Calvet

Figure Bl.27.11. Schematic diagram of a Tian-Calvet heat-flux or heat-conduction calorimeter.

Since heat exchange between the calorimeter vessel and the heat sink is not hindered in a heat-flow calorimeter, the temperature changes produced by the thermal phenomenon under investigation are usually very small (less than 10 4 degree in a Calvet microcalorimeter, for instance) (23). For most practical purposes, measurements in a heat-flow calorimeter may be considered as performed under isothermal conditions. 

The Calvet microcalorimeter (16) is an improved version of the first heat-flow calorimeter described by Tian in 1924 (25). In this micro-... 

Fig. 2. Vertical section of a Tian-Calvet microcalorimetric element (16) inner vessel (A) and hollow truncated cone (B) wedged in the heat sink (C). Reprinted from Calvet and Prat (23) with permission of Dunod.

In heat-flow calorimeters, it is particularly important, as already indicated in Section II, that the heat sink remain, throughout the experiment, at a constant temperature. The construction of the heat sink and thermostat in the Calvet apparatus is shown in Fig. 3. The calorimetric element fits into a conical socket (A), cut in a cylindrical block of aluminium (B). The block is positioned between the bases of two truncated cones (C and C ), placed within a thick metal cylinder (D). The metal cylinder is, in... 

Fig. 3. Vertical section of the Calvet microcalorimeter (16) microcalorimetric element (A) the metal block (B) metallic cones (C and C ) thick metal cylinder (D) thermostat consisting of several metal canisters (E) electrical heater (F) switch (G) thermal insulation (I) and thermal lenses (J and J ). Reprinted from Calvet and Prat (S3) with permission of Dunod.

Calvet and Persoz (29) have discussed at length the question of the sensitivity of the Calvet calorimeter in terms of the number of thermocouples used, the cross section and the length of the wires, and the thermoelectric power of the couples. On the basis of this analysis, the micro-calorimetric elements are designed to operate near maximum sensitivity. The present-day version of a Tian-Calvet microcalorimetric element, which has been presented in Fig. 2, contains approximately 500 chromel-to-constantan thermocouples. The microcalorimeter, now commercially available, in which two of these elements are placed (Fig. 3) may be used from room temperature up to 200°C. 

Fig. 4. Vertical cross section of a high-temperature Calvet calorimeter (16) cell guides (A) thermal insulation (B) top (C) and bottom (N) electrical heaters thermostat consisting of several metal canisters (D, G, and H) switch (E) electrical heater (F) thermometers (I, J, and K) microcalorimetric element (L) and heat sink (M).

Calvet and Guillaud (S3) noted in 1965 that in order to increase the sensitivity of a heat-flow microcalorimeter, thermoelectric elements with a high factor of merit must be used. (The factor of merit / is defined by the relation / = e2/pc, where e is the thermoelectric power of the element, p its electrical resistivity, and c its thermal conductivity.) They remarked that the factor of merit of thermoelements constructed with semiconductors (doped bismuth tellurides usually) is approximately 19 times greater than the factor of merit of chromel-to-constantan thermocouples. They described a Calvet-type microcalorimeter in which 195 semiconducting thermoelements were used instead of the usual thermoelectric pile. 

Calvet, standard model (16) Chromel to constantan couples 30-200 60 (30°C)... 

Calvet, high-temperature version 16) Platinum to platinum-rhodium couples 30-800 (500°C)... 

The basic principle of heat-flow calorimetry is certainly to be found in the linear equations of Onsager which relate the temperature or potential gradients across the thermoelements to the resulting flux of heat or electricity (16). Experimental verifications have been made (89-41) and they have shown that the Calvet microcalorimeter, for instance, behaves, within 0.2%, as a linear system at 25°C (41)-A. heat-flow calorimeter may be therefore considered as a transducer which produces the linear transformation of any function of time f(t), the input, i.e., the thermal phenomenon under investigation]] into another function of time ig(t), the response, i.e., the thermogram]. The problem is evidently to define the corresponding linear operator. 

The efficiency of this method has been demonstrated for several types of heat-flow calorimeters. The rather long time constant of a Calvet-type calorimeter (200 sec), for instance, is decreased to 10 sec, when exact Peltier cooling is used (61). Similarly, the time constant of calorimeters... 

Figure 15 gives a diagrammatic representation of a volumetric line which is used in connection with a high-temperature Calvet microcalorimeter 67). Other volumetric lines which have been described present the same general features (15, 68). In the case of corrosive gases or vapors, metallic systems may be used 69). In all cases, a sampling system (A in Fig. 15) permits the introduction of a small quantity of gas (or vapor) in a calibrated part of the volumetric line (between stopcocks Ri and Ro in Fig. 15) where its pressure Pi is measured (by means of the McLeod gage B in Fig. 15). The gas is then allowed to contact the adsorbent placed in the calorimeter cell C (by opening stopcock Ro in Fig. 15). The heat evolution is recorded and when it has come to completion, the final equi-...

Fig. 15. Volumetric line used in connection with a Calvet microcalorimeter (67).

It is true, however, that many catalytic reactions cannot be studied conveniently, under given conditions, with usual adsorption calorimeters of the isoperibol type, either because the catalyst is a poor heat-conducting material or because the reaction rate is too low. The use of heat-flow calorimeters, as has been shown in the previous sections of this article, does not present such limitations, and for this reason, these calorimeters are particularly suitable not only for the study of adsorption processes but also for more complete investigations of reaction mechanisms at the surface of oxides or oxide-supported metals. The aim of this section is therefore to present a comprehensive picture of the possibilities and limitations of heat-flow calorimetry in heterogeneous catalysis. The use of Calvet microcalorimeters in the study of a particular system (the oxidation of carbon monoxide at the surface of divided nickel oxides) has moreover been reviewed in a recent article of this series (19). 

Calvet microcalorimeters are particularly convenient for such studies. Figure 19 show s, for instance, the evolution of the differential heat of adsorption of oxygen, measured at 30°C with a Calvet calorimeter, as a function of the total amount of oxygen adsorbed on the surface of a sample (100 mg) of nickel oxide, NiO(200) (19, 73). The volume of the first... 

One of the conclusions deduced from the thermochemical cycle 2 in Table V, for instance, is that in the course of the catalytic combustion of carbon monoxide at 30°C, the most reactive surface sites of gallium-doped nickel oxide are inhibited by the reaction product, carbon dioxide. This conclusion ought to be verified directly by the calorimetric study of the reaction. Small doses of the stoichiometric reaction mixture (CO + IO2) were therefore introduced successively in the calorimetric cell of a Calvet microcalorimeter containing a freshly prepared sample of gallium-doped... 

Heat-flow calorimetry may be used also to detect the surface modifications which occur very frequently when a freshly prepared catalyst contacts the reaction mixture. Reduction of titanium oxide at 450°C by carbon monoxide for 15 hr, for instance, enhances the catalytic activity of the solid for the oxidation of carbon monoxide at 450°C (84) and creates very active sites with respect to oxygen. The differential heats of adsorption of oxygen at 450°C on the surface of reduced titanium dioxide (anatase) have been measured with a high-temperature Calvet calorimeter (67). The results of two separate experiments on different samples are presented on Fig. 34 in order to show the reproducibility of the determination of differential heats and of the sample preparation. 

In the various sections of this article, it has been attempted to show that heat-flow calorimetry does not present some of the theoretical or practical limitations which restrain the use of other calorimetric techniques in adsorption or heterogeneous catalysis studies. Provided that some relatively simple calibration tests and preliminary experiments, which have been described, are carefully made, the heat evolved during fast or slow adsorptions or surface interactions may be measured with precision in heat-flow calorimeters which are, moreover, particularly suitable for investigating surface phenomena on solids with a poor heat conductivity, as most industrial catalysts indeed are. The excellent stability of the zero reading, the high sensitivity level, and the remarkable fidelity which characterize many heat-flow microcalorimeters, and especially the Calvet microcalorimeters, permit, in most cases, the correct determination of the Q-0 curve—the energy spectrum of the adsorbent surface with respect to... 

Calvet, E., and Prat, H., eds., Microcalorimetrie, Applications Physicochimiques et Biologiques. Masson, Paris, 1956 Calvet, E., Prat, H., and Skinner, H. A., Recent Progress in Microcalorimetry. Pergamon, Oxford, 1963. 

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