Application of Kramers–Kronig relations to time–temperature superposition for viscoelastic materials

• Shifting procedure when applying the time–temperature superposition principle.
• Shift coefficients optimised to fullfil the best the Kramers–Kronig relations.
• Critical study of the optimized shift coefficients.

Dynamical mechanical analysis (DMA) is an experimental technique commonly used to study the frequency and temperature dependence of the mechanical properties of viscoelastic materials. The measured data are traditionally shifted by application of the time–temperature superposition principle to obtain the master curves of the viscoelastic material. The goal of this work is to present a methodology to determine the horizontal and vertical shift coefficients to be applied to the isotherms of storage and loss moduli measured. The originality lies in the calculation of the shift coefficients by a method requiring fulfilment of the Kramers–Kronig relations conveying the causality condition. The computed vertical shift coefficients are compared to the coefficients predicted by the Bueche–Rouse theory.