Microcalorimeters

Figure Bl.27.8. Schematic view of Picker s flow microcalorimeter. A, reference liquid B, liquid under study P, constant flow circulating pump and 2, Zener diodes acting as heaters T and T2, thennistors acting as temperature sensing devices F, feedback control N, null detector R, recorder Q, themiostat. In the above A is the reference liquid and C2is the reference cell. When B circulates in cell C this cell is the working cell. (Reproduced by pemiission from Picker P, Leduc P-A, Philip P R and Desnoyers J E 1971 J. Chem. Thermo. B41.)...

Recent developments m calorimetry have focused primarily on the calorimetry of biochemical systems, with the study of complex systems such as micelles, protems and lipids using microcalorimeters. Over the last 20 years microcalorimeters of various types including flow, titration, dilution, perfiision calorimeters and calorimeters used for the study of the dissolution of gases, liquids and solids have been developed. A more recent development is pressure-controlled scamiing calorimetry [26] where the thennal effects resulting from varying the pressure on a system either step-wise or continuously is studied. 

The adsorption of NH3 was also measured with a microcalorimeter, and some of the results are shown in Fig. 3. Figure 4 compares the amount of H2 site determined by the deconvolution analysis with that of super strongly adsorbed NH3 with the heat of adsorption above 155 kJ mol . A good correlation shown in the figure indicates the validity of the amounts of Ga sites determined by the deconvolution analysis. 

Fig.4.2. Relative concentration N/Na of hydrogen atoms in a reaction vessel as a function of relative discharge intensity (current) in the Wood tube J/Jg- The measurements were carried out by a semiconductor sensor (/), microcalorimeter (2), and by using the diffusion Wrede method (J).

III. Some Heat-Flow Microcalorimeters That Can Be Used in Heterogeneous Catalysis Research. 196... 

A survey of the literature shows that although very different calorimeters or microcalorimeters have been used for measuring heats of adsorption, most of them were of the adiabatic type, only a few were isothermal, and until recently (14, 15), none were typical heat-flow calorimeters. This results probably from the fact that heat-flow calorimetry was developed more recently than isothermal or adiabatic calorimetry (16, 17). We believe, however, from our experience, that heat-flow calorimeters present, for the measurement of heats of adsorption, qualities and advantages which are not met by other calorimeters. Without entering, at this point, upon a discussion of the respective merits of different adsorption calorimeters, let us indicate briefly that heat-flow calorimeters are particularly adapted to the investigation (1) of slow adsorption or reaction processes, (2) at moderate or high temperatures, and (3) on solids which present a poor thermal diffusivity. Heat-flow calorimetry appears thus to allow the study of adsorption or reaction processes which cannot be studied conveniently with the usual adiabatic or pseudoadiabatic, adsorption calorimeters. In this respect, heat-flow calorimetry should be considered, actually, as a new tool in adsorption and heterogeneous catalysis research. 

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. 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. 

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. 

In recent years, other heat-flow microcalorimeters equipped with commercially available semiconducting thermoelements have been described... 

Fig. 5. The Petit microcalorimeter (31) vertical axles (A and A2) mobile arms (Bi-B3) flux-meter holders (C1-C3) cell guide (D) thermoelectric element (E) cell-positioning block (F) top and bottom flanges (Gi and G2) portholes (Jj and J2) and springs (R). 

The Petit microcalorimeter which is presented in Fig. 5 appears to be particularly suitable for chemisorption studies. 

In this microcalorimeter, the heat sink is not a massive metal block but is divided into several parts which are mobile with respect to each other. Each thermoelectric element (E) and a cell guide (D) are affixed to a fluxmeter holder (C). The holder (C) is mobile with respect to a massive arm (B) which, in turn, rotates around a vertical axle (A). All parts of the heat sink are made of brass. Surfaces in contact are lubricated by silicone grease. Four thermoelectric elements (E) are mounted in this fashion. They enclose two parallelepipedic calorimetric cells, which can be made of glass (cells for the spectrography of liquids are particularly convenient) or of metal (in this case, the electrical insulation is provided by a very thin sheet of mica). The thermoelectric elements surrounding both cells are connected differentially, the Petit microcalorimeter being thus a twin differential calorimeter. 

The purpose of the particular arrangement of the heat sink in the Petit microcalorimeter is to ensure an excellent and reproducible contact, at any temperature, between the surface of the thermoelectric elements and the outside walls of the calorimetric cells (31) and, moreover, to avoid... 

It is clear that in this microcalorimeter, only a fraction of the outside wrall of the inner vessel is covered by thermoelectric elements. Consequently, only a part of the total heat flux emitted by the cell is detected. This may be the cause of a systematic error which, however, can be avoided if the heat transfer via the thermoelectric elements constitutes a constant fraction of the total, irrespective of the process taking place in the calorimeter cell. The present version of the Petit microcalorimeter can be used only at moderate temperatures (<100°C), mainly because some components of the thermoelectric elements wrould be damaged at higher temperatures. 

Intrinsic Sensitivities of Some Heat-Flow Microcalorimeters... 

The intrinsic sensitivity of a heat-flow calorimeter is defined as the value of the steady emf that is produced by the thermoelectric elements when a unit of thermal power is dissipated continuously in the active cell of the calorimeter 38). In the case of microcalorimeters, it is conveniently expressed in microvolts per milliwatt (juV/mW). This ratio, which is characteristic of the calorimeter itself, is particularly useful for comparison purposes. Typical values for the intrinsic sensitivity of the microcalorimeters that have been described in this section are collected in Table I, together with the temperature ranges in which these instruments may be utilized. The intrinsic sensitivity has, however, very little practical importance, since it yields no indication of the maximum amplification that may be applied to the emf generated by the thermoelements without developing excessive noise in the indicating device. 

The value of the time constant depends upon the calorimeter itself p and upon the heat capacity of the calorimeter cell and of its contents p. Typical, but necessarily approximate, values of the time constant for some heat-flow microcalorimeters are given in Table II. 

It must be noted that the heat capacity of the calorimeter cell and of its contents p, which appears in the second term of Tian s equation [Eq. (12)], disappears from the final expression giving the total heat [Eq. (19)]. This simply means that all the heat produced in the calorimeter cell must eventually be evacuated to the heat sink, whatever the heat capacity of the inner cell may be. Changes of the heat capacity of the inner cell or of its contents influence the shape of the thermogram but not the area limited by the thermogram. It is for this reason that heat-flow microcalorimeters, with a high sensitivity, are particularly convenient for investigating adsorption processes at the surface of poor heat-conducting solids similar in this respect to most industrial catalysts. 

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 determination of these curves requires not only the measurement of small amounts of heat in a microcalorimeter, but also the simultaneous determination of the corresponding quantity of adsorbed gas. Volumetric measurements are to be preferred to gravimetric measurements for these determinations because it would be very difficult indeed to ensure a good, and reproducible, thermal contact between a sample of adsorbent, hanging from a balance beam, and the inner cell of a heat-flow calorimeter. 

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).

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