Heat flow signal

As pointed out in Section 8.2, most physical and chemical processes, not just the chemical transformation of reactants into products, are accompanied by heat effects. Thus, if calorimetry is used as an analytical tool and such additional processes take place before, during, or after a chemical reaction, it is necessary to separate their effects from that of the chemical reaction in the measured heat-flow signals. In the following, we illustrate the basic principles involved in applying calorimetry combined with IR-ATR spectroscopy to the determination of kinetic and thermodynamic parameters of chemical reactions. We shall show how the combination of the two techniques provides extra information that helps in identifying processes additional to the chemical reaction which is the primary focus of the investigation. The hydrolysis of acetic anhydride is shown in Scheme 8.1, and the postulated pseudo-first-order kinetic model for the reaction carried out in 0.1 M aqueous hydrochloric acid is shown in Equation 8.22 ... 

Figure 9.2 Recorded data (pressure and heat flow signals) for each dose of probe molecule as a function of time.

A variation of DSC is the MDSC (modulated DSC), wherein heat is applied sinusoidally, such that any thermal events are resolved into reversing and nonreversing components to allow complex and even overlapping processes to be deconvoluted. The heat flow signal in conventional DSC is a combination of... 

From these equations it can be seen that key quantities that can affect the measured heat flow signal in a DSC are ... 

The effect of heating rate on the DSC heat flow signal will be considered in more detail in Subsection 2.4.2. However, it is useful to consider this parameter in terms of calibration protocols. Figure 2.1 shows the onset temperature of the melting peak of indium at seven different heating rates. As the heating rate increases, the thermal lag between the furnace and the sample increases. From Figure 2.1 it can... 

Monitor the heat flow signal and wait for it to stabilize. 

The heat capacity component can then be removed from the averaged modulated heat flow to produce a kinetic heat flow signal. The heat capacity and the kinetic heat flow signals are often described (respectively) as the reversing and nonreversing contributions to the traditional heat flow signal, as measured in traditional DSC experiments. 

Dealing with simple deconvolution first, it can be seen from Equation 4.3 that the heat flow signal is composed of two sets of terms. The first, Cp(b + Bto costow)), is dependent on the magnitudes of the terms b, B, and to (all experimental rather than sample parameters) but has no sample dependence other than the value of Cp. Consequently, this first term is a measure of the sample s heat capacity (as defined previously) and, except in the case of the glass transition (see later discussion), can be considered, for the purposes of this discussion, to be an effectively instantaneous sample response. If we focus on the modulation, we see that this is a cosine wave as opposed to the sine wave in the temperature. This means that, when there is no transition, the modulation in heat flow will, in principle, follow this cosine wave (the modulation in heating rate) with zero phase lag when the convention is adopted that endothermic is up. It will be 180° out of phase when the convention is adopted that endothermic is down. 

The underlying heat flow signal is calibrated by the use of standards with known melting temperatures and enthalpies of fusion. A series of such samples is run over the operating temperature range of the instrument. The sample thermocouple has a nominally known relationship between its output and temperature. Any observed differences between measured (by the sample thermocouple) and expected melting... 

In most cases the heat flow signal approaches the base line almost asymptotically. If the upper integration limit is fixed at a time value which does not coincide with the moment at which the reaction has reached completion, because the signal cannot clearly be distinguished fi om base line noise anymore, the value determined for the gross enthalpy of reaction will be too small. Some reactions will never achieve complete conversion under the conditions proposed for the process. Possible reasons for such a situation may be, for example, chemical equilibria, pH-value dependent inhibitions, or solubility limits. 

The individual calorimeters may be distinguished on one hand by the number of possible modes of operation and on the other hand by the way the heat flow signal is determined. An overview is provided in the following Table 4-7. 

Figure 12. TPR profiles (heat-flow signal v. temperature) of high-loading supported tin dioxide samples [145].

The reversing component of the total heat flow signal is equal to Cpfi. The non-reversing component is the arithmetic difference between the total heat flow and the reversing component ... 

However, the sum of these signals is quantitative. Linearity is maintained in the baseline, permitting accurate measurement of the onset as well as the end of the endothermic and exothermic events [3]. Melting and crystallization neither start nor end at the same temperatures and therefore different integration limits are required. Finally, the total heat flow signal is quantitatively correct regardless of the modulation conditions. Thus the initial crystallinity of the sample can be estimated by TMDSC (see Table 5.1). The data presented in Table 5.1 reveal that the observed initial crystallinity is approximately constant under various experimental conditions. 

Table 5.1. Effect of experimental conditions on the reversing and non-reversing heat flows in the melt region. The sum of the heat flow signals is quantitative and is defined as the initial crystallinity of the quenched PET sample (courtesy of TA Instruments Inc.)...

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