Relaxation In Glass-forming Liquids Research Articles

Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids

Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers.

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature Tg, whether there is an underlying thermodynamic transition at some finite temperature below Tg, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.

Perspective on non-invasive and non-destructive photoacoustic and photothermal applications

This contribution intends to convince readers that by virtue of the rich physics involved, optical excitation, thermal diffusion, thermal expansion, and acoustic wave propagation, and of the optical nature of the involved excitation and detection, photoacoustic and photothermal methods offer a unique combination of features that makes them very attractive for exploitation in a wide area of scientific and technological fields that involve material property evaluation. A perspective is also given on the high potential of these methods for substantial advances beyond the state of the art in a diverse selection of scientific disciplines: biomedical diagnostics, cell and tissue mechanobiology, thin film and interface characterization, characterization of the microstructure of solids, and the physics of relaxation in glass-forming liquids.

Experimental Tests of a Theoretically Predicted Noncausal Correlation between Dynamics and Thermodynamics in Glass-forming Polymer Melts

The connection between slow activated relaxation in glass-forming liquids and various equilibrium thermodynamic properties remains intensely debated. The microscopic elastically collective nonlinea...

Characterization of the secondary relaxations in glass-forming liquids. The contribution of the Starkweather line and of the Coupling Model to the rationalization of TSDC results

This work addresses the study by thermostimulated depolarization currents (TSDC) of Johari-Goldstein (JG) β-relaxations in glass forming systems. Here we analyze the differences between the β-relaxation and the fast secondary (γ, δ, ε, …) relaxations on the one hand, and the α-relaxation on the other.It is shown that TSDC is able to characterize JG although this mobility is often close to, or even partially overlapped with, the α-relaxation.It is also shown that the Starkweather line or zero entropy line (ZEL) can be used as a reference element to identify the secondary relaxations: non-compliance with the ZEL is an indicator of cooperativity.We finally showed that the non-cooperativeness of the Johari-Goldstein relaxation is highlighted by the joint consideration of the Coupling Model and the Starkweather line.

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.

On the molecular mechanisms of α and β relaxations in ionic liquids.

Using 2H NMR, we determine correlation times and motional mechanisms for the α and β relaxations of glass-forming imidazolium-based ionic liquids, explicitly, for the associated cation reorientation dynamics. It is shown that the α relaxation is faster, its nonexponentiality is stronger, and the fragility is higher for bis(trifluoromethylsulfonyl)imide anions than that for tetrafluoroborate anions. 2H NMR stimulated-echo studies reveal that the overall reorientation dynamics involved in the α relaxation is isotropic and composed of jumps about small angles, where the mean jump angles are smaller for larger cations. Moreover, we demonstrate that, in addition to a cation-specific β relaxation, all studied ionic liquids exhibit the genuine Johari-Goldstein β relaxation of glass-forming liquids. Various 2H NMR results consistently indicate that the associated rotational motion is spatially highly restricted. Altogether, our findings show that, despite strong electrostatic interaction and prominent microphase separation of ionic liquids, their glassy dynamics resemble that of their nonionic counterparts, including similar microscopic mechanisms for intrinsic α and β relaxations.

Integral equation theory of thermodynamics, pair structure, and growing static length scale in metastable hard sphere and Weeks-Chandler-Andersen fluids.

We employ the Ornstein-Zernike integral equation theory with the Percus-Yevick (PY) and modified-Verlet (MV) closures to study the equilibrium structural and thermodynamic properties of metastable monodisperse hard sphere and continuous repulsion Weeks-Chandler-Andersen (WCA) fluids under density and temperature conditions where the system is strongly overcompressed or supercooled, respectively. The theoretical results are compared to crystal-avoiding simulations of these dense monodisperse model one-component fluids. The equation of state (EOS) and dimensionless compressibility are computed using both the virial and compressibility routes. For hard spheres, the MV-based virial route EOS and dimensionless compressibility are in very good agreement with simulation for all packing fractions, much better than the PY analogs. The corresponding MV-based predictions for the static structure factor are also very good. The amplitude of density fluctuations on the local cage scale and in the long wavelength limit, and three technically different measures of the density correlation length, are studied with both closures. All five properties grow in a roughly exponential manner with density in the metastable regime up to packing fractions of 58% with no sign of saturation. The MV-based results are in good agreement with our crystal-avoiding simulations. Interestingly, the density dependences of long and short wavelength quantities are closely related. The MV-based theory is also quite accurate for the thermodynamics and structure of supercooled monodisperse WCA fluids. Overall our findings are also relevant as critical input to microscopic theories that relate the equilibrium pair correlation function or static structure factor to dynamical constraints, barriers, and activated relaxation in glass-forming liquids.

NMR Relaxometry: The Canonical Case Glycerol.

We present a quantitative description of the proton spin-lattice relaxation rate R1(T,ω) of glycerol including temperatures from 191 to 360 K and a frequency range 10 kHz < ω/2π < 20 MHz covered by the field-cycling technique. The analysis encompasses the data compiled by Noack and co-workers in 1971, so far, the most complete data set (10 kHz > ω/2π < 117 MHz). Applying frequency-temperature superposition, master curves are constructed extending over 15 decades in frequency/time. They are described by contributions reflecting translational and rotational dynamics mediated by inter- and intramolecular relaxation pathways. The rotational part of the spectral density/susceptibility shows high similarity with those reported by dielectric spectroscopy or photon correlation spectroscopy (PCS). In addition to a Cole-Davidson-like peak, a high-frequency "excess wing" has to be accounted for. Quantitative agreement with the PCS susceptibility is found which probes the same order of the rotational correlation function. The translational contribution is reproduced by applying the force-free hard sphere model, describing diffusion of dipolarly coupled spin systems. Rotational and translational time constants are compared to those from other techniques. Our approach is paradigmatic for the analysis of spin relaxation in glass-forming liquids. It also solves long-standing deficiencies regarding the analyses of deuteron relaxation. Moreover, the case of glycerol is special as its large separation of translation and rotation dynamics, probably because of its hydrogen bond network, is not found in nonassociated liquids.

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.

Fluctuation Effects in the Adam-Gibbs Model of Cooperative Relaxation.

A generalization of the Adam-Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam-Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.

Topological Constraint Theory for Network Glasses and Glass-Forming Liquids: A Rigid Polytope Approach

A variation of the topological constraint theory is proposed where an atomic network is modeled as a collection of rigid polytopes, and which explicitly distinguishes the bond angle constraints as well as rigid bond angles from flexible ones. The proposed theory allows for direct quantitative estimation of the fraction f of zero-frequency or floppy modes of the network. A preliminary model is proposed to connect the theory to the two key experimental observables that characterize glass-forming liquids, i.e., the glass transition temperature Tg and fragility m. The predicted values are tested against the literature data available for binary and ternary chalcogenides in the Ge-As-Se system. The Tg is related to f in this model by the activation entropy associated with the bond scission-renewal dynamics that is at the heart of transport and relaxation in glass-forming liquids. On the other hand, the large and temperature-dependent conformational entropy contribution of the 1-polytopes, i.e., the selenium chain elements in these chalcogenide glass-forming liquids, plays a key role in controlling the variation of m with f.

Influence of Longer Range Transfer of Vapor Interface Modified Caging Constraints on the Spatially Heterogeneous Dynamics of Glass-Forming Liquids

Based on the Elastically Collective Nonlinear Langevin Equation theory of bulk relaxation in glass-forming liquids, and our recent ideas of how interface-nucleated modification of caging constraints are spatially transferred into the interior of a thick film, we present a force-based theory for dynamical gradients in thick films with one vapor interface that includes collective elasticity effects. Quantitative applications to the foundational hard sphere fluid and polymer melts of diverse fragilities are presented. We predict a roughly exponential spatial variation of total activation barrier which is non-perturbatively modified to ~10 particle diameters into film. This leads to prediction of a reduced alpha relaxation time gradient of a double exponential form characterized by a nearly constant spatial decay length, in qualitative accord with simulations. These spatially heterogeneous changes of the temperature variation of the alpha time result in a large and long-range gradient of the local glass transition temperature. An average interfacial layer thickness relevant to ensemble-averaged dielectric and other experiments is also computed. It is predicted to be rather large at the bulk glass transition temperature, decreasing roughly linearly with heating. Spatially inhomogeneous power law decoupling of the alpha relaxation time from its bulk value is predicted, with an effective exponent that decays to zero with distance from the free surface in a nearly exponential manner, trends which are in qualitative accord with recent simulations. This behavior and the double exponential alpha time gradient are related and can be viewed as consequences of an effective quasi-universal factorization of the total barrier in films into the product of its bulk temperature dependent value times a function solely of location in the film.

Connectivity and free-surface effects in polymer glasses

The glass transition is one of the few unsolved problems in condensed matter physics: agreement on the cause of the slowing down of structural relaxation in glass-forming liquids is lacking. Glasses are amorphous solids, which do not possess the long-range crystalline order, yet display arrested dynamics and the shear elastic modulus characteristic of equilibrium elasticity. It has been suggested that due to the influence of intramolecular interactions and chain connectivity, the nature of the glass transition in polymers and in standard glass-formers is fundamentally different. Here, we discuss the role of connectivity in polymer glasses, demonstrating that although covalent bonding promotes glass formation, bonding sequentiality that defines a polymer chain is not critical in the bulk: glassy dynamics is purely a result of the number of connections per particle, independently of how these connections are formed, agreeing with the classical Phillips-Thorpe topological constraint theory. We show that bonding sequentiality does play an important role in the surface effects of the glass, highlighting a major difference between polymeric and colloidal glasses. Further, we identify the heterogenous dynamics of model coarse-grained polymer chains both in ‘bulk’ and near the free surface, and demonstrate characteristic domain patterns in local displacement and connectivity.

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt.

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

Correlation between temperature variations of static and dynamic properties in glass-forming liquids.

Detailed analysis of the static structure factor S(Q) in several glass-forming liquids reveals that the temperature variations of the width of the main diffraction peak ΔQ(T) correlate with the fragility of these liquids. This observation suggests a direct connection between rather subtle structural changes and sharp slowing down of structural relaxation in glass-forming liquids. We show that this observation can be rationalized using the Adam-Gibbs approach, through a connection between temperature variations of structural correlation length, l_{c}∼2π/ΔQ, and the size of cooperatively rearranging regions.

An Overview on Short and Long Time Relaxations in Glass-forming Supercooled Liquids

Density fluctuations in supercooled liquids near the glass transition relax in multiple steps. The short time relaxation is known as β-relaxation and the final long time relaxation is called α-relaxation. It is believed that the long time α-relaxation is a cooperative phenomena associated with a growing length scales, whereas the short-time β-relaxation is often attributed to spatially local processes involving the rattling motion of a particle in the transient cage formed by its neighbors. Using molecular dynamics simulations of few model glass-forming liquids, we show that the β-relaxation is also cooperative in nature and the length scale extracted from the detailed finite-size scaling analysis of β-relaxation is found to be the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime. These results provide a clear connection between short-time dynamics and long-time structural relaxation in glass-forming liquids.

Influence of an amorphous wall on the distribution of localized excitations in a colloidal glass-forming liquid

Elucidating the nature of the glass transition has been the holy grail of condensed matter physics and statistical mechanics for several decades. A phenomenological aspect that makes glass formation a conceptually formidable problem is that structural and dynamic correlations in glass-forming liquids are too subtle to be captured at the level of conventional two-point functions. As a consequence, a host of theoretical techniques, such as quenched amorphous configurations of particles, have been devised and employed in simulations and colloid experiments to gain insights into the mechanisms responsible for these elusive correlations. Very often, though, the analysis of spatio-temporal correlations is performed in the context of a single theoretical framework, and critical comparisons of microscopic predictions of competing theories are thereby lacking. Here, we address this issue by analysing the distribution of localized excitations, which are building blocks of relaxation as per the dynamical facilitation (DF) theory, in the presence of an amorphous wall, a construct motivated by the random first-order transition theory (RFOT). We observe that spatial profiles of the concentration of excitations exhibit complex features such as non-monotonicity and oscillations. Moreover, the smoothly varying part of the concentration profile yields a length scale , which we compare with a previously computed length scale . Our results suggest a method to assess the role of dynamical facilitation in governing structural relaxation in glass-forming liquids.

Characteristic length scales of the secondary relaxations in glass-forming glycerol.

We investigate the secondary relaxations and their link to the main structural relaxation in glass-forming liquids using glycerol as a model system. We analyze the incoherent neutron scattering signal dependence on the scattering momentum transfer, Q , in order to obtain the characteristic length scale for different secondary relaxations. Such a capability of neutron scattering makes it somewhat unique and highly complementary to the traditional techniques of glass physics, such as light scattering and broadband dielectric spectroscopy, which provide information on the time scale, but not the length scales, of relaxation processes. The choice of suitable neutron scattering techniques depends on the time scale of the relaxation of interest. We use neutron backscattering to identify the characteristic length scale of 0.7 Å for the faster secondary relaxation described in the framework of the mode-coupling theory (MCT). Neutron spin-echo is employed to probe the slower secondary relaxation of the excess wing type at a low temperature ( ∼ 1.13T g . The characteristic length scale for this excess wing dynamics is approximately 4.7 Å. Besides the Q -dependence, the direct coupling of neutron scattering signal to density fluctuation makes this technique indispensable for measuring the length scale of the microscopic relaxation dynamics.

Short-Time Beta Relaxation in Glass-Forming Liquids Is Cooperative in Nature.

Temporal relaxation of density fluctuations in supercooled liquids near the glass transition occurs in multiple steps. Using molecular dynamics simulations for three model glass-forming liquids, we show that the short-time β relaxation is cooperative in nature. Using finite-size scaling analysis, we extract a growing length scale associated with beta relaxation from the observed dependence of the beta relaxation time on the system size. We find, in qualitative agreement with the prediction of the inhomogeneous mode coupling theory, that the temperature dependence of this length scale is the same as that of the length scale that describes the spatial heterogeneity of local dynamics in the long-time α-relaxation regime.