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.     

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.     

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.     

Multiple melting peak analysis with gel-spun ultra-high molar mass polyethylene

The multiple melting peaks observed on differential scanning calorimetry (DSC) of ultrahigh molar-mass polyethylene fibers (UHMMPE) are analyzed as a function of sample mass. Using modern DSC capable of recognizing single fibers of microgram size, it is shown that the multiple peaks are in part or completely due to sample packing. Loosely packed fibers fill the entire volume of the pan with rather large thermal resistance to heat flow. On melting, the fibers contract and flow to collect ultimately at the bottom of the pan. This process seems to be able to cause an artifact of multistage melting dependent on the properties of the fibers. A method is proposed to greatly reduce, or even eliminate, errors of this type. The crucial elements of the analysis of melting behavior and melting temperature are decreasing the sample size and packing the individual fibers in a proper geometry, or to introduce inert media to enhance heat transport.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, US Department of Energy at Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the US Department of Energy, under contract number DE-ACOS-96OR22464. Support for instrumentation came from TA Instruments, Inc. and Mettler-Toledo, research support was also given by ICI Paints.     

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.     

Single run heat capacity measurements

A prior study of single-run differential scanning calorimetry that leads directly to heat capacity results is extended to low temperatures (180 K). The instrument considered was the duPont dual sample differential scanning calorimeter with auto sampler and liquid nitrogen cooling accessary-II. The major error is caused by the low temperature isotherm. After optimizing all parameters, heat capacities of selenium, aluminum, quartz, polystyrene, sodium chloride were measured between 180 to 370 K. The root mean square error of all measurements on comparison with well established adiabatic calorimetry is ±2.9%.

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Zusammenfassung In einer vorangehenden Untersuchung wurde single-run DSC zur direkten Ermittlung von WÄrmekapazitÄtswerten angewendet. Diese Methode wird hier auf den niedrigen Temperaturbereich (180 K) ausgedehnt. Das benutzte GerÄt war ein duPont Doppelproben-DSCalorimeter mit Auto-Sampler und einem Flüssigstickstoff-KühlerzusatzgerÄt-II. Der grö\te Fehler wird durch die Niedrigtemperaturisotherme verursacht. Nach Optimierung aller Parameter wurden im Temperaturbereich 180–370 K die WÄrmekapazitÄten von Selen, Aluminium, Quarz, Polystyrol und Natriumchlorid gemessen. Verglichen mit der gutuntersuchten adiabatischen Kalorimetrie betrÄgt der Standardfehler aller Messungen ±2.9 %.

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On leave from the Dept. of Material Science, Fudan University, Shanghai, China.

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This work was supported by the Division of Materials Sciences, 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. In addition, support by the duPont Company in acquisition of the instrumentation is acknowledged.     

Crystallization and melting of poly(oxyethylene) analyzed by temperature-modulated calorimetry

Temperature-modulated calorimetry, TMC, is used to evaluate the temperature region of metastability between crystallization and melting. While crystals like indium can be made to melt practically reversibly during a TMC cycle of low amplitude so that sufficient crystal nuclei remain unmelted, linear macromolecules cannot, because of their need to undergo molecular nucleation. Modulation amplitudes varying from ±0.2 to ±3.0 K are used to assess the temperature gap between the slow crystallization region and the melting of metastable crystals of poly(oxyethylene) (PEO) of molar mass 1500 Da. This low molar mass PEO serves as a model compound with a metastable gap of melting/crystallization that can be bridged by TMC with a large modulation amplitude. © 1997 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

J Polym Sci B: Polym Phys 35 : 1877–1886, 1997     

On the kinetics of melting and crystallization of poly(l-lactic acid) by TMDSC

The crystallization and melting process of poly(l-lactic acid), PLLA, is investigated by temperature modulated differential scanning calorimetry, TMDSC. The sample is cooled from the melt to different temperatures and the crystallization process is followed by subjecting the material to a modulated quasi-isothermal stage. From the average component of the heat flow and the application of the Lauritzen–Hoffman theory two crystallization regimes are identified with a transition temperature around 118 °C. Besides, the oscillating heat flow allows calculating the crystal growth rate via the model proposed by Toda et al., what gives, in addition, an independent determination of the transition temperature from modulated experiments. Further, the kinetics of melting is studied by modulated heating scans at different frequencies. A strong frequency dependence is found both in the real and imaginary part of the complex heat capacity in the transition region. The kinetic response of the material to the temperature modulation is analyzed with the model proposed by Toda et al. Finally, step-wise quasi-isothermal TMDSC was used to investigate the reversible surface crystallization and melting both on cooling and heating and a small excess heat capacity is observed.     

Reversible melting of high molar mass poly(oxyethylene)

The heat capacity, C_p, of poly(oxyethylene), POE, with a molar mass of 900,000 Da, was analyzed by temperature-modulated differential scanning calorimetry, TMDSC. The high molar mass POE crystals are in a folded-chain macroconformation and show some locally reversible melting, starting already at about 250 K. At 335 K the thermodynamic heat capacity reaches the level of the melt. The end of melting of a high-crystallinity sample was analyzed quasi-isothermally with varying modulation amplitudes from 0.2 to 3.0 K to study the reversible crystallinity. A new internal calibration method was developed which allows to quantitatively assess small fractions of reversibly melting crystals in the presence of the reversible heat capacity and large amounts of irreversible melting. The specific reversibility decreases to small values in the vicinity of the end of melting, but does not seem to go to zero. The reversible melting is close to symmetric with a small fraction crystallizing slower than melting, i.e., under the chosen condition some of the melting and crystallization remains reversing. The collected data behave as one expects for a crystallization governed by molecular nucleation and not as one would expect from the formation of an intermediate mesophase on crystallization. The method developed allows a study of the active surface of melting and crystallization of flexible macromolecules.     

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     

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     

Analysis of the complex thermal behavior of poly(L‐lactic acid) film. I. Samples crystallized from the glassy state

The melting behavior of poly(L ‐lactic acid) film crystallized from the glassy state, either isothermally or nonisothermally, was studied by wide angle X‐ray diffraction (WAXD), small angle X‐ray scattering (SAXS), differential scanning calorimetry (DSC), and temperature‐modulated differential scanning calorimetry (TMDSC). Up to three crystallization and two melting peaks were observed. It was concluded that these effects could largely be accounted for on the basis of a “melt‐recrystallization” mechanism. When molecular weight is low, two melting endotherms are readily observed. But, without TMDSC, the double melting phenomena of high molecular weight PLLA is often masked by an exotherm just prior to the final melting, as metastable crystals undergo melt‐recrystallization during heating in the DSC. The appearance of a double cold‐crystallization peak during the DSC heating scan of amorphous PLLA film is the net effect of cold crystallization and melt‐recrystallization of metastable crystals formed during the initial cold crystallization. Samples cold‐crystallized at 80 and 90 °C did not exhibit a long period, although substantial crystallinity developed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3200–3214, 2006     

Crystallization and melting of isotactic polypropylene in response to temperature modulation

Isotactic polypropylene (iPP) was crystallized using temperature modulation in a differential scanning calorimeter (DSC) to thicken the crystals formed on cooling from the melt. A cool-heat modulation method was adopted for the preparation of the samples under a series of conditions. The effect of modulation parameters, such as temperature amplitude and period was monitored with the heating rate that followed. Thickening of the lamellae as a result of the crystallization treatment enabled by the cool-heat method lead to an increase in the peak melting temperature and the final traces of melting. For instance, iPP melting peak shifted by up to 3.5°C with temperature amplitude of 1.0°C while the crystallinity was increased from 0.45 (linearly cooled) to 0.53. Multiple melting endotherms were also observed in some cases, but this was sensitive to the temperature changes experienced on cooling. Even with a slower underlying cooling rate and small temperature amplitudes, some recrystallization and reorganization occurred during the subsequent heating scan. The crystallinity was increased significantly and this was attributed to the crystal perfection that occurred at the crystal growth surface. In addition, temperature modulated differential scanning calorimetry (TMDSC) has been used to study the melting of iPP for various crystallization treatments. The reversing and non-reversing contribution under the experimental time scale was modified by the relative crystal stability formed during crystallization. Much of the melting of iPP was found to be irreversible.This revised version was published online in November 2005 with corrections to the Cover Date.     

Neural network inversion of the Tarasov function used for the computation of polymer heat capacities

The neural network method is trained using back propagation with a series of heat capacities (C _v) in the temperature range 10 to 200 K for the skeletal vibration of 36 linear macromolecules. The trained network could then accurately extract both parameters of the Tarasov function (₁ and ₃) from heat capacities of three computed test cases and a set of experimental measurements for polyethylene. The neural network method offers a major improvement in handling heat capacity data.

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Zusammenfassung Die Neural-Network Methode wird zur Bestimmung der Wärme kapacität (C _v) von 36 linearen Makromolekül-Gerüstschwingungen im Temperaturbereich 10–200 K angewendet. Das präparierte System ist dann in der Lage, bei drei rechnerischen Testfällen und einer Reihe von experimentellen Messungen an Polyethylen aus den Wärmekapazitäten beide Parameter der Tarasov-Funktion (₁ und ₂) genau zu ermitteln. Die Neural-Network Methode stellt eine wesentliche Verbesserung zur Handhabung von Wärmekapazitätsangaben dar.

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Research sponsored by the Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under contract DE-AC05-84 OR21400 with Martin Marietta Energy Systems, Inc. and the Materials Research Division of the National Science Foundation, Polymers Program Grant # DMR-88-18412     

A Detailed Comparison of First Order Transitions by DSC and TMC

Indium was analyzed with both, standard differential scanning calorimetry (DSC) and temperature-modulated DSC (TMDSC) using sinusoidal and saw-tooth modulation. Instrument and sample effects were separated during nucleated, reversible melting and crystallization transitions, and irreversible crystallization with supercooling. The changes in heat flow, time, and sample and reference temperatures were correlated as functions of heating rate, mass, and modulation parameters. The transitions involve three regions of steady state (an initial and a final region before and after melting/crystallization, a region while melting/crystallization is in progress) and one region of approach to steady state (melting peak to final steady state region). Analyses in the time domain show promise when instrument lags, known from DSC, are used for correction of TMDSC. A new method of integral analysis is introduced for quantitative analysis even when irreversible processes occur in addition to reversible transitions. The information was derived from heat-flux calorimeters with control at the heater block or at the reference temperature sensor. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal memory of poly(3‐hydroxybutyrate) using temperature‐modulated differential scanning calorimetry

The influence of thermal history on morphology, melting, and crystallization behavior of bacterial poly(3‐hydroxybutyrate) (PHB) has been investigated using temperature‐modulated DSC (TMDSC), wide‐angle X‐ray diffraction (WAXRD) and polarized optical microscopy (POM). Various thermal histories were imparted by crystallization with continuous and different modulated cooling programs that involved isoscan and cool–heat segments. The subsequent melting behavior revealed that PHB experienced secondary crystallization during heating and the extent of secondary crystallization varied with the cooling treatment. PHB crystallized under slow, continuous, and moderate cooling rates were found to exhibit double melting behavior due to melting of TMDSC scan‐induced secondary crystals. PHB underwent considerable secondary crystallization/annealing that took place under modulated cooling conditions. The overall melting behavior was interpreted in terms of recrystallization and/or annealing of crystals. Interestingly, the PHB analyzed by temperature modulation programs showed a broad exotherm before the melting peak in the nonreversing heat capacity curve and a multiple melting reversing curve, verifying that the melting–recrystallization and remelting process was operative. WAXRD and POM studies supported the correlations from DSC and TMDSC results. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 70–78, 2006     

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.     

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