Temperature-Dependent Heat Capacity Calibration

Commonly, the heat capacity signal is calibrated at a single temperature. However, the experimental error on the heat capacity can further be reduced by a dynamic calibration over the entire temperature range instead of at a single temperature. The heat capacity calibration constant, Kc., shows a gradual evolution over the entire temperature range, with a total variation of 4% between —50 and 300°C. Below —50°C, the deviation increases. 

For the cure studies in this work, this deviation is not so important. Firstly, because most of the MTDSC experiments are performed above —50°C, and secondly, because for quantitative analyses a mobility factor is calculated by normalising the heat capacity between reference heat capacities determined at the same temperature. Thus, changes in Kc with temperature have no effect on this result (section 5.8). 

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Sometimes the empty-pan baseline correction for heat capacity is omitted for the reversing signal because, when closely matched sample and reference pans are used, it is usually small. Whether this is adequate depends on the type of information being sought. For example, if all that is required is the glass transition temperature, then a full heat capacity calibration may be excessive. However, as an absolute minimum, a calibration must be performed to obtain a correction factor for the cyclic heat capacity at one temperature in the range of interest. 

Reaction calorimeters are frequently calibrated using a known heat of a chemical reaction. No standard reaction is internationally accepted. For the measurement of heat capacities, drop calorimeters are frequently used and the calibration is made using a substance, the temperature dependence of which on heat capacity is known. As substances, metals like Cu, Ag, Au, and aluminum oxide in the form of sapphire are used. Calorimeters... 

Unfortunately, K is highly temperature-dependent in the DTA experiment, so it is necessary to calibrate the peak area in the same temperature region as the peak of interest. This may require multiple calibration standards and can be time consuming. As we shall see, the calibration constant K for DSC is not temperature dependent therefore DTA is usually used for qualitative analysis, while DSC is used for quantitative measurements of AH and heat capacity. 

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. 

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. 

The thermocapacitive flow sensor is based on a dielectric material with a temperature-dependent dielectric constant. The sensing module is a capacitor. If the electric power is supplied to a heater that is close to the capacitor, the temperature of the capacitor will increase, causing an increase in the dielectric constant, and thus, an increase in the capacitance of the capacitor. When a fluid flows through the capacitor and if its temperature is lower than that of the capacitor, the temperature of the capacitor wUl decreases due to the convective heat transfer between the fluid and the capacitor. The temperature of the dielectric material of the capacitor will decrease, resulting in a decrease in the capacity. The higher the flow velocity, the lower the capacity. Therefore there is a relationship between the flow velocity and the capacitance. Like the HWA, with a calibration relationship between the flow velocity and the capacitance, the flow velocity can be calculated by measuring the capacity of the capacitor. 

The calibration of DSCs is one of the most important jobs a thermal analyst needs to perform. Thermal analysis instruments need to be calibrated because the indicated temperatures, heats, and heat capacities do not reflect the real values. Thus, certain procedures are necessary to enable the instrumental software to recalculate these values indicated by the instrument, to real temperature, heat, and heat capacity values. This procedure, called calibration, consists of measuring thermal properties of standard materials whose thermal properties are well known. All the results of subsequent actual measurements depend on the validity of the calibration therefore all calibrations have to be carried out carefully. 

With such heat capacity determination it would take a long time to determine temperature dependence of the heat capacity. However, the curves from Ti to steady state and steady state to T2 have similar shape therefore the hs-u (for sample and baseline) amplitude differences are proportional to the heat capacity at every temperature and there is no need to determine the Ss-bi area (shaded area in Fig. 2.19a), but simply to measure the /ts-bi amplitude differences. So, if the instrument is calibrated with a standard for which the temperature dependence of the heat capacity is well known, the heat capacity of the sample can be measured at any temperature. For this, the /isap-w amplitude differences must be used (see Fig. 2.19a, curves Sapphire run and Baseline ). The standard is usually sapphire (crystalline AI2O3), which is readily available from the instrument companies. For low-temperature heat capacity... 

In this relation w denotes the proportionate heat capacity of the calorimeter (a quantity which depends on temperature and on the volume of the calorimeter contents and has to be calibrated for a specific reactor), m and Cp,. are the mass and the specific heat of the mixture under investigation. 

Fig. 6.19. Microcalorimetric recording indicating (A) Heat absorption of a 0.182% lysozyme solution at pH 2.5 the base line is drawn with a calibration label obtained for the solvent. The deviation of the recorded curve from the base line gives the partial heat capacity of the protein. (B) Temperature dependence of partial heat capacity of lysozyme at pH 2.0, 2.5, and 4.5 (from Privalov and Khechinashvili, 1974).

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