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.     

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.     

Study of temperature profile and specific heat capacity in temperature modulated DSC with a low sample heat diffusivity

One important application of temperature modulated DSC (TMDSC) is the measurement of specific heat of materials. When the sample has very good thermal conductivity as in the case of metals, the temperature gradient is not normally an important factor and can be ignored most of the time. However, in the case of materials with poor heat transfer properties, for example, polymers, the thermal conductivity is only in the order of 1/1000 or so of that of metals. This could have a major effect on the test results. In this paper, a round analytical solution is given and a numerical model is used to analyze the effects of thermal diffusivity on temperature distribution inside the test sample and specific heat measurement by TMDSC, PET sample test results are presented to demonstrate the effects of material thermal diffusivity.     

Calorimetric study of the conformational relaxation times in polystyrene

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

Temperature modulated DSC at intermediate-low temperatures

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

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.     

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.     

Investigation of wax deposition and effective diffusion coefficient in water-in-oil emulsion system

As pipeline transportation is widely used in the petroleum industry, the problem of wax deposition is a severe threat to the safety of oil and gas transportation. In addition, the mechanism of wax deposition is very complicated due to the presence of water phase. This paper tries to clarify the effects of water fraction, temperature difference and experimental period on the wax deposition process in water-in-oil emulsion system by a series of static cold finger experiments. The experimental results reveal that the average diffusion rates decrease with increased water fraction, longer experimental period and reduced temperature difference. Furthermore, on the basis of wax deposition experiments in cold finger apparatus and radial temperature distribution simulations via Fluent, the influence of water phase on heat transfer occurring in the wax molecular diffusion process is revealed, and relationship between mass transfer and heat transfer is investigated. Additionally, the effective diffusion coefficient of wax molecules is calculated on the basis of experimental and simulation results. The calculated effective diffusion coefficients using this approach are significantly lower than the calculated results from conventional methods. This explains the remarkable disparity with previous works due to underestimating the influence of dispersed water.     

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.     

Reaction-induced phase separation in polyethersulfone-modified epoxy-amine systems studied by temperature modulated differential scanning calorimetry

In epoxy-amine systems with a thermoplastic additive, the initially homogeneous reaction mixture can change into a multi-phase morphology as a result of the increase in molecular weight or network formation of the curing matrix. Temperature modulated DSC (TMDSC) allows the real-time monitoring of this reaction-induced phase separation. A linear polymerizing epoxy-amine (DGEBA–aniline) and a network-forming epoxy-amine (DGEBA–methylene dianiline), both with an amorphous engineering thermoplastic additive (polyethersulfone, PES), are used to illustrate the effects of phase separation on the signals of the TMDSC experiment. The non-reversing heat flow gives information about the reaction kinetics. The heat capacity signal also contains information about the reaction mechanism in combination with effects induced by the changing morphology and rheology such as phase separation and vitrification. In quasi-isothermal (partial cure) TMDSC experiments, the compositional changes resulting from the proceeding phase separation are shown by distinct stepwise heat capacity decreases. The heat flow phase signal is a sensitive indication of relaxation phenomena accompanying the effects of phase separation and vitrification. Non-isothermal (post-cure) TMDSC experiments provide additional real-time information on further reaction and phase separation, and on the effect of temperature on phase separation, giving support to an LCST phase diagram. They also allow measurement of the thermal properties of the in situ formed multi-phase materials.     

Temperature modulated differential scanning calorimetry (TMDSC) in the region of phase transitions. Part 1: theoretical considerations

For temperature modulated differential scanning calorimetry (TMDSC) a simple model, the low pass filter, is presented which allows to see and calculate the influence of heat transfer into the sample on magnitude and phase shift of the modulated part of the measured heat flow rate and the heat capacity determined from it. A formula is given which enables to correct the measured magnitude of the periodic heat flow rate function and the calculated heat capacity in dependence on the thermal resistance and heat capacity of the sample. The correction becomes very important in regions where the heat capacity changes considerably as in the melting region. The approach is successfully tested with model substances with well-known excess heat capacity in the transition region.     

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 Relationship Between the TMDSC Curve of Frozen Sucrose Solutions and Collapse During Freeze-Drying

This study compares measurements of the collapse temperature of sucrose solutions by freeze drying microscopy with features of TMDSC curves both in the scanning and quasi-isothermal modes. The objective was to determine which feature of the TMDSC curve is predictive of collapse and to provide additional evidence for recent interpretations of the physical significance of the low temperature transitions for sucrose solutions. Interpretations based on the heat capacity signal and the kinetic heat flow using TMDSC are consistent with previous reports based on total heat flow measurement, where the lower temperature transition is the glass transition and the higher temperature transition is associated with the onset of ice melting. Quasi-isothermal experiments further support these conclusions, since additional crystallization of ice is observed only in the region of the lower temperature transition. Collapse of sucrose solutions during freeze-drying begins at the approximate midpoint between the end of the glass transition region and the onset of ice melting. This revised version was published online in July 2006 with corrections to the Cover Date.     

Entropy production in TMDSC

The non-equilibrium process due to irreversible heat exchanges occurring during a temperature modulated differential scanning calorimetry (TMDSC) experiment is investigated in detail. This enables us to define an experimental frequency dependent complex heat capacity from this calorimetric method. The physical meaning of this dynamic heat capacity is discussed. A relationship is clearly established between the imaginary part of this complex quantity and the net entropy created during the experimental time-scale.     

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

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

Behavior of particulates in thermal plasma flows

Injection of particulate matter into a thermal plasma represents one of the approaches used in thermal plasma processing. The injected particles are usually treated as a dispersed phase, governed by the equation of motion and the rate equations for heat and mass transfer in Lagrangian coordinates. A stochastic approach is introduced to take particle dispersion into account due to turbulent fluctuations by randomly sampling instantaneous flow fields. Three-dimensional effects are also considered which are mainly due to particle injection and the presence of a swirl component. A modified approach for investigating noncontinuum effects on plasma-particle heat transfer is proposed, incorporating both electric and aerodynamic effects on the boundary layer around a particle immersed into a thermal plasma. Comparisons of theoretical predictions based on the present model with available experimental data are, in general, in reasonable agreement.     

Thermal characterization of poly-l-lactide by dielectric analysis and modulated DSC

Dielectric analysis (DEA) is a very sensitive technique, which allows for detection of small structural changes at the low scale. An advantage of DEA, with respect to other modulated techniques, is the possibility of using a wider frequency range. Molecular relaxations of the order of only a few nanometers are not observed by any other thermoanalytic method. Nevertheless, these small relaxations involve dipole changes that can be observed by DEA. Thus, this technique is used here, in combination with temperature-modulated differential scanning calorimetry (TMDSC) to obtain insightful information about the thermal transitions of poly-l-lactic acid (PLLA), one of the stereo-isomers of polylactide. Its complex thermal behavior is the subject of ongoing debate, with several overlapping crystallization and melting processes. The combined use of TMDSC and DEA provides a better insight of three important transitions of this polymer: the alpha relaxation, the enthalpic relaxation, and the cold crystallization. The dependences of the enthalpy relaxation on the dynamic glass transition relaxation and on the glass transition as a thermal event are evaluated. On the other hand, it will be shown how the cold crystallization can be identified by TMDSC, and DEA helps us understand the effect of crystallization on the dipole movements. The shape of the dielectric permittivity curve at low frequencies is compared to that of the reversing heat capacity to check whether both signals are sensitive or not to the same events. It is also verified how the experimental results of alpha relaxation of PLLA follow an Arrhenius or a Vogel trend.