Journal of Thermal Analysis and Calorimetry

, Volume 113, Issue 2, pp 453–460 | Cite as

New method for estimating shift factors in time–temperature superposition models

  • Salvador NayaEmail author
  • Antonio Meneses
  • Javier Tarrío-Saavedra
  • Ramón Artiaga
  • Jorge López-Beceiro
  • Carlos Gracia-Fernández


Prediction of polymer properties at short and long observation times is usually performed through time–temperature superposition (TTS) models, which make use of some calculated shift factors. Although TTS principle has been used for many decades, no firm rules have been developed for obtaining the master curves. In the absence of reliable long-term data, it has been a common practice to try to minimize the discrepancy between the individual shifted curves. It was reported that a TTS method is more reliable as that discrepancy is minimized. In this study, a new method for obtaining the shift factors is presented. The optimal shift factors were estimated by minimizing the distance between the single curve derivatives with respect to the derivative of the curve at the reference temperature. That shift factors were tested with some classical models. The data were analyzed by statistical methods, making use of bootstrap resampling and spline estimation. The shift factors obtained from the proposed method allow for obtaining smooth master curves. The accuracy of the estimations was evaluated.


Time–temperature superposition Shift factor WLF equation Arrhenius relation Numerical derivation DMA 



This research was partially supported by the Spanish Ministry of Science and Innovation, Grant MTM2011-22392 (ERDF included).


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  • Salvador Naya
    • 1
    Email author
  • Antonio Meneses
    • 2
  • Javier Tarrío-Saavedra
    • 1
  • Ramón Artiaga
    • 3
  • Jorge López-Beceiro
    • 3
  • Carlos Gracia-Fernández
    • 4
  1. 1.Departamento de Matemáticas, Escuela Politécnica SuperiorUniversidade da CoruñaFerrolSpain
  2. 2.Universidad Nacional de ChimborazoRiobambaEcuador
  3. 3.Departamento de Ingeniería Industrial II, Escuela Politécnica SuperiorUniversidade da CoruñaFerrolSpain
  4. 4.TA InstrumentsMadridSpain

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