What is the Fox equation?

The Fox equation states that 1/Tg(blend) = sum(wi / Tgi) for each component i, where wi is the weight fraction and Tgi is the glass transition temperature in Kelvin. It assumes ideal mixing and is accurate for miscible, weakly interacting blends.

When should I use the Gordon-Taylor equation instead?

Use Gordon-Taylor when the blend is non-ideal — for example, when there are strong specific interactions (hydrogen bonds, dipole-dipole) between components. The k parameter captures the deviation from ideal behavior; k=1 reduces to a linear mass-weighted average, while k values deviating from 1 reflect free-volume asymmetry between components.

What value should I use for the Gordon-Taylor k parameter?

k is typically determined by fitting DSC data. As a starting point, k ≈ Δα2/Δα1, the ratio of the thermal expansion coefficient changes at Tg for each component. Values between 0.3 and 3 cover most practical polymer pairs. If unsure, use k = 1 as a neutral estimate.

Does the tool handle more than two components?

Yes — you can add up to five components. For the multi-component Fox equation, the formula extends naturally: 1/Tg = Σ(wi/Tgi). The Gordon-Taylor equation is formally a binary equation; for blends with 3+ components this tool applies it iteratively using a binary-equivalent approach, which is a common approximation.

Should I enter Tg in Celsius or Kelvin?

The tool accepts either unit — select your preference from the unit toggle. Internally all calculations are performed in Kelvin (as required by the Fox equation), and the result is converted back to your chosen unit for display.

Why must weight fractions sum to 1?

The Fox and Gordon-Taylor equations are mass-fraction weighted averages. If fractions do not sum to 1 the blend composition is undefined. The tool automatically normalizes fractions if they are close to 1 within a small tolerance, and shows an error otherwise.

Glass Transition Temperature Helper

Calculate the glass transition temperature (Tg) of a polymer blend using the Fox equation or Gordon-Taylor mixing rule.

Blend Components

Tg unit:

Mixing Rule

Result

Enter component data and click Calculate Tg.

Formula Reference

Fox Equation

1 / Tg = ∑( w_i / Tg_i )

where w_i = weight fraction, Tg_i in Kelvin.

Summary

The glass transition temperature (Tg) is the temperature at which an amorphous polymer transitions from a rigid, glassy state to a soft, rubbery one. For polymer blends, Tg is not simply the average of each component's Tg — it depends on composition and component interaction. This tool applies the Fox equation (ideal mixing) and the Gordon-Taylor equation (with a fitting parameter k) to give you a quick, reliable estimate for binary or multi-component blends.

How it works

Enter the Tg (in Celsius or Kelvin) and weight fraction for each polymer component.
Select the mixing rule: Fox equation for ideal blends, or Gordon-Taylor for non-ideal blends.
For the Gordon-Taylor rule, set the k parameter (ratio of free-volume increments; often 0.5–2).
Click "Calculate" — the blended Tg is displayed instantly with a component breakdown chart.
Add up to five components using the "Add Component" button.
Switch between Celsius and Kelvin display at any time.

Use cases

Screen polymer blend formulations before running DSC experiments.
Predict Tg shifts when adding a plasticizer or copolymer component.
Validate experimental DSC results against theoretical Fox-equation values.
Teach polymer thermodynamics concepts interactively in a classroom.
Quickly assess miscibility of two polymers via Tg deviation.
Compare ideal (Fox) vs. non-ideal (Gordon-Taylor) blend behavior.
Optimize rubber-toughened polymer formulations for target Tg.
Estimate processing window temperatures for multi-component blends.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu