Papers by Constantine Sandu
Thermochimica Acta, Jul 1, 1985
Based upon the signals of a DSC record, the equation of the transition baseline is analytically d... more Based upon the signals of a DSC record, the equation of the transition baseline is analytically developed for a DuPont 990 thermal analyzer. The equation accounts for the effects on the transition baseline originating from (1) pretransition baseline, (2) heat-capacity change from that of the reactants to that of the products of reaction and (3) the fact that the sample material is subject, during the transition state, to a heating rate which differs from that of the reference material. If there is no change in heat capacities and either the heating rate or the heat transfer resistance are very small, then the transition baseline is merely an extension of the pretransition baseline. Any departure from these conditions makes the calculation of the transition baseline necessary, if correct kinetic parameters are to be expected from a DSC curve.
Thermochimica Acta, 1990
Abstract The present study is a unified mathematical approach to the analysis of DSC data. It add... more Abstract The present study is a unified mathematical approach to the analysis of DSC data. It addresses the baseline correction to the DSC record as well as the solutions of DSC curves of single or multiple, physical and chemical transformations. In this study, previous results in the pertinent literature become particular solutions of the general model. The transition baseline in a physical transformation is identical with the instrumental signal. When an ‘empty’ reference pan is used and the results are extrapolated to zero heating-rate, a pseudo-baseline can be defined. Physical transformations in DSC display a straight line signal during transition, followed by an exponential curve during the post-transition state. The model gives solutions for temperature and heat of transformation in both single and multiple physical transformations. The equation of the transition baseline in a chemical transformation accounts for: the pre-transition baseline; the heat-capacity change from that of the reactants to that of the products of the reaction; and the heating-rate difference between sample and reference materials. If there is no change in the heat capacities and either the reference pan is ‘empty’ or the thermal resistance is negligible, then the transition baseline is an extension of the pre-transition baseline. The DSC curve represents the corrected DSC record. The DSC curve of a chemical transformation is a bell-shaped graph whose skewness depends on the order of reaction. From the distinctive features of the DSC curve (i.e., relations at curve peak, inflection points and curve-bounded area), the apparent kinetic parameters are calculated (order of reaction, activation energy, pre-exponential factor and heat of reaction). The parameters specifically involved in these calculations are: peak temperature, inflection point temperature(s), shape index, area before peak, area after peak, asymmetry index, peak area and partial areas. The larger the asymmetry index, the smaller the reaction order. Final solutions contain the heating rate and the initial concentration (initial amount of reactant) as parameters. A zero-order chemical reaction displays an exponential signal and its solutions are particular. Two multiple reaction systems in DSC are analyzed: (a) two irreversible, first-order, parallel reactions, and (b) two irreversible, first-order, consecutive reactions. In the first case, the apparent kinetic parameters correlate with the area before the maxima/minima of the DSC curve. In the second case, the main parameter is the deflection at the maxima/minima. General-order, mechanistically uncoupled reactions are also discussed. Emphasis is placed on the assumptions and the analytical development as well as on the final solutions and their applicability range. The mathematics of physical transformations are referenced with time as an independent variable, whereas chemical transformations relate to temperature. No attempt was made to express the final solutions in both time and temperature coordinates.
Thermochimica Acta, Sep 1, 1988
... 1982. 2 C. Sandu and D. Lund, Thermochim. Acta, 88 (1985) 453. 3 AP Gray, in RS Porter and JF... more ... 1982. 2 C. Sandu and D. Lund, Thermochim. Acta, 88 (1985) 453. 3 AP Gray, in RS Porter and JF Johnson (Eds.), Analytical Calorimetry, Vol. 1, Plenum, New York, 1968. 4 E. Kamke, Differentialgleichungen. Losungsmethoden ...
Mathematical Modelling in Science and Technology, 1984
Abstract A set of equations, derived from the DSC-curve, is presented to calculate apparent kinet... more Abstract A set of equations, derived from the DSC-curve, is presented to calculate apparent kinetics-parameters including order of reaction, activation energy, heat of reaction, and preexponential factor. The model assumes a homogeneous chemical reaction in a liquid system, characterized by one single extent of reaction. The mathematics of the model is based on the features of the DSC-trace, that is, peak, shape, first inflection-point, and area under the curve, as functions of two main process parameters: heating rate and initial concentration of the reactant. Finally, linear or non-linear regression analysis has to be applied to some of the experimental data to obtain the kinetic parameters. Analysis of DSC-data by our model is best suited for the DSC-equipment having computerized data acquisition and processing.
Thermochimica Acta, 1988
... 1982. 2 C. Sandu and D. Lund, Thermochim. Acta, 88 (1985) 453. 3 AP Gray, in RS Porter and JF... more ... 1982. 2 C. Sandu and D. Lund, Thermochim. Acta, 88 (1985) 453. 3 AP Gray, in RS Porter and JF Johnson (Eds.), Analytical Calorimetry, Vol. 1, Plenum, New York, 1968. 4 E. Kamke, Differentialgleichungen. Losungsmethoden ...
Thermochimica Acta, 1990
Abstract The present study is a unified mathematical approach to the analysis of DSC data. It add... more Abstract The present study is a unified mathematical approach to the analysis of DSC data. It addresses the baseline correction to the DSC record as well as the solutions of DSC curves of single or multiple, physical and chemical transformations. In this study, previous results in the pertinent literature become particular solutions of the general model. The transition baseline in a physical transformation is identical with the instrumental signal. When an ‘empty’ reference pan is used and the results are extrapolated to zero heating-rate, a pseudo-baseline can be defined. Physical transformations in DSC display a straight line signal during transition, followed by an exponential curve during the post-transition state. The model gives solutions for temperature and heat of transformation in both single and multiple physical transformations. The equation of the transition baseline in a chemical transformation accounts for: the pre-transition baseline; the heat-capacity change from that of the reactants to that of the products of the reaction; and the heating-rate difference between sample and reference materials. If there is no change in the heat capacities and either the reference pan is ‘empty’ or the thermal resistance is negligible, then the transition baseline is an extension of the pre-transition baseline. The DSC curve represents the corrected DSC record. The DSC curve of a chemical transformation is a bell-shaped graph whose skewness depends on the order of reaction. From the distinctive features of the DSC curve (i.e., relations at curve peak, inflection points and curve-bounded area), the apparent kinetic parameters are calculated (order of reaction, activation energy, pre-exponential factor and heat of reaction). The parameters specifically involved in these calculations are: peak temperature, inflection point temperature(s), shape index, area before peak, area after peak, asymmetry index, peak area and partial areas. The larger the asymmetry index, the smaller the reaction order. Final solutions contain the heating rate and the initial concentration (initial amount of reactant) as parameters. A zero-order chemical reaction displays an exponential signal and its solutions are particular. Two multiple reaction systems in DSC are analyzed: (a) two irreversible, first-order, parallel reactions, and (b) two irreversible, first-order, consecutive reactions. In the first case, the apparent kinetic parameters correlate with the area before the maxima/minima of the DSC curve. In the second case, the main parameter is the deflection at the maxima/minima. General-order, mechanistically uncoupled reactions are also discussed. Emphasis is placed on the assumptions and the analytical development as well as on the final solutions and their applicability range. The mathematics of physical transformations are referenced with time as an independent variable, whereas chemical transformations relate to temperature. No attempt was made to express the final solutions in both time and temperature coordinates.
Biotechnology Progress, 1985
Page 1. Minimizing Fouling in Heat Exchanger Design Fouling dynamics of heat exchangers - an anal... more Page 1. Minimizing Fouling in Heat Exchanger Design Fouling dynamics of heat exchangers - an analysis of the prevention methods. Constantine Sandu and Daryl Lund, Department of Food Science, University of Wisconsin-Madison ...
Biotechnology Progress, 1986
Constantine Sandu, Department of Food Science, University of Wisconsin-Madison, Madison, Wisconsi... more Constantine Sandu, Department of Food Science, University of Wisconsin-Madison, Madison, Wisconsin 53706 ... When incident upon a physical hody, the radiation in the wavelength range 0.10-100 pin generates heat. The spec-trum of thermal radiation is mostly covered ...
Biotechnology Progress, 1985
The paper describes the physical and mathematical fundamentals of dynamic gravimetry in liquid ph... more The paper describes the physical and mathematical fundamentals of dynamic gravimetry in liquid phase. First, a relation is developed to calculate the apparent weight of a vertical thin cylinder partially immersed Into a liquid. It emphasizes the magnitude of buoyancy forces and surface-tension forces (which act upon fine threads used to suspend a solid object completely immersed into a liquid). Next, the basic relation of dynamic gravimetry is derived to estimate the absolute mass of adsorbed material onto the surface of a submerged solid object. This relation encompasses, apart from the term related to the measured output signal of the balance, three correction terms which originate from the surface tension effects, buoyancy effect of the submerged object, and buoyancy effect due to the adsorbed material.The following sections address adsorption at the air-liquid interface as well as the molecular diffusion process (both being intermingled with concentration and density gradients in the system). Special attention is given to the errors connected with a series of relaxation processes in which the external menisci, the plate-beam system, and the surface tension are involved once their equilibrium conditions are disturbed. The time constants of these relaxation processes can not be exactly predicted. The paper concludes with an experimental illustration of dynamic gravimetry, with the adsorption of beta-lactoglobulin onto stainless steel plates. The validity of predictions based upon the physico-mathematical fundamentals is reconciled with the analytical and technical aspects and difficulties specific to dynamic gravimetry.
Food technology, 1991
RefDoc, THE reference in scientific document supply / Refdoc, la référence en fourniture de docum... more RefDoc, THE reference in scientific document supply / Refdoc, la référence en fourniture de documents scientifiques ...
Thermochimica Acta, 1985
Based upon the signals of a DSC record, the equation of the transition baseline is analytically d... more Based upon the signals of a DSC record, the equation of the transition baseline is analytically developed for a DuPont 990 thermal analyzer. The equation accounts for the effects on the transition baseline originating from (1) pretransition baseline, (2) heat-capacity change from that of the reactants to that of the products of reaction and (3) the fact that the sample material is subject, during the transition state, to a heating rate which differs from that of the reference material. If there is no change in heat capacities and either the heating rate or the heat transfer resistance are very small, then the transition baseline is merely an extension of the pretransition baseline. Any departure from these conditions makes the calculation of the transition baseline necessary, if correct kinetic parameters are to be expected from a DSC curve.
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Papers by Constantine Sandu