Temperature-modulated differential scanning calorimetry through heat diffusion analysis

In the present study, a complete model of thermal diffusion in a TMDSC spec imen is presented. The governing equation takes into account thermal conduc tivity and does not neglect temperature gradients. This model is solved ana lytically for a specimen of cylindrical geometry with two surfaces followin g the block temperature and considering the third surface insulated. The fu ll 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 upo n the sample material, which has not been predicted by existing models. Mor eover, the present model does not require the use of an experimentally dete rmined constant as long as the cell is ideal. It was found that the phase l ag between sample and block temperatures could be described by two effectiv e thermal diffusivities, Lambda' and Lambda ", instead of complex heat capa cities c(p)' and c(p)". These heat capacity parameters were viewed as mathe matical artifacts arising from the use of an over-simplified governing equa tion that does not rake into account thermal conductivity and thermal gradi ents within the specimen.