ASTM E2890-12
(Test Method)Standard Test Method for Kinetic Parameters for Thermally Unstable Materials by Differential Scanning Calorimetry Using the Kissinger Method
Standard Test Method for Kinetic Parameters for Thermally Unstable Materials by Differential Scanning Calorimetry Using the Kissinger Method
SIGNIFICANCE AND USE
6.1 This test method is useful for research and development, quality assurance, regulatory compliance and specification-based acceptance.
6.2 The kinetic parameters determined by this method may be used to calculate thermal hazard figures-of-merit according to Practice E1231.
SCOPE
1.1 This test method describes the determination of the kinetic parameters of Arrhenius activation energy and pre-exponential factor using the Kissinger variable heating rate iso-conversion method (1, 2)2 and activation energy and reaction order by the Farjas method (3) for thermally unstable materials. The test method is applicable to the temperature range from 300 to 900 K (27 to 627°C).
1.2 Both nth order and accelerating reactions are addressed by this method over the range of 0.5 n p n is the nth order reaction order and p is the Avrami reaction order (4). Reaction orders n and p are determined by the Farjas method (3).
1.3 This test method uses the same experimental conditions as Test Method E698. The Flynn/Wall/Ozawa data treatment of Test Method E698 may be simultaneously applied to these experimental results.
1.4 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.
1.5 There is no ISO equivalent to this standard.
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E2890 − 12
StandardTest Method for
Kinetic Parameters for Thermally Unstable Materials by
Differential Scanning Calorimetry Using the Kissinger
Method
This standard is issued under the fixed designation E2890; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope E473Terminology Relating to Thermal Analysis and Rhe-
ology
1.1 This test method describes the determination of the
E537Test Method for The Thermal Stability of Chemicals
kinetic parameters of Arrhenius activation energy and pre-
by Differential Scanning Calorimetry
exponential factor using the Kissinger variable heating rate
2 E691Practice for Conducting an Interlaboratory Study to
iso-conversion method (1, 2) and activation energy and
Determine the Precision of a Test Method
reaction order by the Farjas method (3) for thermally unstable
E698Test Method for Arrhenius Kinetic Constants for
materials. The test method is applicable to the temperature
Thermally Unstable Materials Using Differential Scan-
range from 300 to 900 K (27 to 627°C).
ning Calorimetry and the Flynn/Wall/Ozawa Method
1.2 Both nth order and accelerating reactions are addressed
E967Test Method for Temperature Calibration of Differen-
by this method over the range of 0.5 < n<4and1< p<4
tial Scanning Calorimeters and Differential ThermalAna-
where n is the nth order reaction order and p is the Avrami
lyzers
reaction order (4). Reaction orders n and p are determined by
E968Practice for Heat Flow Calibration of Differential
the Farjas method (3).
Scanning Calorimeters
1.3 This test method uses the same experimental conditions E1142Terminology Relating to Thermophysical Properties
E1231Practice for Calculation of Hazard Potential Figures-
asTestMethodE698.TheFlynn/Wall/Ozawadatatreatmentof
Test Method E698 may be simultaneously applied to these of-Merit for Thermally Unstable Materials
E1860Test Method for Elapsed Time Calibration of Ther-
experimental results.
mal Analyzers
1.4 The values stated in SI units are to be regarded as
E1970PracticeforStatisticalTreatmentofThermoanalytical
standard. No other units of measurement are included in this
Data
standard.
E2041Test Method for Estimating Kinetic Parameters by
1.5 There is no ISO equivalent to this standard.
Differential Scanning Calorimeter Using the Borchardt
1.6 This standard does not purport to address all of the and Daniels Method
safety concerns, if any, associated with its use. It is the E2161Terminology Relating to Performance Validation in
responsibility of the user of this standard to establish appro- Thermal Analysis
priate safety and health practices and determine the applica-
3. Terminology
bility of regulatory limitations prior to use.
3.1 Technical terms used in this test method are defined in
2. Referenced Documents
Terminologies E473, E1142, and E2161. Referenced terms
2.1 ASTM Standards:
include Arrhenius equation, baseline, calibration, Celsius, dif-
ferential scanning calorimeter, endotherm, enthalpy, figure-of-
merit, first-deviation-from baseline, full-width-at-half-
ThistestmethodisunderthejurisdictionofASTMCommitteeE37onThermal
maximum, Kelvin, onset point, peak, peak value, relative
Measurements and is the direct responsibility of Subcommittee E37.01 on Calo-
rimetry and Mass Loss. standard deviation, standard deviation, thermal analysis and
Current edition approved Sept. 1, 2012. Published October 2012. DOI: 10.1520/
thermal curve.
E2890-12.
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
4. Summary of Test Method
this standard.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
4.1 A series of test specimens are heated at a minimum of
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
four different linear rates in a differential scanning calorimeter
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. through a region of exothermic reaction behavior. The rate of
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2890 − 12
-1
heat evolution, created by a chemical reaction, is proportional
E = activation energy (J mol ),
to the rate of reaction and is measured as a function of
T = absolute temperature (K),
-1 -1
temperature and time.
R = gas constant (8.314 J mol K ), and
e = natural logarithm base (2.7182818).
4.2 The temperature corresponding to the maximum rate of
reaction (measured at the heat flow maximum of the exother-
5.4 Eq1andEq4maybecombinedtoyieldthegeneralrate
mic reaction peak) is recorded at each linear heating rate. This
equation:
observed temperature is corrected for instrument thermal
2E⁄RT
da⁄dt 5 f α Ze (5)
~ !
resistance. Activation energy and pre-exponential factor are
derived from the linear regression of the natural logarithm of
5.5 As the temperature increases, the rate of reaction will
the heating rate, normalized to the square of the absolute
increase until a maximum is reached and then the rate declines
temperature,versusthereciprocalabsolutetemperatureofheat
back to “zero” as the reactant is consumed. When the rate of
flow at the peak maximum. The approach is known as the
reaction is displayed as a function of increasing temperature,
Kissinger method (1, 2).
theshapeofthisresponseiscalleda“peak”.Themathematical
4.3 Areaction type is determined for the specimen from the derivative of the reaction rate at the peak maximum equals
zero. Taking the derivative of Eq 5 over time at the maximum
shape of the reaction exotherm under isothermal temperature
conditions. point for the heating with constant rate β, then casting in
logarithmic form and assuming that ln@d ~f ~α!! ⁄dt#50, leads
4.4 Onceareactiontypeisdeterminedkineticparametersof
to Eq 6.
order (either n or p) are determined using the shape of the
reaction exotherm measured by the time at full-width-at-half-
ln β ⁄ T 5 lnZR ⁄ E 2 E⁄RT (6)
@ # @ #
m m
maximum (t ). This approach is known at the Farjas
FWHM
where:
method (3). The activation energy and reaction order are
-1
β = heating rate (K s ), and
derived from the linear regression of the natural logarithm of
T = temperature a peak maximum (K).
thetimeatfull-width-at-half-maximumversusthereciprocalof m
NOTE 2—The assumption of ln@d ~f ~α!! ⁄dt#50 holds strictly only
absolute temperature at maximum reaction rate (heat flow).
for 1st order reaction but is considered a “reasonable” approximation for
other nth order or Avrami reactions.
5. Basis of Methodology
5.6 Eq6isoftheform Y5mX1b.Ifln[β/T ]issetequalto
m
5.1 For reactions that are exothermic in nature, the rate of
Yand1/T issetequaltoX,thenadisplayofYversusXyields
m
heat evolution is proportional to the rate of the reaction.
a slope (m ) equal to –E /R and an intercept (b ) equal to
K K K
Differentialscanningcalorimetrymeasurestheheatflowasthe
ln[ZR/E ] where Z and E are the pre-exponential factor and
dependent experimental parameter versus temperature (or K K
theactivationenergy,respectively,determinedbytheKissinger
time) as the independent parameter.
method.
5.2 Reactions may be modeled with a number of suitable
equations of the form: 5.7 The shape of the reaction exothermic peak may be
characterized by the time at full-width-at-half-maximum
da⁄dt 5 k~T! f~α! (1)
(t ) (3).
fwhm
where:
ln@t # 5 E ⁄RT 1ln@t'⁄ Z# (7)
-1 FWHM F m
da/dt = reaction rate (s ),
α = fraction reacted or conversion (dimensionless), where:
k(T) = specific rate constant at temperature T, and
t = the full-width-at-half-maximum time (s), and
fwhm
-1
f(α) = conversion function (dimensionless).
t’ = an arbitrary function (s ).
Commonly used functions include:
5.8 Eq 7 is of the form Y5mX1b.Ifln[t ] is set equal
FWHM
n
f α 5 1 2 α (2)
~ ! ~ ! to Y and 1/T is set equal to X, then a display of Y versus X
1 m
p 2 1 ⁄p
~ ! yieldsaslope(m )equalto E /Randanintercept(b )equalto
f α 5 p 1 2 α 2 ln 1 2 α (3) F F F
~ ! ~ !@ ~ !#
ln[t’/Z] where E is the activation energy determined by the
F
where:
Farjas method.
n = nth reaction order (dimensionless), and
5.9 The reaction order, n or p, is determined through an
p = Avrami reaction order (dimensionless).
empirical relationship based on t’.
NOTE 1—There are a large number of conversion function expressions
for f(a) (5). Those described here are the more common ones but are not
the only functions suitable for this method. Eq 2 is known as the Law of
6. Significance and Use
Mass Action (6) while Eq 3 is the Avrami equation (4).
6.1 Thistestmethodisusefulforresearchanddevelopment,
5.3 The Arrhenius equation (7) describes how the reaction
quality assurance, regulatory compliance and specification-
rate changes as a function of temperature:
based acceptance.
2E⁄RT
k~T! 5Ze (4)
6.2 The kinetic parameters determined by this method may
where:
be used to calculate thermal hazard figures-of-merit according
-1
Z = pre-exponential factor (s ),
to Practice E1231.
E2890 − 12
7. Interferences 8.3 Ameans, tool or device to close, encapsulate or seal the
container of choice.
7.1 This test method assumes a single reaction mechanism
8.4 Analytical Balance with a capacity of at least 100 mg to
constant over the reaction conversion temperature range of the
weigh specimens or containers, or both to 6 10 µg.
material under evaluation. Some overall reactions of interest
are known to include a series of competing reaction mecha-
8.5 Auxiliary instrumentation considered useful but not
nisms that lead to changes in reaction order with conversion
essential for conducting this method would include cooling
(8). This method addresses the reaction only at a single
capability to hasten cooling to ambient temperature conditions
conversion value at the maximum reaction rate—often about
at the end of the test.
0.7.
9. Hazards
7.2 Method precision is enhanced with the selection of the
appropriate conversion function [f(α)]. The shape of the ther-
9.1 This test method is used to determine the properties of
mal curve, as described in 11.2, may confirm the selection of
thermally reactive materials. The user of this test method shall
the nth order or accelerating reaction models.
use the smallest quantity of material (typically a few milli-
grams) needed to obtain the desired analytical results.
7.2.1 Typically nth reactions include many (but not all)
decompositionreactionsorthosewhereoneoftheparticipating
9.2 Special precautions shall be taken to protect personnel
species is in excess.
andequipmentwhentheapparatusinuserequirestheinsertion
7.2.2 Typical accelerating (Avrami) reactions include ther-
ofspecimensintoaheatedfurnace.Typicalspecialprecautions
moset cure, crystallization, and some pyrotechnic reactions.
include adequate shielding, ventilation of equipment and face
and hand protection for users.Asafety analysis prior to testing
7.3 Since this method uses milligram quantities of material,
is recommended.
it is essential for the test specimens to be homogeneous and
representative of the larger sample from which they are taken.
10. Calibration and Standardization
7.4 Acriticalliteratureevaluationofkineticmethodsreports
10.1 Perform any calibration procedures recommended by
that the Kissinger method is the most accurate method for
the manufacturer as described in the operator’s manual to
determining activation energy in many cases (9).
ensurethattheapparatusiscalibratedateachheatingrateused.
10.2 Calibrate the heat flow signal using 99.99+% indium,
8. Apparatus
Practice E968, and the same type of specimen container to be
8.1 DifferentialScanningCalorimeter(DSC)—Theessential
used in the subsequent test for kinetic parameters.
instrumentation required to provide the minimum differential
10.3 Calibrate the temperature signal using 99.99+%
scanning calorimetric capability for this method includes (a) a
indium, Practice E967, and the same type of specimen con-
furnace(s) to provide uniform controlled heating or cooling of
tainer and heating rates to be used in the subsequent test for
a specimen and reference to a constant temperature or at a
kinetic parameters.
constant rate over the range of 300 K to 900 K, (b) a
temperature sensor to provide a measurement of the specimen 10.4 Calibrate the elapsed time signal using Test Method
temperature to 6 0.01 K, (c) differential sensors to detect a E1860.
heat flow difference between the specimen and reference with
10.5 Determine the thermal resistance (φ) from the leading
a range of 100 mW readable to 6 1µW, (d) a means of
edge slope S 5 ∆ q ⁄ ∆ T in (mW/K) of the indium melting
~ !
sustaining a test chamber environment of inert purge gas at a
endotherm as shown in Fig. 1 and 12.1.
purge rate of 10 to 100 mL/min within 6 5 mL/min, (e) a
temperature controller, capable of executing a specific tem-
11. Procedure
perature program by operating the furnace(s) between selected
11.1 Scouting Experiment:
temperaturelimitsovertherangeofambientto900K(627°C)
11.1.1 Usinga1to5mg test specimen, weighed to a
at a rate of 0.1 to 20 K/min constant to 1% or at an isothermal
precision of 6 0.1 mg, perform a scouting experiment using
temperature constant to 0.1 K, (f) a data collection device,to
Test Method E537 to determine the temperature of first-
provideameansofacquiring,storing,anddisplayingmeasured
deviation-from baseline (T ) and the heat of reaction (∆H).
o
or calculated signals or both. The minimum output signals
required are heat flow, temperature, and time. 11.2 Determination of Reaction Type:
11.2.1 Weighintoaspecimencontainer1to5mgofthetest
8.2 Containers (pans, crucibles, vials, lids, closures, seals,
specimen, with a precision of 60.1 mg, and hermetically seal
etc.) that are inert to the specimen and reference materials (if
the container. DO NOT load the test specimen into the
any) and that are of suitable structural shape and integrity to
apparatus. Load an empty specimen container into the refer-
contain the specimen (even under internal pressure developed
ence chamber. Close the DSC chamber and prepare the
during the reaction) and reference in accordance with the
apparatus for an experimental run.
specific requirements of this test method.
11.2.2 Select an isothermal test temperature corresponding
NOTE3—Manyusersfindglass,goldorgoldcoatedhermeticallysealed
to 10% peak area (∆H) from the scouting experiment per-
containers of low headspace volume advantageous for testing with high
formed in 11.1. Equilibrate the apparatus for 1 min at this test
energy materials. The selected container shall meet the necessary interna
...
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