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.     

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.     

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     

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.     

Reversible Melting During Crystallization of Polymers Studied by Temperature Modulated Techniques (TMDSC, TMDMA)

Quasi-isothermal temperature modulated DSC and DMA measurements (TMDSC and TMDMA, respectively) were performed to determine heat capacity and shear modulus as a function of time during crystallization. Non-reversible and reversible phenomena in the crystallization region of polymers can be observed. The combination of TMDSC and TMDMA yields new information about local processes at the surface of polymer crystals, like reversible melting. Reversible melting can be observed in complex heat capacity and in the amplitude of shear modulus in response to temperature perturbation. The fraction of material involved in reversible melting, which is established during main crystallization, keeps constant during secondary crystallization for PCL PET and PEEK. This shows that also after long crystallization times the surfaces of the individual polymer crystallites are in equilibrium with the surrounding melt. Simply speaking, polymer crystals are ‘living crystals’. This revised version was published online in August 2006 with corrections to the Cover Date.     

Temperature modulated dynamic mechanical analysis

Temperature modulated dynamic mechanical analysis (TMDMA) was performed in the same way as temperature modulated DSC (TMDSC) measurements. Temperature modulation with amplitude 0.5 K and period 20 min was realised by a series of linear heating and cooling cycles (saw-tooth modulation). As in TMDSC TMDMA allows for the investigation of reversible and non-reversible phenomena in the melting and crystallisation region of polymers. The advantage of TMDMA compared to TMDSC is the high sensitivity for small and slow changes in crystallinity, e.g. during re-crystallisation. The combination of TMDMA and TMDSC yields new information about local processes at the surface of polymer crystallites. It is shown that during and after isothermal crystallisation the surface of the individual crystallites is in equilibrium with the surrounding melt.     

Modulated differential scanning calorimetry in the glass transition region

Temperature-modulated calorimetry (TMC) allows the experimental evaluation of the kinetic parameters of the glass transition from quasi-isothermal experiments. In this paper, model calculations based on experimental data are presented for the total and reversing apparent heat capacities on heating and cooling through the glass transition region as a function of heating rate and modulation frequency for the modulated differential scanning calorimeter (MDSC). Amorphous poly(ethylene terephthalate) (PET) is used as the example polymer and a simple first-order kinetics is fitted to the data. The total heat flow carries the hysteresis information (enthalpy relaxation, thermal history) and indications of changes in modulation frequency due to the glass transition. The reversing heat flow permits the assessment of the first and higher harmonics of the apparent heat capacities. The computations are carried out by numerical integrations with up to 5000 steps. Comparisons of the calculations with experiments are possible. As one moves further from equilibrium, i.e. the liquid state, cooperative kinetics must be used to match model and experiment.On leave from Toray Industries, 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 DE-AC05-96OR22464. Support for instrumentation came from TA Instruments, Inc. Research support was also given by ICI Paints, and Toray Industries, Inc.     

Reversible Melting of Thermally Fractionated Polyethylene

Different grades of linear low density polyethylenes (LLDPEs) have been quenched cooled step-wise and crystallised isothermally at (a series of increasing) temperatures in a DSC (thermal fractionated samples). These samples have been investigated by temperature modulated DSC (MDSC). The heat flow curves of the thermal fractionated materials were compared with those obtained from samples crystallised at a relatively slow cooling rate of 2 K min^-1(standard samples). The melting enthalpy obtained from the total heat flow of the thermal fractionated samples was 0-10 J g^-1higher than those of standard samples. The melting enthalpy obtained from the reversing heat flows was 13-31 J g^-1lower in the thermal fractionated samples than in the standard samples. The ratio of the reversing melting enthalpy to the total melting enthalpy increased with decreasing density of the PE. The melting temperature of the endotherms formed by the step-wise cooling was 9 K higher than the crystallisation temperature. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reversible Melting of Semi-Crystalline Polymers 2. Annealing Near to the Melting Point

Annealing experiments have been carried out at a few degrees below the melting point of different polyethylenes (LDPE, LLDPE, HDPE), of polypropylene (PP) and of Nylon-6. The heat capacities decrease during the annealing, within a 2-4 min time scale, to a lower value which corresponds to the extrapolated heat capacity values obtained for the cooling cycle when the polymer is cooled from the melt. Heat capacities in the heating cycle following the cooling cycle of PP, Nylon-6 and HDPE have the same value as during the cooling section. This is not the case for LDPE and LLDPE. Exothermic total heat flow in the cooling section following the annealing indicates that the crystallisation takes place during the cooling rather than during the annealing period. The total melting enthalpy measured before and after the annealing cycle is the same. The reversing heat flow shows an excellent fit to the change of the crystallinity measured by small angle scattering of synchrotron radiation during a heating cycle at temperatures below the melting peak. A coupled thermodynamic interaction of the crystalline and the amorphous phases is concluded from this study. This kind of interaction is possible at the lateral end of polymeric chains incorporated into the crystalline phase. This is an indication of the portion of tie molecules in the system, i.e. the portion of fringed micelle type of crystalline morphology with respect to that of folded chain lamellae. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crystallization of Polymers Studied by Temperature Modulated Calorimetric Measurements at Different Frequencies

Quasi-isothermal temperature modulated DSC (TMDSC) were performed during crystallization to determine heat capacity as function of time and frequency. Non-reversible and reversible phenomena in the crystallization region of polymers were distinguished. TMDSC yields new information about the dynamics of local processes at the surface of polymer crystals, like reversible melting. The fraction of material involved in reversible melting, which is established during main crystallization, keeps constant during secondary crystallization for polycaprolactone (PCL). This shows that also after long crystallization times the surfaces of the individual crystallites are in equilibrium with the surrounding melt. Simply speaking, polymer crystals are living crystals. A strong frequency dependence of complex heat capacity can be observed during and after crystallization of polymers.This revised version was published online in November 2005 with corrections to the Cover Date.     

Recent developments in thermal analysis of polymers: Calorimetry in the limit of slow and fast heating rates

This review focuses on new insights into the crystal melting transition and the amorphous glass transition of polymers that have been gained through recent advances in thermoanalytical methods. The specific heat capacity can now be studied under two extreme limits, that is, under quasi‐isothermal conditions (limit of zero heating rate) and, at the other end of the scale, under rapid heating conditions (heating rates on the order of thousands of degrees per second), made possible through nanocalorimetry. The reversible melting, and multiple reversible melting, of semicrystalline polymers is explored using quasi‐isothermal temperature modulated differential scanning calorimetry, TMDSC. The excess reversing heat capacity, above the baseline, measured under nearly isothermal conditions is attributed to locally reversible surface melting and crystallization processes that do not require molecular nucleation. Observations of double reversible melting endotherms in isotactic polystyrene suggest existence of two distinct populations of crystals, each showing locally reversible surface melting. The second subject of the review, nanocalorimetry, is utilized to study samples of small mass under conditions of very fast heating and cooling. The glass transition properties of thin amorphous polymer films are observed under adiabatic conditions. The glass transition temperature appears to be independent of film thickness, and is observed even in ultra‐thin films. Recrystallization and reorganization during rapid heating are studied by nanocalorimetry of semicrystalline polymers. The uppermost endotherm seen under normal DSC scanning of poly(ethylene terephthalate) is caused by reorganization, and vanishes under the rapid heating conditions (3000K/s) provided by nanocalorimetry. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 629–636, 2005     

TMDSC analysis of single-site copolymer blends after thermal fractionation

Temperature-modulated differential scanning calorimetry (TMDSC) has been used to study the melting of a series of blends containing linear low-density polyethylene (LLDPE) and very low-density polyethylenes (VLDPE) with long chain branches. After the blends were subjected to different thermal histories including thermal fractionation by stepwise isothermal cooling, they were examined by TMDSC. TMDSC curves have been interpreted in terms of a combination of the reversing and non-reversing specific heats that result from reversible and irreversible events at the time and temperature, which they are detected, respectively. It was found that crystals formed at different crystallisation conditions had different internal order; hence they showed different amounts of reversing and non-reversing contributions. There is no exothermic activity seen in the non-reversing signal for the thermally fractionated polymers and their blends suggesting formation of crystals approaching equilibrium. In contrast, polymers and blends cooled at 10°C min^-1 cooling rate showed large exothermic contributions corresponding to irreversible effects. In addition, a true reversible melting contribution is also detected for both fast-cooled and thermally-fractionated samples during the quasi-isothermal measurements. This revised version was published online in July 2006 with corrections to the Cover Date.     

Annealing of Polypropylene/Polyethylene Blends Near to the Melting Points in TMDSC

Annealing experiments have been carried out just below the melting temperature of both polyethylene (LLDPE) and polypropylene (PP) and their blends. The total melting enthalpy measured after the annealing cycle was greater by 10-15% with respect to the value having been measured before it. During the annealing period the heat capacity decreases to a lower value within the first 2-3 min. Heat capacities of PP (either in pure form or in the blends) measured during the heating cycle following the annealing cycle have the same value as during the cooling section. The heat capacities of the LLDPE in the heating cycle following the annealing were those of the preceding heating cycle. The total heat flows in the cooling section following the annealing cycle were greater than those in another cooling cycle at the same temperatures indicating that the crystallisation takes place during the cooling rather than during the annealing periods. The presence of LLDPE decreases the crystallisation temperature of PP. The presence of SEBS in the blend results in a greater crystallisation temperature than that of pure PP. The crystallisation temperature of LLDPE increases with increasing levels of PP. This revised version was published online in July 2006 with corrections to the Cover Date.     

Reversible and irreversible heat capacity of poly[carbonyl(ethylene‐co‐propylene)] by temperature‐modulated calorimetry

The heat capacity of poly[carbonyl(ethylene‐co‐propylene)] with 95 mol % C₂H₄? CO? (Carilon EP®) was measured with standard differential scanning calorimetry (DSC) and temperature‐modulated DSC (TMDSC). The integral functions of enthalpy, entropy, and free enthalpy were derived. With quasi‐isothermal TMDSC, the apparent reversing heat capacity was determined from 220 to 570 K, including the glass‐ and melting‐transition regions. The vibrational heat capacity of the solid and the heat capacity of the liquid served as baselines for the quantitative analysis. A small amount of apparent reversing latent heat was found in the melting range, just as for other polymers similarly analyzed. With an analysis of the heat‐flow rates in the time domain, information was collected about latent heat contributions due to annealing, melting, and crystallization. The latent heat decreased with time to an even smaller but truly reversible latent heat contribution. The main melting was fully irreversible. All contributions are discussed in the framework of a suggested scheme of six physical contributions to the apparent heat capacity. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1565–1577, 2001     

Comparison of reversible melting behaviour of poly(3-hydroxybutyrate) using quasi-isothermal and other modulated temperature differential scanning calorimetry techniques

Melting behaviour of poly(3-hydroxybutyrate) (PHB) has been investigated by conventional DSC and each of several methods of modulated temperature differential scanning calorimetry (mT-DSC) such as heat-cool, iso-scan, step-scan and quasi-isothermal (QI). Thermal properties were investigated after fast and slow cooling crystallisation treatments. Multiple melting peak behaviour was observed for all methods except conventional melting with an average heating rate. Comparison of the mT-DSC data revealed that PHB underwent reversing melting including several reversible events and some non-reversible contributions under the modulation conditions. The main melting of PHB was irreversible, as were crystallisation and annealing, where the crystals can approach equilibrium. The various fusion enthalpy values were measured and they confirmed significant melt-recrystallisation of PHB with different melting conditions. Only the QI method revealed a true reversible contribution.     

Reversible melting in poly(butylene terephthalate)

Crystallized samples of poly(butylene terephthalate) (PBT), examined in the melting region by means of temperature modulated differential scanning calorimetry (TMDSC), show reversible fusion. The analysis of the complex heat capacity reveals that the fusion of poor crystallites can follow temperature modulation more easily than perfect crystals, in agreement with the findings recently reported in the literature, and that the amount of reversible melting decreases with increasing the modulation frequency.     

Obtaining Modulated Temperature DSC Curves Through a Non-conventional DSC Method

The DSC curve obtained in conventional equipment usually only shows the resultant thermal effect due to simultaneous phenomena, which may occur during isothermal or dynamic analyses. This does not allow one to identify the processes properly and may cause an erroneous interpretation of the resulting curves. Modulated DSC equipment enhances the operating conditions and the analysis capacity of conventional DSC by superimposing a sinusoidal temperature modulation on the linear temperature control. Thus reversing and non-reversing heat flow curves are obtained, which are, respectively, the heat capacity and kinetic components of the DSC curve. Therefore, events that are related to these components can be separately analyzed. A method to obtain curves similar to the MDSC reversing and non-reversing components was developed using conventional DSC equipment in a non-conventional way. It was applied to analyze samples of poly(ethylene terephthalate) (PET) taken from bottles of mineral water. The second PET crystallization step that occurs during its melting was quantified and an apparent initial crystallinity was obtained from the resulting data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimating the reversing and non‐reversing heat flow from standard DSC curves in the glass transition region

A mathematical model for the total heat flow obtained in differential scanning calorimetry (DSC) experiments from polymers with enthalpic relaxation is proposed. It is limited to the glass transition and enthalpic relaxation range of temperature and to the cases where the enthalpic relaxation is the only non‐reversing process taking place. The model consists of a mixture of functions representing the heat capacity heat flow of the glassy and non‐glassy fractions, the glass transition progress and the enthalpic relaxation heat flow. Optimal fittings of the model were performed on the experimental total heat flow data, obtained from two thermoplastics with different aging times. Considering which functions of the mixture represent reversing and non‐reversing processes, the reversing and non‐reversing heat flows were also estimated. The estimated reversing and non‐reversing signals were compared with the ones obtained by modulation. On the whole a good match was found, which was even better considering that the estimates are not affected by the frequency effect of the modulated temperature DSC (MTDSC) measurements. The model assumes linear trends for the heat capacity heat flow of the glassy and non‐glassy structures. The glass transition progress is represented by a generalized logistic function and the enthalpic relaxation heat flow by the first derivative of another generalized logistic. It brings about a new approach to these phenomena, where the parameters of these functions represent the temperature at which each event is centered, the change of heat capacity (C_p) at the glass transition and the energy involved in the enthalpic recovery. Copyright © 2011 John Wiley & Sons, Ltd.     

Non isothermal heat capacities and chemical reactions using a modulated DSC

An evaluation of measurements of heat capacities by modulated differential scanning calorimetry, MDSC is presented. Heat capacities were obtained from 130 to 550 K by a non isothermal technique in which a periodic modulation was added to the linear heating rate. Effects of amplitude and period of modulation, sample weight, sample type, pan type, and cell imbalance are described. Results are compared with those obtained using the isothermal technique. Heat capacity could be measured well into the decomposition region and separated from the non reversing signal due to chemical reaction (degradation), thus allowing a precise detection of onsets of the thermal degradation. This additional information will aid in the interpretation of the degradation chemistry, a field vital for the petroleum-industry.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayPart of this paper was presented at the 23rd Conference of the North American Thermal Analysis Society, Toronto, Canada, September 25–28, 1994.The author (MVN) acknowledges the experimental assistance provided by J. Balogh of Exxon Research and Engineering Company, Linden. Helpful discussions with A. Boller of the University of Tennessee at Knoxville, Dr. Y. Jin, General Electrical, and Dr. S. Sauerbrunn formerly of TA Instruments are also acknowledged.     

Crystallization and melting of a branched polyethylene with precisely controlled chemical structure

The heat capacity of a linear polyethylene with dimethyl branches, at every 21st backbone atom was analyzed by differential scanning calorimetry (DSC) and quasi-isothermal temperature-modulated DSC. This novel copolyethylene (PE2M) is relatively difficult to crystallize from the melt. On subsequent heating, a first, sharp melting peak is followed by a sharp cold-crystallization and crystal perfection and a smaller endotherm, before reaching the main melting at 315–320 K, close to the melting temperatures of eicosane and tetracontane. The low-temperature melting is sensitive to the cooling rate and disappears below 1.0 K min⁻¹. The cold crystallization can be avoided by heating with rates faster than 80 K min⁻¹. The PE2M exhibits some reversing and reversible melting, which is typical for chain-folded polymers. The glass transition of semicrystalline PE2M is broadened and reaches its upper limit at about 260 K (midpoint at about 0.355 K). Above this temperature, the crystals seem to have a heat capacity similar to that of the liquid. A hypothesis is that the melting transition can be explained by changes in crystal perfection without major alteration of the crystal structure and the lamellar morphology. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3461–3474, 2006