Testing the paradigm of an ideal glass transition: Dynamics of an ultrastable polymeric glass

Unifying the temperature dependent dynamics of glass formers

Strong changes in bulk properties, such as modulus and viscosity, are observed near the glass transition temperature, Tg, of amorphous materials. For more than a century, intense efforts have been made to define a microscopic origin for these macroscopic changes in properties. Using transition state theory (TST), we delve into the atomic/molecular level picture of how microscopic localized unit relaxations, or "cage rattles," evolve to macroscopic structural relaxations above Tg. Unit motion is broken down into two populations: (1) simultaneous rearrangement occurs among a critical number of units, nα, which ranges from 1 to 4, allowing a systematic classification of glass formers, GFs, that is compared to fragility; and (2) near Tg, adjacent units provide additional free volume for rearrangement, not simultaneously, but within the "primitive" lifetime, τ1, of one unit rattling in its cage. Relaxation maps illustrate how Johari-Goldstein β-relaxations stem from the rattle of nα units. We analyzed a wide variety of glassy materials and materials with a glassy response using literature data. Our four-parameter equation fits "strong" and "weak" GFs over the entire range of temperatures and also extends to other glassy systems, such as ion-transporting polymers and ferroelectric relaxors. The role of activation entropy in boosting preexponential factors to high "unphysical" apparent frequencies is discussed. Enthalpy-entropy compensation is clearly illustrated using the TST approach.

Highly stable petroleum pitches provide access to the deep glassy state

Differential scanning calorimetry (DSC) was used to study the fast aging behavior of two petroleum pitch materials despite being only three to five years old. We observe that these highly aromatic pitches with broad distributions of both molecular weight and aromaticity exhibit large enthalpic relaxation endotherms in initial DSC heating scans, and 20-32 °C reductions in the fictive temperature and 0.35-0.87 of θK, which are indicative of aged glasses similar to ultrastable glasses and 20 MA aged amber. Quantifying the degree of thermodynamic stability relative to the Kauzmann temperature vs. the aging time demonstrates that these materials age just as quickly as low fragility metallic glasses. Additionally, we observe that pitches age faster than polymers reported in the literature when compared using down-jump experiments. We hypothesize that the fraction of higher aromaticity of pitch molecules plays a crucial role in faster dynamics. The unique aging behavior and the ability to produce pitches in bulk quantities using pilot-scale equipment, while being possible to tailor their molecular composition, make them a useful material for studying complex aging dynamics in the deep glassy state.

Surface premelting and melting of colloidal glasses

The nature of liquid-to-glass transition is a major puzzle in science. A similar challenge exists in glass-to-liquid transition, i.e., glass melting, especially for the poorly investigated surface effects. Here, we assemble colloidal glasses by vapor deposition and melt them by tuning particle attractions. The structural and dynamic parameters saturate at different depths, which define a surface liquid layer and an intermediate glassy layer. The power-law growth of both layers and melting front behaviors at different heating rates are similar to crystal premelting and melting, suggesting that premelting and melting can be generalized to amorphous solids. The measured single-particle kinetics reveal various features and confirm theoretical predictions for glass surface layer.

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 T_f reductions relative to the glass transition temperature T_g of the rejuvenated material. T_f was also found to be 11.4 K below the dynamic VFT temperature T_VFT. 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 T_f reduction of 62.6 K relative to the T_g 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 T_K for the material as related to T_VFT. 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 (T_f < T < T_g).

Creating bulk ultrastable glasses by random particle bonding

A recent breakthrough in glass science has been the synthesis of ultrastable glasses via physical vapor deposition techniques. These samples display enhanced thermodynamic, kinetic and mechanical stability, with important implications for fundamental science and technological applications. However, the vapor deposition technique is limited to atomic, polymer and organic glass-formers and is only able to produce thin film samples. Here, we propose a novel approach to generate ultrastable glassy configurations in the bulk, via random particle bonding, and using computer simulations we show that this method does indeed allow for the production of ultrastable glasses. Our technique is in principle applicable to any molecular or soft matter system, such as colloidal particles with tunable bonding interactions, thus opening the way to the design of a large class of ultrastable glasses.

Ultrastable metallic glass by room temperature aging

Glasses have markedly different stability around their glass transition temperature (T_g), and metallic glasses (MGs) are conventionally regarded as metastable compared to other glasses such as silicate glass or amber. Here, we show an aging experiment on a Ce-based MG around its T_g (~0.85T_g) for more than 17 years. We find that the MG with strong fragility could transform into kinetic and thermodynamic hyperstable state after the long-term room temperature aging and exhibits strong resistance against crystallization. The achieved hyperstable state is closer to the ideal glass state compared with that of other MGs and similar to that of the million-year-aged amber, which is attributed to its strong fragility and strong resistance against nucleation. It is also observed through the asymmetrical approaching experiment that the hyperaged Ce-based MG can reach equilibrium liquid state below T_g without crystallization, which supports the idea that nucleation only occurs after the completion of enthalpy relaxation.

Molecular signatures of the glass transition in polymers

The glass transition temperature (T_{g}) is one of the most fundamental properties of polymers. T_{g} is predicted by some theories as a sudden change in a "macroscopic" quantity (e.g., compressibility). However, for systems with "soft" glass transitions where the change is gradual it becomes hard to pinpoint precisely the transition temperature as well as the set of molecular changes occurring during this transition. Here, we introduce two new molecular signatures for the glass transition of polymers that exhibit clear changes as one approaches T_{g}: (i) differential change of the probability distribution of dihedral angles as a function of temperature and (ii) the distribution of fractional of the time spent in the different torsional states. These new signatures provide insights into the glass transition in polymers by directly exhibiting the concept of spatial heterogeneity and dynamical ergodicity breaking in such systems, as well as provide a key step to quantitatively obtain the transition temperature from molecular characteristics of the polymeric systems.

Combined description of polymer PVT and relaxation data using a dynamic "SL-TS2" mean-field lattice model

We develop a combined model to describe the pressure-volume-temperature (PVT) thermodynamics and the α- and β-relaxation time dynamics in glass-forming amorphous materials. The PVT results are described using a two-state modification of the Sanchez-Lacombe equation of state (SL-EoS). The minimization of the Sanchez-Lacombe free energy expression allows one to calculate the density (or specific volume) and the "solid fraction" as a function of temperature and pressure. The solid fraction, ψ(T,P), is then substituted into the TS2 mean-field model (V. V. Ginzburg, Soft Matter, 2020, 16, 810), and the equilibrium relaxation times and the glass transition temperature are calculated. Finally, we use a dynamic model of a Tool-Narayanaswami-Moynihan (TNM)-type to describe the density relaxation as a function of the cooling rate. We applied the new framework to describe experimental data for polystyrene and poly(methylmethacrylate) and found a good qualitative and quantitative agreement.

On a fundamental description of the Kovacs' kinetic signatures in glass-forming systems

The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (T_F) of the glassy structure. We solve for the kinetics of T_F(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of T_F(t) in a set of temperature-jump histories referred to as the Kovacs' signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs' signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally "ideal" glass temperature.

Experimental test of a predicted dynamics-structure-thermodynamics connection in molecularly complex glass-forming liquids

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different "order parameters" including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local-nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Reaching the Ideal Glass in Polymer Spheres: Thermodynamics and Vibrational Density of States

The existence of an ideal glass and the resolution to the Kauzmann paradox is a long-standing open question in materials science. To address this problem, we exploit the ability of glasses with large interfacial area to access low energy states. We submit aggregates of spheres of a polymeric glass former to aging well below their glass transition temperature, T_{g}; and characterize their thermodynamic state by calorimetry, and the vibrational density of state (VDOS) by inelastic neutron scattering (INS). We show that, when aged at appropriate temperatures, glassy spheres attain a thermodynamic state corresponding to an ideal glass in time scales of about one day. In this state, the boson peak, underlying the deviation from the Debye level of the VDOS, is essentially suppressed. Our results are discussed in the framework of the link between the macroscopic thermodynamic state of glasses and their vibrational properties.

"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.

How to "measure" a structural relaxation time that is too long to be measured?

It has recently become possible to prepare ultrastable glassy materials characterized by structural relaxation times, which vastly exceed the duration of any feasible experiment. Similarly, new algorithms have led to the production of ultrastable computer glasses. Is it possible to obtain a reliable estimate of a structural relaxation time that is too long to be measured? We review, organize, and critically discuss various methods to estimate very long relaxation times. We also perform computer simulations of three dimensional ultrastable hard spheres glasses to test and quantitatively compare some of these methods for a single model system. The various estimation methods disagree significantly, and non-linear and non-equilibrium methods lead to a strong underestimate of the actual relaxation time. It is not yet clear how to accurately estimate extremely long relaxation times.

Distinct dynamics of structural relaxation in the amorphous phase of poly(l-lactic acid) revealed by quiescent crystallization

Fast scanning calorimetry (FSC) experiments were performed to investigate physical aging in amorphous and semi-crystalline poly(l-lactic acid)s (PLLAs) that were thermally crystallized under conditions leading to the α'- or α-crystalline form, and either favouring or inhibiting the development of a rigid amorphous fraction (RAF). The enthalpy of recovery was calculated after two procedures of rescaling to the content of the whole amorphous phase and also to the only content of the mobile amorphous fraction (MAF), which helped in clarifying the contribution of the RAF. From the dependence of the structural relaxation rate on the aging temperature, two regimes were evidenced for all samples. In the aging temperature domain situated close to the glass transition, the structural relaxation occurs significantly faster in the MAF. Its rate is independent of the aging temperature and is not influenced by the microstructure. However, the distance to equilibrium is higher in samples for which the coupling is strong between crystal and amorphous, implying that the time to reach equilibrium is also higher. In contrast, at low aging temperatures, for which the whole amorphous phase can be considered as solid, MAF and RAF exhibit the same structrural relaxation rate. This convergence in the relaxation kinetics by decreasing the temperature of physical aging was interpreted as the evolution of relaxation dynamics in the MAF from segmental to local. This change is highlighted by the comparison between MAF and RAF relaxation kinetics, but it occurs similarly in a pure amorphous system.

A model-free analysis of configurational properties to reduce the temperature- and pressure-dependent segmental relaxation times of polymers

The segmental relaxation time data for poly(vinyl acetate), poly(vinyl chloride), and linear and star polystyrene are analyzed using a model-free method to determine how the temperature- and pressure-dependent relaxation times, τ, scale with the relative configurational thermodynamic properties. The model-free method assumes no specific mathematical form, such as reciprocal linearity, and the configurational properties are referred to an isochronal state to eliminate the bias associated with the definition of the ideal glassy state. The scaling ability of a given configurational property is strongly material-dependent with the logarithm of τ scaling better with TS_c and H_c for poly(vinyl acetate), with TS_c, H_c, and U_c for poly(vinyl chloride), and with TS_c, H_c, and V_c for linear and star polystyrene. The choice of the isochronal reference state does not qualitatively affect the results.

A simple mean-field model of glassy dynamics and glass transition

We propose a phenomenological model to describe the equilibrium dynamic behavior of amorphous glassy materials. It is assumed that a material can be represented by a lattice of cooperatively re-arranging regions (CRRs), with each CRR having two states, the low-temperature "solid" and the high-temperature "liquid". At low temperatures, the material exhibits two characteristic relaxation times, corresponding to the slow large-scale motion between the "solid" CRRs (α-relaxation) and the faster local motion within individual CRRs (β-relaxation). At high temperatures, the α- and β-relaxation times merge, as observed experimentally and suggested by the "Coupling Model" framework. Our new approach is labeled "Two-state, two (time)scale model" or TS2. It is shown that the TS2 treatment can successfully describe the "two-Arrhenius" relaxation time behavior described in several recent experiments. We also apply TS2 to describe the pressure- and molecular-weight dependence of the glass transition temperature in bulk polymers, as well as its dependence on film thickness in thin films.

LOOKING AT THE GLASS TRANSITION: CHALLENGES OF EXTREME TIME SCALES AND OTHER INTERESTING PROBLEMS

The behavior of glass-forming materials is examined with emphasis on the below-glass transition behavior. A major question that is related to the super-Arrhenius behavior of the dynamics of glass-forming systems is whether the apparent divergence at finite temperature continues below the kinetic or laboratory glass transition that is related to the limits of measurement and is standardized so that the material relaxation time is near 100 s. The problem arises because as the temperature decreases, the time scales required to reach equilibrium (or metastable equilibrium) become geologically long. Yet the apparent finite temperature divergence is fundamental to many theories of glasses; therefore, it becomes essential to find ways to finesse the extreme time scales related to the so-called Kauzmann paradox to bring new information to the ongoing conversation concerning the existence or not of an ideal glass transition at either the Kauzmann temperature or the Vogel–Fulcher–Tammann temperature. After describing the framework of the glassy state that is formed by the early ideas of a fictive temperature, we examine the use of extremely low fictive temperature glasses as a means to potentially get around the long time-scale problem. The challenge is to find ways to create such glasses and measure their properties. In addition to looking at the dynamic behavior of a 20-million-year-old amber and a vapor-deposited amorphous perfluoropolymer whose fictive temperature was the same as the Kauzmann temperature for the material, we also examine the possibility of directly testing the thermodynamics of an ideal glass transition by making athermal solutions of a poly(α-methyl styrene) and its pentamer, where we find that the entropy surface determined from extrapolation of the heat capacity to zero pentamer shows no distinct transition at as much as 180 K below the Kauzmann temperature. The significance of the dynamics of the stable glasses and the thermodynamics of the polymer solutions is discussed in terms that challenge the idea of an ideal glass transition. We also look in more detail at the ability to use vapor deposition to make ethylbenzene, a small-molecule organic, into an ultra-stable glass with a fictive temperature that is possibly below the Kauzmann temperature of this material. We end with remarks on the question of decoupling of different relaxation mechanisms as something not treated by current theories of glass, and we consider some open questions related to the fact that the glass transition remains an unresolved and important problem.

Surface-Bulk Interplay in Vapor-Deposited Glasses: Crossover Length and the Origin of Front Transformation

Thin film stable glasses transform into a liquid by a moving front that propagates from surfaces or interfaces with higher mobility. We use calorimetric data of vapor-deposited glasses of different thicknesses and stabilities to identify the role of glassy and liquid dynamics on the transformation process. By invoking the existence of an ultrathin intermediate layer whose transformation strongly depends on the properties of both the liquid and the glass, we show that the recovery to equilibrium is driven by the mismatch in the dynamics between glass and liquid. The lifetime of this intermediate layer associated with the moving front is the geometric mean between the bulk transformation time and the alpha relaxation time. Within this view, we explain the observed dependencies of the growth front velocity and the crossover length with both stability and temperature. Extrapolation of these results points towards ordinary thin film glasses transforming via a frontlike transformation mechanism if heated sufficiently fast, establishing a close connection between vapor-deposited and liquid-cooled glasses.

Activation volume in superpressed glass-formers

In pressurized glass-forming systems, the apparent (changeable) activation volume Va(P) is the key property governing the previtreous behavior of the structural relaxation time (τ) or viscosity (η), following the Super-Barus behavior: [Formula: see text], T = const. It is usually assumed that Va(P) = V#(P), where [Formula: see text] or [Formula: see text]. This report shows that Va(P) ≪ V#(P) for P → Pg, where Pg denotes the glass pressure, and the magnitude V#(P) is coupled to the pressure steepness index (the apparent fragility). V#(P) and Va(P) coincides only for the basic Barus dynamics, where Va(P) = Va = const in the given pressure domain, or for P → 0. The simple and non-biased way of determining Va(P) and the relation for its parameterization are proposed. The derived relation resembles Murnaghan - O'Connel equation, applied in deep Earth studies. It also offers a possibility of estimating the pressure and volume at the absolute stability limit. The application of the methodology is shown for diisobutyl phthalate (DIIP, low-molecular-weight liquid), isooctyloxycyanobiphenyl (8*OCB, liquid crystal) and bisphenol A/epichlorohydrin (EPON 828, epoxy resin), respectively.

Configurational entropy of glass-forming liquids

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraught with difficulties, misconceptions, and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, nonambiguous, and experimentally relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems.