Glass Transition Temperature
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The glass–liquid transition, or glass transition, is the gradual and reversible transition in
amorphous In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("wi ...
materials (or in amorphous regions within
semicrystalline Crystallinity refers to the degree of structural order in a solid. In a crystal, the atoms or molecules are arranged in a regular, periodic manner. The degree of crystallinity has a big influence on hardness, density, transparency and diffusion ...
materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased.
ISO ISO is the most common abbreviation for the International Organization for Standardization. ISO or Iso may also refer to: Business and finance * Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007 * Iso ...
11357-2: Plastics – Differential scanning calorimetry – Part 2: Determination of glass transition temperature (1999).
An amorphous solid that exhibits a glass transition is called a
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
. The reverse transition, achieved by
supercooling Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid or a gas below its melting point without it becoming a solid. It achieves this in the absence of a seed crystal or nucleus around which a crystal ...
a
viscous liquid In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous (see Viscosity of amorphous ma ...
into the glass state, is called
vitrification Vitrification (from Latin ''vitreum'', "glass" via French ''vitrifier'') is the full or partial transformation of a substance into a glass, that is to say, a non- crystalline amorphous solid. Glasses differ from liquids structurally and glasses po ...
. The glass-transition temperature ''T''g of a material characterizes the range of temperatures over which this glass transition occurs (as an experimental definition, typically marked as 100 s of relaxation time). It is always lower than the melting temperature, ''T''m, of the crystalline state of the material, if one exists. Hard plastics like
polystyrene Polystyrene (PS) is a synthetic polymer made from monomers of the aromatic hydrocarbon styrene. Polystyrene can be solid or foamed. General-purpose polystyrene is clear, hard, and brittle. It is an inexpensive resin per unit weight. It is a ...
and
poly(methyl methacrylate) Poly(methyl methacrylate) (PMMA) belongs to a group of materials called engineering plastics. It is a transparent thermoplastic. PMMA is also known as acrylic, acrylic glass, as well as by the trade names and brands Crylux, Plexiglas, Acrylite, ...
are used well below their glass transition temperatures, i.e., when they are in their glassy state. Their ''T''g values are both at around . Rubber
elastomer An elastomer is a polymer with viscoelasticity (i.e. both viscosity and elasticity) and with weak intermolecular forces, generally low Young's modulus and high failure strain compared with other materials. The term, a portmanteau of ''elastic p ...
s like
polyisoprene Polyisoprene is strictly speaking a collective name for polymers that are produced by polymerization of isoprene. In practice polyisoprene is commonly used to refer to synthetic ''cis''-1,4-polyisoprene, made by the industrial polymerisation of i ...
and
polyisobutylene Polyisobutene (polyisobutylene) is a class of organic polymers prepared by polymerization of isobutene. The polymers often have the formula Me3C H2CMe2sub>nX (Me = CH3, X = H, F). They are typically colorless gummy solids. Polymerization is typ ...
are used above their ''T''g, that is, in the rubbery state, where they are soft and flexible;
crosslinking Cross-linking may refer to *Cross-link In chemistry and biology a cross-link is a bond or a short sequence of bonds that links one polymer chain to another. These links may take the form of covalent bonds or ionic bonds and the polymers ca ...
prevents free flow of their molecules, thus endowing rubber with a set shape at room temperature (as opposed to a viscous liquid). Despite the change in the physical properties of a material through its glass transition, the transition is not considered a
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
; rather it is a phenomenon extending over a range of temperature and defined by one of several conventions. Such conventions include a constant cooling rate () and a viscosity threshold of 1012 Pa·s, among others. Upon cooling or heating through this glass-transition range, the material also exhibits a smooth step in the thermal-expansion coefficient and in the
specific heat In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
, with the location of these effects again being dependent on the history of the material. The question of whether some phase transition underlies the glass transition is a matter of ongoing research.


Introduction

The glass transition of a liquid to a solid-like state may occur with either cooling or compression. The transition comprises a smooth increase in the viscosity of a material by as much as 17
orders of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...
within a temperature range of 500 K without any pronounced change in material structure. The consequence of this dramatic increase is a
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
exhibiting solid-like mechanical properties on the timescale of practical observation. This transition is in contrast to the
freezing Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liquid ...
or crystallization transition, which is a first-order
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
in the Ehrenfest classification and involves discontinuities in thermodynamic and dynamic properties such as volume, energy, and viscosity. In many materials that normally undergo a freezing transition, rapid cooling will avoid this phase transition and instead result in a glass transition at some lower temperature. Other materials, such as many
polymers A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic an ...
, lack a well defined crystalline state and easily form glasses, even upon very slow cooling or compression. The tendency for a material to form a glass while quenched is called glass forming ability. This ability depends on the composition of the material and can be predicted by the rigidity theory. Below the transition temperature range, the glassy structure does not relax in accordance with the cooling rate used. The expansion coefficient for the glassy state is roughly equivalent to that of the crystalline solid. If slower cooling rates are used, the increased time for structural relaxation (or intermolecular rearrangement) to occur may result in a higher density glass product. Similarly, by annealing (and thus allowing for slow structural relaxation) the glass structure in time approaches an equilibrium density corresponding to the supercooled liquid at this same temperature. ''T''g is located at the intersection between the cooling curve (volume versus temperature) for the glassy state and the supercooled liquid. Moynihan, C. et al. (1976) in ''The Glass Transition and the Nature of the Glassy State'', M. Goldstein and R. Simha (Eds.), Ann. N.Y. Acad. Sci., Vol. 279. . The configuration of the glass in this temperature range changes slowly with time towards the equilibrium structure. The principle of the minimization of the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and ...
provides the thermodynamic driving force necessary for the eventual change. At somewhat higher temperatures than ''T''g, the structure corresponding to equilibrium at any temperature is achieved quite rapidly. In contrast, at considerably lower temperatures, the configuration of the glass remains sensibly stable over increasingly extended periods of time. Thus, the liquid-glass transition is not a transition between states of
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
. It is widely believed that the true equilibrium state is always crystalline. Glass is believed to exist in a kinetically locked state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon. Time and temperature are interchangeable quantities (to some extent) when dealing with glasses, a fact often expressed in the
time–temperature superposition The time–temperature superposition principle is a concept in polymer physics and in the physics of glass-forming liquids. This superposition principle is used to determine temperature-dependent mechanical properties of linear viscoelastic mat ...
principle. On cooling a liquid, ''internal degrees of freedom successively fall out of equilibrium''. However, there is a longstanding debate whether there is an underlying second-order phase transition in the hypothetical limit of infinitely long relaxation times. In a more recent model of glass transition, the glass transition temperature corresponds to the temperature at which the largest openings between the vibrating elements in the liquid matrix become smaller than the smallest cross-sections of the elements or parts of them when the temperature is decreasing. As a result of the fluctuating input of thermal energy into the liquid matrix, the harmonics of the oscillations are constantly disturbed and temporary cavities ("free volume") are created between the elements, the number and size of which depend on the temperature. The glass transition temperature ''T''g0 defined in this way is a fixed material constant of the disordered (non-crystalline) state that is dependent only on the pressure. As a result of the increasing inertia of the molecular matrix when approaching ''T''g0, the setting of the thermal equilibrium is successively delayed, so that the usual measuring methods for determining the glass transition temperature in principle deliver ''T''g values that are too high. In principle, the slower the temperature change rate is set during the measurement, the closer the measured ''T''g value ''T''g0 approaches. Techniques such as
dynamic mechanical analysis Dynamic mechanical analysis (abbreviated DMA) is a technique used to study and characterize materials. It is most useful for studying the viscoelastic behavior of polymers. A sinusoidal stress is applied and the strain in the material is measured, ...
can be used to measure the glass transition temperature.


Transition temperature ''T''g

Refer to the figure on the bottom right plotting the heat capacity as a function of temperature. In this context, ''T''g is the temperature corresponding to point A on the curve.Tg measurement of glasses
. Glassproperties.com. Retrieved on 2012-06-29.
Different operational definitions of the glass transition temperature ''T''g are in use, and several of them are endorsed as accepted scientific standards. Nevertheless, all definitions are arbitrary, and all yield different numeric results: at best, values of ''T''g for a given substance agree within a few kelvins. One definition refers to the
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
, fixing ''T''g at a value of 1013 poise (or 1012 Pa·s). As evidenced experimentally, this value is close to the annealing point of many glasses. In contrast to viscosity, the
thermal expansion Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic ...
,
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity ...
, shear modulus, and many other properties of inorganic
glass Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of ...
es show a relatively sudden change at the glass transition temperature. Any such step or kink can be used to define ''T''g. To make this definition reproducible, the cooling or heating rate must be specified. The most frequently used definition of ''T''g uses the energy release on heating in differential scanning calorimetry (DSC, see figure). Typically, the sample is first cooled with 10 K/min and then heated with that same speed. Yet another definition of ''T''g uses the kink in dilatometry (a.k.a. thermal expansion): refer to the figure on the top right. Here, heating rates of are common. The linear sections below and above ''T''g are colored green. ''T''g is the temperature at the intersection of the red regression lines. Summarized below are ''T''g values characteristic of certain classes of materials.


Polymers

Dry
nylon-6 Nylon 6 or polycaprolactam is a polymer, in particular semicrystalline polyamide. Unlike most other nylons, nylon 6 is not a condensation polymer, but instead is formed by ring-opening polymerization; this makes it a special case in the comp ...
has a glass transition temperature of . Nylon-6,6 in the dry state has a glass transition temperature of about . Whereas
polyethene Polyethylene or polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most commonly produced plastic. It is a polymer, primarily used for packaging (plastic bags, plastic films, geomembranes and containers including bott ...
has a glass transition range of The above are only mean values, as the glass transition temperature depends on the cooling rate and molecular weight distribution and could be influenced by additives. For a semi-crystalline material, such as
polyethene Polyethylene or polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most commonly produced plastic. It is a polymer, primarily used for packaging (plastic bags, plastic films, geomembranes and containers including bott ...
that is 60–80% crystalline at room temperature, the quoted glass transition refers to what happens to the amorphous part of the material upon cooling.


Silicates and other covalent network glasses


Kauzmann's paradox

As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By
extrapolating In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between know ...
the
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity ...
of the supercooled liquid below its
glass transition temperature The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rub ...
, it is possible to calculate the temperature at which the difference in entropies becomes zero. This temperature has been named the Kauzmann temperature. If a liquid could be supercooled below its Kauzmann temperature, and it did indeed display a lower entropy than the crystal phase, the consequences would be paradoxical. This Kauzmann paradox has been the subject of much debate and many publications since it was first put forward by
Walter Kauzmann Walter J. Kauzmann (18 August 1916 – 27 January 2009) was an American chemist and professor emeritus of Princeton University. He was noted for his work in both physical chemistry and biochemistry. His most important contribution was recognizin ...
in 1948. One resolution of the Kauzmann paradox is to say that there must be a
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
before the entropy of the liquid decreases. In this scenario, the transition temperature is known as the ''calorimetric ideal glass transition temperature'' ''T''0c. In this view, the glass transition is not merely a
kinetic Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory of gases, Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to i ...
effect, i.e. merely the result of fast cooling of a melt, but there is an underlying
thermodynamic Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
basis for glass formation. The glass transition temperature: : T_g \to T_ \text \frac \to 0. The Gibbs–DiMarzio model from 1958 specifically predicts that a supercooled liquid's configurational entropy disappears in the limit T \to T_^+, where the liquid's existence regime ends, its microstructure becomes identical to the crystal's, and their property curves intersect in a true second-order phase transition. This has never been experimentally verified due to the difficulty of realizing a slow enough cooling rate while avoiding accidental crystallization. The Adam–Gibbs model from 1965 suggested a resolution of the Kauzmann paradox according to which the relaxation time diverges at the Kauzmann temperature, implying that one can never equilibrate the
metastable In chemistry and physics, metastability denotes an intermediate Energy level, energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of me ...
supercooled liquid here. A critical discussion of the Kauzmann paradox and the Adam–Gibbs model was given in 2009. Data on several supercooled organic liquids do not confirm the Adam–Gibbs prediction of a diverging relaxation time at any finite temperature, e.g. the Kauzmann temperature.


Alternative resolutions

There are at least three other possible resolutions to the Kauzmann paradox. It could be that the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly decreases to a smaller value. It could also be that a first order phase transition to another liquid state occurs before the Kauzmann temperature with the heat capacity of this new state being less than that obtained by extrapolation from higher temperature. Finally, Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached.


In specific materials


Silica, SiO2

Silica Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is one ...
(the chemical compound SiO2) has a number of distinct
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
line forms in addition to the quartz structure. Nearly all of the crystalline forms involve
tetrahedral In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
SiO4 units linked together by ''shared vertices'' in different arrangements ( stishovite, composed of linked SiO6
octahedra In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet a ...
, is the main exception). Si-O bond lengths vary between the different crystal forms. For example, in α-quartz the bond length is , whereas in α-tridymite it ranges from . The Si-O-Si bond angle also varies from 140° in α-tridymite to 144° in α-quartz to 180° in β-tridymite. Any deviations from these standard parameters constitute microstructural differences or variations that represent an approach to an
amorphous In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid, glassy solid) is a solid that lacks the long-range order that is characteristic of a crystal. Etymology The term comes from the Greek ''a'' ("wi ...
, vitreous or glassy solid. The transition temperature ''T''g in silicates is related to the energy required to break and re-form covalent bonds in an amorphous (or random network) lattice of
covalent bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
s. The ''T''g is clearly influenced by the chemistry of the glass. For example, addition of elements such as B, Na, K or Ca to a silica glass, which have a valency less than 4, helps in breaking up the network structure, thus reducing the ''T''g. Alternatively, P, which has a valency of 5, helps to reinforce an ordered lattice, and thus increases the ''T''g. ''T''g is directly proportional to bond strength, e.g. it depends on quasi-equilibrium thermodynamic parameters of the bonds e.g. on the enthalpy ''H''d and entropy ''S''d of configurons – broken bonds: ''T''g = ''H''d /  'S''d + R ln[(1 − ''f''c)/ ''f''cwhere R is the gas constant and ''f''c is the percolation threshold. For strong melts such as Si''O''2 the percolation threshold in the above equation is the universal Scher–Zallen critical density in the 3-D space e.g. ''f''c = 0.15, however for fragile materials the percolation thresholds are material-dependent and ''f''c ≪ 1. The enthalpy ''H''d and the entropy ''S''d of configurons – broken bonds can be found from available experimental data on viscosity.


Polymers

In polymers the glass transition temperature, ''T''g, is often expressed as the temperature at which the
Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and ...
is such that the
activation energy In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules pe ...
for the cooperative movement of 50 or so elements of the polymer is exceeded . This allows molecular chains to slide past each other when a force is applied. From this definition, we can see that the introduction of relatively stiff chemical groups (such as
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms, ...
rings) will interfere with the flowing process and hence increase ''T''g. The stiffness of thermoplastics decreases due to this effect (see figure.) When the glass temperature has been reached, the stiffness stays the same for a while, i.e., at or near ''E''2, until the temperature exceeds ''T''m, and the material melts. This region is called the rubber plateau. Coming from the low-temperature side, the shear modulus drops by many orders of magnitude at the glass transition temperature ''T''g. A molecular-level mathematical relation for the temperature-dependent
shear modulus In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: :G \ \stackre ...
of the polymer glass on approaching ''T''g from below has been developed by Alessio Zaccone and
Eugene Terentjev Eugene M. Terentjev (born 21 June 1959) is professor of Polymer physics at the University of Cambridge, and fellow of Queens' College where he is the Director of Studies in Natural Sciences. Terentjev earned his MSc in Physics from Moscow State U ...
. Even though the shear modulus does not really drop to zero (it drops down to the much lower value of the rubber plateau), upon setting the shear modulus to zero in the Zaccone–Terentjev formula, an expression for ''T''g is obtained which recovers the
Flory–Fox equation In polymer chemistry and polymer physics, the Flory–Fox equation is a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system. The equation was first proposed in 1950 by Paul J. Flory and Th ...
, and also shows that ''T''g is inversely proportional to the thermal expansion coefficient in the glass state. This procedure provides yet another operational protocol to define the ''T''g of polymer glasses by identifying it with the temperature at which the shear modulus drops by many orders of magnitude down to the rubbery plateau. In
ironing Ironing is the use of a machine, usually a heated tool (an iron), to remove wrinkles and unwanted creases from fabric. The heating is commonly done to a temperature of 180–220 °Celsius (356-428 Fahrenheit), depending on the fabric. Ironing wor ...
, a fabric is heated through this transition so that the polymer chains become mobile. The weight of the iron then imposes a preferred orientation. ''T''g can be significantly decreased by addition of
plasticizer A plasticizer ( UK: plasticiser) is a substance that is added to a material to make it softer and more flexible, to increase its plasticity, to decrease its viscosity, and/or to decrease friction during its handling in manufacture. Plasticiz ...
s into the polymer matrix. Smaller molecules of plasticizer embed themselves between the polymer chains, increasing the spacing and free volume, and allowing them to move past one another even at lower temperatures. Addition of plasticizer can effectively take control over polymer chain dynamics and dominate the amounts of the associated free volume so that the increased mobility of polymer ends is not apparent. The addition of nonreactive
side groups In IUPAC nomenclature of chemistry, a pendant group (sometimes spelled pendent) or side group is a group of atoms attached to a backbone chain of a long molecule, usually a polymer. Pendant groups are different from pendant chains, as they are n ...
to a polymer can also make the chains stand off from one another, reducing ''T''g. If a plastic with some desirable properties has a ''T''g that is too high, it can sometimes be combined with another in a
copolymer In polymer chemistry, a copolymer is a polymer derived from more than one species of monomer. The polymerization of monomers into copolymers is called copolymerization. Copolymers obtained from the copolymerization of two monomer species are some ...
or
composite material A composite material (also called a composition material or shortened to composite, which is the common name) is a material which is produced from two or more constituent materials. These constituent materials have notably dissimilar chemical or ...
with a ''T''g below the temperature of intended use. Note that some plastics are used at high temperatures, e.g., in automobile engines, and others at low temperatures. In
viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly ...
materials, the presence of liquid-like behavior depends on the properties of and so varies with rate of applied load, i.e., how quickly a force is applied. The silicone toy
Silly Putty Silly Putty is a toy based on silicone polymers that have unusual physical properties. It bounces, but it breaks when given a sharp blow, and it can also flow like a liquid. It contains a viscoelastic liquid silicone, a type of non-Newtonian f ...
behaves quite differently depending on the time rate of applying a force: pull slowly and it flows, acting as a heavily viscous liquid; hit it with a hammer and it shatters, acting as a glass. On cooling,
rubber Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymers of the organic compound isoprene, with minor impurities of other organic compounds. Thailand, Malaysia, and ...
undergoes a ''liquid-glass transition'', which has also been called a ''rubber-glass transition''.


Mechanics of vitrification

Molecular motion in condensed matter can be represented by a
Fourier series A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''p ...
whose physical interpretation consists of a superposition of
longitudinal Longitudinal is a geometric term of location which may refer to: * Longitude ** Line of longitude, also called a meridian * Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long axis of the vehicl ...
and
transverse Transverse may refer to: *Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle *Transverse flute, a flute that is held horizontally * Transverse force (or ''Euler force''), the tangen ...
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
s of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called ''
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
fluctuations''. (In polyatomic systems, they may also include
composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
al fluctuations.) Thus,
thermal motion A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
in liquids can be decomposed into elementary longitudinal vibrations (or acoustic
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s) while transverse vibrations (or shear waves) were originally described only in
elastic Elastic is a word often used to describe or identify certain types of elastomer, elastic used in garments or stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rubber used to hold objects togeth ...
solids exhibiting the highly ordered crystalline state of matter. In other words, simple liquids cannot support an applied force in the form of a
shearing stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the o ...
, and will yield mechanically via macroscopic
plastic deformation In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain ...
(or viscous flow). Furthermore, the fact that a
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
deforms locally while retaining its rigidity – while a
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
yields to macroscopic
viscous flow The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...
in response to the application of an applied
shearing force In solid mechanics, shearing forces are unaligned forces acting on one part of a body in a specific direction, and another part of the body in the opposite direction. When the forces are collinear (aligned with each other), they are called ...
– is accepted by many as the mechanical distinction between the two. The inadequacies of this conclusion, however, were pointed out by Frenkel in his revision of the
kinetic theory of solids In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical ...
and the
theory of elasticity Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and ...
in
liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, a ...
s. This revision follows directly from the continuous characteristic of the
viscoelastic In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly ...
crossover from the liquid state into the solid one when the transition is not accompanied by crystallization—ergo the supercooled
viscous liquid In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous (see Viscosity of amorphous ma ...
. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon
vitrification Vitrification (from Latin ''vitreum'', "glass" via French ''vitrifier'') is the full or partial transformation of a substance into a glass, that is to say, a non- crystalline amorphous solid. Glasses differ from liquids structurally and glasses po ...
, as described by Bartenev in his mechanical description of the vitrification process. This concept leads to defining the glass transition in terms of the vanishing or significant lowering of the low-frequency shear modulus, as shown quantitatively in the work of Zaccone and Terentjev on the example of polymer glass. In fact, the shoving model stipulates that the activation energy of the relaxation time is proportional to the high-frequency plateau shear modulus, a quantity that increases upon cooling thus explaining the ubiquitous non-Arrhenius temperature dependence of the relaxation time in glass-forming liquids. The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
that levels out temperature differentials between compressed and expanded volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
" for lattice phonons, and that the value of the mean free path is of the
order of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic di ...
of the scale of disorder in the molecular structure of a liquid or solid. The thermal phonon mean free paths or relaxation lengths of a number of glass formers have been plotted versus the glass transition temperature, indicating a linear relationship between the two. This has suggested a new criterion for glass formation based on the value of the phonon mean free path. It has often been suggested that
heat transport Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
in
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic scattering of acoustic phonons by lattice defects (e.g. randomly spaced vacancies). These predictions were confirmed by experiments on commercial
glasses Glasses, also known as eyeglasses or spectacles, are vision eyewear, with lenses (clear or tinted) mounted in a frame that holds them in front of a person's eyes, typically utilizing a bridge over the nose and hinged arms (known as temples or ...
and glass
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant materials made by shaping and then firing an inorganic, nonmetallic material, such as clay, at a high temperature. Common examples are earthenware, porcelain ...
s, where mean free paths were apparently limited by "internal boundary scattering" to length scales of . The relationship between these transverse waves and the mechanism of vitrification has been described by several authors who proposed that the onset of correlations between such phonons results in an orientational ordering or "freezing" of local shear stresses in glass-forming liquids, thus yielding the glass transition.


Electronic structure

The influence of
thermal A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
phonon In physics, a phonon is a collective excitation in a periodic, Elasticity (physics), elastic arrangement of atoms or molecules in condensed matter physics, condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phon ...
s and their interaction with
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
ic structure is a topic that was appropriately introduced in a discussion of the resistance of liquid metals. Lindemann's theory of melting is referenced, and it is suggested that the drop in
conductivity Conductivity may refer to: *Electrical conductivity, a measure of a material's ability to conduct an electric current **Conductivity (electrolytic), the electrical conductivity of an electrolyte in solution ** Ionic conductivity (solid state), ele ...
in going from the
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
line to the liquid state is due to the increased scattering of conduction electrons as a result of the increased
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
of atomic
vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum ...
. Such theories of localization have been applied to transport in
metallic glass An amorphous metal (also known as metallic glass, glassy metal, or shiny metal) is a solid metallic material, usually an alloy, with disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a high ...
es, where the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
of the electrons is very small (on the order of the interatomic spacing). The formation of a non-crystalline form of a gold-silicon alloy by the method of
splat quenching Splat quenching is a metallurgical, metal morphing technique used for forming metals with a particular crystal structure by means of extremely rapid quenching, or cooling. A typical technique for splat quenching involves casting molten metal by pou ...
from the melt led to further considerations of the influence of electronic structure on glass forming ability, based on the properties of the
metallic bond Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. It may be descri ...
. Other work indicates that the
mobility Mobility may refer to: Social sciences and humanities * Economic mobility, ability of individuals or families to improve their economic status * Geographic mobility, the measure of how populations and goods move over time * Mobilities, a conte ...
of localized
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s is enhanced by the presence of dynamic phonon modes. One claim against such a model is that if
chemical bonds A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
are important, the
nearly free electron model In solid-state physics, the nearly free electron model (or NFE model) or quasi-free electron model is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model i ...
s should not be applicable. However, if the model includes the buildup of a
charge distribution In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...
between all pairs of atoms just like a chemical bond (e.g., silicon, when a band is just filled with electrons) then it should apply to
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
s. Thus, if the
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
is low, the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
of the electrons is very short. The electrons will only be sensitive to the short-range order in the glass since they do not get a chance to scatter from atoms spaced at large distances. Since the short-range order is similar in glasses and crystals, the electronic energies should be similar in these two states. For alloys with lower resistivity and longer electronic mean free paths, the electrons could begin to sense that there is
disorder Disorder may refer to randomness, non-order, or no intelligible pattern. Disorder may also refer to: Healthcare * Disorder (medicine), a functional abnormality or disturbance * Mental disorder or psychological disorder, a psychological pattern a ...
in the glass, and this would raise their energies and destabilize the glass with respect to crystallization. Thus, the glass formation tendencies of certain alloys may therefore be due in part to the fact that the electron mean free paths are very short, so that only the short-range order is ever important for the energy of the electrons. It has also been argued that glass formation in metallic systems is related to the "softness" of the interaction potential between unlike atoms. Some authors, emphasizing the strong similarities between the local structure of the glass and the corresponding crystal, suggest that chemical bonding helps to stabilize the amorphous structure. Other authors have suggested that the electronic structure yields its influence on glass formation through the directional properties of bonds. Non-crystallinity is thus favored in elements with a large number of polymorphic forms and a high degree of
bond Bond or bonds may refer to: Common meanings * Bond (finance), a type of debt security * Bail bond, a commercial third-party guarantor of surety bonds in the United States * Chemical bond, the attraction of atoms, ions or molecules to form chemica ...
ing
anisotropy Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
. Crystallization becomes more unlikely as bonding anisotropy is increased from
isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
lic to
anisotropic Anisotropy () is the property of a material which allows it to change or assume different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material's physic ...
metal A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
lic to
covalent A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
bonding, thus suggesting a relationship between the group number in the
periodic table The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
and the glass forming ability in
elemental An elemental is a mythic being that is described in occult and alchemical works from around the time of the European Renaissance, and particularly elaborated in the 16th century works of Paracelsus. According to Paracelsus and his subsequent fo ...
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
s.


See also

* Gardner transition *
glass formation A glass is an amorphous solid completely lacking long range periodic atomic structure that exhibits a region of glass transformation. This broad definition means that any material be it organic, inorganic, metallic, etc. in nature may form a gla ...


References


External links


Fragility

VFT Eqn.





Angell: Aqueous media

DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers"

Glass Transition Temperature short overview
{{DEFAULTSORT:Glass Transition Cryobiology Glass engineering and science Glass physics Phase transitions Polymer chemistry Rubber properties Threshold temperatures