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.     

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.     

Phase behavior at low temperature of poly(tetrafluoroethylene) by temperature-modulated calorimetry

Temperature modulated differential calorimetry (TMDSC) is used to examine the crystal-crystal transitions of poly(tetrafluoroethylene). This study gives new information about the dynamic thermal behavior of such transitions. The involvement of reversible and irreversible processes during the phenomenon is observed, which are related to the order-disorder changes occurring during the transition.This study adds a new example to the response of TMDSC during first order transitions.     

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.     

Modeling the heat flow and heat capacity of modulated differential scanning calorimetry

Modulated differential scanning calorimetry (MDSC) uses an abbreviated Fourier transformation ?r the data analysis and separation of the reversing component of the heat flow and temperature signals. In this paper a simple spread-sheet analysis will be presented that can be used to better understand and explore the effects observed in MDSC and their link to actual changes in the instrument and sample. The analysis assumes that instrument lags and other kinetic effects are either avoided or corrected for.     

Heat capacity measurements on uranium–cerium mixed oxides by differential scanning calorimetry

Uranium–cerium mixed oxides of three different compositions (U_0.2Ce_0.8)O₂, (U_0.5Ce_0.5)O₂ and (U_0.8Ce_0.2)O₂, were prepared by combustion synthesis and characterized by XRD. The compositional characterization was done by ICP-AES. Heat capacity measurements employed a heat flux type differential scanning calorimeter from 280 to 820 K. The heat capacity values of (U_0.2Ce_0.8)O₂, (U_0.5Ce_0.5)O₂ and (U_0.8Ce_0.2)O₂ at 298 K are 62.8, 64.2 and 70.1 J K⁻¹ mol⁻¹, respectively. Enthalpy increment, entropy and Gibbs energy function were computed from the heat capacity data.     

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.     

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.     

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.     

Simulation of temperature-modulated DSC of transitions represented by abrupt changes in heat capacity

Computer simulations have been applied to elucidate the response of a sample to temperaturemodulated differential scanning calorimetry (tm-DSC) during transitions. Two cases have been simulated; a latent heat without supercooling (represented by an abrupt heat capacity pulse with perfect reversibility) and a latent heat with perfect supercooling or large hysteresis (an abrupt heat capacity change without reversibility, i.e. the change in heat capacity is seen on heating, but not on cooling). Because the simulation was applied to these well-characterized phenomena, the results are useful to reveal actual sample thermal responses during transitions. The non-reversible component was observed in both cases and has no distinct difference. Higher harmonics due to non-linearity of the transitions were also observed. Furthermore, by inspecting thermal response of the sample and the essential feature of tm-DSC, a new method of data analysis has been devised.     

Temperature-modulated differential scanning calorimetry of reversible and irreversible first-order transitions

Temperature-modulated differential scanning calorimetry of first-order transitions has led to many new observations. Some of these involve non-linear processes or deal with transformations of practically instantaneous response. The latter may cause serious lags within the calorimeter due to limited thermal conductivity of the sample and the instrument. In both cases the “reversing heat capacity” or a “complex heat capacity” is not a precise representation of the transition since both are computed from abbreviated Fourier transforms, limited to the evaluation of the first harmonic component. One has in these cases to work in the time-domain with the raw output. But even from these analyses in the time-domain many interesting new insights about the transition and the calorimeter performance can be generated.     

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:

Heat balances and heat capacity calculations

We present enthalpy and heat capacity calculations under reversible conditions in which a system is allowed to reach equilibrium after incremental steps in temperature. We focus on the binary systems Ag–Cu and 1,3,5 tri-bromo-benzene and 1,3,5 tri-chloro-benzene and show that due to the compositional effect, thermodynamic properties differ up to an order of magnitude in two-phase regions relative to values in single-phase regions. We demonstrate that Planck’s definition of heat capacity needs a minor extension to include the change of phase assemblages due to phase transitions. Dedicated to Professor Su-II Pyun on the occasion of his 65th birthday     

Calorimetric glass transition temperature and absolute heat capacity of polystyrene ultrathin films

The absolute heat capacity and glass transition temperature (T_g) of unsupported ultrathin films were measured with differential scanning calorimetry with the step-scan method in an effort to further examine the thermodynamic behavior of glass-forming materials on the nanoscale. Films were stacked in layers with multiple preparation methods. The absolute heat capacity in both the glass and liquid states decreased with decreasing film thickness, and T_g also decreased with decreasing film thickness. The magnitude of the T_g depression was closer to that observed for films supported on rigid substrates than that observed for freely standing films. The stacked thin films regained bulk behavior after the application of pressure at a high temperature. The effects of various preparation methods were examined, including the use of polyisobutylene as an interleaving layer between the polystyrene films. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3518–3527, 2006     

Isobaric specific heat capacity of typical lithium chloride liquid desiccants using scanning calorimetry

Three kinds of lithium chloride desiccants were selected, which are considered to be potential and interesting working fluids for a desiccant/dehumidification or absorption refrigeration system, and their isobaric specific heat capacities were determined in this context. Experiments were conducted at a high accuracy twin-cell scanning calorimeter. The temperature accuracy and heat flux resolution of the calorimeter are ±0.05 K and 0.1 μW respectively. The data of lithium chloride + water and lithium chloride + triethylene glycol (TEG)/propylene glycol (PG) + water systems were achieved at temperatures from 308.15 K to 343.15 K and atmospheric pressure. The mass fraction of LiCl ranged from 15% to 45% in the LiCl + H₂O system, and the mass fraction of LiCl and glycol ranged from 10% to 23.3% and 20% to 46.7% in the ternary systems respectively. Based on the experimental heat capacity data, a universal empirical formula was correlated as a function of temperature and solute mass fraction. In the experimental mass fractions and temperatures range, the average absolute deviation (AAD) between experiment results and calculated values is no more than 0.15%, and maximum absolute deviation (MAD) is within 0.38%. These thermodynamic data of lithium chloride solutions can be effectively used for analysis and design of desiccant/dehumidification systems and absorption refrigeration systems in both refrigeration and chemical industry.     

Low-temperature heat capacity and thermodynamic properties of crystalline carboxin (C12H13NO2S)

Carboxin was synthesized and its heat capacities were measured with an automated adiabatic calorimeter over the temperature range from 79 to 380 K. The melting point, molar enthalpy (Δ_fusH_m) and entropy (Δ_fusS_m) of fusion of this compound were determined to be 365.29±0.06 K, 28.193±0.09 kJ mol⁻¹ and 77.180±0.02 J mol⁻¹ K⁻¹, respectively. The purity of the compound was determined to be 99.55 mol% by using the fractional melting technique. The thermodynamic functions relative to the reference temperature (298.15 K) were calculated based on the heat capacity measurements in the temperature range between 80 and 360 K. The thermal stability of the compound was further investigated by differential scanning calorimetry (DSC) and thermogravimetric (TG) analysis. The DSC curve indicates that the sample starts to decompose at ca. 290 °C with the peak temperature at 292.7 °C. The TG-DTG results demonstrate the maximum mass loss rate occurs at 293 °C corresponding to the maximum decomposition rate.     

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.     

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.