Supercooled Regime Research Articles

Relaxation, crystal nucleation, kinetic spinodal and Kauzmann temperature in supercooled zinc selenide

Structural relaxation and crystallization are crucial phenomena in physics, chemistry, and materials science. A thorough study of their relationship could clarify some critical open questions. In this article, we focus on thermodynamic and kinetic properties: the Kauzmann temperature, TK (where the excess entropy tends to zero), the kinetic spinodal temperature, Tks (where the relaxation and crystal nucleation curves cross), and the glass transition temperature, Tg. We used zinc selenide (ZnSe) as a model system for which a reliable potential is available and obtained the self-diffusion coefficient, viscosity, critical nucleus birth times, relaxation times, entropy, Tg, Tks and TK by molecular dynamics (MD) simulations. We confirmed that the Stokes-Einstein equation breaks down in the moderate supercooled regime, impacting the relationships between the dynamic and thermodynamic properties. Two relaxation times were determined in the supercooled liquid (SCL) state: i) using the shear viscosity and the Maxwell equation, τη, and ii) from the self-intermediate scattering function and the Kohlrausch equation, τR. We found that in the whole supercooling regime, τη ≪ τR confirming two recent experimental studies for other substances. The nucleus birth times, τN, were also obtained for two system sizes. The τRT and τNT curves indeedcrossover,confirming the existence of a kinetic spinodal temperature for this system. Hence, for temperatures somewhat above and below the Tks, crystallization of the SCL could be affected by structural relaxation. Finally, our results demonstrate that if the Kauzmann temperature existed, it would be well below the Tks. Hence, crystal nucleation intervenes on the cooling path, and SCL ZnSe cannot reach this temperature, thus averting the paradoxical entropic situation. These findings shed light on some central problems related to supercooled liquids.

Temperature dependent onset of shear thinning in supercooled glass-forming network liquids.

The onset of shear thinning and the transition from Newtonian to non-Newtonian behavior in the viscous flow of select chalcogenide and oxide network glass-forming liquids in the deeply supercooled regime and its temperature dependence are studied using parallel plate rheometry. In all cases, the onset occurs at a shear rate γ̇c that is several orders of magnitude lower than the shear relaxation rate τ0 -1 and the former increases with increasing temperature. These results are in good qualitative agreement with the predictions of the existing models of shear relaxation and shear thinning based on the nonlinear Langevin equation theory, random first order transition theory, and the free volume model. However, in contrast to the theoretical predictions, the reduced shear rate W0 (=τ0γ̇c) at the onset is found to range between 10-3 and 10-5 and decrease with increasing temperature. This temperature dependence becomes stronger with increasing fragility of the liquid. These results likely indicate that the shear thinning mechanism in network liquids could be fundamentally different from those in molecular, metallic, or polymeric glass-formers.

Relations between thermodynamics, structures, and dynamics for modified water models in their supercooled regimes.

We use molecular dynamics simulations to study relations between thermodymamic, structural, and dynamical properties of TIP4P/2005 water models with systematically reduced partial charges and, thus, weaker hydrogen bonds. Observing a crossing of isochores in the P-T diagram, we show that these water-like models have a readily accessible liquid-liquid critical point (LLCP) associated with a transition between high-density liquid (HDL) and low-density liquid (LDL) forms and determine the dependence of the critical temperature Tc, pressure Pc, and density ρc on the charge-scaling factor from fits to a two-structure equation of states. The results indicate that the water-like models exhibit liquid polyamorphism in a wide range of interaction parameters. Considering elongated systems, we observe a decomposition into extended and stable HDL-like and LDL-like regions at appropriate pressures and low temperatures and analyze the respective structural and dynamical properties. We show that the diverse local order results in very different correlation times of local dynamics, while the fragility is hardly changed. The results yield insights into the origin of a dynamical crossover, which is observed when lowering the temperature along isobars and was previously interpreted in terms of a fragile-to-strong transition. Our findings imply that the effect does not involve two liquid phases with an exceptionally large difference of the fragility but rather a high temperature dependence near the LLCP results from a rapid conversion from HDL-like environments with faster dynamics to LDL-like ones with slower dynamics.

MD simulations of charged binary mixtures reveal a generic relation between high- and low-temperature behavior.

Experimental studies of the glassy slowdown in molecular liquids indicate that the high-temperature activation energy E∞ of glass-forming liquids is directly related to their glass transition temperature Tg. To further investigate such a possible relation between high- and low-temperature dynamics in glass-forming liquids, we analyze the glassy dynamics of binary mixtures using molecular dynamics simulations. We consider a binary mixture of charged Lennard-Jones particles and vary the partial charges of the particles and, thus, the high-temperature activation energy and the glass transition temperature of the system. Based on previous results, we introduce a phenomenological model describing relaxation times over the whole temperature regime from high temperatures to temperatures well inside the supercooled regime. By investigating the dynamics of both particle species on molecular and diffusive length scales along isochoric and isobaric pathways, we find a quadratic charge dependence of both E∞ and Tg, resulting in an approximately constant ratio of both quantities independent of the underlying observable, the thermodynamic ensemble, and the particle species, and this result is robust against the actual definition of Tg. This generic relation between the activation energy and the glass transition temperature indicates that high-temperature dynamics and the glassy slowdown are related phenomena, and the knowledge of E∞ may allow us to approximately predict Tg.

Structural relaxation in quantum supercooled liquids: A mode-coupling approach

We study supercooled dynamics in a quantum hard-sphere liquid using quantum mode-coupling formulation. In the moderate quantum regime, classical cage effects lead to slower dynamics compared to the strongly quantum regime, where tunneling overcomes classical caging, leading to faster relaxation. As a result, the glass transition critical density can become significantly higher than for the classical liquids. A perturbative approach is used to solve time dependent quantum mode-coupling equations to study in detail the dynamics of the supercooled liquid in the moderate quantum regime. Similar to the classical case, the relaxation time shows the power-law increase with the increase in the density in the supercooled regime. However, the power-law exponent is found to be dependent on the quantumness; it increases linearly as the quantumness is increased in the moderate quantum regime.

Core-softened water-alcohol mixtures: the solute-size effects.

Water is the most anomalous material on Earth, with a long list of thermodynamic, dynamic and structural behaviors that deviate from what is expected. Recent studies have indicated that these anomalies may be related to a competition between two liquids, which means that water has a potential liquid-liquid phase transition (LLPT) that ends at a liquid-liquid critical point (LLCP). In a recent study [J. Mol. Liq., 2020, 320, 114420], using molecular dynamics simulations and a core-softened potential approach, we have shown that adding a simple solute such as methanol can "kill" the density-anomalous behavior as the LLCP is suppressed by spontaneous crystallization in a hexagonal close packing (HCP) crystal near the LLPT. Now, we extend this work to realize how longer-chain alcohols will affect the complex behavior of water-alcohol mixtures in the supercooled regime. Besides core-softened (CS) methanol, ethanol and 1-propanol were added to a system of identical particles that interact through the continuous shouldered well (CSW) potential. We observed that the density anomaly gradually decreases its extension in phase diagrams until it disappears with the growth of the non-polar chain and the alcohol concentration, different from the liquid-liquid phase transition (and the LLCP), which remained present in all analyzed mixtures, according to Nature, 2001, 409, 692. For our model, the longer non-polar chains and higher concentrations gradually impact the competition between the scales in the CS potential, leading to a gradual disappearing of the anomalies until the TMD total disappearance is observed when the first coordination shell structure is also affected: short-range ordering is favored, leading to less competition between short- and long-range ordering and, consequently, to the extinction of anomalies. Also, the non-polar chain size and concentration have an effect on the solid phases, favoring the hexagonal close packed (HCP) solid and the amorphous solid phase over the body-centered cubic (BCC) crystal. These findings help to elucidate the behavior of water solutions in the supercooled regime and indicate that the LLCP can be observed in systems without density-anomalous behavior.

Microscopic theory for elastic modulus of colloidal polymers: Effect of bond length

Colloidal polymers have attracted increasing attention in condensed physics, statistical mechanics and polymer science and engineering due to their advances in synthesis and visualization. Many useful properties and applications of colloidal polymers make them an ideal model to explore fundamental problems in slow dynamics and rheology of chain-like molecules in supercooled regime. With temperature decreasing or density rapidly increasing, amorphous materials often exhibit nonzero shear moduli. In this article, we are to investigate the nonzero shear modulus and bulk modulus of colloidal polymer in supercooled regime based on recent microscopic theoretical development. At the segmental-scale level, an analytical derivation for elastic modulus of colloidal polymer is constructed based on the standard approximation in naïve mode-coupling theory (NMCT). In the framework of nonlinear Langevin equation theory (NLET), the derivation combines the concept of dynamic free energy, localization and NMCT crossover volume fraction. Taking the chain connectivity into account, an explicit expression for shear modulus including intrachain structure factor, interchain correlation and localized length is formulated. Bulk modulus can be obtained by relating it to long wavelength part of static structure factor. Firstly, our calculation for discrete wormlike chain shows that intrachain structure factor has a power law decay at intermediate wavevector which is similar to flexible linear chain. Secondly, we find that colloidal polymer with long bond length has a lower NMCT crossover volume fraction. Furthermore, inputting the localized length, long wavelength density fluctuation and static intrachain and interchain structures into the theoretical expression, the effect of bond length on shear modulus and bulk modulus are investigated. Interestingly, we find the bond length plays a critical and unique role in localized length and bulk modulus. For instance, when the supercooling degree is used as an independent variable, the local length and bulk elastic modulus of the chain with the same bond length can be collapsed onto a universal curve, which is independent of chain length and local bending energy. However, in the aspect of shear modulus, the bond length is not a unique quantity and the above universal curve cannot be found. The shear modulus depends on other parameters of chain, such as chain length and rigidity. According to the universal behavior of zero-wavevector static structure factor versus bond length, we guess that the nonuniversal curve of shear modulus is due to the bond length effect on long wavevector static structure factor. This work provides a theoretical foundation for controlling various properties of chain-like supercooled materials in the future.

Anomalously strong viscosity behavior in mixed oxy-sulfide Na4P2S7-xOx invert glasses

In this report, the first observations of the anomalously strong viscosity behavior in the melt quenched (MQ) invert mixed oxy-sulfide Na4P2S7-xOx, 0 ≤ x ≤ 5, (NaPSO) glass series. We find that these glasses even with 67 mole% modifier, Na2S, exhibit a calorimetric fragility index, mcal, as small as 29 compared to typical values of ~ 60 to 80 for alkali silicate glasses with > 50 mole% SiO2. We find that the calorimetric fragility of these glasses varies systematically with the extent of network forming bridging oxygens (BOs) in the glasses. The mcal values were converted to kinetic fragility (mvis) values and used with the measured Tgs to produce viscosity curves for the glasses using the Mauro-Yue-Ellison-Gupta-Allan (MYEGA) model. The viscosity of the glass with a minimum mcal value of x = 2.5 was then shown to exhibit a viscosity that was as strong as some alkali aluminosilicate glasses.In this report, the first observations have been made of anomalously strong viscosity behavior and correspondingly strong bulk glass formation and resistance to crystallization in a melt quenched (MQ) prepared series of invert, modifier content greater than the glass former content, mixed oxy-sulfide Na4P2S7-xOx, 0 ≤ x ≤ 5, (NaPSO) glasses. We find that these glasses even with 67 mole % modifier, Na2S, and only 33 mole% glass former P2S5-xOx, exhibit a calorimetric fragility index, mcal, as small as 29 compared to typical values of ~ 60 to 80 for alkali silicate glasses with > 50 mole% SiO2 and the theoretical minimum mcal of ~ 15. The mcal values were converted to kinetic viscosity fragility, mvis, values and used with the measured glass transition temperatures, Tgs, to produce viscosity curves for the glasses using the Mauro-Yue-Ellison-Gupta-Allan (MYEGA) model. The viscosity of the glass with a minimum mcal value of x = 2.5 was then shown to exhibit a viscosity that was as strong as, and for some compositions stronger than, the viscosity of alkali aluminosilicate glasses which have three dimensional network structures compared to the one dimensional chain structures observed in these MOS invert glasses. Consistent with these small values of fragility indices and therefore predicted higher viscosity above the glass transition temperature, Tg, in the supercooled liquid regime, these glasses are also particularly resistant to crystallization. For example, the x = 2.5 glass composition exhibits a crystallization temperature, TC, more than 150K above its Tg. We find that the calorimetric fragility of these glasses varies systematically with the extent of network forming bridging oxygens (BOs) in the glasses. The structural change caused by incrementally replacing sulfur with oxygen has been found to have consistent, large effects on the thermal properties.

Experimental tests for a liquid-liquid critical point in water

Water is a fascinating material. Its composition is simple—one oxygen andtwo hydrogen atoms—but its chemistry and physics are extremely complex andexhibit 75 documented anomalies. Although these anomalies and theirmolecular origin are not completely understood, we know that hydrogen bondsplay key roles in all of the phases of water. Moreover, there isexperimental evidence that the polymorphism of the ice structure extendsinto the liquid phase and is associated with a liquid-liquid coexistenceline. This is currently a topic of great interest in water research becausethere are indications that the end point of the coexistence line correspondsto a second critical point inside the supercooled liquid regime. We examinethe recent progress in understanding water anomalies and the liquid-liquidphase transition hypothesis, including the results of recent experimentalwork and molecular simulations of both bulk and confined water. We examineexperimental results that test whether the behavior of liquid water isconsistent with the textquotedblleft liquid polymorphismtextquotedblrighthypothesis that liquid water can exist in two distinct phases of differingdensities. We also examine recent research on the anomalies of nanoconfinedwater and, in particular, on water in biological environments. We find thatthe concept of liquid polymorphism can also describe the properties of otherliquids that have two characteristic length scales.

Competing interactions near the liquid-liquid phase transition of core-softened water/methanol mixtures

Water is a unique material with a long list of thermodynamic, dynamic and structural anomalies, which are usually attributed to the competition between two characteristic length scales in the intermolecular interaction. It has been argued that a potential liquid-liquid phase transition (LLPT) ending at a liquid-liquid critical point (LLCP) lies at the core of the anomalous behavior of water. This transition which has been evidenced in multiple simulation studies seems to be preempted experimentally by spontaneous crystallization. Here, in order to expose the connection between the spontaneous crystallization observed in the supercooled regime in the vicinity of the LLPT, and the density anomaly, we perform extensive Molecular Dynamics simulations of a model mixture of core-softened water and methanol. The pure water-like fluid exhibits a LLPT and a density anomaly. In contrast, our pure methanol-like model does have a LLPT but lacks the density anomaly. Our results illustrate the relation between the vanishing of the density anomaly and an increase in the temperature of the spontaneous crystallization: once this temperature surpasses the LLCP critical temperature, no density anomaly is observed. This peculiar feature illustrates how fine tuning the competitive interactions determine the anomalous behavior of water/alcohol mixtures.

Cooperatively rearranging regions change shape near the mode-coupling crossover for colloidal liquids on a sphere

The structure and dynamics of liquids on curved surfaces are often studied through the lens of frustration-based approaches to the glass transition. Competing glass transition theories, however, remain largely untested on such surfaces and moreover, studies hitherto have been entirely theoretical/numerical. Here we carry out single particle-resolved imaging of dynamics of bi-disperse colloidal liquids confined to the surface of a sphere. We find that mode-coupling theory well captures the slowing down of dynamics in the moderate to deeply supercooled regime. Strikingly, the morphology of cooperatively rearranging regions changed from string-like to compact near the mode-coupling crossover—a prediction unique to the random first-order theory of glasses. Further, we find that in the limit of strong curvature, Mermin–Wagner long-wavelength fluctuations are irrelevant and liquids on a sphere behave like three-dimensional liquids. A comparative evaluation of competing mechanisms is thus an essential step towards uncovering the true nature of the glass transition.

Some Aspects of the Liquid Water Thermodynamic Behavior: From The Stable to the Deep Supercooled Regime.

Liquid water is considered to be a peculiar example of glass forming materials because of the possibility of giving rise to amorphous phases with different densities and of the thermodynamic anomalies that characterize its supercooled liquid phase. In the present work, literature data on the density of bulk liquid water are analyzed in a wide temperature-pressure range, also including the glass phases. A careful data analysis, which was performed on different density isobars, made in terms of thermodynamic response functions, like the thermal expansion and the specific heat differences , proves, exclusively from the experimental data, the thermodynamic consistence of the liquid-liquid transition hypothesis. The study confirms that supercooled bulk water is a mixture of two liquid “phases”, namely the high density (HDL) and the low density (LDL) liquids that characterize different regions of the water phase diagram. Furthermore, the isobars behaviors clearly support the existence of both a liquid–liquid transition and of a liquid–liquid critical point.

Recipe for ultrafast and persistent phase-change memory materials

The contradictory nature of increasing the crystallization speed while extending the amorphous stability for phase-change materials (PCMs) has long been the bottleneck in pursuing ultrafast yet persistent phase-change random-access memory. Scandium antimony telluride alloy (ScxSb2Te3) represents a feasible route to resolve this issue, as it allows a subnanosecond SET speed but years of reliable retention of the RESET state. To achieve the best device performances, the optimal composition and its underlying working mechanism need to be unraveled. Here, by tuning the doping dose of Sc, we demonstrate that Sc0.3Sb2Te3 has the fastest crystallization speed and fairly improved data nonvolatility. The simultaneous improvement in such ‘conflicting’ features stems from reconciling two dynamics factors. First, promoting heterogeneous nucleation at elevated temperatures requires a higher Sc dose to stabilize more precursors, which also helps suppress atomic diffusion near ambient temperatures to ensure a rather stable amorphous phase. Second, however, enlarging the kinetic contrast through a fragile-to-strong crossover in the supercooled liquid regime should require a moderate Sc content; otherwise, the atomic mobility for crystal growth at elevated temperatures will be considerably suppressed. Our work thus reveals the recipe by tailoring the crystallization kinetics to design superior PCMs for the development of high-performance phase-change working memory technology.

Tagged-particle dynamics in confined colloidal liquids

We present numerical results for the tagged-particle dynamics by solving the mode-coupling theory in confined geometry for colloidal liquids (cMCT). We show that neither the microscopic dynamics nor the type of intermediate scattering function qualitatively changes the asymptotic dynamics in vicinity of the glass transition. In particular, we find similar characteristics of confinement in the low-frequency susceptibility spectrum which we interpret as footprints of parallel relaxation. We derive predictions for the localization length and the scaling of the diffusion coefficient in the supercooled regime and discover a pronounced nonmonotonic dependence on the confinement length. For dilute liquids in the hydrodynamic limit we calculate an analytical expression for the intermediate scattering functions, which is in perfect agreement with event-driven Brownian dynamics simulations. From this, we derive an expression for persistent anticorrelations in the velocity autocorrelation function (VACF) for confined motion. Using numerical results of the cMCT equations for the VACF we also identify a crossover between different scalings corresponding to a transition from unconfined to confined behavior.

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.

Dynamical Accuracy of Water Models on Supercooling.

Molecular dynamics (MD) simulations are commonly used to explore the structural and dynamical properties of supercooled bulk water in the so-called "no man's land" (NML) (150-227 K), where crystallization occurs almost instantaneously. This approach has provided significant insight into experimentally inaccessible phenomena. In this paper, we compare the dynamics of simulations using one-, three-, and four-body water models to experimentally measured quasielastic neutron scattering spectra. We show that the agreement between simulated and experimental data becomes substantially worse with a decrease in temperature toward the deeply supercooled regime. It was found that it is mainly the nature of the local dynamics that is poorly reproduced, as opposed to the macroscopic properties such as the diffusion coefficient. This strongly implies that the molecular mechanism describing the water dynamics is poorly captured in the MD models, and simulated structural and dynamical properties of supercooled water in NML must be interpreted with care.

The progression of thermodynamic anomalies in MX2 networks with local tetrahedral geometries

Key thermodynamic anomalies in density and compressibility, as well as the related stability limits, are determined using an ionic model for BeF2 which includes many-body polarization terms. BeF2 is chosen as an example of an archetypal network-forming system whose structure can be rationalised in terms of connected local tetrahedral coordination polyhedra. The anion dipole polarizability (which effectively controls the bond angles linking neighbouring tetrahedra) is used as a single free parameter in order to help rationalise the changes in the anomaly locations in phase space, whilst all other potential parameters remain fixed. The anomalies and stability limits systematically shift to lower temperature and higher pressure as the anion polarizability is increased. At high dipole polarizabilities the temperature of maximum density anomaly locus becomes suppressed into the supercooled regime of the phase space. The movements of the anomaly loci are analysed in terms of the network structure and the correlation with the inter-tetrahedral bond angles is considered. The high sensitivity of the anomalies to the details of the potential models applied is discussed with reference to previous works on related systems. The relationship to analogous studies on Stillinger–Weber liquids is discussed.

The dynamics of supercooled water can be predicted from room temperature simulations.

There is strong interest in understanding the behavior of water in its supercooled state. While many of the qualitative trends of water dynamical properties in the supercooled regime are well understood, the connections between the structure and dynamics of room temperature and supercooled water have not been fully elucidated. Here, we show that the reorientational time scales and diffusion coefficients of supercooled water can be predicted from simulations of room temperature liquid water. Specifically, the derivatives of these dynamical time scales with respect to inverse temperature are directly calculated using the fluctuation theory applied to dynamics. These derivatives are used to predict the time scales and activation energies in the supercooled regime based on the temperature dependence in one of two forms: that based on the stability limit conjecture or assuming an equilibrium associated with a liquid-liquid phase transition. The results indicate that the retarded dynamics of supercooled water originate from structures and mechanisms that are present in the liquid under ambient conditions.

Liquid‐liquid phase transitions in glass‐forming systems and their implications for memory technology

AbstractWhile it is broadly known that solid compounds may exist in distinct crystalline arrangements (polymorphs), the notion that some liquids may also adopt distinct phases with dissimilar structures and densities is much less widespread. One of the reasons is that these liquid‐liquid (L‐L) transitions often occur in the supercooled equilibrium regime below the melting line and can be challenging to observe experimentally. Glass‐forming liquids that supercool over significant temperature ranges can therefore constitute useful systems for investigating these transitions. In this paper we review experimental evidence for L‐L transitions in chalcogenide systems. In that respect, L‐L transitions are found to be associated with transitions from fragile to strong viscous behavior in these glass‐forming liquids. Moreover, they are signaled by extrema in multiple thermodynamic functions and sharp change in physical properties such as electrical conductivity. Finally, while the physical principles underlying these transitions are still unclear, they have been shown to play a critical role in the function of PCMs that are poised to transform fast computing technologies.

A collective elastic fluctuation mechanism for decoupling and stretched relaxation in glassy colloidal and molecular liquids.

We propose a microscopic theory for the decoupling of self-diffusion and structural relaxation in glass-forming liquids within the Elastically Collective Nonlinear Langevin Equation (ECNLE) activated dynamics framework. Our central hypothesis is that the heterogeneity relevant to this problem is static fluctuations of local density on the scale of 3-4 particle diameters and how this changes local packing correlations. These fluctuations modify the degree of dynamical cage expansion that mechanistically couples intracage large amplitude hopping and longer range collective elasticity in ECNLE theory. Decoupling only emerges in the deeply supercooled regime where the strongly temperature dependent elastic barrier becomes non-negligible relative to its noncooperative local analog. The theory makes predictions for various aspects of the decoupling phenomenon, including apparent fractional power law Stokes-Einstein behavior, that appear to be consistent with experiments and simulations on hard sphere fluids and molecular liquids. Of central importance is a microscopic connection between the barrier fluctuation variance and most probable barrier height. Sensible results are also obtained for the nonexponential stretching of a generic relaxation time correlation function and its temperature evolution. Nonuniversality can arise from the relative importance of the local and collective barriers (related to fragility) and the precise magnitude of the length scale that defines the transition from local cage to elastic physics. Comparison is made with a traplike model based on a Gaussian distribution of barriers.