The Calorimetric Signal

Calorimeters essentially record power as a function of time by a direct measurement or by conversion from temperature changes. Both kinetic and thermodynamic information is accessible from the same calorimetric data set. The calorimetric signal, power as a function of time, is a measure of the rate of the reaction as shown in (23)  

The reaction rate, defined as dx/dt, is proportional to the quantity of reactant that is available for reaction. For solution reactions, the reaction volume V should be included in the equation. Equation (25) describes a reaction where (A) reacts to form (B) in a single mechanism  

The integral of equation (27) provides a relationship between power and time, the calorimetric signal  

It is possible to derive the parameters n, k, and AH from the calorimetric data and hence predict the course of a reaction from start to finish. Equation (28) is useful for simulating calorimetric data, where values of k, AH, A, V and n can be used to construct a model calorimetric curve 

These types of equations can be applied to more complex reaction schemes such as sequential reactions,parallel reactions and solid state reactions.Table 1 shows some of the reaction schemes where such equations can be written. 

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If the assumptions made above are not valid, and/or information about the rate constants of the investigated reactions is required, model-based approaches have to be used. Most of the model-based measurements of the calorimetric signal are based on the assumption that the reaction occurs in one single step of nth order with only one rate-limiting component concentration in the simplest case, this would be pseudo-first-order kinetics with all components except one in excess. The reaction must be carried out in batch mode (Vr = constant) in order to simplify the determination, and the general reaction model can, therefore, be written as Equation 8.14 with component A being rate limiting ... 

CALORIMETRIC MEASOREMEMTS Solution calorimetry was performed at 298.2 0.1 K by using a C-80 differential flux calorimeter manufactured by Setaram. The energy equivalent of the calorimetric signal was determined by electric calibration. The reliability of the equipment was checked by the dissolution of tris-(hydroxymethyl) aminomethane (THAM). Agreement within 0.4% with the published value of +17.75 kJ. mol-1 ( 21) was obtained. 

Finally, the systematic determination of the time constants (or thermokinetic parameters) of the calorimetric signal peaks gives information on the diffusion... 

The objective of this work is to simulate an industrial process on a bench scale, allowing a wide spectrum of operation conditions and measurements. Taking into account the complexity of the process as well as the fact that the calorimetric signal reflects the sum of physicochemical changes in the reaction system, an additional on-line mini-spectrometer (OceanOptics, S2000 spectrometer) for simultaneous in situ measurements as well as some off-line data furnished by TMDSC and gravimetric measurements have been used. 

Note that it is not possible to distinguish kinetically between different rapid (with respect to the time constant of the instrument) reactions, i.e. the calorimetric signal appears zero order in nature regardless of the actual reaction order. 

In the pulse flow method, the procedure consists of the injection of a precise and well-defined gas volume (probe molecule + carrier gas) into the stream which flows through the catalyst bed held on flie fritted glass of a specially designed calorimetric cell. For each pulse, the calorimetric signal is recorded and the amount of gas which has not been retained by the catalyst is measured by a gas chromatogr h (or mass spectrometer) connected on-line to flie calorimetric cell. The major disadvantage of this technique is that the weakly chemisorbed portion of the probe gas is not held by the catalyst and gives rise to an endothermic peak of desorption which follows immediately the exothermic peak of adsorption, and thus necessitates peak deconvolution. 

To express such behavior, the calorimetric signal must shift, starting from the initial instant, from a value representing a post-reaction equilibrium where V = 0 to the value corresponding to the initial rate V = a, which in this case equals 40. 

After the leaetion has taken off, it is possible to observe other situations due especially to the existence of a stationary process. In such a case, the calorimetric signal will be constant at a value lower than or equal to the initial value. 

A point worth noting is that introducing additional oxygen has practically no effect on the calorimetric signal. 

The role played by metals can be interpreted by considering the formation of a new exothermic oxygen species whose bound amount constantly decreases while the temperature rises. The exothermic nature of this species makes it possible to explain why its contribution to the heat exchange continually decreases with temperature the calorimetric signal corresponding to the composite material of alumina + metal then joins up with the signal corresponding to alumina alone. 

From a kinetic point of view, the comparison between the calorimetric signal relative to the adsorption of the oxygenated species and the response of the sensor (see Figure 10.16) indicates that the endothermic species take abont as mnch time as the signal of the sensor to reach eqnilibrium. 

Figure 10.16. Comparison between the calorimetric signal and the response of a sensor placed in the same conditions, and comparison with the gradient of the sensor response as a function of time...

One of the main advantages of reaction calorimetry on the larger scale is the possibility of inserting into the reactor special analytical probes for on-line measurements. Some preliminary results obtained by coupling an ultrasonic sensor with calorimetry are presented in Fig. 5.17. The sensor is directly inserted into the reactor, its contribution in terms of heat accumulation having been previously determined so that the calorimetric signal is only related to the chemical reaction and process. At the moment, only the sound wave measurement is compared to the... 

In this method, first used by Navarro et al. [230, 231] and by van Bokhoven [232, 233], the convolution recorded in the frequency domain is accepted as the transformation equation [Eq. (2.8)] of the calorimeter. For the determination of an unknown heat effect, it is assumed that the spectrum transmittance H(jheat effect Px(t) is generated and the calorimetric signal Tx(t) is measured. After determination of the spectrum transmittance H(jcalorimeter response Tft), the thermokinefics Px(t) is obtained as the inverse Fourier transform... 

It is very important to observe that the response time of the calorimetric signals when a kinetic process occurs is much higher than in a typacal binding process. In this way, the catalyzed reaction progress can be followed from analysis of the calorimetric peaks (first or second injections). Thus, the reaction rate can be calculated since the heat flow (dQ/ dt) is directly proportional to the rate of reaction (Eq. 21). The area under each peak gives the... 

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