Temperature-modulated DSC using higher harmonics of the Fourier transform

Abstract

In this paper, experiments with temperature-modulated calorimetry are described in which use is made of multiple modulation frequencies for the evaluation of the heat capacity. The different harmonics of the Fourier series of the heat-flow rate and heating rate of a single sawtooth-modulation experiment were deconvoluted to extract data pertaining to different frequencies. In the normally employed temperature-modulated differential scanning calorimetry (TMDSC), one uses only the first harmonic of the Fourier series. In such a typical TMDSC experiment with a period of less than about 150 s, one needs to correct the measurements by extrapolation to zero frequency, utilizing data taken at different frequencies. It is shown that the extrapolation of the heat capacity from the amplitudes of the first and higher harmonics of the Fourier-transforms of heat-flow rate and heating rate permits the evaluation of the correct heat capacity from a single experiment. The number of harmonics which can be used for the correction depends on the chosen period of the sawtooth. In case of the power-compensation calorimeter employed in this study, the upper limit of frequency of the highest harmonic is about 2 π/10 rad s −1 (0.1 Hz), i.e., for modulation with a period of 120 s, up to the eleventh harmonic can be utilized, although the amplitude (and precision) decreases for the higher harmonics.