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.     

Melting and crystallization of poly(butylene terephthalate) by temperature‐modulated and superfast calorimetry

Quantitative temperature‐modulated differential scanning calorimetry (TMDSC) and superfast thin‐film chip calorimetry (SFCC) are applied to poly(butylene terephthalate)s (PBT) of different thermal histories. The data are compared with those of earlier measured heat capacities of semicrystalline PBT by adiabatic calorimetry and standard DSC. The solid and liquid heat capacities, which were linked to the vibrational and conformational molecular motion, serve as references for the quantitative analyses. Using TMDSC, the thermodynamic and kinetic responses are separated between glass and melting temperature. The changes in crystallinity are evaluated, along with the mobile–amorphous and rigid–amorphous fractions with glass transitions centered at 314 and 375 K. The SFCC showed a surprising bimodal change in crystallization rates with temperature, which stretches down to 300 K. The earlier reported thermal activity at about 248 K was followed by SFCC and TMDSC and could be shown to be an irreversible endotherm and is not caused by a glass transition and rigid–amorphous fraction, as assumed earlier. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1364–1377, 2006     

Temperature-modulated Calorimetry of the Crystallization of Polymers Analyzed by Measurements and Model Calculations

The response of temperature-modulated differential scanning calorimetry (TMDSC) to irreversible crystallization of linear polymers was investigated by model calculations and compared to a number of measurements. Four different exotherms were added to a typical modulated, reversible heat-flow rate in order to simulate irreversible crystallization. It was found that the reversing heat-flow rate of the TMDSC in response to such irreversible crystallization exotherms is strongly affected by tbe shape of the transition and the phase-angle where the exotherm occurs. A comparison with the experimental data gave valuable insight into the transitions, as well as the nature of the TMDSC response which is usually limited to an analysis of the first harmonic term of the Fourier series that describes the heat-flow rate.This revised version was published online in November 2005 with corrections to the Cover Date.     

Temperature modulated DSC at intermediate-low temperatures

In this paper we present a new cooling system for temperature modulated DSC (TMDSC) working down to about 60 K. In order to demonstrate the features of this new system in combination with commercial TMDSC apparatus, we present measurements of the specific heat capacity (c_p) around the phase transitions of betaine borate and betaine phosphate. For SilGel 604 we report c_p and sound velocity data around the melt, as well as around the glass transition.     

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.     

Optimization of Experimental Parameters in TMDSC. The influence of non-linear and non-stationary thermal response

To treat data from temperature modulated differential scanning calorimetry (TMDSC) in terms of complex or reversing heat capacity firstly one should pay attention that the response is linear and stationary because this is a prerequisite for data evaluation. The reason for non-linear and non-stationary thermal response is discussed and its influence on complex (reversing) heat capacity determination is shown. The criterion for linear and stationary response is proposed. This allows to choose correct experimental conditions for any complex heat capacity measurement. In the case when these conditions can not be fulfilled because of experimental restrictions one can estimate the influence of non-linearity and non-stationarity on measured value of complex or reversing heat capacity. This revised version was published online in July 2006 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.     

Quasi-isothermal measurement by TMDSC in isotactic polypropylene

We measure the frequency dependences of complex heat flows for isothermally crystallized isotactic polypropylene (iPP) by the quasi-isothermal TMDSC. Regarding the quasi-isothermal melting processes as a kind of the single relaxation process, we analyze them by the Debye model. The resultant heat capacity of iPP is larger (about 11%) than usual thermodynamic heat capacity. We also found that the excess of the heat capacity, C _p (excess), has non-monotonous temperature dependence. A simple model introducing some kinetic modes into amorphous producing after and during temperature modulation can reproduce the temperature dependence of C _p (excess) very well.     

Reversed Annealing of Thermal Fractionated Polyethylenes by TMDSC

Polyethylene samples prepared by thermal fractionation (TF) were annealed in several consecutive cycles in a temperature modulated DSC (TMDSC) at a temperatures one °C below the peak temperatures, increased from cycle to cycle relative to these peaks. The transition enthalpy of each cooling cycle was greater or equal to that of the preceding heating cycle. The total heat-flows of each heating cycle corresponded to those of the samples in the reference state up until the vicinity of the annealing temperature. During the annealing, the heat capacities decreased to a lower value over a one minute period. The thermal memory effect caused by the thermal fractionation was eliminated by a small overheating of the material for a short time. The fast disappearance of the thermal memory by a relatively very small degree of heating above their melting temperature denies a long range physical separation of macromolecules by TF. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

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.     

Calorimetric study of the conformational relaxation times in polystyrene

The temperature dependence of the relaxation times of the structural relaxation process of polystyrene is determined by temperature-modulated differential scanning calorimetry (TMDSC) and by conventional differential scanning calorimetry (DSC) in the latter by modelling the experimental heat capacity curves measured in heating scans after different thermal histories. The good agreement between both measuring techniques in the temperature interval just above the glass-transition temperature is a guide for the interpretation of the results of the TMDSC technique in the glass-transition region. In addition, the same model applied to DSC scans is used to simulate the TMDSC experiment and the calculated response is compared with the measured scans. Received: 22 February 1999 Accepted in revised form: 11 June 1999     

Thermodynamic properties and thermal stability of the synthetic zinc formate dihydrate

Zinc formate dihydrate has been synthesized and characterized by powder X-ray diffraction, elemental analysis, FTIR spectra and thermal analysis. The molar heat capacity of the coordination compound was measured by a temperature modulated differential scanning calorimetry (TMDSC) over the temperature range from 200 to 330 K for the first time. The thermodynamic parameters such as entropy and enthalpy vs. 298.15 K based on the above molar heat capacity were calculated. The thermal decomposition characteristics of this compound were investigated by thermogravimetric analysis (TG) and differential scanning calorimetry (DSC). TG curve showed that the thermal decomposition occurred in two stages. The first step was the dehydration process of the coordination compound, and the second step corresponded to the decomposition of the anhydrous zinc formate. The apparent activation energy of the dehydration step of the compound was calculated by the Kissinger method using experimental data of TG analysis. There are three sharply endothermic peaks in the temperature range from 300 to 650 K in DSC curve.     

Can one measure precise heat capacities with DSC or TMDSC?</o:p>

Summary During a prior study of gel-spun fibers of ultrahigh-molar-mass polyethylene, a substantial error was observed on calculating the heat capacity with a deformed pan, caused by the lateral expansion of the fibers on shrinking during fusion. In this paper, the causes of this and other effects that limit the precision of heat capacity measurements by DSC and TMDSC are explored. It is shown that the major cause of error in the DSC is not a change in thermal resistance due to the limited contact of the fibers with the pan or the deformed pan with the platform, but a change in the baseline. In TMDSC, the frequency-dependence is changed. Since irreversible changes in the baseline can occur also for other reasons, inspections of the pan after the measurement are necessary for precision measurements.     

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.     

Temperature Modulated DSC for the Investigation of Polymer Materials: A brief account of recent studies

Temperature modulated differential scanning calorimetry (TMDSC), the most recent development that adds periodic modulation to the conventional DSC, has recently seen a fast growth due to availability of commercial instrumentation. The use of the technique necessitates a total control of all of the experimental parameters. The paper focuses on recent applications to investigate polymers [1].This revised version was published online in November 2005 with corrections to the Cover Date.     

On the frequency-dependent specific heat and TMDSC: Constitutive modelling based on thermodynamics with internal state variables

To develop constitutive models to represent the thermomechanically chemically coupled behaviour of curing resins, vulcanizing elastomers or melting and crystallizing polymers the technique of DSC is extremely helpful. In the present study, the method of TMDSC is interpreted and evaluated in the context of thermodynamics with internal state variables. The balance equation of energy and the dissipation principle in the form of the Clausius–Duhem inequality form the theoretical basis of our study. Since the pressure and the temperature are the external variables in DSC, the specific Gibbs free energy is used as thermodynamic potential. It depends on temperature, stress and a set of internal state variables to represent the microstructure of the material on a phenomenological basis. The temperature- and internal variable-induced changes in the Gibbs free energy are approximated by a Taylor series up to second order terms. As a substantial result of this work, closed-form expressions for the dynamic calorimetric response due to harmonic temperature perturbations and the frequency-dependent complex heat capacity are derived. The theory allows a physical interpretation of the complex heat capacity and its underlying phenomena and is in accordance with experimental observations from literature.