Fulcher-Tammann (VFT)-type expectations and the super-Arrhenius signature disappears above the glass transition volume fraction. The non-equilibrium aging response shows that the time for the structural evolution into equilibrium and the α-relaxation time are decoupled. The DWS investigation of the aging behavior after different volume fraction jumps reveals a different non-equilibrium or aging behavior for the considered colloidal systems compared with either molecular glasses or the macroscopic rheology of a similar colloidal dispersions.

Correlation between Molecular Mobility and Physical Stability in Pharmaceutical Glasses.

We investigated a possible correlation between molecular mobility and physical stability in glassy celecoxib and indomethacin and identified the specific mobility mode responsible for physical instability (crystallization). In the glassy state, because the structural relaxation times are very long, the measurement was enabled by time domain dielectric spectroscopy. However, the local motions in the glassy state were characterized by frequency domain dielectric spectroscopy. Isothermal crystallization was monitored by powder X-ray diffractometry using either a laboratory source (supercooled state) or synchrotron source (glassy state). Structural (α) relaxation time correlated well with characteristic crystallization time in the supercooled state. On the other hand, a stronger correlation was observed between the Johari-Goldstein (ß) relaxation time and physical instability in the glassy state but not with structural relaxation time. These results suggest that Johari-Goldstein relaxation is a potential predictor of physical instability in the glassy state of these model systems.

Dynamic and temperature dependent response of physical vapor deposited Se in freely standing nanometric thin films.

Here, we report results from an investigation of nano-scale size or confinement effects on the glass transition and viscoelastic properties of physical vapor deposited selenium films. The viscoelastic response of freely standing Se films was determined using a biaxial membrane inflation or bubble inflation method [P. A. O'Connell and G. B. McKenna, Science 307, 1760-1763 (2005)] on films having thicknesses from 60 to 267 nm and over temperatures ranging from Tg, macroscopic - 15 °C to Tg, macroscopic + 21 °C. Time-temperature superposition and time-thickness superposition were found to hold for the films in the segmental dispersion. The responses are compared with macroscopic creep and recoverable creep compliance data for selenium [K. M. Bernatz et al., J. Non-Cryst. Solids 307, 790-801 (2002)]. The time-temperature shift factors for the thin films show weaker temperature dependence than seen in the macroscopic behavior, being near to Arrhenius-like in their temperature dependence. Furthermore, the Se films exhibit a "rubbery-like" stiffening that increases as film thickness decreases similar to prior observations [P. A. O'Connell et al., Macromolecules 45(5), 2453-2459 (2012)] for organic polymers. In spite of the differences from the macroscopic behavior in the temperature dependence of the viscoelastic response, virtually no change in Tg as determined from the thickness dependence of the retardation time defining Tg was observed in the bubble inflation creep experiments to thicknesses as small as 60 nm. We also find that the observed rubbery stiffening is consistent with the postulate of K. L. Ngai et al. [J. Polym. Sci., Part B: Polym. Phys. 51(3), 214-224 (2013)] that it should correlate with the change of the macroscopic segmental relaxation.

Molecular mobility in glassy dispersions.

Dielectric spectroscopy was used to characterize the structural relaxation in pharmaceutical dispersions containing nifedipine (NIF) and either poly(vinyl) pyrrolidone (PVP) or hydroxypropyl methylcellulose acetate succinate (HPMCAS). The shape of the dielectric response (permittivity versus log time) curve was observed to be independent of temperature. Thus, for the pure NIF as well as the dispersions, the validity of the time-temperature superposition principle was established. Furthermore, though the shape of the full dielectric response varied with polymer concentration, the regime related to the α- or structural relaxation was found to superimpose for the dispersions, though not with the response of the NIF itself. Hence, there is a limited time-temperature-concentration superposition for these systems as well. Therefore, in this polymer concentration range, calculation of long relaxation times in these glass-forming systems becomes possible. We found that strong drug-polymer hydrogen bonding interactions improved the physical stability (i.e., delayed crystallization) by reducing the molecular mobility. The strength of hydrogen bonding, structural relaxation time, and crystallization followed the order: NIF-PV P>NIF-HPMCAS>NIF. With an increase in polymer concentration, the relaxation times were longer indicating a decrease in molecular mobility. The temperature dependence of relaxation time, in other words fragility, was independent of polymer concentration. This is the first application of the superposition principle to characterize structural relaxation in glassy pharmaceutical dispersions.

Dynamics of a thermo-responsive microgel colloid near to the glass transition.

In a previous study, we used diffusing wave spectroscopy (DWS) to investigate the aging signatures of a thermo-sensitive colloidal glass and compared them with those of molecular glasses from the perspective of the Kovacs temperature-jump, volume recovery experiments [X. Di, K. Z. Win, G. B. McKenna, T. Narita, F. Lequeux, S. R. Pullela, and Z. Cheng, Phys. Rev. Lett. 106, 095701 (2011)]. In order to further look into the glassy behavior of colloidal systems, we have synthesized a new core/shell particle with lower temperature sensitivity and studied the aging signatures of concentrated systems, again following Kovacs' protocol. Similar signatures of aging to those observed previously were seen in this new system. Moreover, a systematic study of the temperature dependence of the dynamics of the new system for different weight concentrations was performed and the dynamic fragility index m was determined. We have also explored the use of the properties determined from the DWS measurements to obtain macroscopic rheological parameters - storage modulus G(')(ω) and loss modulus G(″)(ω) - using a generalized Stokes-Einstein approach. The micro-rheological and macro-rheological values are in reasonable agreement.

Evaluation of heterogeneity measures and their relation to the glass transition.

For most phase transitions, dynamic slowdown is accompanied by a static structure change. However, in the case of the supercooled liquid, which is a special liquid state below the melting temperature, one observes pronounced dynamic slowdown, i.e., diffusion coefficient, relaxation time, and viscosity change 10-14 orders of magnitude within a relatively small temperature range. This occurs without the pronounced static structure change observed in other phase transitions. Over the past several decades, there has been extensive research aimed to understand why the glass transition occurs, to establish what the glass transition exactly is, and to improve our understanding of how molecules move near to the glass transition. In the present work, we have examined the idea that the dramatic reduction in molecular mobility or dynamic slowdown in a supercooled liquid during cooling from above T(g) occurs because of the increasing length scale of heterogeneous subregions, or the cooperatively rearranging regions (CRR) proposed by Adam and Gibbs. Although there is little doubt about the existence of microscopic heterogeneous regions, the absence of the "universal" parameters to characterize the temperature dependent heterogeneity data and type of temperature divergence among different parameters over the same temperature range suggests the possibility that the heterogeneity itself may not relate to the CRR directly and thus may not be the key cause of the glass transition phenomenon. It remains an important research challenge to identify which, if any, of the heterogeneity parameters relates in a causal manner to the glass transition.

Challenging the Kauzmann paradox using an ultra-stable perfluoropolymer glass with a fictive temperature below the dynamic VFT temperature.

Ultra-stable fluoropolymer glasses were created using vacuum pyrolysis deposition that show large fictive temperature Tf reductions relative to the glass transition temperature Tg of the rejuvenated material. Tf was also found to be 11.4 K below the dynamic VFT temperature TVFT. Glass films with various thickness (200-1150 nm) were deposited onto different temperature substrates. Glassy films were characterized using rapid-chip calorimetry, Fourier-transform infrared spectroscopy and intrinsic viscosity measurements. Large enthalpy overshoots were observed upon heating and a Tf reduction of 62.6 K relative to the Tg of 348 K was observed. This reduction exceeds values reported for a 20-million-year-old amber and another amorphous fluoropolymer and is below the putative Kauzmann temperature TK for the material as related to TVFT. These results challenge the importance of the Kauzmann paradox in glass-formation and illustrates a powerful method for the exploration of material dynamics deep in the glassy state (Tf < T < Tg).

Gelation via ion exchange in discotic suspensions.

The phase behavior of charged disk suspensions displays a strong dependence on ionic strengths, as the interplay between excluded volume and electrostatic interactions determines the formation of glasses, gels, and liquid crystal states. The various ions in natural soil or brine, however, could present additional effects, especially considering that most platelet structures bear a momentous ion-exchange capacity. Here we observed how ion exchange modulates and controls the interaction between individual disks and leads to unconventional phase transitions from isotropic gel to nematic gel and finally to nematic liquid crystals.

Temperature divergence of the dynamics of a poly(vinyl acetate) glass: dielectric vs. mechanical behaviors.

The dynamics of glass forming liquids as the glass transition temperature (T(g)) is traversed has become of special interest because of the continuing question as to whether or not the dynamics diverge towards an ideal glass transition/Kauzmann temperature or if the apparent Vogel-Fulcher-Tammann (VFT) divergence is lost as one goes below the conventional T(g) but remains in equilibrium. Here we examine the response of a poly(vinyl acetate) PVAc polymer glass-former using both dielectric and mechanical methods in the vicinity of T(g). Isothermal measurements were performed to study the aging behavior of the PVAc and to assure that the equilibrium state was achieved for temperatures as much as 16 K below the calorimetric T(g). Surprisingly, we found that the mechanical response took much longer to age into its equilibrium than did the dielectric response. Also, the temperature dependence of the time-temperature shift factors obtained from the two methods is different and the dielectric response shows a turnover to an apparent Arrhenius behavior rather than a continuation of the VFT extrapolated divergence at the lowest temperatures tested.