ASTM E2890-12(2018)

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, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.7 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Historical
• Publication Date: 31-Mar-2018
• ICS: 17.200.10 - Heat. Calorimetry
• Technical Committee: E37 - Thermal Measurements
• Drafting Committee: E37.01 - Calorimetry and Mass Loss

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E2890 − 12 (Reapproved 2018)
Standard Test 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 mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
1.1 This test method describes the determination of the
kinetic parameters of Arrhenius activation energy and pre-
2. Referenced Documents
exponential factor using the Kissinger variable heating rate
2.1 ASTM Standards:
iso-conversion method (1, 2) and activation energy and
E473Terminology Relating to Thermal Analysis and Rhe-
reaction order by the Farjas method (3) for thermally unstable
ology
materials. The test method is applicable to the temperature
E537Test Method for The Thermal Stability of Chemicals
range from 300 to 900 K (27 to 627°C).
by Differential Scanning Calorimetry
1.2 Both nth order and accelerating reactions are addressed
E691Practice for Conducting an Interlaboratory Study to
by this method over the range of 0.5 < n<4and1< p<4
Determine the Precision of a Test Method
where n is the nth order reaction order and p is the Avrami
E967Test Method for Temperature Calibration of Differen-
reaction order (4). Reaction orders n and p are determined by
tial Scanning Calorimeters and Differential ThermalAna-
the Farjas method (3).
lyzers
E968Practice for Heat Flow Calibration of Differential
1.3 This test method uses the same experimental conditions
Scanning Calorimeters
asTestMethodE698.TheFlynn/Wall/Ozawadatatreatmentof
E698Test Method for Kinetic Parameters for Thermally
Test Method E698 may be simultaneously applied to these
Unstable Materials Using Differential Scanning Calorim-
experimental results.
etry and the Flynn/Wall/Ozawa Method
1.4 The values stated in SI units are to be regarded as
E1142Terminology Relating to Thermophysical Properties
standard. No other units of measurement are included in this
E1231Practice for Calculation of Hazard Potential Figures
standard.
of Merit for Thermally Unstable Materials
1.5 There is no ISO equivalent to this standard.
E1860Test Method for Elapsed Time Calibration of Ther-
mal Analyzers
1.6 This standard does not purport to address all of the
E1970PracticeforStatisticalTreatmentofThermoanalytical
safety concerns, if any, associated with its use. It is the
Data
responsibility of the user of this standard to establish appro-
E2041Test Method for Estimating Kinetic Parameters by
priate safety, health, and environmental practices and deter-
Differential Scanning Calorimeter Using the Borchardt
mine the applicability of regulatory limitations prior to use.
and Daniels Method
1.7 This international standard was developed in accor-
E2161Terminology Relating to Performance Validation in
dance with internationally recognized principles on standard-
Thermal Analysis and Rheology
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
3. Terminology
3.1 Technical terms used in this test method are defined in
ThistestmethodisunderthejurisdictionofASTMCommitteeE37onThermal
Terminologies E473, E1142, and E2161. Referenced terms
Measurements and is the direct responsibility of Subcommittee E37.01 on Calo-
include Arrhenius equation, baseline, calibration, Celsius,
rimetry and Mass Loss.
Current edition approved April 1, 2018. Published May 2018. Originally
approved in 2012. Last previous approval in 2012 as E2890 – 12. DOI: 10.1520/ For referenced ASTM standards, visit the ASTM website, www.astm.org, or
E2890-12R18. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof Standards volume information, refer to the standard’s Document Summary page on
this standard. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E2890 − 12 (2018)
differential scanning calorimeter, endotherm, enthalpy, figure-
p = Avrami reaction order (dimensionless).
of-merit, first-deviation-from baseline, full-width-at-half-
NOTE 1—There are a large number of conversion function expressions
maximum, Kelvin, onset point, peak, peak value, relative 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
standard deviation, standard deviation, thermal analysis, and
Mass Action (6) while Eq 3 is the Avrami equation (4).
thermal curve.
5.3 The Arrhenius equation (7) describes how the reaction
rate changes as a function of temperature:
4. Summary of Test Method
2E⁄RT
k T 5Ze (4)
~ !
4.1 A series of test specimens are heated at a minimum of
four different linear rates in a differential scanning calorimeter
where:
through a region of exothermic reaction behavior. The rate of
-1
Z = pre-exponential factor (s ),
heat evolution, created by a chemical reaction, is proportional
-1
E = activation energy (J mol ),
to the rate of reaction and is measured as a function of
T = absolute temperature (K),
temperature and time. -1 -1
R = gas constant (8.314 J mol K ), and
4.2 The temperature corresponding to the maximum rate of e = natural logarithm base (2.7182818).
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
derivative of the reaction rate at the peak maximum equals
4.3 Areaction type is determined for the specimen from the
zero. Taking the derivative of Eq 5 over time at the maximum
shape of the reaction exotherm under isothermal temperature
point for the heating with constant rate β, then casting in
conditions.
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
ln β ⁄ T 5 lnZR ⁄ E 2 E⁄RT (6)
reaction exotherm measured by the time at full-width-at-half- @ # @ #
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).
m
thetimeatfull-width-at-half-maximumversusthereciprocalof
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
K K
dependent experimental parameter versus temperature (or theactivationenergy,respectively,determinedbytheKissinger
time) as the independent parameter. method.
5.2 Reactions may be modeled with a number of suitable 5.7 The shape of the reaction exothermic peak may be
equations of the form:
characterized by the time at full-width-at-half-maximum
(t ) (3).
fwhm
da⁄dt 5 k T f α (1)
~ ! ~ !
ln t 5 E ⁄RT 1ln t'⁄ Z (7)
@ # @ #
FWHM F m
where:
-1
where:
da/dt = reaction rate (s ),
α = fraction reacted or conversion (dimensionless),
t = the full-width-at-half-maximum time (s), and
fwhm
-1
k(T) = specific rate constant at temperature T, and
t’ = an arbitrary function (s ).
f(α) = conversion function (dimensionless).
5.8 Eq 7 is of the form Y5mX1b.Ifln[t ] is set equal
FWHM
Commonly used functions include:
to Y and 1/T is set equal to X, then a display of Y versus X
m
n
yieldsaslope(m )equalto E /Randanintercept(b )equalto
f ~α! 5 ~1 2 α! (2)
1 F F F
ln[t’/Z] where E is the activation energy determined by the
~p 2 1!⁄p
F
f ~α! 5 p~1 2 α!@2 ln ~1 2 α!# (3)
Farjas method.
where:
5.9 The reaction order, n or p, is determined through an
n = nth reaction order (dimensionless), and
empirical relationship based on t’.
E2890 − 12 (2018)
6. Significance and Use any) and that are of suitable structural shape and integrity to
contain the specimen (even under internal pressure developed
6.1 Thistestmethodisusefulforresearchanddevelopment,
during the reaction) and reference in accordance with the
quality assurance, regulatory compliance and specification-
specific requirements of this test method.
based acceptance.
NOTE3—Manyusersfindglass,goldorgoldcoatedhermeticallysealed
6.2 The kinetic parameters determined by this method may
containers of low headspace volume advantageous for testing with high
energy materials. The selected container shall meet the necessary internal
be used to calculate thermal hazard figures-of-merit according
pressure rating to withstand internal pressure buildup.
to Practice E1231.
8.3 Ameans, tool or device to close, encapsulate or seal the
7. Interferences container of choice.
8.4 Analytical Balance with a capacity of at least 100 mg to
7.1 This test method assumes a single reaction mechanism
constant over the reaction conversion temperature range of the weigh specimens or containers, or both to 610 µg.
material under evaluation. Some overall reactions of interest
8.5 Auxiliary instrumentation considered useful but not
are known to include a series of competing reaction mecha-
essential for conducting this method would include cooling
nisms that lead to changes in reaction order with conversion
capability to hasten cooling to ambient temperature conditions
(8). This method addresses the reaction only at a single
at the end of the test.
conversion value at the maximum reaction rate—often about
0.7.
9. Hazards
7.2 Method precision is enhanced with the selection of the 9.1 This test method is used to determine the properties of
appropriate conversion function [f(α)]. The shape of the ther-
thermally reactive materials. The user of this test method shall
mal curve, as described in 11.2, may confirm the selection of use the smallest quantity of material (typically a few milli-
the nth order or accelerating reaction models.
grams) needed to obtain the desired analytical results.
7.2.1 Typically nth reactions include many (but not all)
9.2 Special precautions shall be taken to protect personnel
decompositionreactionsorthosewhereoneoftheparticipating
andequipmentwhentheapparatusinuserequirestheinsertion
species is in excess.
ofspecimensintoaheatedfurnace.Typicalspecialprecautions
7.2.2 Typical accelerating (Avrami) reactions include ther-
include adequate shielding, ventilation of equipment and face
moset cure, crystallization, and some pyrotechnic reactions.
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
10. Calibration and Standardization
representative of the larger sample from which they are taken.
10.1 Perform any calibration procedures recommended by
7.4 Acriticalliteratureevaluationofkineticmethodsreports
the manufacturer as described in the operator’s manual to
that the Kissinger method is the most accurate method for
ensurethattheapparatusiscalibratedateachheatingrateused.
determining activation energy in many cases (9).
10.2 Calibrate the heat flow signal using 99.99+ % indium,
8. Apparatus
Practice E968, and the same type of specimen container to be
used in the subsequent test for kinetic parameters.
8.1 DifferentialScanningCalorimeter(DSC)—Theessential
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, Test Method E967, and the same type of specimen
furnace(s) to provide uniform controlled heating or cooling of
containerandheatingratestobeusedinthesubsequenttestfor
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
10.4 Calibrate the elapsed time signal using Test Method
temperature sensor to provide a measurement of the specimen
E1860.
temperatureto 60.01K, (c) differential sensorstodetectaheat
10.5 Determine the thermal resistance (φ) from the leading
flow difference between the specimen and reference with a
edge slope ~S 5 ∆ q ⁄ ∆ T! in (mW/K) of the indium melting
rangeof100mWreadableto 61µW, (d)ameansofsustaining
endotherm as shown in Fig. 1 and 12.1.
a test chamber environmentofinertpurgegasatapurgerateof
10 to 100 mL/min within 65 mL/min, (e) a temperature
11. Procedure
controller,capableofexecutingaspecifictemperatureprogram
byoperatingthefurnace(s)betweenselectedtemperaturelimits 11.1 Scouting Experiment:
over the range of ambient to 900 K (627°C) at a rate of 0.1 to 11.1.1 Usinga1to5mg test specimen, weighed to a
20 K/min constant to 1% or at an isothermal temperature precision of 60.1 mg, perform a scouting experiment using
constant to 0.1 K, (f) a data collection device, to provide a Test Method E537 to determine the temperature of first-
means of acquiring, storing, and displaying measured or deviation-from baseline (T ) and the heat of reaction (∆H).
o
calculated signals or both. The minimum output signals re-
11.2 Determination of Reaction Type:
quired are heat flow, temperature, and time.
11.2.1 Weighintoaspecimencontainer1to5mgofthetest
8.2 Containers (pans, crucibles, vials, lids, closures, seals, specimen, with a precis
...