Non-isothermal Kinetic Analysis Method
Solid state kinetics lays its foundation on the basis of the experiments that are carried out in absolute isothermal conditions. However, although it is known that thermally activated processes involve gradual heating up of the reactants and the reactions
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Non-isothermal Kinetic Analysis Method
Solid state kinetics lays its foundation on the basis of the experiments that are carried out in absolute isothermal conditions. However, although it is known that thermally activated processes involve gradual heating up of the reactants and the reactions progress under rising and fluctuating temperature conditions, conventional kinetic studies were confined to only isothermal conditions due to limitation of performing. In addition, the mathematical procedures developed for analysing non-isothermal kinetic data contain numerous approximations, assumptions and controversies [1–5]. These procedures fail to reflect the characteristics of a realistic situation. In addition to this, a priori knowledge of the reaction mechanism is required. The reaction mechanism is either assumed or identified by carrying out isothermal kinetic experiments. The methods [6–9] most widely used to evaluate activation energy from the non-isothermal calorimetric data are also based on a particular type of assumed mechanism. Nonetheless, characteristic reaction mechanism(s) do exist for all the reactions occurring under non-isothermal conditions. Therefore, the development of a more reliable and accurate non-isothermal kinetic analysis method is long overdue. In the present study, it has been shown that the actual reaction mechanism under non-isothermal conditions can be directly identified unambiguously through a newly developed technique.
3.1 Identification of the Kinetic Law The analysis is based on the fact that the general kinetic equation for solid state processes is generally represented by gðaÞ ¼ kðT Þt
ð3:1Þ
where g(a) is the reaction mechanism and is expressed as an appropriate function of fractional reaction (a), k(T) is the specific rate constant at a specified temperature T and t is the time [10]. Here, the fractional conversion (a) values are required to be recorded against rising temperature T at different heating rates. The variation in P. Deb, Kinetics of Heterogeneous Solid State Processes, SpringerBriefs in Materials, DOI: 10.1007/978-81-322-1756-5_3, The Author(s) 2014
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Non-isothermal Kinetic Analysis Method
fractional conversion as a function of temperature at specified heating rate bi can be expressed conveniently by a relationship of the type abi ¼ ubi ðT Þ
ð3:2Þ
where abi is the fractional conversion at a heating rate bi at temperature T and ubi (T) is an appropriate function of temperature and is the heating rate identity. Therefore, at any intermediate temperature within the limits of experimental temperature range abi can be easily evaluated by using spline interpolation technique [11]. During the non-isothermal experimentation, a linear rise in temperature can be represented by Tf ¼ Ti þ bi tbi
ð3:3Þ
where Ti is the starting temperature of the reaction corresponding to the heating rate bi and tbi is the time spent in attaining the desired temperature Tf. Therefore, tbi ¼ Tf Ti =bi : ð3:4Þ Now, considering any one of the experimental heating rate bn
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