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 specific heat capacity of two nanocomposite systems

Thermal investigations on two selected model-nanocomposites have been made. They differ with regard to the type of the anorganic nanoparticles that have been filled into an organic oligomer matrix. The properties of nanocomposites may vary between those of a simple mixture of independent components and those of a system, where specific interfacial interactions between the constituting parts lead to ‘new’ properties. Depending on the type of the nanoparticles filled into the matrix, the resulting properties might be closer to one or to the other extreme. We used temperature modulated differential scanning calorimetry (TMDSC) to investigate a matrix of the oligomer diglycidyl ether of bisphenol A (DGEBA) filled either with SiO₂- or Al₂O₃-nanoparticles. The dependence of the complex specific heat capacity () on the concentration of nanoparticles shows a clear difference between the two systems as far as the glass transition of the oligomer is concerned. The SiO₂ composite seems to behave more like a simple mixture, whereas the Al₂O₃ composite shows ‘new’ properties.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Simple derivation of the frequency dependent complex heat capacity

This paper gives a simple derivation of the well-known expression of the frequency dependent complex heat capacity in modulated temperature experiments. It aims at clarified again that the generalized calorimetric susceptibility is only due to the non-equilibrium behaviour occurring in the vicinity of thermodynamic equilibrium of slow internal degrees of freedom of a sample when the temperature oscillates at a well determined frequency.     

Non-debye nature in thermal relaxation and thermal properties of lithium borate glasses studied by modulated DSC

Complex heat capacity, C _p ^*=C _p ^'–iC _p ^', of lithium borate glasses xLi₂O·(1–x)B₂O₃ (molar fraction x=0.00–0.30) has been investigated by Modulated DSC. We have analyzed the shape of C _p ^* by the Cole-Cole plot, performed fitting by the Havriliak-Negami equation, and then determined the parameters related to the non-Debye nature of thermal relaxation. Moreover, the concentration dependence of the thermal properties has been investigated. Glass transition temperatures become higher with the increase of molar fraction of Li₂O and shows the board peak around x=0.26. Temperature ranges of glass transitions become narrower with the increase of Li₂O concentration.     

Reversible and irreversible heat capacity of poly(trimethylene terephthalate) analyzed by temperature‐modulated differential scanning calorimetry

The heat capacity of poly(trimethylene terephthalate) (PTT) has been analyzed using temperature‐modulated differential scanning calorimetry (TMDSC) and compared with results obtained earlier from adiabatic calorimetry and standard differential scanning calorimetry (DSC). Using quasi‐isothermal TMDSC, the apparent reversing and nonreversing heat capacities were determined from 220 to 540 K, including glass and melting transitions. Truly reversible and time‐dependent irreversible heat effects were separated. The extrapolated vibrational heat capacity of the solid and the total heat capacity of the liquid served as baselines for the analysis. As one approaches the melting region from lower temperature, semicrystalline PTT shows a reversing heat capacity, which is larger than that of the liquid, an observation that is common also for other polymers. This higher heat capacity is interpreted as a reversible surface or bulk melting and crystallization, which does not need to undergo molecular nucleation. Additional time‐dependent, reversing contributions, dominating at temperatures even closer to the melting peak, are linked to reorganization and recrystallization (annealing), while the major melting is fully irreversible (nonreversing contribution). © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 622–631, 2000     

The heat capacity of fluorinated propane and butane derivatives by differential scanning calorimetry

The constant pressure liquid-phase heat capacities of 21 hydrogen containing fluorinated propane and butane derivatives and one fluorinated ether (CF₃OCF₂H) with boiling points ranging from -34.6° to 76.7°C have been measured to 3% accuracy by differential scanning calorimetry at 40°C. The measurements are needed to help identify alternative refrigerants and blowing agents that do not deplete the stratospheric ozone layer. The DSC method has two significant advantages for this purpose, which are:

Static pressure and heat flux measurements of a thermal argon plasma flow in a water-cooled tube

The momentum and energy transfer phenomena with large temperature difference were investigated experimentally and theoretically, using an argon atmospheric thermal plasma. The plasma was generated by an arc discharge, 4–6 kW, and flowed into a water-cooled copper tube for static pressure measurements and into a copper block with the same size hole (8 mm i.d.) for measuring heat fluxes using a transient method. The argon flow rate was 2.77–8.31×10^–4 kg/s. The static pressure of the plasma flow shows a different variation from that of an ordinary flow and does not decrease monotonically. The axial distributions of the numerical calculations are in fair agreement with those of the experiments, and it is concluded that the contributions of recombination and of physical properties play important roles in the behavior of the confined thermal plasma flow.     

Thermal expansivity,volume and the effect of pressure on the isobaric heat capacity of 1-hexanamine-1 hexanol mixtures from 0.1 to 400 MPa at 303 K up to 453 K

Thermal expansivities of liquid mixtures of 1-hexanol and 1-hexanamine have been determined as a function of pressure up to 400 MPa over the temperature range from 303 to 453 K. Measurements were performed in a pressure-scanning calorimeter by the stepwise technique. Compressibilities of the mixtures under study were determined at 303 K using the technique described before. Molar volumes under atmospheric pressure were determined for each mixture from the density measurements with a Paar instrument. From both the molar volume as a function of pressure at 303 K and the thermal expansivities the effects of pressure on the isobaric heat capacity were determined over the whole pressure and temperature range under study.

---

Zusammenfassung Im Temperaturbereich 303–453 K wurde der thermische Ausdehungskoeffizient flüssiger Gemische aus 1-Hexanol und 1-Aminohexan als Funktion des Druckes bis 400 MPa bestimmt. Die Messungen wurden in einem Druck-Scanningkalorimeter nach der Schritt-für-Schritt-Methode ausgeführt. Die Kompressibilität der untersuchten Gemische wurde bei 303 K mittels der bereits beschriebenen Methode bestimmt. Mittels Dichtemessungen in einem Paar-Gerät wurde für jedes Gemisch das molare Volumen bei Atmosphärendruck ermittelt. Anhand der Druckabhängigkeit des molaren Volumens bei 303 K sowie der thermischen Ausdehnungskoeffizienten wurde der Einflu\ des Druckes auf die isobare Wärmekapazität im gesamten untersuchten Druck- und Temperaturintervall bestimmt.

     

Partial molal heat capacity of aqueous ferrous chloride from measurements of integral heats of dilution

Heats of dilution of concentrated aqueous solutions (4.43 moles-kg^–1) of FeCl₂ were measured at 15, 25, and 35°C. The heat capacities of these concentrated solutions were also measured at the same temperatures. From these data the partial molal heat capacity, C _p2 ⁰ (FeCl₂, aq, 298.15°K)=–2.56±30 J–°K^–1–mole^–1, was calculated. The partial molal heat capacity of Fe²⁺(aq), –2±30 J-°K^–1-mole^–1, was correlated with the correspondence principle equations of Criss and Cobble.     

Evaluation of the Compatibility of EPDM and IIR I. Specific heat capacity

The thermal effect of mixing of EPDM and IIR was studied by differential scanning calorimetry over the temperature range between 335 and 435 K. O'Neill's method was used for calculating the specific heat capacity with alumina as standard. The greater the butyl rubber content, the lower the heat capacity. The presence of butyl rubber induces a marked thermal instability because of isobutylene units. It is possible that a rearrangement occurs in the molecular sequence, accompanied by secondary reactions involving free radicals. The contribution of each component to the cP of the tested polymeric systems is discussed. Differences between theoretical and experimental specific heat capacities increase as the operation temperature is raised. The relationship between the contributions of the two components to the specific heat capacity values of mixtures can be described by a first order equation, named the law of reciprocal thermal affinity. This aspect can be ascribed to the interaction of various reacting entities, which form certain units with low molar heat capacity. This revised version was published online in July 2006 with corrections to the Cover Date.