Glass transition

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Glassblowing at temperatures just above the glass transition

Glass transition or vitrification refer to the transformation of a glass-forming liquid into a glass, which usually occurs upon rapid cooling. It is a dynamic phenomenon occurring between two distinct states of matter (liquid and glass), each with different physical properties. Upon cooling through the temperature range of glass transition (a "glass transformation range"), without forming any long-range order or significant symmetry of atomic arrangement, the liquid contracts more continuously at about the same rate as above the melting point until there is a decrease in the expansion coefficient. ^[1]

Amorphous silica particles (average particle diameter 600 nm) prepared from basic TEOS solution . This SEM micrograph illustrates the short-range order evidenced in most liquids. A similar microstructure becomes thermally arrested or "frozen in" as a result of rapid cooling during the liquid → glass transition.

The glass transition temperature T_g is lower than melting temperature, T_m, due to supercooling; it depends on the time scale of observation which must be defined by convention. One approach is to agree on a standard cooling rate of 10 K/min. Another approach is by requiring a viscosity of 10¹³ poise. Otherwise, one can only talk about a glass transformation range.

[edit] Introduction

The glassy or vitreous state of matter is typically formed by rapid cooling and solidification from the molten (or liquid) state. If the liquid were allowed to crystallize on cooling, then according to the Ehrenfest classification of first-order phase transitions, there would be a discontinuous change in volume (and thus a discontinuity in the slope or first derivative with respect to temperature, dV/dT) at the melting point. In this context, glass and melt are distinct phases with an interfacial discontinuity having a surface of tension with a positive surface energy. Thus, a metastable parent phase is always stable with respect to the nucleation of small embryos or droplets from a daughter phase, provided it has a positive surface of tension. Such first-order transitions must proceed by the advancement of an interfacial region whose structure and properties vary discontinuously from the parent phase. ^[2][3][4][5]

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. ^{[6][7][8][9][10]}

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 (see Physics of glass). It should be noted here that 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 metastable 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. ^{[11][11][12][13] [14]}

[edit] Transition temperature T_g

Measurement of T_g by differential scanning calorimetry

Determination of T_g by dilatometry.

Refer to the figure on the 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. The linear sections below and above T_g are colored green. T_g is the temperature at the intersection of the red regression lines. ^[15]

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. ^[16]

In contrast to viscosity, the thermal expansion, heat capacity, 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. Here, heating rates of 3-5 K/min are common. Summarized below are T_g values characteristic of certain classes of materials.

These are only mean values, as the glass transition temperature depends on the cooling rate, molecular weight distribution and could be influenced by additives.

Note also that for a semi-crystalline material, such as polyethylene 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.

[edit] Classes of materials

[edit] Silicates and ceramics

The amorphous structure of glassy silica (SiO₂). No long-range order is present, however there is local ordering with respect to the tetrahedral arrangement of oxygen (O) atoms around the silicon (Si) atoms.

Many ceramics are produced in a vitrification process. Vitrification may also occur naturally when lightning strikes sand, where the extreme and immediate heat can create hollow, branching rootlike structures of glass, called fulgurite. When applied to whiteware ceramics, vitreous means the material has an extremely low permeability to liquids, often but not always water, when determined by a specified test regime. The microstructure of whiteware ceramics frequently contain both amorphous and crystalline phases.

Ideal glass formers are typically composed of molecular networks whose intricate geometries do not lend themselves easily to long-range order formation and higher orders of symmetry. The most common example are SiO₄ tetrahedra, with 4 oxygen atoms surrounding a central Si atom. In each of its 7 thermodynamically stable crystalline forms (e.g. quartz) only 2 out of 4 of each the edges of the terahedra are shared with others, yielding the net chemical formula for silica: SiO₂.

The transition temperature T_g in ceramics and silicates is related to the energy required to break and re-form covalent bonds in a somewhat less than perfect (may be regarded as an understatement) 3D lattice of covalent bonds. The T_g is therefore influenced by the chemistry of the glass. For example, addition of elements B, Na, K or Ca to a silica glass, which have a valency less than 4, helps breaking up the 3D lattice and reducing the T_g. On the contrary, P which has a valency of 5, helps to re-establish the 3D lattice, and thus increase the T_g.

[edit] Nuclear waste

A vitrification experiment for the study of nuclear waste disposal

Vitrification is a proven technique in the disposal and long-term storage of nuclear waste or other hazardous wastes^[19]. Waste is mixed with a glass-forming chemical (usually simply with sugar) to form molten glass that then solidifies, immobilizing the waste. The final waste form resembles a black glossy substance, such as obsidian, and is a non-leaching, durable material that effectively traps the waste inside. The waste can be stored for relatively long periods in this form without concern for air or groundwater contamination. Bulk vitrification uses electrodes to melt soil and wastes where they lie buried. The hardened waste may then be disinterred with less danger of widespread contamination. Vitrification locks dangerous materials into a stable glass form that will last for thousands of years.^[20]

[edit] Polymers

T_g depends on the properties of viscoelastic materials 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.

In polymers, 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. 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.

The stiffness of thermoplastics decreases due to this effect. (This is shown in the figure below.) 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.

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.

Stiffness versus temperature

T_g can be significantly decreased by addition of plasticisers 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. The "new-car smell" is due to the initial outgassing of volatile small-molecule plasticizers used to modify interior plastics (e.g., dashboards) to keep them from cracking in the cold, winter weather. 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 which 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.

Another example of practical lowering of T_g is ethylene glycol, which is used as automotive antifreeze and propylene glycol added to ice cream to reduce ice crystals and make ice cream smoother.

[edit] Rubber

In ironing, a fabric is heated through the glass-rubber transition.

Rubber is a highly non-Newtonian fluid. On cooling, it undergoes a liquid-glass transition, which may also be called rubber-glass transition.

The Space Shuttle Challenger disaster was caused by rubber O-rings that were below their glass transition temperature on an unusually cold Florida morning, and thus could not flex adequately to form proper seals between sections of the two solid-fuel rocket boosters.

[edit] Biomaterials

When sucrose is cooled slowly, the result is crystal sugar (or rock candy), but, when cooled rapidly, the result can be in the form of syrupy cotton candy (candyfloss).

Vitrification can also occur when starting with a liquid such as water, usually through very rapid cooling or the introduction of agents that suppress the formation of ice crystals. Additives used in cryobiology or produced naturally by organisms living in polar regions are called cryoprotectants. Arctic frogs and some other ectotherms naturally produce glycerol or glucose in their livers to reduce ice formation. When glucose is used as a cryoprotectant by Arctic frogs, massive amounts of glucose are released at low temperature^[21], and a special form of insulin allows for this extra glucose to enter the cells. When the frog rewarms during spring, the extra glucose must be rapidly removed from the cells and recycled via renal excretion and storage in the bladder. Arctic insects also use sugars as cryoprotectants. Arctic fish use antifreeze proteins, sometimes appended with sugars, as cryoprotectant.

Vitrification technology is being used to cryopreserve cells, tissues and organs for transplantation. For years, glycerol has been used in cryobiology as a cryoprotectant for blood cells and bull sperm, allowing storage at liquid nitrogen temperatures. However, glycerol cannot be used to protect whole organs from damage. Instead, many biotechnology companies are currently^[update] researching the development of other cryoprotectants more suitable for such uses. A successful discovery may eventually make possible the bulk cryogenic storage (or "banking") of transplantable human and xenobiotic organs. A substantial step in that direction has already occurred. At the July 2005 annual conference of the Society for Cryobiology^[22], Twenty-First Century Medicine announced the vitrification of a rabbit kidney to -135°C with their proprietary vitrification cocktail. Upon rewarming, the kidney was successfully transplanted into a rabbit, with complete functionality and viability.

In the context of cryonics, especially in preservation of the human brain, vitrification of tissue is thought to be necessary to prevent destruction of the tissue or information encoded in the brain. At present, vitrification techniques have only been applied to brains (neurovitrification) by Alcor and to the upper body by the Cryonics Institute, but research is in progress by both organizations to apply vitrification to the whole body.

The scientific basis behind the cryonics is that proteins possess a glass transition temperature below which both anharmonic motions and long-range correlated motion within a single molecule are quenched. The origin of this transition is primarily due to "caging" by glassy water^[23], but can also be modeled in the absence of explicit water molecules, suggesting that part of the transition is due to internal protein dynamics.^[24]

[edit] Amorphous metals

Samples of amorphous metal

In the past, small batches of amorphous metals with high surface area configurations (ribbons, wires, films, etc.) have been produced through the implementation of extremely rapid rates of cooling. This was initially termed "splat cooling" by Doctoral student W. Klement at Cal Tech, who showed that cooling rates on the order of millions of degrees per second is sufficient to impede the formation of crystals, and the metallic atoms becomes "locked into" a glassy state. Amorphous metal wires have been produced by sputtering molten metal onto a spinning metal disk. More recently a number of alloys have been produced in layers with thickness exceeding 1 millimeter. These are known as bulk metallic glasses (BMG). Liquidmetal Technologies sell a number of titanium-based BMGs. Batches of amorphous steel have also been produced that demonstrate mechanical properties far exceeding those found in conventional steel alloys. ^{[25] [26] [27] [28]}

In 2004, NIST researchers presented evidence that an isotropic non-crystalline metallic phase (dubbed "q-glass") could be grown from the melt. This phase is the first phase, or "primary phase," to form in the Al-Fe-Si system during rapid cooling. Interestingly, experimental evidence indicates that this phase forms by a first-order transition. Transmission electron microscopy (TEM) images show that the q-glass nucleates from the melt as discrete particles, which grow spherically with a uniform growth rate in all directions. The diffraction pattern shows it to be an isotropic glassy phase. Yet there is a nucleation barrier, which implies an interfacial discontinuity (or internal surface) between the glass and the melt. ^{[29] [30]}

[edit] Colloidal glasses

Electron micrograph of surface of colloidal glass. Structure and morphology consist of short-range order with both interdomain and intradomain lattice defects.

The term colloid is used primarily to describe a broad range of solid-liquid (and/or liquid-liquid) mixtures, all of which contain distinct solid (and/or liquid) particles which are dispersed to various degrees in a liquid medium. The term is specific to the size of the individual particles, which are larger than atomic dimensions but small enough to exhibit Brownian motion. If the particles are large enough, then their dynamic behavior in any given period of time in suspension would be governed by forces of gravity and sedimentation. But if they are small enough to be colloids, then their irregular motion in suspension can be attributed to the collective bombardment of a myriad of thermally agitated molecules in the liquid suspending medium, as described originally by Albert Einstein in his dissertation. Einstein proved the existence of water molecules by concluding that this erratic particle behavior could adequately be described using the theory of Brownian motion, with sedimentation being a possible long-term result. This critical size range (or particle diameter) typically ranges from nanometers (10⁻⁹ m) to micrometers (10⁻⁶ m). ^[31]

A colloidal crystal is a highly ordered array of colloidal particles which can be formed over a very long range (from a few millimeters to one centimeter) in length, and which appear analogous to their atomic or molecular counterparts. One of the finest natural examples of this phenomenon can be found in precious opal, where brilliant regions of pure spectral color result from close-packed domains of colloidal spheres of amorphous silicon dioxide (or silica, SiO₂).

Thus, it has been known for many years that, due to repulsive Coulombic interactions, electrically charged macromolecules in an aqueous environment can exhibit long-range crystal-like correlations with separation between the particles often being considerably greater than the individual particle diameter. Colloidal solids (both crystals and glasses) are receiving increased attention, largely due to their mechanisms of solidification and self-assembly, cooperative motion, structures similar to those observed in condensed matter (liquids, crystals and glasses) and structural phase transitions including the glass transition. Phase equilibrium has been considered within the context of their physical similarities (with appropriate scaling) to classical elastic solids. In contrast to atomic systems, however, the length or spatial scale is mesoscopic and determined by the spacing between the particles l (the cube root of the particle concentration or vol% solids). Thus, colloidal crystals can also exhibit the microstructure of a glass-like amorphous solid on an appropriately larger spatial scale. Concentrated colloidal suspensions may exhibit a distinct glass transition as function of particle concentration or density. ^{[32] [33] [34] [35]}

[edit] Kauzmann's paradox

Entropy difference between crystal and undercooled melt

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, consequences would be paradox. This Kauzmann paradox has been the subject of much debate and many publications since it was first put forward in 1948.^[36]

One resolution of the Kauzmann paradox is to say that there must be a phase change 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 → T_0c  as   ^dT⁄_dt → 0.

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.

[edit] See also

[edit] References

[edit] Further reading

• For glass transition temperatures of various resins, see Engineered Materials Handbook—Desk edition. (1995). ASM International. ISBN 0871702835. p. 369.
• For glass transition temperatures of various glasses, see Mazurin, O.V. Handbook of Glass Data. (1993). Elsevier. ISBN 0444816356.
• Prediction of high weight polymers glass transition temperature using RBF neural networks Journal of Molecular Structure: THEOCHEM, Volume 716, Issues 1-3, 7 March 2005, Pages 193-198 Antreas Afantitis, Georgia Melagraki, Kalliopi Makridima, Alex Alexandridis, Haralambos Sarimveis and Olga Iglessi-Markopoulou
• Wilkes, Charles E.; Summers, James W.; Daniels, Charles Anthony; Berard, Mark T. (2005), PVC Handbook (illustrated ed.), Hanser Verlag, ISBN 9781569903797, http://books.google.com/books?id=YUkJNI9QYsUC .

[edit] External links

• Vitrification in Cryonics
• CRYOBIOLOGY 48(1):22-35 (2004)
• Vitrification: Putting the Heat on Waste
• Fragility thy name is glass
• Liquid fragility and the glass transition in water and aqueous solutions
• Vogel-Tammann-Fulcher Equation Parameters
• On the glassy state of multiphase and pure polymer materials
• Liquid fragility and the glass transition in water and aqueous solutions
• Colloidal Glasses