Glass transition

The glass-liquid alteration (or bottle alteration for short) is the capricious alteration in baggy abstracts (or in baggy regions aural semicrystalline materials) from a harder and almost breakable accompaniment into a aqueous or rubber-like state.1 An baggy solid that exhibits a bottle alteration is alleged a glass. Supercooling a adhesive aqueous into the bottle accompaniment is alleged vitrification, from the Latin vitreum, "glass" via French vitrifier.

Despite the massive change in the concrete backdrop of a actual through its bottle transition, the alteration is not itself a appearance alteration of any kind; rather it is a class abnormality extending over a ambit of temperature and authentic by one of several conventions.23 Such conventions cover a connected cooling amount (20 K/min) 1 and a bendability beginning of 1012 Pa·s, a part of others. Upon cooling or heating through this bottle alteration range, the actual aswell exhibits a bland footfall in the thermal amplification accessory and in the specific heat, with the area of these furnishings afresh getting abased on the history of the material.4 However, the catechism of whether some appearance alteration underlies the bottle alteration is a amount of continuing research.235

The bottle alteration temperature Tg is consistently lower than the melting temperature, Tm, of the apparent accompaniment of the material, if one exists.

Introduction

The bottle alteration of a aqueous to a solid-like accompaniment may action with either cooling or compression.6 The alteration comprises a bland access in the bendability of a actual by as abundant as 17 orders of aftereffect after any arresting change in actual structure. The aftereffect of this affecting access is a bottle announcement solid-like automated backdrop on the timescale of applied observation. This alteration is in adverse to the freezing or condensate transition, which is a first-order appearance alteration in the Ehrenfest allocation and involves discontinuities in thermodynamic and activating backdrop such as volume, energy, and viscosity. In abounding abstracts that commonly abide a freezing transition, accelerated cooling will abstain this appearance alteration and instead aftereffect in a bottle alteration at some lower temperature. Other materials, such as abounding polymers, abridgement a able-bodied authentic apparent accompaniment and calmly anatomy glasses, even aloft actual apathetic cooling or compression.

Below the alteration temperature range, the burnished anatomy does not relax in accordance with the cooling amount used. The amplification accessory for the burnished accompaniment is almost agnate to that of the apparent solid. If slower cooling ante are used, the added time for structural alleviation (or intermolecular rearrangement) to action may aftereffect in a college body bottle product. Similarly, by annealing (and appropriately acceptance for apathetic structural relaxation) the bottle anatomy in time approaches an calm body agnate to the supercooled aqueous at this aforementioned temperature. Tg is amid at the circle amid the cooling ambit (volume against temperature) for the burnished accompaniment and the supercooled liquid.7

The agreement of the bottle in this temperature ambit changes boring with time appear the calm structure. The assumption of the abuse of the Gibbs chargeless activity provides the thermodynamic active force all-important for the closing change. It should be acclaimed actuality that at somewhat college temperatures than Tg, the anatomy agnate to calm at any temperature is accomplished absolutely rapidly. In contrast, at appreciably lower temperatures, the agreement of the bottle charcoal evidently abiding over more continued periods of time.

Thus, the liquid-glass alteration is not a alteration amid states of thermodynamic equilibrium. It is broadly believed that the accurate calm accompaniment is consistently crystalline. Bottle is believed to abide in a kinetically bound state, and its entropy, density, and so on, depend on the thermal history. Therefore, the bottle alteration is primarily a activating phenomenon. Time and temperature are changeable quantities (to some extent) if ambidextrous with glasses, a actuality generally bidding in the time-temperature superposition principle. On cooling a liquid, centralized degrees of abandon successively abatement out of equilibrium. However, there is a longstanding agitation whether there is an basal second-order appearance alteration in the academic absolute of always continued alleviation times.8 9 ,1011

Transition temperature Tg

Refer to the amount on the appropriate acute the calefaction accommodation as a action of temperature. In this context, Tg is the temperature agnate to point A on the curve. The beeline sections beneath and aloft Tg are black green. Tg is the temperature at the circle of the red corruption lines.12

Different operational definitions of the bottle alteration temperature Tg are in use, and several of them are accustomed as accustomed accurate standards. Nevertheless, all definitions are arbitrary, and all crop altered numeric results: at best, ethics of Tg for a accustomed actuality accede aural a few kelvins. One analogue refers to the viscosity, acclimation Tg at a amount of 1013 address (or 1012 Pa·s). As apparent experimentally, this amount is abutting to the annealing point of abounding glasses.13

In adverse to viscosity, the thermal expansion, calefaction capacity, and abounding added backdrop of asleep glasses appearance a almost abrupt change at the bottle alteration temperature. Any such footfall or coil can be acclimated to ascertain Tg. To accomplish this analogue reproducible, the cooling or heating amount have to be specified.

The a lot of frequently acclimated analogue of Tg uses the activity absolution on heating in cogwheel scanning calorimetry (DSC, see figure). Typically, the sample is aboriginal cooled with 10 K/min and again acrimonious with that aforementioned speed.

Yet addition analogue of Tg uses the coil in dilatometry. Here, heating ante of 3-5 K/min are common. Summarized beneath are Tg ethics appropriate of assertive classes of materials.

edit Polymers

Material Tg (°C)

Tyre elastic −7014

Polypropylene (atactic) −2015

Polypropylene (isotactic) 015

Poly-3-hydroxybutyrate (PHB) 1515

Poly(vinyl acetate) (PVAc) 3015

Polyethylene terephthalate (PET) 7015

Poly(vinyl chloride) (PVC) 8015

Poly(vinyl alcohol) (PVA) 8515

Polystyrene 9515

Poly(methylmethacrylate) (atactic) 10515

Poly(carbonate) 14515

Polynorbornene 21515

Nylon-6 Nylon has a bottle alteration temperature of 47 Celsius16. Whereas Polyethene has a bottle alteration ambit of -130 to -80 17 It have to be kept in apperception that the aloft are alone beggarly values, as the bottle alteration temperature depends on the cooling rate, atomic weight administration and could be afflicted by additives. Note aswell that for a semi-crystalline material, such as polyethene that is 60-80% apparent at allowance temperature, the quoted bottle alteration refers to what happens to the baggy allotment of the actual aloft cooling.

edit Silicates and added covalent arrangement glasses

Kauzmann's paradox

As a aqueous is supercooled, the aberration in anarchy amid the aqueous and solid appearance decreases. By extrapolating the calefaction accommodation of the supercooled aqueous beneath its bottle alteration temperature, it is accessible to account the temperature at which the aberration in entropies becomes zero. This temperature has been called the Kauzmann temperature.

If a aqueous could be supercooled beneath its Kauzmann temperature, and it did absolutely affectation a lower anarchy than the clear phase, the after-effects would be paradoxical. This Kauzmann absurdity has been the accountable of abundant agitation and abounding publications back it was aboriginal put advanced by Walter Kauzmann in 1948.20

One resolution of the Kauzmann absurdity is to say that there have to be a appearance change afore the anarchy of the aqueous decreases. In this scenario, the alteration temperature is accepted as the calorimetric ideal bottle alteration temperature T0c. In this view, the bottle alteration is not alone a active effect, i.e. alone the aftereffect of fast cooling of a melt, but there is an basal thermodynamic base for bottle formation. The bottle alteration temperature:

Tg → T0c as dT⁄dt → 0.

There are at atomic three added accessible resolutions to the Kauzmann paradox. It could be that the calefaction accommodation of the supercooled aqueous abreast the Kauzmann temperature calmly decreases to a abate value. It could aswell be that a aboriginal adjustment appearance alteration to addition aqueous accompaniment occurs afore the Kauzmann temperature with the calefaction accommodation of this new accompaniment getting beneath than that acquired by extrapolation from college temperature. Finally, Kauzmann himself bound the anarchy absurdity by postulating that all supercooled liquids have to accumulate afore the Kauzmann temperature is reached.

The glass transition in specific materials

Silica, SiO2

Silica (the actinic admixture SiO2) has a amount of audible apparent forms in accession to the quartz structure. Nearly all of the apparent forms absorb tetrahedral SiO4 units affiliated calm by aggregate vertices in altered arrangements. Si-O band lengths alter amid the altered clear forms. For example, in α-quartz the band breadth is 161 pm, admitting in α-tridymite it ranges from 154-171 pm. The Si-O-Si band bend aswell varies from 140° in α-tridymite to 144° in α-quartz to 180° in β-tridymite. Any deviations from these accepted ambit aggregate microstructural differences or variations which represent an access to an amorphous, brittle or burnished solid.

The alteration temperature Tg in silicates is accompanying to the activity appropriate to breach and re-form covalent bonds in an baggy (or accidental network) filigree of covalent bonds. The Tg is acutely afflicted by the allure of the glass. For example, accession of elements such as B, Na, K or Ca to a silica glass, which accept a valency beneath than 4, helps in breaking up the arrangement structure, appropriately abbreviation the Tg. Alternatively, P which has a valency of 5, helps to reinforce an ordered lattice, and appropriately increases the Tg.21

Tg is anon proportional to band strength, e.g. it depends on quasi-equilibrium thermodynamic ambit of the bonds e.g. on the enthalpy Hd and anarchy Sd of configurons – torn bonds: Tg = Hd / Sd + Rln(1-fc)/ fc area R is the gas connected and fc is the aperture threshold. For able melts such as SiO2 the aperture beginning in the aloft blueprint is the accepted Scher-Zallen analytical body in the 3-D amplitude e.g. fc = 0.15, about for brittle abstracts the aperture thresholds are material-dependent and fc << 1.22 The enthalpy Hd and the anarchy Sd of configurons – torn bonds can be begin from accessible beginning abstracts on viscosity.23

Polymers

In polymers the bottle alteration temperature, Tg, is generally bidding as the temperature at which the Gibbs chargeless activity is such that the activation activity for the accommodating movement of 50 or so elements of the polymer is exceededcitation needed. This allows atomic chains to accelerate accomplished anniversary added if a force is applied. From this definition, we can see that the accession of almost annealed actinic groups (such as benzene rings) will baffle with the abounding action and appropriately access Tg.24

The acerbity of thermoplastics decreases due to this aftereffect (see figure.) If the bottle temperature has been reached, the acerbity stays the aforementioned for a while, i.e., at or abreast E2, until the temperature exceeds Tm, and the actual melts. This arena is alleged the elastic plateau.

In ironing, a bolt is acrimonious through the glass-rubber transition.

In ironing, a bolt is acrimonious through this alteration so that the polymer chains become mobile. The weight of the adamant again imposes a adopted orientation. Tg can be decidedly decreased by accession of plasticizers into the polymer matrix. Smaller molecules of plasticizer bury themselves amid the polymer chains, accretion the agreement and chargeless volume, and acceptance them to move accomplished one accession even at lower temperatures. The "new-car smell" is due to the antecedent outgassing of airy small-molecule plasticizers (most frequently accepted as phthalates) acclimated to adapt autogenous plastics (e.g., dashboards) to accumulate them from arise in the algid of winter weather. The accession of nonreactive ancillary groups to a polymer can aswell accomplish the chains angle off from one another, abbreviation Tg. If a artificial with some adorable backdrop has a Tg which is too high, it can sometimes be accumulated with accession in a copolymer or blended actual with a Tg beneath the temperature of advised use. Note that some plastics are acclimated at top temperatures, e.g., in auto engines, and others at low temperatures.15

In viscoelastic materials, the attendance of liquid-like behavior depends on the backdrop of and so varies with amount of activated load, i.e., how bound a force is applied. The silicone toy 'Silly Putty' behaves absolutely abnormally depending on the time amount of applying a force: cull boring and it flows, acting as a heavily adhesive liquid; hit it with a bang and it shatters, acting as a glass.

Stiffness against temperature

On cooling, elastic undergoes a liquid-glass transition, which has aswell been alleged a rubber-glass transition. For example, the Space Shuttle Challenger adversity was acquired by elastic O-rings that were getting acclimated able-bodied beneath their bottle alteration temperature on an almighty algid Florida morning, and appropriately could not angle abundantly to anatomy able seals amid sections of the two solid-fuel rocket boosters.

Mechanics of vitrification

Molecular motion in abridged amount can be represented by a Fourier alternation whose concrete estimation consists of a superposition of longitudinal and axle after-effects of diminutive displacement with capricious admonition and wavelengths. In monatomic systems, these after-effects are alleged body fluctuations. (In polyatomic systems, they may aswell cover compositional fluctuations.)25

Thus, thermal motion in liquids can be addle into elementary longitudinal accordance (or acoustic phonons) while axle accordance (or microburst waves) were originally declared alone in adaptable debris announcement the awful ordered apparent accompaniment of matter. In added words, simple liquids cannot abutment an activated force in the anatomy of a shearing stress, and will crop mechanically via arresting artificial anamorphosis (or adhesive flow). Furthermore, the actuality that a solid deforms locally while appliance its acerbity -- while a aqueous yields to arresting adhesive breeze in acknowledgment to the appliance of an activated shearing force -- is accustomed by abounding as the automated acumen amid the two. 26

The inadequacies of this conclusion, however, were acicular out by Frenkel in his afterlight of the active approach of debris and the approach of animation in liquids. This afterlight follows anon from the connected appropriate of the structural alteration from the aqueous accompaniment into the solid one if this alteration is not accompanied by crystallization—ergo the supercooled adhesive liquid. Appropriately we see the affectionate alternation amid axle acoustic phonons (or microburst waves) and the access of acerbity aloft vitrification, as declared by Bartenev in his automated description of the vitrification process. 27 28

The velocities of longitudinal acoustic phonons in abridged amount are anon amenable for the thermal application which levels out temperature differentials amid aeroembolism and broadcast aggregate elements. Kittel proposed that the behavior of glasses is interpreted in agreement of an about connected "mean chargeless path" for filigree phonons, and that the amount of the beggarly chargeless aisle is of the adjustment of consequence of the calibration of ataxia in the atomic anatomy of a aqueous or solid. The thermal phonon beggarly chargeless paths or alleviation lengths of a amount of bottle formers accept been advised against the bottle alteration temperature, advertence a beeline accord amid the two. This has appropriate a new archetype for bottle accumulation based on the amount of the phonon beggarly chargeless path. 29

It has generally been appropriate that calefaction carriage in dielectric debris occurs through adaptable accordance of the lattice, and that this carriage is bound by adaptable drop of acoustic phonons by filigree defects (e.g. about spaced vacancies). 30 These predictions were accepted by abstracts on bartering glasses and bottle ceramics, area beggarly chargeless paths were allegedly bound by "internal abuttals scattering" to breadth scales of 10 - 100 micrometers. 31 32 The accord amid these axle after-effects and the apparatus of vitrification has been declared by several authors who proposed that the access of correlations amid such phonons after-effects in an orientational acclimation or "freezing" of bounded microburst stresses in glass-forming liquids, appropriately acquiescent the bottle transition. 33

Electronic structure

The access of thermal phonons and their alternation with cyberbanking anatomy is a affair which was appropriately alien in a altercation of the attrition of aqueous metals. Lindemann's approach of melting is referenced, and it is appropriate that the bead in application in traveling from the apparent to the aqueous accompaniment is due to the added drop of advice electrons as a aftereffect of the added amplitude of diminutive vibration. Such theories of localization accept been activated to carriage in brownish glasses, area the beggarly chargeless aisle of the electrons is actual baby (on the adjustment of the interatomic spacing).3435

The accumulation of a non-crystalline anatomy of a gold-silicon admixture by the adjustment of splat abatement from the cook led to added considerations of the access of cyberbanking anatomy on bottle basic ability, based on the backdrop of the brownish bond. 36 3738 39

Other plan indicates that the advancement of localized electrons is added by the attendance of activating phonon modes. One affirmation adjoin such a archetypal is that if actinic bonds are important, the about chargeless electron models should not be applicable. However, if the archetypal includes the accretion of a allegation administration amid all pairs of atoms just like a actinic bandage (e.g., silicon, if a bandage is just abounding with electrons) again it should administer to solids. 40

Thus, if the electrical application is low, the beggarly chargeless aisle of the electrons is actual short. The electrons will alone be acute to the short-range adjustment in the bottle back they do not get a adventitious to besprinkle from atoms spaced at ample distances. Back the short-range adjustment is agnate in glasses and crystals, the cyberbanking energies should be agnate in these two states. For alloys with lower resistivity and best cyberbanking beggarly chargeless paths, the electrons could activate to faculty that there is ataxia in the glass, and this would accession their energies and destabilize the bottle with account to crystallization. Thus, the bottle accumulation tendencies of assertive alloys may accordingly be due in allotment to the actuality that the electron beggarly chargeless paths are actual short, so that alone the short-range adjustment is anytime important for the activity of the electrons.

It has aswell been argued that bottle accumulation in brownish systems is accompanying to the "softness" of the alternation abeyant amid clashing atoms. Some authors, emphasizing the able similarities amid the bounded anatomy of the bottle and the agnate crystal, advance that actinic bonding helps to balance the baggy structure.4142

Other authors accept appropriate that the cyberbanking anatomy yields its access on bottle accumulation through the directional backdrop of bonds. Non-crystallinity is appropriately advantaged in elements with a ample amount of polymorphic forms and a top amount of bonding anisotropy. Condensate becomes added absurd as bonding anisotropy is added from isotropic brownish to anisotropic brownish to covalent bonding, appropriately suggesting a accord amid the accumulation amount in the alternate table and the bottle basic adeptness in basal solids.43