Self-Diffusion of Supercooled o-Terphenyl near the Glass Transition Temperature

Importance of Experiments That Can Test Theories Critically

General dynamic and thermodynamic properties of complex materials, including amorphous polymers and molecular glass-formers, have been established from the wealth of experimental data accumulated over the years. Naturally, these general properties attract researchers to construct theories and models to address and explain them. Often more than one theory with contrasting or even conflicting theoretical bases can equally explain a general property rather well. The correct explanation becomes unclear, and progress is stopped. The resolution of the problem comes when an innovative experiment is performed with insightful results that can critically test the premise and assumptions of each theory. This important role played by experimentalists is exemplified by the contributions of Mark Ediger in several general properties considered in this paper: (1) dynamics of the components in binary polymer blends; (2) breakdown of the Stokes-Einstein and the Debye-Stokes-Einstein relations; (3) enhancement of surface mobility and in relation to formation of ultrastable glasses; and (4) the Johari-Goldstein β-relaxation in ultrastable glasses. Different theories proposed to explain these properties are discussed, including the Coupling Model of the author.

Understanding dynamics in coarse-grained models. IV. Connection of fine-grained and coarse-grained dynamics with the Stokes-Einstein and Stokes-Einstein-Debye relations

Applying an excess entropy scaling formalism to the coarse-grained (CG) dynamics of liquids, we discovered that missing rotational motions during the CG process are responsible for artificially accelerated CG dynamics. In the context of the dynamic representability between the fine-grained (FG) and CG dynamics, this work introduces the well-known Stokes-Einstein and Stokes-Einstein-Debye relations to unravel the rotational dynamics underlying FG trajectories, thereby allowing for an indirect evaluation of the effective rotations based only on the translational information at the reduced CG resolution. Since the representability issue in CG modeling limits a direct evaluation of the shear stress appearing in the Stokes-Einstein and Stokes-Einstein-Debye relations, we introduce a translational relaxation time as a proxy to employ these relations, and we demonstrate that these relations hold for the ambient conditions studied in our series of work. Additional theoretical links to our previous work are also established. First, we demonstrate that the effective hard sphere radius determined by the classical perturbation theory can approximate the complex hydrodynamic radius value reasonably well. Furthermore, we present a simple derivation of an excess entropy scaling relationship for viscosity by estimating the elliptical integral of molecules. In turn, since the translational and rotational motions at the FG level are correlated to each other, we conclude that the "entropy-free" CG diffusion only depends on the shape of the reference molecule. Our results and analyses impart an alternative way of recovering the FG diffusion from the CG description by coupling the translational and rotational motions at the hydrodynamic level.

Implications of Low-concentration Polymer on the Physical Stability of Glassy Griseofulvin: Role of the Segmental Mobility

Crystallization of amorphous pharmaceutical solids are widely reported to be affected by the addition of polymer, while the underlying mechanism require deep study. Herein, crystal growth behaviors of glassy griseofulvin (GSF) doped with various 1% w/w polymer were systematically studied. From the molecular structure, GSF cannot form the hydrogen bonding interactions with the selected polymer poly(vinyl acetate), polyvinyl pyrrolidone (PVP), 60:40 vinyl pyrrolidone-vinyl acetate copolymer (PVP/VA 64), and poly(ethylene oxide) (PEO). 1% w/w polymer exhibited weak or no detectable effects on the glass transition temperature (Tg) of GSF. However, crystal growth rates of GSF was altered from 4.27-fold increase to 2.57-fold decrease at 8 ℃ below Tg of GSF. Interestingly, the ability to accelerate and inhibit the growth rates of GSF crystals correlated well with Tg of polymer, indicating the controlling role of segmental mobility of polymer. Moreover, ring-banded growth of GSF was observed in the polymer-doped systems. Normal compact bulk and ring-banded crystals of GSF were both characterized as the thermodynamically stable form I. More importantly, formation of ring-banded crystals of GSF can significantly weaken the inhibitory effects of polymer on the crystallization of glassy GSF.

Molecular Dynamics and Diffusion in Amorphous Solid Dispersions Containing Imidacloprid

The main goal of this study is to develop an experimental toolbox to estimate the self-diffusion coefficient of active ingredients (AI) in single-phase amorphous solid dispersions (ASD) close to the glass transition of the mixture using dielectric spectroscopy (DS) and oscillatory rheology. The proposed methodology is tested for a model system containing the insecticide imidacloprid (IMI) and the copolymer copovidone (PVP/VA) prepared via hot-melt extrusion. For this purpose, reorientational and the viscoelastic structural (α-)relaxation time constants of hot-melt-extruded ASDs were obtained via DS and shear rheology, respectively. These were then utilized to extract the viscosity as well as the fragility index of the dispersions as input parameters to the fractional Stokes-Einstein (F-SE) relation. Furthermore, a modified version of Almond-West (AW) formalism, originally developed to describe charge diffusion in ionic conductors, was exercised on the present model system for the estimation of the AI diffusion coefficients based on shear modulus relaxation times. Our results revealed that, at the calorimetric glass-transition temperature (T_g), the self-diffusion coefficients of the AI in the compositional range from infinite dilution up to 60 wt % IMI content lied in the narrow range of 10^-18-10^-20 m² s^-1, while the viscosity values of the dispersions at T_g varied between 10⁸ Pa s and 10¹⁰ Pa s. In addition, the phase diagram of the IMI-PVP/VA system was determined using the melting point depression method via differential scanning calorimetry (DSC), while mid-infrared (IR) spectroscopy was employed to investigate the intermolecular interactions within the solid dispersions. In this respect, the findings of a modest variation in melting point at different compositions stayed in agreement with the observations of weak hydrogen bonding interactions between the AI and the polymer. Moreover, IR spectroscopy showed the intermolecular IMI-IMI hydrogen bonding to have been considerably suppressed, as a result of the spatial separation of the AI molecules within the ASDs. In summary, this study provides experimental approaches to study diffusivity in ASDs using DS and oscillatory rheology, in addition to contributing to an enhanced understanding of the interactions and phase behavior in these systems.

Amorphous Solid Dispersions: Role of the Polymer and Its Importance in Physical Stability and In Vitro Performance

Amorphous solid dispersions stabilized by one or more polymer(s) have been widely used for delivering amorphous drugs with poor water solubilities, and they have gained great market success. Polymer selection is important for preparing robust amorphous solid dispersions, and considerations should be given as to how the critical attributes of a polymer can enhance the physical stability, and the in vitro and in vivo performances of a drug. This article provides a comprehensive overview for recent developments in the understanding the role of polymers in amorphous solid dispersions from the aspects of nucleation, crystal growth, overall crystallization, miscibility, phase separation, dissolution, and supersaturation. The critical properties of polymers affecting the physical stability and the in vitro performance of amorphous solid dispersions are also highlighted. Moreover, a perspective regarding the current research gaps and novel research directions for better understanding the role of the polymer is provided. This review will provide guidance for the rational design of polymer-based amorphous pharmaceutical solids with desired physicochemical properties from the perspective of physical stability and in vitro performance.

Physical stability and dissolution behaviors of amorphous pharmaceutical solids: Role of surface and interface effects

Amorphous pharmaceutical solids (APS) are single- or multi-component systems in which drugs exist in high-energy states with long-range disordered molecular packing. APSs have become one of the most effective and widely used pharmaceutical delivery approaches for poorly water-soluble drugs in the last several decades. Considerable efforts have been made to investigate the physical stability and dissolution behaviors of APSs, however, the underlying mechanisms remain imperfectly understood. Recent studies reveal that surface and interface properties of APSs could strongly affect the physical stability and dissolution behaviors. This paper provides a comprehensive overview of recent studies focusing on the physical stability and dissolution behaviors of APSs from both surface and interface perspectives. We highlight the role of surface or interface properties in nucleation, crystal growth, phase separation, dissolution, and supersaturation. Meanwhile, the challenges and scope of research on surface and interface properties in the future are also briefly discussed. This review contributes to a better understanding of the surface- and interface-facilitated processes, which will provide more efficient and rational guidance for the design of APSs.

Upper bound of fragility from spatial fluctuations of shear modulus and boson peak in glasses

It is shown that the normalized rms fluctuation of the shear modulus on the medium-range order scale in glasses correlates with fragility: the higher fragility, the smaller the fluctuation amplitude. The latter is calculated within the heterogeneous elasticity theory using the data on the boson peak in glasses. On a smaller scale corresponding to cooperative structural relaxation, the normalized rms fluctuation of the infinite-frequency shear modulus was estimated using the data on the decoupling of viscosity and diffusion in supercooled liquids. These fluctuations are much smaller in amplitude, and, in contrast, they increase with increasing fragility. Extrapolation predicts intersection of both rms fluctuations and disappearing of the boson peak at the upper limit to fragility ≈180.

Single molecule demonstration of Debye-Stokes-Einstein breakdown in polystyrene near the glass transition temperature

Rotational-translational decoupling, in which translational motion is apparently enhanced over rotational motion in violation of Stokes-Einstein (SE) and Debye-Stokes-Einstein (DSE) predictions, has been observed in materials near their glass transition temperatures (T_g). This has been posited to result from ensemble averaging in the context of dynamic heterogeneity. In this work, ensemble and single molecule experiments are performed in parallel on a fluorescent probe in high molecular weight polystyrene near its T_g. Ensemble results show decoupling onset at approximately 1.15T_g, increasing to over three orders of magnitude at T_g. Single molecule measurements also show a high degree of decoupling, with typical molecules at T_g showing translational diffusion coefficients nearly 400 times higher than expected from SE/DSE predictions. At the single molecule level, higher degree of breakdown is associated with particularly mobile molecules and anisotropic trajectories, providing support for anomalous diffusion as a critical driver of rotational-translational decoupling and SE/DSE breakdown.

Experiments with high-molecular-weight polystyrene provide insights into the mechanisms behind rotational-translational decoupling in glassy systems. Specifically, particularly mobile molecules exhibiting anisotropic trajectories are found to play a key role in Debye-Stokes-Einstein breakdown.

The Interplay between the Theories of Mode Coupling and of Percolation Transition in Attractive Colloidal Systems

In the recent years a considerable effort has been devoted to foster the understanding of the basic mechanisms underlying the dynamical arrest that is involved in glass forming in supercooled liquids and in the sol-gel transition. The elucidation of the nature of such processes represents one of the most challenging unsolved problems in the field of material science. In this context, two important theories have contributed significantly to the interpretation of these phenomena: the Mode-Coupling theory (MCT) and the Percolation theory (PT). These theories are rooted on the two pillars of statistical physics, universality and scale laws, and their original formulations have been subsequently modified to account for the fundamental concepts of Energy Landscape (EL) and of the universality of the fragile to strong dynamical crossover (FSC). In this review, we discuss experimental and theoretical results, including Molecular Dynamics (MD) simulations, reported in the literature for colloidal and polymer systems displaying both glass and sol-gel transitions. Special focus is dedicated to the analysis of the interferences between these transitions and on the possible interplay between MCT and PT. By reviewing recent theoretical developments, we show that such interplay between sol-gel and glass transitions may be interpreted in terms of the extended F13 MCT model that describes these processes based on the presence of a glass-glass transition line terminating in an A3 cusp-like singularity (near which the logarithmic decay of the density correlator is observed). This transition line originates from the presence of two different amorphous structures, one generated by the inter-particle attraction and the other by the pure repulsion characteristic of hard spheres. We show here, combining literature results with some new results, that such a situation can be generated, and therefore experimentally studied, by considering colloidal-like particles interacting via a hard core plus an attractive square well potential. In the final part of this review, scaling laws associated both to MCT and PT are applied to describe, by means of these two theories, the specific viscoelastic properties of some systems.

Surface diffusion of a glassy discotic organic semiconductor and the surface mobility gradient of molecular glasses

Surface diffusion has been measured in the glass of an organic semiconductor, MTDATA, using the method of surface grating decay. The decay rate was measured as a function of temperature and grating wavelength, and the results indicate that the decay mechanism is viscous flow at high temperatures and surface diffusion at low temperatures. Surface diffusion in MTDATA is enhanced by 4 orders of magnitude relative to bulk diffusion when compared at the glass transition temperature T_g. The result on MTDATA has been analyzed along with the results on other molecular glasses without extensive hydrogen bonds. In total, these systems cover a wide range of molecular geometries from rod-like to quasi-spherical to discotic and their surface diffusion coefficients vary by 9 orders of magnitude. We find that the variation is well explained by the existence of a steep surface mobility gradient and the anchoring of surface molecules at different depths. Quantitative analysis of these results supports a recently proposed double-exponential form for the mobility gradient: log D(T, z) = log D_v(T) + [log D₀ - log D_v(T)]exp(-z/ξ), where D(T, z) is the depth-dependent diffusion coefficient, D_v(T) is the bulk diffusion coefficient, D₀ ≈ 10^-8 m²/s, and ξ ≈ 1.5 nm. Assuming representative bulk diffusion coefficients for these fragile glass formers, the model reproduces the presently known surface diffusion rates within 0.6 decade. Our result provides a general way to predict the surface diffusion rates in molecular glasses.

Impact of Molecular Surface Diffusion on the Physical Stability of Co-Amorphous Systems

In this study, surface diffusion of l-aspartic acid-carvedilol (ASP-CAR) co-amorphous systems at different ASP concentrations is measured and correlated with their physical stability. ASP-CAR films at ASP concentrations of 1-5% (w/w) were prepared by a newly developed method based on a vacuum compression molding process. Surface diffusion measurements were conducted on these systems based on the surface grating decay method using atomic force microscopy (AFM). The results demonstrate that a small amount of ASP (i.e., ≤ 5% w/w) in the co-amorphous systems could significantly slow down the grating decay process compared with that of pure amorphous CAR, indicating a reduced surface diffusion of CAR molecules. The decay time gradually increased in co-amorphous systems with increasing ASP concentration from 1 to 5% (w/w), with the longest observed decay time of around 800 h for the 5%ASP-CAR system, which was more than 200 times longer compared to the decay time of pure amorphous CAR (approximately 3 h). A good correlation between the decay constants of the pure amorphous CAR and co-amorphous films at ASP concentrations of 1-5% (w/w) and the physical stability of corresponding amorphous powder samples was found. Overall, this study provides a new method to prepare co-amorphous films for surface property measurements and reveals the impact of surface diffusion on the physical stability of co-amorphous systems.

Surface Diffusion Is Controlled by Bulk Fragility across All Glass Types

Surface diffusion is vastly faster than bulk diffusion in some glasses, but only moderately enhanced in others. We show that this variation is closely linked to bulk fragility, a common measure of how quickly dynamics is excited when a glass is heated to become a liquid. In fragile molecular glasses, surface diffusion can be a factor of 10^{8} faster than bulk diffusion at the glass transition temperature, while in the strong system SiO_{2}, the enhancement is a factor of 10. Between these two extremes lie systems of intermediate fragility, including metallic glasses and amorphous selenium and silicon. This indicates that stronger liquids have greater resistance to dynamic excitation from bulk to surface and enables prediction of surface diffusion, surface crystallization, and formation of stable glasses by vapor deposition.

Fast crystal growth of amorphous nimesulide: implication of surface effects

Understanding crystallization behaviors is of utmost importance for developing robust amorphous pharmaceutical solids. Herein, the crystal growth behaviors of amorphous anti-inflammatory drug nimesulide (NIME) are systemically investigated in the glassy and supercooled liquid state as a function of temperature. A sudden over-tenfold increase is observed in the bulk crystal growth of NIME on cooling below its glass transition temperature (T_g). This fast growth behavior is known as a glass-to-crystal (GC) mode and has been reported in some molecular glasses. Fast surface crystal growth of NIME can persist up to T_g + 57°C with a weak jump in its growth rates at 30-40°C. In addition, surface crystal growth and GC growth of NIME exhibit an almost identical temperature dependence, supporting the view that GC growth is indeed a surface-facilitated process. Moreover, the bubble-induced fast crystal growth of NIME is observed in the interior of its supercooled liquid with approximately the same growth kinetics as surface crystal growth. These findings are relevant for a full understanding of the surface-related crystallization behaviors and physical stability of amorphous pharmaceutical formulations.

Bubble-induced fast crystal growth of indomethacin polymorphs in a supercooled liquid

Physical stability is one of the main challenges when developing robust amorphous pharmaceutical formulations. This article reports fast crystal growth behaviors of the γ and α forms of indomethacin (IMC) initiated by bubbles in the interior of a supercooled liquid. Bubble-induced crystal growth of γ-IMC exhibits approximately the same kinetics as its surface crystal growth, supporting the view that bubble-induced crystal growth is a surface-facilitated process. In contrast, the rates of bubble-induced crystal growth of α-IMC are much faster than those of its surface crystal growth. These results indicate that the bubble-induced crystal growth not only depends on the interface created by the bubble but also strongly correlates with the true cavitation of the bubble. Moreover, bubble-induced fast crystal growth of γ- and α-IMC can be terminated at different temperatures by cooling. These outcomes are meaningful for the in-depth understanding of physical stability and pre-formulation study of amorphous pharmaceutical solids showing surface-facilitated crystal growth.

Glass Dynamics Deep in the Energy Landscape

When a liquid is cooled, progress down the energy landscape is arrested near the glass transition temperature T_g. In principle, lower energy states can be accessed by waiting for further equilibration, but the rough energy landscape of glasses quickly leads to kinetics on geologically slow time scales below T_g. Over the past decade, progress has been made probing deeper into the energy landscape via several techniques. By looking at bulk and surface diffusion, using layered deposition that promotes equilibration, imaging glass surfaces with faster dynamics below T_g, and optically exciting glasses, experiments have moved into a regime of ultrastable, low energy glasses that was difficult to access in the past. At the same time, both simulations and energy landscape theory based on a random first order transition (RFOT) have tackled systems that include surfaces, optical excitation, and interfacial dynamics. Here we review some of the recent experimental work, and how energy landscape theory illuminates glassy dynamics well below the glass transition temperature by making direct connections between configurational entropy, energy landscape barriers, and the resulting dynamics.

Rheology based estimates of self- and collective diffusivities in viscous liquids

The self-diffusion coefficient of viscous liquids is estimated on the basis of a simple analysis of their rheological shear spectra. To this end, the Almond-West approach, previously employed to access single-particle diffusivities in ionic conductors, is generalized for application to molecular dynamics in supercooled liquids. Rheology based estimates, presented for indomethacin, ortho-terphenyl, and trinaphthylbenzene, reveal relatively small, yet systematic differences when compared with diffusivity data directly measured for these highly viscous liquids. These deviations are discussed in terms of mechanical Haven ratios, introduced to quantify the magnitude of collective translational effects that have an impact on the viscous flow.

Temperature and Thickness Dependence of the Time Scale of Crystallization of Polymers under 1D Confinement

Confined in nanodomains, polymers crystallize much slower than in bulk due to both finite size and interfacial effects. These two factors are successfully disentangled in our phenomenological framework, which provides a measurement of the time scale of crystallization via a product of probabilities involving nucleation and of chain diffusion. In this Letter, we demonstrate that our model allows determining the Gibbs free energy of the formation of a critical size nucleus indicated by the classical nucleation theory for bulk polymer melts. In addition to that, by means of segmental mobility data and one single set of isothermal crystallization measurements at different confinement degrees, our model predicts the right temperature and thickness dependence of the crystallization time.

Diffusion in dense supercritical methane from quasi-elastic neutron scattering measurements

Methane, the principal component of natural gas, is an important energy source and raw material for chemical reactions. It also plays a significant role in planetary physics, being one of the major constituents of giant planets. Here, we report measurements of the molecular self-diffusion coefficient of dense supercritical CH₄ reaching the freezing pressure. We find that the high-pressure behaviour of the self-diffusion coefficient measured by quasi-elastic neutron scattering at 300 K departs from that expected for a dense fluid of hard spheres and suggests a density-dependent molecular diameter. Breakdown of the Stokes-Einstein-Sutherland relation is observed and the experimental results suggest the existence of another scaling between self-diffusion coefficient D and shear viscosity η, in such a way that Dη/ρ=constant at constant temperature, with ρ the density. These findings underpin the lack of a simple model for dense fluids including the pressure dependence of their transport properties.

Diffusion-controlled and `diffusionless' crystal growth: relation between liquid dynamics and growth kinetics of griseofulvin

Understanding how liquid dynamics govern crystallization is critical for maintaining the physical stability of amorphous pharmaceutical formulations. In the present study, griseofulvin (GSF), a classic antifungal drug, was used as the model system to investigate the correlations between crystal growth kinetics and liquid dynamics. The temperature dependence of the kinetic part of the bulk crystal growth in a supercooled liquid of GSF was weaker than that of the structural relaxation time τα and scaled as τα −0.69. In the glassy state, GSF exhibited the glass-to-crystal (GC) growth behavior, whose growth rate was too fast to be under the control of the α-relaxation process. Moreover, from the perspective of τα, the GC growth of GSF also satisfied the general condition for GC growth to exist: D/u < 7 pm, where D is the diffusion coefficient and u the speed of crystal growth. Also compared were the fast surface crystal growth rates u s and surface relaxation times τsurface predicted by the random first-order transition theory. Here, the surface crystal growth rate u s of GSF exhibited a power-law dependence upon the surface structural relaxation time: u s ∝ τsurface −0.71, which was similar to that of the bulk growth rate and τα. These findings are important for understanding and predicting the crystallization of amorphous pharmaceutical solids both in the bulk and at the surface.

Physical stability of amorphous pharmaceutical solids: Nucleation, crystal growth, phase separation and effects of the polymers

Compared to their crystalline forms, amorphous pharmaceutical solids present marvelous potential and advantages for effectively improving the oral bioavailability of poorly water-soluble drugs. A central issue in developing amorphous pharmaceutical solids is the stability against crystallization, which is particularly important for maintaining their advantages in solubility and dissolution rate. This review provides a comprehensive overview of recent studies focusing on the physical stability of amorphous pharmaceutical solids affected by nucleation, crystal growth, phase separation and the addition of polymers. Moreover, we highlight the novel technologies and theories in the field of amorphous pharmaceutical solids. Meanwhile, the challenges and strategies in maintaining the physical stability of amorphous pharmaceutical solids are also discussed. With a better understanding of physical stability, the more robust amorphous pharmaceutical formulations with desired pharmaceutical performance would be easier to achieve.

Coarse-graining strategy for modeling effective, highly diffusive fluids with reduced polydispersity: A dynamical study

We present a coarse-graining strategy for reducing the number of particle species in mixtures to achieve a simpler system with higher diffusion while preserving the total particle number and characteristic dynamic features. As a system of application, we chose the bidisperse Lennard-Jones-like mixture, discovered by Kob and Andersen [Phys. Rev. Lett. 73, 1376 (1994)], possessing a slow dynamics due to the fluid's multi-component character with its apparently unconventional choice for the pair potential of the type-A-type-B arrangement. We further established in a so-formed coarse-grained and temperature-independent monodisperse system an equilibrium structure with a radial distribution function resembling its mixture counterpart. This one-component system further possesses similar dynamic features such as glass transition temperature and critical exponents while subjected to Newtonian mechanics. This strategy may finally lead to the manufacturing of new nanoparticle/colloidal fluids by experimentally modeling only the outcoming effective pair potential(s) and no other macroscopic quantity.

Excess-entropy scaling in supercooled binary mixtures

Transport coefficients, such as viscosity or diffusion coefficient, show significant dependence on density or temperature near the glass transition. Although several theories have been proposed for explaining this dynamical slowdown, the origin remains to date elusive. We apply here an excess-entropy scaling strategy using molecular dynamics computer simulations and find a quasiuniversal, almost composition-independent, relation for binary mixtures, extending eight orders of magnitude in viscosity or diffusion coefficient. Metallic alloys are also well captured by this relation. The excess-entropy scaling predicts a quasiuniversal breakdown of the Stokes-Einstein relation between viscosity and diffusion coefficient in the supercooled regime. Additionally, we find evidence that quasiuniversality extends beyond binary mixtures, and that the origin is difficult to explain using existing arguments for single-component quasiuniversality.

A Mechanistic Model for Predicting the Physical Stability of Amorphous Solid Dispersions

In this paper, we establish a mechanistic model for the prediction of amorphous solid dispersion (ASD) stability. The novel approach incorporates fundamental physical parameters, principally supersaturation, diffusivity, and interfacial energy, to model crystallization in ASDs accounting for both kinetic and thermodynamic drivers. API dependent decoupling coefficients were also considered which allowed dynamic mechanical analysis to probe molecular mobility, with viscosity measurements, across an exceptionally broad range of temperatures to support ASD stability simulations. ASDs are multicomponent systems in which the amorphous form of active pharmaceutical ingredients (APIs) are molecularly dispersed within a carrier. This gives rise to a transiently supersaturated API solution upon dissolution which increases the driving force for oral absorption and results in increased bioavailability as compared to that of the crystalline API. A major shortcoming of ASDs, however, is that there is the potential for amorphous APIs to revert to their more stable crystalline form during storage, despite the use of polymer carriers to stabilize formulations and limit recrystallization. Hot melt extrusion (HME) has been employed as the preparation method for ASDs used in this study as it is well-suited for the formation of uniform dispersions. The ASDs were stored under controlled temperature conditions, in the absence of humidity, to determine recrystallization kinetics. Our mechanistic model, considering both crystal nucleation and growth processes, describes temporal ASD stability through a system of coupled differential equations that connect the physiochemical properties of the ASD system to drug recrystallization. The model and prolonged time scale of crystallization observed highlight the importance of considering both thermodynamic and kinetic factors in the preparation of stable ASDs. Experimental observations were found to be in good agreement with predictions of the model confirming its utility in predicting the temporal physical stability of amorphous solid dispersions through a mechanistic lens.

Surface diffusion in glasses of rod-like molecules posaconazole and itraconazole: effect of interfacial molecular alignment and bulk penetration

The method of surface grating decay has been used to measure surface diffusion in the glasses of two rod-like molecules posaconazole (POS) and itraconazole (ITZ). Although structurally similar antifungal medicines, ITZ forms liquid-crystalline phases while POS does not. Surface diffusion in these systems is significantly slower than in the glasses of quasi-spherical molecules of similar volume when compared at the glass transition temperature T_g. Between the two systems, ITZ has slower surface diffusion. These results are explained on the basis of the near-vertical orientation of the rod-like molecules at the surface and their deep penetration into the bulk where mobility is low. For molecular glasses without extensive hydrogen bonds, we find that the surface diffusion coefficient at T_g decreases smoothly with the penetration depth of surface molecules and the trend has the double-exponential form for the surface mobility gradient observed in simulations. This supports the view that these molecular glasses have a similar mobility vs. depth profile and their different surface diffusion rates arise simply from the different depths at which molecules are anchored. Our results also provide support for a previously observed correlation between the rate of surface diffusion and the fragility of the bulk liquid.

Direct Measurement of Lateral Molecular Diffusivity on the Surface of Supersaturated Amorphous Solid Dispersions by Atomic Force Microscopy

Quantifying molecular surface diffusivity is of broad interest in many different fields of science and technology. In this study, the method of surface grating decay is utilized to investigate the surface diffusion of practical relevant amorphous solid dispersions of indomethacin and the polymeric excipient Soluplus (a polyvinyl caprolactam-polyvinyl acetate-polyethylene glycol graft copolymer) at various polymer concentrations (1-20% w/w). The study confirms that measuring surface diffusivity below the system's glass transition temperature is possible with a simplified atomic force microscopy setup. Results highlight a striking polymer influence on the surface diffusivity of drug molecules at low polymer concentrations and a turnover point to a polymer dominated diffusion at around three percent (w/w) polymer concentration. The surface diffusion measurements further correlate well with the observed increase in physical stability of the system as measured by X-ray powder diffraction. These findings are of vital interest in both the applied use and fundamental understanding of amorphous solid dispersions.

Continuous time random walk concepts applied to extended mode coupling theory: a study of the Stokes-Einstein breakdown

In an attempt to extend the mode coupling theory (MCT) to lower temperatures, some years back an Unified theory was proposed which within the MCT framework incorporated the activated dynamics via the random first order transition theory (RFOT). The theory successfully showed that there is hopping induced diffusive dynamics and the modified MCT coupled to the activated motion continues till low temperatures. Here we show that the theory although successful in describing other properties of supercooled liquids is unable to capture the Stokes-Einstein breakdown. We then show using continuous time random work (CTRW) formalism that the Unified theory is equivalent to a CTRW dynamics in presence of two waiting time distributions. It is known from earlier work on CTRW that in such cases the total dynamics is dominated by the fast motion. This explains the failure of the Unified theory in predicting the SE breakdown as both the structural relaxation and the diffusion process are described by the comparatively fast MCT like dynamics. The study also predicts that other forms of extended MCT with Markovian hopping kernel will face a similar issue. We next modify the Unified theory by applying the concept of renewal theory, usually used in CTRW models where the distribution has a long tail. According to this theory the first jump given by the persistent time is slower than the subsequent jumps given by the exchange time. We first show that for systems with two waiting time distributions even when both the distributions are exponential the persistent time is larger than the exchange time. We also identify the persistent time with the slower activated process. The extended Unified theory can now explain the SE breakdown. In this extended theory at low temperatures the structural relaxation is described by the activated dynamics whereas the diffusion is primarily determined by the MCT like dynamics leading to a decoupling between them. We also calculate a dynamic lengthscale from the wavenumber dependence of the relaxation time. We find that this dynamic length scale grows faster than the static length scale.

Progress towards a phenomenological picture and theoretical understanding of glassy dynamics and vitrification near interfaces and under nanoconfinement

The nature of alterations to dynamics and vitrification in the nanoscale vicinity of interfaces-commonly referred to as "nanoconfinement" effects on the glass transition-has been an open question for a quarter century. We first analyze experimental and simulation results over the last decade to construct an overall phenomenological picture. Key features include the following: after a metrology- and chemistry-dependent onset, near-interface relaxation times obey a fractional power law decoupling relation with bulk relaxation; relaxation times vary in a double-exponential manner with distance from the interface, with an intrinsic dynamical length scale appearing to saturate at low temperatures; the activation barrier and vitrification temperature T_g approach bulk behavior in a spatially exponential manner; and all these behaviors depend quantitatively on the nature of the interface. We demonstrate that the thickness dependence of film-averaged T_g for individual systems provides a poor basis for discrimination between different theories, and thus we assess their merits based on the above dynamical gradient properties. Entropy-based theories appear to exhibit significant inconsistencies with the phenomenology. Diverse free-volume-motivated theories vary in their agreement with observations, with approaches invoking cooperative motion exhibiting the most promise. The elastically cooperative nonlinear Langevin equation theory appears to capture the largest portion of the phenomenology, although important aspects remain to be addressed. A full theoretical understanding requires improved confrontation with simulations and experiments that probe spatially heterogeneous dynamics within the accessible 1-ps to 1-year time window, minimal use of adjustable parameters, and recognition of the rich quantitative dependence on chemistry and interface.

Molecular Dynamics Simulation of the Capillary Leveling of a Glass-Forming Liquid

Motivated by recent experimental studies probing (i) the existence of a mobile layer at the free surface of glasses and (ii) the capillary leveling of polymer nanofilms, we study the evolution of square-wave patterns at the free surface of a generic glass-forming binary Lennard-Jones mixture over a wide temperature range, by means of molecular dynamics simulations. The pattern's amplitude is monitored, and the associated decay rate is extracted. The evolution of the latter as a function of temperature exhibits a crossover between two distinct behaviors, over a temperature range typically bounded by the glass-transition temperature and the mode-coupling critical temperature. Layer-resolved analysis of the film particles' mean-squared displacements further shows that diffusion at the surface is considerably faster than in the bulk, below the glass-transition temperature. The diffusion coefficient of the surface particles is larger than its bulk counterpart by a factor that reaches 10⁵ at the lowest temperature studied. This factor decreases upon heating, in agreement with recent experimental studies.

Isochronal superpositioning in the equilibrium regime of superpressed propylene carbonate to ∼ 1.8 GPa: A study by diffusivity measurement of the fluorescent probe Coumarin 1

We address the problem of glass-forming of liquids by superpressing. We study the pressure-induced dynamic change of the fragile van der Waals liquid propylene carbonate towards the glassy state in the equilibrium regime by measuring the diffusivity of the fluorescent probe Coumarin 1 embedded in the host liquid. The probe diffusivity is measured by the fluorescence recovery after photobleaching (FRAP) technique across a bleached volume generated by the near-field diffracted pattern of a laser beam. The recovered fluorescence intensity fits to a stretched exponential with the diffusive time [Formula: see text] and the stretched exponent [Formula: see text] as free parameters. In the pressure range [0.3-1.0]GPa the diffusivity decouples from the Stokes-Einstein relation. The decoupling correlates well to a decrease of [Formula: see text]. The variation of [Formula: see text] is non-monotonous with [Formula: see text] showing a minimum at [Formula: see text] s. We evidence an isochronal superpositioning over about 3 decades of [Formula: see text] between ∼ 10 s and [Formula: see text] s and a density scaling in the whole investigated pressure range. The pressure at which [Formula: see text] is minimum coincides to the dynamical crossover pressure measured by other authors. This crossover pressure is compatible with the critical point of MCT theory. As our studied pressure range encompasses the critical pressure, the non-monotonous variation of [Formula: see text] opens new insight in the approach to the critical point.

Spurious violation of the Stokes-Einstein-Debye relation in supercooled water

The theories of Brownian motion, the Debye rotational diffusion model, and hydrodynamics together provide us with the Stokes–Einstein–Debye (SED) relation between the rotational relaxation time of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\ell }}$$\end{document}ℓ-th degree Legendre polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ, and viscosity divided by temperature, η/T. Experiments on supercooled liquids are frequently performed to measure the SED relations, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓk_BT/η and D_t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ, where D_t is the translational diffusion constant. However, the SED relations break down, and its molecular origin remains elusive. Here, we assess the validity of the SED relations in TIP4P/2005 supercooled water using molecular dynamics simulations. Specifically, we demonstrate that the higher-order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ values exhibit a temperature dependence similar to that of η/T, whereas the lowest-order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\tau }}}_{{\boldsymbol{\ell }}}$$\end{document}τℓ values are decoupled with η/T, but are coupled with the translational diffusion constant D_t. We reveal that the SED relations are so spurious that they significantly depend on the degree of Legendre polynomials.

Formation of Ultrastable Glasses via Precipitation: A Modeling Study

The precipitation of a glass forming solute from solution is modeled using a lattice model previously introduced to study dissolution kinetics of amorphous materials. The model includes the enhancement of kinetics at the surface of a glass in contact with a plasticizing solvent. We demonstrate that precipitation can produce a glass substantially more stable than that produced by very long time annealing of the bulk glass former. The energy of these ultrastable amorphous precipitates is found to be dominated by residual solvent rather than high energy glass configurations.

Perspective: Searching for simplicity rather than universality in glass-forming liquids

This article gives an overview of experimental results on dynamics in bulk glass-forming molecular liquids. Rather than looking for phenomenology that is universal, in the sense that it is seen in all liquids, the focus is on identifying the basic characteristics, or "stylized facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner.

Origin of the emergent fragile-to-strong transition in supercooled water

Liquids can be broadly classified into two categories, fragile and strong ones, depending on how their dynamical properties change with temperature. The dynamics of a strong liquid obey the Arrhenius law, whereas the fragile one displays a super-Arrhenius law, with a much steeper slowing down upon cooling. Recently, however, it was discovered that many materials such as water, oxides, and metals do not obey this simple classification, apparently exhibiting a fragile-to-strong transition far above [Formula: see text] Such a transition is particularly well known for water, and it is now regarded as one of water's most important anomalies. This phenomenon has been attributed to either an unusual glass transition behavior or the crossing of a Widom line emanating from a liquid-liquid critical point. Here by computer simulations of two popular water models and through analyses of experimental data, we show that the emergent fragile-to-strong transition is actually a crossover between two Arrhenius regimes with different activation energies, which can be naturally explained by a two-state description of the dynamics. Our finding provides insight into the fragile-to-strong transition observed in a wide class of materials.

Experimental evidence of low-density liquid water upon rapid decompression

To understand water’s anomalous behavior, a two-liquid model with a high-density liquid and a low-density liquid (LDL) has been proposed from theoretical simulations, and is gradually gaining ground. However, it has been experimentally challenging to probe the region of the phase diagram of H₂O where the LDL phase is expected to occur. We overcome the experimental challenge by using a technique of rapid decompression integrated with fast synchrotron measurements, and show that the region of LDL is accessible via decompression of a high-pressure crystal. We report the experimental evidence of the LDL from in situ X-ray diffraction and its crystallization process, providing a kinetic pathway for the appearance of LDL as an intermediate phase in the crystal–crystal transformation upon decompression.

Water is an extraordinary liquid, having a number of anomalous properties which become strongly enhanced in the supercooled region. Due to rapid crystallization of supercooled water, there exists a region that has been experimentally inaccessible for studying deeply supercooled bulk water. Using a rapid decompression technique integrated with in situ X-ray diffraction, we show that a high-pressure ice phase transforms to a low-density noncrystalline (LDN) form upon rapid release of pressure at temperatures of 140–165 K. The LDN subsequently crystallizes into ice-I_c through a diffusion-controlled process. Together with the change in crystallization rate with temperature, the experimental evidence indicates that the LDN is a low-density liquid (LDL). The measured X-ray diffraction data show that the LDL is tetrahedrally coordinated with the tetrahedral network fully developed and clearly linked to low-density amorphous ices. On the other hand, there is a distinct difference in structure between the LDL and supercooled water or liquid water in terms of the tetrahedral order parameter.

From elemental tellurium to Ge2Sb2Te5 melts: High temperature dynamic and relaxation properties in relationship with the possible fragile to strong transition

We investigate the dynamic properties of Ge-Sb-Te phase change melts using first principles molecular dynamics with a special emphasis on the effect of tellurium composition on melt dynamics. From structural models and trajectories established previously [H. Flores-Ruiz et al., Phys. Rev. B 92, 134205 (2015)], we calculate the diffusion coefficients for the different species, the activation energies for diffusion, the Van Hove correlation, and the intermediate scattering functions able to substantiate the dynamics and relaxation behavior of the liquids as a function of temperature and composition that is also compared to experiment whenever possible. We find that the diffusion is mostly Arrhenius-like and that the addition of Ge/Sb atoms leads to a global decrease of the jump probability and to an increase in activated dynamics for diffusion. Relaxation behavior is analyzed and used in order to evaluate the possibility of a fragile to strong transition that is evidenced from the calculated high fragility (M = 129) of Ge₂Sb₂Te₅ at high temperatures.

Influence of Hydrogen Bonding on the Surface Diffusion of Molecular Glasses: Comparison of Three Triazines

Surface grating decay measurements have been performed on three closely related molecular glasses to study the effect of intermolecular hydrogen bonds on surface diffusion. The three molecules are derivatives of bis(3,5-dimethyl-phenylamino)-1,3,5-triazine and differ only in the functional group R at the 2-position, with R being C₂H₅, OCH₃, and NHCH₃, and referred to as "Et", "OMe", and "NHMe", respectively. Of the three molecules, NHMe forms more extensive intermolecular hydrogen bonds than Et and OMe and was found to have slower surface diffusion. For Et and OMe, surface diffusion is so fast that it replaces viscous flow as the mechanism of surface grating decay as temperature is lowered. In contrast, no such transition was observed for NHMe under the same conditions, indicating significantly slower surface diffusion. This result is consistent with the previous finding that extensive intermolecular hydrogen bonds slow down surface diffusion in molecular glasses and is attributed to the persistence of hydrogen bonds even in the surface environment. This result is also consistent with the lower stability of the vapor-deposited glass of NHMe relative to those of Et and OMe and supports the view that surface mobility controls the stability of vapor-deposited glasses.

A New Phenomenon: Sub-Tg, Solid-State, Plasticity-Induced Bonding in Polymers

Polymer self-adhesion due to the interdiffusion of macromolecules has been an active area of research for several decades. Here, we report a new phenomenon of sub-T_g, solid-state, plasticity-induced bonding; where amorphous polymeric films were bonded together in a period of time on the order of a second in the solid-state at ambient temperatures, up to 60 K below their glass transition temperature (T_g), by subjecting them to active plastic deformation. Despite the glassy regime, the bulk plastic deformation triggered the requisite molecular mobility of the polymer chains, causing interpenetration across the interfaces held in contact. Quantitative levels of adhesion and the morphologies of the fractured interfaces validated the sub-T_g, plasticity-induced, molecular mobilization causing bonding. No-bonding outcomes (i) during the uniaxial compressive straining of films (a near-hydrostatic setting which strongly limits plastic flow) and (ii) between an 'elastic' and a 'plastic' film further established the explicit role of plastic deformation in this newly reported sub-T_g solid-state bonding.

Evidence for Anomalous Dynamic Heterogeneities in Isostatic Supercooled Liquids

Upon cooling, the dynamics of supercooled liquids exhibits a growing transient spatial distribution of relaxation times that is known as dynamic heterogeneities. The relationship between this now well-established crucial feature of the glass transition and some underlying liquid properties remains challenging and elusive in many respects. Here we report on computer simulations of liquids with a changing network structure (densified silicates), and show that there is a deep and important link between the mechanical nature characterized by topological constraints and the spatial extent of such fluctuations. This is not only revealed by a maximum in the dynamic correlation length ξ_{4} for fluctuations when the liquid becomes isostatically rigid, but also by a contraction of the volume of relaxing structural correlations upon the onset of stressed rigidity.

Decoupling energetic modifications to diffusion from free volume in polymer/nanoparticle composites

Diffusion coefficients of small molecules in a model composite of spherical nanoparticles and polymer with attractive interfacial interactions are reduced from that in the pure polymer, to a degree far below the level expected from geometric tortuosity arguments. We determine whether such dramatic reductions are due to modifications to the matrix polymer free volume near the nanoparticle surface, or alternatively are due to energetic attractions between the diffusants and nanoparticle surface. We performed ethyl acetate sorption experiments within the vicinity of the polymer glass transition (T_g ≤ T ≤ T_g + 25 K) for a model polymer/nanoparticle composite, silica-filled poly(methyl acrylate). By application of the Vrentas-Duda free volume theory of diffusion we have decoupled the energetic effects from those related to free-volume and segmental dynamics. While the latter is unaffected by addition of nanoparticles, the energy needed for the ethyl acetate diffusant to overcome neighboring attractive forces doubles after adding 40 vol% nanoparticles with a diameter of 14 nm. This is qualitatively consistent with hydrogen bonding interactions between the silica surface and ethyl acetate slowing its rate of diffusion. On the other hand for benzene, which does not hydrogen bond to the silica surface, diffusion coefficients that can be explained by tortuosity effects were obtained. This work provides quantitative evidence that the diffusant-filler energetic interactions and geometric blocking effects can be fully responsible for the substantially reduced diffusivity commonly observed in polymer/nanoparticle composite systems.

Growth rate of crystalline ice and the diffusivity of supercooled water from 126 to 262 K

Understanding deeply supercooled water is key to unraveling many of water's anomalous properties. However, developing this understanding has proven difficult due to rapid and uncontrolled crystallization. Using a pulsed-laser-heating technique, we measure the growth rate of crystalline ice, G(T), for 180 K < T < 262 K, that is, deep within water's "no man's land" in ultrahigh-vacuum conditions. Isothermal measurements of G(T) are also made for 126 K ≤ T ≤ 151 K. The self-diffusion of supercooled liquid water, D(T), is obtained from G(T) using the Wilson-Frenkel model of crystal growth. For T > 237 K and P ∼ 10-8 Pa, G(T) and D(T) have super-Arrhenius ("fragile") temperature dependences, but both cross over to Arrhenius ("strong") behavior with a large activation energy in no man's land. The fact that G(T) and D(T) are smoothly varying rules out the hypothesis that liquid water's properties have a singularity at or near 228 K at ambient pressures. However, the results are consistent with a previous prediction for D(T) that assumed no thermodynamic transitions occur in no man's land.