J. Ortin

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: identification by means of modulating functions

Abstract This 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 modulating functions are used directly on the thermogram. The method is used twice: to obtain the time constants and the amplitudes. Its feasibility 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: identification and deconvolution in microcalorimetric systems with continuous injection for the study of liquid mixtures

The results obtained by means of different identification methods, tested on the experimental thermograms of calorimeters with a continuous injection device, are compared. The experimental system is specially suited to investigating the thermodynamic properties of mixtures. Particular attention is devoted to defining the conditions that allow a satisfactory approach to the transfer function of the system at the beginning of the injection. The accuracy of such an approach determines that of the excess enthalpies measured at large dilutions.

Thermogenesis: An approach to nearly exact deconvolution in time-varying systems

Abstract Particular experimental conditions in calorimetry of mixing by continuous injection of a reactant open the possibility of building a simple model to study the performance of such devices. The characteristic equations of the model lead to an exact formulation of a deconvolutive procedure based on variable inverse filtering. The way in which the parameters of the filter may be obtained from experimental work is established.

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.

Deconvolution in microcalorimetry and an application to mass-varying systems

The behaviour of the calorimetric response in continuous injection devices, which are well suited for measurement of excess partial molar enthalpies at different concentrations, is analysed by means of heat transport models. Signal analysis of the thermal response gives the enthalpy values at very low concentrations. We establish an operating routine for the identification of the time-varying device, and a generalized deconvolution procedure to obtain, with high accuracy, the power released in the calorimeter as a function of time. The main features considered are the changes in sensitivity and dynamic properties of the experimental system due to the injection of one component in the mixture. A formal decomposition of the heat transport equations shows that typically time-invariant methods are able to deal with deconvolution in non-invariant systems.