Calibration heat flow rate

E. Gmelin, S. M. Sarge. Temperature, Heat and Heat Flow Rate Calibration of Differential Scanning Calorimeters. Thermochim. Acta 2000, 347, 9-13. 

Sarge, S.M. Hohne, G.W.H. Cammenga, H.K. Eysel, W. Gmehn, E. Temperature, heat and heat flow rate calibration of scanning calorimeters in the cooling mode. Thermochim. Acta 2000, 361, 1-20. 

Mathematically this simation without a AT loop is expressed by the upper three boxed equations in Fig. 4.60, where dQs/dt and dQs/dt are the heat-flow rates into the reference and sample calorimeters, respectively. The measured and true temperatures are represented by T and T. For simplicity, one can assume that the proportionality constant K is the same for the sample and reference calorimeters. Differences are assessed by calibration. Both bottom equations are then equal to the power input from the average temperature amplifier. Wav (ill W or J s ). 

Differential scanning calorimetry is not an absolute measuring technique, calibrations are thus of prime importance. Calibrations are necessary for the measurement of temperature, T (in K) amplitude, expressed as temperature difference, AT (in K) or as heat-flow rate, dQ/dt (in J s or W) peak area AH (in J) and time, t (in s or min). Figure 4.62 shows the analysis of a typical first-order transition, a melting transition. 

The use of the corrections B in Fig. A.l 1.2 needs two calibration runs of the DSC of Fig. 4.54. The heat capacities of the calorimeter platforms, C pi and C pi, and the resistances to the constantan body, R pi and R pi, must be evaluated as a function of temperature. First, the DSC is ran without the calorimeters, next a run is done with sapphire disks on the sample and reference platforms without calorimeter pans. From the empty run one sets a zero heat-flow rate for and This allows to calculate the temperature-dependent time constants of the DSC, written as = C piRspi and Tr = CrpiRrpi, and calculated from the equations in the lower part of Fig. A. 11.2. For the second run, the heat-flow rates are those into the sapphire disks, known to be mCpQ, as suggested in Figs. 4.54 and 4.70. The heat-capacity-correction terms are zero in this second calibration because no pans were used. From these four equations, all four platform constants can be evaluated and the DSC calibrated. 

Figure 4.67[A] shows a typical isothermal experiment carried out with a DSC. Similar experiments could be carried out with isothermal calorimeters, dilatometry and other teehniques sensitive to crystallinity changes. After attainment of steady state at point 0, the experiment begins. At point 1, the first heat flow rate is observed, and when the heat flow rate reaches 0 again, the transition is complete. The shaded area is the time integral of the heat flow rate, and if there is only a negligible instrument lag, it represents the overall kinetics. In case of an excessive heat flow-rate amplitude, lag calibrations with sharply melting substances of similar thermal conductivity may have to be made (see Figure 4.22). Processes faster than about 1 min...

In Section 4.3, it is shown with Figure 4.55 that the heat of fusion and its calibration to 100% crystallinity can be best accomplished by standard DSC, but the baseline is best checked or established by MTDSC. A well-established baseline of heat flow rate of the liquid is sufficient if the temperature dependence of the heat capacity is known (see Figures 4.23,4.25 and 4.57). A detailed, simple description of the kinetics of the glass transition of semicrystalline samples is illustrated in the example of PET (Figures 4.58. 60). Both frequency of measurement and the existing crystallinity affect the appearance of the glass transition as can be seen from the data in Table 4.1. 

For precise measurements it is necessary to correct (calibrate) the measured heat flow rate magnitude and phase shift for influences from the apparatus, as well as from the heat transport, which also is a time-dependent process and therefore influences the measured heat flow rate function [43],... 

The TMDSC enables another elegant possibility of Cp (magnitude) determination from the amplitude of the modulated part of the measured heat flow rate function both in the isothermal and. scanning modes of operation. This method is especially advantageous in cases of noisy signals with low sample masses or low heating rates. Precise calibration of the heat flow rate amplitude is a prerequisite for obtaining reliable results [43]. 

The difference between the heat flow rates to the two measuring systems, the differential heat flow rate, is proportional to the (negative) measured temperature difference between the sample and reference sides. At any rate, the calibration factor fC (T) is usually not constant over large temperature ranges, and the respective calibration function has to be determined empirically in most cases. 

Differential heat flow rate between sample and reference system (with known calibration function) as a function of time or temperature... 

Heat conduction in solid bodies is particularly suitable for quantitative measurements of heat exchanged (i.e., generated or consumed in the calorimeter system) vdth the surroundings. In a suitably designed instrument, the heat flow rate

solid body with a defined thermal resistance between the calorimeter system and the surroundings can be made entirely dependent on the temperature difference AT measured at the said thermal resistance. On these grounds, a record of the time course of this local temperature difference provides a means for the measurement of heat flow rates if the specific calibration factor K is known 0= KAT... 

Owing to the complex nature of heat conduction inside a real instrument, it is generally impossible to calculate the thermal resistance i th lhat quantitatively connects the measured temperature difference and the corresponding heat flow rate. Instead, the apparent thermal resistance must be determined by proper calibration. 

This calorimeter (Picker, Jolicoeur, and Desnoyers, 1969) represents a twin instrument with countercurrent auxiliary circulation (Figure 7.24). All liquids are brought to a constant temperature at the inlet. The reactants are mixed with one another before entering the first flow tube, and the heat of reaction is transferred in a heat exchanger from the reaction product to the auxiliary liquid, which flows in the opposite direction. In the second flow tube - also connected by means of a second heat exchanger with a counterflowing auxiliary liquid - a nonreacting reference liquid (e.g., the reaction product) flows. The temperature difference between the two countercurrents is measured it is proportional to the heat flow rate of the reaction. The calorimeter is equipped with electric calibration heaters. 

From Eq. (7.24), it follows that the vibrational (static) heat capacity of the sample can be determined in the usual way from the first summand as well as from the amplitude of the modulated component of the measured heat flow rate function. In absence of other processes, the two results must coincide this can be used for calibration purposes. If other processes take place in the sample, the apparent heat capacity from the modulated part, the reversing heat capacity, may differ from the apparent heat capacity, the total heat capacity determined from the first summand of the right-hand side in Eq. (7.24). The difference between these two apparent heat capacities is the so-called nonreversing heat capacity . To obtain the frequency-dependent complex heat capacity from the measured heat flow rate function, different evaluation methods exist. It is not within the scope of this book to explain this ambitious matter in detail interested readers are referred to the special literature (e.g., Hohne, Hemminger, and Flammersheim, 2003 Schick, 2002). 

At the times when the classical calorimeters were built, no computers existed and all evaluation was done by hand. Therefore, there was a need for simple formulas to calculate the quantities of interest from the measured curves. The construction of the calorimeters was such to give a signal strictly proportional to the heat flow rate into the sample itself with a calibration factor almost not influenced by the heat transfer to the sample and its heat capacity. The price to be paid for this comfort was a rather low sensitivity of the calorimeter with a need for large samples and large time constants in the range from some seconds up to many minutes in the case of very sensitive microcalorimeters (see Section 7.9.2). 

If the calibration factor depends on further parameters (e.g., sample mass, temperature, heat evolved), it is recommended that K be presented graphically as a function of the respective parameter. A good linearity exists when K is constant (horizontal line). The linearity error 3K/K equals the maximum deviation from the horizontal line. A good linearity of the apparatus is a precondition for the existence of an apparatus function (see Section 6.3), which makes it essential for a reconstruction of the tme heat flow rate function in(f) from the measured curve out-... 

A number of heat flow rate calibration materials have also been suggested for the calibration of the heat capacity scale of calorimeters. Table 9.2 describes these materials and the applicable temperature ranges. 

Table 9.2 Heat flow rate calibration materials (Della Catta et ai, 2006).

First, the heat (peak area) and the heat capacity (heat flow rate) calibration of the DSC were verified using the same heating rate as in the planned experiments. Indium was used as the reference substance for heat calibration and sapphire for heat capacity calibration. 

Figure 1. 2 (a) Temperature profile and measured heat flow rate for empty pans, sapphire calibration standard (34 mg), and initially amorphous PEEK (29 mg), Heating rate = 20 K/ min, Perkin Ehner Pyris Diamond DSC. (b) Specific heat capacity versus temp>erature. Reference data (straight fines) for the fuUy amorphous (liquid) and crystaUine (solid) PEEK from ATHAS-DB [124],... 

---