Glass transition#Silicates and other covalent network glasses

The glass transition of a liquid to a solid-like state may occur with either cooling or compression.{{cite book|last=Hansen|first=J.-P.|title=Theory of Simple Liquids|isbn=978-0123705358|url=https://books.google.com/books?id=Uhm87WZBnxEC|year=2007|publisher=Elsevier|pages=250–254|author2=McDonald, I. R.|access-date=2016-09-23|archive-date=2013-09-21|archive-url=https://web.archive.org/web/20130921052911/http://books.google.com/books?id=Uhm87WZBnxEC|url-status=live}} The transition comprises a smooth increase in the viscosity of a material by as much as 17 orders of magnitude within a temperature range of 500 K without any pronounced change in material structure.{{cite book|author1=Adam, J-L|author2=Zhang, X.|title=Chalcogenide Glasses: Preparation, Properties and Applications|url=https://books.google.com/books?id=IuNRAwAAQBAJ&pg=PA94|date=14 February 2014|publisher=Elsevier Science|isbn=978-0-85709-356-1|page=94|access-date=2 May 2017|archive-date=17 July 2017|archive-url=https://web.archive.org/web/20170717080736/https://books.google.com/books?id=IuNRAwAAQBAJ&pg=PA94|url-status=live}} This transition is in contrast to the freezing or crystallization transition, which is a first-order phase transition 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, 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.{{cite journal|last=Phillips|first=J.C.|title=Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys|journal=Journal of Non-Crystalline Solids|year=1979|volume=34|issue=2|page=153|doi=10.1016/0022-3093(79)90033-4|bibcode = 1979JNCS...34..153P }}

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. {{ISBN|0890720533}}.

{{cite journal|doi=10.1016/0022-3697(88)90002-9|title=Perspective on the glass transition|year=1988|last1=Angell|first1=C. A.|journal=Journal of Physics and Chemistry of Solids|volume=49|issue=8|pages=863–871|bibcode = 1988JPCS...49..863A }}{{cite journal|doi=10.1021/jp953538d|title=Supercooled Liquids and Glasses|year=1996|last1=Ediger|first1=M. D.|last2=Angell|first2=C. A.|last3=Nagel|first3=Sidney R.|journal=The Journal of Physical Chemistry|volume=100|issue=31|pages=13200}}{{cite journal|doi=10.1126/science.267.5206.1924|title=Formation of Glasses from Liquids and Biopolymers|year=1995|last1=Angell|first1=C. A.|journal=Science|volume=267|issue=5206|pages=1924–35|pmid=17770101|bibcode = 1995Sci...267.1924A |s2cid=927260}}

{{cite journal|doi=10.1126/science.267.5206.1935|title=A Topographic View of Supercooled Liquids and Glass Formation|year=1995|last1=Stillinger|first1=F. H.|journal=Science|volume=267|issue=5206|pages=1935–9|pmid=17770102|bibcode = 1995Sci...267.1935S |s2cid=30407650}}

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 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. 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 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.{{clarify|date=June 2016}}{{Cite book

|url=https://books.google.com/books?id=D7Z8ywb3QggC

|author=Zarzycki, J.

|title=Glasses and the Vitreous State

|isbn=978-0521355827

|publisher=Cambridge University Press

|year=1991

|access-date=2016-09-23

|archive-date=2020-08-02

|archive-url=https://web.archive.org/web/20200802204950/https://books.google.com/books?id=D7Z8ywb3QggC

|url-status=live

}}

{{Cite book

|vauthors=Nemilov SV

|title= Thermodynamic and Kinetic Aspects of the Vitreous State

|publisher=CRC Press

|year=1994|isbn=978-0849337826

}}

{{Cite book

|author=Gibbs, J. H.

|editor=MacKenzie, J. D.

|title=Modern Aspects of the Vitreous State

|publisher=Butterworth

|year=1960

|oclc=1690554

}}

{{cite journal|doi=10.1016/j.jnoncrysol.2010.05.012|title=Connectivity and glass transition in disordered oxide systems|year=2010|last1=Ojovan|first1=Michael I|last2=Lee|first2=William (Bill) E|journal=Journal of Non-Crystalline Solids|volume=356|issue=44–49|pages=2534|bibcode = 2010JNCS..356.2534O }}

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.{{cite journal|journal=Ceramics|last=Sturm|first=Karl Günter|date=2017|title=Microscopic-Phenomenological Model of Glass Transition I. Foundations of the model (Revised and enhanced version) (Former title: Microscopic Model of Glass Transformation and Molecular Translations in Liquids I. Foundations of the Model-October 2015)|url=http://rgdoi.net/10.13140/RG.2.2.19831.73121|language=en|doi=10.13140/RG.2.2.19831.73121}} Techniques such as dynamic mechanical analysis can be used to measure the glass transition temperature.{{Cite web|date=2018|title=What is Dynamic Mechanical Testing (DMA)?|url=https://coventivecomposites.com/explainers/dynamic-mechanical-analysis-dma/|language=en|access-date=2020-12-09|archive-date=2020-11-17|archive-url=https://web.archive.org/web/20201117144756/https://coventivecomposites.com/explainers/dynamic-mechanical-analysis-dma/|url-status=live}}

The definition of the glass and the glass transition are not settled, and many definitions have been proposed over the past century.{{Cite journal |last1=Zanotto |first1=Edgar D. |last2=Mauro |first2=John C. |date=September 2017 |title=The glassy state of matter: Its definition and ultimate fate |url=https://linkinghub.elsevier.com/retrieve/pii/S0022309317302685 |journal=Journal of Non-Crystalline Solids |language=en |volume=471 |pages=490–495 |doi=10.1016/j.jnoncrysol.2017.05.019|bibcode=2017JNCS..471..490Z }}

Franz Simon:{{Cite journal |last=Simon |first=Franz |date=1927-04-01 |title=Zum Prinzip von der Unerreichbarkeit des absoluten Nullpunktes |url=https://doi.org/10.1007/BF01395487 |journal=Zeitschrift für Physik |language=de |volume=41 |issue=4 |pages=806–809 |doi=10.1007/BF01395487 |bibcode=1927ZPhy...41..806S |issn=0044-3328}} Glass is a rigid material obtained from freezing-in a supercooled liquid in a narrow temperature range.

Zachariasen:{{Cite journal |last=Zachariasen |first=W. H. |date=October 1932 |title=The Atomic Arrangement in Glass |url=https://pubs.acs.org/doi/abs/10.1021/ja01349a006 |journal=Journal of the American Chemical Society |language=en |volume=54 |issue=10 |pages=3841–3851 |doi=10.1021/ja01349a006 |issn=0002-7863}} Glass is a topologically disordered network, with short range order equivalent to that in the corresponding crystal.{{Cite journal |last=Gupta |first=Prabhat K. |date=February 1996 |title=Non-crystalline solids: glasses and amorphous solids |url=https://linkinghub.elsevier.com/retrieve/pii/0022309395005021 |journal=Journal of Non-Crystalline Solids |language=en |volume=195 |issue=1–2 |pages=158–164 |doi=10.1016/0022-3093(95)00502-1|bibcode=1996JNCS..195..158G }}

Glass is a "frozen liquid” (i.e., liquids where ergodicity has been broken), which spontaneously relax towards the supercooled liquid state over a long enough time.

Glasses are thermodynamically non-equilibrium kinetically stabilized amorphous solids, in which the molecular disorder and the thermodynamic properties corresponding to the state of the respective under-cooled melt at a temperature T* are frozen-in. Hereby T* differs from the actual temperature T.{{Cite book |last1=Gutzow |first1=Ivan S. |url=https://link.springer.com/10.1007/978-3-642-34633-0 |title=The Vitreous State: Thermodynamics, Structure, Rheology, and Crystallization |last2=Schmelzer |first2=Jürn W.P. |date=2013 |publisher=Springer Berlin Heidelberg |isbn=978-3-642-34632-3 |location=Berlin, Heidelberg |pages=124 |language=en |doi=10.1007/978-3-642-34633-0}}

Glass is a nonequilibrium, non-crystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent supercooled liquids (SCL), and they spontaneously relax toward the SCL state. Their ultimate fate is to solidify, i.e., crystallize.

{{anchor|Transition temperature}}

{{More citations needed section|date=July 2009}}

File:Tgdilatometric.gif.]]

File:Tgdscenglish.svg

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.[http://www.glassproperties.com/tg/ Tg measurement of glasses] {{Webarchive|url=https://web.archive.org/web/20090417092926/http://glassproperties.com/tg/ |date=2009-04-17 }}. 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, 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.{{GoldBookRef |title=glass-transition temperature |file=G02641 }}

In contrast to viscosity, the thermal expansion, heat capacity, shear modulus, and many other properties of inorganic glasses 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 {{Convert|3|-|5|K/min|abbr=on|F/min}} 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.

Dry nylon-6 has a glass transition temperature of {{Convert|47|C}}.[http://www.polymerprocessing.com/polymers/PA6.html nylon-6 information and properties] {{Webarchive|url=https://web.archive.org/web/20120110015535/http://www.polymerprocessing.com/polymers/PA6.html |date=2012-01-10 }}. Polymerprocessing.com (2001-04-15). Retrieved on 2012-06-29. Nylon-6,6 in the dry state has a glass transition temperature of about {{Convert|70|C}}.{{cite journal | last1 = Jones | first1 = A | year = 2014 | title = Supplementary Materials for Artificial Muscles from Fishing Line and Sewing Thread | journal = Science | volume = 343 | issue = 6173| pages = 868–72 | doi = 10.1126/science.1246906 | pmid = 24558156 |bibcode = 2014Sci...343..868H | s2cid = 16577662 }}[https://web.archive.org/web/20150520110712/http://www.tainstruments.co.jp/application/pdf/Thermal_Library/Applications_Briefs/TA133.PDF Measurement of Moisture Effects on the Mechanical Properties of 66 Nylon]. TA Instruments Thermal Analysis Application Brief TA-133 Whereas polyethene has a glass transition range of {{Convert|-130|to|-80|C}}[http://www.polyesterconverters.com/pcl_apps/stage1/stage2/applications_and_enduses/polyethene.htm PCL | Applications and End Uses | Polythene] {{Webarchive|url=https://web.archive.org/web/20130605113814/http://www.polyesterconverters.com/pcl_apps/stage1/stage2/applications_and_enduses/polyethene.htm |date=2013-06-05 }}. Polyesterconverters.com. Retrieved on 2012-06-29.

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.

File:Specific_heat_of_several_glassy_solids.png

In 1971, Zeller and Pohl discovered that {{Cite journal |last1=Zeller |first1=R. C. |last2=Pohl |first2=R. O. |date=1971-09-15 |title=Thermal Conductivity and Specific Heat of Noncrystalline Solids |url=https://link.aps.org/doi/10.1103/PhysRevB.4.2029 |journal=Physical Review B |volume=4 |issue=6 |pages=2029–2041 |doi=10.1103/PhysRevB.4.2029|bibcode=1971PhRvB...4.2029Z }} when glass is at a very low temperature ~1K, its specific heat has a linear component: $c\; \backslash approx\; c\_1\; T\; +\; c\_3\; T^3$. This is an unusual effect, because crystal material typically has $c\; \backslash propto\; T^3$, as in the Debye model. This was explained by the two-level system hypothesis,{{Cite journal |last1=Anderson |first1=P. w. |last2=Halperin |first2=B. I. |last3=Varma |first3=c. M. |date=January 1972 |title=Anomalous low-temperature thermal properties of glasses and spin glasses |url=http://www.tandfonline.com/doi/abs/10.1080/14786437208229210 |journal=Philosophical Magazine |language=en |volume=25 |issue=1 |pages=1–9 |doi=10.1080/14786437208229210 |bibcode=1972PMag...25....1A |issn=0031-8086}} which states that a glass is populated by two-level systems, which look like a double potential well separated by a wall. The wall is high enough such that resonance tunneling does not occur, but thermal tunneling does occur. Namely, if the two wells have energy difference $\backslash Delta\; E\; \backslash sim\; k\_BT$, then a particle in one well can tunnel to the other well by thermal interaction with the environment. Now, imagine that there are many two-level systems in the glass, and their $\backslash Delta\; E$ is randomly distributed but fixed ("quenched disorder"), then as temperature drops, more and more of these two-level levels are frozen out (meaning that it takes such a long time for a tunneling to occur, that they cannot be experimentally observed).

Consider a single two-level system that is not frozen-out, whose energy gap is $\backslash Delta\; E\; =\; O(1/\backslash beta)$. It is in a Boltzmann distribution, so its average energy $=\; \backslash frac\{\backslash beta\; \backslash Delta\; E\}\{e^\{\backslash beta\; \backslash Delta\; E\}\; -\; 1\}\; \backslash beta^\{-1\}$.

Now, assume that the two-level systems are all quenched, so that each $\backslash Delta\; E$ varies little with temperature. In that case, we can write $n(\backslash Delta\; E)$ as the density of states with energy gap $\backslash Delta\; E$. We also assume that $n(\backslash Delta\; E)$ is positive and smooth near $\backslash Delta\; E\; \backslash approx\; 0$.

Then, the total energy contributed by those two-level systems is$$\backslash bar\; E\; \backslash sim\; \backslash int\_0^\{O(1/\backslash beta)\}\; \backslash frac\{\backslash beta\; \backslash Delta\; E\}\{e^\{\backslash beta\; \backslash Delta\; E\}\; -\; 1\}\; \backslash beta^\{-1\}\; \backslash ;\; n(\backslash Delta\; E)\; d\backslash Delta\; E\; =$$

\beta^{-2}\int_0^{O(1)} \frac{a}{e^a-1} n(a/\beta)da \propto \beta^{-2} n(0)

The effect is that the average energy in these two-level systems is $\backslash bar\; E\; \backslash sim\; T^2$, leading to a $\backslash partial\_T\; \backslash bar\; E\; \backslash propto\; T$ term.

In experimental measurements, the specific heat capacity of glass is measured at different temperatures, and a $(T^2,\; c/T)$ graph is plotted. Assuming that $c\; \backslash approx\; c\_1\; T\; +\; c\_3\; T^3$, the graph should show $c/T\; \backslash approx\; c\_1\; +\; c\_3\; T^2$, that is, a straight line with slope showing the typical Debye-like heat capacity, and a vertical intercept showing the anomalous linear component.

File:KauzmannParadox.png

As a liquid is supercooled, the difference in entropy between the liquid and solid phase decreases. By extrapolating the heat capacity of the supercooled liquid below its glass transition temperature, 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, this would be paradoxical, as the liquid phase should have the same vibrational entropy, but much higher positional entropy, as the crystal phase. This is the Kauzmann paradox, still not definitively resolved.{{cite journal|doi=10.1021/cr60135a002|title=The Nature of the Glassy State and the Behavior of Liquids at Low Temperatures|year=1948|last1=Kauzmann|first1=Walter|journal=Chemical Reviews|volume=43|issue=2|pages=219–256}}{{cite web |last1=Wolchover |first1=Natalie |title=Ideal Glass Would Explain Why Glass Exists at All |url=https://www.quantamagazine.org/ideal-glass-would-explain-why-glass-exists-at-all-20200311 |website=Quanta Magazine |access-date=3 April 2020 |date=11 March 2020 |archive-date=7 April 2020 |archive-url=https://web.archive.org/web/20200407071119/https://www.quantamagazine.org/ideal-glass-would-explain-why-glass-exists-at-all-20200311/ |url-status=live }}

There are many possible resolutions to the Kauzmann paradox.

Kauzmann himself resolved the entropy paradox by postulating that all supercooled liquids must crystallize before the Kauzmann temperature is reached.

Perhaps at the Kauzmann temperature, glass reaches an ideal glass phase, which is still amorphous, but has a long-range amorphous order which decreases its overall entropy to that of the crystal. The ideal glass would be a true phase of matter.{{Cite journal |last1=Gibbs |first1=Julian H. |last2=DiMarzio |first2=Edmund A. |date=1958-03-01 |title=Nature of the Glass Transition and the Glassy State |url=https://pubs.aip.org/jcp/article/28/3/373/75478/Nature-of-the-Glass-Transition-and-the-Glassy |journal=The Journal of Chemical Physics |language=en |volume=28 |issue=3 |pages=373–383 |doi=10.1063/1.1744141 |bibcode=1958JChPh..28..373G |issn=0021-9606}} The ideal glass is hypothesized, but cannot be observed naturally, as it would take too long to form. Something approaching an ideal glass has been observed as "ultrastable glass" formed by vapor deposition,{{Cite journal |last1=Swallen |first1=Stephen F. |last2=Kearns |first2=Kenneth L. |last3=Mapes |first3=Marie K. |last4=Kim |first4=Yong Seol |last5=McMahon |first5=Robert J. |last6=Ediger |first6=M. D. |last7=Wu |first7=Tian |last8=Yu |first8=Lian |last9=Satija |first9=Sushil |date=2007-01-19 |title=Organic Glasses with Exceptional Thermodynamic and Kinetic Stability |url=https://www.science.org/doi/10.1126/science.1135795 |journal=Science |language=en |volume=315 |issue=5810 |pages=353–356 |doi=10.1126/science.1135795 |pmid=17158289 |bibcode=2007Sci...315..353S |issn=0036-8075}}

Perhaps there must be a phase transition 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 basis for glass formation. The glass transition temperature:

: $T\_g\; \backslash to\; T\_\{0c\}\; \backslash text\{\; as\; \}\; \backslash frac\{dT\}\{dt\}\; \backslash to\; 0.$

Perhaps the heat capacity of the supercooled liquid near the Kauzmann temperature smoothly decreases to a smaller value.

Perhaps 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.

Silica (the chemical compound SiO₂) has a number of distinct crystalline forms in addition to the quartz structure. Nearly all of the crystalline forms involve tetrahedral SiO₄ units linked together by shared vertices in different arrangements (stishovite, composed of linked SiO₆ octahedra, is the main exception). Si-O bond lengths vary between the different crystal forms. For example, in α-quartz the bond length is {{convert|161|pm}}, whereas in α-tridymite it ranges from {{convert|154|–|171|pm|abbr=on}}. 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, 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 bonds. 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.{{Cite journal|author=Ojovan M.I.|title=Configurons: thermodynamic parameters and symmetry changes at glass transition|journal=Entropy|volume=10|issue=3|pages=334–364|year=2008|url=http://www.mdpi.org/entropy/papers/e10030334.pdf|doi=10.3390/e10030334|bibcode=2008Entrp..10..334O|doi-access=free|access-date=2009-09-25|archive-date=2009-07-11|archive-url=https://web.archive.org/web/20090711015530/http://www.mdpi.org/entropy/papers/e10030334.pdf|url-status=live}}

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_c] where R is the gas constant and f_c is the percolation threshold. For strong melts such as SiO₂ 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.{{cite journal|author=Ojovan, M.I.|title=Configurons: thermodynamic parameters and symmetry changes at glass transition|journal=Entropy|volume=10|pages=334–364|year=2008|url=http://www.mdpi.org/entropy/papers/e10030334.pdf|doi=10.3390/e10030334|issue=3|bibcode=2008Entrp..10..334O|doi-access=free|access-date=2009-09-25|archive-date=2009-07-11|archive-url=https://web.archive.org/web/20090711015530/http://www.mdpi.org/entropy/papers/e10030334.pdf|url-status=live}} The enthalpy H_d and the entropy S_d of configurons – broken bonds can be found from available experimental data on viscosity.{{cite journal|doi=10.1088/0953-8984/19/41/415107|pmid=28192319|title=Thermodynamic parameters of bonds in glassy materials from viscosity–temperature relationships|year=2007|last1=Ojovan|first1=Michael I|last2=Travis|first2=Karl P|last3=Hand|first3=Russell J|journal=Journal of Physics: Condensed Matter|volume=19|issue=41|pages=415107|bibcode=2007JPCM...19O5107O|s2cid=24724512 |url=http://eprints.whiterose.ac.uk/4058/1/ojovanm1.pdf|access-date=2019-07-06|archive-date=2018-07-25|archive-url=https://web.archive.org/web/20180725094232/http://eprints.whiterose.ac.uk/4058/1/ojovanm1.pdf|url-status=live}} On the surface of SiO₂ films, scanning tunneling microscopy has resolved clusters of ca. 5 SiO₂ in diameter that move in a two-state fashion on a time scale of minutes. This is much faster than dynamics in the bulk, but in agreement with models that compare bulk and surface dynamics.{{cite journal|doi=10.1038/nphys1432|title=Multi-scale dynamics at the glassy silica surface|year=2019|last1=Nguyen|first1=Huy|last2=Lia|first2=Can|last3=Wallum|first3=Alison|last4=Lyding|first4=Joseph|last5=Gruebele|first5=Martin|journal= J. Chem. Phys.|volume=151|issue=1 |pages=62–68|pmid=20336168 |pmc=2844102 }}{{cite journal|doi=10.1063/1.5123228|title=A universal origin for secondary relaxations in supercooled liquids and structural glasses|year=2009|last1=Wolynes|first1=PG|last2=Stevenson|first2=JD|journal= Nature Physics|volume=6|issue=1 |pages=62–68|pmid=20336168 |doi-access=free|pmc=2844102 }}

In polymers the glass transition temperature, T_g, is often expressed as the temperature at which the Gibbs free energy is such that the activation energy for the cooperative movement of 50 or so elements of the polymer is exceeded {{Citation needed|date=September 2010}}. 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 rings) will interfere with the flowing process and hence increase T_g.Cowie, J. M. G. and Arrighi, V., Polymers: Chemistry and Physics of Modern Materials, 3rd Edn. (CRC Press, 2007) {{ISBN|0748740732}}

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 E₂, until the temperature exceeds T_m, and the material melts. This region is called the rubber plateau.

File:Ironing.jpg

In 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 plasticizers 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.{{Citation

|last1= Capponi

|first1= S.

|last2= Alvarez

|first2= F.

|last3= Racko

|first3= D.

|title= Free Volume in a PVME Polymer–Water Solution

|journal= Macromolecules

|volume= 53

|pages= 4770–4782

|year= 2020

|issue= 12

|doi= 10.1021/acs.macromol.0c00472 |bibcode= 2020MaMol..53.4770C

|hdl= 10261/218380

|s2cid= 219911779

|hdl-access= free

}}

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 or 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.

File:rubber plateau.svgIn viscoelastic 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 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 undergoes a liquid-glass transition, which has also been called a rubber-glass transition.

{{Main|Vitrification}}

Molecular motion in condensed matter can be represented by a Fourier series whose physical interpretation consists of a superposition of longitudinal and transverse waves of atomic displacement with varying directions and wavelengths. In monatomic systems, these waves are called density fluctuations. (In polyatomic systems, they may also include compositional fluctuations.)Slater, J.C., Introduction to Chemical Physics (3rd Ed., Martindell Press, 2007) {{ISBN|1178626598}}

Thus, thermal motion in liquids can be decomposed into elementary longitudinal vibrations (or acoustic phonons) while transverse vibrations (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 (or viscous flow). Furthermore, the fact that a solid deforms locally while retaining its rigidity – while a liquid yields to macroscopic viscous flow in response to the application of an applied shearing force – is accepted by many as the mechanical distinction between the two.{{cite journal|doi=10.1017/S0305004100017138|title=On the stability of crystal lattices. I|date=April 1940|last1=Born|first1=Max|authorlink1=Max Born|journal=Mathematical Proceedings of the Cambridge Philosophical Society|volume=36|issue=2|pages=160–172|bibcode = 1940PCPS...36..160B |s2cid=104272002 }}{{cite journal| doi=10.1063/1.1750497| title=Thermodynamics of Crystals and Melting| year=1939| last1=Born| first1=Max| journal=The Journal of Chemical Physics| volume=7| issue=8| pages=591–603|bibcode = 1939JChPh...7..591B }}

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 in liquids. This revision follows directly from the continuous characteristic of the viscoelastic crossover from the liquid state into the solid one when the transition is not accompanied by crystallization—ergo the supercooled viscous liquid. Thus we see the intimate correlation between transverse acoustic phonons (or shear waves) and the onset of rigidity upon vitrification, as described by Bartenev in his mechanical description of the vitrification process.{{cite book|author=Frenkel, J.|title=Kinetic Theory of Liquids|url=https://archive.org/details/in.ernet.dli.2015.53485|publisher=Clarendon Press, Oxford|year=1946}}

Bartenev, G. M., Structure and Mechanical Properties of Inorganic Glasses (Wolters – Noordhoof, 1970) {{ISBN|9001054501}}

The velocities of longitudinal acoustic phonons in condensed matter are directly responsible for the thermal conductivity 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" for lattice phonons, and that the value of the mean free path is of the order of magnitude 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.

{{cite journal

|author=Reynolds, C. L. Jr.

|title=Correlation between the low temperature phonon mean free path and glass transition temperature in amorphous solids

|journal=J. Non-Cryst. Solids

|volume=30

|issue=3 |page=371

|year=1979

|doi=10.1016/0022-3093(79)90174-1|bibcode = 1979JNCS...30..371R }}

It has often been suggested that heat transport in dielectric 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).Rosenburg, H. M. (1963) Low Temperature Solid State Physics. Clarendon Press, Oxford.

These predictions were confirmed by experiments on commercial glasses and glass ceramics, where mean free paths were apparently limited by "internal boundary scattering" to length scales of {{convert|10|–|100|µm}}.{{cite journal|author=Kittel, C.

|title=Ultrasonic Propagation in Liquids|journal=J. Chem. Phys.|volume=14|issue=10|page=614|year=1946|doi=10.1063/1.1724073|bibcode = 1946JChPh..14..614K |hdl=1721.1/5041|hdl-access=free}}

{{cite journal|author=Kittel, C.|title=Interpretation of the Thermal Conductivity of Glasses|journal=Phys. Rev.|volume=75|issue=6|page=972|year=1949|doi=10.1103/PhysRev.75.972|bibcode = 1949PhRv...75..972K }}

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.{{cite journal|doi=10.1016/0022-3093(85)90256-X|title=Orientational ordering of local shear stresses in liquids: A phase transition?|year=1985|last1=Chen|first1=Shao-Ping|last2=Egami|first2=T.|last3=Vitek|first3=V.|journal=Journal of Non-Crystalline Solids|volume=75|issue=1–3|pages=449|bibcode = 1985JNCS...75..449C }}

The influence of thermal phonons and their interaction with electronic structure is a topic that was appropriately introduced in a discussion of the resistance of liquid metals. Lindemann's theory of melting is referenced,{{cite thesis |last=Sorkin |first=Viacheslav |date=2005 |title=Point Defects, Lattice Structure and Melting |type=MSc |chapter=Lindemann criterion |chapter-url=http://phycomp.technion.ac.il/~phsorkin/thesis/thesis.pdf |access-date=6 January 2022 |pages=5–8 |publisher=Israel Institute of Technology |archive-date=19 August 2019 |archive-url=https://web.archive.org/web/20190819095312/http://phycomp.technion.ac.il/~phsorkin/thesis/thesis.pdf |url-status=live }} and it is suggested that the drop in conductivity in going from the crystalline to the liquid state is due to the increased scattering of conduction electrons as a result of the increased amplitude of atomic vibration. Such theories of localization have been applied to transport in metallic glasses, where the mean free path of the electrons is very small (on the order of the interatomic spacing).

{{cite journal

|author=Mott, N. F.

|title=The Resistance of Liquid Metals

|journal=Proceedings of the Royal Society A

|volume=146

|issue=857 |page=465

|year=1934

|doi=10.1098/rspa.1934.0166

|bibcode = 1934RSPSA.146..465M |doi-access=free

}}

{{cite journal

|author=Lindemann, C.

|title=On the calculation of molecular natural frequencies

|journal=Phys. Z.

|volume=11 |page=609

|year=1911

}}

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.{{cite journal|doi=10.1038/187869b0|title=Non-crystalline Structure in Solidified Gold–Silicon Alloys|year=1960|last1=Klement|first1=W.|last2=Willens|first2=R. H.|last3=Duwez|first3=POL|journal=Nature|volume=187|issue=4740|pages=869|bibcode=1960Natur.187..869K |s2cid=4203025}}{{cite journal|doi=10.1063/1.1735777|title=Continuous Series of Metastable Solid Solutions in Silver-Copper Alloys|year=1960|last1=Duwez|first1=Pol|last2=Willens|first2=R. H.|last3=Klement|first3=W.|journal=Journal of Applied Physics|volume=31|issue=6|pages=1136|bibcode=1960JAP....31.1136D|url=http://authors.library.caltech.edu/3755/1/DUWjap60.pdf|access-date=2018-05-16|archive-date=2017-12-02|archive-url=https://web.archive.org/web/20171202104916/https://authors.library.caltech.edu/3755/1/DUWjap60.pdf|url-status=live}}{{cite journal|doi=10.1063/1.1735778|title=Metastable Electron Compound in Ag-Ge Alloys|year=1960|last1=Duwez|first1=Pol|last2=Willens|first2=R. H.|last3=Klement|first3=W.|journal=Journal of Applied Physics|volume=31|issue=6|pages=1137|bibcode=1960JAP....31.1137D|url=https://authors.library.caltech.edu/33559/1/DUWjap60b.pdf|access-date=2019-07-06|archive-date=2020-04-18|archive-url=https://web.archive.org/web/20200418184208/https://authors.library.caltech.edu/33559/1/DUWjap60b.pdf|url-status=live}}{{cite journal|pmid=17841932|year=1978|last1=Chaudhari|first1=P|last2=Turnbull|first2=D|title=Structure and properties of metallic glasses|volume=199|issue=4324|pages=11–21|doi=10.1126/science.199.4324.11|journal=Science|bibcode = 1978Sci...199...11C |s2cid=7786426}}

{{cite journal

|author=Chen, J. S.

|title=Glassy metals

|journal=Reports on Progress in Physics

|volume=43

|issue=4 |page=353

|year=1980

|doi=10.1088/0034-4885/43/4/001|bibcode = 1980RPPh...43..353C |s2cid=250804009

}}

Other work indicates that the mobility of localized electrons is enhanced by the presence of dynamic phonon modes. One claim against such a model is that if chemical bonds are important, the nearly free electron models should not be applicable. However, if the model includes the buildup of a charge distribution 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 solids.

{{cite journal

|author1=Jonson, M. |author2=Girvin, S. M. |title=Electron-Phonon Dynamics and Transport Anomalies in Random Metal Alloys

|journal=Phys. Rev. Lett.

|volume=43

|issue=19 |page=1447

|year=1979

|doi=10.1103/PhysRevLett.43.1447

|bibcode=1979PhRvL..43.1447J

}}

Thus, if the electrical conductivity is low, the 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 {{dubious|date=July 2019}} 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.

{{cite journal

|author=Turnbull, D.

|title=Amorphous Solid Formation and Interstitial Solution Behavior in Metallic Alloy System

|journal=J. Phys. C

|volume=35

|issue=C4 |page=C4–1

|year=1974

|doi=10.1051/jphyscol:1974401

|citeseerx=10.1.1.596.7462

|s2cid=52102270

}}

{{cite journal

|author1=Chen, H. S. |author2=Park, B. K. |title=Role of chemical bonding in metallic glasses

|journal=Acta Metall.

|volume=21

|issue=4 |page=395

|year=1973

|doi=10.1016/0001-6160(73)90196-X

}}

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 bonding anisotropy. Crystallization becomes more unlikely as bonding anisotropy is increased from isotropic metallic to anisotropic metallic to covalent bonding, thus suggesting a relationship between the group number in the periodic table and the glass forming ability in elemental solids.

{{cite journal

|author1=Wang, R. |author2=Merz, D. |title=Polymorphic bonding and thermal stability of elemental noncrystalline solids

|journal=Physica Status Solidi A

|volume=39

|issue=2 |page=697

|year=1977

|doi=10.1002/pssa.2210390240

|bibcode = 1977PSSAR..39..697W }}

• Gardner transition
• Glass formation

{{Reflist|30em}}

{{Commons category|Glass-liquid transitions}}

• [http://eprints.iisc.ernet.in/archive/00000257/01/kjrao.pdf Fragility] {{Webarchive|url=https://web.archive.org/web/20070628185015/http://eprints.iisc.ernet.in/archive/00000257/01/kjrao.pdf |date=2007-06-28 }}
• [http://www.iop.org/EJ/abstract/0953-8984/12/46/305 VFT Eqn.]
• [https://web.archive.org/web/20190115195943/http://pslc.ws/macrog/tg.htm Polymers I]
• [http://www.lasalle.edu/academ/chem/ms/polymersRus/Resources/GlassTrans.htm Polymers II] {{Webarchive|url=https://web.archive.org/web/20100111055937/http://www.lasalle.edu/academ/chem/ms/polymersRus/Resources/GlassTrans.htm |date=2010-01-11 }}
• [http://www.public.asu.edu/~caangell/Abstracts/395.pdf Angell: Aqueous media]
• [http://www.doitpoms.ac.uk/tlplib/glass-transition/index.php DoITPoMS Teaching and Learning Package- "The Glass Transition in Polymers"]
• [https://coatings.specialchem.com/coatings-properties/glass-transition-temperature Glass Transition Temperature short overview]

{{Glass science}}

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