J. Viñals

Thermogenesis: Identification by means of pade approximants

Abstract The paper describes how to obtain an analytic approximation to the transfer function of a conduction calorimeter, namely, a procedure to identify the calorimetric system. In this case Pade approximants are used on the Laplace transform of the thermogram. The feasibility of the method is tested on two models which span the frequency range usually attained by actual calorimeters. The influence of random noise and baseline drift have also been analyzed. The results show that three or four time constants are correctly obtained.

Thermogenesis: response given by calorimeters whose physical parameters change in time

Abstract The response given by conduction calorimeters whose physical parameters change in time is analysed in terms of heat transport equations particularly through “localized time constants” or RC models including variable coefficients. The results obtained in simple models exhibit several anomalies concerning the sensibility of the device: its value usually differs from that given by classical models and also from the temperature of the stationary state (corresponding to a constant power release inside the laboratory cell). These facts could question the standard calibration procedures in the case of phase transitions and liquid mixtures.

Thermogenesis: Relative kinetic limits

Abstract This work presents kinetic limits for conduction calorimeters taken from experimental data and given in reduced units (ν τ 1 ). Two different criteria are proposed concerning either a full reconstruction of a rectangular heat pulse (used in calibration procedures) or a complete separation of elementary pulses to provide a fair reconstruction of the thermogenesis. These upper limits are given for several signal to noise ratios.

Thermogenesis: deconvolution in non time-invariant calorimetric systems

Abstract Most conduction calorimeters do not behave, strictly speaking, as time invariant systems (e.g., calorimeters used to study titrations). In this communication the performance of standard deconvolutive techniques applied on thermograms calculated from discrete variable models is analysed (RC models whose physical parameters change with time). Secondly, two new algorithms are developed which yield the power released inside the calorimetric cell even when the parameters of the system are changing during the experiment. The first algorithm takes advantage of the system of differential equations ruling the time evolution of the discrete model whereas the second deals with inverse filters with variable time constants. In the cases studied, both methods produce equivalent results.

Thermogenesis: Smoothing techniques in Z-transform and harmonic analysis

Abstract This work analyses how the standard smoothing techniques affect the thermogenesis given by harmonic analysis or Z-transform methods. The analysis has allowed an optimization of their efficiency. The results concerning signal/noise ratios of 40, 60, 80 and 100 dB are tabulated and generalized to a reduced frequency representation.

Thermogenesis: Harmonic analysis and universal transference function

Abstract This work considers how the ratio signal/noise and the introduction of a cut-off frequency affect the calculus of the thermogenesis. In particular, the validity of the experimental criterion used to calculate this frequency inside the deconvolutive calculus is studied. The deconvolutive efficiency of the universal transference function is also presented comparatively.

Thermogenesis: experimental approach to a reduced transference function

The dynamic treatment of conduction microcalorimeters must be accomplished through their transference function (TF). A systematic analysis of experimental TFs belonging to calorimeters whose dynamic characteristics are quite different (the first time constants ratio is roughly 16) shows: 1. in order to verify the relative dynamic characteristics it is convenient to use a reduced representation of modulus (dB) and phase (rad) against a reduced scale ντ 1. Such a representation between 0 and 30 dB does not depend on the laboratory cell and the kind of detector: 2. in this representation, TFs associated with materials of high conductivity coincide within the range 0 < ντ1 < 4. For materials of low conductivity, the TFs group in the range 0 < ντ1 < 1. It seems feasible, then, to use a reduced TF irrespective of the type of calorimeter.

Thermogenesis: determination of thermokinetic parameters

Abstract This work analyses the performance of the method of obtaining the time constant (rate reaction constant) defining a first-order process after the deconvolution of the experimental record given by a heat conduction calorimeter. The analysis is carried out for different signal/noise ratios and the results given in relative time and frequency scales.

Verification of calorimetric models based on physical parameters by frequential characteristics

Abstract Quantitative criteria to ascertain the quality of calorimetric models based on physical parameters are presented. These include not only a comparison between model and experimental pulse responses, especially for the larger time constants, but also an analysis of their spectra up to the frequential limit brought about by the experimental noise. A calorimetric model based on the physical parameters of a Unipan 600 calorimeter is used to reconstruct a given power dissipation. The results are then compared to those given by other methods, i.e. dynamic optimization, inverse filtering and harmonic analysis.

Microcalorimetrie et thermogenese: Identification des dispositifs experimentaux permettant de mesurer directement les enthalpies d'exces

Abstract Heat-conduction microcalorimetry is an interesting technique for measuring excess enthalpies at very high dilution. The deconvolution of the instrumental response is, however, strictly necessary. In this paper, the results of a comparative application of two techniques giving a good representation of the transfer function of the calorimetric system are presented.