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The glass–liquid transition, or glass transition, is the gradual and
reversible
reversible
transition in
amorphous In condensed matter physics Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science th ...
materials (or in amorphous regions within
semicrystalline Crystallinity refers to the degree of structural order in a solid Solid is one of the four fundamental states of matter (the others being liquid, gas and plasma). The molecules in a solid are closely packed together and contain the le ...
materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased.
ISO The International Organization for Standardization (ISO ) is an international standard An international standard is a technical standard A technical standard is an established norm (social), norm or requirement for a repeatable technical task w ...
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 transparency and translucency, 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 ...

glass
. The reverse transition, achieved by
supercooling Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isoch ...
a
viscous liquid In condensed matter physics Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that s ...
into the glass state, is called
vitrification 300px, A vitrification experiment, using molten glass. Vitrification (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area ar ...

vitrification
. The glass-transition temperature ''T''g of a material characterizes the range of temperatures over which this glass transition occurs. It is always lower than the
melting temperature
melting temperature
, ''T''m, of the crystalline state of the material, if one exists. Hard plastics like
polystyrene Polystyrene (PS) is a synthetic aromatic forms of benzene (top) combine to produce an average structure (bottom) In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, com ...

polystyrene
and
poly(methyl methacrylate) Poly(methyl methacrylate) (PMMA), also known as acrylic, acrylic glass, or plexiglass, as well as by the trade names Crylux, Plexiglas, Acrylite, Astariglas, Lucite, Perclax, and Perspex, among several others ( see below), is a transparent the ...
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 A polymer (; Greek ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules, or macromolecules, composed of many Repeat unit, repe ...
s like
polyisoprene Polyisoprene is a collective name for polymers A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy imag ...
and
polyisobutylene Polyisobutene (polyisobutylene) is a class of organic polymers prepared by polymerization of isobutene Isobutylene (or 2-methylpropene) is a hydrocarbon with the formula (CH3)2C=CH2. It is a four-carbon branched alkene , the simplest alkene. ...

polyisobutylene
are used above their ''T''g, that is, in the rubbery state, where they are soft and flexible;
crosslinkingCross-linking may refer to *Cross-link In chemistry and biology a cross-link is a bond that links one polymer A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecule F ...
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 , , and many other related fields, phase transitions (or phase changes) are the of transition between a state of a medium, identified by some parameters, and another one, with different values of the parameters. Commonly the term is used to ...
; 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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quant ...
, 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 continuing 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 In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geome ...
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 transparency and translucency, 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 ...

glass
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 o ...

freezing
or
crystallization Crystallization or crystallisation is the process by which a solid Solid is one of the four fundamental states of matter (the others being liquid, gas and plasma). The molecules in a solid are closely packed together and contain the ...

crystallization
transition, which is a first-order
phase transition In , , and many other related fields, phase transitions (or phase changes) are the of transition between a state of a medium, identified by some parameters, and another one, with different values of the parameters. Commonly the term is used to ...
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 ''wikt:poly-, poly-'', "many" + ''wikt:-mer, -mer'', "part") is a Chemical substance, substance or material consisting of very large molecules, or macromolecules, composed of many Repeat unit, repeating subunits. Due to thei ...

polymers
, 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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
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 An axiom, postulate or assumption is a statement that is taken to be true True most commonly refers to truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online ...
. 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 400px, Temperature dependence of elastic modulus of a viscoelastic material under periodic excitation. The frequency is ''ω'', ''G' '' is the elastic modulus, and ''T''0 T_0 \quad \implies \quad a_ < 1 \\ & T < T_0 \quad \implies \quad a_ > ...
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 polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substa ...
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 In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, ...

viscosity
, 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 A shape or figure is the form of an object or its external boundary, outline, or external surface File:Water droplet lying on a damask.jpg, Water droplet lying on a damask ...
,
heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
, shear modulus, and many other properties of inorganic
glass Glass is a non- crystalline, often transparency and translucency, 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 ...

glass
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 Differential scanning calorimetry (DSC) is a thermoanalytical technique in which the difference in the amount of heat In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than Work (thermodynam ...

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 (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.Tg measurement of glasses
Glassproperties.com. Retrieved on 2012-06-29.
Summarized below are ''T''g values characteristic of certain classes of materials.


Polymers

Dry has a glass transition temperature of . Nylon-6,6 in the dry state has a glass transition temperature of about . Whereas polyethene 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 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 the
heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
of the supercooled liquid below its
glass transition temperature The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous In condensed matter physics Condensed matter physics is the field of that deals with the macroscopic and microscopic physical propert ...
, 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 A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist A scientist is a person who conducts Scient ...
in 1948. One resolution of the Kauzmann paradox is to say that there must be a
phase transition In , , and many other related fields, phase transitions (or phase changes) are the of transition between a state of a medium, identified by some parameters, and another one, with different values of the parameters. Commonly the term is used to ...
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 effect, i.e. merely the result of fast cooling of a melt, but there is an underlying
thermodynamic Thermodynamics is a branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ...
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 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 metastability. I ...

metastable
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 An oxide () is a chemical compound A chemical compound is a chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any su ...

Silica
(the chemical compound SiO2) has a number of distinct
crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformatio ...

crystal
line forms in addition to the quartz structure. Nearly all of the crystalline forms involve
tetrahedral In , a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular , is a composed of four , six straight , and four . The tetrahedron is the simplest of all the ordinary and the only one that has fewer than 5 faces. The t ...

tetrahedral
SiO4 units linked together by ''shared vertices'' in different arrangements (
stishovite Stishovite is an extremely hard, dense tetragonal form ( polymorph) of silicon dioxide Silicon dioxide, also known as silica, is an oxide of rutile. Ti(IV) centers are grey; oxygen centers are red. Notice that oxygen forms three bonds to titani ...

stishovite
, composed of linked SiO6 , 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 Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science th ...
, 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 electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they s ...
s. The ''T''g is clearly influenced by the chemistry of the glass. For example, addition of elements such as , , or to a
silica glass Fused quartz, fused silica or quartz glass is a glass Glass is a non- crystalline, often transparency and translucency, transparent amorphous solid, that has widespread practical, technological, and decorative use in, for example, window pa ...
, which have a valency less than 4, helps in breaking up the network structure, thus reducing the ''T''g. Alternatively, , 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 Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these qua ...
is such that the
activation energy In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo during ...

activation energy
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 Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), organ Chemistry * Organic matter, matter that has come from a once-living organ ...

benzene
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 The interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of two or more academic disciplines into one activity (e.g., a research project). It draws knowledge from several other ...
of the polymer glass on approaching ''T''g from below has been developed by Alessio Zaccone and
Eugene TerentjevEugene 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 Univ ...
. 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, 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 Iron () is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the comp ...

ironing
, 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 Plasticity may refer to: Science * Plasticity (physics), in engineering and physics, the propensity of ...
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 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 Polymer chemistry is a sub-discipline of chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structu ...
or
composite material A composite material (also called a composition material or shortened to composite, which is the common name) is a material Material is a substance Substance may refer to: * Substance (Jainism), a term in Jain ontology to denote the base or o ...

composite material
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 The interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of two or more academic discipline An academic discipline or academic field is a subdivision of knowledge that is Edu ...
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 A silicone or polysiloxane is a polymer A polymer (; Greek ''poly- Poly, from the Greek :wikt:πολύς, πολύς meaning "many" or "much", may refer to: Businesses * China Poly Group Corporation, a Chinese business group, and its sub ...

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 viscoelasticity, viscoelastic liquid silicone, a type of ...
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 polymer A polymer (; Greek ''poly- Poly, from the Greek :wikt:πολύς, πολύς meaning "many" or "much" ...

rubber
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 In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gen ...
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 (geography), meridian * Longitudinal engine, an internal combustion engine in which the crankshaft is oriented along the long ...

longitudinal
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 *Euler force, Transverse force (or ''Euler force''), ...

transverse
wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

wave
s of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called ''
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its per unit . The symbol most often used for density is ''ρ'' (the lower case Greek letter ), although the Latin letter ''D'' can also ...

density
fluctuations''. (In polyatomic systems, they may also include
composition Composition or Compositions may refer to: Arts * Composition (dance), practice and teaching of choreography * Composition (music), an original piece of music and its creation *Composition (visual arts) The term composition means "putting togethe ...
al fluctuations.) Thus,
thermal motion of the ideal gas is proportional to the average kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a bod ...
in liquids can be decomposed into elementary (or acoustic
phonon In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
s) while (or shear waves) were originally described only in elastic 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, and will yield mechanically via macroscopic
plastic deformation In engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad ra ...
(or viscous flow). Furthermore, the fact that a
solid Solid is one of the four fundamental states of matter 4 (four) is a number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is an ...

solid
deforms locally while retaining its rigidity – while a
liquid A liquid is a nearly incompressible In fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, ...

liquid
yields to macroscopic
viscous flow The viscosity of a fluid In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, ...
in response to the application of an applied – 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 and the
theory of elasticity Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics Continuum mechanics is a branch of mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical object ...
in
liquid A liquid is a nearly incompressible In fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, ...

liquid
s. This revision follows directly from the continuous characteristic of the
viscoelastic In materials science The interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of two or more academic discipline An academic discipline or academic field is a subdivision of knowledge that is Edu ...
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 Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that s ...
. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon
vitrification 300px, A vitrification experiment, using molten glass. Vitrification (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area ar ...

vitrification
, 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 ...

thermal conductivity
that levels out temperature differentials between
compressed Compression may refer to: Physical science *Compression (physics), size reduction due to forces *Compression member, a structural element such as a column *Compressibility, susceptibility to compression *Gas compression *Compression ratio, of a co ...
and expanded volume elements. Kittel proposed that the behavior of glasses is interpreted in terms of an approximately constant "
mean free path In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...

mean free path
" 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 In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contain ...
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 in
dielectric In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force i ...

dielectric
solids occurs through elastic vibrations of the lattice, and that this transport is limited by elastic
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagnetic radiation within the portion of the electromagneti ...

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, consisting of glass or hard plastic lenses 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 ...

glasses
and glass
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant Corrosion is a Erosion, natural process that converts a refined metal into a more chemically stable form such as oxide, hydroxide, carbonate or sulfide. ...
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 Example of a thermal column between the ground and a cumulus A thermal column (or thermal) is a column of rising air File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie represe ...

thermal
phonon In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
s and their interaction with
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

electron
ic structure is a topic that was appropriately introduced in a discussion of the
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
of liquid metals
Lindemann's theory of melting
is referenced, and it is suggested that the drop in conductivity in going from the
crystal A crystal or crystalline solid is a solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformatio ...

crystal
line to the liquid state is due to the increased
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagnetic radiation within the portion of the electromagneti ...

scattering
of conduction electrons as a result of the increased
amplitude The amplitude of a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Period, a descriptor for ...

amplitude
of atomic
vibration Vibration is a mechanical phenomenon whereby oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparentl ...

vibration
. Such theories of localization have been applied to transport in metallic glasses, where the
mean free path In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...

mean free path
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 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 bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has m ...
. 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 contempo ...
of localized
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

electron
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 atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyd ...
are important, the
nearly free electron model In solid-state physics Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state ...
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 Systeme Internati ...
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 four fundamental states of matter 4 (four) is a number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is an ...

solid
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 An electric current is a stream of charged particle In p ...
is low, the
mean free path In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...

mean free path
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 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) In finance Finance is the study of financial institutions, financial markets and how they operate within the financial system. It is concerned with the creation and management of ...
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 Physica ...
. Crystallization becomes more unlikely as bonding anisotropy is increased from
isotropic Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...
metal A metal (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...

metal
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 Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, ...
metal A metal (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...

metal
lic to
covalent A covalent bond is a chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and take ...

covalent
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 tabular display of the chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is ...

periodic table
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 The Renaissance ( , ) , from , with the same meanings. was a period in European history marking the transiti ...
solid Solid is one of the four fundamental states of matter 4 (four) is a number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is an ...

solid
s.


See also

* Gardner transition


References


External links


Fragility

VFT Eqn.





Angell: Aqueous media

DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers"
{{DEFAULTSORT:Glass Transition
Condensed matter physics Condensed matter physics Condensed matter physics is the field of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that s ...
Cryobiology Glass engineering and science Glass physics Phase transitions Polymer chemistry Rubber properties Threshold temperatures