The glass–liquid transition, or glass transition, is the gradual and reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle "glassy" state into a viscous or rubbery state as the temperature is increased.^[2] An amorphous solid that exhibits a glass transition is called a glass. The reverse transition, achieved by supercooling a viscous liquid into the glass state, is called vitrification.

The glass-transition temperature T_g of a material characterizes the range of temperatures over which this glass transition occurs (as an experimental definition, typically marked as 100 s of relaxation time). It is always lower than the melting temperature, T_m, of the crystalline state of the material, if one exists, because the glass is a higher energy state (or enthalpy at constant pressure) than the corresponding crystal.

Hard plastics like polystyrene and poly(methyl methacrylate) 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 100 °C (212 °F). Rubber elastomers like polyisoprene and polyisobutylene are used above their T_g, that is, in the rubbery state, where they are soft and flexible; crosslinking prevents free flow of their molecules, thus endowing rubber with a set shape at room temperature (as opposed to a viscous liquid).^[3]

Despite the change in the physical properties of a material through its glass transition, the transition is not considered a phase transition; rather it is a phenomenon extending over a range of temperature and defined by one of several conventions.^[4][5] Such conventions include a constant cooling rate (20 kelvins per minute (36 °F/min))^[2] 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, with the location of these effects again being dependent on the history of the material.^[6] The question of whether some phase transition underlies the glass transition is a matter of ongoing research.^{[4][5][7][when?]}

Characteristics

The glass transition of a liquid to a solid-like state may occur with either cooling or compression.^[10] 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.^[11] 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.^[12]

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.^{[13][14][15][16][17]}

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.^{[clarification needed][6][18][19][20]}

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.^[21] Techniques such as dynamic mechanical analysis can be used to measure the glass transition temperature.^[22]

Formal definitions

The definition of the glass and the glass transition are not settled, and many definitions have been proposed over the past century.^[23]

Franz Simon:^[24] Glass is a rigid material obtained from freezing-in a supercooled liquid in a narrow temperature range.

Zachariasen:^[25] Glass is a topologically disordered network, with short range order equivalent to that in the corresponding crystal.^[26]

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.^[27]

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.^[23]

Transition temperature T_g

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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.^[28]

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.^[29]

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 3–5 K/min (5.4–9.0 °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.^[28]

Summarized below are T_g values characteristic of certain classes of materials.

Polymers

Dry nylon-6 has a glass transition temperature of 47 °C (117 °F).^[35] Nylon-6,6 in the dry state has a glass transition temperature of about 70 °C (158 °F).^[36][37] Whereas polyethene has a glass transition range of −130 to −80 °C (−202 to −112 °F)^[38] 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

Linear heat capacity

In 1971, Zeller and Pohl discovered that ^[42] when glass is at a very low temperature ~1K, its specific heat has a linear component: ${\displaystyle c\approx c_{1}T+c_{3}T^{3}}$. This is an unusual effect, because crystal material typically has ${\displaystyle c\propto T^{3}}$, as in the Debye model. This was explained by the two-level system hypothesis,^[43] 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 ${\displaystyle \Delta E\sim k_{B}T}$, 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 ${\displaystyle \Delta E}$ 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 ${\displaystyle \Delta E=O(1/\beta )}$. It is in a Boltzmann distribution, so its average energy ${\displaystyle ={\frac {\beta \Delta E}{e^{\beta \Delta E}-1}}\beta ^{-1}}$.

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

Then, the total energy contributed by those two-level systems is