Calorimeter cells

Figure Bl.27.7. Schematic diagram of isothennal displacement calorimeter A, glass calorimeter cell B, sealed heater C, stainless steel stirrer D, thennistor E, inlet tube F, valve G, window shutters Ft, silver rod ...

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. 

Fia. 6. The Petit-Eyraud calorimeter calorimeter cells (A) cylinders made of insulating material (B) metal block (C) and plate of alumina supporting the thermoelectric pile (D). Reprinted from 3/f) with permission of Gauthier-Villars. 

Several features of the early model (Fig. 6) have been modified in the present-day, high-temperature version of this calorimeter (Fig. 7) (37). Depending upon the temperature range envisaged, the block is made of refractory steel, alumina, or beryllium oxide and is machined to house the calorimeter itself. The thermoelectric pile (about 50 platinum to platinum-rhodium thermocouples) is affixed in the grooves of an alumina plate (A), which is permanently cemented to two cylindrical tubes of alumina (B). Cylindrical containers of platinum (C) ensure the uniformity of the temperature distribution within the calorimeter cells. 

Fig. 7. The Eyraud calorimeter the thermoelectric pile (1) the heat sink (2) horizontal section of the calorimeter (3) plate of alumina (A) calorimeter cells (B) and platinum cylinders (C). Reprinted from (37) with permission.

The relation between the emf of the thermoelectric pile and the heat flux from the calorimeter cell will be first established. Let us suppose (Fig. 8) that the process under investigation takes place in a calorimeter vessel (A), which is completely surrounded by n identical thermoelectric junctions, each separated from one another by equal intervals. The thermocouples are attached to the external surface of the calorimeter cell (A), which constitutes the internal boundary (Eint) of the pile and to the inside wall of the heat sink (B), constituting the external boundary (Eext) of the thermoelectric pile. The heat sink (B) is maintained at a constant temperature (6e). 

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. 

When a Joule heating or a Peltier cooling are used to compensate part of the heat absorbed or liberated in the calorimeter cell, Eq. (17) gives... 

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. 

Laville (43) has supposed that the calorimeter is composed of a heat-conducting body (the internal boundary in Fig. 8) which receives, on a fraction (Si) of its surface at temperature 0i, a heat flux (t) generated within the calorimeter cell. Another fraction of its surface S2, at temperature 02, emits a heat flux which diffuses towards the heat sink at temperature 03-... 

In the calculations proposed by Camia (44), a heat pulse is produced within the calorimeter cell, which is initially in thermal equilibrium. The heat pulse diffuses through the heat-conducting body toward the heat sink which is maintained at a constant temperature 03. 

This simplified equation is equivalent to Tian s equation [Eq. (16)], and it appears that n is indeed the time constant r of the calorimeter. Thence, the successive coefficients n in Eq. (29) may be called the calorimeter time constants of 1st, 2nd,. .., ith order. When the Tian equation applies correctly, all time constants r, except the first r may be neglected. Since the value of the coefficients n of successive order decreases sharply [the following values, for instance, have been reported (40) n = 144 sec, r2 = 38.5 sec, r3 = 8.6 sec, ri 1 sec], this approximation is often valid, and the linear transformation of many thermal phenomena produced by the thermal lag in the calorimeter may actually be represented correctly by Eqs. (16) or (30). It has already been shown (Section IV.A) that the total heat produced in the calorimeter cell is then proportional to the area limited by the thermogram. 

The differential equations Eqs. (10) and (29)3, which represent the heat transfer in a heat-flow calorimeter, indicate explicitly that the data obtained with calorimeters of this type are related to the kinetics of the thermal phenomenon under investigation. A thermogram is the representation, as a function of time, of the heat evolution in the calorimeter cell, but this representation is distorted by the thermal inertia of the calorimeter (48). It could be concluded from this observation that in order to improve heat-flow calorimeters, one should construct instruments, with a small... 

Although most heat-flow calorimeters are multipurpose instruments, it is clear that for each particular type of experiment, the inner calorimeter cell must be especially designed and carefully tested. The reliability of the calorimetric data and, thence, the precision of the results depend, to a large extent, upon the arrangement of the inner cell. Typical arrangements for adsorption studies are described in the next section (Section VI.A). 

As already indicated (Section IV.A), the quantity of heat evolved in the calorimeter cell is measured, in the case of usual heat evolutions, by the area limited by the thermogram. The integration of the calorimetric curves is, therefore, often needed. This may be achieved by means of integrating devices which may be added to the recorder. From our experience, however,... 

The development of the theory of heat-flow calorimetry (Section VI) has demonstrated that the response of a calorimeter of this type is, because of the thermal inertia of the instrument, a distorted representation of the time-dependence of the evolution of heat produced, in the calorimeter cell, by the phenomenon under investigation. This is evidently the basic feature of heat-flow calorimetry. It is therefore particularly important to profit from this characteristic and to correct the calorimetric data in order to gain information on the thermokinetics of the process taking place in a heat-flow calorimeter. 

It should be recalled, at this point, that the value of the time constant is related to the heat capacity of the calorimeter cell and of its contents [Eq. (15)]. For meaningful results, it is therefore essential that the arrangement of the inner cell remain identical for both the Joule heating and the thermal phenomenon under investigation. Strictly speaking, the time constant would be unchanged if it were possible to keep the thermal paths completely identical in both cases. This condition is, of course, very difficult to meet. 

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-...

The adsorption cell (C in Fig. 15) which contains the adsorbent must be placed in the inner cell of the calorimeter and a good thermal contact must be established between the sample and the sensing elements of the calorimeter. The mechanical contact between the volumetric line and the calorimeter occurs, therefore, in the calorimeter cell itself. Thence, any relative movement or vibrations between these parts of the apparatus must be strictly avoided. This necessitates the very careful installation of the whole apparatus, especially if experiments of long duration are to be made. 

The adsorbent—a powder generally, but it could be a metal or oxide film— is placed in a glass tube (the adsorption cell C in Fig. 15) which is connected to the volumetric and vacuum lines. The bottom part of the tube, which contains the adsorbent and is located in the calorimeter cell, is made of thin-walled (0.2-0.3 mm) blown tubing (A in Fig. 18). In order to avoid the slow diffusion of gases through a thick layer of adsorbent (see Section VII.A), the sample is often placed in the annular space between the inner wall of the adsorption cell and the outer wall of a cylinder made of glass,... 

It must be noted that although the calibration cell is very different from the adsorption cell [Fig. 18, cells (1) and (2)3, the heat capacity of both cells is not very different, as the similar values of the time constant of the calorimeter containing one cell or the other indeed show (350 sec in the case of the calibration cell and 400 sec in the case of the adsorption cell) (55). This is explained by the fact that in both eases, the calorimeter cell is almost completely filled with a metal. However, the glass tube which is immersed in the calorimeter cell and the pressure changes which occur in the course of the adsorption experiments may be the sources of variable thermal leaks. The importance of these leaks was appreciated by means of the following control experiments. 

Proper calibration of the DSC instruments is crucial. The basis of the enthalpy calibration is generally the enthalpy of fusion of a standard material [21,22], but electrical calibration is an alternative. A resistor is placed in or attached to the calorimeter cell and heat peaks are produced by electrical means just before and after a comparable effect caused by the sample. The different heat transfer conditions during calibration and measurement put limits on the improvement. DSCs are usually limited to temperatures from liquid nitrogen to 873 K, but recent instrumentation with maximum temperatures close to 1800 K is now commercially available. The accuracy of these instruments depends heavily on the instrumentation, on the calibration procedures, on the type of measurements to be performed, on the temperature regime and on the... 

Simple visual observation of the samples upon removal from the calorimeter cell after the experiments revealed that varying degrees of coagulation had taken place in some of the samples during the experimental cycle. At sample loadings in the neighborhood of 1.0 mg/mL, the samples scanned at pH 8.34 and pH 7.5 were clear upon removal from the cell. The pH 6.32 samples were somewhat milky in appearance, and the pH 4.8 samples were virtually opaque. 

Methods. The differential heats of adsorption of reagents and the differential heat of their interaction on the nickel oxide surface were measured in a Calvet microcalorimeter with a precision of 2 kcal. per mole. The apparatus has been described (18). For each adsorption of a single gas, small doses of gas are allowed to interact with a fresh nickel oxide sample (100 to 200 mg.) placed in the calorimeter cell maintained at 30°C. At the end of the adsorption of the last dose, the equilibrium pressure is, in all cases, 2 torr. Duplication of any adsorption experiment on a new sample gives the same results within 2 kcal. per mole of heat evolved and 0.02 cc. of gas adsorbed per gram. Electrical conductivities of the nickel oxide sample are measured in an electrical conductivity cell with platinum electrodes (1) by a d.c. bridge. 

The calorimeter cell contained 80 pM protein (0.6 ml) and a solution containing 0.6 mM ligand was added in 5 pi increments. The reac-... 

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