Calculate the glass transition temperature (Tg) of a polymer blend with the Fox or Gordon–Taylor equation, or find the composition for a target Tg.
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Common Polymer Tg Reference Values
These are illustrative typical values, not a verified set measured under one protocol. Use grade-specific measured values with a stated method, Tg criterion and thermal history for calculator inputs.
| Polymer | Tg (°C) | Tg (K) | State at 23°C |
|---|---|---|---|
| PDMS (silicone rubber) | -127 | 146 | Rubbery |
| HDPE | -120 to -80 | 153-193 | Semicrystalline |
| LDPE | -110 | 163 | Semicrystalline |
| Polybutadiene (PBd) | -90 | 183 | Rubbery |
| Polyisoprene (NR) | -60 | 213 | Rubbery |
| Polypropylene (iPP) | -10 | 263 | Semicrystalline |
| Nylon 6 | 50 | 323 | Semicrystalline |
| Nylon 6,6 | 50-57 | 323-330 | Semicrystalline |
| PLA (amorphous) | 55-60 | 328-333 | Glassy |
| PET | 75-80 | 348-353 | Semicrystalline |
| PVC (rigid) | 80-87 | 353-360 | Glassy |
| Polystyrene (PS) | 95-105 | 368-378 | Glassy |
| PMMA (atactic) | 100-120 | 373-393 | Glassy |
| PEEK | 143 | 416 | Semicrystalline |
| Polycarbonate (PC) | 145-150 | 418-423 | Glassy |
| Polyimide (PI) | 360-410 | 633-683 | Glassy |
Blend Tg Models
These empirical mixing rules estimate Tg for a compatible amorphous phase. The calculator converts inputs to kelvin and provides Fox, inverse Fox composition and Gordon–Taylor modes; the linear rule is a reference comparison.
Fox Equation (most widely used):
Gordon-Taylor Equation (uses a material-specific k parameter):
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: for this component order, the volume-additivity expression is (density A / density B) × (DeltaAlphaB / DeltaAlphaA), where DeltaAlpha is the expansion-coefficient jump at Tg. A fitted k must match the material pair and component order. See NIST journal equations 1–2.
Phase-separated blends can exhibit separate transitions. Mixing-rule outputs alone do not establish miscibility; use experimental evidence.
Gordon-Taylor k Parameter Reference
Use a fitted or appropriately derived k for the same material pair, component order and test conditions. Swapping components requires replacing k by 1/k. k = 1 is an arithmetic reference assumption, with no guaranteed conservative direction.
| Available evidence | How to choose k |
|---|---|
| Measured blend data | Fit and validate for the stated materials and conditions |
| Literature value | Check material grade, component order and definition |
| No validated k | Do not assume a conservative value; k = 1 is only a linear reference |
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 (with material-dependent rate sensitivity), 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 can fall substantially and the amorphous phase becomes more mobile. Tg alone does not establish a safe service temperature or load-bearing performance.
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
| Factor | Effect on Tg | Quantitative Example |
|---|---|---|
| Molecular weight | Increases asymptotically (Flory-Fox: Tg = Tg,inf – K/Mn) | PS: Tg rises ~40°C from Mn 1,000 to 100,000 g/mol |
| Plasticizer content | Lowers Tg | 10 wt% water in Nylon 6,6 depresses Tg by 15-20°C |
| Crosslink density | Raises Tg | Epoxy Tg increases with amine hardener stoichiometry |
| Backbone stiffness | Stiffer backbone raises Tg | Tg order: polyimide (~400°C) > PC (147°C) > PS (100°C) |
| Side chain length | Longer flexible side chains lower Tg (internal plasticization) | Poly(n-hexyl methacrylate): -5°C vs. PMMA: 105°C |
| Tacticity | Can shift Tg 30-60°C | Syndiotactic PMMA: 115-130°C vs. isotactic PMMA: 45°C |
| Hydrostatic pressure | Raises Tg (~0.02°C/bar) | PS at 500 bar: Tg rises ~10°C above atmospheric value |
| Film thickness (<50 nm) | Free surface lowers Tg; attractive substrate can raise it | PS free-standing films <30 nm: Tg suppressed up to 30°C below bulk |
Tg Measurement Methods
| Method | Tg Definition | vs. DSC Midpoint | Best For |
|---|---|---|---|
| DSC (differential scanning calorimetry) | Midpoint of heat capacity step | Reference baseline | General screening, small samples, blends |
| DMA (tan delta peak, 1 Hz) | Peak of loss factor | Method- and frequency-dependent | Structure-property relationships, composites |
| DMA (E’ onset) | Storage modulus drop onset | Criterion-dependent | Engineering use-temperature estimation |
| TMA (thermomechanical analysis) | Slope change in linear thermal expansion | Material- and protocol-dependent | Coatings, adhesives, thin films |
| Dilatometry | Change in specific volume slope | Material- and protocol-dependent | Fundamental research, pressure dependence studies |
Report the measurement method, Tg criterion, heating rate or DMA frequency and thermal history; there is no universal numerical offset between methods. TA Instruments compares these measurement responses. 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 = 360.65 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.
The model spread depends on the inputs and chosen k. Even miscible blends can deviate from these mixing rules; neither agreement nor disagreement is a stand-alone miscibility test. Validate an estimate against measurements for the intended material.
