Download Practical Specific Heat Determination by Dual

a p p l i c at i o n N o t e
Differential Scanning Calorimetry
Authors
Phil Robinson
PerkinElmer, Inc.
Seer Green, U.K.
Practical Specific
Heat Determination
by Dual Furnace DSC
Introduction
This application note outlines the practical
considerations when making specific heat
determinations by Dual Furnace (Power
Compensation) DSC and explains the
way that specific heat may be calculated
from DSC data. This will give thermal
analysts sufficient information to make successful and accurate specific heat
measurements using their calorimeters and understand how to avoid some of
the common errors encountered.
Background
The DSC 1 of 1963 was used by Michael J. O’Neill of the Perkin-Elmer
Corporation, who discussed measurement of specific heat (Cp) by DSC as an
alternative to using drop calorimeters and adiabatic calorimeters. Shortly after
the introduction of the DSC 1, O’Neill detailed determination of Cp data,1 and
modern software is based on this methodology.
Applicability
Specific heat determination may be made on most, if not all, types of solid and
liquid material, although it is necessary that the material is thermally stable over
the temperature range used for the determination and that no mass loss occurs.
The temperature range normally specified is between -100 °C and 600 °C
although it is possible to work beyond these values. For a broader discussion
of experimental parameters and applicability, see ASTM® standard test
method E1269.
Overview of Methods of Determining Cp by DSC
Experimental Considerations
There are three basic methods of determining specific heat,
each with advantages, differing levels of accuracy achievable
and ease of use. However it should be noted that designs
of DSC analyzer differ and some types are inherently more
accurate than others. The accuracies mentioned below are
based on using a dual furnace DSC: measurements using
single furnace (heat-flux) DSC require additional care to
produce acceptable data.
As with any analytical technique, the care exercised by the
user can have a large influence on the overall accuracy of
the determination, and it is a combination of small factors
which must be considered for successful measurements to
be made. For all methods of specific heat determination,
including modulated temperature DSC, the same
consideration apply, and these are:
1.Traditional 2-Curve Method
• The sample pan and the sample presentation
Here, the same sample pan is used for two identical tests
consisting of:
– Sample pan flatness
• A baseline run using an empty pan and cover
• A sample of the material whose specific heat is being
determined run using the same pan and cover as the
baseline run.
With care, specific heat data with around 1.5% absolute
accuracy or slightly better should be obtained.
• Accuracy in sample mass measurement
– Sample shape and flatness
– Sample pan placement in furnace
– Reference pan
• Furnace cover placement
– Furnace cover shape and “fit” to the furnace (avoids
baseline errors)
• Experiment design
2.Traditional 3-Curve Method
This method uses the same approach as the 2-curve
method except that a third curve is generated using a
reference material, the one most often used is a sapphire
disk. This reference data is used to “correct” sample data
at every temperature, giving improved accuracy which,
with care, can be up to 0.8% absolute accuracy. This
method also allows different sample pans to be used for
each part of the test.
3.Modulated-Temperature DSC Method
This newest approach to specific heat determination
involves subjecting the material being tested to a nonlinear temperature program, with the specific heat data
extracted from the resulting heat-flow curve. Data can
be obtained with an absolute accuracy of up to 0.5%
of the literature value with suitable care and correct
use of baselines. The method is generally extremely
slow due to the nature of the temperature program
and the requirement to have a baseline. However the
improvement in accuracy makes it worth considering for
some situations, although it is not discussed further in
this application note.
The influences shown above are discussed in more detail
below and explain how, when all factors are correctly
implemented, accurate specific heat measurements can
be obtained.
Required Accuracy in Measurement of Sample Mass
If the weight of the sample is not recorded with
sufficient accuracy, an unacceptable error in specific heat
measurement can result. An example is shown in Table 1.
Since errors are cumulative, each individual error will
increase the error of the final specific heat measurement.
Note that in circumstances where the sample pan is weighed
separately, (e.g. when a different sample pan is used for the
baseline, sample run and reference run) errors from weighing
would approximately double or worse, significantly affecting
the overall accuracy of the specific heat determination. It
is recommended that samples and sample pans are always
weighed to an accuracy of 0.001 mg to maximize the accuracy
of the specific heat data.
Table 1. Example of a measured heat-flow at 95 °C = 13.735 mW with an actual mass of 5.133 mg.
2
3-place grams
4-place grams
5-place grams
6-place grams
Sample Mass (mg)
5 mg
5.1 mg
5.13 mg
5.133 mg
Possible Error (mg)
±1 mg
± 0.1 mg
±0.01 mg
±0.001 mg
Specific Heat (J/g/°C)
0.915667
0.897712
0.892463
Accuracy of Specific Heat
102.66%
100.6471%
100.0595%
0.891941
100.0000%
The Sample Pan
Instrumental Conditions
Choice of sample pan will have an influence on accuracy,
and also how well the sample is prepared into the pan.
In most cases, It is useful if the sample pan can be used
without the need for crimping, allowing the same sample
pan to be used for the baseline test and the sample test.
In this way, the specific heat contribution from the sample
pan mass is eliminated. Where this is not possible, then the
pans should be weighed at least as accurately as the sample.
For thermally stable solid samples, it is recommended to use
standard aluminum sample pans 0219-0041 which can be
used without crimping.
To make successful specific heat measurements, it is vital
that the analyzer is clean and stable in temperature and
environment before attempting to make a measurement.
Preparation of the DSC analyzer before starting such testing
might involve the following:
Sample Pan Flatness
• Ensure that the Sample Holder is Clean
It is recommended that a furnace clean is carried out
before starting measurements, removing both sample and
reference pans before starting. This will do two things.
Firstly, it will clean any sample residues from the furnace,
and secondly it will “condition” the sample holder, giving
a highly repeatable baseline.
Since all measurements involve heat flow between the
sample holder sensor system through the bottom of
the sample pan and into the sample, it is clear that the
flatness of the sample pan will have an influence on the
measurement. Correct use of either a standard crimper or
universal crimper will encapsulate the sample and produce a
pan with a flat bottom. It is recommended that you inspect
the pan visually to ensure that the bottom of the pan is flat
after samples have been sealed in the pan before loading
them into the analyzer.
• Ensure that the Sample Holder Block Temperature
is Stable
Sample Form and Shape
• Ensure that the Platinum Covers Fit Well
It follows that if the sample pan bottom must make good
contact with the heat source, then the sample itself should
make good contact with the sample pan in order to minimize
the thermal resistance. This suggests that the sample should
ideally be flat and thin, allowing a large surface to touch the
sample pan in relation to the thickness of the sample. It is
recommended that the sample is thin and flat e.g. 1 mm thick
by 5-6 mm diameter with flat surfaces top and bottom. Where
this is not possible, at least the bottom of the sample should
be made as flat as possible.
Sample Size
The sample size makes a difference to the measurement
since errors resulting from the accuracy of weighing become
significant with very small samples. In general, sample sizes
should be between 5 mg and 100 mg, with the preferred
weight between 20 mg and 40 mg. It may be necessary
to reduce the heating rate when using larger samples to
minimize temperature gradients within the sample.
Reference Pan
The pan used in the reference furnace should generally
be of the same type as the pan used for the sample. The
reference sample pan should not be disturbed or changed
in any way until all tests have been completed, otherwise
errors in specific heat determination may be introduced.
If the temperature of the sample holder is not stable,
baseline drift will be seen from run to run, leading to
significant errors in specific heat determinations. Ideally,
the analyzer should be left turned on overnight, and the
cooling accessory should be switched on at least 2 hours
before measurements commence. A cooling accessory of
some type should always be operational during specific
heat determinations.
If the covers to not fit easily, then the external “shape”
of the furnace can vary from run to run as the lids tilt
slightly. Some surprisingly small effects in the “fit” of
the lids can cause some large errors in the repeatability
of the baseline.
It is recommended that you use the manually fitted
platinum furnace covers and not the autosampler covers.
The autosampler covers do not always “sit” in the same
orientation or flatness, and this results in changes to the
baseline, which affects the accuracy
Reform the normal covers (the type with two tweezer
holes) using reforming tool 0319-0030 or fit a pair
of new covers 0419-0299 before starting to make
measurements for best accuracy.
• Keep each Platinum Cover on the Same Furnace
It is particularly important that each cover remains on the
same furnace throughout the measurement as differences
in their mass would give errors in the measured specific
heat. Recent changes to the platinum cover design
provide an indent in the center of one of the lids when
purchasing a pair of covers (0419-0299) which allows
easy identification of each cover. New furnace covers are
made from a platinum-iridium alloy which is less prone
to bending through mishandling than the earlier pure
platinum covers of the type.
3
• Platinum Cover Orientation
For most work on a DSC, the orientation of the platinum
furnace covers has little effect if any. However for specific
heat work, orientation matters rather more, especially
if the covers are deformed slightly. For maximum
repeatability, use the tweezer-holes in the cover as a
guide to orientate the covers in the same way each time.
• Purge Gas
The settings will depend on which analyzer you are using.
Diamond DSC, P1, DSC and DSC 7
Ensure that your purge gas is flowing by using an inlet
pressure of about 2 bar, giving a flow of about 30 mL/
min through each of the two furnaces. Note that the
total flow from the exhaust of the analyzer will be around
60 mL/min.
DSC 8000 and DSC 8500
Use a flow of 60 nL/min since the mass flow control
regulates the total flow into the analyzer.
Sample Preparation and Encapsulation
As with any thermal analysis measurement, correct sample
presentation is of paramount importance, and the sample
should be:
• A thin flat layer of sample to minimize temperature
gradients within the sample.
• Evenly distributed over the base of the pan to ensure
good contact with the pan base and the sample holder
sensor.
• Sandwiched by the sample pan lid to promote fast heatflow through good thermal contact between the pan
and the sample. This also minimizes sample movement
which can also cause some undesirable effects on the
measurement.
• A flat bottom to the sample pan to ensure good thermal
contact with the furnace sensor system.
To meet the above criteria, it is recommended that the
sample size should be typically between 10 mg and 100 mg,
and that sample pans are selected as follows:
The amount of time required to purge the system (and
therefore achieve a stable heat-flow) may vary with the
type of purge gas being used.
a). Standard Aluminium Pans (0219-0041)
I. Nitrogen or Air – no purging time is necessary
after closing the sample holder cover (see note below
concerning oxygen).
b). Universal Crimper Aluminium Pans (Robotic Crimper)
II.
Helium or Argon – To completely displace air or
nitrogen after closing the sample holder cover,
a purging time of 6-8 minutes is necessary (at the
recommended flow rates above) since helium and
argon both have a much higher thermal conductivity
than either air or nitrogen. After closing the sample
holder cover, the changing concentration of these
higher-thermal conductivity gases have the effect
of causing some apparent drift in the heat-flow
reading from the sample holder until purging
has completed.
III. Oxygen – Due to the high reactivity of oxygen, it
is likely that samples will be changed by the effects of
heating in this atmosphere; therefore it is recommended
that specific heat determinations should not be carried
out in the presence of oxygen. This comment will also
apply to air with sample types of sample.
Use sample pan bases and cover, but do not seal or crimp
them for the baseline run or sapphire disk.
If heating the sample to temperatures above 100 °C, consider
piercing the top pan in the center to allow the air inside
the pan to expand. Alternatively, consider using a pan with
holes as the top pan. Note that having the top pan with
holes will allow any material ejected from within the pan to
be collected in the well at the top of the pan, avoiding the
need to clean out the sample furnace after such a spillage.
This “spillage” can also indicate an interpretation of any
anomalies seen on the DSC curve. Using a sample pan as a
cover can fulfill the requirement of “sandwiching” the sample
between the pan base and the cover.
c). Other Pan Types
Other pans should be selected where circumstances require
their use, but allowance should be made for the differing
thermal resistances. Pans made of material other than the
aluminum types above are acceptable but it should be noted
that aluminum has a relatively higher thermal conductivity
compared with other metals and this will affect the thermal
resistance constant (Ro) values obtained. See Appendix 1 for
Ro determination.
The prime reason for considering using pans of different
design is to prevent volatilization (or sublimation) occurring.
In this case it may be necessary to use a large volume
stainless steel pan in order to contain the sample in the
temperature range required, and, if necessary, determine Ro
for this type of pan.
4
Experimental Design for the 2-Curve and 3-Curve Cp
Determinations
Starting Temperature and Isotherm
Figure 1
The starting temperature chosen should be at least 30 °C
above the “block” temperature of the DSC (i.e. the
background temperature from the cooling accessory); any
lower and the furnace control is not reliable, resulting in
inaccurate heat-flow readings. It may be necessary to wait
for several minutes before starting to record data while the
heat-flow reading stabilizes.
Ending Temperature and Ending Isotherm
The maximum temperature span for a single specific heat
test is best kept to between 150 °C and 200 °C since small
changes in the instrument stability may become significant
with larger temperature ranges. Where specific heat over a
larger temperature range is required, it is recommended that
a series of overlapping temperature ranges is used, and it is
suggested that a 50 °C overlap should be made. With each
portion treated as a separate test, the overlapping portions
can be used to confirm that the data is continuous,
The length of the ending isothermal at the upper
temperature should be selected so that a good steady
isothermal heat-flow reading is obtained, and it should
be recognized that this may take between three and five
minutes, with larger samples requiring even longer than this.
It is generally found that three to five minutes is sufficient
for acceptable stability, although the accuracy can be
significantly compromised if the heat flow is not completely
stable at the end of this isothermal period.
Figure 2 is a display of the ending isothermal for an empty
sample pan and a sample pan containing a sapphire disk
(0219-1269) 6 mm diameter x 1 mm thick and weighing
approximately 130 mg.
It is recommended that the heat-flow reading should be
stable to 0.001 mW over one minute for the best specific
heat data.
The data displayed in Figure 1 shows two curves – one where
the heat flow is completely stable at the start of the test (red)
and where the analyzer was not completely stable (blue).
Heating Rate
The size of the signal from which the specific heat is
calculated is directly proportional to the heating rate used,
so it follows that heating faster rates will produce larger
signals, which would give more accurate data. However if
the heating rate is too high, the temperature gradients in
the sample will be large and this may introduce other errors
in the measurement.
It is normal to use heating rates between 5 °C/min and
20 °C/min, with 20 °C/min being preferred in most
circumstances. If low heating rates are required, larger
samples should be considered to produce heat-flow signals
of a reasonable size and minimize measurement errors from
this source.
While for 3 curve Cp technique it is not so important, for
all other Cp methods it is essential that the instrument be
calibrated using two temperature calibration standards to
ensure that the scan rate is accurate.
Figure 2
It will be seen that the empty pan with much lower mass
achieves a steady baseline much sooner than the much
larger mass sapphire test, and that the isothermal drift from
the sapphire test is much greater despite the 4 minutes
at isothermal. The significance of this drift is that it will
introduce an error into the measurement, and it is suggested
that a longer time is used to allow better stability.
It should also be noted that the Y difference between the
two curves (~15.7 mW – ~15.57 mW) is related to the
difference in mass between the empty pan and the pan plus
sapphire.
5
Typical Temperature Program
Testing
Based on the guidelines above, a typical experiment to measure
heat capacity from 20 °C to 200 °C would be as follows:
With 0219-0041 pans and covers, the same aluminum
pan is used for all three tests, so the aluminum weight is
a constant and therefore can be ignored. Therefore each
measurement, consisting of three data sets, uses only one
single pan for all three tests.
• Stabilize the analyzer at 0 °C for each test before starting
to record data
–
It may be useful to use the “Start Run” criteria in Pyris™
software under the “Initial Conditions” settings to
automatically stabilize the heat-flow signal before data
collection starts. Use the “right mouse button” to
“change” the “start run” parameters.
• In Pyris, use the following method:
Test 1 – Baseline Run
Sample furnace contains an empty aluminum pan and lid
(do not crimp) with furnace cover fitted. Sample weight in
Pyris = 0 mg.
Reference furnace is not disturbed.
1. Isothermal at 0 °C to 1 minute
2. Heat from 0 °C to 200 °C at 20 °C/min
Test 2 – Sapphire Reference Run
3. Isothermal at 200 °C for 5 minutes
Sample furnace contains the sapphire reference in the same
aluminum pan as for Test 1, with the flat aluminum lid on
top of sapphire (do not crimp), and furnace cover fitted.
Sample weight in Pyris = weight of sapphire disk.
4. End condition = “go to load”
Although the data is required from 20 °C, the test must
start from 0 °C since the first minute of the heating data is
required for stabilization, and at 20 °C/min, this is required
to be 20 °C below the temperature at which the first
measurement is needed.
Typical Test Procedure
The best pans to use are the standard aluminum sample
pans (0219-0041) for solid samples such as powders or
polymers since there is no need to weigh the pan itself. This
is because the pan used is a constant since the same pan
is used for all three tests. Using this pan type is assumed in
these instructions:
Initial Situation
At the start of the test, the situation should be like this:
Sample Furnace Empty standard pan plus lid (0219-0041) – not crimped.
Furnace cover fitted.
Reference Furnace
Empty standard pan plus lid (0219-0041) – it does not
matter if the lid is crimped or not crimped.
Furnace cover fitted.
It is important not to disturb the reference furnace in any
way during testing (do not move either the pan, lid or the
furnace cover) since this will affect the “balance” of the two
furnaces and give errors in heat capacity measurement.
6
Reference furnace is not disturbed.
Test 3 – Sample Run
Sample furnace contains the sample in the same aluminum
pan and lid (crimped with sample) used for Test 1 and Test 2,
with furnace cover fitted. Sample weight in Pyris = weight
of sample.
Reference furnace is not disturbed.
Placing the furnace cover each time the sample is changed
is important – the orientation of the platinum lid and how
flat it sits on the furnace will affect the heat capacity
values obtained.
If you use universal crimper pans, then you must crimp each
pan (which cuts off the ring of aluminum) and weigh the
amount of aluminum as well as the amount of the sample.
The heat capacity software has a place to enter the weight
of the aluminum pan if you use the 3-curve method (i.e.
with sapphire as reference).
Data Analysis Following the DSC Tests
Pyris software automatically optimizes the data during the
Cp calculation, performing shifting and sloping of the data
in the process. For manual calculations the user must make
these corrections, which should involve the following steps:
Use “Shift Y” to move the start of all curves to a nominal
milliwatt value (Figure 3).
Verification of Data Quality
Figure 6 shows data from a sapphire disk (0219-1269)
collected at 20 °C/min. The data has been optimized by
aligning the start and ending isothermal using the “slope”
function in Pyris software.
Figure 3
Use the “slope” command on the “rescale” toolbar and
select “align endpoints” option. The slope should normally
be set from the first data point of the lower temperature
isothermal and the last data point of the upper temperature
isothermal (Figure 4).
Figure 6
The calculated difference between the two curves seen in
Figure 6 is shown in Figure 7.
Figure 4
The baseline curve is then subtracted from the sample curve,
giving the heat-flow difference due only to the sample
(Figure 5). This must then be further calculated to take into
account the mass of the sample and the heating rate used
for the test.
Figure 7
It is normal to remove the heat-flow curves to make the
display more clear, and to switch the x-axis to temperature
before creating a table of results using <Tools> <Tables>
from the Pyris top menus.
Figure 5
7
Specific Heat Calculation
Table 2
The calculation is extremely straightforward. The difference
between the sample curve and the baseline curve is measured
in milliwatts and converted to specific heat as follows:
Temperature
(°C)
Measured Cp
NBS (1971)
Error
(J/g*°C) (J/g*°C)%
42
0.449
0.809239 -44.5
47
0.791
0.818851 -3.4
52
0.832
0.828168 0.5
57
0.845
0.837289 0.9
62
0.856
0.846214 1.2
67
0.864
0.854845 1.1
Mass mg
72
0.873
0.863182 1.1
77
0.882
0.871322 1.2
82
0.890
0.879364 1.2
87
0.898
0.887113 1.2
97
0.913
0.902020 1.2
Identifying Common Problems in Specific Heat
Determination
100
0.917
0.906532 1.2
Problem: Measured Specific Heat Data is Inaccurate
107
0.927
0.916144 1.2
117
0.941
0.929580 1.2
127
0.953
0.942330 1.1
137
0.966
0.954492 1.2
147
0.980
0.966065 1.4
157
0.992
0.977050 1.5
167
1.003
0.987544 1.6
177
1.014
0.997548 1.6
• Sample weights are not measured accurately enough
187
1.025
1.007062 1.8
• Platinum covers exchanged
The data in the table is taken from Figure 7. Points to note are:
• First minute of the data is inaccurate (in this instance
equivalent to 20 °C) and should be discarded. This is
related to heat-flow equilibration at the start of heating.
Specific Heat =
Heat Flow
Mass x Heating Rate
Units: Heat Flow
Heating rate
mW (=mJ/s)
˚C/second
The specific heat is then given in J/g/°C.
Likely causes:
• Insufficient time for instrument stabilization after start-up
• Cooling accessory not stable
• More equilibration time needed at initial isothermal or
ending isothermal
• Instrument not in control at the starting temperature
• Pan weights are not measured accurately enough (only
important if different pans are used for different parts of
the test)
• Instrument has not been calibrated using two
temperature standards
• Data above 150 °C shows an increasing error. This
demonstrates that the span used for the specific heat
determination should be kept to no more than 150 °C to
maximize accuracy.
Problem: Initial Isothermal Drifting at Start of Test
• Column 3 data is based on published information from
the National Bureau of Standards in the U.S. in 1971.
–Cooling system has not been fully stabilized, e.g.
Intracooler not left for minimum 1.5 hours
When used as an internal reference in the three curve
method, sample data is corrected according to the values
determined from the reference material test, reducing the
error in the sample determination.
Likely causes:
• Instrument not fully stable at start of test
• Program not sent to initial test temperature and held
isothermal before test start
–Manually go to start temperature, wait for stability and
then start test
• Purge gas concentration still changing after sample
loading (helium or argon)
–Increase waiting time after loading samples
8
Problem: End Isothermal of the Test Still Drifting When
Test Ends
Likely causes:
• Ending isothermal wait is too short
–Increase end isothermal time
Reasons to Adjust Ro
Ro will require adjusting if the pan type is changed from the
standard aluminum sample pan to, for example, alumina or
graphite, which have different thermal resistances. It may
also be necessary to check Ro if working below -50 °C or
above 400 °C with any pan type.
• Sample is very large and requires more time to stabilize
–Increase end isothermal time
• Instrument not stable
–Cooling system unstable or not fully stabilized
Problem: Baselines Drift During Test
Likely causes:
• Sample movement in sample pan
–Improve crimping and sample loading
• Platinum covers not replaced flat
–May need to be re-shaped using the reforming tool
0319-0030
• Cooling accessory not fully stable
–Need to wait longer before using the analyzer
There are of course many other possible reasons; however
these are among the more common.
Conclusion
The specific heat of a material may be determined with
reasonable accuracy if sufficient care is taken. The primary
advantage of the DSC approach to measuring specific heat
is the simplicity of the sample preparation, the speed of data
collection and analysis.
References
1.Measurement of Specific Heat Functions by Differential
Scanning Calorimetry, M.J. O’Neill, Perkin-Elmer
Corporation. Reprinted from Analytical Chemistry,
Vol. 38, page 1331, September 1966.
Appendix 1. Determination of Thermal Resistance
Constant, Ro
The thermal resistance constant, Ro, is a measure of the
speed of heat transfer between the sample holder of the
DSC and the sample itself. The speed of heat transfer is
affected, among other things, by the flatness of the base
of the sample pan, the thermal conductivity of the sample
pan material, sample pan type and by the heating rate.
Once determined, it is used in the specific heat calculation
to correct the measured temperatures in relation to the
height of the specific heat “peak”. It is important that Ro be
measured accurately under the conditions that the sample is
to be analyzed.
Figure 8. Calculation of Ro from an Indium Curve run at 0.8 ˚C/min.
To measure the thermal resistance constant, prepare a 3 mg
piece of indium metal and flatten it on a sheet of glass
before encapsulating it in a suitable DSC pan. The indium
sample should then be analyzed at the same heating rate
used for the specific heat determination.
The plot in Figure 1 shows a Delta Y calculation performed
on the leading edge of an indium melting peak. The Ro is
calculated as follows:
Ro =
DT
DY
=
(155.58 – 155.35) ˚C
(19.36 – 7.37) mW
=
0.23 ˚C
11.98 mW
=
0.0192
˚C/mW
This value of 0.0192 °C/mWatt for Ro is shown in Figure 8
as a label.
Typical values are between 0.02 °C/mWatt and 0.08 °C/mWatt
but these values are for guidance and are very sample
pan type dependent. Some software (Pyris for Microsoft®
Windows® for example) requires that Ro is given in °C/Watt.
To obtain this value, convert the Delta Y calculation from
milliwatts to Watts by dividing by 1000.
9
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