Non-isothermal methods

In this method, data are obtained for reaction proceeding at a series of different heating rates [539,560,561]. This reduces the advantage of the non-isothermal method and one might just as well perform a series of isothermal measurements for which the subsequent analysis will be both more accurate and much simpler. Use of the technique can be illustrated by reference to the work of Ozawa [561] which is quoted as typical. The Doyle equation [eqn. (25)] above can be written... 

Solid-state reactions have usually been studied either by isothermal or by non-isothermal methods, with few attempts to combine the advantages of these alternative and sometimes complementary approaches. For reasons stated in Chap. 3, the kinetic information obtained from isothermal studies appears to be more accurate and reliable, and these studies are emphasised in this review. Wherever appropriate, however, account is taken of non-isothermal studies as a valuable source of complementary information. 

The lanthanide formates decompose above 670 K [1040] and the chemical changes proceed through the oxyformate [1041] and the oxy-carbonate to Ln203. Values of E determined by non-isothermal methods [1040] decreased with increase in atomic number for reaction in air but were approximately equal for reactions in vacuum. 

It is believed [1135,1136] that the decomposition of metal complexes of salicyaldoxime and related ligands is not initiated by scission of the coordination bond M—L, but by cleavage of another bond (L—L) in the chelate ring which has been weakened on M—L bond formation. Decomposition temperatures and values of E, measured by several non-isothermal methods were obtained for the compounds M(L—L)2 where M = Cu(II), Ni(II) or Co(II) and (L—L) = salicylaldoxime. There was parallel behaviour between the thermal stability of the solid and of the complex in solution, i.e. Co < Ni < Cu. A similar parallel did not occur when (L—L) = 2-indolecarboxylic acid, and reasons for the difference are discussed... 

The second section will concentrate on methods of determining phase diagrams. The first part will examine non-isothermal methods, such as differential thermal analysis and cooling curve determinations, while the second will concentrate on isothermal methods, such as metallography, X-ray measurements, etc. The various limitations of both methods will be discussed and some novel techniques introduced. 

The accuracy of some isothermal techniques, particularly those that rely on observation of phases, is limited by the number of different compositions that are prepared. For example, if two samples are separated by a composition of 2at%, and one is single-phase while the other two-phase, dien formally the phase boundary can only be defined to within an accuracy of 2at%. This makes isothermal techniques more labour intensive than some of the non-isothermal methods. However, because it is now possible to directly determine compositions of phases by techniques such as electron microprobe analysis (EPMA), a substantially more quantitative exposition of the phase equilibria is possible. 

Gonzalez, J. L., and Salvador, F. (1984), Comparative studies of non-isothermal methods in Unear and non-linear temperature variation, React. Kinet. Catal. Lett., 25(1-2), 125-130. 

Litwinienko, G, Kasprzyska-Guttman, T., and Studzinski, M. 1997. Effects of Selected Phenol Derivatives on the Autoxidation of Linolenic Acid Investigated by DSC Non-Isothermal Methods. Thermochim. Acta., 307, 97-106. 

The survey of the investigations and results covers the release of water from salts and hydroxides, the calcination of carbonates and oxalates, the reactions of metallic oxides and carbonates with SO2, and reactions on the surface of carbon. The application of the non-isothermal method to the thermal decomposition of carboxylic acids and polymeric plastics as well as to the pyrolyses of natural substances, in particular bituminous coal, is explained. Finally, chemical reactions in a liquid phase, the desorption of gases from solids, annihilation processes in disturbed crystal lattices and the emission of exo-electrons from metallic surfaces are discussed. 

Up to now the preparation of calibration methods to analyse permanent gases has finished. Two different non isothermal methods have been prepared. The first one is meant to be used when gases pass directly through the gas chromatograph. The second one analyses gases collected in sample bags and therefore at a lower pressure. The methods use two packed columns connected in series (10 Ft Porapak N, 80/100 GR 5.3 packed column and 6 Ft Molecular Sieve 5 A 60/80 MESH packed column). 

Isothermal and non-isothermal methods provide complementary routes to a common objective, the determination of the kinetic parameters for a selected... 

If reversibihty is ignored, the significance of reported Arrhenius parameters is diminished because of a possible compensation effect dependent on reaction conditions [93,168], Assessment of the reUability of measured Arrhenius parameters, particularly when using non-isothermal methods, requires demonstration that they are not dependent upon experimental variables, other than temperature, such as sample mass, etc. Evidence that a reaction is (or is not) reversible... 

The heat of polymerization of acrylonitrile has been reported as around 18 kcal/mole. Joshi (12), using an isothermal distillation calorimeter (13) at 74°C, determined values of 18.3 and 18.5 kcal/mole for bulk polymerization and for polymerization in benzene solution, respectively these values are about 1 kcal/mole higher than those reported previously by Tong and Kenyon (13) for bulk polymerization. Baxendale and Madras (14) used a non-isothermal method to determine a value of 18.3 kcal/mole for the polymerization of 5% aqueous solutions at 25°C. The lowest reported value is that of Suzuki, Miyama, and Fujimoto (10) 16.0 kcal/mole at 20°C. The highest reported value is that of Chiu (11) 20.5 kcal/mole for bulk polymerization. This last result was apparently obtained at a temperature of 140°C so the equivalent value for a temperature of 60°C would probably be slightly lower. 

Numerous studies have been performed in this field during the last few decades. A non-isothermal method, traditionally used in thermal analysis was applied to measure the rate constants, which were then used in an Arrhenius plot to determine the E parameter. The magnitude of E has been compared with the enthalpies (A Ef ) of various possible reactions and this was used to elucidate the actual atomization mechanism. In spite of this, the mechanism of matrix modification, as well as some other evaporation/atomization problems, still remains unrevealed. 

Two methods (15) of using these transducers can be identified. The first method, the most widely used in commercial gas detectors, is a non-isothermal method. In this case the temperature of the sensing element is allowed to rise as a result of chemical reaction at the catalyst surface and the rate of reaction, and hence the concentration of flammable gas is derived from the increase in temperature. In the second method the temperature of the sensing element is maintained constant during the reaction, and the reaction rate is obtained in terms of a difference in electrical power dissipation of the element under reacting and non-reacting conditions. 

In the non-isothermal method the catalytically active sensing element and a similar but catalytically inert element form two arms of a Wheatstone s bridge. Power is supplied to the circuit to heat the elements to their operating temperature, and the values of the fixed resistors selected such that the bridge balances in air. When flammable gas is passed over the elements, reaction takes place on the sensing element, imparting power to the element and thus... 

The non-isothermal method does, however, have advantages which have ensured that it has been the most widely applicable method in the past. These are simplicity of circuitry, direct voltmeter display and compensation for variations in ambient conditions. The isothermal method has been used successfully for several fundamental studies (18,19), and is now beginning to be exploited in practical devices where rapid response is required (14). 

The crystallization kinetics of amorphous materials can be investigated either isothermally or non-isothermally by using thermal analysis techniques. In the isothermal method, the sample is heated above the glass transition temperature and the heat absorbed during the crystallization process is measured as a function of time. On the other hand, in the non-isothermal method, the sample is heated at a fixed rate and then the change in enthalpy is recorded as a function of temperature. Thermal analysis techniques such as differential thermal analysis (DTA) and differential scanning calorimetry (DSC) are quite popular for kinetic analysis of crystallization processes in amorphous solids (Araujo Idalgo, 2009 Malek, 2000 Prasad Varma, 2005). 

Fig. 16. Computation of the volume fraction crystallized, x, in non-isothermal method (Celikbilek et al., 2011 Prasad Varma, 2005)...

Therefore, this chapter covers the investigation of the crystallization kinetics of amorphous materials by studying the crystallization mechanism in terms of isothermal and non-isothermal methods and describing different thermal analysis techniques used in crystallization kinetic studies and explaining the structural characterization techniques used to determine the crystallization mechanism... 

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