Glass Transition Temperature (Tg) Calculator

Enter the weight fractions and select materials to calculate the Tg blend, target ratio, or comparison with Gordon-Taylor.

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Common Polymer Tg Reference Values

Values are DSC midpoint at 10°C/min heating rate. DMA tan-delta peak (1 Hz) typically reads 15-25°C higher for the same material. Ranges reflect molecular weight and tacticity variation.

Blend Tg Models

Three empirical models predict blend Tg for miscible systems. All require temperatures in Kelvin for calculation.

Fox Equation (most widely used):

\frac{1}{T_g}=\frac{w_A}{T_{gA}}+\frac{w_B}{T_{gB}}

Gordon-Taylor Equation (accounts for volume change on mixing via the k parameter):

T_g=\frac{w_A\,T_{gA}+k\,w_B\,T_{gB}}{w_A+k\,w_B}

Linear Mixing Rule: Tg = wA x TgA + wB x TgB (in Kelvin). Equivalent to Gordon-Taylor with k = 1.

Variables:

• Tg: glass transition temperature of the blend (K)
• wA, wB: weight fractions of components A and B (wA + wB = 1)
• TgA, TgB: glass transition temperatures of pure components (K)
• k: Gordon-Taylor interaction parameter (k = DeltaAlphaA / DeltaAlphaB, ratio of thermal expansion coefficient jumps at Tg)

If a blend is immiscible, two separate Tg values appear near each component's Tg rather than a single blended value.

Gordon-Taylor k Parameter Reference

When Deltaα values are unavailable, fitted k values from literature can be used. When k is unknown and no data exists, k = 1.0 (linear mixing) is the default assumption.

What is Glass Transition Temperature?

The glass transition temperature is not a sharp thermodynamic phase transition. It is a kinetically controlled event: Tg shifts with measurement rate (approximately 3-5°C per decade change in DSC heating rate), meaning the same material can yield different Tg values depending on test method and thermal history.

Below Tg, backbone chain segments lack sufficient thermal energy to overcome rotational energy barriers, locking the material into a rigid, glassy state with high modulus and low creep. Above Tg, cooperative segmental motion activates, modulus drops by 3-4 orders of magnitude, and the material enters a viscoelastic (rubbery) state. This transition governs the practical upper use temperature of amorphous and semi-crystalline engineering plastics.

A useful structural heuristic: Tg/Tm (both in Kelvin) falls between 0.5 and 0.67 for most synthetic polymers. Symmetric backbone repeat units trend toward 0.5; asymmetric or rigid-chain architectures trend toward 0.67. This two-thirds approximation holds broadly across hundreds of polymers and can serve as a rough sanity check when a Tg is reported without a Tm reference.

Factors That Shift Tg

Tg Measurement Methods

A Tg value without a stated method and heating rate carries 20-30°C of inherent ambiguity. ASTM E1356 covers DSC Tg measurement; ISO 11357-2 applies to plastics specifically.

Example Calculation

Blend: 60 wt% Polymer A (TgA = 100°C = 373.15 K) and 40 wt% Polymer B (TgB = 50°C = 323.15 K).

Fox equation: 1/Tg = 0.60/373.15 + 0.40/323.15 = 0.001608 + 0.001238 = 0.002846 K-1, so Tg = 351.4 K = 78.3°C.

Gordon-Taylor (k = 0.5): Tg = (0.60 x 373.15 + 0.5 x 0.40 x 323.15) / (0.60 + 0.5 x 0.40) = (223.89 + 64.63) / 0.80 = 360.6 K = 87.5°C.

Linear mix (k = 1): Tg = 0.60 x 373.15 + 0.40 x 323.15 = 353.2 K = 80.0°C.

For a truly miscible blend, all three models should agree within 5-10°C. Large discrepancies signal partial immiscibility or an inappropriate k value, not a calculation error.