Non-isothermal Measurement

An abrupt start to a large release of heat and its frequent and intensive fluctuation in the measuring kettle also causes in the intermediate thermostat a prolonged disturbance in the controlled equilibrium due to the thermal inertia. 

Because of the small amount of injected mass, pst2 — Pst2w and (k F)2 = (k f )2v are valid, and the combination of both relations gives 

The final temperature T2oo can differ somewhat from the initial temperature T2v (Fig. 6.1) 

Therefore, sometimes it is necessary to obtain the exact equality of T and T v hy physical means. In particular is the case where the generally small heat of a mixture Qui must be determined. For such a problem it is advisable to install in the stirring shaft a closed chamber with the liquid batch flowing around it in the measuring 

To calculate Q, we must know the accurate heat capacity of the mixture C2. The usual method used to determine it is labour intensive and prone to error. Hence, for the exact estimation of Qm another way is preferred  

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Constant rate thermo gravimetry has been described [134—137] for kinetic studies at low pressure. The furnace temperature, controlled by a sensor in the balance or a pressure gauge, is increased at such a rate as to maintain either a constant rate of mass loss or a constant low pressure of volatile products in the continuously evacuated reaction vessel. Such non-isothermal measurements have been used with success for decomposition processes the rates of which are sensitive to the prevailing pressure of products, e.g. of carbonates and hydrates. 

The techniques referred to above (Sects. 1—3) may be operated for a sample heated in a constant temperature environment or under conditions of programmed temperature change. Very similar equipment can often be used differences normally reside in the temperature control of the reactant cell. Non-isothermal measurements of mass loss are termed thermogravimetry (TG), absorption or evolution of heat is differential scanning calorimetry (DSC), and measurement of the temperature difference between the sample and an inert reference substance is termed differential thermal analysis (DTA). These techniques can be used singly [33,76,174] or in combination and may include provision for EGA. Applications of non-isothermal measurements have ranged from the rapid qualitative estimation of reaction temperature to the quantitative determination of kinetic parameters [175—177]. The evaluation of kinetic parameters from non-isothermal data is dealt with in detail in Chap. 3.6. 

Isothermal and non-isothermal measurements of enthalpy changes [76] (DTA, DSC) offer attractive experimental approaches to the investigation of rate processes which yield no gaseous product. The determination of kinetic data in non-isothermal work is, of course, subject to the reservations inherent in the method (see Chap. 3.6). 

Non-isothermal measurements of the temperatures of dehydrations and decompositions of some 25 oxalates in oxygen or in nitrogen atmospheres have been reported by Dollimore and Griffiths [39]. Shkarin et al. [606] conclude, from the similarities they found in the kinetics of dehydration of Ni, Mn, Co, Fe, Mg, Ca and Th hydrated oxalates (first-order reactions and all values of E 100 kJ mole-1), that the mechanisms of reactions of the seven salts are probably identical. We believe, however, that this conclusion is premature when considered with reference to more recent observations for NiC204 2 H20 (see below [129]) where kinetic characteristics are shown to be sensitive to prevailing conditions. The dehydration of MnC204 2 H20 [607] has been found to obey the contracting volume... 

Although the decompositions of FeS04 and Fe2(S04)3 have received considerable attention, there is a lack of close agreement between isothermal and non-isothermal measurements [528]. Kinetic parameters are sensitive to the nature of the prevailing atmosphere and the particular salt preparation used [381]. The decomposition of iron(II) sulphate [319, 381,524] in vacuum or in an inert atmosphere (748—848 K) proceeds with the transitory formation of the intermediate Fe202(S04), viz. 

There have been comparatively few kinetic studies of the decompositions of solid malonates [1103]. The sodium and potassium salts apparently melt and non-isothermal measurements indicate second-order rate processes with high values of E (962 125 and 385 84 kJ mole-1, respectively). The reaction of barium malonate apparently did not involve melting and, from the third-order behaviour, E = 481 125 kJ mole-1. 

From non-isothermal measurements, based on apparent first-order obedience, values of E for the overall reactions were 528 and 302 kJ mole-1 for the Na and K salts, respectively. During dehydration at 450 K, Rochelle salt formed [1104] a mixture of separate crystallites of the Na and K salts which then decomposed as above. 

The corresponding chromium compounds [Cr(en)3]X3 evolve ethylenediamine [1131] and the values of E determined using non-isothermal measurements were 105 and 182 kJ mole 1 for X = Cl" and SCN", respectively. Hughes [1132] reported a value of E = 175 kJ mole"1 for X = Cl" and showed that the decomposition rate is sensitive to sample disposition. Amine evolution from both the (en) and propenediamine (pn) compounds was catalyzed by NH4C1 [1132,1133] or NH CN [1133,1285], addition of small amounts of these substances resulting in a substantial reduction of E. The influence of NH4C1 is ascribed [1132] to the dissociation products, since HC1 promoted the reaction but NH r and NH4I showed no such effect. 

It is apparent, from the above short survey, that kinetic studies have been restricted to the decomposition of a relatively few coordination compounds and some are largely qualitative or semi-quantitative in character. Estimations of thermal stabilities, or sometimes the relative stabilities within sequences of related salts, are often made for consideration within a wider context of the structures and/or properties of coordination compounds. However, it cannot be expected that the uncritical acceptance of such parameters as the decomposition temperature, the activation energy, and/or the reaction enthalpy will necessarily give information of fundamental significance. There is always uncertainty in the reliability of kinetic information obtained from non-isothermal measurements. Concepts derived from studies of homogeneous reactions of coordination compounds have often been transferred, sometimes without examination of possible implications, to the interpretation of heterogeneous behaviour. Important characteristic features of heterogeneous rate processes, such as the influence of defects and other types of imperfection, have not been accorded sufficient attention. 

While non-isothermal measurements can provide a rapid and useful qualitative indication of the occurrence of one or more reactions and the main features of behaviour (such as reaction temperatures, phase transitions, melting etc.), the method cannot be recommended as providing the most accurate kinetic data, particularly when the reaction is reversible. 

Thermal decomposition was performed using a SDT Q-600 simultaneous DSC-TGA instrument (TA Instruments). The samples (mass app. 10 mg) were heated in a standard alumina 90 il sample pan. All experiments were carried out under air with a flow rate of 0.1 dm3/min. Non-isothermal measurements were conducted at heating rates of 3, 6, 9, 12, and 16 K/min. Five experiments were done at each heating rate. 

The determination of absolute or ideal energies of activation is handicapped by the fact that the variation of the cell temperature introduces undertainties either at the reference electrode—solution interface, when both working and reference electrodes are at the same temperature, or from the thermal liquid junction potential in a non-isothermal measurement [5,36]. 

The situation becomes more complicated if experiments are carried out in non-isothermal conditions. First of all,many non-isothermal measurement procedures are possible. The selection of a particular method depends on the process characteristics and methods of interpretation. Scanning calorimeters, which measure the quantity of heat released as the ambient temperature is varied linearly. The rate of temperature change can be varied by the experimenter. 

Non-isothermal measurements may enable steps in a sequence of chemical processes to be distinguished in what might otherwise be incorrectly regarded as a single reaction. 

Flynn [34] has emphasized the importance of using accurate calculated data for the temperature integral in determining the magnitudes of E, and A fi om non-isothermal measurements. He points out that modem computer methods make the use of approximations unnecessary. 

Non-isothermal measurements (Chapter 2) have yielded valuable information about reaction temperatures and the successive steps in the removal of water from crystalline hydrates, e g. oxalates [14], sulfates [15-17]. DTA and DSC studies have sometimes provided additional information on the recrystallization of the dehydrated product [18]. The problems of relating kinetic parameters obtained by non-isothermal measurements to those from isothermal experiments are discussed in Chapter 5. The effects of heat transfer and diffusion of water vapour may be of even greater consequence in non-isothermal work. Rouquerol [19,20] has suggested that some of the above problems may be significantly decreased through the use of constant rate thermal analysis. 

The dehydration of MnC204.2Fl20 in air and in nitrogen (373 to 473 K) was described [135] by the contracting volume equation with E = 10 k3 mol" . Similar values were obtained from non-isothermal measurements. Recrystallization of the product to give crystalline anhydrous salt may occur more readily at higher reaction... 

Many of the experimental studies of the thermal decompositions of coordination compounds have been restricted to non-isothermal measurements primarily directed towards identification of the occurence of a reaction and the characterization of the major products of this change. The improved sensitivity of experimental methods (notably TG and DSC or DTA) has revealed the chemical complexity of the thermal reactions of solid coordination compounds. Much comparative information concerning the relative reactivities of related materials has been obtained. While... 

The kinetics of processes with a latent heat, such as crystallisation and melting, can be measured either directly by isothermal or non-isothermal measurement of the latent heat or by observation of the change of the heat... 

The activation energies for the decomposition of sodium n-propoxide and sodium iso-propoxide derived from the isothermal data are slightly higher than those of non-isothermal data. There could be two possible reasons (1) the temperature ranges of the isothermal and non-isothermal measurements are not the same and (2) the initial stage of decomposition under isothermal conditions includes a retardation period and also the specimen experiences a non-isothermal condition till the isothermal temperature is reached. Similar observations are reported in the literature [58,67]. 

The following heats of physicochemical processes can be determined by means of both isothermal and non-isothermal measuring modes using the previously described apparatus. 

However, providing the materials that can be made reproducibly, these problems do not prevent the application of the principles of polymer physics to the analysis of crystallisation in these systems. It is interesting to note that this type of crystallisation, observable on the DSC, will also occur in commercial products, such as confectionery chew-like materials with a porous aerated structure. With this industrial aspect in mind, it is relevant to develop methods to measiue crystallisation rates. Methods for isothermal and non-isothermal analysis exist to do this. These methods are considerably easier in fats where there are no difficult-to-control variables, such as the level of plasticiser/water. Nevertheless this has been attempted in sucrose using the approach of Chan et al. [31, 32]. Rates were obtained for experiments on isothermal crystallisation of amorphous sucrose [33] and crystallisation exotherms were measured from DSC curves scanned at different rates. Shift factors were then calculated for both isothermal and non-isothermal measurements and are plotted in Figure 9.9. 

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