Glass Transition Temperature

A plastic that softens without melting

Take a length of rubber tubing and dunk it in liquid nitrogen. Pull it out and it has become a glass rod — rigid, brittle, and it will shatter if you tap it on the bench. Let it warm back up and the very same material becomes floppy and elastic again. Nothing melted. No crystals formed or vanished. The molecules are in exactly the same chemical arrangement at both temperatures. What changed is whether the polymer chains can move.

The temperature at the middle of that change is the glass transition temperature, Tg. Below Tg the long chain molecules are jammed against each other and frozen in place — only their bonds vibrate. The material is a glass: hard, transparent, and brittle. Above Tg the chains have enough thermal energy that whole segments of the backbone can swing and slither past their neighbors. The material is rubbery: soft, leathery, able to stretch and recover.

This only happens in the amorphous (disordered) regions of a polymer. A perfectly crystalline solid melts at a sharp melting point, Tm, by destroying its ordered lattice. An amorphous solid has no lattice to destroy — so instead of melting it goes through this gradual mobility transition. Most everyday plastics are either fully amorphous (polystyrene, PMMA, polycarbonate) or semicrystalline (PET, polyethylene, nylon), and the semicrystalline ones show both a Tg for their amorphous fraction and a higher Tm for their crystals.

Free volume: the room a chain needs to wiggle

The clearest physical picture of Tg is the free-volume theory. Picture the polymer as a tangle of cooked spaghetti. The total volume is split into the volume actually occupied by the chains and the empty gaps between them — the free volume, V_f. For a segment of chain to rotate or translate, an empty pocket of free volume has to be available right next to it for the segment to swing into.

As you heat the polymer, it expands and the free volume grows. As you cool it, the free volume shrinks. Free-volume theory says cooperative segmental motion shuts off once the fractional free volume f = V_f/V falls to a near-universal value:

f(Tg) ≈ 0.025      (about 2.5% free volume at the glass transition)

This is the Williams–Landel–Ferry "universal" free volume. Below Tg there is simply not enough empty space for a segment to move into, so the chains lock and only local vibrations survive. The macroscopic fingerprint is a kink in the volume-versus-temperature curve: the thermal expansion coefficient drops by roughly a factor of two to three as you cross from rubber to glass, because the glass can only expand by stretching bonds, not by opening new gaps.

Specific
volume V
  │                              ╱  rubbery / liquid
  │                           ╱      (high expansion: α_liquid)
  │                        ╱
  │                     ╱←── kink at Tg
  │                  ╱
  │            ────╱  glassy
  │       ────       (low expansion: α_glass)
  │  ────
  └────────────────────────────────────→  Temperature
                     Tg

The WLF equation and the kinetics of freezing

Here is the subtle part that trips up most students: the glass transition is not a true thermodynamic phase transition at all. It is a kinetic event. On cooling, the chains keep relaxing toward equilibrium until their relaxation time grows longer than the time you give them. The moment the relaxation time exceeds the experimental timescale (about 100 s for a typical lab measurement), the structure can no longer keep up and it freezes. That freezing temperature is Tg.

The temperature dependence of the relaxation time (and of viscosity) near Tg is captured by the Williams–Landel–Ferry (WLF) equation, valid roughly from Tg to Tg + 100 K:

log₁₀(aT) = −C₁ (T − Tg) / [C₂ + (T − Tg)]

  with "universal" constants  C₁ ≈ 17.4,  C₂ ≈ 51.6 K  (when referenced to Tg)

Here aT is the shift factor — the ratio of relaxation times at temperature T versus at Tg. The WLF form is not Arrhenius; the apparent activation energy itself blows up as you approach Tg from above, which is why the slowdown is so dramatic. At Tg the viscosity of a glass-former reaches about 10¹² Pa·s — twelve orders of magnitude stiffer than honey — which is the practical definition of "a glass" for inorganic systems too.

Because the transition is kinetic, Tg depends on the cooling rate. Cool ten times faster and the chains run out of time at a higher temperature, so Tg rises by roughly 3 °C. Cool ten times slower and Tg drops about 3 °C. A Tg quoted without a heating rate is incomplete; DSC values are almost always reported at 10 or 20 °C/min.

What sets Tg: chain stiffness, side groups, and forces

Tg is fundamentally about how easily the backbone can rotate. Anything that hinders bond rotation raises Tg; anything that lubricates it lowers Tg.

• Backbone flexibility. A flexible —Si—O—Si— backbone (silicone) rotates freely, giving the lowest Tg of any common polymer (≈ −125 °C). A stiff backbone studded with aromatic rings (polycarbonate, polyimide) resists rotation and pushes Tg up to 150 °C or beyond.
• Side groups. A bulky pendant group raises Tg by getting in the way of rotation. Polyethylene (no side group) has Tg ≈ −110 °C; swap one hydrogen for a phenyl ring to make polystyrene and Tg jumps to ≈ 100 °C.
• Intermolecular forces. Strong attractions between chains make them harder to pull apart. The amide hydrogen bonds in nylon-6,6 lift its Tg to ≈ 50 °C and give it a high Tm of 265 °C.
• Crosslinking. Chemical crosslinks tie chains together; a densely crosslinked thermoset (cured epoxy, vulcanized hard rubber) can have a Tg above 200 °C and no melting point at all because it cannot flow.
• Molecular weight. Chain ends carry extra free volume. Short chains have many ends and a depressed Tg. The Fox–Flory relation captures it: Tg = Tg^∞ − K/M_n, where Tg^∞ is the high-molecular-weight limit and K is a polymer-specific constant. Above ~20,000 g/mol the dependence flattens out.

Glass transition temperatures of common polymers

Polymer	Tg (°C)	Tm (°C)	State at 25 °C
Polydimethylsiloxane (silicone)	−125	−40	Rubbery liquid
Polyethylene (LDPE)	−110	110	Semicrystalline, tough
Polyisoprene (natural rubber)	−70	—	Rubbery
Polypropylene	−10	165	Semicrystalline
Nylon-6,6	50	265	Tough, semicrystalline
PET (drink bottle)	76	255	Glassy / semicrystalline
Rigid PVC	80	—	Hard glass
Polystyrene	100	—	Brittle glass
PMMA (acrylic / "Plexiglas")	105	—	Hard glass
Polycarbonate	147	—	Tough glass

Notice the pattern: every polymer that feels hard and rigid at room temperature (PS, PMMA, PVC, PC) has a Tg above 25 °C; every polymer that feels soft and elastic (silicone, natural rubber, polyethylene's amorphous regions) has a Tg below 25 °C. Room temperature literally sits in the gap between these two families — which is no coincidence, since materials are usually engineered to be on the right side of Tg for their job.

Plasticizers, copolymers, and the Fox equation

You can move a polymer's Tg on purpose by blending in a second component. The Fox equation predicts the Tg of a miscible blend or random copolymer from the weight fractions w and the component Tg values (in kelvin):

  1/Tg = w₁/Tg,₁ + w₂/Tg,₂

The most important application is plasticization. A plasticizer is a small, low-Tg molecule — typically a phthalate ester such as DEHP (di-2-ethylhexyl phthalate) or a citrate ester — that slips between the chains, forces them apart, and donates free volume. The chains unlock at a lower temperature, so Tg drops.

Worked example. Rigid PVC has Tg ≈ 80 °C (353 K). DEHP has an effective Tg ≈ −85 °C (188 K). Blend 65 % PVC with 35 % plasticizer by weight:

1/Tg = 0.65/353 + 0.35/188
     = 0.001841 + 0.001862
     = 0.003703 K⁻¹
  Tg = 270 K = −3 °C

That single calculation explains an entire industry: pure PVC is a rigid pipe and window-frame plastic, but a third of its weight in plasticizer drags Tg below room temperature and turns it into flexible tubing, cling film, vinyl flooring, and the soft coating on electrical cable. Water is the universal plasticizer of biological and food polymers — a dry cracker (high Tg, crisp glass) goes soggy and leathery once humidity pushes its Tg below room temperature.

Where the glass transition decides everyday outcomes

• Chewing gum and chocolate. Gum base is engineered with a Tg just below mouth temperature: rigid in the wrapper, rubbery once warmed by your mouth. Chocolate's fat phase and the staling of bread are both Tg-driven texture changes.
• The O-ring that doomed Challenger. The 1986 Space Shuttle Challenger disaster traced to a fluoroelastomer (Viton) O-ring. On the near-freezing launch morning the cold seal stiffened toward its glass transition, lost its resilience, and recovered too slowly to reseal the booster joint in time. The glass transition was, quite literally, a matter of life and death.
• Pharmaceutical amorphous drugs. Many drugs are stored as amorphous glasses because they dissolve faster than their crystals. Formulators must keep storage temperature well below the drug's Tg, or the glass relaxes, crystallizes, and the dose loses potency.
• 3D printing. Filament printers (FDM) heat plastic above Tg so it flows and fuses, then let it freeze below Tg to hold the shape. PLA prints around 200 °C precisely because its Tg (≈ 60 °C) is conveniently low.
• Food freezing. The "glass transition of the freeze-concentrated matrix," Tg′, sets the safe storage temperature of frozen foods; storing ice cream below its Tg′ stops the sugar matrix from flowing and growing gritty ice crystals.

Common misconceptions and pitfalls

• "Tg is melting." No. Melting destroys crystalline order at a sharp, fixed temperature with a latent heat. Tg is a gradual, rate-dependent freezing of motion in disordered regions, with no latent heat — only a step in heat capacity.
• "Tg is a fixed material constant." It is not. Because the transition is kinetic, the same polymer gives a Tg that shifts with heating rate, sample history (aging), and measurement method. Always report the technique and rate.
• "Glass transition only happens in plastics." Window glass, hard candy, amber, and even cryogenically vitrified cells all have a glass transition. Any liquid cooled fast enough to skip crystallization becomes a glass with its own Tg.
• "Above Tg the polymer is a liquid that flows away." For a high-molecular-weight or crosslinked polymer, above Tg you get a rubbery plateau, not free flow. Chain entanglements (or crosslinks) hold the shape; true viscous flow needs an even higher temperature (or, for thermosets, never comes).
• "Physical aging doesn't matter." A glass stored below Tg slowly densifies as the trapped excess free volume leaks out (enthalpy relaxation). Over months a polycarbonate part becomes denser and more brittle — a real failure mode that depends on how far below Tg it sits.