Applicability condition of time-temperature superposition principle (TTSP) to a multi-phase system

The applicability condition of the time-temperature superposition principle (TTSP) to a multi-phase system is analytically discussed assuming a mixture law. It was concluded that the TTSP does not hold for a multi-phase system in general but does hold for a multi-component system in which some components have the same temperature dependence and the others have no temperature dependence. On the basis of the results, the application of the TTSP to plant materials such as wood and bamboo was examined using a mixture law and a stretched-exponential function having a characteristic relaxation time tau (0) and a stretching parameter beta. Wood can be treated as a multi-phase system consisting of a framework (f) and matrix (m). In this case, it was expected that the TTSP holds for the matrix in the shorter time region ta parts per thousand(a)tau (0f) under T < T (gf) , while the TTSP holds for the framework in the longer time region ta parts per thousand < T (gm) , where t and T (g) is a measurement time and the glass transition temperature, respectively.