Differential thermal analysis theory

Smothers, W. J., and Y. Chiang Differential Thermal Analysis Theory and Practice. Chem. Publishing Co., New York (1958). 

David, D.J. Determination of specific heat and heat of fusion by differential thermal analysis. Study of theory and operating parameters, Aural Chem., 36(11) 2162-2166, 1964. 

There are several different types of instrument covered under the term DSC, which have evolved from differential thermal analysis (DTA) and measure the temperature difference between sample and reference pans located in the same furnace. This is then converted to heat flow using a calibration factor. A detailed analysis of DSC requires consideration of the various sources of heat loss, and these are generally captured in the calibration routine for the instrument. Absolute temperature calibration is achieved through the use of pure indium (156.6 °C) and tin (231.9 °C) melting-point standards. A comprehensive analysis of the theory of DSC contrasted with DTA may be found in several reference works (Richardson, 1989, Gallagher, 1997). 

The porous and amorphous structure of the resulting oxide overlayer is also interesting to discuss. The differential thermal analysis showed that at least six water molecules per C03O4 are involved in the overlayer structure. This is not surprising when one deals with a hydrous metal hydroxide layer, and the fact that such a structure behaves as amorphous in x-ray diffractometry does not preclude the existence of the crystalline domains of dimensions lower than 5x5 nm. The catalytic activity of this system is probably explained better in terms of the local interactions of the oxygen molecules with the cations of the oxide by considering a microscopic approach based on the quantum-chemical theory of the chemical bond in the small-sized solid clusters. 

The first question of any solid-state chemist thinking in terms of structure and energetics will definitely be What is the stable polymorph, mercury carbodiimide, HgNCN(I), or mercury cyanamide, HgNCN(ll) Unfortimately, it is impossible to answer this question by means of differential thermal analysis because both polymorphs decompose, prior to interconversion, at about 230 °C to yield a white polymer and mercury metal. Thus, theoretical reasoning and/or electronic-structure theory is needed. Let us attempt to argue using both classical and quantum-chemical means. 

DETERMINATION OF SPECIFIC HEAT AND HEAT OF FUSION BY DIFFERENTIAL THERMAL ANALYSIS. STUDY OF THEORY AND OPERATING PARAMETERS. 

Wunderlich B (1971) Differential Thermal Analysis. In Weissberger A, RossiterBW, eds Physical Methods of Chemistry, Vol 1, Part V, Chapter 8, pp 427-500. Wiley, New York. Debye P, Huckel E (1923) The Theory of Electrolytes. I. Lowering of Freezing Point and Related Phenomena. Physikal. Z 24 185-206 see also your favorite Physical Chemistry... 

With this link between the microscopic and macroscopic description of matter securely established, the next chapter of the book will concentrate on the description of the various theories needed for the understanding of thermal analysis, namely equilibrium and irreversible thermodynamics and kinetics. The Introduction will then be completed with a summary of the specific functions needed for the six basic branches of thermal analysis thermometry, differential thermal analysis, calorimetry, thermomechanical analysis, dilatometiy, and thermogravimetiy. 

With this brief discussion of the functions needed for thermal analysis and the basic theories of the description of matter we are now ready to treat the various thermal analysis techniques one at a time. In this text we start with the simplest measurement, thermometry, go to the most basic techniques, differential thermal analysis and calorimetry, and finish with thermomechanical analysis, dilatometry, and thermogravimetry. Each of the techniques is illustrated with a selection of problems fi om various applications of thermal analysis. An effort has been made to cover as many types as possible, but also to try to avoid any duplication of the description of the phenomena to be measured. A detailed discussion of any particular aspect of melting, for example, will thus only be given for the techniques where it can most easily be measured. If other techniques can achieve the same, reference will be made to where the full description is given. 

Reuter, J. Buesing, D. Tamarit, J. L. Wiirflinger, A. High-pressure differential thermal analysis of the phase behavior in some rm-butyl compounds, J. Mater. Chem. 1997,7,41 6. This paper also discusses some phenomenological theories of crystal melting (like the Pople-Karasz theory, 1961) that take into account orientational disorder in the solid, based on ideas presented in 1939 by Lennard-Jones and Devonshire. The essential parameter of such a theory is the ratio of the barriers to reorientation and to diffusion, which is also a measure for the anisotropy in molecular shape. 

Despite the delay and difficulties in derivation of a suitable theoretical treatment for differential thermal analysis, it is clear that such derivations have not only justified certain aspects that had been empirically established—such as the relationship between peak area and amount of reactant and the necessity for dilution of the specimen with reference material— but have also revealed aspects that were not fully appreciated—such as the fact that the proportionality relationship holds strictly only for a ATf curve and the importance of heat conduction along thermocouple wires. Further developments in quantitative application obviously depend on designing experimental conditions compatible with those demanded by theory Wilburn [1972]. 

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