# Extending Cooling Rate Performance of Fast Scanning Chip Calorimetry by Liquid Droplet Cooling
## 1 Introduction  
The option of fast cooling is important for the analysis of crystallization and vitrification of materials, as it allows for designing specific solidification pathways, including crystallization at high melt-supercooling or full suppression of crystallization [1]. In the case of metal alloys, the critical cooling rate, avoiding the precipitation of alloying elements on cooling, is of particular importance for optimizing the age hardening processes, needed for understanding precipitation kinetics (commonly from 0.5 to 1000 K/s) [2, 3]. Industrially important polymers exhibit critical cooling rates for avoiding crystallization on cooling covering a wide range: 0.5 K/s for poly(L-lactic acid) [4], 800 K/s for isotactic polypropylene [5] and more than \(10^{6}\) K/s for linear polyethylene [6]. Generally, there are two ways to reach high cooling rates for fast scanning chip calorimetry (FSC). The first option is reducing the mass of the sample and of the lateral dimensions of the measuring cell, as proposed by [PERSON] et al. [6, 7]. In the case of fast scanning chip calorimetry (FSC), the cooling of nanogram-size samples is possible with rates up to \(10^{7}\) K/s [8]. However, decreasing the sample mass typically results in a reduced signal-to-noise (S/N) ratio. Rapid cooling of larger samples is possible with a cooling medium with a higher thermal effusivity, e.g., using a liquid or solid as a heat sink instead of a gas. Nevertheless, as already discussed in reference [9], the maximum cooling rate cannot be increased by such an approach because, during heating, too much energy is stored in the cooling medium. Suppose the cooling medium is in thermal contact to the sample only during cooling, e.g., by immersing the hot part into a liquid quenching bath, gun technique of splat-quenching [10], melt-spinning techniques [11], sliding the sample from a hot to a cold place [12], or moving it into a region with a water spray [13]. Then, the limitation of too much stored energy in the device is not valid anymore. Such approaches are used in numerous homemade experimental setups for polymer-quenching experiments [14; 15; 16; 17; 18] or for producing amorphous metals [19]. So far, we are not aware of attempts to combine liquid quenching and FSC. However, this method would allow us to quench larger samples at higher cooling rates and measure them on heating at the device's optimum heating rate. In this work, we introduce such a combination and demonstrate its advantages and limitations. It is accepted and common practice to minimize the sample size in FSC experiments to reach high cooling rates, because fast cooling requires fast removal of the heat stored in the sample-calorimeter system. The maximum possible cooling rate in FSC is limited by the heat exchange between the sample and the surroundings and the sample size/heat capacity. As the measured heat flow is proportional to the apparent heat capacity multiplied by the temperature scanning rate, larger samples exhibit an increased S/N ratio, being important when scanning at lower rates. On the other side, smaller samples can be cooled fast without significant thermal lag. Though the dynamic range of FSC is already much larger than that of the conventional DSC, sensors of different sizes are presently used (Figure 1). Reduction in the sensor membrane thickness, of the lateral size of the heated spot and of the sample mass allows for increasing the cooling rate up to a few ten Megakelvin per second (MK/s). However, the small sample has a correspondingly low S/N ratio and a large surface-to-volume ratio. FSC commonly consists of a differential measurement scheme, where the heat losses from the sample and empty reference side are supposed to compensate each other. In the case of big samples, the different surface contributions to the heat losses are often neglected or corrected for heat capacity measurements [20; 21; 22; 23].