Glass Transition Simulator: Polymer Tg and Modulus vs Temperature

simulator intermediate ~10 min
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Tg ≈ 373 K (100°C) — typical of polystyrene

At Mₙ=100 kDa with no plasticizer, the glass transition occurs near 373 K. Below this temperature the modulus jumps by three orders of magnitude from ~1 MPa (rubbery) to ~3 GPa (glassy).

Formula

Tg(Mₙ) = Tg∞ - K / Mₙ  (Fox–Flory)
log(aT) = -C₁·(T - Tg) / (C₂ + T - Tg)  (WLF)
fᵥ = fg + αf·(T - Tg)  (free volume)

The Glass Transition Phenomenon

Cool a polymer melt slowly and at some temperature it abruptly stiffens — not by crystallizing, but by falling out of equilibrium. The glass transition is the temperature where cooperative segmental motion of 10–50 backbone atoms freezes out on the experimental timescale. The modulus jumps by roughly three orders of magnitude, transforming a pliable rubber into a rigid glass. Every amorphous polymer has a Tg, and it is arguably the single most important property for material selection.

Free Volume Theory

Above Tg, chain segments can rearrange because sufficient free volume — the unoccupied space between packed chains — allows cooperative motion. As temperature decreases, free volume shrinks linearly until it reaches a critical fraction fg ≈ 2.5% at Tg. Below Tg, the structure is essentially frozen: free volume can no longer redistribute fast enough to accommodate molecular rearrangement, and the material becomes a non-equilibrium glass.

Molecular Weight and Plasticizer Effects

Chain ends have more free volume than mid-chain segments, so shorter chains have lower Tg following the Fox-Flory relation Tg = Tg∞ - K/Mₙ. Plasticizers work similarly: small molecules inserted between chains increase free volume and chain mobility, depressing Tg proportionally to their loading. The simulation lets you blend in plasticizer and observe the transition temperature shift in real time.

Engineering Significance

Tg determines a polymer's service temperature range. Polystyrene (Tg ≈ 100°C) is rigid at room temperature; polyisoprene (Tg ≈ -70°C) is rubbery. Tire rubber must remain far above Tg for grip, while aircraft canopies need Tg well above operating temperature for structural integrity. Predicting and controlling Tg through copolymerization, crosslinking, and additive blending is central to polymer product design.

FAQ

What is the glass transition temperature?

The glass transition temperature (Tg) is the temperature range where an amorphous polymer transitions from a hard, glassy state to a soft, rubbery state. Unlike melting, it is not a true phase transition but a kinetic phenomenon — the temperature where molecular relaxation times exceed the observation timescale.

How do plasticizers lower Tg?

Plasticizers are small molecules that intercalate between polymer chains, increasing free volume and chain mobility. Each weight-percent of plasticizer typically lowers Tg by 1–3 K. Common plasticizers include phthalates (DOP) for PVC and water for biopolymers like gelatin.

Why does cooling rate affect Tg?

Faster cooling gives chains less time to rearrange into equilibrium configurations, freezing in more excess free volume at a higher apparent Tg. A tenfold increase in cooling rate typically raises the measured Tg by 3–5 K. This is why Tg is a kinetic, not thermodynamic, property.

What is the WLF equation?

The Williams-Landel-Ferry equation log(aT) = -C₁(T-Tg)/(C₂+T-Tg) describes the dramatic temperature dependence of relaxation times near Tg. With universal constants C₁≈17.4 and C₂≈51.6 K, it predicts a 10-decade change in viscosity over a 50 K range around Tg.

Sources

Embed

<iframe src="https://homo-deus.com/lab/polymer-science/glass-transition/embed" width="100%" height="400" frameborder="0"></iframe>
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