hi,

pay attention the the macromolecular mobility effect, which induces a decrease of some termination rate constants. see:

Thermooxidative aging of polydicyclopentadiene in glassy state. Polymer Degradation and Stability, Volume 102, April 2014, Pages 95-104

by E. Richaud, PY Le Gac, J Verdu

regards

Hi Dr Flor,

There was an article by the ICTAC comittee:

doi:10.1016/j.tca.2011.03.034

In which this matter is discussed. Personally in my work I have found that non-isothermal kinetics is as accurate as isothermal. Several "ease-of-use"  reasons of non-isothermal kinetics makes it the prefer method for many researchers. 

I also realise there are good arguments for using isothermal methods instead, but it's rather the exception, than the rule, that these (isothermal) methods give superior results.

regards,

The formalized methodology of nonisothermal kinetics using thermoanalytical methods does not necessarily guarantee the reliability of the kinetic parameters evaluated experimentally. We should more seriously approach to the actual reaction phenomena occurring in the solid state. We are still continuing this challenging for making our methodology to be useful in modern material sciences.

In my opinion the situation has not changed very much. The mentioned problems are still matter of discussion. And solid state kinetics is not an easy task. The question whether isothermal is "better" than non-isothermal kinetic analysis seems me in this context of secondary order.

In older methods for the evaluation of kinetic parameters, many approximations are applied so that the kinetic parameters were very unreliable. There are newer approaches, please see the papers attached.

Actually I have a related question. In case of reactions it is sometimes problematic to perform "isothermal" tests. It is impossible to heat the sample to the selected temperature immediately. Either we use maximum heating rate where we have temperature overshoot, or we heat up the sample linearly and keep it constant afterwards. In both cases it is hard to select the "zero" time for kinetic calculations. I remember two cases when I met this difficulty: one was an epoxy composite study, the other was a polymerization kinetics measurement. Non-isothermal tests with scanned temperatures can be performed easily but (especially if the kinetics is complicated and cannot be described by a single empirical equation) the data processing is more complicated.

In reply to the question of Gyorgy Banhegyi. I solved, in a satisfactory way, the “zero” time problem, in a thermal dehydration study with TGA, replacing the original furnace with a red light source focused on the sample, and controlled by a proper unit. This allowed to reach the working temperature in not more than 30 sec. (see G. Flor, V. Berbenni and A, Marini Z. Naturforsch.,34a, 1117 ,1979).

Dear Dr Flor - this is a good idea, but it is not provided with standard thermoanalytical systems.

And you should have in mind, that real isothermal conditions don't exist in reality, there is always a temperature field and a temperature gradient inside the sample which is needed for the heat to flow. consequently the measured signal is "smeared" (i.e. the convolution product of different reaction rates at different places with different temperatures inside the sample). You should know all these conditions to get precise knowledge of the reaction in question. (By the way similar problems exist also for non-isothermal methods).

(1) If the reaction under investigation is fulfilled with the prerequisite of the fundamental kinetic equation of solid-state reaction and the kinetic rate data that are free form the undesired effect of mass and heat transfer phenomena. The isothermal and nonisothermal methods including other sample controlled methods are equally useful for the kinetic analysis. This ideal situation can be realized in the practical kinetic study. For example; doi: 10.1021/jp2094017

 Even in this case,  the kinetic calculation should be logically designed for avoiding the possible distortion of the kinetic parameters due to the mutual dependence of these parameters as a mathematical consequence. In this ideal case, we do not need take care the zero time in the isothermal kinetic rate data, because the kinetic rate data at any temperature profiles can be analyzed on the basis of the fundamental kinetic equation (differential form). doi: 10.1021/jp0022205

(2) Even if the reaction were approximately described on the basis of single step assumption, the kinetic rate data in which the mass and heat transfer phenomena are negligible are not easy to obtain, Therefore, large cares must be taken to trace the kinetic behavior using thermal analysis. In this point, isothermal measurements are suitable for the purpose of the kinetic analysis in comparison with the nonisothermal measurements, because in general the lower the reaction rate is the lower the gradients in partial pressure of evolved gas and temperature during the reaction. Sample controlled thermal analysis, especially constant rate thermal analysis, can be more suitable. The recommendation of the ICTAC kinetic committee address this problem: doi: 10.1016/j.tca.2014.05.036

However, the recommendation of the ICTAC kinetic committee is just to support the researchers who use the kinetic analysis by thermal analysis as a tool for characterizing their samples and reactions. Specialists are more carefully addressing this problem. For example, in our case, we use nearly 100 runs for publication of one kinetic article, but behind the study a larger number of preliminary thermoanalytical runs have been carried out to find the region of sample and measurement conditions applicable to kinetic analysis. This is because the criteria of the appropriate sample and measurement conditions depends on the sample and reaction under investigation. Please visit my profile in RG.

(3) Even the kinetic measurements have been carried out with great care, many reaction is far from the idealized single step reaction that is described as the functions of only temperature and fractional reaction (alpha). Many other factors influence on the kinetic behavior and the reaction is in many cases a overlapping multistep reaction in the kinetic meanings. doi:10.1016/s0040-6031(02)00051-5. If we apply the kinetic analysis based on the single step assumption to such real reaction process, the determined kinetic parameters are largely distorted showing the variation of the kinetic parameters as the reaction advances and even negative activation energy. In a strict sense, these kinetic parameters can not have physical significance. However, it is not easy to model the real kinetics of the complex reaction system. Therefore, the just apparent kinetic parameters are used to discuss some characteristics of the reaction through a kind of correlation analysis. Although I do not support the terminology, in this case the superficial kinetic parameters are sometimes called as effective kinetic parameters.

(4) A certain practical significance should be admitted for the approaches in (4); however, it is apparent that the reliability of the approach is limited. Therefore, we should seek a possibility to solve the problem in more rigorous  way. doi: 10.1007/s10973-012-2882-5. The kinetic deconvolution analysis is one of such trails to find the possible physical and chemical factors that influence the kinetic behavior. doi: 10.1007/s10973-012-2500-6

Although this approach is also just empirical, we expect to obtain many useful information concerning the solid-state reaction through the challenging and contribute notably towards the provision of a theoretical foundation for the further understanding of solid-state reactions. Please find our recent publications.

(5) In conclusion, our challenging is endless.

Please comment. Thank you very much in advance.

Very interesting and challenging question. Galwey (and others) made a number of important  papers on this subject, and in my opinion, he rightly poinetd that the theory for solid state reaction (and more generally kinetics), requires new developments.

See A. K. Galwey. What theoretical and/or chemical significance is to be attached to the magnitude of an activation energy determined for a solid-state decomposition ? J. Therm. Anal. Calorim. 2006,86(1),267-286