The results of a muitinational concerted programme on the determination of thermokinetics are presented. The purpose of the programme was to compare different numerical methods which have been independently proposed for the determination of thermokinetics from experimental calorimetric data. To achieve this end, the same experimental data, obtained from two heat-flow calorimeters, were distributed and successively analyzed by the different methods. Numerical methods based on the state function theory, on Fourier transform analysis, on dynamic optimization and on a simple differentiation of the data were thus critically tested.During the last few years, dynamic calorimetry has developed significantly. Its function is to determine not only the total heat effect associated with the thermal phenomenon under study, but also the changes of thermal power with time, the "thermoyenesis" W(t) [1 ], expressed by dQ(t) W(t) -dt where Q is the amount of evolved heat and t is the time. Since the reaction progress and the associated heat effects are simultaneous, any calorimetric measurement in which W(t) is correctly determined can be a source of information on the kinetics of the reaction under study. However, experimental calorimetric data, i.e. directly or indirectly temperature changes vs. time O(t), never exactly correspond to W(t). Because of thermal lags in the calorimeter, a distortion always occurs. Hence, in order to reconstruct W(t) from O(t), it is necessary to define a relation between these functions:
W(t) = M[O(t)](1) Several methods [1-5] have been proposed for the determination of thermokinetics, which make use of a Ist-order differential equation. However, these methods are not adapted to the study of rapidly changing heat effects, measured in
A vertebra from the Albian of Mesnil-Saint-Père (Aube, eastern Paris Basin), previously identified as the first caudal of a sauropod dinosaur, is shown to be a dorsal vertebra of a large pliosaur. The specimen resembles vertebrae from the Albian of England and eastern France that have been referred to the pliosaur Polyptychodon, a taxon in need of revision.
A simple method for removing the distortion due to thermal lags from calorimetric curves is described and tested. The method is based upon the use of numerical inverse filters. Its results are equivalent to those of the more sophisticated deconvolution methods, using Fourier transform analysis or state function theory. The new method is easily adapted to the on-line reconstruction of calorimetric data by means of a microprocessor.The calorimetric determination of the kinetics of fast reactions is often hindered by the distortion in the calorimetric curves which is caused by thermal lags in the instrument.However, several methods are available to correct ("to reconstruct") the calorimetric curves:(1) a graphical method [1 ]; (2) (automatic) analog methods [2][3][4][5][6][7]; (3) numerical methods, based on Fourier transform analysis [8][9] or state function theory [10][11][12].The graphical methods is simple and yields acceptable results. However, its application requires long and strenuous work which, moreover, must be accomplished after the calorimetric data have been completely collected ("off-line") [1 ].Correction by analog methods can be achieved "on-line". Results are good; however, the instruments performing the reconstruction must be manually adjusted for each calorimeter and even for each new experiment. Moreover, the analog signal should be amplified when a multi-stage correction system is used, with an unavoidable increase of the noise level [2][3][4][5][6][7].Numerical methods also yield good results. When Fourier transform analysis is used, the correction must be achieved off-line and, in the case of long experiments, a medium-sized computer (,,~ 16 Kbytes for 2000 points) must be available [8][9]. The representation of the calorimetric system (calorimeter and dataacquisition line) by state functions and the resulting data reconstruction may be performed on-line [10][11][12]. The method requires a smaller-sized memory than the method based on Fourier transform analysis. However, both numerical methods are equally sensitive to noise in the data.
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