Effect of Cross-Linking Density on Horizontal and Vertical Shift Factors in Linear Viscoelastic Functions of Epoxy Resins

Abstract

Epoxy resins are an important class of thermosetting resins, and their network structure, obtained by the curing reaction of epoxy and amine compounds, plays an important role in the material properties. We here revisited a time–temperature superposition (TTS) principle applied to the dynamic viscoelastic functions of epoxy resins, in which the network was well defined and systematically varied on the basis of the length of n-alkyl diamine. The superimposition of isothermal curves in the frequency domain required not only a horizontal shift but also a vertical shift, regardless of the length of n-alkyl diamine. The temperature dependence of the horizontal shift factor, aT, could be well expressed by the Williams–Landel–Ferry equation. The fitting parameter, called C2, increased with decreasing alkyl chain length of the diamine, meaning that the thermal expansion of the free volume was suppressed due to greater cross-linking density. This was qualitatively confirmed by a full-atomistic molecular dynamics (MD) simulation. Meanwhile, the vertical shift factor, bT, increased with increasing temperature, and the extent was smaller with increasing cross-linking density. This can be explained in terms of the entropic contribution to the modulus in the temperature region above the glass transition temperature. The entropy change estimated using the isobaric molar heat capacity from the MD simulation strongly supported this hypothesis. The knowledge here obtained should be useful for a better design of thermosetting polymers as well as for the prediction of long-term durability.