Glass transition temperature

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The glass transition temperature, T_g, is the temperature at which an amorphous solid, such as glass or a polymer, becomes brittle on cooling, or soft on heating. More specifically, it defines a pseudo second order phase transition in which a supercooled melt yields, on cooling, a glassy structure and properties similar to those of crystalline materials e.g. of an isotropic solid material.^[1] T_g is usually applicable to wholly or partially amorphous solids such as common glasses and plastics (organic polymers).

Below the glass transition temperature, T_g, amorphous solids are in a glassy state^[2] and most of their joining bonds are intact. In inorganic glasses, with increased temperature more and more joining bonds are broken by thermal fluctuations so that broken bonds (termed configurons) begin to form clusters. Above T_g these clusters become macroscopic large facilitating the flow of material. In organic polymers, secondary, non-covalent bonds between the polymer chains become weak above T_g. Above T_g glasses and organic polymers become soft and capable of plastic deformation without fracture. This behavior is one of the things which make most plastics useful.^[3]

It is important to note that the glass transition temperature is a kinetic parameter, and thus parametrically depends on the melt cooling rate. Thus the slower the melt cooling rate, the lower T_g. In addition, T_g depends on the measurement conditions, which are not universally defined.^[4]

The bond system of an amorphous material changes its Hausdorff dimension from Euclidian 3 below T_g (where the amorphous material is solid), to fractal 2.55±0.05 above T_g, where the amorphous material is liquid.^[5]

[edit] Time dependency

Consider a molecular liquid which is slowly cooling down. At a certain temperature, the average kinetic energy of molecules no longer exceeds the binding energy between neighboring molecules and growth of organized solid crystal begins. Formation of an ordered system takes a certain amount of time since the molecules must move from their current location to energetically preferred points at crystal nodes. As temperature falls, molecular motion slows down further and, if the cooling rate is fast enough, molecules never reach their destination — the substance enters into dynamic arrest and a disordered, glassy solid (or supercooled liquid) forms. In fact, Walter Kauzmann has argued that if such an arrest did not happen, at still lower temperatures a thermodynamically paradoxical situation would arise, where the undercooled liquid would have to be denser and of a lower enthalpy than the crystalline phase. Such arrest apparently takes place at certain temperature, which is called the calorimetric ideal glass transition temperature T_0c. This means that 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.^[6] The glass transition temperature T_g → T_0c as ^dT⁄_dt → 0.

A full discussion of T_g requires an understanding of mechanical loss mechanisms (vibrational and resonance modes) of specific (usually common in a given material) functional groups and molecular arrangements. Factors such as heat treatment and molecular re-arrangement, vacancies, induced strain and other factors affecting the condition of a material may have an effect on T_g ranging from the subtle to the dramatic. T_g is dependent on the viscoelastic materials properties, and so varies with rate of applied load. The silicone toy 'Silly Putty' is a good example of this: pull slowly and it flows; hit it with a hammer and it shatters.

In contrast to the melting points of crystalline materials the glass transition temperature is therefore somewhat dependent on the time-scale of the imposed change. To some extent time and temperature are interchangeable quantities when dealing with glasses, a fact often expressed in the time-temperature superposition principle. An alternative way to discuss the same issue is to say that a glass transition temperature is only truly a point on the temperature scale if the change is imposed at one particular frequency. This is why the ability to modulate the temperature in a DSC experiment has made determining T_g considerably more precise. Since T_g is cooling-rate (or frequency) dependent as the glass is formed, the glass transition is not considered a true thermodynamic phase transition by many in the field. They reserve this epithet rather for a transition that is sharp and history-independent.

The glass-liquid transition has universal characteristics of phase transitions including symmetry breaking for the system of bonds.^[7]

The IUPAC Compendium of Chemical Terminology, 1997, 66, 583 defines the glass transition as a second order phase transition in which a supercooled melt yields, on cooling, a glassy structure and properties similar to those of crystalline materials e.g. of an isotropic solid material. Phase transitions are associated with the symmetry breaking^[8]. The translation-rotation symmetry in the distribution of atoms and molecules is unchanged at the liquid-glass transition, which retains the topological disorder of fluids. Symmetry changes at glass transition can be viewed when considered not for atoms but for bonds. The disordered material changes its symmetry, namely the Hausdorff dimension of bonds, from Euclidian 3D below to fractal 2.55±0.05- dimensional above the glass transition temperature.^[9]

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. With thermoplastics, the stiffness of the material will drop due to this effect. This is shown in the figure below. It can be seen that when the glass temperature has been reached, the stiffness stays the same for a while, until the material melts. This region is called the rubber plateau.

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.

In glasses (including amorphous metals and gels), T_g 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. E.g., add B, Na, K or Ca to a silica glass, which have a valency less than 4 and they help break up the 3D lattice and reduce the T_g. Add P which has a valency of 5 and it helps re-establish the 3D lattice, increasing T_g.

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] Measurement of T_g for glasses

Measurement of T_g by DSC. T_g is the temperature corresponding to point A.^[10]

Determination of T_g for glasses by dilatometry. The linear sections below and above T_g are marked green; T_g is the temperature at the point of intersection of the corresponding red regression lines.^[10]

In contrast to the viscosity the thermal expansion, heat capacity, and many other properties of inorganic glasses show a relatively sudden change at the glass transition temperature. This effect is used for measurement by Differential scanning calorimetry (DSC) and dilatometry.

The viscosity at the glass transition temperature depends on the sample preparation (especially the cooling curve), the heating or cooling curve during measurement and the chemical composition.^[4] In general, the glass transition temperature is close to the annealing point of glasses at 10¹³ poise = 10¹² Pa·s. For dilatometric measurements heating rates of 3-5 K/min are common, for DSC measurements 10 K/min, considering that the heating rate during measurement should equal the cooling rate during sample preparation.^[4]

[edit] Biophysics

Proteins also 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^[11], but can also be modeled in the absence of explicit water molecules, suggesting that part of the transition is due to internal protein dynamics.^[12]

Vitrification (glass formation below the melting point) can 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. This is in contrast to ordinary freezing which results in ice crystal formation. Additives used in cryobiology or produced naturally by organisms living in polar regions are called cryoprotectants. Vitrification technology is being used to cryopreserve cells, tissues and organs for transplantation.

[edit] Glass transition temperature of some materials

These are only mean values, as the glass transition temperature depends on the cooling-ratio, 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 as the temperature is dropped

[edit] References and footnotes

• 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

[edit] External links

• Vogel-Tammann-Fulcher Equation Parameters
• Fragility thy name is glass
• On the glassy state of multiphase and pure polymer materials
• Liquid fragility and the glass transition in water and aqueous solutions
• Colloidal Glasses