Heat-flow calorimeters

Heat-flow Calorimeters.— In calorimeters of the adiabatic or isoperibol types, heat-exchange between the calorimeter and its surroundings is either eliminated or is restricted to a small, accurately determined amount. An alternative method is to transfer the heat of reaction completely to a heatsink, so that both the calorimeter and the heat-sink remain essentially isothermal and the calorimetric determination consists of measuring the heat transferred. Two main types have been employed. 

Although isothermal phase-change calorimeters operate on the heat-flow principle, the use of the term heat-flow is usually restricted to calorimeters of the second type where thermometry is used to measure the small temperature differences which arise. In the most widely used form of heat-flow calorimeter, a thermopile provides the main thermal conduction path between the reaction vessel and the heat-sink and is also used to measure the small temperature difference between them. The enthalpy change is calculated from the area under the temperature-time curve, or thermogram. 

Calorimeters based on the heat-flow principle are most useful for the measurement of small quantities of heat absorbed or evolved over long periods, but have also been used for the study of rapid reactions. 

The application of calorimeters of these main classes to the measurement of enthalpies of reaction will be described in subsequent sections. For many of the techniques described much greater detail is available in the two excellent volumes on Experimental Thermochemistry, prepared under the auspices of the I.U.P.A.C., which no new worker in the field can afford not to read. A very useful review entitled Recent Developments in Calorimetry has been published by Wilhoit in which he includes references to many commercially available calorimeters. 

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B. General Equations for the Heat Transfer in a Heat-Flow Calorimeter. 211... 

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. 

Finally, in the ease of heat-flow calorimeters (3 in Fig. 1), the inner vessel and its surroundings are connected by a heat conductor (C in Fig. 1). 

It appears therefore that during the operation of all usual calorimeters, temperature gradients are developed between the inner vessel and its surroundings. The resulting thermal head must be associated, in all cases, to heat flows. In isoperibol calorimeters, heat flows (called thermal leaks in this case) are minimized. Conversely, they must be facilitated in isothermal calorimeters. All heat-measuring devices could therefore be named heat-flow calorimeters. However, it must be noted that in isoperibol or isothermal calorimeters, the consequences of the heat flow are more easily determined than the heat flow itself. The temperature decrease... 

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-... 

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... 

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. 

No theory can possibly take into account the arrangement of a real heat-flow calorimeter in all its details. Theoretical models of heat-flow calorimeters, which are necessarily simplified versions of the actual instruments, will therefore be used in the following calculations. It must be remarked that because of the limitations of the theory, no absolute measurements can be made with a heat-flow calorimeter, nor with any calorimeter. It is possible, however, to compare successive measurements with precision. A calorimetric study necessarily involves the calibration of the calorimeter and, upon this operation, depends the accuracy of the whole series of measurements. 

Now the thermal balance of the inner cell of a heat-flow calorimeter may be established. Let the thermal power developed in the cell, at time t, be called W. 

This fundamental equation of heat-flow calorimeters is called the Tian equation. 

The reciprocal value of the constant p/fi has a dimension of [<] and is called the calorimeter time constant r. This is another important characteristic of a heat-flow calorimeter ... 

As already indicated, Tian s equation supposes (1) that the temperature of the external boundary of the thermoelectric element 8e, and consequently of the heat sink, remains constant and (2) that the temperature Oi of the inner cell is uniform at all times. The first condition is reasonably well satisfied when the heat capacity of the heat sink is large and when the rate of the heat flux is small enough to avoid the accumulation of heat at the external boundary. The second condition, however, is physically impossible to satisfy since any heat evolution necessarily produces heat flows and temperature gradients. It is only in the case of slow thermal phenomena that the second condition underlying Tian s equation is approximately valid, i.e., that temperature gradients within the inner cell are low enough to be neglected. The evolution of many thermal phenomena is indeed slow with respect to the time constant of heat-flow calorimeters (Table II) and, in numerous cases, it has been shown that the Tian equation is valid (16). 

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 calorimeter response to a unit impulse must therefore be determined. This may be achieved by solving the Fourier equation [Eq. (23)] for a theoretical model of a heat-flow calorimeter and for this particular heat evolution. 

The combination of Eqs. (28) and (22) gives the Laplace transform of the impulse response H(p) which allows us to solve Eq. (21). By the inverse transformation, the relation which gives the output of the linear system g(t) (the thermogram) to any input/(0 (the thermal phenomenon under investigation) is obtained. This general equation for the heat transfer in a heat-flow calorimeter may be written (40, 46) ... 

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... 

In any case, thermal inertia may be decreased but never completely removed (48). Data from heat-flow calorimeters must therefore be recorded in such a way that (1) the total amount of heat produced by the phenomenon under investigation is measured with precision, and (2) the correction of the thermograms is easily performed. 

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). 

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. 

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... 

The large amount of calorimetric data, which can be conveniently stored in a digital form, may, of course, be used in a computer to solve the general equation for the heat transfer in a heat-flow calorimeter (Section IV.B) ... 

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. 

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). 

Finally, experimental procedures differing from that described in the preceding examples could also be employed for studying catalytic reactions by means of heat-flow calorimetry. In order to assess, at least qualitatively, but rapidly, the decay of the activity of a catalyst in the course of its action, the reaction mixture could be, for instance, either diluted in a carrier gas and fed continuously to the catalyst placed in the calorimeter, or injected as successive slugs in the stream of carrier gas. Calorimetric and kinetic data could therefore be recorded simultaneously, at least in favorable cases, by using flow or pulse reactors equipped with heat-flow calorimeters in place of the usual furnaces. 

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... 

Chemical composition was determined by elemental analysis, by means of a Varian Liberty 200 ICP spectrometer. X-ray powder diffraction (XRD) patterns were collected on a Philips PW 1820 powder diffractometer, using the Ni-filtered C Ka radiation (A, = 1.5406 A). BET surface area and pore size distribution were determined from N2 adsorption isotherms at 77 K (Thermofinnigan Sorptomatic 1990 apparatus, sample out gassing at 573 K for 24 h). Surface acidity was analysed by microcalorimetry at 353 K, using NH3 as probe molecule. Calorimetric runs were performed in a Tian-Calvet heat flow calorimeter (Setaram). Main physico-chemical properties and the total acidity of the catalysts are reported in Table 1. 

A heat-flow calorimeter of Tian-Calvet type from Setaram maintained at a desired temperature, from room temperature up to 400°C, was used in connection with a volumetric apparatus equipped with a Me Leod gauge. Sample weights were typically 100 mg and ammonia doses 0.1 cm NTP. 

Heat flow calorimeters simulate closely the operation of plant reactors. Removing the heat of reaction at the same rate as it is generated results in a constant reaction temperature. The temperature difference between the reactor and vessel jacket is a measure of the rate of heat production. 

Figure 6.2 Schematic representation of (a) an adiabatic calorimeter, (b) an isoperibol calorimeter, and (c) a heat conduction (or heat flow) calorimeter. fc and 7] are the temperatures of the calorimeter proper and the external jacket, respectively, and is the heat flow rate between the calorimeter proper and the external jacket.

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