Phase Transition Calorimeters

A thermogram from a differential scanning calorimeter. The peak indicates a phase change in the sample, and the difference in base line before and after the phase transition is due to the difference in heat capacities of the two phases. 

The heat flux and energy calibrations are usually performed using electrically generated heat or reference substances with well-established heat capacities (in the case of k ) or enthalpies of phase transition (in the case of kg). Because kd, and kg are complex and generally unknown functions of various parameters, such as the heating rate, the calibration experiment should be as similar as possible to the main experiment. Very detailed recommendations for a correct calibration of differential scanning calorimeters in terms of heat flow and energy have been published in the literature [254,258-260,269]. 

Calorimeters of Historical and Special Interest Around 1760 Black realized that heat applied to melting ice facilitates the transition from the solid to the liquid stale at a constant temperature. For the first time, the distinction between the concepts of temperature and heat was made. The mass of ice that melted, multiplied by the heal of fusion, gives the quantity of heal. Others, including Bunsen, Lavoisier, and Laplace, devised calorimeters based upon this principle involving a phase transition. The heat capacity of solids and liquids, as well as combustion heats and the production of heat by animals were measured with these caloritnelers. 

Figure 45. The configurational entropies of the ferroelectric phase transition for crystals 1 (A) and 2 (+). The difference in entropy between the two crystals, AS, is 0.79 x 10-3Jg-1 this is assigned to the Cu+ dopants. The DSC measurements were made with the cooling and heating rates 5 K/min in an interval ranging from 373 K to 220 K using a DSC 2920 calorimeter (TA Instruments) [179]. (Reproduced with permission from Ref. 179. Copyright 2004, The American Physical Society.)...

Mention should be made here of the recently developed technique of pressure perturbation calorimetry (PPC), which measures the temperature-dependent volume change of a solute or colloidal particle in aqueous solution. PPC can also be used to detect thermotropic phase transitions in lipid model membranes and to characterize the accompanying volume changes and the kinetics of the phase transition. PPC essentially measures the heat change that results from small pressure changes at a constant temperature in a high-sensitivity isothermal calorimeter. For an excellent recent review on PPC as applied to lipid systems, the reader is referred to Heerklotz (19). 

In the high-temperature region, the main method of measurement is the drop calorimetry, where the sample is heated to the chosen temperature outside the calorimeter in a furnace and the heat capacity is calculated from the temperature dependence of the enthalpy changes measured after dropping the sample into the calorimeter. The application of this technique affects, however, the behavior of the sample heated in the furnace (decomposition, reaction with the crucible, etc. should be avoided) as well as at the cooling from the furnace temperature to that of the calorimeter. Sometimes the sample does not complete its phase transition at cooling (e.g. at the temperature of fusion, a part of the sample crystallizes while the other part becomes glassy). In such a case, the drop calorimeter must be supplemented by a solution calorimeter in order to get the enthalpy differences of all the samples to a defined reference state. 

Another useful tool that the automotive chemist will use is the differential scanning calorimeter. The component will be measured against a reference as heat is applied to both samples. A constant temperature will be maintained and the difference in temperature (AT) required to raise the temperature of the sample in relation to the reference sample is measured. Because the reference sample is not undergoing phase transitions, the AT of the measured sample will show an endothermic (melting point) or exothermic (crystallization) peak as heat is applied [7-9],... 

Takahashi, H., Yashima, M., Kakihana, M., and Yoshimura, M. (2001) A differential scanning calorimeter study of the monoclinic (P21/b) - hexagonal (P63/m) reversible phase transition in hydroxyapatite. Thermochim. Acta, 371, 53—56. 

Hohne (145) pointed out that the function principle of DSC can give rise to calibration errors in case of phase transitions disturbing the steady-state conditions. The cause of this problem is the temperature dependence of the coefficients of heat transfer, leading to weak nonlinearity of the calorimeter. This results in a dependence of the calibration factor on parameters such as mass and thermal conductivity of the sample, heating rate, peak shape, and temperature. By theoretical considerations and calculations, the uncertainty of the calibration factor due to the variation of sample parameters can be 1-5%, depending on the temperature and the instrument involved. 

These authors were aware of the difficulty of establishing a comprehensive classification of calorimeters In every classification there are certain calorimeters which do not clearly belong to a particular category.The Calvet calorimeter, for instance, can be used eidier isothermally with electric compensation... or in an isoperibol manner involving the measurement of a local temperature difference. Moreover, a number of existing calorimeters remain outside our classification. One example is a calorimeter involving a compensation of the thermal effect other than by thermoelectric means or by phase transition. But such devices can be easily included in our classification by analogy. ... 

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