12821 IUPAC Gold Book - Williams–Landel–Ferry equation 10.1351/goldbook.12821 12821 current synonym: WLF Equation 1 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. 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 \(T_{\rm{g}}\) + \(\pu{50 K}\). shift factor https://goldbook.iupac.org//terms/view/12801 time–temperature superposition https://goldbook.iupac.org//terms/view/12813 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) https://goldbook.iupac.org/terms/view/12821/html https://goldbook.iupac.org/terms/view/12821/json https://goldbook.iupac.org/terms/view/12821/plain 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 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-06-06T02:05:38+00:00