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The extrapolated onset-temperature (according to DIN EN ISO 11357-1:2010-03) is the designed intersection point of the extrapolated baseline and the inflectional tangent at the beginning of the melting or crystallization peak. The baseline and the inflectional tangent are determined from the temperature-dependent heat flow signal. In the case of pure and homogeneous materials, the onset-temperature can be indicated as melting temperature. In contrast to peak-temperature, the onset-temperature is less dependent on heating rate and sample mass. Furthermore onset-temperatures are usually used for temperature calibration of a DSC.

Heat flow and enthalpy diagramm. Onset temperature is marked as T onset. The dotted line represents crystallization, the continous line represents melting

(acc. to DIN EN ISO 11357-1:2010-03) The virtual baseline corresponds to the heat flow signal if the phase change enthalpy would be zero. It is usually constructed by a straight line between the peak start temperature and peak end temperature. If the heat capacity between liquid and solid phase is very different, the use of a sigmoidal baseline is recommended. Since the baseline is used, among other things, to determine the heat of fusion, the determination of heat of fusion depends on the "correct" choice of the baseline. In addition to the curve progression (linear or sigmoid), the baseline is dependent on the selected start and end temperatures. Therefore it is crucial to measure a sufficiently wide temperature range to identify the course of the heat flow signal outside the peak.

Baselines top left: sigmoidal, others: clockwise linear1-3 with different start and end temperatures. The influence on the heat of fusion is indicated by the table below.

The nucleation or crystallization temperature T_n is the temperature at which the cristal growth starts (nucleation) and is determined from the first deviation of the DSC signal from the baseline. The nucleation is a stochastic process that depends on the purity of the PCM, the sample volume, the interface to the measuring vessel and the cooling rate. Therefore, the nucleation temperature is subject to a certain degree of distribution, which is usually greater than the measurement uncertainties of a DSC instrument. Besides the nucleation or crystallization temperature as material property, on system level an isothermal equilibrium temperature depending on certain boundary conditions is also often named as crystallization temperature.

The peak temperature marks the point at which the largest deviation of the heat flow signal from the virtual baseline is measured. In the case of pure, homogeneous substances, the sample material in the DSC is completely melted at this temperature.

The amount of heat that is supplied or withdrawn from a system is expressed in isobaric processes by the enthalpy change of the system. Outside of a phase transition, the enthalpy change depends on the heat capacity and the temperature change of the system. It is also called sensitive heat. The phase change itself is indicated by the phase change enthalpy or heat of fusion. Since the change in temperature is relatively small compared to the enthalpy change, it is also called latent heat. The enthalpy change measured in the DSC during a phase change is therefore the sum of sensitive and latent heat. The enthalpy change is the integral form (over time) of the heat flow signal in the DSC. Phase change enthalpy is determined by the integral between the heat flow signal and the virtual baseline. Since the "real" shape of the baseline can only be interpreted during a continuous measurement, the phase change should occur in a narrow temperature range in order to be able to determine the phase change enthalpy as precisely as possible. Therefore, the heating rate should be chosen as low as possible. The sensitive component is determined by the absolute integral of the heat flow signal. In conventional DSC devices, the heat flow signal is calculated by the difference of the heat capacities to a reference system. Therefore, possible heat flow signals of the measuring system without sample must be subtracted from the sample measurement to determine the sensitive part. Compared to the phase change, the heat flow signal in the sensitive area is relatively low, which is why high heating rates are recommended for the determination of the sensitive enthalpy.

The zeroline is a straight line constructed from the offset of the two isotherms at the beginning and end of heating or cooling. The start and end times correspond to the start and end times of the heating or cooling cycles. The Y-value is taken from the heat flow value at the end of the respective isotherms. The zeroline is constructed over time and subtracted from the heat flow signal of the measurement. With well calibrated DSC and small temperature measuring ranges, the zero line corresponds approximately to the heat flow signal of the empty furnace. However, the linear behaviour is usually no longer given at large temperature ranges, which is why non-linear curves should be corrected by measurements with empty crucibles (blank measurements). After this correction, the zero line should be redetermined and subtracted from the measurement.

Zeroline construction is a correction to 0 heatflow if the DSC shows a heatflow signal at constant temperatures

Supercooling is the process of cooling a liquid or a gas below its freezing point without it becoming a solid. (see also Wikipedia). 

Supercooling during the liquid-solid phase change is the phenomenon when a material’s crystallization initiation occurs at a temperature below its freezing temperature. That is, the nucleation starts at a temperature below the real freezing point of the material. Thus, a material that tends to supercool should be cooled considerably below its expected freezing point to initiate freezing. Once its nucleation initiates, the material temperature rises to its real freezing point, and then continues freezing at that temperature.

If supercooling is considerable, it is disadvantageous in a PCM as it negatively affects the functionality of the TES system. That is because, then the freezing does not start at the expected freezing temperature, but only way below, with a practical requirement of a large operating temperature range. In addition, the higher the degree of supercooling, the less the energy released (as it is released as sensible heat, which is lesser than the expected latent heat release).

Many materials undergo supercooling. Supercooling is related to the material’s nucleation and solidification mechanisms. The degree of its supercooling is influenced by the sample size, homogeneity, cooling rate and sample container surface morphology (influencing the availability of nucleation sites), among other factors. A pure (i.e., unary) material which undergoes supercooling, will rise-up to its real freezing temperature and then will freeze within a narrow temperature range (ideally: at constant temperature). 

Figure 1 is an example of a pure material: n-dodecane (purity: 99%), that supercools. In Figure 1 (a), the supercooling region is enclosed by a red circle. When the temperature is -12.42 °C the nucleation starts. Right after, the temperature rises back to its real freezing point around -10.6 °C and remains rather constant around this temperature till freezing completion. The supercooling is characterized also in the enthalpy and specific heat profiles of n-dodecane, as in Figure 1 (b) and (c) respectively, indicated with the crystallization initiation and the real freezing (initial) temperatures. 

Blends could also undergo supercooling. Supercooling in blends will cause phase separation, if these are incongruent melting compositions. Only congruent melting compositions will not phase separate even with supercooling. 

Peritectic compounds (they are a type of incongruent melting compositions) will inherently supercool, as their solidification occurs through coring. Coring is a process where each solidifying block forms a core with a higher melting point surrounded by outer layers of increasingly lower melting points. To initiate this core formation, the material should be cooled below its real freezing point. As peritectics will always supercool, they will always phase separate, and therefore are unsuitable as PCMs.

If a eutectic supercools, it will also have phase separation. That is because a eutectic is not a congruent melting blend. Therefore eutectics are suitable as PCMs only in the absence of supercooling. That is because the eutectic solidification (of all the involved components) occurs simultaneously (if supercooling is absent), such that their total composition is the same as the composition of the liquid. Therefore, if there is a eutectic that does not undergo supercooling, it freezes rather similar to a congruent melting composition, and is thus suitable as a PCM.  

How is supercooling determined:

For very pure and homogeneous substances, supercooling is determined by the difference between the onset melting temperature and the nucleation temperature. It should be noted here that the nucleation is a stochastic process which, in contrast to the melting point, depends on the measuring conditions (e. g. cooling rate, sample volume, etc.). Therefore the measured value referes to these settings.

This definition is not applicable to PCMs that do not show a nucleation temperature such as blends of paraffins. These materials show not a clear nucleation temperature, the behaviour is more like a hysteresis. Figure 2 - figure 4 show different approaches to determine the value for supercooling of RT27. Reference points are: peak-peak, offset-offset and onset-onset temperature.

Peak-peak (figure 3) and offset-offset (figure 4) are very much dependent on the heating rate, sample mass and the DSC device. Therefore, these differences are only comparable within the same DSC if the same heating rate and approximately the same thermal mass have been used. As the difference between onset temperature of the melting peak and  crystallisation peak can be  negative this is not an indicator for the degree of supercooling.

The challenge with blends or other inhomogeneous materials is that they have a melting and crystallization. So no nucleation point is visible.

Figure 1: Supercooling in pure materials: e.g. n-dodecane, as seen in its (a) temperature-profile, (b) enthalpy profile and (c) specific heat profile.

Figure 2: Possibility offset-offset temperature

 Figure 3: Possibility peak-peak temperature

 Figure 4: Possibility onset-onset temperature

Many solid-liquid PCM exhibit supercooling, i.e. the crystallisation of the PCM upon cooling starts at a lower temperature than the melting temperature. The temperature at the starting point for crystallisation is called nucleation temperature. Nucleation theory of the liquid-solid phase change describes the formation of a solid particle in the bulk of the liquid phase. This process is spontaneous under isobaric and isothermal conditions if it is associated with a reduction in the Gibbs’ potential, which applies for temperatures below the equilibrium melting temperature. In the course of the phase change, the liquid and the solid phase meet at an interface which is associated with an interface energy. The formation of the interface, however, is in any case an endothermic process associated with the surface tension. Thus, at a temperature below the equilibrium melting temperature, the net change in Gibbs’ potential is negative only beyond a certain cluster size, the so-called critical radius. Only clusters larger than the critical radius will grow spontaneously and the whole material will solidify consequently. This nucleation barrier can be overcome by thermal fluctuations. Since these fluctuations are local stochastic events, nucleation is a probabilistic phenomenon. Thermal fluctuations as well as the nucleation barrier depend on temperature, and therefore the nucleation rate is also dependent on temperature.

Two types of nucleation can be distinguished: homogeneous and heterogeneous nucleation. In the case of homogeneous nucleation, only the phase changing substance is involved and the surface tension refers to the interface between solid and liquid. Homogeneous nucleation can take place at any location in the system, and the whole volume is a potential nucleation site. Hence the nucleation rate is a function of the bulk volume. However, if a suitable foreign substance is present providing a smaller surface tension with respect to the solid, nucleation will occur preferably at the interface to this foreign substance (heterogeneous nucleation). Substances with a particularly small surface tension for a given solid (nucleating agents) can be added to enhance nucleation. In principle any impurity or surface in contact with the liquid has the potential to offer a reduced surface tension and to overcome the nucleation barrier.

Summarising, the observed nucleation temperature depends on the volume and the purity of the sample under investigation. The larger the volume and the more impurities are present, the higher the absolute probability for a nucleation event is and the closer the observed nucleation temperature is expectably to the melting temperature. In addition, the nucleation temperature depends on the applied cooling rate: the lower the applied cooling rate, the closer the observed nucleation temperature is expectably to the melting temperature.

Literature:

• Günther, E., Huang, L., Mehling, H., and Dötsch, C. Subcooling in pcm emulsions – Part 2: Interpretation in terms of nucleation theory. Thermochim Acta 2011;522(1-2):199-204.
• Kashchiev, D., 2000. Nucleation – Basic Theory with Applications, Butterworth, Heinemann.
• Skripov, V.P., 1974. Metastable Liquids, John Wiley & Sons, New York.

Nucleation temperature T_n of a PCM sample cooled down exposed to a constant ambient temperature

General definition

According to the ASTM standard E473, Differential Scanning Calorimetry (DSC)[1]is a technique where the heat flow rate difference into a substance and a reference is measured as a function of temperature, while the sample is subjected to a controlled temperature program. This way, quantitative calorimetric information of the sample can be obtained, such as melting and crystallization temperatures; heat of fusion; heat capacity; heat of reaction and others. DSC is considered an accurate, simple and user-friendly technique and, consequently, it is probably the most popular thermal analysis method. It is widely used for the characterization of materials in the field of thermal energy storage [1,2].

[1] Note that the acronym DSC can refer either to the technique (differential scanning calorimetry) or to the measuring device itself (differential scanning calorimeter)

Main advantages and limitations

Nowadays, DSC is a routine technique and the instruments are relatively inexpensive; therefore, it can be found in numerous characterization laboratories. It allows a cost-effective determination of certain relevant thermal properties of materials with a moderate effort. Unfortunately, this implies some drawbacks. It is a popular misconception that a DSC experiment can be successfully completed just by recording a DSC peak [2]. This is not true, especially for research purposes, where reproducibility of the results is essential. Literature [3] demonstrates that significant differences can arise between DSC results for the same material when they measured in different laboratories. Standard procedures are yet to be developed in order to avoid these uncertainties. Besides, DSC shows other limitations, like the reduced sample size to be measured. The dynamic nature of the technique can be also considered a drawback for certain applications, because it implies a “lack of equilibrium” conditions whereas the properties to be determined they are inherently equilibrium properties.

Main DSC types

Two main types of DSC exist nowadays: power compensation DSC and heat flux DSC. Power compensation DSC was created by Gray and O’ Neil at the Perkin-Elmer Corporation [4] in 1963. Alternatively, heat flux DSC grew out of Differential Thermal Analysis (DTA).

A heat flux DSC usually consist of a cell containing the reference and sample holders surrounded by a heating block that acts as a homogeneous-temperature body. The two holders are heated (or cooled) by means of the heating block and therefore they are submitted to the same temperature program. The measured signal is the temperature difference, which is computed by temperature sensors located below (or surrounding[1]) the sample and reference holders. If during the temperature program there is thermal symmetry between the two holders, no heat exchange will occur between them. Conversely, if any thermal asymmetry occurs, owed for instance to a phase transition within the sample or to the different thermal capacity of the sample and the reference, then a temperature difference will take place. This temperature difference is used to calculate the heat exchanged between the holders and, eventually, to determine the thermal properties of the sample.

The power compensation DSC[2] consists of two microfurnaces of the same type, each of which contains a temperature sensor and a heating resistor. Upon heating, the same heating power is supplied to both microfurnaces via a control circuit. If there is thermal symmetry, the temperature of both microfurnaces is always the same. When an asymmetry occurs, for example as a result of a phase change in the sample, a temperature difference results between the microfurnace accommodating the sample and that containing the reference sample. That temperature difference is used as the input signal of a second control circuit, which tries to reduce it by increasing or decreasing an additional heating power. This compensating heating is proportional to the heat consumed or released in the sample during the event that led to the asymmetry and, therefore, can be used to determine the thermal properties of the sample.

Calvet-type DSC is a heat flux DSC developed by the company Setaram Inc [5]. It is based on the Calvet detector construction. In contrast to the traditional plate-shaped heat flow sensors, the Calvet type is based on a three dimensional heat flow meter sensor, formed by an array of thermocouples surround the tubular sample and reference holders. This radial arrangement of the thermopiles guarantees an almost complete integration of the heat, which leads to an increased accuracy. Besides, the sensitivity of the DSC is no longer significantly affected by the type of crucible, type of purge gas and flow rate. In addition, 3D Calvet sensors can be calibrated by the Joule Effect method, avoiding the need of certified reference materials and allowing for a calibration at almost any temperature, with the consequent advantages. This arrangement also allows the use of larger sample sizes and higher pressures compared to traditional DSC devices.