Diagnosis of Phase Shift in a Temperature-Modulated Calorimetric Method

In a temperature-modulated calorimetric method using the same apparatus as a standard differential scanning calorimeter, we have to pay attention to the thermophysical parameters of the apparatus, which cause phase shift in ac temperatures, such as heat capacity of base plate, heat capacity of a pan, thermal conductance between a heater and base plate, and thermal conductance between a pan and base plate. We performed the analysis of the thermal system of the apparatus with these parameters. Beside the theoretical consideration, we carried out heat capacity measurement in a wide range of modulation periods. We found that the experimental results were well-expressed in terms of these thermophysical parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

The heat capacity of polymers

The long path to an understanding of heat capacity is traced from isothermal and adiabatic calorimetries to the most recent three methods of isoperibol, scanning, and temperature-modulated calorimetry (TMDSC). These latter three methods are: the traditional method of scanning thermal analysis; the quasi-isothermal method of finding the maximum amplitude of the periodic heat flow in response to a temperature modulation at a constant base temperature; and the pseudo-isothermal analysis of a temperature-modulated scanning experiment by subtracting the effect due to the underlying constant heating rate. In parallel, the development of the knowledge about phases and molecules is traced from its beginning to present-day nanophases and macromolecules.     

Single run heat capacity measurements

An outline for the data analysis of single-run heat capacity measurments by dual sample DSC is presented with the following features: 1. Heat flow correction by subtracting the contribution due to the sample pan, including correction for mismatched pan masses. 2. Heat flow and temperature correction with a nonlinear temperature calibration, temperature lag correction, and heating rate correction. 3. Calculation of the cell constants for both cell positions and evaluation of the asymmetry factor between cell positions A and B. 4. Heat capacity calibration and calculation with slope and asymmetry correction. 5. Calculation of heat capacity for multiple runs. 6. Data curve fitting for heat capacity.This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 8818412 and the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-84OR21400 with Martin Marietta Energy Systems, Inc. Thanks are given to TA Instruments, Inc. (New Castle, DE) for providing the commercial heat capacity software and helping with the acquisition of the calorimeter.     

Cell asymmetry correction for temperature modulated differential scanning calorimetry

The quality of measurement of heat capacity by differential scanning calorimetry (DSC) is based on strict symmetry of the twin calorimeter. This symmetry is of particular importance for temperature-modulated DSC (TMDSC) since positive and negative deviations from symmetry cannot be distinguished in the most popular analysis methods. The heat capacities for sapphire-filled and empty aluminum calorimeters (pans) under designed cell imbalance caused by different pan-masses were measured. In addition, the positive and negative signs of asymmetry have been explored by analyzing the phase-shift between temperature and heat flow for sapphire and empty runs. The phase shifts change by more than 180° depending on the sign of the asymmetry. Once the sign of asymmetry is determined, the asymmetry correction for temperature-modulated DSC can be made.On leave from Toray Research Center, Inc., Otsu, Shiga 520, JapanThis work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 90-00520 and the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy at Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy, under contract number DE-AC05-960R22464.     

Melting of polymers by non-isothermal, temperature-modulated calorimetry: analysis of various irreversible latent heat contributions to the reversing heat capacity

This paper provides an analysis of contributions to the apparent, reversing heat capacity when measured by temperature-modulated differential scanning analysis (TMDSC) with an underlying heating rate in the temperature range where irreversible transitions with latent heats occur. To deconvolute the data of a TMDSC scan into a total and reversing part, it is common practice to use the sliding averages and the first harmonics of the Fourier series of temperature and heat-flow rate. Under certain conditions, this procedure produces erroneous reversing contributions which are detailed by experiment and simulation. Unless the response to the temperature modulation is linear, the total heat-flow rate is stationary, and the transition is truly reversible and occurs only once during the temperature scan, one cannot expect a true deconvolution of total and reversible effects. In the presence of multiple, irreversible transitions within a modulation period, however, each process involving latent heat can increase the modulation amplitude, as demonstrated by computer-simulation of polymer melting. As a result, the multiple transitions may give erroneously high latent heats when integrating the apparent reversing heat capacity with respect to temperature.     

Data Analysis Without Fourier Transformation for Sawtooth-type Temperature-modulated DSC

The response of a differential scanning calorimeter (DSC) to sawtooth-type temperature modulation has been analyzed in the time domain using a standard treatment of the DSC data without Fourier transformation into the frequency domain. This method has some of the advantages of a temperature-modulated DSC (TMDSC) and may achieve a reasonable accuracy with more transparent and less time-consuming data analysis than the current TMDSC. The limits of linearity and stationarity of the thermal response, a prerequisite for the validity of the calculation of the reversing heat capacity by Fourier transformation, can be easily recognized in standard DSC. In contrast to the common handling of TMDSC, where the non-reversing contributions are calculated as difference between the total and reversing parts, we define a new, directly measured quantity, called the imbalance in heat capacity. It represents the difference between heating and cooling due to the non-reversing thermal process. This quantity is also of value for the representation of irreversible contributions inquasi-isothermal processes, such as cold crystallization and the annealing of crystallites in the melting range. This revised version was published online in July 2006 with corrections to the Cover Date.     

随机温度调制DSC技术TOPEM的理论和应用

介绍一种称作TOPEM的温度调制差示扫描量热技术[1],由瑞士梅特勒-托利多公司开发.该技术基于随机温度调制,是一般温度调制DSC理论的结果.无需进一步校准,在单次实验中就能测定准稳态比热和宽频范围的频率依赖的复合比热.而且,从测试的数据可直接测定可逆和不可逆热流,并可从热力学上将这两个热流分别与显热流和潜热流相关联.应用实例显示了TOPEM实验的线性行为测试和稳态测试(一致性检查)、玻璃化转变的频率依赖性、热固性树脂的等温固化、固-固转变、可逆熔融和不可逆熔融等.     

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.     

Determination of cell asymmetry in temperature-modulated DSC

The quality of measurement of heat capacity by differential scanning calorimetry (DSC) is based on the symmetry of the twin calorimeters. This symmetry is of particular importance for the temperature-modulated DSC (TMDSC) since positive and negative deviations from symmetry cannot be distinguished in the most popular analysis methods. Three different DSC instruments capable of modulation have been calibrated for asymmetry using standard non-modulated measurements and a simple method is described that avoids potentially large errors when using the reversing heat capacity as the measured quantity. It consists of overcompensating the temperature-dependent asymmetry by increasing the mass of the sample pan.On leave from Toray Industries, Inc., Otsu, Shiga 520, JapanOn leave from Toray Research Center, Inc., Otsu, Shiga 520, JapanThis work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 90-00520 and the Division of Materials Sciences, Office of Basic Energy Sciences, U. S. Department of Energy at Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U. S. Department of Energy, under contract number DE-AC0S-96OR22464. Support for instrumentation came from TA Instruments, Inc. and Mettler-Toledo, Research support was also given by ICI Painls, and Toray Industries, Inc.     

Melting of indium by temperature-modulated differential scanning calorimetry

The melting and crystallization of a sharply melting standard has been explored for the calibration of temperature-modulated differential scanning calorimetry, TMDSC. Modulated temperature and heat flow have been followed during melting and crystallization of indium. It is observed that indium does not supercool as long as crystal nuclei remain in the sample when analyzing quasi-isothermally with a small modulation amplitude. For standard differential scanning calorimetry, DSC, the melting and crystallization temperatures of indium are sufficiently different not to permit its use for calibration on cooling, unless special analysis modes are applied. For TMDSC with an underlying heating rate of 0.2 K min^–1 and a modulation amplitude of 0.5–1.5 K at periods of 30–90 s, the extrapolated onsets of melting and freezing were within 0.1 K of the known melting temperature of indium. Further work is needed to separate the effects originating from loss of steady state between sample and sensor on the one hand and from supercooling on the other.On leave from Toray Research Center, Inc., Otsu, Shiga 520, Japan.This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant # DMR 90-00520 and the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy at Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy, under contract number DEACOS-960R22464. Support for instrumentation came from TA Instruments, Inc. and Mettler-Toledo Inc. Research support was also given by ICI Paints.     

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).     

Evaluation of heat capacity measurements by temperature-modulated differential scanning calorimetry

Temperature-modulated differential scanning calorimetry (TMDSC) is known to have the ability to measure heat capacity of materials more accurately than the conventional differential scanning calorimeter. However, the accuracy of the measured heat capacity displays significant dependence on various experimental parameters such as period of modulation (p), amplitude of modulation (a), geometry of sample (g), heating rate (r), etc. One of the key features of this system is the ability to measure heat capacity under quasi-isothermal conditions. In the present investigation, heat capacity of a well-established system namely sapphire and thoria was measured by TMDSC under dynamic mode and also under quasi-isothermal mode. The experimental parameters, mentioned above p, a, g, and r are varied to establish the conditions for measuring heat capacity accurately.     

A Method for Analysis of the Measured Curves of TMDSC Investigation in the Melting Region of Polymers

The measured signal of the temperature-modulated differential scanning calorimetry (TMDSC) is discussed in the case of polymer melting. The common data evaluation procedure of TMDSC-signals is the Fourier analysis. The resulting information is the amplitude and the phase shift of the first harmonic of the periodic heat flow component. It is shown that this procedure is not sufficient for quantitative discussions if deviations from the symmetric curve shape occur in the measured heat flow curves. For polymer melting it is demonstrated that asymmetric curves will be measured if the experimental temperature amplitude is too large. In this paper a data evaluation method is presented, which is based on the Fourier transform of the measured curves. The peaks of the first and second harmonics in the resulting spectra are used for the analysis of the asymmetry of the measured curves. In the case of polymer melting this analysis yields the maximum temperature amplitude which follows a correct linear data evaluation. This maximum temperature amplitude depends on the material. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat capacity measurement and DSC study of hafnium hydrides

Heat capacities, electrical conductivities and phase transition temperature of hafnium hydrides, HfH_x (0.99≤x≤1.83), were studied using a direct heating pulse calorimeter and a differential scanning calorimeter from room temperature to above 500 K. The heat capacity of HfH_1.83 was larger than that of pure hafnium and showed no anomaly of heat capacity. In contrast, there were λ-type peaks for the heat capacity and DSC curves for HfH_x (1.1≤x≤1.6) near 385 and 356 K. The anomalies of heat capacity and electrical conductivity of HfH_x (1.1≤x≤1.6) were considered the result of phase transition and order-disorder phase transition for hydrogen in the hafnium hydride lattice for HfH_x (1.1≤x≤1.3).     

Comparison of simulated and actual DSC measurements for first-order transitions

A system of differential equations modeling a heat flux DSC is solved and the results are compared with those obtained using a TA Instruments Q1000™ DSC.¹ It incorporates a new heat flow rate measurement technique that determines the heat flow rate between the sample and its pan. Two types of first-order transitions are investigated: melting of a pure substance and solidification of a pure substance including super-cooling. In both transitions, the peak shape obtained using the new heat flow rate measurement and predicted by the model is quite different from that measured using conventional DSC. It is shown that the differences are the result of simplifications implicit in the conventional heat flow rate measurement that is based solely on the difference between sample and reference calorimeter temperatures. Heat flow rates measured using the improved measurement agree very well with the model predictions for heat exchange between the sample and its pan.     

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.     

Study of the crystallization and melting region of PET and PEN and their blends by TMDSC

The cold crystallization and melting of poly(ethylene therephthalate) (PET), poly(ethylene 2,6-naphthalene dicarboxylate) (PEN) and their blends were studied using temperature modulated differential scanning calorimetry (TMDSC) at underlying heating rates of between 1 and 3 K min^-1 and periods ranging from 30 to 90 s. The amplitude of modulation was selected in order to give an instantaneous heating rate β≥0. Heat flow is analyzed by the total heat flow signal o, which is equivalent to the conventional DSC signal, and the reversing heat flow o_REV, which only detects the glass transition and the melting processes. The dependence of the melting region in the reversing heat flow on the frequency of modulation is analyzed. The use of the so-called non-reversing heat flow o_NREV (=o-o_REV)) and the effect of frequency and amplitude on the complex heat capacity are also studied. The results show the complexity of these magnitudes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Characterization of Reacting Polymer Systems by Temperature-Modulated Differential Scanning Calorimetry

The benefits of temperature-modulated differential scanning calorimetry to characterize reacting polymers are illustrated for different experimental systems. The effects of combined isothermal and non-isothermal cure paths on (de)vitrification, mobility-restricted reactions, and relaxation during vitrification are discussed for anhydride- and amine-cured epoxies. The simultaneous measurement of heat capacity, heat flow, and heat flow phase provides an excellent tool for mechanistic interpretations. The influence of the metakaolinite particle size on the production of inorganic silicate-metakaolinite polymer glasses is treated as an example. These principles are further illustrated for primary and secondary amine-epoxy step growth reactions, and for styrene-cured unsaturated polyester chain growth reactions with ‘gel effect’. Finally, the effects of isothermal cure and temperature on reaction-induced phase separation in a polyethersulfone modified epoxy-amine system are highlighted. This revised version was published online in July 2006 with corrections to the Cover Date.     

Temperature modulated differential scanning calorimetry (TMDSC) in the region of phase transitions. Part 1: theoretical considerations

For temperature modulated differential scanning calorimetry (TMDSC) a simple model, the low pass filter, is presented which allows to see and calculate the influence of heat transfer into the sample on magnitude and phase shift of the modulated part of the measured heat flow rate and the heat capacity determined from it. A formula is given which enables to correct the measured magnitude of the periodic heat flow rate function and the calculated heat capacity in dependence on the thermal resistance and heat capacity of the sample. The correction becomes very important in regions where the heat capacity changes considerably as in the melting region. The approach is successfully tested with model substances with well-known excess heat capacity in the transition region.