ASTM E2958-21

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Designation: E2958 − 19 E2958 − 21
Standard Test Methods for
Kinetic Parameters by Factor Jump/Modulated
Thermogravimetry
This standard is issued under the fixed designation E2958; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 These test methods describe the model-free determination of Arrhenius activation energy by thermogravimetry using the factor
jump (1) (Test Method A) or modulated thermogravimetry (2) (Test Methods B and C) techniques. With the assumption of a
first-order kinetic model, the pre-exponential factor is additionally determined.
1.2 These test methods are applicable to materials with well-defined decomposition profiles, namely, a smooth, continuous mass
change.
1.3 These test methods are applicable to decomposition occurring in the range from 400 K to 1200 K (nominally 100 °C to 900
°C). The temperature range may be extended depending on the instrumentation and material used.
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 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.
1.6 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.
2. Referenced Documents
2.1 ASTM Standards:
E473 Terminology Relating to Thermal Analysis and Rheology
E1142 Terminology Relating to Thermophysical Properties
E1582 Test Method for Temperature Calibration of Thermogravimetric Analyzers
E1641 Test Method for Decomposition Kinetics by Thermogravimetry Using the Ozawa/Flynn/Wall Method
E1877 Practice for Calculating Thermal Endurance of Materials from Thermogravimetric Decomposition Data
E1970 Practice for Statistical Treatment of Thermoanalytical Data
E2040 Test Method for Mass Scale Calibration of Thermogravimetric Analyzers
These test methods are under the jurisdiction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.01 on Calorimetry
and Mass Loss.
Current edition approved Sept. 1, 2019Oct. 1, 2021. Published September 2019November 2021. Originally approved in 2014. Last previous edition approved in 20142019
as E2958 – 14.19. DOI: 10.1520/E2958-19.10.1520/E2958-21.
The boldface numbers in parentheses refer to a list of references at the end of this standard.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
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E2550 Test Method for Thermal Stability by Thermogravimetry
E3007 Practice for Selection and Use of Kinetic Reference Values in the Study of Decomposition Reactions by Thermogravi-
metry
3. Terminology
3.1 Definitions—Technical terms used in these test methods are defined in Terminologies E473 and E1142 include Arrhenius
equation, activation energy, Celsius, failure criterion, modulated temperature, pre-exponential factor, reaction order, and
thermogravimetric analysis.
4. Summary of Test Methods
4.1 These test methods consist of heating a test specimen weighing a few milligrams 2 mg to 4 mg at a heating rate of about 1
K/min with a superimposed step-and-hold (factor jump) or sinusoidal (modulated) temperature program through the decomposition
temperature region. The specimen mass rate-of-change is continuously calculated and recorded as a function of temperature. The
activation energy is then determined from the mass rate-of-change at two (or more) closely spaced temperature regions. The
activation energy thus determined is based on no assumed reaction model or mechanism and thus is model free.
4.2 AssumingIf a first-order reaction model (n = 1), the additional 1) is assumed, the reaction parameter logarithm-of-the-pre-
exponential-factor (ln[Z]) is additionally determined.
4.3 Activation energy and logarithm-of-the-pre-exponential-factor may be displayed as a function of average temperature or
conversion to provide additional information about the constancy of the decomposition reaction relative to these experimental
parameters.
5. Significance and Use
5.1 The activation energy may be used to calculate thermal endurance and an estimate of the lifetime of the material at specified
temperatures using Test Method E1877.
5.2 The kinetic parameters determinedetermined by these test methods may be used in quality assurance, specification acceptance,
research, and development.
5.3 The kinetic parameters of activation energy and logarithm of the pre-exponential factor determined by these test methods have
little intrinsic value in themselves. Most practical applications of this information, such as lifetime estimation (see Test Method
E1877), also require an estimation of the precision of the respective values. Determination of that precision by replicated
determination is a non-manditory part of these test methods.
6. Apparatus
6.1 The essential equipment required to provide minimum thermogravimetric analytical capability of these test methods include:
6.1.1 A thermobalance, composed of (a) a furnace to provide uniform controlled heating of a specimen at a constant rate up to
100 K/min within the temperature range from ambient to 1200 K; (b) a temperature sensor to provide an indication of the
specimen/furnace temperature readable to within 60.160.01 K; (c) an electrobalance to continuously measure the specimen mass
with a minimum capacity of 20 mg and a sensitivity of 650 μg; and (d) a means of sustaining the specimen/container under
atmospheric control of an inert or reactive purge gas of 99.99 % purity at a rate of 20 mL/min to 50 mL/min 6 5 mL/min.
6.1.2 A temperature controller, capable of executing a specific temperature program by operating the furnace between selected
temperature limits at a rate of temperature change of 1 K/min to 100 K/min constant to within 61 % or an isothermal temperature
which is maintained constant to within 60.05 K.
6.1.3 A data collection device, to provide a means of acquiring, storing, and displaying measured or calculated signals, or both.
The minimum output signals required for these test methods are mass, mass rate-of-change, temperature, and time.
6.1.4 Auxiliary instrumentation or data analysis capability considered useful in conducting these test methods include:
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6.1.4.1 For Test Method B, the ability to apply a sinusoidal temperature program of a 100 s to 300 s period and 60.01 K to 66
K amplitude upon the underlying linear temperature program or isothermal conditions.
6.1.4.2 For Test Method B, the capability to continuously calculate activation energy and logarithm of the pre-exponential factor.
NOTE 1—Alternative capabilities are described in Refs (3-7).
6.2 Containers (pans, crucibles, and so forth) that are inert to the specimen and that will remain dimensionally stable over the
temperature range from ambient to 1200 K.
6.3 High-Purity (99.99 %) Nitrogen Supply, for purge gas.
NOTE 2—Other atmospheres may be used but shall be reported.
6.4 Cryogenic Mill capable of grinding up to 4 mg of material at a temperature less than 173 K (–100 °C).
7. Sampling, Test Specimens, and Test Units
7.1 Since milligram quantities of specimens are used, it is essential that the specimens be representative of the samples from which
they are taken. All specimens should be thoroughly mixed prior to sampling and should be sampled by removing portions form
various parts of the sample. These portions should in turn be combined and mixed well to ensure a representative specimen for
the determination.
7.2 Powdered or granular specimens that have a high surface-to-volume ratio, are preferred, although films, fibers, and fabric may
be used providing that care is taken to ensure that all specimens are uniform in size and shape. Where the sample is a part or is
in the form of pellets, the specimen may be prepared by filling, rasping or cryogenic milling.
NOTE 3—The specimen size and surface-to-volume ratio are known to affect the results of this test. A narrow range of specimen sizes should be used as
noted in 10.1 and 12.1. Uniformity in particle size can be achieved, without the loss of volatiles, by using a cryoscopy (liquid nitrogen) mill to grind the
sample to a powder. To prevent the condensation of moisture, the mill should be opened only after returning to ambient temperature, or the operation
should be performed in a glove box filled with dry gas.
7.2.1 The specimen size and surface-to-volume ratio are known to affect the results of this test. A narrow range of specimen sizes
should be used as noted in 10.1 and 12.1. Uniformity in particle size can be achieved, without the loss of volatiles, by using a
cryoscopy (liquid nitrogen) mill to grind the sample to a powder. To prevent the condensation of moisture, the mill should be
opened only after returning to ambient temperature, or the operation should be performed in a glove box filled with dry gas.
7.3 In the absence of other information, the samples are assumed to be analyze as-received except for the mechanical treatment
noted in 7.2. If some heat treatment, such as drying, is applied to the sample prior to analysis, this treatment and any resulting mass
loss shall be reported.
7.4 Some materials may require more sophisticated conditioning, such as maintaining the sample in a specified temperature and
relative humidity for an extended period of times. Such conditioning may be conducted, but procedural details shall be included
in the report.
8. Preparation of Apparatus and Experimental Conditions
8.1 Prepare the thermogravimetric analyzer using the procedures described in the manufacturer’s operations manual.manual
including positioning the temperature sensor as close as practical to the test specimen.
8.2 Identify the weight loss to be used as the failure criterion. Report this value.
NOTE 3—The value of 5 % mass loss of the specific decomposition step is commonly used as a default value in thermogravimetry and accelerated lifetime
testing as the failure criteria (see Test Method E1641).
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9. Calibration and Standardization
9.1 Calibrate the temperature scale of the thermogravimetric analyzer at 1 K/min using Practice E1582.
9.2 Calibrate the mass loss scale of the thermogravimetric analyzer using Test Method E2040.
TEST METHOD A
FACTOR JUMP METHOD
10. Procedure
10.1 Place 2 mg to 4 mg of the specimen into a clean, tared instrument specimen container.
NOTE 4—Other specimen size to 61 mg may be used but shall be reported.
NOTE 5—Powdered or granular specimens should be distributed evenly over the specimen holder so as to maximize the exposed surface.
10.2 Equilibrate the specimen for 1 minute at a temperature at least 20 K below the known decomposition onset temperature.
Establish the mass scale at the conversion fraction of zero (α = 0.0 %).
NOTE 6—The decomposition onset temperature may be obtained from a scouting experiment using Test Method E2550 at 5 K/min.
10.3 Begin recording experimental data. Initiate an isothermal temperature program for 150 s. At the end of this isothermal period,
measure and record the mass rate-of-change (dα /dt), temperature (T ) and conversion (α ).
v v v
10.4 Initiate a temperature step-and-hold sequence by increasing the temperature by 10.0 K 6 0.2 K K, avoiding overshoot, and
holding that temperature to within 0.05 K for 150 s. At the end of this isothermal period, record the mass rate-of change (dα /dt),
p
temperature (T ) and conversion (α ).
p p
NOTE 7—The time required to establish temperature equilibrium and to make an accurate mass rate-of-change measurement may vary by instrument and
temperature. These conditions are thought to embrace those achievable by all instrument designs. Other temperature steps and isothermal hold periods
may be used but shall be reported (see Appendix X1).
10.5 Using the data obtained in 10.3 and 10.4, determine the activation energy, logarithm of the pre-exponential factor and
temperature (T) using Eq 1, Eq 2, and Eq 4. Record these values along with the conversion (α) at the end of the second isothermal
region.
10.6 Initiate a second step-and-hold cycle by decreasing the temperature by 5.0 K 6 0.1 K and holding that temperature to within
0.05 K for 150 s. At the end of the isothermal region, record the mass-rate-of change (dα /dt), temperature (T ) and conversion
v v
(α ).
v
10.7 Using the data obtained in 10.4 and 10.6, determine the activation energy, logarithm of the pre-exponential factor, and
temperature using Eq 1, Eq 2, Eq 3, and Eq 4. Record these values along with the conversion (α) at the end of the second isothermal
region.
10.8 Repeat 10.4 – 10.7 until the decomposition weight loss is complete or until the upper temperature limit of the apparatus is
reached.
10.9 Create a table of activation energy and logarithm of the pre-exponential factor versus conversion. Select the activation energy
and logarithm of the pre-exponential factor nearest the failure criterion conversion level from 8.2.
NOTE 8—Most uses of activation energy and logarithm of the pre-exponential factor required an estimation of their precision. Mean values and standard
deviations for both values may be obtained from a minimum of three replicate determinations (see Practice E1970).
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10.10 Report the mean activation energy (E) and its percent relative standard deviation (σE/E) and the mean logarithm of the
pre-exponential factor (ln[Z]) and its percent relative standard deviation (σln[Z]/ln[Z]) at the temperature closest to the failure
criterion of 8.2.
11. Calculations
11.1 Calculations are as follows:
E 5 $R T T ln @~dα ⁄ dt!⁄~dα ⁄ dt!#%⁄~T 2 T ! (1)
p v p v p v
ln@Z , min # 5 ln@~dα ⁄ dt!⁄~1 2 α ⁄ 100 %!#1E⁄RT (2)
v
log Z , min 5 log dα ⁄ dt ⁄ 1 2 α ⁄ 100 % 10.434 E⁄RT (3)
@ # @~ ! ~ !#
T 5 T 1 T ⁄2 (4)
~ !
p v
where:
E = activation energy, J/mol,
R = gas constant (= 8.31451 J/(mol K)),
T = temperature at the end of the higher temperature isothermal plateau, K,
p
T = temperature at the end of the lower temperature isothermal plateau, K,
v
T = average temperature between T and T , K,
p v
dα /dt = mass rate-of-change at the end of the higher temperature isothermal plateau, % / min,
p
dα /dt = mass rate-of-change at the end of the lower temperature isothermal plateau, % / min,
v
ln = natural logarithm to the Napier base e,
α = fraction reacted or conversion, %,
-1
Z = pre-exponential factor, min , and
dα/dt = mean mass rate-of-change for two adjacent step-and-hold segments = (dα dt + dα /dt)/2.
v p
NOTE 9—The logarithm of the pre-exponential factor (ln[Z]) calculated in Eq 2 is determined assuming a first-order kinetics reaction.
TEST METHOD B
MODULATED THERMOGRAVIMETRY METHOD
12. Procedure
12.1 Place 2 mg to 4 mg of the specimen into a clean, tared instrument specimen container.
NOTE 10—Other specimen size to 61 mg may be used but shall be reported.
NOTE 11—Powdered or granular specimens should be distributed evenly over the specimen holder so as to maximize the exposed surface.
12.2 Equilibrate the specimen for 1 minute at a temperature at least 20 K below the known decomposition onset temperature.
Establish the percent mass loss scale at 100 % (α = 0 %).
NOTE 12—The decomposition onset temperature may be obtained from a scouting experiment using Test Method E2550 at 5 K/min.
12.3 Begin recording experimental data including average temperature, average mass, conversion, activation energy and logarithm
of the pre-exponential factor. Initiate a modulated temperature program with amplitude of 64.9 K to 65.1 K (that is, 9.8 K to 10.2
K peak-to-peak) and a period of 300 s.
NOTE 13—The time
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