basic theory & experimental considerationsbasic theory & experimental considerations thermal...
TRANSCRIPT
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MODULATED DSCTM COMPENDIUM
Basic Theory & ExperimentalConsiderations
Thermal Analysis & Rheology
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BACKGROUND
Differential scanning calorimetry (DSC) is a thermal analysis technique which has been used for more thantwo decades to measure the temperatures and heat flows associated with transitions in materials as a functionof time and temperature. Such measurements provide quantitative and qualitative information about physicaland chemical changes that involve endothermic or exothermic processes, or changes in heat capacity. DSC isthe most widely used thermal analysis technique with applicability to polymers and organic materials, as well asvarious inorganic materials.
DSC has many advantages which contribute to its widespread usage, including fast analysis time (usually lessthan 30 minutes), easy sample preparation, applicability to both solids and liquids, wide temperature range, andexcellent quantitative capability. On the other hand, DSC does have some limitations. In order of importancethese limitations are:
� The ability to properly analyze complex transitions
Many transitions are complex because they involve multiple processes. Examples include the enthalpicrelaxation that occurs at the glass transition, and the crystallization of amorphous or metastable crystallinestructures prior to or during melting. Enthalpic relaxation is an endothermic process that can vary inmagnitude depending on the thermal history of the material. Under some circumstances, it can make theglass transition appear to be a melting transition. Simultaneous crystallization and melting make it nearlyimpossible to determine the real crystallinity of the sample prior to the DSC experiment. These problemsare compounded further when analyzing blends of materials.
Conventional DSC does not allow these complex transitions to be properly analyzed since conventionalDSC measures only the sum of all thermal events in the sample. Hence, when multiple transitions occur inthe same temperature range, results are often confusing and misinterpreted.
� The presence of sufficient sensitivity
The ability of DSC to detect weak transitions is dependent on both short-term (seconds) noise in the heatflow signal and long-term (minutes) variations in the shape of the heat flow baseline. However, sinceshort-term noise can be effectively eliminated by signal averaging, the real limitation for reproduciblydetecting weak transitions is variation in baseline rectilinearity. Because of the need to use differentmaterials in the construction of DSC cells and because of changes in the properties of these materials andthe purge gas with temperature, all commercial DSC instruments have varying degrees of baseline driftand related effects.
� The presence of adequate resolution
High resolution, or the ability to separate transitions that are only a few degrees apart, requires the use ofsmall samples and low heating rates. However, the size of the heat flow signal decreases with reducedsample size and heating rate. This means that any improvement in resolution results in a reduction insensitivity and vice versa. Conventional DSC results are always a compromise between sensitivity andresolution.
� The need for complex experiments
Some DSC measurements such as heat capacity and thermal conductivity require multiple experiments ormodifications to the standard DSC cell which increase the opportunity for error as well as the experimen-tal time. Hence, they are not commonly made by the average user.
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Figure 1. HEAT FLUX DSC SCHEMATIC
Modulated DSC (MDSC) is a new technique which provides not only the same information as conven-tional DSC, but also provides unique information not available from conventional DSC by overcoming most ofthe limitations of conventional DSC. The result is an exciting new way to significantly increase the basicunderstanding of material properties.
THEORY
The theory supporting modulated DSC can be easily understood by comparing it to conventional DSC. Inconventional DSC, the difference in heat flow between a sample and an inert reference is measured as afunction of time and temperature as both the sample and reference are subjected to a controlled environmentof time, temperature, and pressure. The most common instrument design for making those DSC measure-ments is the heat flux design shown in Figure 1. In this design, a metallic disk (made of constantan alloy) is theprimary means of heat transfer to and from the sample and reference. The sample, contained in a metal pan,and the reference (an empty pan) sit on raised platforms formed in the constantan disc. As heat is transferredthrough the disc, the differential heat flow to the sample and reference is measured by area thermocouplesformed by the junction of the constantan disc and chromel wafers which cover the underside of the platforms.These thermocouples are connected in series and measure the differential heat flow using
the thermal equivalent of Ohm�s Law, , where = heat flow, ∆T = the temperature difference
between reference and sample and RD = the thermal resistance of the constantan disc. Chromel and alumelwires attached to the chromel wafers form thermocouples which directly measure sample temperature. Purgegas is admitted to the sample chamber through an orifice in the heating block before entering the samplechamber. The result is a uniform, stable thermal environment which assures better baseline flatness andsensitivity (signal-to-noise) than alternative DSC designs. In conventional DSC, the temperature regime seenby the sample and reference is linear heating or cooling at rates from as fast as 100°C/minute to rates as slowas 0°C/minute (isothermal).
GAS PURGEINLET
LID
REFERENCEPAN
THERMOELECTRICDISC (CONSTANTAN)
THERMOCOUPLEJUNCTION
HEATING BLOCK
CHROMEL WIRE
ALUMELWIRE
CHROMELDISC
SAMPLEPAN
dQ
dt=
T
R D
∆ dQ
dt
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Modulated DSC is a technique which also measures the difference in heat flow between a sample and an inertreference as a function of time and temperature. In addition, the same �heat flux� cell design is used. How-ever, in MDSC a different heating profile (temperature regime) is applied to the sample and reference. Spe-cifically, a sinusoidal modulation (oscillation) is overlaid on the conventional linear heating or cooling ramp toyield a profile in which the average sample temperature continuously changes with time but not in a linearfashion. The solid line in Figure 2 shows the profile for a MDSC heating experiment. The net effect ofimposing this more complex heating profile on the sample is the same as if two experiments were run simulta-neously on the material - one experiment at the traditional linear (average) heating rate [dashed line in Figure2] and one at a sinusoidal (instantaneous) heating rate [dashed-dot line in Figure 2]. The actual rates for thesetwo simultaneous experiments is dependent on three operator-selectable variables:
� Underlying heating rate (range 0-100°C/minute)� Period of modulation (range 10-100 seconds)� Temperature amplitude of modulation (range ±0.01-10°C)
(Note: The ranges shown here for these variables are the settable ranges. Not all values in therange produce acceptable MDSC results. See the section on Optimization of Results in ModulatedDSC Compendium TA-210 for recommendations on the actual values to choose depending on themeasurement of interest.)
In the example shown in Figure 2, the underlying heating rate is 1°C/minute, the modulation period is 30seconds, and the modulation amplitude is ±1°C. This set of conditions results in a sinusoidal heating profilewhere the instantaneous heating rate varies between +13.44°C/minute and -11.54°C/minute (i.e., coolingoccurs during a portion of the modulation). Although the actual sample temperature changes in a sinusoidalfashion during this process (Figure 3), the analyzed signals are ultimately plotted versus the linear averagetemperature which is calculated from the average value as measured by the sample thermocouple (essentiallythe dashed line in Figure 2). [Note: As in conventional DSC, MDSC can also be run in a cooling or isothermalmode rather than heating mode.]
Figure 2. TYPICAL MDSC HEATING PROFILE
108.0 108.5 109.0 109.5 110.0106
107
108
109
110
111
112
-15
-10
-5
0
5
10
15
Temperature (°C)
Mod
ulat
ed T
empe
ratu
re (
°C)
[
] D
eriv
. Mod
. Tem
p. (
°C/m
in)
109.8°C
110.3°C
13.44°C/min
107.6°C
108.1°C
108.6°C
-11.54°CUnderlying Heating Rate
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The general equation which describes the resultant heat flow at any point in a DSC or MDSC experiment is:
[1]
where: = total heat flow
Cp = heat capacityβ = heating ratef(T,t) = heat flow from kinetic (absolute temperature and
time dependent) processes
As can be seen from the equation, the total heat flow ( ), which is the only heat flow measured by conven-tional DSC, is composed of two components. One component is a function of the sample�s heat capacity andrate of temperature change, and the other is a function of absolute temperature and time.
Modulated DSC determines the total, as well as these two individual heat flow components, to provide in-creased understanding of complex transitions in materials. MDSC is able to do this based on the two heatingrates seen by the material - the average heating rate which provides total heat flow information and thesinusoidal heating rate which provides heat capacity information from the heat flow that responds to the rate oftemperature change.
These individual heat flow components are often referred to by different names. In the remainder of thisdocument the terms �heat capacity component� [Cpβ] and �reversing heat flow� will be used interchangeably.Likewise, �kinetic component� [f(T,t)] and �nonreversing heat flow� will be used interchangeably.
dQ
dt= C + (T, t)pβ
dQ
dt
dQ
dt
50 100 150 200 250-0.8
-0.6
-0.4
-0.2
0.0
0
2
4
6
8
10
12
14
Temperature (°C)
Mo
du
late
d H
eat
Flo
w (
W/g
)
Mod
ulat
ed H
eatin
g R
ate
(°C
/min
)
Figure 3. MDSC RAW SIGNALS - QUENCHED PET
MODULATED HEAT FLOW
MODULATED HEATINGRATE5.01 mg sample
helium purge2oC/minute heating rate +0.5oC amplitude, 100 second period
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All of these MDSC heat flow signals are calculated from three measured signals - time, modulated heat flow,and modulated heating rate (the derivative of modulated temperature). Figure 3 shows the the latter twosignals for amorphous polyethyleneterephthalate (PET). Since these raw signals are visually complex, theyneed to be deconvoluted to obtain the more standard DSC heat flow curves. The following sections describethat process using quenched PET as the example material. (Note: Although deconvolution is required to obtainthe final quantitative results provided by MDSC, the raw signals, particularly the modulated heat flow, can stillbe used to obtain valuable insights as to what is occurring in the material, as well as to troubleshoot experimen-tal conditions and to detect artifacts. Hence, it is generally recommended that the raw modulated heat flowand modulated heating rate signals be stored as part of the MDSC data file.)
Heat Capacity
The heat capacity (Cp) of the sample is continuously determined by dividing the modulated heat flow amplitudeby the modulated heating rate amplitude. This approach is based on the well-accepted procedures for deter-mining Cp in conventional DSC. In conventional DSC, Cp is generally calculated (equation [2]) from thedifference in heat flow between a blank (empty pan) run and a sample run under identical conditions. Curves1 and 2 in Figure 4 show typical curves for sapphire.
[2]
where KCp = calibration constant
Cp can also be calculated, however, by comparing the difference in heat flow between two runs on an identi-cal sample at two different heating rates. Curve 3 in Figure 4 represents the same sapphire sample as curve 2run at a higher heating rate. In this case:
[3]
Cp = K xHeat Flow (Sample) - Heat Flow (Blank)
Heating RateCp
Cp = xHeat Flow at Heat Rate 2 - Heat Flow at Heat Rate 1
Heating Rate 2 - Heating Rate 1CpΚ
Figure 4. SAPPHIRE Cp MEASUREMENT - CONVENTIONAL DSC
10 20 30 40 50 60-1.5
-1.0
-0.5
0.0
Temperature (°C)
Hea
t F
low
(m
W)
Empty Pans
Sapphire @ 3°C/min
Sapphire @ 6°C/min
50.00°C-0.01200mW
50.00°C-0.6158mW
Delta 0.60mW
50.00°C-1.169mW
Delta 1.16mW
(1)
(2)
(3)
17.35 mg samplehelium purge
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In MDSC, the heating rate changes during the modulation cycle. In Figure 5, the MDSC conditions arechosen so that the modulated heating rate varies between two heating rates which are essentially the same asthose chosen for curves 2 and 3 in Figure 4 (i.e., approximately 3 and 6oC/minute). Overlaying the resultantmodulated heat flow curve from Figure 5 on curves 2 and 3 from Figure 4, shows (Figure 6) that taking thedifference in modulated heat flow and dividing it by the difference in modulated heating rate is equivalent tothe conventional DSC approach using two different heating rates and equation [3]. [Note: The heat capacitysignal is actually calculated in modulated DSC based on a Discrete Fourier Transformation where the mea-sured amplitudes of the sample temperature and heat flow modulation are compared to a reference sine waveof the same frequency. The equation used is:
Cp = KCp (Qamp/Tamp) (Modulation Period/2π) [4]
where: Cp = heat capacityKCp = heat capacity calibration constantQamp = heat flow amplitudeTamp = temperature amplitude
For a complete description of the Discreet Fourier Transformation technique, see Press, W.H.; Flannetry, B.P.;Teukolsky, S.A.; and Vetterling, W.T., Numerical Recipes, the Art of Scientific Computing, 1986, CambridgeUniversity Press, Cambridge, pp. 386-390.]
Reversing Heat Flow
The heat capacity (reversing) component of total heat flow is calculated by converting the measured heatcapacity into heat flow using equation [1] where β is the average (underlying) heating rate used in the experi-ment. [Note: -Cp is used in the actual calculation so that endotherms and exotherms occur in the properdownward and upward directions respectively. See Figure 7.]
Reversing Heat Flow = (-Cp) x Average Heating Rate [5]
Figure 5. SAPPHIRE Cp MEASUREMENT - MDSC
10 20 30 40 50 60-1.5
-1.0
-0.5
0.0
-4
-2
0
2
4
6
Temperature (°C)
Mo
du
late
d H
eat
Flo
w (
mW
)
[
] M
odul
ated
Hea
ting
Rat
e (°
C/m
in
+
+
MDSC Cp Measurement
Modulated Heating Rate
Modulated Heat Flow
5.932°C/min
3.152°C/min
-0.6495mW
-1.132mW
17.35 mg samplehelium purge4.5°C/minute heating rate, +0.4°C amplitude, 100 second period
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Figure 6. DSC & MDSC Cp MEASUREMENTS (SAPPHIRE)
10 20 30 40 50 60-1.5
-1.0
-0.5
0.0
Temperature (°C)
Hea
t F
low
(m
W)
Standard DSC Cp Measurement
3°C/minute
6°C/minuteModulated Heat Flow used forCp Measurement
Figure 7. REVERSING HEAT FLOW (QUENCHED PET)
HEAT CAPACITY
REVERSING HEAT FLOW
50 100 150 200 250-10
-5
0
5
10
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Temperature (°C)
Hea
t Cap
acity
(J/
g/°C
)
Rev
Hea
t Flo
w (
W/g
)
5.5 mg samplehelium purge2oC/minute heating rate, + 1oC amplitude, 100 second period
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Figure 8. TOTAL HEAT FLOW (QUENCHED PET)
25 50 75 100 125 150 175 200 225 250 275-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
Temperature (°C)
Mo
du
late
d H
eat
Flo
w (
W/g
)
[
]H
eat
Flo
w (
W/ g
)
5.5 mg samplehelium purge2°C/minute heating rate, +1°C amplitude, 100 second period
Figure 9. ALL HEAT FLOW SIGNALS - QUENCHED PET
0.2
0.1
0.0
-0.1
-0.2
-0.350 100 150
Temperature (°C)
H
eat F
low
(W
/g)
0.3
0.2
0.1
0.0
-0.1
-0.2
-0.3
[
] R
ev H
eat F
low
(W
/g)
5.5 mg sample helium purge 2°C/minute rate ±1°C amplitude 100 second period
200 250 300
0.1
0.0
-0.1
-0.2
-0.3
[
] Non
rev
Hea
t Flo
w (
W/g
)
NONREVERSING
TOTAL
REVERSING
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Total Heat Flow
The total heat flow in MDSC is continuously calculated as the moving average of the raw modulated heat flowsignal (Figure 8). [Note: As Figure 8 shows, the raw modulated heat flow is not corrected for real-time fortemperature by the current TA Instruments MDSC software and, hence transitions appear to occur lower intemperature in this raw signal than in the calculated signals. This difference is a result of the time delayassociated with �real-time� deconvolution (about 1.5 cycles).]
Nonreversing Heat Flow
The kinetic (nonreversing) component of the total heat flow is determined as the arithmetic difference be-tween the total heat flow and the heat capacity component. Figure 9 shows the three heat flows for quenchedPET.
Nonreversing Heat Flow = Total Heat Flow - Reversing Heat Flow [6]
TYPICAL APPLICATIONS
Modulated DSC provides many unique measurement capabilities. Several of those are included here forillustration. However, new applications for modulated DSC continue to be found. Contact your local TAInstruments Representative for applications notes describing these additional measurements.
Analysis of Complex Transitions
The blending of two or more polymers is becoming a common method for developing new materials fordemanding applications such as impact resistant parts and packaging films. Since the ultimate properties ofblends can be significantly affected by what polymers are present, as well as by small changes in the blendcomposition, suppliers of those materials are interested in rapid tests which provide verification that the correctpolymers and amount of each polymer are present in the blend. Conventional DSC has proven to be aneffective technique for characterizing blends such as polyethylene/polypropylene where the crystalline meltingendotherms or other transitions (e.g., glass transition) associated with the polymer components are sufficientlyseparated to allow identification and/or quantitation. However, many blends do not exhibit this convenientseparation and thus are difficult to accurately evaluate by conventional DSC.
Figure 10, for example, shows the conventional DSC result for the first heat on a polymer blend (solid line)containing polyethyleneterephthalate (PET) and acrylonitrile-butadiene-styrene (ABS). There are threeobvious transitions indicative of the glass transition, cold crystallization, and crystalline melting of the PET, seenat 67, 121, and 235°C respectively. However, no apparent ABS transitions are observed. Upon reheating,after cooling at a controlled rate (10°C/minute), the conventional DSC result changes (broken line). Now onlytwo transitions are observed - a glass transition at 106°C and a crystalline melt at 238°C. Explanation of thesechanges on reheating, particularly the apparent shift in the glass transition temperature, is difficult based ononly these results.
The MDSC results for the �as received� material shown in Figure 11 helps to resolve these interpretationissues. Phenomena such as glass transitions are reversing under MDSC, while cold crystallization isnonreversing. Hence, separation of the total heat flow into its reversing and nonreversing components sepa-rates overlapping thermal events with different behavior. The nonreversing curve in this case shows only theexotherm associated with the PET cold crystallization, as well as a weak endotherm about 70°C associatedwith relaxation phenomena. The reversing curve shows two transitions - the glass transition (67°C) for PET,as well as a second glass transition (at 105°C) associated with the ABS. In conventional DSC, this latter glasstransition is hidden under the PET cold crystallization peak and thus only becomes visible on reheating.
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Figure 10. PET/ABS BLEND - CONVENTIONAL DSC
50 100 150 200 250-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
Temperature (°C)
Hea
t F
low
(W
/g)
120.92°C
67.38°C70.262°C (H) 235.36°C
22.63J/g
111.82°C9.016J/g
249.75°C
FIRST HEAT ON MOLDED PART
SECOND HEAT AFTER 10°C/min COOLING(Curve shifted on Y axis to avoid overlap)
9.22mg samplenitrogen purge10°C/minute heating rate
Figure 11. PET/ABS BLEND - MODULATED DSC
NONREVERSING
TOTAL
REVERSING
PET Tg
ABS Tg
FIRST HEAT ON MOLDED PART
20 40 60 80 100 120 140 160 180 200-0.15
-0.14
-0.13
-0.12
-0.11
-0.10
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
Temperature (°C)
Hea
t F
low
(W
/g)
[
] N
on
rev
Hea
t F
low
(W
/g)
-0.02
-0.03
-0.04
-0.05
-0.06
[
] R
ev H
eat
Flo
w (
W/g
)
67.00°C72.89°C(H)
104.45°C
107.25°C(H)
8.46mg samplenitrogen purge2°C/minute heating rate, +1°C amplitude, 60 second period
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Increased Sensitivity For Detecting Weak Transitions
Weak transitions such as the glass transition are measured in DSC based on the change in heat capacity whichoccurs during the transition. Since this heat capacity change appears as a step change in the heat flow curve,it is important that other �baseline effects� in the heat flow curve are minimal. Unfortunately, this is notalways the case. Figure 12 shows a polymer resin where the presence of moisture has such severe effects onthe baseline that the glass transition is difficult to determine definitively. However, in modulated DSC theseeffects, which are nonreversing, are separated from the transition of interest, which is reversing.
Increased Resolution
Sensitivity and resolution in DSC are both affected by heating rate. Faster heating rates improve sensitivitybut decrease resolution, while the converse is true for slower heating rates. Therefore, choosing a heating ratein conventional DSC is always a compromise. Modulated DSC eliminates this need to compromise by essen-tially exposing the sample to two different heating rates simultaneously - a slow average (underlying) heatingrate and a fast instantaneous heating rate. The result is both good resolution and sensitivity in the sameexperiment. Figure 13 shows the results for sodium nitrite where an underlying heating rate of 0.05°C/minuteis necessary to provide adequate resolution of the two weak heat capacity changes associated with phasetransitions between 163 and 166°C. Despite this slow heating rate, the sensitivity is still sufficient to readilydetect these transitions.
Direct Measurement of Heat Capacity
Heat capacity (Cp) measurement by conventional DSC is a tedious process requiring multiple experiments andconsiderable operator expertise to obtain results with reasonable accuracy and precision. MDSC provides theability to measure heat capacity more directly and measure it even at slow (including isothermal) heating rateconditions. In addition, MDSC can measure heat capacity changes during certain transitions. Figure 14 shows
Figure 12. Tg IN POLYMER RESIN
NOTE: ALL CURVES @SAME SENSITIVITY
TOTAL
NONREVERSING
REVERSING
0 50 100 150 200-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
-0.4
-0.2
0.0
0.2
0.4
0.6
Temperature (°C)
Hea
t F
low
(W
/g)
[
] R
ev H
eat
Flo
w (
W/g
)
[
] N
on
rev
Hea
t F
low
(W
/g)
-0.2
-0.4
-0.6
-0.8127.79°C
131.17°C(H)
3.08 samplenitrogen purge5°C/minute heating rate, +1°C amplitude, 60 second period
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Figure 13. SODIUM NITRITE - MDSC
Figure 14. ISOTHERMAL EPOXY CURE - MDSC
Non
rev
Hea
t Flo
w (
mW
)
6
4
2
0
DM A 1H z
Tim e (m in)
15 20 25 35 40301050
H eat
Capacity
(
) H
eat C
apac
ity (
mJ/
°C)
14.5
14.0
13.5
13.0
12.5
12.0
11.5
(
)
E' (
GP
a)
30
20
10
0
∆H of Cure
Isothermal 80°Chelium purge+0.5°C amplitude60 second period
161 162 163 164 165 166 1672
3
4
5
6
7
Temperature (°C)
Com
plex
Cp
(J/g
/°C
)
32.96mg samplehelium purge0.05°C/minute heating rate, +0.1°C, amplitude, 80 second period
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the heat capacity change occurring during the isothermal cure of an epoxy thermoset. As expected, the heatcapacity decreases during cure as the material�s free volume and mobility decrease because of crosslinking.The onset of the heat capacity decrease occurs after the exothermic peak maximum which implies that heatcapacity changes more dramatically during the final stage of cure (crosslinking) than during linear polymeriza-tion (the first stage of cure). Evaluation by dynamic mechanical analysis (DMA) supports this conclusionsince the modulus (E') increases at exactly the same time as heat capacity decreases.
Thermal Conductivity Measurement
Thermal conductivity is a measure of the ease with which heat is transmitted through a material and is a basicmaterial property. Materials with high thermal conductivity are called �conductors� and those with lowconductivity are called �insulators�. Solid conductors (such as metals) typically have thermal conductivities inthe range of 10 to 400 W/°C m while insulators (such as polymers, glasses and ceramics) have values in therange of 0.1 to 2 W/°C m. Furthermore, thermal conductivity changes as a weak function of temperature andrarely changes by a factor of ten within a general class of materials.
Conventional DSC can be used to measure the thermal conductivity of insulating materials. However, themeasurement requires modification of the DSC cell and a very tedious experimental procedure. ModulatedDSC provides a much better way to obtain similar information. MDSC is applicable to materials whosethermal conductivity are in the range 0.1 to 1.5 W/°Cm. MDSC measurement does not require any modifica-tions to the DSC system. With proper calibration, accuracy and precision equivalent to accepted ASTMprocedures are obtained.
Comparative Thermal Conductivities
MDSC MDSC MDSCExp�t. Literature Var. from Coeff. Var.
Material (W/°Cm) (W/°Cm)** Lit. (%) (%)*
Polystyrene 0.14 0.14 0 2.2Polytetrafluoroethylene 0.34 0.33 3 2.3Soda Lime Glass 0.73 0.71 3 7.5Pyrex 7740 1.09 1.10 1 4.7
* average based on 4 measurements** Thermal Conductivity of Selected Materials, NIST Reference Series (1996).
CALIBRATION
Modulated DSC requires the same basic calibrations as conventional DSC (baseline, temperature, and heatflow). In addition, however, because heat capacity determination is a necessary first step to calculatingreversing and nonreversing heat flow, a heat capacity calibration must be performed for MDSC. Note: In allcalibrations, the experimental conditions (e.g., pan type, purge gas, heating rate, modulation amplitude andperiod) should be identical to those used in subsequent sample evaluations.
Baseline calibration is based on a conventional DSC experiment in which an empty cell is heated over abroad temperature range. The resultant curve is used to correct for cell heat flow imbalance between thesample and reference positions.
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Temperature calibration is based on a conventional DSC experiment in which a reference material is heatedthrough a well-characterized transition (e.g. indium melting). The transition temperature obtained is comparedwith its literature value to determine a calibration factor. At least two calibration standards which bracket thetemperature range of interest are recommended.
Heat flow calibration is also based on a conventional DSC experiment in which a reference material isheated through a well-characterized transition (e.g. indium melting). The heat flow associated with thetransition is compared with the literature value to determine a calibration factor.
Heat capacity calibration is based on an MDSC experiment with a known standard such as sapphire. Asingle calibration value is used and it should be determined near the middle of the desired temperature range(when using an underlying heating rate) and near the transition of interest (when making isothermal measure-ments). Alternatively, multiple calibrations which bracket the temperature region of interest can be averagedand used. Best results are obtained using 25mg (nominal) of sapphire at the same conditions as the subse-quent sample runs. Note: Long periods (100 seconds) provide the best accuracy for heat capacity measure-ments because they provide maximum time for heat transfer through the sample.
OPTIMIZATION OF RESULTS
This section contains a general discussion of experimental parameters which can affect MDSC results, as wellas recommended settings for those parameters in both general applications and specific situations (e.g. glasstransition measurement). These recommendations are not intended to be absolute, but rather areintended to be good starting points.
Recommended General Conditions
� Prepare the sample to maximize effective heat transfer and to minimize thermal gradients- Spread the sample uniformly across the bottom of the pan. Use a thin film or a piece of sample withits flat side towards the pan. Do not use large irregular chunks.- Weigh the sample before and after the experiment to assure that no weight loss has occurred.- Use 5-15 mg (organics and polymers) or 20-50 mg (inorganics) samples.
� Select and prepare the sample pan to minimize gradients- Use standard, crimped pans if possible. Liquids and volatile materials may require hermetic pans.- Ensure that the bottom of the pan after sealing/crimping is as flat as possible. Lightly sanding thebottom of the pan with fine sand paper sometimes improves flatness.- Match weights of sample and reference pans as closely as possible.
� Select an appropriate purge gas
A purge gas should be used in modulated DSC experiments since it helps provide uniform heat trans-fer in the cell. Higher thermal conductivity purge gases such as helium are recommended. Typicalflow rates are 25-50 ml/minute. Purge through both the PURGE GAS (at 25 ml/minute) andVACUUM (at 50 ml/minute) ports on the DSC module. The latter purge improves modulation athigher amplitudes.
� Use a cooling accessory
For most MDSC experiments it is necessary to have a source of cooling present so that the instanta-neous heating rate fluctuations required by the chosen conditions can be achieved. A RefrigeratedCooling system (RCS), or a Liquid Nitrogen Cooling Accessory (LNCA) are two options. SinceMDSC experiments are longer than conventional DSC experiments (because slower underlying
16
heating rates and/or �quasi-isothermal� conditions are used), the RCS, which does not consumecoolant, is recommended unless its temperature range (-70 to 400°C) does not cover the region ofinterest.
� Select a modulation period of 40-100 secondsFor most samples in standard crimped pans, 60 seconds is the recommended period of oscillation.Larger periods may be necessary for the larger mass hermetic pans. For higher thermal conductivitypurge gases (e.g., helium), a 40 second period is sufficient for many measurements. Periods of 30seconds or less are generally not recommended.
� Select an underlying heating rate of 1-5°C/minuteThe maximum practical heating rate for MDSC experiments is 5°C/minute. The ideal heating rate isone that provides at least 4 temperature oscillations (periods) over the temperature range ofeach transition studied.
� Use a modulation amplitude between ±0.5 and 3°CLarger amplitudes (±1.5 to 3°C) should be used when measuring weak glass transitions. Smalleramplitudes should be used for analysis of sharp transitions which are only a few oC wide. Amplitudessmaller than ±0.03°C should be avoided since they are difficult to control.
The modulation amplitude in combination with the period determines the range of instantaneousheating/cooling rates obtained during modulation. The amplitude can be chosen to achieve heat only,heating/cooling (as in Figure 15), or heat/isothermal (see the section on recommended conditions forstudying melting phenomena on page 19).
Note: Both the purge gas and DSC cell cooling capacity affect the range of achievable modulationamplitudes. Larger amplitudes and shorter periods require greater cell cooling capacity. A possibleconcern when using larger amplitudes, especially at low temperatures, is that some amplitude settingscannot be achieved at some periods.
Figure 15. POLYMER COMPOSITE - MDSC MODULATED HEATING RATE
80 85 90 95 100-30
-20
-10
0
10
20
Temperature (°C)
Mod
ulat
ed H
eatin
g R
ate
(°C
/min
) MODULATED HEAT RATE: DIFFERENCE OF 32°C/MIN
30.5 mg samplenitrogen purge1°C/minute heating rate, +2.5°C amplitude, 60 second period
COOLING
HEATING
17
� Use a data storage rate of 1 second/data point and store both the raw and deconvoluted signals.
The data storage rate in MDSC may be selected from the same range of values as for conventionalDSC, namely 0.2 to 1000 seconds/ data point. The default is 0.2 seconds/point. However, increasingthe storage interval helps reduce the size of the MDSC files without compromising the quality of thedata. This is because the data used to calculate the stored data is always collected at 0.2 seconds/data point. Data storage at 1 second/data point is recommended.
Since deconvolution of the MDSC heat capacity and heat flow signals occurs essentially in real-time(there is a 1.5 cycle delay), the option exists for not storing the raw modulated signals. Nevertheless,it is recommended that these raw signals be stored since they often provide useful troubleshootingassistance (see next section) and/or visual confirmation of specific thermal events. The list of recom-mended signals for storage includes time, temperature, modulated heat flow, modulated temperature,heat flow phase, heat capacity, total heat flow, reversing heat flow, and nonreversing heat flow.Storage of all these MDSC signals, however, makes file sizes larger.
Verifying Acceptability of Conditions Chosen
Just as with conventional DSC, good reproducibility and accuracy of results in MDSC are based on theassumption that the sample is able to follow the heating/cooling regime imposed on it. Said another way, if theexperimental conditions result in a modulated heating profile which the sample cannot follow, goodresults will not be obtained. The modulated heat flow profile (Figure 16) provides an excellent way todetermine if the sample is following the modulation. A smooth, regular sine wave indicates reasonable experi-mental conditions.
Examination of the modulated heating rate profile or the Lissajous plot of modulated heat flow versus modu-lated heating rate (Figure 17), also provides an indication that reasonable experimental conditions are chosen.Note: Lissajous plots are only possible using Thermal Solutions Software.
Figure 16. MODULATED SIGNAL INDICATES QUALITY RESULTS
135 140 145 150 155 160Temperature (°C)
Mo
du
late
d H
eat
Flo
w (
mW
)
+1.5°C Amplitude
+3.5°C Amplitude
+5.5°C Amplitude
5°C/min Ramp
No Distortion
Distortion
40 Seconds Period
18
Figure 17. LISSAJOUS PLOT INDICATES QUALITY RESULTS
Typical Conditions for Studying Glass Transitions (The conditions described here reflect minor changesto the General Conditions described earlier and are designed to optimize glass transition results).
� 10-30 mg sample weight
� Crimped aluminum pans (matched ±0.1 mg).
� Underlying Heating RateUse a rate up to 5°C/minute. Use lower heating rates if necessary to achieve at least fourmodulation cycles over the temperature range of the transition.
� Amplitude = ±1°CUse larger values (up to ±3°C) for very weak transitions.
� Period = 60 seconds
� Helium purge at 25 mL/minute
� 1 second/data point storage rate
Recommended Conditions for Polymer Melting (Initial Crystallinity) [The conditions described herereflect minor changes to the General Conditions described earlier and are designed to optimize studies of themelt region].
In semicrystalline, broad melting polymers, MDSC has the unique ability to separate melting from simultaneouscrystallization/crystalline perfection on the basis that these phenomena are reversing and nonreversing respec-tively. Hence, MDSC provides more accurate measurement of the onset and temperature range of melting, aswell as initial crystallinity.
� 10-15 mg sample weight
-12 -8 -4 0 4 8 12-0.4
-0.2
0.0
0.2
0.4
Modulated Heatin g Rate (°C/min )
Mo
du
late
d H
eat
Flo
w (
W/g
)
In Control
Out of Control
19
� Crimped aluminum pans (matched ±0.1 mg)
� 5°C/minute Underlying Heating Rate
� Period = 40-60 secondsUse longest period possible to still achieve at least 4 modulations at half-height of the melting peak.
� Select the amplitude to achieve an instantaneous heating rate that varies between some positive value andzero (isothermal). The table shown in Figure 18 provides guidance in choosing that amplitude. Thereare two reasons for adjusting conditions to periodically achieve a 0°C/minute minimum instantaneousheating rate. First, by not cooling the material at any time during the modulation, the possibility for�artificially� affecting any crystallization phenomena observed is eliminated. Second, and more impor-tantly, when the heating rate is zero, there is no heat flow associated with heat capacity-related
(reversing) events [recall the earlier equation governing heat flow dQ
dtC f T tp= +β ( , ) ] and hence any
heat flow observed must be the result of kinetic phenomena. Figure 19, for example, shows themodulated heat flow curve for quenched polyethyleneterephthalate (PET) with the conditions set toperiodically achieve a zero heating rate. The exothermic behavior observed above the cold crystalliza-tion is associated with ongoing crystallization/crystalline perfection processes which cannot be ob-served by conventional DSC. The deconvoluted nonreversing heat flow (solid line) as expectedcorresponds exactly with the raw heat flow until steady state is lost in the melt above 230°C.
� Helium purge at 25 mL/minute
� 1 second/data point storage rate
Figure 18. SELECTION OF AMPLITUDE FOR �HEAT / ISO� EXPERIMENTS
0.1 0.2 0.5 1 2 5 10
10 0.003 0.005 0.013 0.027 0.053 0.133 0.265
20 0.005 0.011 0.027 0.053 0.106 0.265 0.531
30 0.008 0.016 0.040 0.080 0.159 0.398 0.796
40 0.011 0.021 0.053 0.106 0.212 0.531 1.062
50 0.013 0.027 0.066 0.133 0.265 0.663 1.327
60 0.016 0.032 0.080 0.159 0.318 0.796 1.592
70 0.019 0.037 0.093 0.186 0.372 0.929 1.858
80 0.021 0.042 0.106 0.212 0.425 1.062 2.123
90 0.024 0.048 0.119 0.239 0.478 1.194 2.389
100 0.027 0.053 0.133 0.265 0.531 1.327 2.654
Heating Rate (°C/min)
Per
iod
(sec
)
T = H * P
2 *60amp r πwhere: T
amp = maximum temperature amplitude for "heat only" (°C)
Hr = Average heating rate (°C/min)P = period (seconds)
20
Figure 19. EXOTHERMIC EVENTS IN QUENCHED PET
Typical Conditions for Heat Capacity Measurements (The conditions described here reflect minorchanges to the General Conditions described earlier and are designed to optimize heat capacity results.)
In situations where accurate heat capacity is the parameter of primary interest (rather than total, reversing andnonreversing heat flows), it is worthwhile to invest additional experimental time to ensure optimum accuracyand reproducibility.
� Sample weight: 10-15 mg polymers, 15-25 mg sapphire, 25-50 mg metals
� Crimped aluminum pans (matched within ±0.1 mg)
� Underlying Heating Rate 0-5°C/minuteGenerally, comparable results are obtained from any heating rate in this range. However, there aresituations where a heating rate of zero (�quasi-isothermal� conditions) are desirable. For example,Figure 20 shows the heat capacity curves for polystyrene during its glass transition when heating andcooling at 1°C/minute (solid lines). The curves are different because of time-dependent hysteresiseffects in the region of the glass transition. The dashed line, on the other hand, represents the heatcapacity values obtained using quasi-isothermal experiments which remove this time-dependency.These values are the same whether the transition is approached from lower or higher temperature.MDSC, therefore, provides the steady state glass transition shape and temperature, as well as Cpvalue as a function of temperature.
Another situation where quasi-isothermal conditions are valuable is shown in Figure 21. The measure-ment of Cp during melting is complicated by the fact that two �apparently reversing� phenomena (Cpand melting) simultaneously contribute to the modulated heat flow amplitude and hence create anartificially high value for Cp. However, using quasi-isothermal conditions where the heat of melting iseffectively spread over an extremely large number of modulations, it is possible to reduce the effectattributable to melting and obtain Cp trends which agree with theory. Note: This measurement of Cpduring melting may not work for materials which rapidly crystallize (e.g., polyethylene).
50 100 150 200 250-0.05
0.00
0.05
0.10
0.15
-0.05
0.00
0.05
0.10
0.15
Temperature (°C)
Mo
du
late
d H
eat
Flo
w (
W/g
)
No
nre
v H
eat
Flo
w (
W/g
)
MODULATED HEATFLOW
NONREVERSINGHEAT FLOW
5.70mg sample sizehelium purge2°C/minute heating rate, +0.318°C amplitude, 60 second period
21
Figure 20. POLYSTYRENE Tg UNDER DIFFERENT MDSC CONDITIONSH
eat C
apac
ity (
J/g/
°C)
2.0
1.8
1.6
1.4
Cooling
Comparison of Heating and Cooling Ramps @ 1°C/minwith Isothermal Measurements
Heating
Temperature (°C)
90 95 100 110 115 12010585
Isothermal
+0.5°C amplitude, 60 second period
Figure 21. HEAT CAPACITY - SLOW COOLED PET
50 100 150 200 2500
2
4
6
8
Temperature (°C)
Hea
t Cap
acity
(J/
g/°C
)
9.55mg samplehelium purge+0.531°C amplitude, 40 second period
HEATED @ 5°C/MIN
ISOTHERMAL MEASUREMENTSPERFORMED OVER 6 DAYS
22
Typical Conditions for Heat Capacity Measurements (cont.)
� Amplitude = ±0.5 to 1.0°C
� Period = 80-100 seconds
� Helium purge at 25 mL/minute
� 1 second/data point storage rate
Recommended Conditions for Thermal Conductivity
Thermal conductivity measurement by MDSC is based on two experiments using the same sample materialbut different sample thickness. In one experiment, a thin sample is used, and the experimental conditions arechosen to ensure that accurate heat capacity information is obtained (i.e., the sample follows the appliedmodulation). In the other experiment, a thick sample without a pan is used so that the temperature modulationoccurs only in part of the sample (the side in contact with the pan) and the remainder of the sample, in effect,becomes a heat sink. [For a complete discussion of the theory associated with this measurement, see publica-tion TA 086.]
Specific experimental recommendations include:
� Sample weight:- 10-15 mg (thin sample) for accurate heat capacity measurement. Sample is run in a crimped aluminumpan.- 100-150 mg (thick sample). Cut sample to be a right circular cylinder 3.4 - 3.8 mm high. Use of a largediameter (6.3 mm) sample is preferred to minimize heat losses through the sides of the sample. Thisthick sample is run directly on the DSC cell platform without a sample pan. However, an aluminum foildisk and a drop of silicone oil should be used to improve thermal contact.
� Underlying heating rate = 0. This is a quasi-isothermal measurement.Allow 10-15 minutes for equilibration before taking data.
� Amplitude = ±0.5°C
� Period = 80 seconds
� Use polystyrene to obtain the additional calibration required to compensate for heat losses through thesides of the sample.
� Helium purge at 25 mL/minute
� 1 second/data point storage rate
� Thermal conductivity experiments are generally run at specific temperatures of interest (e.g., ambienttemperature). This MDSC procedure should not be used in a region above the melting or softening pointof the material because the thick sample may adhere to the DSC cell platform causing contamination.
23
21 22 23 24 25 26-4
-2
0
2
4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Time (min)
Mod
ulat
ed H
eatin
g R
ate
(°C
/min
)
[
] Mod
ulat
ed H
eat F
low
(m
W)
21.92min
21.97min
ADDITIONAL EXPERIMENTAL CONSIDERATIONS
There are several additional experimental considerations which may influence the results obtained, includingphase lag, frequency effects at the glass transition, and separation of reversing and nonreversing heat flowduring melting. These are described here along with an indication of their impact.
Phase Lag
The general heat flow equation used to describe modulated DSC as stated earlier is dQ
dtC f T tp= +β ( , ) . This
equation assumes that, in regions where the sample material has no time dependent (kinetic) phenomena, thesample responds instantaneously and directly tracks the sinusoidal heating profile. As Figure 22 shows, thismeans that the modulated heat flow is 180o out-of-phase with respect to the modulated heating rate [when themodulated heating rate is maximum, the resultant heat flow is most endothermic]. In reality, this assumption isnot completely valid. There is actually a phase shift (lag) between the two measured raw signals due to non-instantaneous heat transfer between the DSC cell and the sample. In regions where no thermal events areoccurring in the sample, this lag is due entirely to experimental effects (e.g., sample pan-to-DSC cell diskcontact). In regions where the sample exhibits thermal events, this lag is a combination of experimental andsample effects. As a result, the heat capacity measured in modulated DSC is actually the complex heatcapacity (Cp*) which can be split into a component Cp' (usually considered the �real� or thermodynamic heatcapacity) which is in-phase with temperature modulation and an out-of-phase, imaginary component Cp".[The relationship between these heat capacity components is Cp* = (Cp'2 + Cp"2)½.] To obtain a quantitativemeasure of Cp", and hence Cp', it is first necessary to compensate (calibrate) for the lag associated withexperimental effects. This is easily accomplished by selecting �baseline� areas outside the transition regionand adjusting the phase angle to the theoretically expected 0° or zero-phase lag. Any remaining lag is thenattributable to the sample and can be used to calculate Cp' and Cp". Figure 23 shows that there is a smallpeak in Cp" at the glass transition for amorphous PET. However, its resultant effect on Cp' is <1%. Figure 24shows, furthermore, that the effect of Cp" becomes significant for this material only in the melt where steadystate is lost. Correction for Cp" is hence currently only of interest academically. However, future work withsuitable models may enable additional information about the material�s structure and behavior to be obtainedfrom quantifying Cp".
Figure 22. PHASE SHIFT BETWEEN MODULATED TEMPERATURE & HEAT FLOW
24
Figure 23. CONTRIBUTIONS TO HEAT CAPACITY (QUENCHED PET)
Figure 24. PHASE-CORRECTED HEAT FLOW SIGNALS (QUENCHED PET)
50 100 150 200 250 300-0.3
-0.2
-0.1
0.0
0.1
-0.2
-0.1
0.0
0.1
0.2
Temperature (°C)
Rev
Hea
t F
low
(W
/g)
No
nre
v H
eat
Flo
w (
W/g
)
NONREVERSING
REVERSING
Solid Line = Cp* x Aver. Heating RateDashed Line = Cp’ x Aver. Heating Rate
50 100 150 200 250 3000
1
2
3
4
5
6
0
1
2
3
4
5
6
Temperature (°C)
Com
plex
Cp
(J/g
/°C
)
[---
----
---]
Rev
Hea
t Cap
acity
(J/
g/°C
)
4
3
2
1
0
[
]
Kin
etic
Hea
t Cap
acity
(J/g
/°C
)
Cp*Cp’
Cp"
25
Frequency Effects
Material transitions such as the glass transition may exhibit a temperature and time dependency. This meansthat those transitions may shift to higher temperatures as the frequency of measurement increases. Hence,particularly in techniques such as dynamic mechanical analysis (DMA) where several decades of frequencyare commonly covered, it is important to calibrate and compare materials at the same frequency.
Modulated DSC, because it involves a sinusoidal modulation, also imposes frequency effects on the collecteddata. Normally, those effects are of no concern provided the modulation period, which determines frequency,is constant when comparing materials. Even in situations where the period varies, frequency effects should besmall because of the narrow range of useable MDSC periods (25-100 seconds). Nevertheless, there areapplications where it still must be considered. For example, the separation of endothermic relaxation pro-cesses from the glass transition.
In amorphous polymers, it is common for an enthalpic relaxation to be present over the glass transition region.This relaxation, which has been described in the literature using several names including stress relaxation andvolume relaxation, is endothermic and increases in size with longer aging times and increased aging tempera-tures. Hence, measuring the size of this relaxation is of interest because end-use applications such as wear-dated carpet fibers and packaging are affected by changes in internal polymer structure due to aging. Unfor-tunately, in conventional DSC overlap of the glass transition and the enthalpic relaxation is often sufficient tomake interpretation difficult and measurement of the energy associated with the relaxation essentially impos-sible even using sigmoidal baseline treatments to account for baseline shifts. Modulated DSC, because itseparates nonreversing phenomena such as relaxation processes from reversing phenomena like the glasstransition, should be an ideal technique for quantifying the heat associated with the relaxation. However, theresults obtained by modulated DSC are dependent on experimental conditions. The reason for this is readilyexplained by comparing the reversing and total heat flow curves used to generate those results as shown forpolystyrene in Figure 25. The total heat flow profile is unaffected by the change in modulation period (fre-quency). The reversing heat flow, on the other hand, is affected, shifting as expected to higher temperatures
Figure 25. EFFECT OF MODULATION FREQUENCY ONTOTAL AND REVERSING SIGNALS
85 90 95 100 105 110 115 120-0.14
-0.13
-0.12
-0.11
-0.10
-0.07
-0.06
-0.05
-0.04
-0.03
Temperature (°C)
Hea
t F
low
(W
/g)
Rev
Hea
t F
low
(W
/g)
TOTAL
REVERSING
EFFECT OF PERIOD (on Tg)SOLID = 100 sec PERIODDASH-DOT = 50 sec PERIODDASH = 25 sec PERIOD
9.5mg samplehelium purge2°C/minute heating rate, +0.4°C amplitude
104.68°C-0.05993W/g
106.79°C-0.05989W/g
26
Figure 26. EFFECT OF DIFFERENT MODULATION FREQUENCIES ON CALCULATEDNONREVERSING (ENTHALPIC RELAXATION) SIGNAL
Figure 27. COOLING CURVES FOR RELAXATION CORRECTION
NONREVERSING
50 60 70 80 90 100 110
-0.16
-0.14
-0.12
-0.10
-0.08
Temperature (°C)
Hea
t F
low
(W
/g)
REVERSING HEAT FLOW CURVESAT TWO FREQUENCIES
ADDITIONAL NONREVERSING AREA MEASURED ATHIGHER FREQUENCY
AREA MEASUREDAT LOWER
FREQUENCY
TOTAL HEAT FLOWCURVE
85 90 95 100 105 110 115 120-0.035
-0.030
-0.025
-0.020
-0.015
-0.010
0.045
0.050
0.055
0.060
0.065
0.070
0.075
0.080
Temperature (°C)
Hea
t Flo
w (
W/g
)
Rev
Hea
t Flo
w (
W/g
)
EFFECT OF PERIOD (frequency)ON GLASS TRANSITIONTEMPERATURE
TOTAL
REVERSING
+ +103.59°C0.05891W/g
105.70°C0.05892W/g
SOLID = 100 sec PERIODDASH-DOT = 50 sec PERIODDASH = 25 sec PERIOD
27
as modulation period decreases. Since the nonreversing heat flow is determined by subtracting the reversingheat flow from the total heat flow, this shift makes the nonreversing heat flow larger than expected. (SeeFigure 26). If the ultimate interest is constructing a correlation curve for comparing the area of the relaxationendotherm with other end-use properties, then this error in nonreversing heat flow can be ignored provided acommon modulation period is used. Conversely, to obtain an absolute measure of the heat of relaxationrequires another series of experiments. Those experiments are cooling curves at the corresponding frequen-cies (See Figure 27). Comparing the total and reversing heat flow curves on cooling provides a �frequencyshift correction factor� which accounts for the error in the calculated nonreversing heat flow directly related tothe frequency shift. When that correction is made, the accuracy and reproducibility of the heat of enthalpicrelaxation measurement is excellent (Figure 28). [Note: The glass transition temperature in the reversing heatflow is also affected by the modulation period (frequency). This effect needs to be considered when compar-ing results.]
Separation of Reversing and Nonreversing Heat Flow
As stated earler, the total heat flow obtained from modulated DSC is equivalent to the heat flow signal ob-tained from conventional DSC. In additon, the total heat flow is not affected by the selected experimentalconditions, provided good modulation is obtained (see page 17). The separation of the total heat flow intoits reversing and nonreversing components is, however, affected by the selected experimentalconditions expecially in temperature regions where time-dependent (nonreversing) events occur(e.g., the melting region). Figure 29 shows typical differences in the reversing and nonreversing heat flowsfor quenched PET in the melting region. These results where obtained under equivalent experimental condi-tions except for modulation amplitude. Nevertheless, despite these differences, the initial crystallinity (which isthe sum of the two heat flows and therefore the total heat flow over that region) is constant and more impor-tantly agrees well with that obtained from x-ray diffraction measurements. Note: The separation of the total
Figure 28. FREQUENCY EFFECT ON ENTHALPIC RELAXATION (POLYSTYRENE)
FrequencyEnthalpic
Relaxation(Uncorrected)
Correction FromNonreversing
Cooling
EnthalpicRelaxation(Corrected)
.04 Hz (25 sec) 1.82 J/g 1.12 J/g 0.70 J/g
.01 Hz (100 sec) 1.32 J/g 0.60 J/g 0.72 J/g
2oC/minute heating rate, +0.4oC amplitude
28
Figure 29. EFFECT OF EXPERIMENTAL CONDITIONS ON REVERSING/NONREVERSING HEAT FLOWS IN MELT REGION
Amplitude Reversing Nonreversing InitialCrystallinity
+0.51°C 126 J/g 125 J/g 1 J/g
0.75 113 111 2
1.00 103 102 1
1.25 89 84 5
heat flow into its reversing and nonreversing components during melting is also affected by the loss of steadystate (see Figure 19). This further affects the quantitative reproducibility and accuracy of these two heat flowcomponents but does not affect the total heat flow or initial crystallinity values.
Additional theory and studies are needed before the reversing and nonreversing heat flows themselves can becorrelated to specific material phenomena once steady state is lost in the melting region.
ADDITIONAL MODULATED DSC REFERENCES
The following is a compilation of technical publications from the open literature (compilation date 8/96) whichmay be helpful in further broadening your knowledge of MDSC and its applications. See TA InstrumentsPublication TN-33 for the latest additions to this list.
�AC Calorimetric aspect of dynamic differential scanning calorimetry�, Ichiro Hatta, Thermochimica Acta, 272, 49-52 (1996).
�A Mathematical Model for Modulated Differential Scanning Calorimetry�, A.A. Lacey, C. Nikolopoulos, and M. Reading, submittedfor publication (Jan. 1996).
�Heat Capacity Measurements by Modulated DSC at Constant Temperature�, Y. Jin, A. Boller and B. Wunderlich, J. ThermalAnalysis, submitted 2 July 1993.
�High Precision Heat Capacity Measurements by Dynamic Differential Scanning Calorimetry�, Ichiro Hatta and Satashi Muramatsu,submitted for publication to Jpn. J. Appl. Phys. 35, L858-L860 (1996).
5oC/minute heating rate, 40 second period
29
�Modeling the Heat Flow Capacity of Modulated Differential Scanning Calorimetry�, Bernhard Wunderlich, submitted for publicationin J. Thermal Anal. (Feb. 1996).
�Modulated Differential Scanning Calorimetry: VIII Interface Development Between Films of Polyepichlorohydrin and Poly (vinylacetate)�, M. Song, D.J. Hourston, H.M. Pollock, A. Hammiche, and M. Reading, submitted for publication (8/96).
�Modulated Differential Scanning Calorimetry in the Glass Transition Region, VI - Model Calculations Based on Poly(ethyleneTerephthalate)�, Bernhard Wunderlich and Iwao Okazaki, submitted for publication in J. Therm. Anal. June, 1996.
�Modulated Differential Scanning Calorimetry in The Glass Transition Region, V: Activation Energies and Relaxation Times ofPoly(ethylene terephthalate)�, Iwao Okazaki and Bernhard Wunderlich, submitted for publication in J. Polymer Sci., Part B,Polymer Physics, Dec. 1996 issue.
�Modulated Differential Scanning Calorimetry in the Glass Transition Region, III - Evaluation of Polystyrene and Poly(ethyleneterephthalate)�, A. Boller, I. Okazaki, and B. Wunderlich, Thermochim. Acta , 286, 1-19 (1996).
�Simulation of Dynamic DSC of Temperature Dependent Heat Capacity�, Katsuhido Knari and Takeo Ozawa, submitted forpublication to Thermochim Acta (1996).
�Utility of Phase Correction in MDSC�, P.S. Gill and S.R. Aubuchon, submitted for publication to Proc. 11th ICTAC Conference(1996).
�A Study of Calcium Oxalate Monohydrate Using Dynamic Differential Scanning Calorimetry and other Thermoanalytical Tech-niques�, Keith J. Kociba, M.S. Thesis, Ohio State University (1995).
�A Study on the Curing Process of Epoxy Resins with DDSC�, K. Yokokawa, S. Tatsumiya and K. Miki, Proc. 31st JapaneseConference on Calorimetry and Thermal Analysis, 118-119 (1995).
�Application of Dynamic Differential Scanning Calorimetry to the Study of Phase Transitions�, I. Hatta, H. Ichikawa, and M. Todoki,Thermochim. Acta, 267, 83 (1995).
�Applications of Modulated Temperature Differential Scanning Calorimetry to a Range of Problems in Polymer Science�, D.Hourston, M. Song, H. Pollock, A. Hammiche, Proc. 21st North American Thermal Analysis Society Conference, 109-114(1995).
�Approach to Study of Heat Denaturation of Protein Using Dynamic DSC�, S. Muramatsu and I. Hatta, Proc. 31st JapaneseConference on Calorimetry and Thermal Analysis, 116-117 (1995).
�Cyclic Differential Scanning Calorimetry and the Melting and Solidification of Pure Metals�, K. A. Q. O�Reilly and B. Cantor,submitted for publication to Thermochim. Acta (1995).
�Determination of Initial Crystallinity in Polymers by Modulated Differential Scanning Calorimetry�, S. Sauerbrunn and L. Thomas,Amer. Lab., 27, 19-22 (January 1995).
�Direct Measurement of Thermal Conductivity Using Modulated DSC�, S. Aubuchon, R. Blaine, Proc. 21st North American ThermalAnalysis Society Conference, 142-147 (1995).
�Enhanced Thermal Properties and Morphology of Ion-Exchanged Polypyrolle Films�, V. T. Trung, B. C. Ennis and M. Forsyth,Polymer, 36 (1995).
�Investigation of the Curie Temperature via Modulated DSC�, S. Aubuchon and R. Blaine, Proc. 31st Japanese Conference onCalorimetry and Thermal Analysis, 126-127 (1995).
�Investigation of the Curie Transition via Modulated DSC�, S. Aubuchon, R. Blaine, Proc. 21st North American Thermal AnalvsisSociety Conference, September 1995.
�Investigation on Phase Transition of Phospholipids by Dynamic DSC�, H. Takenouchi and I. Hatta, Proc. 31st Japanese Conferenceon Calorimetry and Thermal Analysis, 114-115 (1995).
�Linearity and Non-Linearty in DSC: A critique on Modulated DSC�, Takeo Ozawa and Katsuhido Kanari, Thermochim Acta, 253,183-188 (1995).
�Linearity, Steady State, and Complex Heat Capacity in Modulated Differential Scanning Calorimetry�, B. Wunderlich, A. Boller, I.Okazaki and S. Kreitmeur, submitted for publication to Thermochim. Acta (Sept. 1995).
30
�Method and Apparatus for Parsed Dynamic Differential Analysis�, Michael Reading, U.S. Patent 5,474,385 (12 Dec. 1995).�Method and Apparatus for AC Differential Thermal Analysis�, M. Reading, U.S. Patent 5,439,291 (8 August 1995).
�Method and Appartus for Modulated Differential Analysis�, M. Reading, B. Hahn, B. Crowe, Canadian Patent 2,089,225 (July1995).
�Modulated Differential Scanning Calorimetry: VI Thermal Characterization of Multi-component Polymers and Interfaces�, D.J.Hourston, M. Song, A. Hammiche, H.M. Pollock, and M. Reading, submitted for publication (Nov. 1995).
�Modulated Differential Scanning Calorimetry: V. The Physical Ageing Process in a Binary and Polymer Blend of Poly (methylmethacrylate) and Poly (styrene-coacrylonitrile)�, D. J. Hourston, A. Hammiche, H. M. Pollock,M. Song, snd M. Reading, submitted for publication to Macromolecules (1995).
�Modulated Differential Scanning Calorimetry: IV Miscibility and Glass Transition Behavior in Poly (methyl methacrylate) and Poly(epichlorohydrin) Blends�, M. Song, A. Hammiche, H.M. Pollock, D.J. Hourston, and M. Reading, submitted for publica-tion to Polymer (Sept. 1995).
�Modulated Differential Scanning Calorimetry: III. Application to Glass Transition Temperature Measurements�, M. Song, A.Hammiche, H. M. Pollock, D. J. Hourston and M. Reading, submitted for publication.
�Modulated Differential Scanning Calorimetry in the Glass Transition Region, II: The Mathematical Treatment of the Kinetics of theGlass Transition�, B. Wunderlich, A. Boller, I. Okazaki and S. Kreitmeier, Thermochimica Acta, September 1995 (submittedfor publication).
�Modulated Differential Scanning Calorimetry: I. A study of the Glass Transition behavior of Blends of Poly (Methylmethacylate) andPoly (Styrene-co-acrylonitrile)�, M. Song, A Hammiche, H. M. Pollock, D. J. Hourston, and M. Reading; preprint (1995).
�Modulated Differential Scanning Calorimetry in the Glass Transition Region�, A. Bollar, C. Schick, and B. Wunderlich, submitted forpublication in Thermochimica Acta, January 1995.
�Modulated Diffierential Scanning Calorimetry - Capabilities and Limits�, B. Wunderlich, A. Boller, Proc. 21st North AmericanThermal Analysis Society Conference, 136-141 (1995).
�Modulated Differential Scanning Calorimetry: Isothermal Cure and Vitrification of Thermosetting Systems�, G. Van Assche, A. VanHemelrijck, H. Rahier, and B. Van Mele, Thermochimica Acta, August 1995 (accepted for publication).
�Modulated Differential Scanning Calorimetry (MDSC)�, A. Boller, Advanced Thermal Analysis Laboratory, Eighth Report, Univer-sity of Tennessee Knoxville, 4-8 (1995).
�Modulated Differential Scanning Calorimetry: V. Studies of Physical Aging in Polystyrene�, D. J. Hourston, M. Song, A. Hammiche,H. M. Pollock, and M. Reading; preprint (1995).
�Observations on Real and Imaginary Differences in Proposed Schemes for the Analysis of Data from Modulated-TemperatureDifferential Scanning Calorimetry�, M. Reading, submitted for publication to Thermochim. Acta (Sept. 1995).
�Compatibility of differential scanning calorimetry and ac calorimetry�, Ichiro Hatta, Jpn. J. Appl. Phys., 33, L686-688 (1994).
�Evaluation of Non-Isothermal Heat Capacities and Applications of Modulated DSC�, B. Wunderlich, M. Varma-Nair, J.J. Balogh,and H Aldrich, Proc. 23rd NATAS Conf. (1994).
�Mathematical Description of Differential Scanning Calorimetry Based on Periodic Temperature Modulation�, B. Wunderlich, Y. Jinand A. Boller, Thermochim. Acta, 238, 277-293 (1994).
�Method and Apparatus for Modulated Differential Analysis�, M. Reading, B. K. Hahn, and B. S. Crowe, U.S. Patent 5,346,306 (13September 1994).
�Method and Apparatus for Thermal Conductivity Measurements�, S.M. Marcus, and M. Reading, U.S. Patent 5,335,993 (9 August1994).
�Modulated Differential Scanning Calorimetry: A New Method for Thermal Conductivity of Polymers, Glasses, and Ceramics�, S. M.Marcus and R. L. Blaine, T. W. Tong (ed.), Thermal Conductivity 22, Technomic Publishing, Lancaster, PA, pp. 826-833(1994).
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�Modulated Differential Scanning Calorimetry�, M. Reading, A. Luget, and R. Wilson, Thermochimica Acta, 239, 295-307 (1994).
�Modulated DSC: The Melting Transition�, S.R. Sauerbrunn, and L.C. Thomas, Proc. 23rd NATAS Conf. (1994).
�Modulated DSC: The Effect of Period�, S.R. Sauerbrunn, P.S. Gill, and J.A. Foreman, Proc. 23rd NATAS Conf. (1994).�Modulated DSC: The Effect of Amplitude�, S.R. Sauerbrunn, and R.L. Blaine, Proc. 23rd NATAS Conf. (1994).
�Modulated Differential Scanning Calorimetry in the Glass Transition Region�, B. Wunderlich, A. Boller, and C Schick, Proc. 23rdNATAS Conf. (1994).
�Phase Transitions in Solid C70: Supercooling, Metastable Phases, and Impurity Effect�, A.R. McGhie, J.E. Fischer, P.A. Heiney, P.W.Stephens, R.L. Cappelletti, D.A. Neumann, W.H. Mueller, H.Mohn, and H.U. ter Meer, Phys.Rev. B, 49, 12614-12618 (1994).
�Thermal Conductivity of Polymers, Glasses, and Ceramics by Modulated DSC�, S. M. Marcus and R. L. Blaine, Thermochim. Acta.243, 231-239 (1994).
�A Modulated DSC Analysis of Microbial Biocompatible Polyester�, A. Cesaro, L. Navarini, and R. Pepi, Thermochim. Acta, 227,157-166 (1993)
�A Technique for Differential Scanning Calorimetry�, S. Sauerbrunn and P. Gill, Amer.Lab., 25, 54-58 (September 1993).
�Effect of Aging on the Enthalpic Relaxation of Amorphous PET�, S.R. Sauerbrunn, R.L. Blaine and J.A. Foreman, Proc. 22nd NATASConf., 514-519 (1993).
�Method and Apparatus for Modulated Differential Analysis�, M. Reading, B.K. Hahn and B.S. Crowe, U.S. Patent 5,224,775 (6 July1993).
�Method and Apparatus for Spacially Resolved Modulated Differential Analysis�, M. Reading, U.S. Patent 5,248,199, (28 September1993).
�Modulated Differential Scanning Calorimetry�, D.R. Kamm, B.S. Crowe, and M.Reading, Proc. 9th National Symposium on ThermalAnalysis, pages 19-26 (1993).
�Modulated DSC: The Newest Innovation in Thermal Analysis�, N. Buckman, Chemistry in Australia, 666-667 (December 1993).
�Modulated Differential Scanning Calorimetry�, P.S. Gill, S.R. Sauerbrunn, and M. Reading, J. Therm. Anal., 40, 931-939 (1993).
�Modulated Differential Scanning Calorimetry- A New Way Forward in Materials Characterization�, M. Reading, Trends in PolymerScience, 1, 248-253 (1993).
�Quantifying PET/PC Blends with Modulated DSC�, S.R. Sauerbrunn, P.S. Gill and C.L. Marcozzi, Proc. 22nd NATAS Conf., 313-318 (1993).
�Thermal Conductivity of Polymers, Glasses and Ceramics by Modulated DSC�, S.M. Marcus and R.L. Blaine, Proc. 22nd NATASConf., 102-108 (1993).
�Characterization of Polymeric Materials by Modulated Differential Scanning Calorimetry�, J. Seferis, et.al., Proc. Greek Academy ofScience, submitted 17 November 1992.
�Modulated Differential Scanning Calorimetry�, S.R. Sauerbrunn, B.S. Crowe, and M. Reading, Proc. 21st NATAS Conf., 137-144(1992).
�Modulated Differential Scanning Calorimetry�, S. Sauerbrunn, B. Crowe, and M. Reading, Amer. Lab., 24, 44-47 (August 1992).
�Some Aspects of the Theory and Practice of Modulated Differential Scanning Calorimetry�, M. Reading, D. Elliott and V. Hill, Proc.21st NATAS Conf., 145-150 (1992).
FUTURE UPDATES
By conventional DSC standards, modulated DSC is a relatively new technique, having been available about 4years compared to 35 years for conventional DSC. As a result, it is reasonable to expect that the capabilitiesand applications for modulated DSC will continue to grow over at least the next decade. Please watch futureissues of the TA Instruments Hotline Newsletter for announcements of these new capabilities.
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