Glasses are disordered materials that lack the periodicity of crystals but behave mechanically like solids. The most common way of making a glass is by cooling a viscous liquid fast enough to avoid crystallization. Although this route to the vitreous state-supercooling-has been known for millennia, the molecular processes by which liquids acquire amorphous rigidity upon cooling are not fully understood. Here we discuss current theoretical knowledge of the manner in which intermolecular forces give rise to complex behaviour in supercooled liquids and glasses. An intriguing aspect of this behaviour is the apparent connection between dynamics and thermodynamics. The multidimensional potential energy surface as a function of particle coordinates (the energy landscape) offers a convenient viewpoint for the analysis and interpretation of supercooling and glass-formation phenomena. That much of this analysis is at present largely qualitative reflects the fact that precise computations of how viscous liquids sample their landscape have become possible only recently.

Supercooled liquids and the glass transition

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.

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Stochastic thermodynamics, fluctuation theorems and molecular machines

Although it has long been recognized that dynamics in supercooled liquids might be spatially heterogeneous, only in the past few years has clear evidence emerged to support this view. As a liquid is cooled far below its melting point, dynamics in some regions of the sample can be orders of magnitude faster than dynamics in other regions only a few nanometers away. In this review, the experimental work that characterizes this heterogeneity is described. In particular, the following questions are addressed: How large are the heterogeneities? How long do they last? How much do dynamics vary between the fastest and slowest regions? Why do these heterogeneities arise? The answers to these questions influence practical applications of glass-forming materials, including polymers, metallic glasses, and pharmaceuticals.

Spatially Heterogeneous Dynamics in Supercooled Liquids

The field of viscous liquid and glassy solid dynamics is reviewed by a process of posing the key questions that need to be answered, and then providing the best answers available to the authors and their advisors at this time. The subject is divided into four parts, three of them dealing with behavior in different domains of temperature with respect to the glass transition temperature, Tg , and a fourth dealing with ‘‘short time processes.’’ The first part tackles the high temperature regime T.Tg ,i n which the system is ergodic and the evolution of the viscous liquid toward the condition at Tg is in focus. The second part deals with the regime T;Tg , where the system is nonergodic except for very long annealing times, hence has time-dependent properties ~aging and annealing!. The third part discusses behavior when the system is completely frozen with respect to the primary relaxation process but in which secondary processes, particularly those responsible for ‘‘superionic’’ conductivity, and dopart mobility in amorphous silicon, remain active. In the fourth part we focus on the behavior of the system at the crossover between the low frequency vibrational components of the molecular motion and its high frequency relaxational components, paying particular attention to very recent developments in the short time dielectric response and the high Q mechanical response. © 2000 American Institute of Physics.@S0021-8979~00!02213-1#

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1065&context=mse_pubs

Relaxation in glassforming liquids and amorphous solids

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerical diagonalization and by applying the single-bond coherent potential approximation. The results for the density of states $g(\ensuremath{\omega})$ are in excellent agreement with each other. If the system is near the borderline of stability a low-frequency peak appears in the quantity $g(\ensuremath{\omega})/{\ensuremath{\omega}}^{2}$ as a precursor of the instability. We argue that this peak is the analogon of the ``boson peak,'' observed in structural glasses and other disordered solids. By means of the level distance statistics we show that the peak is not associated with localized states.

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Harmonic Vibrational Excitations in Disordered Solids and the “Boson Peak”

Dynamics of supercooled liquids and glassy solids

Several experimental methods feature the potential to distinguish between slow and fast contributions to the non-exponential, ensemble averaged primary response in glass-forming materials. Some of these techniques are based on the selection of subensembles using multi-dimensional nuclear magnetic resonance, optical bleaching, and non-resonant spectral hole burning. Others, such as the time-dependent solvation spectroscopy, measure microscopic responses induced by local perturbations. Using several of these methods it could be demonstrated for various glass-forming materials that the non-exponential relaxation results from a superposition of dynamically distinguishable entities. The experimental observation that subensembles can be selected efficiently indicates a large degree of heterogeneity. The intrinsic response is compatible with single exponential relaxation.

Nature of the Non-exponential Primary Relaxation in Structural Glass-formers Probed by Dynamically Selective Experiments

Using deuteron NMR, we have studied molecular reorientation rates and rate exchange processes in supercooled ortho-terphenyl. We monitor the re-equilibration of differently selected subensembles through four-time stimulated echo experiments. A comparison of the two-time with the four-time echoes suggests that the characteristic time scales for reorientation and dynamical exchange are relatively similar. The four-time correlation functions were described using various multi-state rate exchange models.

https://iopscience.iop.org/article/10.1209/epl/i1996-00186-5/pdf

Dynamic heterogeneity in supercooled ortho-terphenyl studied by multidimensional deuteron NMR

The nonexponential response of propylene carbonate and glycerol near their glass transitions could be selectively altered using nonresonant spectral hole burning (NSHB) experiments. This observation provides evidence of the existence of a distribution of relaxation times in these supercooled liquids. NSHB is based on a pump, wait, and probe scheme and uses low-frequency large amplitude electrical fields to modify the dielectric relaxation. The temporal evolution of the polarization of the sample is then measured subsequent to a small voltage step. By variation of a recovery time inserted between pump and probe, the refilling of the spectral features could be monitored and was found to take place on the time scale set by the peak in the distribution. The recovery time and pump frequency dependences of the spectral modifications were successfully simulated using a set of coupled rate equations.

Gregor Diezemann

Papers

Harmonic Vibrational Excitations in Disordered Solids and the “Boson Peak”

Dynamics of supercooled liquids and glassy solids

Nature of the Non-exponential Primary Relaxation in Structural Glass-formers Probed by Dynamically Selective Experiments

Dynamic heterogeneity in supercooled ortho-terphenyl studied by multidimensional deuteron NMR

Nonresonant dielectric hole burning spectroscopy of supercooled liquids