Institute for Complex Systems - Sapienza - CNR

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ISC Sapienza Glass-forming liquids Structural Glasses and Glass Forming Liquids: an introduction

Structural Glasses and Glass Forming Liquids: an introduction

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Glass is a very present element in everyday life, so much so that it becomes a complicated and long exercise to imagine being without it: no windows, no spectacles, no bottles, no street lamps, no screens for computer, mobile phone and television, no windscreen in the car, no light bulbs, no watches, just to mention a few examples. Indeed, it is a necessary material. Yet, besides its practical use, glass, e.g., in the form of lenses, mirrors, flasks or pipes, has been fundamental in the development of scientific research and visual art, helping and guiding the human sight to look at things in different perspectives and on widely different length-scales, from the microscopic world of cells and bacteria to the open space of planets and stars.
From the point of view of physics, all glasses represent an excited state, and may, in due course, relax to the crystalline ground state. Crystallization involves two steps: (i)the nucleation of microscopic bubbles of crystal in the liquid phase and (ii) their growth, rapidly transforming the whole material into a solid whose structure is an ordered pattern. Nucleation processes tend to be extremely slow in glassy systems on experimental times.

Glass relaxation times may be very long, 70-million-year-old silica-rich volcanic glasses not being uncommon. As a typical example consider window glass. Each window glass everywhere in the world is far from equilibrium, a cubic micron of such glass neither being a crystal nor an ordinary undercooled liquid. It is, in some sense, an undercooled liquid that in the glass-forming process has fallen out of its own metastable equilibrium. The glassy state is inherently a nonequilibrium state: a substance that is glassy in daily life, i.e. on a timescale of years, may behave like a liquid on a geological timescale.

Any liquid cooled down sufficiently fast to low enough temperature will become glassy, i.e., it will lack time to evolve into a long-range ordered crystalline array. Two types of mechanisms conceivably play a role in this quenching process: (i) fast interactions, which happen on a short timescale, characterize relaxation processes that are rapid enough to remain in thermal equilibrium at every step of the cooling (beta relaxation processes), and (ii) slow mechanisms, mainly reconstructive transformations involving many molecules, that practically``carry" the structural, off-equilibrium, relaxation (called alpha relaxation). In principle, the larger the variety of molecules is, the easier the glass formation becomes. The alpha processes start lagging behind the thermal state of the system during cooling already in the molten state. Their relaxation time, then, exceeds the time needed to reach equilibrium and they progressively get out of phase with the forcing thermal field, becoming increasingly more decoupled from it.

Relaxation times in glassy systems scale with viscosity, which indicates the resistance to flow of a system and is a measure of its internal friction. The International System unit of viscosity is Pa s = kg/(m s). An older unit is Poise, 1 Poise = 0.1 Pa s. Water of 20 degrees Celsius has viscosity 1 centiPoise. An undercooled liquid is called glass, when it has a viscosity of 1013 Poise, one thousand-million-million times as large. Viscosity has, in general, a strong temperature dependence varying, e.g., in silica-based glassy systems, over fifteen orders of magnitude.


As a parameter, viscosity fixes the different manufacturing processes in a glass tank and industrial terms like strain point, anneal point, softening and working point are all defined for a specific viscosity. Despite its ubiquitous operational use in industry, it is perhaps the least understood of all glass properties. In silica-based systems the viscosity is dominated by the silica concentration in the system, with high silica percentage having an enormously higher viscosity. This manifests itself in nature in very fluid lava for low-silica-containing fluids, or else as explosive volcanism for high-silica-containing ones, where the high viscosity prevents softer energy release.

The point at which the viscosity, or relaxation time, are so large that equilibrium no longer exists between the thermal state of the glass-forming system and the surrounding heat bath, is called the glass transition temperature, commonly occurring at about two thirds of the melting temperature in silica-based glasses. This transition temperature, with its measurable heat effect, discriminates between a glass and an undercooled liquid.

There are two typical phenomenological behaviors of the viscosity as a function of the temperature, as
temperature decreases towards the glass transition, that have been identified so far. The first one is the so-called Arrhenius relaxation, according to which the viscosity grows exponentially at a low temperature, as exp(A/T), where A is the activation energy for viscous flow. The second one is the Vogel-Fulcher law, expressed as exp[B/(T-T_0)], that diverges even faster than the Arrhenius one, as it can be expressed defining a temperature-dependent activation energy A=BT/(T-T_0), even diverging at the low but finite temperature T_0. Both laws indicate a very large increase in viscosity or, equivalently, in relaxation time, preventing the material from reaching thermal equilibrium. During the last decennia two categories of glasses have been distinguished according to the above-mentioned temperature dependence around the glass transition: the strong glasses and the fragile glasses. Neither the ``strong'' nor ``fragile'' property of glass refers to resistance to crashes or heating, rather to the difficulty for macroscopically rearranging its amorphous packing (into another, equivalent, amorphous packing), following an external perturbation. The distinction is based on the flow behavior of glasses in the molten state. The materials belonging to the Arrhenius family are designated as strong. They display a very high viscosity above the melting point. For instance, SiO2 has a viscosity of 2.400 Pa s about 300 degrees above its melting point (ca. 2100 K). The materials whose viscosity follows the Vogel-Fulcher law are designated as fragile.

A glass can be viewed as a liquid in which a huge slowing down of the diffusive motion of the particles has destroyed its ability to flow on experimental timescales. The slowing down is expressed through the relaxation time, that is, generally speaking, the characteristic time at which the slowest measurable processes relax to equilibrium.

Cooling down from the liquid phase, the slow degrees of freedom of the glass former are no longer accessible and the viscosity of the undercooled melt grows several orders of magnitude in a relatively small temperature interval. As a result, in the cooling process, from some point on, the time effectively spent at a certain temperature is not enough to attain equilibrium: the system is said to have fallen out of equilibrium.

The preparation plays a fundamental role to get a glass out of a liquid, thus avoiding the crystallization of the substance. Depending on the material, the ways of obtaining a glass are very diverse and consist not only in the cooling of a liquid but also include compression, intense grinding or irradiation of crystals with heavy particles, decompression of crystals that are stable at high pressure, chemical reactions, polymerization, evaporation of solvents, drying, deposition of chemical vapors, etc. Many kinds of materials present a glass phase at a given external condition if prepared in the proper way: silica, halide and chalkline based glasses, as well as carbon-based polymer glasses, e.g., polyvinylchloride (PVC), germanate dioxide (GeO2), orthoterphenyl (OTP), K+Ca2+NO3- and open network liquids, just to mention a few.

Main lines of research on complex liquids and structural glasses:

- Amorphous-amorphous transition in mean-field models.

- Competition between glass formation and crystal growth.

- Complex free energy landscape and the role of saddles.

- Random first order transition theory.

- Thermodynamics of the glassy state.

-   Inverse transitions

-  The growth of amorphous order in supercooled liquids

- Viscoelasticity and metastability in supercooled liquids.



Luca Angelani, Andrea Cavagna, Irene Giardina, Luca Leuzzi, Antonio Scala