Temperature-Modulated Differential Scanning Calorimetry through Heat Diffusion Analysis

Abstract

In the present study, a complete model of thermal diffusion in a TMDSC specimen is presented. The governing equation takes into account thermal conductivity and does not neglect temperature gradients. This model is solved analytically for a specimen of cylindrical geometry with two surfaces following the block temperature and considering the third surface insulated. The full analytical solution consists of a transient and an asymptotic expression. The asymptotic expression is divided into an underlying and a cyclic part to allow comparison with existing models. The present model finds that the phase angle between the temperatures of sample and block are dependent upon the sample material, which has not been predicted by existing models. Moreover, the present model does not require the use of an experimentally determined constant as long as the cell is ideal. It was found that the phase lag between sample and block temperatures could be described by two effective thermal diffusivities, Λ′ and Λ″, instead of complex heat capacities $c'_p {\text{ and }}c''_{\text{p}}$ and $c'_p {\text{ and }}c''_{\text{p}}$. These heat capacity parameters were viewed as mathematical artifacts arising from the use of an over-simplified governing equation that does not take into account thermal conductivity and thermal gradients within the specimen.