Equivalent-circuit modeling of a heat-flux differential scanning calorimetry cell. Analysis of thermal resistance factors and comparison with experimental data

Abstract

An equivalent-clrcult model Is presented for a commerclal heat-flux dlff erentlal scanning calorlmetry (DSC) cell. Thls model Is developed In a form that permlts dlrect comparlson wlth experlmental data. The varlous thermal resistance factors In the cell are computed vla this model. Comparlsons of model predlctlons wlth experlmental data are presented for the melting endotherms of In, Sn, and Zn. I n partlcular, the Influence of varlables, such as the heatlng rate and the thermal characterlstlcs of sample and the purge gas atmosphere, Is crltlcally examlned. Thls study demonstrates for the first time, both vla model as well as by experiments, the Importance of heat exchange between the sample and reference channels and heat leakage through the purge gas.Differential scanning calorimetry (DSC) is rapidly becoming a powerful tool in the arsenal of techniques that is currently available to the analytical chemist ( I ) . However, theoretical developments have lagged somewhat behind the many innovations that have characterized the practical application of this technique. For example, equivalent-circuit models have been presented by many authors for the description of DSC systems, both of the heat-flux type (2-6) as well as of the power-compensation design (7,8). However, in the majority of cases, the model implications were developed within a framework that rendered direct testing via experimentation a difficult task. The main contribution of this paper, thenefore, is the development and experimental testing of an equivalent-circuit model for a commercial DSC cell of the heat-flux type. We focus in particular on the various resistance factors in this cell and their sensitivity to variables such as heating rate, sample characteristics, and purge gas atmosphere.A Du Pont 1090 Thermal Analysis System fitted with the Model 910 DSC accessory module, was used in this study. The software supplied by the manufacturer was used for the most part for the analyses of DSC thermograms. All fusion endotherms were recorded only after one or two initial "conditioning" heat-cool cycles through the transition. mmmercial samples of In, Sn, and Zn (99.999% purity or better) were used as received. The purge gas was flushed through the DSC cell at the rate of ca. 80 mL/min. Sealed sample pans were used in all the cases. The sample sensor thermal resistance was varied by inserting an A1 disk in the sample and reference pan bottoms. These disks were fashioned out of the Al pans supplied by the manufacturer. Programmed heating rates were nominally in the range from 1 'C/min to 40 'C/min, for the results presented herein. In selected instances, heating rates down to 0.2 "C/min were utilized to check thermal lag effects. Nominal sample mass was ca. 10 mg. THEORYThe starting point for our model development utilizes, as in previous studies (2,9,10) two basic relationships, namely one describing the conservation of energy and the other arising from the linear dependence of heat-flow on temperature differential (Newton's law). Figure 1 presents this...

Computer simulation of differential scanning calorimetry: influence of thermal resistance factors and simplex optimization of peak resolution

“…The manner in which thermal resistances manifest themselves in the morphology of a DSC thermogram perhaps is best treated in terms of electrical equivalent circuits (2, [5][6][7][8][9]. Figure 1 illustrates the equivalent circuit thát was used by us earlier (2) for a DSC cell of the heat-flux type. In Figure 1, Ts is the sample temperature, TR is the reference temperature, TP is the heater (source) temperature, TSH is the sample platform temperature, TRH is the reference platform temperature, Rq is the thermal resistance between heater and sample (or reference) platforms, fig is the thermal resistance between temperature sensor and sample, fiR is the thermal resistance between temperature sensor and reference, Rq' is the thermal resistance of the disk between sample and reference platforms, fiG is the gas thermal resistance between heater and sample (or reference), and Rq is the gas thermal resistance between sample and reference.…”

“…Expressions for the endotherm slope, S, as well as the endotherm amplitude, H, are also available from our model (2) as follows:…”

“…dq/dt = g(TRH -TSH). Because of the above difficulties, we have chosen to use largely our earlier model (2) to generate the required simulation parameters.…”