Data-driven de-smearing of DSC signals

Abstract

In heat flux differential scanning calorimetry, a pair of identical crucibles, one empty as reference and the other filled with the sample, is heated in a furnace with a prescribed rate. The (empty) reference crucible heats faster, resulting in a temperature difference that is detected by thermocouples. Slow heating of the furnace results in weak and noisy signals; higher heating rates induce strong signals but lead to smearing if applied to materials undergoing a phase transition: The recorded peak signal is shifted toward higher temperatures. To determine the peak, the onset/endset temperatures, and the phase transition enthalpy, multiple heating rates are used to find a trade-off between noise and smearing. When plotting the melting peaks over temperature and heating rate, the visual similarity to the time evolution of a probability density under drift and diffusion catches the eye. Such a density evolution can be described by the Fokker–Planck equations. In this analogon, the de-smeared signal corresponds to the initial distribution. We propose a data-driven de-smearing approach, based on an extrapolation to a (hypothetical) zero heating rate signal. This zero rate signal is low-dimensionally parameterized and its parameters together with the drift and diffusion of the Fokker–Planck equation are fitted against the calorimetric measurements. The method is successfully tested on heat capacity data of a technical-grade high-density polyethylene (HDPE) using mid-range heating rates. The data are strongly affected by smearing, and the proposed de-smearing method {FPEX}_{0} delivers reliable estimates of characteristic shape parameters of the phase transition peak effectively overcoming the problem of a deteriorating signal-to-noise ratio for heating rates approaching zero.