Relaxation phenomenon measured as dynamic specific heat in the first-order phase transition of a molecular crystal

Abstract

We found that the specific heat becomes a frequency-dependent complex quantity at and around the two first-order phase transition points of n-hexatriacontane $(n\ensuremath{-}{\mathrm{C}}_{36}{\mathrm{H}}_{74}).$ One is the rotator phase transition point, and the other is the melting point. The dynamic specific heat was measured by using temperature-modulated calorimetry in the low-frequency range of $0.0003l~f/\mathrm{Hz}l~0.05.$ The frequency range is sufficient to discuss the dispersion of the dynamic specific heat. The dynamic specific heat can be described by the Debye relaxation. The relaxation parameters show different trends in the lower-half temperature region and a higher half-temperature region in each phase transition. We label the former by ${I}_{R}$ and ${I}_{M},$ and the latter as ${\mathrm{II}}_{R}$ and ${\mathrm{II}}_{M}$ ${(I}_{R}$ and ${\mathrm{II}}_{R}$ are in the rotator phase transition, and ${I}_{M}$ and ${\mathrm{II}}_{M}$ are in the melting). The values of the relaxation time are about 600 s in ${I}_{R}$ and ${I}_{M}.$ The values reduce to about 40 s in ${\mathrm{II}}_{R}$ and about 120 s in ${\mathrm{II}}_{M}.$ The relaxation strengths in ${I}_{R}$ and ${I}_{M}$ are smaller than those in ${\mathrm{II}}_{R}$ and ${\mathrm{II}}_{M}.$ We found that the thermal conductivity is a real and frequency-independent quantity in the entire temperature region including the phase transition points. The relaxation time of the dynamic specific heat measured in the end of ${\mathrm{II}}_{R}$ agrees with the characteristic time measured by using a polarizing microscope. This agreement reveals that the origin of the obtained dynamic specific heat in the temperature region is the weight fractional fluctuation of the rotator phase.