Glass_transition - Wikiparency

# Glass transition **Glass transition** is the reversible change, on cooling, by which a [[Supercooling|supercooled]] liquid stops flowing on the timescale of the experiment and becomes an [[Amorphous_solid|amorphous solid]] — a [[Glass|glass]] — without ever crystallising. Nothing discontinuous happens to the structure: the atomic arrangement of the glass is the arrangement the liquid had when it stopped rearranging, frozen in place. What changes is the rate of rearrangement, and it changes enormously. Over a temperature interval of a hundred kelvin or so, the [[Viscosity|viscosity]] of a silicate melt climbs through ten orders of magnitude, and somewhere in that climb the liquid ceases to be a liquid in any practical sense. In the microsim below the reader moves the temperature along a Vogel–Fulcher–Tammann curve, `log10(η) = A + B/(T − T₀)`, drawn on a logarithmic viscosity axis against *T*. Four horizontal lines mark the glassmaker's reference viscosities — the working point at 10³ Pa·s, the softening point at 10^6.6 Pa·s, the annealing point at 10^12 Pa·s and the strain point at 10^13.5 Pa·s — and the readout names which of them the melt has crossed. A second control is the cooling rate, which slides the glass transition temperature *T*g down the same curve, because a slower experiment gives the liquid longer to keep up. Presets cover [[Soda–lime_glass|soda–lime]], [[Borosilicate_glass|borosilicate]] and fused [[Silicon_dioxide|silica]] glass and polystyrene, so a single sim spans the silicate and the polymer halves of the subject. On the [[Materials_science|Materials science]] flagship this article serves the *Ceramics and glasses* section of Part VIII; the [[Viscosity|viscosity]], [[Thermal_shock|thermal shock]] and [[Thermoplastic|thermoplastic]] pages reuse the same curve with their own presets. ## Characteristics The glass transition announces itself in every property that depends on whether the structure can rearrange. Volume and enthalpy are continuous through it, but their temperature derivatives — the thermal expansion coefficient and the [[Heat_capacity|heat capacity]] — drop by a step on cooling, because the liquid's configurational contribution switches off while the vibrational contribution continues. On a dilatometer trace the expansion curve shows a knee; on a calorimeter trace, a step. That pattern, continuity in the quantity and a step in its derivative, is the signature of a second-order transition, and it is the reason the glass transition is often, and misleadingly, described as one. It is not a [[Phase_transition|phase transition]] in the thermodynamic sense, for a decisive reason: the temperature at which it occurs depends on how fast the experiment is done. A thermodynamic transition temperature does not. Cool a melt more slowly and the liquid stays in equilibrium to a lower temperature, so *T*g falls; heat a glass faster and the apparent *T*g rises. The transition is a kinetic event — the point where the material's internal relaxation time overtakes the experimenter's clock — dressed in the clothes of a thermodynamic one. The glass below *T*g is not at equilibrium. Held just below the transition it slowly contracts and stiffens as its structure keeps relaxing towards the equilibrium it was denied — physical ageing, which changes [[Density|density]], modulus and toughness over months. Reheating through *T*g recovers the lost enthalpy in a burst, so a calorimeter scan taken on heating shows an overshoot peak on top of the step that a cooling scan does not. ## Formal definitions Because the transition is kinetic, every definition of *T*g is a convention that fixes an observation time, and the three in common use do not agree exactly. The viscometric convention places *T*g where the shear viscosity reaches 10^12 Pa·s, the same viscosity that defines the annealing point. The calorimetric convention takes the midpoint of the heat-capacity step at a stated heating rate, commonly 10 K/min. The dilatometric convention takes the intersection of the glass and liquid expansion lines. Comparisons between materials mean something only when the convention and the rate are stated with the number. The conventions are not arbitrary, and the viscometric one can be read as a statement about time. Maxwell's relation gives a structural relaxation time `τ ≈ η/G∞`, with `G∞` the instantaneous shear modulus of the melt, which for a silicate is of order 10 GPa. At η = 10^12 Pa·s this gives τ ≈ 100 s (derived) — a couple of minutes, which is roughly the timescale of a laboratory cooling run. The 10^12 Pa·s convention therefore says, in disguise, that the glass transition is where the material stops keeping up with an experiment of human duration. ## Transition temperature <i>T</i><sub>g</sub> The temperature *T*g is not a material constant but a material property under stated conditions, and its magnitude is set by how strongly the structural units are bonded to one another and how easily they can exchange neighbours. Network glasses with strong directional bonds sit high; molecular and polymer glasses, held together by weaker forces, sit low. ### Polymers For a [[Polymer|polymer]] the transition is the onset of large-scale segmental motion along the chain, and *T*g rises with anything that hinders it: stiff backbone units, bulky side groups, polar interactions, cross-links. [[Polyethylene|Polyethylene]], whose chain is a flexible string of methylene units, has a *T*g well below room temperature and is leathery at ambient conditions; polystyrene, carrying a phenyl ring on every second carbon, has one near 100 °C and is glassy and brittle. Chain length matters too, through the excess free volume that chain ends contribute: *T*g rises with molar mass and saturates, the dependence described by the Fox–Flory relation `Tg = Tg∞ − K/Mn`.[^foxflory] Below *T*g a [[Thermoplastic|thermoplastic]] is a hard glass; above it, and below its melting or flow range, it is the rubbery solid that [[Rubber_elasticity|rubber elasticity]] describes. ### Silicates and other covalent network glasses In a silicate the structural unit is the SiO₄ tetrahedron, and the glass is a continuous random network of corner-sharing tetrahedra with no long-range order — the model Zachariasen proposed in 1932 and the reason such a network can accept a wide range of compositions without crystallising.[^zachariasen] Pure silica's network is fully connected, its *T*g is above 1,100 °C and its viscosity falls only slowly with temperature. Adding soda and lime breaks bridging Si–O–Si links into non-bridging oxygens terminated by sodium and calcium ions; the network is cut, and both the transition temperature and the whole viscosity curve collapse by hundreds of kelvin. That is the entire trick of window glass: a melt workable in a furnace rather than a plasma. The microsim's soda–lime preset is a three-point fit to the law Vogel proposed in 1921 and Fulcher applied to glass viscosity data in 1925:[^vogel1921][^fulcher1925] `A = −3.63`, `B = 5,183 K`, `T₀ = 491 K`, anchored on the working, softening and annealing points at 1,000, 725 and 550 °C. Its one free prediction is the strain point, placed at 521 °C (derived). The fit is ILLUSTRATIVE — a display curve through the standard reference viscosities, not measured constants for any particular batch — and the sim prints its three numbers on screen. ## Linear heat capacity Two distinct heat-capacity anomalies belong to glasses, and they live at opposite ends of the temperature scale. Near *T*g there is the configurational step already described, of order a few tenths of a joule per gram per kelvin for a polymer. Far below it, near and under 1 K, glasses show a contribution to the [[Specific_heat_capacity|specific heat]] that is very nearly linear in temperature, where a crystal of the same composition follows the *T*³ law of the [[Debye_model|Debye model]]. The excess is attributed to two-level tunnelling systems: pairs of nearly equivalent local configurations, present only because the structure is disordered, between which an atom or small group can tunnel. The model was proposed independently by two groups in 1972 and remains the standard account.[^ahv][^phillips] ### Experimental data Differential scanning calorimetry is the routine measurement. A sample is cooled and reheated at a fixed rate and the heat flow is recorded; the transition appears as a step in the baseline, with the enthalpy-recovery overshoot on the heating leg. Repeating the scan at several rates makes the kinetics visible directly: each decade of rate moves the apparent *T*g by a fixed amount, and the size of that shift measures how steeply the relaxation time depends on temperature. The steepness is quantified by the fragility index *m*, the slope of `log10(η)` against `Tg/T` at `T = Tg`. Strong liquids such as silica have *m* near 20; fragile ones such as polymers and many molecular glasses reach 100 or more. The shift in *T*g per decade of cooling rate is approximately `Tg/m`, so the microsim's soda–lime fit, whose fragility works out to about 39, moves its transition about 21 K per decade, while a polymer glass at *T*g = 373 K with *m* ≈ 140 moves only about 2.7 K (both derived). A slower furnace makes a denser glass, and for silicates it makes a measurably different one. ### Dynamic heterogeneity and cooperative motion near the glass transition Approaching *T*g, relaxation stops being exponential and stops being uniform. The response to a perturbation decays as a stretched exponential, `exp(−(t/τ)^β)` with β falling towards 0.5, and the reason is that different regions of the sample relax at rates differing by orders of magnitude at the same instant — dynamic heterogeneity. Rearrangement requires the cooperation of a region a few nanometres across, and the growth of that cooperative region as temperature falls is the usual physical picture behind the Vogel–Fulcher–Tammann divergence. ## Kauzmann's paradox Kauzmann pointed out in 1948 that the arithmetic of supercooling cannot be extrapolated indefinitely.[^kauzmann] A supercooled liquid has more [[Entropy|entropy]] than the crystal of the same substance, but it also has the larger heat capacity, so the excess entropy shrinks as the liquid is cooled. Extrapolating the measured excess to lower temperatures, it reaches zero at a finite temperature *T*K, the Kauzmann temperature, typically some tens of kelvin below the observed *T*g. Below *T*K the extrapolation would give the disordered liquid less entropy than the ordered crystal, which is absurd. Something must intervene, and in practice the glass transition always does — but only because of a kinetic accident, which is unsatisfying as an explanation of a thermodynamic impossibility. ### Possible resolutions Three families of answer are current. The first says an ideal glass transition, a genuine thermodynamic transition to a unique amorphous ground state, occurs at *T*K and is merely hidden by the kinetic one; the Adam–Gibbs theory, which makes the relaxation time diverge as the configurational entropy vanishes, supports this by deriving the Vogel–Fulcher–Tammann form with `T₀ = TK`, and the near-coincidence of fitted `T₀` with measured *T*K is its main evidence.[^adamgibbs] The second says the extrapolation itself is wrong, because the liquid's heat capacity falls away before *T*K is reached. The third says the question is unphysical, since no experiment can equilibrate a liquid below *T*g anyway. The paradox is unresolved, which is a fair summary of the theory of the glass transition as a whole. ## Time-temperature superposition and master curves Because a single relaxation process dominates, measurements made at different temperatures can often be collapsed onto one master curve by shifting them horizontally in log time by a factor `a_T`. The shift factor above *T*g follows the Williams–Landel–Ferry equation, `log10(a_T) = −C₁·(T − T_ref)/(C₂ + T − T_ref)`, with values near C₁ = 17.4 and C₂ = 51.6 K for many polymers when *T*ref is taken as *T*g.[^wlf] The equation is not independent of the curve the microsim draws: it is algebraically the Vogel–Fulcher–Tammann form with `T₀ = T_ref − C₂` and `B = C₁·C₂`, written for relaxation time instead of viscosity. The practical payoff is large. A [[Viscoelasticity|viscoelastic]] property needed over ten decades of time — the creep of a polymer over thirty years — can be measured over three decades at several temperatures and assembled, which is how long-term design data for plastics are generated. The same superposition fails whenever more than one relaxation mechanism is active, in semicrystalline polymers and in blends, and a failure to superpose is itself informative. ## In specific materials The transition looks the same on a viscosity plot across materials whose bonding could hardly be more different, which is the main argument that it is a generic consequence of kinetic arrest rather than of any particular chemistry.[^flowers-solidstate] ### Silica, SiO<sub>2</sub> Fused silica is the archetypal strong glass: fully polymerised, fragility near 20, and a viscosity that falls almost exponentially with reciprocal temperature over many decades, close to [[Arrhenius_equation|Arrhenius]] behaviour. Its transition lies above 1,100 °C, which is why it is worked with an oxy-hydrogen flame, and its low thermal expansion gives it the [[Thermal_shock|thermal shock]] resistance that makes it the material of furnace tubes and telescope blanks. ### Polymers Polymer glasses are the fragile extreme. Their transitions are broad, strongly rate-dependent and easily moved by additives, and the modulus falls by about three decades across the transition — from a glassy few gigapascals to a rubbery few megapascals — the single most consequential fact in plastics engineering, fixing the service ceiling of a glassy plastic and the service floor of an [[Elastomer|elastomer]]. ### Effect of polymer blending on glass transition A miscible blend or a random copolymer shows one transition, at a temperature between those of its components, described to a good approximation by the Fox equation `1/Tg = w₁/Tg₁ + w₂/Tg₂` with `w` the mass fractions.[^fox] An immiscible blend shows two, one for each phase, which makes the calorimeter a miscibility test. Plasticisers exploit the same arithmetic deliberately: adding a low-*T*g liquid to poly(vinyl chloride) drags the blend's transition below room temperature and turns a rigid pipe material into a flexible sheet. ### Bulk metallic glasses (BMGs) Metals crystallise so readily that the earliest metallic glasses needed cooling rates near 10⁶ K/s, got by splat-quenching a melt onto a chilled wheel. Bulk metallic glasses are alloys — typically four or five elements of very different atomic size, near a deep eutectic — whose crystallisation is so frustrated that centimetre sections vitrify at a few kelvin per second.[^peker-johnson] Between *T*g and the crystallisation temperature they have a supercooled-liquid window in which they can be blow-moulded like a [[Thermoplastic|thermoplastic]], and below it they combine high strength with elastic strains near 2 %. See [[Amorphous_metal|amorphous metal]]. ## Mechanics of vitrification The mechanical account of vitrification is a race between two timescales: the structural relaxation time τ, rising steeply as the melt cools, and the time available, set by the cooling rate. While τ is short the liquid stays in equilibrium and its volume follows the equilibrium line. When τ becomes comparable to the time spent in each temperature interval, the structure can no longer fully adjust, and the volume curve bends away onto the glass line. Everything below that knee is a frozen record of the structure the liquid had when it fell out of equilibrium — which is why the fictive temperature, at which the frozen structure would be the equilibrium one, is used as a state variable for glasses. Annealing near the transition lowers it and densifies the glass, the industrial operation the annealing point is defined for. ### Electronic structure Disorder survives into the electronic properties. An amorphous [[Semiconductor|semiconductor]] has no sharp band edges: the loss of long-range order smears them into exponential band tails whose states are spatially localised, separated from extended states by a mobility edge, so conduction near the edge proceeds by hopping rather than by band transport. The same disorder that makes the glass transition possible makes amorphous silicon a usable thin-film electronic material and makes chalcogenide glasses switch resistance when they crystallise. ## See also - [[Glass]] - [[Ceramic]] - [[Amorphous_solid]] - [[Soda–lime_glass]] - [[Borosilicate_glass]] - [[Thermoplastic]] - [[Viscosity]] - [[Thermal_shock]] - [[Sintering]] - [[Amorphous_metal]] ## References [^flowers-solidstate]: Flowers, P.; Neth, E. J.; Robinson, W. R.; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax (Portal Book 051). Chapter 10, Liquids and Solids, §10.5 The Solid State of Matter (amorphous solids and glass), chapter pp. 475–544 (section page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^vogel1921]: Vogel, H. (1921). "Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten." *Physikalische Zeitschrift* 22: 645–646. (Page range to pin; no DOI.) [^fulcher1925]: Fulcher, G. S. (1925). "Analysis of recent measurements of the viscosity of glasses." *Journal of the American Ceramic Society* 8 (6): 339–355. https://doi.org/10.1111/j.1151-2916.1925.tb16731.x [^zachariasen]: Zachariasen, W. H. (1932). "The atomic arrangement in glass." *Journal of the American Chemical Society* 54 (10): 3841–3851. (DOI to pin.) [^kauzmann]: Kauzmann, W. (1948). "The nature of the glassy state and the behavior of liquids at low temperatures." *Chemical Reviews* 43 (2): 219–256. (DOI to pin.) [^adamgibbs]: Adam, G.; Gibbs, J. H. (1965). "On the temperature dependence of cooperative relaxation properties in glass-forming liquids." *Journal of Chemical Physics* 43 (1): 139–146. (DOI to pin.) [^wlf]: Williams, M. L.; Landel, R. F.; Ferry, J. D. (1955). "The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids." *Journal of the American Chemical Society* 77 (14): 3701–3707. (DOI to pin.) [^foxflory]: Fox, T. G.; Flory, P. J. (1950). "Second-order transition temperatures and related properties of polystyrene." *Journal of Applied Physics* 21 (6): 581–591. (DOI to pin.) [^fox]: Fox, T. G. (1956). "Influence of diluent and of copolymer composition on the glass temperature of a polymer system." *Bulletin of the American Physical Society* 1: 123. (Abstract; page to pin.) [^ahv]: Anderson, P. W.; Halperin, B. I.; Varma, C. M. (1972). "Anomalous low-temperature thermal properties of glasses and spin glasses." *Philosophical Magazine* 25 (1): 1–9. (DOI to pin.) [^phillips]: Phillips, W. A. (1972). "Tunneling states in amorphous solids." *Journal of Low Temperature Physics* 7 (3–4): 351–360. (DOI to pin.) [^peker-johnson]: Peker, A.; Johnson, W. L. (1993). "A highly processable metallic glass: Zr41.2Ti13.8Cu12.5Ni10.0Be22.5." *Applied Physics Letters* 63 (17): 2342–2344. (DOI to pin.) ## External links - [Chemistry: Atoms First, 2nd edition](https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first), OpenStax via the Open Textbook Library — Chapter 10 for the solid state, amorphous solids and glass. - Further links, including the glass-industry viscosity standards and the interactive fragility databases, are listed on the Wikipedia pair.  **Microsim — three.js (Wikitube framework), pending deploy:** *Glass transition* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Glass_transition.html` is live.   ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Glass_transition) : [Wikitube](https://en.wikitube.io/wiki/Glass_transition) · pinned revision [1372313063](https://en.wikipedia.org/w/index.php?oldid=1372313063) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Materials_science]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Materials_science row M45 · sim pending (matter/Glass_transition).*