Title: Williams–Landel–Ferry equation
Long Title: IUPAC Gold Book - Williams–Landel–Ferry equation
DOI: 10.1351/goldbook.12821
Status: current

Definition
Equation describing the temperature dependence of the shift factor, \(a_{T}\), for time–temperature superposition \[\log_{10}a_{\rm{T}} = \frac{-C_{1}(T_{1} - T_{0})}{C_{2} + (T_{1} - T_{0})}\] \(C_{1}\) and \(C_{2}\) are empirical constants, \(T\) is the temperature of measurement, and \(T_{0}\) is the reference temperature.

Note
The WLF equation is usually applied with the reference temperature, \(T_{0}\), equal to the glass-transition temperature, \(T_{\rm{g}}\). The values of the constants \(C_{1}\) and \(C_{2}\) depend on the type of polymer and are valid over a limited range of temperature, from \(T_{\rm{g}}\) to about \(T_{\rm{g}}\) + \(\pu{50 K}\).

Related Terms
- shift factor: https://goldbook.iupac.org//terms/view/12801
- time–temperature superposition: https://goldbook.iupac.org//terms/view/12813

Source
- PAC, 2013, 85, 1017. 'Glossary of terms relating to thermal and thermomechanical properties of polymers (IUPAC Recommendations 2013)' on page 1044 (https://doi.org/10.1351/PAC-REC-12-03-02)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/12821/html
- json: https://goldbook.iupac.org/terms/view/12821/json
- xml: https://goldbook.iupac.org/terms/view/12821/xml

Citation: Citation: 'Williams–Landel–Ferry equation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.12821
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Accessed: 2026-06-06T02:05:37+00:00