Sensitivity heat flow microcalorimeters

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. 

Intrinsic Sensitivities of Some Heat-Flow Microcalorimeters... 

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. 

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... 

Building a heat flow microcalorimeter is not trivial. Fortunately, a variety of modern commercial instruments are available. Some of these differ significantly from those just described, but the basic principles prevail. The main difference concerns the thermopiles, which are now semiconducting thermocouple plates instead of a series of wire thermocouples. This important modification was introduced by Wadso in 1968 [161], The thermocouple plates have a high thermal conductivity and a low electrical resistance and are sensitive to temperature differences of about 10-6 K. Their high thermal conductivity ensures that the heat transfer occurs fast enough to avoid the need for the Peltier or Joule effects. 

An apparatus with high sensitivity is the heat-flow microcalorimeter originally developed by Calvet and Prat [139] based on the design of Tian [140]. Several Tian-Calvet type microcalorimeters have been designed [141-144]. In the Calvet microcalorimeter, heat flow is measured between the system and the heat block itself. The principles and theory of heat-flow microcalorimetry, the analysis of calorimetric data, as well as the merits and limitations of the various applications of adsorption calorimetry to the study of heterogeneous catalysis have been discussed in several reviews [61,118,134,135,141,145]. The Tian-Calvet type calorimeters are preferred because they have been shown to be reliable, can be used with a wide variety of solids, can follow both slow and fast processes, and can be operated over a reasonably broad temperature range [118,135]. The apparatus is composed by an experimental vessel, where the system is located, which is contained into a calorimetric block (Figure 13.3 [146]). 

A Tian—Calvet heat-flow microcalorimeter which, due to the 480 thermocouples of its thermopile, ensures all at once a good isothermicity of the experiment and a high sensitivity allowing to use a small sample (for an activated carbon, typically 50-100 mg) relatively easy to wet. 

The measurement of the heat of adsorption by a suitable calorimeter is the most reliable method for evaluating the strength of adsorption (either physical or chemical). Tian-Calvet heat-flow microcalorimeters are an example of high sensitivity apparatus which are suitably adapted to the study of gas-solid interactions when connected to sensitive volumetric systems [10-14, 50-55]. Volumetric-calorimetric data reported in the following were measured by means of either a C-80 or MS standard heat-flow microcalorimeter (both by Setaram, F), connected to ahigh vacuum (residual pressure... 

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. 

Other instruments include the Calvet microcalorimeters [113], some of which can also run in the scanning mode as a DSC. These are available commercially from SETARAM. The calorimeters exist in several configurations. Each consists of sample and reference vessels placed in an isothermally controlled and insulated block. The side walls are in intimate contact with heat-flow sensors. Typical volumes of sample/reference vessels are 0.1 to 100 cm3, The instruments can be operated from below ambient temperatures up to 300°C (some high temperature instruments can operate up to 1000°C). The sensitivity of these instruments is better than 1 pW, which translates to a detection limit of 1 x 10-3 W/kg with a sample mass of 1 g. 

Very high sensitivity and the concomitant use of minute samples justify the descriptor microcalorimeter for many heat flow instruments. In general, a calorimeter can be labeled a microcalorimeter when its sensitivity is better than 10 (xW. Note, however, that some authors adopt a tighter definition, indicating 1 (x W as the sensitivity upper limit [160], The cell volume is usually in the range of 0.5-25 cm3. 

Microcalorimetry has gained importance as one of the most reliable method for the study of gas-solid interactions due to the development of commercial instrumentation able to measure small heat quantities and also the adsorbed amounts. There are basically three types of calorimeters sensitive enough (i.e., microcalorimeters) to measure differential heats of adsorption of simple gas molecules on powdered solids isoperibol calorimeters [131,132], constant temperature calorimeters [133], and heat-flow calorimeters [134,135]. During the early days of adsorption calorimetry, the most widely used calorimeters were of the isoperibol type [136-138] and their use in heterogeneous catalysis has been discussed in [134]. Many of these calorimeters consist of an inner vessel that is imperfectly insulated from its surroundings, the latter usually maintained at a constant temperature. These calorimeters usually do not have high resolution or accuracy. 

Standard heat capacities of transfer can be derived from the temperature dependence of standard enthalpies of solution (8). While this technique can give general trends in the transfer functions from water to mixed solvents (9), it is not always sufficiently precise to detect the differences between similar cosolvents, and the technique is rather laborious. Direct measurements of the difference between heat capacities per unit volume of a solution and of the solvent a — gq can be obtained with a flow microcalorimeter (10) to 7 X 10 5 JK 1 cm-3 on samples of the order of 10 cm3. A commercial version of this instrument (Picker dynamic flow calorimeter, Techneurop Inc.) has a sensitivity improved by a factor oi about two. 

The essential requirements for the application of this direct method are a sensitive microcalorimeter (preferably of the heat-flow type, as described in Section 3.2.2) combined with equipment for the determination of the amount adsorbed. Although the assemblage of the apparatus is somewhat demanding, once the effort has been made the advantages of calorimetry are as follows ... 

Immersion calorimetry has much to offer for the characterization of powders and porous solids or for the study of adsorption phenomena. The technique can provide both fundamental and technologically useful information, but for both purposes it is essential to undertake carefully designed experiments. Thus, it is no longer acceptable to make ill-defined heat of immersion measurements. To obtain thermodynamically valid energy, or enthalpy, or immersion data, it is necessary to employ a sensitive microcalorimeter (preferably of the heat-flow isothermal type) and adopt a technique which involves the use of sealed glass sample bulbs and allows ample time (usually one day) for outgassing and the subsequent temperature equilibration. 

The high sensitivity of the latest versions of flow microcalorimeter permits accurate determination of the heats of adsorption produced by the injection of nanomole quantities of solutes into the carrier liquids. This means that the heats of adsorption can be determined on solids having very low specific surface areas, or, on the other hand, the differential heats can be obtained at very low surface coverages for high surface area adsorbents. 

The best-known calorimeter of this type was developed by Tian and Calvet (Fig. 17). Here the defined heat-conduction path to the thermostated surroundings (a large aluminum block) consists of a large number of differential thermocouples coupled in series (thermopile). This arrangement permits optimum determination of the heat flow rate to the surroundings, and such an instrument can be very sensitive (microcalorimeter). 

At the times when the classical calorimeters were built, no computers existed and all evaluation was done by hand. Therefore, there was a need for simple formulas to calculate the quantities of interest from the measured curves. The construction of the calorimeters was such to give a signal strictly proportional to the heat flow rate into the sample itself with a calibration factor almost not influenced by the heat transfer to the sample and its heat capacity. The price to be paid for this comfort was a rather low sensitivity of the calorimeter with a need for large samples and large time constants in the range from some seconds up to many minutes in the case of very sensitive microcalorimeters (see Section 7.9.2). 

Single microbes produce a very small metabolic heat of 1-3 pW per cell, which cannot be detected even with the most sensitive calorimeter. But the exponential replication of bacteria in culture allows their detection in sensitive so-called microcalorimeters. To decide whether a product is infected or not, it is sufficient to put it in a calorimeter vessel under ideal growth conditions at 37 °C. If the material is aseptic, no signal will develop, but in the presence of germs, an exothermic heat flow rate will be measured. To identify the different relevant bacteria, it is necessary to follow the growth behavior of the culture and see whether they can be distinguished from one another. Furthermore, the detection limit (the minimum bacteria concentration) has to be determined, and the significance of the measurement for different contaminations has to be proved. 

In order to establish the correct functioning of the microcalorimeter, which is then connected to the volumetric adsorption unit, the sensitivity is evaluated determining the calorimeter constant. The calibration constant reports the voltage generated by the calorimeter when a heat flow is emitted from inside the micro-calorimetric cell. There are two methods to determine the calibration constant K by application of electric power and by the stationary method [9, 10]. 

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