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 $${FPEX}_{0}$$ 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.

Sub-nL thin-film differential scanning calorimetry chip for rapid thermal analysis of liquid samples

“…Because of the low thermal inertia of the twin arms, the tfDSC chip can accommodate scan speeds up to 100 °C min −1 before the smearing becomes intolerable. For the results obtained at rates in excess of 100 °C min −1 , de-smearing procedures 23 can be applied to minimize the thermal lag influence. The fast scan capability of the tfDSC chip enhances the sensitivity while shortening the analysis time compared to commercial instruments.…”

Material Search for a Li10GeP2S12-Type Solid Electrolyte in the Li–P–S–X (X = Br, I) System via Clarification of the Composition–Structure–Property Relationships

“…The abovementioned phase-formation temperatures are consistent with the synthetic result for LPSBr (#8 in Figure ) but not with that for LPSI, which could be synthesized at 473 K (#18 in Figure ). The inconsistence of LPSI was considered due to the difference in measurements or synthesis conditions, such as heating rate. − Based on results of both synthesis and DTA combined with HT-XRD, we concluded that LPSBr and LPSI are synthesized with relatively high purity over the temperature range of 473–493 K. Within this temperature range, the synthetic temperatures were re-examined to obtain highly crystalline samples. The tetragonal phases of LPSBr and LPSI synthesized at 483 and 478 K, respectively, were selected for crystal structure analysis; Figure shows the synchrotron XRD patterns collected at 298 K. As this study aimed to identify a structural analogue of LGPS in the Li–P–S– X system, the XRD patterns of the two synthesized phases are compared with that of an original LGPS sample with tetragonal symmetry ( P 4 2 / nmc , no.…”

Effect of Mass and Temperature Rate on the Thermal Properties of High-Density Polyethylene Using Differential Scanning Calorimetry

“…The curve is then analyzed to determine the crystallinity of the polymers. If the polymer is completely amorphous, the crystallinity will be zero, but less than unity for semi-crystalline polymers [13]. A sample of various masses was tested at a constant heating rate, and the effect on the thermal characteristics of HDPE was investigated.…”

“…The temperature difference is plotted on a heating curve as a function of temperature. The analysis of the heating curve to calculate the peak, on-set, and end-set temperatures, phase transition (melting and crystallization) temperatures, and enthalpies [13].…”