Some elements in specific heat capacity measurement and numerical simulation of temperature modulated DSC (TMDSC) with R/C network

One important application of temperature modulated DSC (TMDSC) is the measurement of specific heat of materials. In this paper, a thermal resistance/capacitance (R/C) numerical model is used to analyze the effects of experimental parameters and calibration on the measurement of specific heat in TMDSC under isothermal conditions. The actual TMDSC experiments were conducted with sapphire and pure copper samples, respectively. Both simulation and experiments showed that in TMDSC, the measured sample specific heat is a non-linear function of many factors such as sample mass, the heat transfer properties of the TMDSC instrument, temperature modulation period, the heat capacity difference between calibration material and the test material, but modulation amplitude has very little effect on the results. The typical behavior of a heat flux type TMDSC can be described as a low pass filter in terms of specific heat capacity measurement when the instrument heat transfer properties are taken into account. At least for metallic materials, where the temperature gradient inside the sample can normally be ignored, the sample should be chosen in such a way that its total heat capacity (mass times specific heat) is close to that of the calibration material in order to get a more accurate result. Also, a large modulation period is beneficial to improving the test accuracy.     

Experimental investigation into the heat capacity measurement using an modulated DSC

Experiments using a commercial modulated DSC (MDSC) for the measurement of specific heat capacity of a sample have been carried out. It is found that because the amplitude of heat flow of MDSC is a complicated non-linear function of various experimental conditions such as the modulation frequency and the heat capacities of a sample and pan, the methodology of heat capacity determination using an MDSC in a single run has not been justified. The experimental results, on the other hand, agree with the theoretical equation of one of the authors. It is therefore concluded that the capabilities of MDSC should be further examined.     

Low-temperature heat capacities and derived thermodynamic functions of cyclohexane

The low-temperature heat capacities of cyclohexane were measured in the temperature range from 78 to 350 K by means of an automatic adiabatic calorimeter equipped with a new sample container adapted to measure heat capacities of liquids. The sample container was described in detail. The performance of this calorimetric apparatus was evaluated by heat capacity measurements on water. The deviations of experimental heat capacities from the corresponding smoothed values lie within ±0.3%, while the inaccuracy is within ±0.4%, compared with the reference data in the whole experimental temperature range. Two kinds of phase transitions were found at 186.065 and 279.684 K corresponding solid-solid and solid-liquid phase transitions, respectively. The entropy and enthalpy of the phase transition, as well as the thermodynamic functions {H_(T)-H _{298.15 K}} and {S _(T)-S_{298.15 K}}, were derived from the heat capacity data. The mass fraction purity of cyclohexane sample used in the present calorimetric study was determined to be 99.9965% by fraction melting approach. This revised version was published online in July 2006 with corrections to the Cover Date.     

Measuring the Glass Transition of Thermosets by Alternating Differential Scanning Calorimetry

The glass transition temperature of thermosets is determined by alternating differential scanning calorimetry (ADSC), which is a temperature modulated DSC technique. The different values of the glass transition obtained from heat flow measurements (total and reversible) and heat capacity (modulus of the complex heat capacity) are analysed and compared with the values obtained by conventional DSC. The effect of the sample mass on the values of T_g, heat capacity and phase angle has been analysed. The effect of the thermal contact between sample and pan has been studied using samples cured directly inside the pan and disc-shaped samples of different thickness. The results obtained for the thermal properties and the phase angle are compared and analysed. The modulus of the complex heat capacity enables the determination of the dynamic glass transition, T_g, which is frequency dependent. The apparent activation energy ofthe relaxation process associated with the glass transition has been evaluated from the dependence of T_g on the period of the modulation.This revised version was published online in November 2005 with corrections to the Cover Date.     

Complex heat capacity measurements by TMDSC Part 1. Influence of non-linear thermal response

To treat data from temperature modulated differential scanning calorimetry (TMDSC) in terms of complex or reversing heat capacity one should know heat transfer and apparatus influences on experimental results. On the other hand one should pay attention that the response is linear because this is a prerequisite for data evaluation. The reason for non-linear thermal response is discussed and its influence on complex heat capacity determination is shown. The criterion for linear response is proposed. This allows to choose correct experimental conditions for any complex heat capacity measurements. In the case when these conditions cannot be fulfilled because of experimental restrictions one can estimate the influence of non-linear response on measured value of complex or reversing heat capacity.     

Finite-element calculations on the behaviour of a DSC in temperature-modulated mode

The influence of changes of sample properties on the amplitude and phase shift of the differential-temperature signal as well as the influence of frequency changes has been calculated for a one-dimensional model of a temperature-modulated DSC (TMDSC) using a computer program for finite-element-method (FEM) calculations. Amplitude and phase shift of the measured signal ΔT (which is proportional to the differential heat-flow rate) is strongly influenced by the heat capacity of the sample. The connection is only linear for rather small heat capacities. The influence of the heat-transfer coefficient between sample and sample pan on amplitude and phase shift of the signal is not so large and linear (within the framework of our calculations). The influence of the heat-transfer coefficient between sample and sample pan on amplitude and phase shift of the signal is not so large and linear (within the framework of our calculations). For precise measurements, a very careful “calibration” is needed, which must take all the aforementioned influences into account.     

An adiabatic low-temperature calorimeter for heat capacity measurement of small samples

A small sample adiabatic calorimeter for measuring heat capacities in the temperature range 60–350 K using the Nernst method has been constructed. The sample cell of the calorimeter is 6 cm³ in the internal volume, equipped with a miniature platinum thermometer and surrounded by two adiabatic shields. Two sets of 6-junction chromel-copel thermocouples were mounted between the cell and the shields to indicate the temperature differences between them. The adiabatic conditions of the cell were automatically controlled by two sets of temperature controller. A mechanical pump was used to pump out the vapour of liquid nitrogen in the cryostat to solidify N₂ (1), and 60 K or even lower temperature was obtained. The performance of this apparatus was evaluated by heat capacity measurements on α-alumina. The deviations of experimental results from a smoothed curve lie within ±0.2%, while the inaccuracy is within ±0.5% compared with the recommended reference data in the wole temperature range.     

Some remarks on heat capacity measurements by temperature-modulated calorimetry

In temperature-modulated calorimetry, the condition in sample amount, especially thickness, required for high-accuracy heat capacity measurement should be made clear. We propose the condition of maximum thickness of a sample for measuring heat capacity within an accuracy of 1%. The other important factor for high-accuracy heat capacity measurement is thermal contact conductance between a sample and a sample pan and also that between a pan and a base plate of an apparatus. The conditions in these thermal contact conductances required for high-accuracy heat capacity measurement are discussed. Among them, if only thermal contact conductance between a pan and a base plate is significant, there is an ingenious method to measure heat capacity with high accuracy. Furthermore, if the thermal contact conductance between a pan and a base plate is infinite, we offer a simple method to obtain complex heat capacity.     

Specific heat capacities of pure triglycerides by heat-flux differential scanning calorimetry

The specific heat capacities of some triglycerides commonly found in palm oil were determined with a heat-flux differential scanning calorimeter. The specific heat capacity measurements were made under the optimum operating conditions determined earlier: scan rate 17 deg·min^?1, sample mass 21 mg and purge gas (nitrogen) flow rate 50 ml/min. Pure triglycerides (four simple and four mixed) were used in the experiments. The four simple triglycerides were trilaurin, trimyristin, tripalmitin and tristearin, and the mixed triglycerides were 1,2-dimyristoyl-3-oleoyl, 1,2-dimyristoyl-3-palmitoyl, 1,2-dipalmitoyl-3-oleoyl and 1,2-dioleoyl-3-palmitoyl. The results of this study are compared with literature values and also with values obtained by using estimation methods. The experimental specific heat capacities are within ±1% precision with a 95% confidence level.     

Review of heat transport properties of solar heat transfer fluids

The present article reviews the test techniques for some of the important heat transport properties of oils such as viscosity, density, specific heat capacity and thermal conductivity mainly used for characterization of heat transfer fluids. It can be seen that while density of oils can be tested at higher temperatures, the other heat transport properties of oils like viscosity, specific heat capacity and thermal conductivity have a limitation of being tested at low temperatures below 100–150 °C. While quite a few number of researchers have reported evaluation of heat transfer properties like specific heat capacity and thermal conductivity of oils by different methods, there remains a huge scope of debate and discussions on the repeatability and reproducibility of such tests, especially in case of oils used in high-temperature applications. A lot of insight has been gathered with respect to testing of thermal conductivity of oils, and several common test methods have been compared with each other. Lastly, two mathematical models, reported in the literature in open domain, have been reviewed and compared with each other. If the oils are to be used at elevated temperatures, like heat transfer fluids used in concentrated solar power generation where temperatures go as high as 400 °C and beyond, there is an urgent need to standardize a laboratory test method for performance evaluation of heat transport properties, which can help in formulating new generation oils based on novel chemistries and technologies like nanofluids, synthetic oils of novel chemistries, molten salts and molten metals.     

Estimation of the heat capacity of individual substances on the basis of experimental enthalpy increments

A method of determination of the high-temperature (T > 298.15 K) heat capacity function of individual substances by differentiation of enthalpy increment measurements with respect to temperature has been suggested. The approach is based on approximation of enthalpy increment measurements by a polynomial without free term, which makes it possible to strictly meet the boundary conditions of differentiation determined by the properties of the enthalpy increment function. In combination with the Shomate method, the approach enables the optimal choice of the form of temperature dependence of heat capacity that is consistent best of all with the concepts of classical thermodynamics and provides the best reproducibility of enthalpy increment measurements. When low-temperature heat capacity measurements for individual substances are not available, i.e., the Shomate method is inapplicable, the suggested strategy makes it possible to obtain the heat capacity change function in the temperature range of enthalpy increment measurements and to estimate the heat capacity of the substance at standard temperature.     

Improved conditions for measurement of the specific heat capacities of pure triglycerides by differential scanning calorimetry

Reproducible specific heat capacities (C _p) of triglycerides can be obtained by using heat-flux DSC under improved operating conditions. The improved operating parameters, such as the scanning rate, the sample mass and the atmosphere within the DSC chamber, were established via statistical analysis of the experimental data with trilaurin as a sample. The specific heat capacity results on trilaurin were compared with the values calculated by using estimation methods. The precision of the specific heat capacity measured for trilaurin under these conditions was within ±1%.     

Development of heat capacity measurement system for single crystals of molecule-based compounds

We report on construction of a new low temperature heat capacity measurement system. This system was designed for performing thermodynamic investigation by thermal relaxation technique for small amount of samples at extremely low temperature region between 70 mK and 10 K. Two different calorimetry cells for this system were designed. One is a usual-type calorimetry cell consisting of tiny chip-type thermometer and strain gauge heater. The size of the sample stage has been reduced for measuring small samples. The other is designed for performing heat capacity measurements under magnetic fields of which magnitude and direction are accurately controlled. The calorimetry cells with heat capacity measurement unit can be mounted on a handy top-loading type dilution refrigerator of which outer diameter including the adiabatic space is 27 mm. We discuss basic performance and specification of the constructed cells and low temperature heat capacity data of an organic charge transfer salt obtained by this system.     

Experimental Evaluation of Procedures for Heat Capacity Measurement by Differential Scanning Calorimetry

Experimental evaluation of the procedures adopted for heat capacity measurements employing differential scanning calorimetry (DSC) has been carried out by taking nickel and sapphire as test samples. Among the various methodologies reported in literature, the absolute dual step method was chosen for this purpose due to its simplicity and minimum number of measurements required. By proper temperature and heat flux calibration employing indium as reference, it was possible to obtain the calibration factor independent of temperature. This was ascertained by analysing other pure metals namely Sn, Zn, Cd, and Pb and determining their melting temperatures and heats of melting. Various operator- and sample-dependent parameters such as heating rate, sample mass, the structure of the sample, reproducibility and repeatability in the measurements were investigated. Heat capacities of both nickel and sapphire have been determined using the above method. Further, the heat capacity of nickel has also been determined using the widely employed three-step method taking sapphire as the heat flux calibration standard. Both methods yielded the comparable heat capacity values for nickel. Based on the parameters investigated and their influence, it could be concluded that reasonably precise and accurate heat capacity measurements are possible with DSC. One advantage of this method is the elimination of a separate calibration run using a reference material of known heat capacity. This revised version was published online in August 2006 with corrections to the Cover Date.     

Study of temperature profile and specific heat capacity in temperature modulated DSC with a low sample heat diffusivity

One important application of temperature modulated DSC (TMDSC) is the measurement of specific heat of materials. When the sample has very good thermal conductivity as in the case of metals, the temperature gradient is not normally an important factor and can be ignored most of the time. However, in the case of materials with poor heat transfer properties, for example, polymers, the thermal conductivity is only in the order of 1/1000 or so of that of metals. This could have a major effect on the test results. In this paper, a round analytical solution is given and a numerical model is used to analyze the effects of thermal diffusivity on temperature distribution inside the test sample and specific heat measurement by TMDSC, PET sample test results are presented to demonstrate the effects of material thermal diffusivity.     

Modulated differential scanning calorimetry in the glass transition region

Temperature-modulated differential scanning calorimetry (TMDSC) is based on heat flow and represents a linear system for the measurement of heat capacity. As long as the measurements are carried out close to steady state and only a negligible temperature gradient exists within the sample, quantitative data can be gathered as a function of modulation frequency. Applied to the glass transition, such measurements permit the determination the kinetic parameters of the material. Based on either the hole theory of liquids or irreversible thermodynamics, the necessary equations are derived to describe the apparent heat capacity as a function of frequency.Presented in part at the 24th Conference of the Northamerican Thermal Analysis Society, San Francisco, CA, September 10–13, 1995.     

Particle dynamics and particle heat and mass transfer in thermal plasmas. Part II. Particle heat and mass transfer in thermal plasmas

This paper is concerned with a review of heat and mass transfer between thermal plasmas and particulate matter. In this situation various effects which are not present in ordinary heat and mass transfer have to be considered, including unsteady conditions, modified convective heat transfer due to strongly varying plasma properties, radiation, internal conduction, particle shape, vaporization and evaporation, noncontinuum conditions, and particle charging. The results indicate that (i) convective heat transfer coefficients have to be modified due to strongly varying plasma properties; (ii) vaporization, defined as a mass transfer process corresponding to particle surface temperatures below the boiling point, describes a different particle heating history than that of the evaporation process which, however, is not a critical control mechanism for interphase mass transfer of particles injected into thermal plasmas; (iii) particle heat transfer under noncontinuum conditions is governed by individual contributions from the species in the plasma (electrons, ions, neutral species) and by particle charging effects.     

Advanced two-channel ac calorimeter for simultaneous measurements of complex heat capacity and complex thermal conductivity

The advanced construction of a two-channel ac calorimeter for simultaneous measurements of frequency-dependent complex heat capacity C(ω) and complex thermal conductivity λ(ω) is presented. In the new calorimeter, the number of interfaces with thermal-wave reflections was reduced. Thus, the new construction can be easily calibrated with higher precision and is simpler in handling than the previous one. The new construction allows to measure thermal conductivity in steady-state mode, as well as frequency-dependent complex thermal properties in ac mode, in the same measuring cell. The capabilities of this technique were demonstrated, being applied for simultaneous measurements of complex effusivity, diffusivity, heat capacity, and thermal conductivity of glycerol in the glass transition region. The so-called ac and dc thermal conductivities of glycerol were measured as a function of temperature. It was shown that the double-channel ac calorimetry is a technique, which can be used for reliable distinguishing of relaxation processes related to relaxing thermal conductivity or relaxing heat capacity.In the region apart from phase transitions, the calorimeter provides the unique possibility of simultaneous measurements of the thermal contact properties together with the sample’s thermal parameters. The improvement of the accuracy gave us the possibility to observe the thermal contact resistance, leading to a step of 1 and 5% in the temperature-modulation amplitude at the cell/sample interface in the case of liquid samples such as Apiezon™-H grease and glycerol, respectively. A step of 25% was observed in the case of a dry thermal contact between the cell and an ethylene-1-octene copolymer sample. Thus, the thermal contact resistance must be taken into account in the temperature-modulated calorimetry, especially in the case of a dry cell/sample contact.     

A New Theoretical Approach to Steady State of Temperature Modulated Heat Flux DSC

The steady state of temperature modulated heat flux DSC, in which the sample temperature is controlled at a fixed frequency, a fixed amplitude and a constant underlying heating rate, is theoretically investigated for complex heat capacity of the sample, taking accounts of heat capacities of heat paths, heat loss to the environment and mutual heat exchange between the sample and the reference material. Rigorous and general solutions for the temperature difference oscillation are obtained in relation to the sample temperature as a reference oscillation. The results are quite different from those obtained in functions of the heat source temperature as a reference oscillation. From these solutions, application of the technique to heat capacity measurements is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.