Modulated DSC Paper #5 Measurement Of Glass Transitions .
Modulated DSC Paper #5Measurement of Glass Transitions andEnthalpic RecoveryLeonard C. ThomasTA Instruments, 109 Lukens Drive, New Castle, DE 19720, USAABSTRACTThis paper provides a summary of recommendations designed to permitoptimization of Modulated DSC results. It also describes two important aspects(frequency dependence and enthalpic recovery) of the important glass transitionmeasurement that can be readily determined from DSC and MDSC experiments.INTRODUCTIONMeasurement of the glass transition and glass transition temperature are probablythe most common measurements made with the DSC and MDSC techniques. In aprevious paper in this series entitled “Optimization of MDSC Experimental Conditions”(1), recommendations were provided for selection of experimental conditions(modulation amplitude and period, and heating rate). As discussed therein, selection ofexperimental conditions can significantly affect measurement sensitivity and resolution.A summary of these effects is given in the following section.SELECTION OF OPTIMUM EXPERIMENTAL CONDITIONSIn general, it may be said that sensitivity increases with use of slower heatingrates, and larger modulation amplitudes and periods. A larger temperature amplitudeincreases the amplitude of the modulated heating rate, which in turn magnifies the size ofthe measured heat flow signal. Also, a longer modulation period provides more time forheat transfer to occur. Although higher heating rates improve sensitivity in DSCexperiments, slower heating rates improve MDSC sensitivity by providing moremodulation cycles over the temperature region of the transition.Resolution improves with slower heating rates, smaller modulation amplitudes,and slightly shorter modulation periods. The reason that smaller modulation amplitudesimprove resolution is due to the way that MDSC signals are calculated (2). Since thesignals are calculated over a full modulation cycle, the larger the temperature amplitudefor that cycle, the more temperature averaging will occur for each data point.RECOMMENDED STARTING CONDITIONS FOR MEASUREMENT OFGLASS TRANSITIONSThese largely depend on characteristics (size, shape etc.) of the transition and aregiven below. After the initial experiment, conditions can be adjusted to improvesensitivity, resolution or both.TP 0101
For "Standard" Glass TransitionsSample Size: 10-15mgModulation Amplitude: 2X Table Value*Period: 40 secondsHeating Rate: 3 C/minFor "Hard-to-Detect" Glass TransitionsSample Size: 10-20mgModulation Amplitude: 4X Table Value*Period: 60 secondsHeating Rate: 2 C/minFor Tg with "Enthalpic Recovery" PeakSample Size: 5-10mgModulation Amplitude: 1.5X Table Value*Period: 40 secondsHeating Rate: 1 C/minThe "Table Value" (*) indicated above is taken from the table shown below,which displays the temperature modulation amplitude, for a given period and heatingrate, that would cause the heating rate to go to a minimum value of zero with no cooling.The table is supplied in the “Help” section of the “On-Line” manual and greatlyfacilitates the ease of the calculation for the older DSC 2910 and 2920 instruments. Thelatest Q Series instruments have software “templates” that calculate the modulationamplitude directly upon input of the selected period and underlying heating rate.When measuring glass transitions or heat capacity, it is always recommended tohave some cooling during temperature modulation. This is obtained by selecting amodulation amplitude larger than the value given in the table. For example, a modulationamplitude larger than 0.159 C would cause some cooling during temperature modulationfor a heating rate of 1 C/min and modulation period of 60 seconds.HeatingRatePeriod (sec)4050607080901000.10.011 0.013 0.016 0.019 0.021 0.024 0.0270.20.021 0.027 0.032 0.037 0.042 0.048 0.0530.50.053 0.066 0.080 0.093 0.106 0.119 0.1331.00.106 0.133 0.159 0.186 0.212 0.239 0.2652.00.212 0.265 0.318 0.371 0.424 0.477 0.5315.00.531 0.663 0.796 0.928 1.061 1.194 1.326This table is additive, i.e. the heat only amplitude for a periodof 40 sec and heating rate of 2.5 C/min. is the sum of thevalues for 2.0 C/min and 0.5 C/min:Amplitude (40s, 2.5 C/min) 0.212 0.053 0.265 CTP 0102
EFFECT OF TEST FREQUENCY ON THE GLASS TRANSITIONTEMPERATUREWhen conducting a standard DSC experiment, the analyst does not select a testfrequency as one of the experimental parameters and therefore, does not need to considerthe effect of frequency on the measured glass transition temperature. However, becausethe macro-molecular motion associated with the glass transition is a time-dependentprocess, the higher the heating rate in DSC, the higher will be the measured glasstransition temperature. In contrast, with MDSC, the analyst selects a test frequencyindirectly with selection of a modulation period, which is the inverse of frequency.Frequency cycles/secondModulation Period 1/Frequency seconds/cycleThermal analysts working with other thermal-analytical techniques(e.g., Dynamic Mechanical Analysis, Dielectric Analysis or Rheology) that use a knowntest frequency, are well acquainted with the fact that the measured glass transitiontemperature increases as the test frequency is raised. This can be seen in Figure 1 forDMA results on Polyethylene Terephthalate (PET).The glass transition is a frequency-dependent transition, asdemonstrated by the Dynamic Mechanical Analysis (DMA) ofpoly(ethyleneterephthalate) (PET).Figure 1Storage Modulus (MPa)50000.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.0 & 20.0Hz4000IncreasingFrequency 300020001000020604010080140120160Temperature ( C)As indicated above, the MDSC user is indirectly selecting a temperaturemodulation frequency with selection of a modulation period. As with DMA, this affectsthe measured glass transition temperature. The shorter the period, the higher the testfrequency and the higher is the measured glass transition temperature. This is seen inFigure 2, which is a comparison of MDSC experiments run at the same heating rate butwith different modulation periods on quench-cooled PET.TP 0103
Figure 2Although the shorter modulation period causes a shift in the measured glasstransition temperature in the Reversing Heat Flow and Reversing Heat Capacity signals,it does not affect the glass transition temperature as measured in the Total Heat Flow orTotal Heat Capacity signals. The reasons for this are beyond the scope of this paper butthere are two important effects of this difference in response between the Reversing andTotal signals. Collectively, these effects are known as the "Frequency Effect" of MDSCand are illustrated in Figure 3.The glass transition temperature, as measured with the Reversing signal, is at ahigher temperature than that measured using the Total signal from either DSC or MDSC.The effect is only a few degrees but sometimes this can be very important when settingspecifications for a proposed product.An endothermic peak is created in the Nonreversing signal at the glass transitiontemperature. The area of this peak is superimposed on the endothermic peak caused byenthalpic recovery as discussed in the next section.TP 0104
Figure 3The "Frequency Effect" of MDSC causes the glasstransition temperature to be higher in theReversing signal and causes an endothermic peakin the Nonreversing signal which is additive to thepeak caused by Enthalpic RecoveryMEASUREMENT OF ENTHALPIC RECOVERYFor the MDSC user, who may not be familiar with "enthalpic recovery" at theglass transition temperature (Tg), a brief introduction is provided prior to a discussion ofhow to make the measurement with MDSC.Background InformationPhysical properties (heat capacity, modulus or stiffness, impact resistance,coefficient of thermal expansion etc.) of amorphous materials are very different from thephysical properties of crystalline materials. In addition, the physical properties ofamorphous materials can change with time as the sample relaxes ("enthalpic relaxation")toward an equilibrium state. This can complicate their analysis. The process of enthalpicrelaxation or "physical aging" results in a decrease in the energy content of the material.Since DSC and MDSC can measure the energy (heat) content of a sample, they areexcellent tools to compare differences in equilibrium between samples and thereforedifferences in expected end-use physical properties.At temperatures below the glass transition (Tg) of a material, amorphous structurehas very low molecular mobility and is not in thermal equilibrium. That is, the energycontent is higher than it should be and the material will gradually decrease in energy as it"ages" toward an equilibrium state. Once the material is heated above Tg, it has highmolecular mobility and is in thermal equilibrium. "Enthalpic Recovery" is the recovery ofenergy that the sample gave-up (dissipated) as it relaxed toward an equilibrium state overtime. It is seen in a DSC or MDSC experiment as the sample is heated from below TgTP 0105
(non-equilibrium) to a temperature above Tg. Since equilibrium is the lowest energystate, the more energy required to heat a sample over the temperature range of the glasstransition, the closer the sample is to equilibrium. The effect of this aging or enthalpicrelaxation can be seen in Figure 4 for a sample of Polycarbonate (PC) that was aged at135 C for up to 5 days. The Total heat flow signal (like DSC) shows both the stepchange in heat flow (heat capacity) at Tg and the enthalpic recovery peak, while theMDSC Reversing signal shows just the change in heat flow caused by the change in heatcapacity.Figure 4An aging temperature of 135 C was used to create Figure 4 because it isrelatively close to the Tg and the sample ages relatively quickly. At temperatures wellbelow the Tg (e.g., Tg – 40 C), aging occurs much more slowly. If the experiment wereperformed with an aging temperature of 100 C, the aging process would be so slow thatvery little difference would be seen in the samples after just five days.MEASUREMENT OF ENTHALPIC RECOVERYIn order to measure enthalpic recovery, it is necessary to separate the change inheat capacity (heat flow) at Tg from the endothermic peak caused by the enthalpicrecovery process. This is not possible with standard DSC. With MDSC, the change inheat capacity occurs in the Reversing signal while enthalpic recovery, which is a kineticprocess, occurs in the Nonreversing signal. This can be seen in Figure 5, where theMDSC signals are shown in heat capacity units on a sample of Polystyrene (PS) that wasaged at 85 C for up to 8 hours. It would be easy to integrate the peaks in theTP 0106
Nonreversing signal and measure differences in energy content between the samples dueto aging (enthalpic relaxation). As mentioned above and in MDSC Paper #3 (1), a heatingrate of 1 C/min is recommended in order to obtain sufficient modulation cycles (aminimum of 4 is recommended) over the transition region and therefore to obtain a goodseparation of the enthalpic recovery peak from the change in heat capacity at the glasstransition (Tg).Aging Time @ 85 C0.68.0 Hours2.62.64.0 Hours0.5 Hours[ –– –– – ] Nonrev Cp (J/g/ C)2.0 HoursHeat Capacity (J/g/ C)1.0 Hours0 HoursNonreversing2.28.0 Hours0 Hours1.80.22.2-0.21.8[ ––––– · ] Rev Cp (J/g/ C)Figure 5ReversingTotal-0.68.0 Hours1.41.47090110Temperature ( C)130Universal V3.8A TA InstrumentsCorrection of the “Frequency Effect”As previously stated, the "frequency effect" of MDSC causes an endothermicpeak in the Nonreversing signal that is superimposed on the peak due to enthalpicrecovery. In order to more accurately measure the energy caused only by enthalpicrecovery, it is necessary to subtract the apparent energy caused by the "frequency effect".This can be done in one of two ways as explained below.After measuring the peak area in the Nonreversing signal of the aged sample, thesample can be rapidly cooled back to the starting temperature and heated a second timeunder the same MDSC experimental conditions. The area of the peak from the secondheat (non-aged sample) can then be subtracted from the first heat (aged sample) to obtainthe peak area in the first heat caused by just enthalpic recovery. This is illustrated inFigure 5 where the second heat is identified as "0 Hours".Since the "frequency effect" is seen in both heating and cooling modes, the agedsample can be heated to a temperature above Tg and then cooled under the same MDSCconditions as used for heating. Any peak area in the Nonreversing signal on cooling canonly be caused by the "frequency effect". This area can then be subtracted from the peakarea on heating to obtain the peak area on heating which was just due to enthalpicrecovery. This is illustrated in Figure 6.TP 0107
0 .0 0R evHeat Flow (W/g)-0 .0 2Figure 6To ta lH e a tin g N o n re v-0 .0 4-0 .0 6fre q . e ffe c t e n th a lp ic re la xa tio n2 .8 8 8 J/g-0 .0 8T g o ccu rs a t d ifferen t tem p s.G iv es rise to p ea k in N o n rev ersin g sig n a lsin ce N R ev To ta l - R evTo ta lR ev-0 .1 0fre q . e ffe ct 0 .9 2 7 4 J /g C o o lin gP eak from freq . effectN o n re v-0 .1 260657075Te m p e ra tu re ( C )808590E n th alp ic E ven t F req . E ffect 2 .8 88 J /g fro m h ea tin g cu rveF req .effect 0 .9 27 4 J/g (from coo lin g cu rv e)E n th a lp ic even t 2 .88 8 - 0.92 74 1.96 06 J/gSUMMARYModulated DSC is an extremely useful technique for measurement of the glasstransition. Like all analytical techniques, it is important to select optimum experimentalcondition in order to obtain the highest quality results and to state those experimentalconditions when reporting results. Because MDSC applies a temperature modulationperiod (inverse of frequency), the measured glass transition temperature differs betweenthe Total and Reversing signals and increases with decreasing period (increasingfrequency). Because of the difference in response to frequency between the Total andReversing signals, it is necessary to correct for the "frequency effect" when measuringquantitative peak areas in the Nonreversing signal that are associated with enthalpicrecovery.REFERENCES1.Modulated DSC Paper # 3, Optimization of MDSC Experimental Conditions; TATechnical Paper (TP 008).2.Modulated DSC Paper # 2, Calculation and Calibration of MDSC Signals; TATechnical Paper (TP 007).KEY WORDSmodulated differential scanning calorimetry, mdsc, dsc, glass transition, glass transitiontemperature, reversing signal, non reversing signal, enthalpic, recoveryTP 0108
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the effect of frequency on the measured glass transition temperature. However, because the macro-molecular motion associated with the glass transition is a time-dependent process, the higher the heating rate in DSC, the higher will be the measured glass transition temperature. In
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Exo Up 7 DSC Heat Flow Equation (T,t) dt dT Cp dt dH f) s mJ (mW or DSC heat flow signal dt dH Sample Specific Heat x Sample Weight Cp Sample Heat Capacity Heating Rate (C/min) dt dT at an absolute temperature (kinetic) f (T,t) Heat flow that is function of time 8 7 8
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