1、Designation: E2070 08E2070 13Standard Test Method forKinetic Parameters by Differential Scanning CalorimetryUsing Isothermal Methods1This standard is issued under the fixed designation E2070; the number immediately following the designation indicates the year oforiginal adoption or, in the case of r
2、evision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 Test Method A determines Methods A, B, and C determine kinetic parameters for activation energy,
3、pre-exponential factorand reaction order using differential scanning calorimetry from a series of isothermal experiments over a small (; 10( 10 K)temperature range. This treatment Test Method A is applicable to low nth order reactions and to autocatalyzedreactions. TestMethods B and C are applicable
4、 to accelerating reactions such as thermoset curing or pyrotechnic reactions and crystallizationtransformations in the temperature range from 300 to 900 K (30 to 630 C). (nominally 30 to 630C). This test method is applicableonly to these types of exothermic reactions when the thermal curves do not e
5、xhibit shoulders, double peaks, discontinuities or shiftsin baseline.1.2 Test Method B Methods D and E also determines the activation energy of a set of time-to-event and isothermal temperaturedata generated by this or other procedures.procedures1.3 Test Method C determines the activation energy and
6、 initial heat flow from a series of isothermal experiments over a smalltemperature range. Because this approach only determines kinetic parameter of activation energy, no knowledge of the kineticmodel is required. Therefore it is considered to be “model free”. This approach is broadly applicable to
7、a variety of complicatedreactions including those not well understood.1.3 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard.1.4 This test method is similar but not equivalent toISO DIS 11357, to ISO DIS 11357, Part 5, and provid
8、es more informationthan the ISO standard.1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatoryl
9、imitations prior to use. Specific precautionary statements are given in Section 8.2. Referenced Documents2.1 ASTM Standards:2D3550D3350 Practice for Thick Wall, Ring-Lined, Split Barrel, Drive Sampling of SoilsSpecification for Polyethylene PlasticsPipe and Fittings MaterialsD3895 Test Method for Ox
10、idative-Induction Time of Polyolefins by Differential Scanning CalorimetryD4565 Test Methods for Physical and Environmental Performance Properties of Insulations and Jackets for TelecommunicationsWire and CableD5483 Test Method for Oxidation Induction Time of Lubricating Greases by Pressure Differen
11、tial Scanning CalorimetryD6186 Test Method for Oxidation Induction Time of Lubricating Oils by Pressure Differential Scanning Calorimetry (PDSC)E473 Terminology Relating to Thermal Analysis and RheologyE537 Test Method for The Thermal Stability of Chemicals by Differential Scanning CalorimetryE698 T
12、est Method for Arrhenius Kinetic Constants for Thermally Unstable Materials Using Differential Scanning Calorimetryand the Flynn/Wall/Ozawa MethodE967 Test Method for Temperature Calibration of Differential Scanning Calorimeters and Differential Thermal Analyzers1 This test method is under the juris
13、diction of ASTM Committee E37 on Thermal Measurements and is the direct responsibility of Subcommittee E37.01 on Calorimetryand Mass Loss.Current edition approved Feb. 1, 2008Sept. 15, 2013. Published March 2008October 2013. Originally approved in 2000. Last previous edition approved in 20032008 asE
14、2070 03.E2070 08. DOI: 10.1520/E2070-08.10.1520/E2070-13.2 For referencedASTM standards, visit theASTM website, www.astm.org, or contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This
15、 document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior edition
16、s as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official document.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E968 Practice for Heat Flow Calibration of Different
17、ial Scanning CalorimetersE1142 Terminology Relating to Thermophysical PropertiesE1445 Terminology Relating to Hazard Potential of ChemicalsE1858 Test Method for Determining Oxidation Induction Time of Hydrocarbons by Differential Scanning CalorimetryE1860 Test Method for Elapsed Time Calibration of
18、Thermal AnalyzersE1958 Guide for Sensory Claim SubstantiationE1970 Practice for Statistical Treatment of Thermoanalytical DataE2041 Test Method for Estimating Kinetic Parameters by Differential Scanning Calorimeter Using the Borchardt and DanielsMethodE2046 Test Method for Reaction Induction Time by
19、 Thermal Analysis2.2 ISO Standard:3ISO DIS 11357 Part 5: Determination of Temperature and/or Time of Reaction and Reaction Kinetics3. Terminology3.1 Specific technical terms used in this test method are defined in Terminologies E473, E1142, and E1445., including the termscalorimeter, Celsius, crysta
20、llization, differential scanning calorimetry, general rate law, isothermal, peak, and reaction.4. Summary of Test Method4.1 A test specimen is held at a constant temperature in a differential scanning calorimeter throughout an exothermic reaction.The rate of heat evolution, developed by the reaction
21、, is proportional to the rate of reaction. Integration of the heat flow as afunction of time yields the total heat of reaction.4.2 An autocatalytic, accelerating (Sestak-Berggren or Avrami models), nth th order data, or model free treatment4,5,6 is used toderive the kinetic parameters of activation
22、energy, pre-exponential factor and reaction order from the heat flow and total heat ofreaction information obtained in 4.1 (See Basis for Methodology, Section 5.)5. Basis of Methodology5.1 Reactions of practical consideration are exothermic in nature; that is, they give off heat as the reaction prog
23、resses.Furthermore, the rate of heat evolution is proportional to the rate of the reaction. Differential scanning calorimetry measures heatflow as a dependent experimental parameter. parameter as a function of time under isothermal experimental conditions. DSC isuseful for the measurement of the tot
24、al heat of a reaction and the rate of the reaction as a function of time and temperature.5.2 Reactions may be modeled with a number of suitable equations of the form of:d/dt5kT! f! (1)where:d/dt = reaction rate (min1),d/dt = reaction rate (s1), = fraction reacted or conversion (dimensionless), = fra
25、ction reacted (dimensionless),k (T) = specific rate constant at temperature T (min1 ),k (T) = specific rate constant at temperature T (s1 ),f () = conversion function. Commonly used functions include:f1!512!n (2)f2!5m 12!n (3)f2!5 12!n (3)f3!5p1 2 !21n 1 2 !#p 21!p (4)where:n and m = partial reactio
26、n order terms.n, , and p = partial reaction order terms.NOTE 1There are a large number of conversion function expressions for f()f().4. Those described here are the moremost common but are notthe only functions suitable for this test method. Eq 21 is known as the general rate equation while Eq 3 is
27、the autocatalyticaccelerating (or3 Available from American National Standards Institute (ANSI), 25 W. 43rd St., 4th Floor, New York, NY 10036, http:/www.ansi.org.4 Sbirrazzuoli, N.; Brunel, D.; Elegant, L., J. Therm. Anal., 38, 1509-1524, 1992.Sbirrazzuoli, N., Brunel, D., and Elegant, L., Journal o
28、f Thermal Analysis, Vol 38, 1992,pp. 15091524.5 Sestak, J.; Berggren, G.; Thermochim. Acta, 3, 1, 1971.Sestak, J., and Berggren, G., Thermochimica Acta, Vol 3, 1971, p. 1.6 Gorbachiev, V.M., J. Therm. Anal., 18, 193197, 1980.Gorbachiev, V.M., Journal of Thermal Analysis, Vol 18, 1980, pp. 193197.E20
29、70 132Sestak-Berggren) equationequation.5,6. Eq 4 is the accelerating Avrami equation. Eq 2 is used for nth order reactions while Eq 3 isor Eq 4 are used foraccelerating reaction, such as thermoset cure and crystallization transformations.5.3 For a reaction conducted at temperature (T), the autocata
30、lyticaccelerating rate Eq 3equation of and the rate equation Eq 15.2may be cast in itstheir logarithmic form.d/dt5kT! m 12!n (5)d/dt5kT! 12!n (5)lnd/dt# 5lnkT!#1m ln#1n ln12# (6)lnd/dt# 5lnkT!#1 ln#1n ln12# (6)This equation has the form z = a + bx + cy and may be solved using multiple linear regress
31、ion analysis.analysis where x = ln,y = ln1 , z = lnd/dt, a = lnk(T), b = and c = n.NOTE 2Subsequent discussions use the autocatalytic form of the The rate equation (Eq 3). It ) reduces to the simpler general rate equation (Eq 2)when the value of reaction order parameter m equals zero thereby reducin
32、g the number of kinetic parameters to be determined.5.4 For reactions conducted at temperature (T), the accelerating rate equation of Eq 4 may be cast as:ln2ln 1 2 !#5p lnk T!#1p lnt# (7)This equation has the form of y = mx + b and may be solved by linear regression where x = lnt, y = ln-ln(1 ), wit
33、h p =m,b = p lnk(T), and t = time.5.5 The Arrhenius equation describes how the reaction rate changes as a function of temperature:kT! 5Z e2E/RT (8)where:Z = pre-exponential factor (min1),Z = pre-exponential factor (s1),E = activation energy (J mol1),T = absolute temperature (K),R = gas constant = (8
34、.314 J mol1 K1), ande = natural logarithm base = 2.7182818.5.6 Eq 68 cast in its logarithmic form is:lnkT!# 5lnZ# 2E/RT (9)lnkT!# 5lnZ# 2E/RT (9)Eq 79 has the form of a straight line, y = xmx + b, where a plot of the logarithm of the reaction rate constant (lnlnk(T) versusthe reciprocal of absolute
35、temperature (l/T)(l/T) is linear with the slope equal to E/R and an intercept equal to lnZ.5.7 As an alternative to 5.3Eq 6 and 5.5Eq 7, the rate and Arrhenius equations combined and cast in logarithmic form is:lnd/dt# 5lnZ# 2E/RT1m ln#1n ln12# (10)lnd/dt# 5lnZ# 2E/RT1m ln#1n ln12# (10)Eq 810 has th
36、e form, z = a + bwbx + cxcy + dy,dw, and may be solved using multiple linear regression analysis.where:z = lnd/dta = lnZb = -E/Rx = 1/Tc = y = ln1 d = n, andw = ln1 .5.8 If activation energy values only are of interest, Eq 811 may be solved under conditions of constant conversion to yield:lnt# 5E/RT
37、1c (11)lnt# 5E/RT1b (11)where:t = lapsed time, (min), at isothermal temperature, T, andc = constant.E2070 133t = lapsed time (s), at constant conversion and at isothermal temperature, T, andb = constant.Eq 911 has the form of a straight line, y = xmx + b, where a plot of the logarithm of the lapsed
38、time under a series of differingisothermal conditions versus the reciprocal of absolute temperature (l/T) is linear with a slope equal to E/R.5.9 If activation energy values only are of interest, Eq 811 may be solved under conditions of constant conversion and theequality d/dtd/dt = dH/dt/HdH/dt / (
39、H) to yield:lndH/dt# 5E/RT1b 5m/T1b (12)lndH/dt# 52E/RT1b 5m/T1b (12)where:H = total heat of reaction (J/g),H = total heat of reaction (mJ),dH/dt = instantaneous heat flow (W/g),dH/dt = instantaneous heat flow (mW),b = constant, andm = slope (kK)m = slope (K)Eq 1012 has the form of a straight line y
40、 = mx + b, where a plot of the logarithm of the heat flow (lnlndH/dtdH)/dt) at thepeak of the exotherm under a series of differing isothermal temperature conditions versus the reciprocal of the absolute temperature(1/T) is linear with a slope equal to E/R.5.10 A series of isothermal experiments by T
41、est Method AA, B, and C described in Section 11 at four or more temperatures,determines the kinetic parameters of activation energy, pre-exponential factor and reaction order. Alternatively, a series ofisothermal experiments byTest MethodAdescribed in Section 11 at four or more temperatures may be u
42、sed to determine activationenergy and initial heat flow by test Method C described in Section 15.Alternatively, the time to a condition of constant conversionfor a series of experiments at four or more temperatures obtained by this or alternative Test Method B,D, described in Section 12,may be used
43、to determine activation energy only.5.11 Aseries of not less than four isothermal DSC experiments, covering a temperature range of approximately 10 K and a timeless than 100 min (such as those shown in Fig. 1) provides values for d/dt, , (1 ) and T to solve Eq 56, Eq 7, Eq 9, and Eq810.5.12 Aseries
44、of not less than four isothermal DSC experiments covering a temperature range of approximately 10 K and a timeless than 100 min provides dH/dt and T to solve Eq 10125.13 Avariety of time-to-event experiments such as oxidation induction time methods (Practice D3550D3350 and Test MethodsD3895, D4565,
45、D5483, and D6186, and Guide E1958E1858) and reaction induction time methods (Test Method E2046) providevalues for t and T to solve equation Eq 115.76. Significance and Use6.1 This test method is useful for research and development, quality assurance, regulatory compliance and specificationacceptance
46、 purposes.6.2 The determination of the order of a chemical reaction or transformation at specific temperatures or time conditions is beyondthe scope of this test method.6.3 The activation energy results obtained by this test method may be compared with those obtained from Test Method E698for nth ord
47、er and autocatalyticaccelerating reactions. Activation energy, pre-exponential factor, and reaction order results by thistest method may be compared to those for Test Method E2041 for nth order reactions.7. Interferences7.1 The approach is applicable only to exothermic reactions.NOTE 3Endothermic re
48、actions are controlled by the rate of the heat transfer of the apparatus and not by the kinetics of the reaction and may not beevaluated by this test method.7.2 This test method is intended for a reaction mechanism that does not change during the transition. This test method assumesa single reaction
49、 mechanism when the shape of the thermal curve is smooth (as in Fig. 2 and Fig. 3) and does not exhibit shoulders,multiple peaks or discontinuation steps.7.3 Method Test method precision is enhanced with the selection of the appropriate conversion function f() that minimizesthe number of experimental parameters determined. The shape of the thermal curve, as described in Section Appendix X111,
