ASTM E2070-2013(2018) Standard Test Methods for Kinetic Parameters by Differential Scanning Calorimetry Using Isothermal Methods.pdf

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1、Designation: E2070 13 (Reapproved 2018)Standard Test Methods 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 th

2、e case of revision, 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 Methods A, B, and C determine kinetic parametersfor activation energy, pre-expone

3、ntial factor and reaction orderusing differential scanning calorimetry from a series of isother-mal experiments over a small ( 10 K) temperature range. TestMethod A is applicable to low nth order reactions. TestMethods B and C are applicable to accelerating reactions suchas thermoset curing or pyrot

4、echnic reactions and crystallizationtransformations in the temperature range from 300 to 900 K(nominally 30 to 630C). These test methods are applicableonly to these types of exothermic reactions when the thermalcurves do not exhibit shoulders, double peaks, discontinuitiesor shifts in baseline.1.2 T

5、est Methods D and E also determines the activationenergy of a set of time-to-event and isothermal temperaturedata generated by this or other procedures1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 These test methods ar

6、e similar but not equivalent toISO DIS 11357, Part 5, and provides more information than theISO standard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety, he

7、alth, and environmental practices and deter-mine the applicability of regulatory limitations prior to use.Specific precautionary statements are given in Section 8.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established i

8、n the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D3350 Specification for Polyethylene Plastics Pipe and Fit-tings Materi

9、alsD3895 Test Method for Oxidative-Induction Time of Poly-olefins by Differential Scanning CalorimetryD4565 Test Methods for Physical and Environmental Per-formance Properties of Insulations and Jackets for Tele-communications Wire and CableD5483 Test Method for Oxidation Induction Time of Lubri-cat

10、ing Greases by Pressure Differential Scanning Calorim-etryD6186 Test Method for Oxidation Induction Time of Lubri-cating Oils by Pressure Differential Scanning Calorimetry(PDSC)E473 Terminology Relating to Thermal Analysis and Rhe-ologyE537 Test Method for The Thermal Stability of Chemicalsby Differ

11、ential Scanning CalorimetryE698 Test Method for Kinetic Parameters for ThermallyUnstable Materials Using Differential Scanning Calorim-etry and the Flynn/Wall/Ozawa MethodE967 Test Method for Temperature Calibration of Differen-tial Scanning Calorimeters and Differential Thermal Ana-lyzersE968 Pract

12、ice for Heat Flow Calibration of DifferentialScanning CalorimetersE1142 Terminology Relating to Thermophysical PropertiesE1445 Terminology Relating to Hazard Potential of Chemi-calsE1858 Test Methods for Determining Oxidation InductionTime of Hydrocarbons by Differential Scanning Calorim-etryE1860 T

13、est Method for Elapsed Time Calibration of Ther-mal AnalyzersE1970 Practice for Statistical Treatment of ThermoanalyticalData1These test methods are under the jurisdiction of ASTM Committee E37 onThermal Measurements and is the direct responsibility of Subcommittee E37.01 onCalorimetry and Mass Loss

14、.Current edition approved April 1, 2018. Published May 2018. Originallyapproved in 2000. Last previous edition approved in 2013 as E2070 13. DOI:10.1520/E2070-13R18.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Bo

15、ok of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recogn

16、ized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1E2041 Test Method for Estimating Kinetic Parameters byDifferentia

17、l Scanning Calorimeter Using the Borchardtand Daniels MethodE2046 Test Method for Reaction Induction Time by ThermalAnalysis2.2 ISO Standard:3ISO DIS 11357 Part 5: Determination of Temperature and/orTime of Reaction and Reaction Kinetics3. Terminology3.1 Specific technical terms used in these test m

18、ethods aredefined in Terminologies E473, E1142, and E1445, includingthe terms calorimeter, Celsius, crystallization, differentialscanning calorimetry, general rate law, isothermal, peak, andreaction.4. Summary of Test Method4.1 A test specimen is held at a constant temperature in adifferential scann

19、ing calorimeter throughout an exothermicreaction. The rate of heat evolution, developed by the reaction,is proportional to the rate of reaction. Integration of the heatflow as a function of time yields the total heat of reaction.4.2 An accelerating (Sestak-Berggren or Avrami models),nth order data,

20、or model free treatment4,5,6is used to derive thekinetic parameters of activation energy, pre-exponential factorand reaction order from the heat flow and total heat of reactioninformation obtained in 4.1. (See Basis for Methodology,Section 5.)5. Basis of Methodology5.1 Reactions of practical conside

21、ration are exothermic innature; that is, they give off heat as the reaction progresses.Furthermore, the rate of heat evolution is proportional to therate of the reaction. Differential scanning calorimetry measuresheat flow as a dependent experimental parameter as a functionof time under isothermal e

22、xperimental conditions. DSC isuseful for the measurement of the total heat of a reaction andthe rate of the reaction as a function of time and temperature.5.2 Reactions may be modeled with a number of suitableequations of the form of:d/dt 5 kT! f! (1)where:d/dt = reaction rate (s1), = fraction react

23、ed (dimensionless),k (T) = specific rate constant at temperature T (s1),f() = conversion function. Commonly used functionsinclude:f1! 5 1 2 !n(2)f2! 5 1 2 !n(3)f3! 5 p1 2 !2 1 n 1 2 !#p 2 1!p(4)where:n, , and p = partial reaction order terms.NOTE 1There are a large number of conversion function expr

24、essionsfor f().4Those described here are the most common but are not the onlyfunctions suitable for these test methods Eq 1 is known as the general rateequation while Eq 3 is the accelerating (or Sestak-Berggren) equation.5,6Eq 4 is the accelerating Avrami equation. Eq 2 is used for nth orderreactio

25、ns while Eq 3 or Eq 4 are used for accelerating reaction, such asthermoset cure and crystallization transformations.5.3 For a reaction conducted at temperature (T), the accel-erating rate Eq 3 and the rate equation Eq 1 may be cast in theirlogarithmic form.d/dt 5 kT! 1 2 !n(5)lnd/dt# 5 lnkT!#1 ln#1n

26、 ln1 2 # (6)This equation has the form z = a + bx + cy and may be solvedusing multiple linear regression analysis where x = ln, y =ln1 , z = lnd/dt, a = lnk(T), b = and c = n.NOTE 2The rate equation (Eq 3) reduces to the simpler general rateequation (Eq 2) when the value of reaction order parameter

27、equals zerothereby reducing the number of kinetic parameters to be determined.5.4 For reactions conducted at temperature (T), the acceler-ating rate equation of Eq 4 may be cast as:ln2 ln 1 2 !# 5 p lnk T!#1p lnt# (7)This equation has the form of y = mx + b and may be solvedby linear regression wher

28、e x = lnt, y = ln-ln(1 ), with p= m, b = p lnk(T), and t = time.5.5 The Arrhenius equation describes how the reaction ratechanges as a function of temperature:kT! 5 Ze2E/RT(8)where:Z = pre-exponential factor (s1),E = activation energy (J mol1),T = absolute temperature (K),R = gas constant = (8.314 J

29、 mol1K1), ande = natural logarithm base = 2.7182818.5.6 Eq 8 cast in its logarithmic form is:lnkT!# 5 lnZ# 2 E/RT (9)Eq 9 has the form of a straight line, y = mx + b, where a plotof the logarithm of the reaction rate constant (lnk(T) versusthe reciprocal of absolute temperature (l/T) is linear with

30、theslope equal to E/R and an intercept equal to lnZ.5.7 As an alternative to Eq 6 and Eq 7, the rate andArrhenius equations combined and cast in logarithmic form is:lnd/dt# 5 lnZ# 2 E/RT1m ln#1n ln1 2 # (10)Eq 10 has the form, z = a + bx + cy + dw, and may be solvedusing multiple linear regression a

31、nalysis.where:z = lnd/dta = lnZb =-E/Rx =1/Tc = y = ln1 3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.4Sbirrazzuoli, N., Brunel, D., and Elegant, L., Journal of Thermal Analysis,Vol38, 1992, pp. 15091524.5Sestak, J., an

32、d Berggren, G., Thermochimica Acta, Vol 3, 1971, p. 1.6Gorbachiev, V.M., Journal of Thermal Analysis, Vol 18, 1980, pp. 193197.E2070 13 (2018)2d = n, andw = ln1 .5.8 If activation energy values only are of interest, Eq 11may be solved under conditions of constant conversion toyield:lnt# 5 E/RT1b (11

33、)where:t = lapsed time (s), at constant conversion and at isothermaltemperature, T, andb = constant.Eq 11 has the form of a straight line, y = mx + b, where a plotof the logarithm of the lapsed time under a series of differingisothermal conditions versus the reciprocal of absolute tem-perature (l/T)

34、 is linear with a slope equal to E/R.5.9 If activation energy values only are of interest, Eq 11may be solved under conditions of constant conversion and theequality d/dt = dH/dt /(H) to yield:lndH/dt# 52E/RT1b 5 m/T1b (12)where:H = total heat of reaction (mJ),dH/dt = instantaneous heat flow (mW),b

35、= constant, andm = slope (K)Eq 12 has the form of a straight line y =mx + b, where a plotof the logarithm of the heat flow (lndH/dt) at the peak of theexotherm under a series of differing isothermal temperatureconditions versus the reciprocal of the absolute temperature(1/T) is linear with a slope e

36、qual to E/R.5.10 A series of isothermal experiments by Test Method A,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, the time toa condition of constant conversion for a seri

37、es of experimentsat four or more temperatures obtained by this or alternativeTest Method D, described in Section 12, may be used todetermine activation energy only.5.11 A series of not less than four isothermal DSCexperiments, covering a temperature range of approximately10 K and a time less than 10

38、0 min (such as those shown in Fig.1) provides values for d/dt, ,(1) and T to solve Eq 6, Eq7, Eq 9, and Eq 10.5.12 A series of not less than four isothermal DSC experi-ments covering a temperature range of approximately 10 K anda time less than 100 min provides dH/dt and T to solve Eq 125.13 A varie

39、ty of time-to-event experiments such as oxida-tion induction time methods (Specification D3350 and TestMethods D3895, D4565, D5483, D6186, and E1858) andreaction induction time methods (Test Method E2046) providevalues for t and T to solve equation Eq 11.6. Significance and Use6.1 These test methods

40、 are useful for research anddevelopment, quality assurance, regulatory compliance, andspecification acceptance purposes.6.2 The determination of the order of a chemical reaction ortransformation at specific temperatures or time conditions isbeyond the scope of these test methods.6.3 The activation e

41、nergy results obtained by these testmethods may be compared with those obtained from TestMethod E698 for nth order and accelerating reactions. Activa-tion energy, pre-exponential factor, and reaction order resultsby these test methods may be compared to those for TestMethod E2041 for nth order react

42、ions.7. Interferences7.1 The approach is applicable only to exothermic reactions.NOTE 3Endothermic reactions are controlled by the rate of the heattransfer of the apparatus and not by the kinetics of the reaction and maynot be evaluated by these test methods.7.2 These test methods are intended for a

43、 reaction mecha-nism that does not change during the transition. These testmethods assume a single reaction mechanism when the shapeof the thermal curve is smooth (as in Fig. 2 and Fig. 3) and doesnot exhibit shoulders, multiple peaks, or discontinuation steps.7.3 Test method precision is enhanced w

44、ith the selection ofthe appropriate conversion function f() that minimizes thenumber of experimental parameters determined. The shape ofthe thermal curve, as described in Section 11, may confirm theselection of the nth order or accelerating models.7.4 Typical nth order reactions include those in whi

45、ch allbut one of the participating species are in excess.7.5 Typical accelerating reactions include thermoset cure,crystallization and pyrotechnic reactions.7.6 For nth order kinetic reactions, these test methodsanticipate that the value of n is small, non-zero integers, suchas 1 or 2. These test me

46、thods should be used carefully whenvalues of n are greater than 2 or are not a simple fraction, suchas12 = 0.5.7.7 Accelerating kinetic reactions anticipate that m and n arefractions between 0 and 2 and that their sum (m + n) is less than3.7.8 Accelerating kinetic reactions anticipate that p is anin

47、teger often with a value of 4.7.9 Since these test methods use milligram quantities, it isessential that the test specimens are homogeneous and repre-sentative of the larger samples from which they are taken.7.10 Test specimens may release toxic and corrosive efflu-ents that may be harmful to person

48、nel or apparatus. Operationwith a venting or exhaust system is recommended.E2070 13 (2018)38. Hazards8.1 Special precautions shall be taken to protect personneland equipment when the apparatus in use requires the insertionof specimens into a heated furnace. These special precautionsinclude adequate

49、shielding and ventilation of equipment andface and hand protections for users (see Note 6).9. Apparatus9.1 A differential scanning calorimeter (DSC) that providesthe minimum calorimetric capability for these test methodsincludes:9.1.1 A DSC Test Chamber, composed of:9.1.1.1 A Furnace(s), that provides uniform controlled heat-ing of a specimen and reference to constant temperature at aconstant rate between 300 and 900 K.9.1.1.2 A Temperature S