A Theoretical Approach to Temperature Modulated Power Compensation DSC

The steady state of temperature modulated power compensation DSC has been theoretically investigated for measurements of complex heat capacity, taking accounts of heat capacities of heat paths, heat loss to the environment, and mutual heat exchange between the sample and the reference material. Thermal contact between the sample cell and the cell holder is also taken into accounts. Rigorous and general solutions are obtained. From these solutions application of the technique to heat capacity measurements is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

General Theory of Steady State of tm-DSC and its Application to Complex Heat Capacity Measurements

For complex heat capacity measurements, steady state of various types of temperature modulated DSC is theoretically investigated by a set of common comprehensive fundamental equations of heat balance. Heat capacities of heat paths, heat loss to the environment and mutual heat exchange between the sample and the reference material are taken into accounts together with thermal contact effect between the cell and its holder plate. Rigorous and general solutions have been obtained, and useful relations for complex heat capacity measurements have been derived for each type of DSC. They are compared with each other to elucidate unique features of each type of DSC.This revised version was published online in November 2005 with corrections to the Cover Date.     

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.     

A new version of differential flow heat capacity calorimeter; tests of heat loss corrections and heat capacities of aqueous NaCl from T = 300 K to T = 623 K

A new differential flow heat capacity calorimeter was constructed. It is designed to operate at temperatures up to 700 K and pressures up to 35 MPa and its primary use is for determining the massic heat capacities at constant pressure of dilute aqueous solutions. The instrument works in the so-called isoperibol regime, where the fluid sample flowing through the cell is heated by an electrical heater and the power necessary to provide a constant temperature rise is measured relative to that for a reference fluid (water). From the two values of power for sample and water the ratio of massic heat capacities of the sample to that of water can be calculated. A thorough investigation of calibration techniques showed that the calorimetric performance is very sensitive to the thermal conductivities of the sample and reference fluids. Measurements under turbulent flow conditions are questionable since there is no guarantee that by changing the flow rate the experiments and the calibrations would be performed at the same flow conditions. The procedure is very accurate and sensitive when measuring the difference in heat capacity between a solvent and a dilute solution of solute in the same solvent. The calorimeter was used to measure heat capacities of aqueous solutions of NaCl at eight temperatures up to 623 K and pressures to 30 MPa. The newly obtained values show consistency with previously published results and enlarge the database of experimental values aboveT =  573 K, where experimental data are rare.     

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.     

Heat capacity measurement by modulated DSC at constant temperature

The mathematical equations for step-wise measurement of heat capacity (C _p ) by modulated differential scanning calorimetry (MDSC) are discussed for the conditions of negligible temperature gradients within sample and reference. Using a commercial MDSC, applications are evaluated and the limits explored. This new technique permits the determination ofC _p by keeping the sample continually close to equilibrium, a condition conventional DSC is unable to meet. Heat capacity is measured at ‘practically isothermal condition’ (often changing not more than ±1 K). The method provides data with good precision. The effects of sample mass, amplitude and frequency of temperature modulation were studied and methods for optimizing the instrument are proposed. The correction for the differences in sample and reference heating rates, needed for high-precision data by standard DSC, do not apply for this method. Presented in preliminary from at the 22nd NATAS Conference in Denver, CO 9/19-22/93 (Proceedings, pages 59–64, editor K. R. Williams).     

A small sample-size automated adiabatic calorimeter from 70 to 580 K

An automatic adiabatic calorimeter for measuring heat capacities in the temperature range 70-580 K, equipped with a small sample cell of 7.4 cm³ in the internal volume has been developed. In order to obtain a good adiabatic condition of the calorimeter at high temperature, the calorimeter was surrounded in sequence by two adiabatic shields, three radiation shields and an auxiliary temperature-controlled sheath. The main body of the cell made of copper and the lid made of brass are silver-soldered and the cell is sealed with a copper screw cap. A sealing gasket made of Pb-Sn alloy is put between the cap and the lid to ensure a high vacuum sealing of the cell in the whole experimental temperature range. All the leads are insulated and fixed with W30-11 varnish, thus a good electric insulation is obtained at high temperature. All the experimental data, including those for energy and temperature are collected and automatically with a personal computer using a predetermined program. To verify the accuracy of the calorimeter, the heat capacities of α-Al₂O₃ of the calorimetric standard reference material is measured. The standard deviations of experimental heat capacity values from the smoothed values are within ± 0.28%, while the inaccuracy is within ±0.4% compared with those of the National Bureau of Standards over the entire working temperature range. Project supported by the National Natural Science Foundation of China (Grant No. 29573133).     

Temperature Modulated Differential Scanning Calorimetry Part IV. Effect of heat transfer on the measurement of heat capacity using quasi-isothermal ADSC

An analysis developed in previous work has been further refined in order to study the effect of heat transfer on the heat capacity and phase angle measurements by TMDSC. In the present model, a temperature gradient within the sample has been taken into account by allowing for heat transfer by thermal conduction within the sample. The influence of the properties of the sensors, the heat transfer conditions between the sensor and sample,and the properties of the sample have been investigated by varying each parameter in turn. The results show that heat capacity measurements are reliable only within a restricted frequency range, for which the experimental conditions are such that the heat transfer phase angle depends linearly on the modulation frequency. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new tool for an old job: Using fixed cell scanning calorimetry to investigate dilute aqueous solutions

The development of fixed twin cell temperature scanning calorimeters has enabled the more efficient determination of heat capacities of dilute aqueous solutions with a precision comparable to that of the Picker flow heat capacity calorimeters developed nearly 40 years ago. Experiments require less than 0.5 cm³ of solution, and results can be obtained routinely over the temperature range (278 to 395) K at pressures up to a few bars. Multiple scanning of samples by both increasing and decreasing temperature allows assessment of instrument drift, solute stability, and reproducibility of results. Chemical calibration is essential to take full advantage of the precision and sensitivity of the calorimeters. The calorimetric output is a direct measure of the difference in heat capacity per unit volume of a solution and of a reference liquid, usually water. Thus, densities of the solution and reference liquid are needed to transform the results into heat capacities per unit mass of solution. Examples of solutes that have been investigated include a variety of inorganic and organic compounds that dissolve to give simple ionic or neutral species, or that produce complexes or species that exist in equilibrium distributions that can change as the temperature is scanned. Appropriate selection of the results from experiments on combinations of solutes allows calculation of standard state (zero concentration) thermodynamic quantities for chemical processes and reactions over the ranges of temperature scanned at the solution compositions investigated. Results for a few specific systems are presented and discussed for some representative classes of solutes that have been investigated in our laboratory since 1998.     

Thermal conductivity measurements using the flash method

Thermal diffusivity is the speed with which heat propagates through a material. It has a multitude of direct applications, such as determining heat transfer through brake pads at the moment of contact, etc., but more often it is used to derive thermal conductivity from the fundamental relationship tying it with specific heat capacity and density. Using a new multi-sample configuration system, and testing a reference sample adjacent to the unknown, specific heat capacity can be obtained parallel with thermal diffusivity. Thus, a single test yields thermal diffusivity and thermal conductivity with prior knowledge of density. The method is fast and produces results with high accuracy and very good repeatability. The sample size, 12 to 30 mm diameter and 2 to 5 mm thickness, is easy to handle and is well suited for a broad range of materials, even for composites, often a problem for other methods. Typical data on two polymers, Pyrex glass and Pyroceram 9606 are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

苯氧威 (C17H19NO4) 的热容和热力学性质

通过小样品精密自动绝热量热计测定了自己合成并提纯的苯氧威 (C₁₇H₁₉NO₄) 在79 ～ 360 K温区的低温摩尔热容。量热实验发现, 该化合物在320 ~ 330 K温区, 有一固 - 液熔化相变过程, 其熔化温度为（326.31±0.14）K, 摩尔熔化焓、摩尔熔化熵及化合物的纯度分别为：(26.98±0.04) kJ• mol^-1和（82.69 0.09）J•mol^-1•K^-1和 (99.53±0.01 )%。并计算出了80-360 K的热力学参数。用分步熔化法得到绝对纯化和物的熔点为326.60±0.06 K。用差示扫描量热 (DSC) 技术对该物质的固-液熔化过程作了进一步研究，结果与绝热量热法一致。     

Experimental Considerations for Temperature Modulated DSC at Low Temperature

Temperature modulated DSC (TMDSC) at low temperatures requires attention to the selection of experimental parameters that are within the capability of the instrumentation as well as special care in calibration of heat capacity measurement when high precision is required. Data are presented to facilitate selection of appropriate modulation periods and amplitudes at low temperature when using a mechanical cooling accessory. The standard error of the mean heat capacity measurement for a sapphire standard increased with decreasing temperature, decreasing period, and increasing pan mass. For ice in hermetically sealed pans, the standard error of the mean heat capacity measurement was larger than for sapphire and did not follow a predictable trend with changes in temperature and period of modulation. This was attributed to changes in sample geometry between successive measurements due to melting and resolidification. A simple one-point temperature calibration by TMDSC may be unsuitable for precise measurement of heat capacity because of the random error caused by sample placement and the systematic error caused by cell asymmetry, temperature dependence of the calibration constant, and different sample thermal conductivities. An alternative calibration procedure using standard DSC and either a linear or second order fit of the calibration constant over the temperature range of interest is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Heat capacity of alcohols in aqueous solutions in the temperature range from 5 to 125°C

Using a precise technique of scanning microcalorimetry the heat capacity differences between water and dilute aqueous solutions of ethanol, n-propanol, n-butanol and n-pentanol were measured from 5 to 125°C and the partial molar heat capacities of these substances in water were determined. It was found that the heat capacity increment for alcohol disolved in water is proportional to the number of the-CH ₂ ^– groups and decrease with a temperature increase. The heat capacity increment of hydration of non-polar groups is shown to be positive and large at room temperature and decreases in magnitude as the temperature increases. In contrast, the heat capacity increment of hydration of polar groups is negative at room tempreature and increases as the temperature increases. From the temperature dependence of the heat capacity increment one can assume that the water molecules solvated by the non-polar groups of the alcohols behave in a non-cooperative manner.     

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.     

Measurement of thermal diffusivity and specific heat capacity of polymers by laser flash method

We measured thermal diffusivity and heat capacity of polymers by laser flash method, and the effects of measurement condition and sample size on the accuracy of the measurement are discussed. Thermal diffusivities of PTFE films with thickness 200–500 μm were the same as those data that have been reported. But, the data for film thickness less than 200 μm have to be corrected by an equation to cancel thermal resistance between sample film and graphite layers for receiving light and detecting temperature. Thermal diffusivity was almost unaffected by the size of area vertical to the direction of laser pulse, because heat flow for the direction could be negligible. Specific heat capacity of polymer film was exactly measured at room temperature, provided that low absorbed energy (< 0.3 J) and enough sample mass (> 25 mg) were satisfied as measuring conditions. Thermal diffusivity curve of PS or PC versus temperature had a terrace around T_g, whereas that of PE decreased monotonously with increasing in temperature until T_m. Further, we estimated relative specific heat capacity (RC_p) by calculating ratios of heat capacities at various temperatures to the one at 299 K. RC_p for PS obtained by laser flash method was larger than that obtained by DSC method, whereas the RC_ps for PE obtained by the both methods agreed with one another until T_m (305 K). RC_p for PS decreased linearly, with increase in temperature after it increased linearly until T_g (389 K), showing similarity to temperature dependency of thermal conductivity. RC_p for PE also decreased until T_m, similar to thermal conductivity. ©1995 John Wiley & Sons, Inc.     

Heat capacity of poly(butylene terephthalate)

The low‐temperature heat capacity of poly(butylene terephthalate) (PBT) was measured from 5 to 330 K. The experimental heat capacity of solid PBT, below the glass transition, was linked to its approximate group and skeletal vibrational spectrum. The 21 skeletal vibrations were estimated with a general Tarasov equation with the parameters Θ₁ = 530 K and Θ₂ = Θ₃ = 55 K. The calculated and experimental heat capacities of solid PBT agreed within better than ±3% between 5 and 200 K. The newly calculated vibrational heat capacity of the solid from this study and the liquid heat capacity from the ATHAS Data Bank were applied as reference values for a quantitative thermal analysis of the apparent heat capacity of semicrystalline PBT between the glass and melting transitions as obtained by differential scanning calorimetry. From these results, the integral thermodynamic functions (enthalpy, entropy, and Gibbs function) of crystalline and amorphous PBT were calculated. Finally, the changes in the crystallinity with the temperature were analyzed. With the crystallinity, a baseline was constructed that separated the thermodynamic heat capacity from cold crystallization, reorganization, annealing, and melting effects contained in the apparent heat capacity. For semicrystalline PBT samples, the mobile‐amorphous and rigid‐amorphous fractions were estimated to complete the thermal analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4401–4411, 2004     

对MDTA中测样品热容量的准恒温法的评述

对用调制差热分析（ＭＤＴＡ）准恒温法测样品热容量的情形进行了讨论。通过结合最基本的热传导定律和ＭＤＴＡ模型，指出了目前国际上测量样品热容量的准恒温法只能得到在所测温度范围内的物质热容量平均值，调制温度的幅度越大或调制频率越高，所得到的热容量数据越平滑。在所测温度范围内样品热容量基本不变时，用ＭＤＴＡ准恒温法较好；但当样品热容量在所测温度范围内有明显变化时，用传统差热分析法（ＤＴＡ）更好一些。     

Miscibility of polymer blends studied by a simplified method of data analysis using light heating modulated temperature DSC

A simple method of application of light heating modulated temperature DSC to a study of miscibility of polymer blends has been developed. In this method only the sample was measured and the standard materials were not used. The total heat flow, the complex heat capacity, the reversing and non-reversing heat flows were obtained as values measured from those quantities in hypothetical glassy state at T>T_g. The values of the hypothetical glassy state were calculated by extrapolation from T<T_g. The present method gives relative values but useful information can be obtained from the results. Some results from miscible and immiscible polymer blends are shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

硝酸肼的量热研究

用精密自动绝热量热计测定了在220 K—370 K温度范围内硝酸肼的热容、熔化热、熔化温度和熔化熵。所得热容数据的精密度以百分偏差的均方根值表示为±0.2％。三次熔化热测定的相对偏差为±0.1％。为验证结果的可靠性, 用该装置测定了冰的熔化热和熔化温度, 其结果与文献值一致; 又用法国SETARAM公司的高温量热计测定了硝酸肼的熔化热和熔化温度, 其结果与我们用量热法测定的结果一致; 从量热结果计算出了该试样的纯度, 该结果亦与化学分析的结果一致。这些均可说明我们所测得的数据是可靠的。