1、Designation: E 2070 08Standard Test Method forKinetic Parameters by Differential Scanning CalorimetryUsing Isothermal Methods1This standard is issued under the fixed designation E 2070; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revisio
2、n, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 Test Method A determines kinetic parameters for acti-vation energy, pre-exponential factor and reactio
3、n order usingdifferential scanning calorimetry from a series of isothermalexperiments over a small (; 10 K) temperature range. Thistreatment is applicable to low nth order reactions and toautocatalyzed reactions such as thermoset curing or pyrotech-nic reactions and crystallization transformations i
4、n the tem-perature range from 300 to 900 K (30 to 630 C). This testmethod is applicable only to these types of exothermic reac-tions when the thermal curves do not exhibit shoulders,discontinuities or shifts in baseline.1.2 Test Method B also determines the activation energy ofa set of time-to-event
5、 and isothermal temperature data gener-ated by this or other procedures.1.3 Test Method C determines the activation energy andinitial heat flow from a series of isothermal experiments over asmall temperature range. Because this approach only deter-mines kinetic parameter of activation energy, no kno
6、wledge ofthe kinetic model is required. Therefore it is considered to be“model free”. This approach is broadly applicable to a varietyof complicated reactions including those not well understood.1.4 SI units are the standard.1.5 This test method is similar but not equivalent to ISO11357, Part 5, and
7、 provides more information than the ISOstandard.1.6 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 and health practices and determine the applica-bility of reg
8、ulatory limitations prior to use. Specific precau-tionary statements are given in Section 8.2. Referenced Documents2.1 ASTM Standards:2D 3550 Practice for Thick Wall, Ring-Lined, Split Barrel,Drive Sampling of SoilsD 3895 Test Method for Oxidative-Induction Time of Poly-olefins by Differential Scann
9、ing CalorimetryD 4565 Test Methods for Physical and Environmental Per-formance Properties of Insulations and Jackets for Tele-communications Wire and CableD 5483 Test Method for Oxidation Induction Time of Lu-bricating Greases by Pressure Differential Scanning Calo-rimetryD 6186 Test Method for Oxid
10、ation Induction Time of Lu-bricating Oils by Pressure Differential Scanning Calorim-etry (PDSC)E 473 Terminology Relating to Thermal Analysis and Rhe-ologyE 537 Test Method for The Thermal Stability Of ChemicalsBy Differential Scanning CalorimetryE 698 Test Method for Arrhenius Kinetic Constants for
11、Thermally Unstable Materials Using Differential ScanningCalorimetry and the Flynn/Wall/Ozawa MethodE 967 Test Method for Temperature Calibration of Differ-ential Scanning Calorimeters and Differential ThermalAnalyzersE 968 Practice for Heat Flow Calibration of DifferentialScanning CalorimetersE 1142
12、 Terminology Relating to Thermophysical PropertiesE 1445 Terminology Relating to Hazard Potential ofChemicalsE 1860 Test Method for Elapsed Time Calibration of Ther-mal AnalyzersE 1958 Guide for Sensory Claim SubstantiationE 1970 Practice for Statistical Treatment of Thermoanalyti-cal Data1This test
13、 method is under the jurisdiction ofASTM Committee E37 on ThermalMeasurements and is the direct responsibility of Subcommittee E37.01 on ThermalTest Methods and Practices.Current edition approved Feb. 1, 2008. Published March 2008. Originallyapproved in 2000. Last previous edition approved in 2003 a
14、s E 2070 03.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Dr
15、ive, PO Box C700, West Conshohocken, PA 19428-2959, United States.E 2041 Method for Estimating Kinetic Parameters by Dif-ferential Scanning Calorimeter Using the Borchardt andDaniels MethodE 2046 Test Method for Reaction Induction Time by Ther-mal Analysis2.2 ISO Standard:ISO DIS 11357 Part 5 Determ
16、ination of Temperature and/orTime of Reaction and Reaction Kinetics33. Terminology3.1 Specific technical terms used in this test method aredefined in Terminologies E 473, E 1142, and E 1445.4. Summary of Test Method4.1 A test specimen is held at a constant temperature in adifferential scanning calor
17、imeter 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 autocatalytic, nthorder data or model free treat-ment4,5,6is used to deri
18、ve the kinetic parameters of activationenergy, pre-exponential factor and reaction order from the heatflow and total heat of reaction information obtained in 4.1 (SeeBasis for Methodology, Section 5.)5. Basis of Methodology5.1 Reactions of practical consideration are exothermic innature; that is, th
19、ey 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. DSC isuseful for the measurement of the total heat of a reaction andthe rate of t
20、he reaction as a function of time and temperature.5.2 Reactions may be modeled with a number of suitableequations of the form of:da/dt 5 kT! fa! (1)where:da/dt = reaction rate (min1),a = fraction reacted or conversion (dimensionless),k (T) = specific rate constant at temperature T (min1),f(a) = conv
21、ersion function. Commonly used functionsinclude:f1a! 5 1a!n(2)f2a! 5am1a!n(3)where:n and m = partial reaction order terms.NOTE 1There are a large number of conversion function expressionsfor f(a)4. Those described here are the more common but are not theonly functions suitable for this method. Eq 2
22、is known as the general rateequation while Eq 3 is the autocatalytic (or Sestak-Berggren) equation5,6.Eq 2 is used for nth order reactions while Eq 3 is used for thermoset cureand crystallization transformations.5.3 For a reaction conducted at temperature (T), the auto-catalytic rate equation of 5.2
23、 may be cast in its logarithmicform.da/dt 5 kT! am1a!n(4)lnda/dt 5 lnkT!# 1 mlna 1 nln1 a (5)This equation has the form z = a + bx + cy and may be solvedusing multiple linear regression analysis.NOTE 2Subsequent discussions use the autocatalytic form of the rateequation (Eq 3). It reduces to the sim
24、pler general rate equation (Eq 2)when the value of reaction order parameter m equals zero thereby reducingthe number of kinetic parameters to be determined.5.4 The Arrhenius equation describes how the reaction ratechanges as a function of temperature:kT! 5 Ze2E/RT(6)where:Z = pre-exponential factor
25、(min1),E = activation energy (J mol1),T = absolute temperature (K),R = gas constant = (8.314 J mol1K1), ande = natural logarithm base = 2.7182818.5.5 Eq 6 cast in its logarithmic form is:lnkT!# 5 lnZE/RT (7)Eq 7 has the form of a straight line, y = x + b, where a plotof the logarithm of the reaction
26、 rate constant (lnk (T) versusthe reciprocal of absolute temperature (l/T) is linear with theslope equal to E/R and an intercept equal to lnZ.5.6 As an alternative to 5.3 and 5.5, the rate and Arrheniusequations combined and cast in logarithmic form is:lnda/dt 5 lnZE/RT 1 mlna 1 nln1 a (8)Eq 8 has t
27、he form, z = a + bw + cx + dy, and may be solvedusing multiple linear regression analysis.5.7 If activation energy values only are of interest, Eq 8 maybe solved under conditions of constant conversion to yield:ln Dt 5 E/RT 1 c (9)where:Dt = lapsed time, (min), at isothermal temperature, T, andc = c
28、onstant.Eq 9 has the form of a straight line, y = x + 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) is linear with a slope equal to E/R.5.8 If activation energy values only are of interest, Eq
29、8 maybe solved under conditions of constant conversion and theequality d/dt = dH/dt/H to yield:lndH/dt 5 E/RT 1 b 5 m/T 1 b (10)where:H = total heat of reaction (J/g),dH/dt = instantaneous heat flow (W/g),3Available from American National Standards Institute, 11 W. 42nd St., 13thFloor, New York, NY
30、10036.4Sbirrazzuoli, N.; Brunel, D.; Elegant, L., J. Therm. Anal., 38, 1509-1524, 1992.5Sestak, J.; Berggren, G.; Thermochim. Acta, 3, 1, 1971.6Gorbachiev, V.M., J. Therm. Anal., 18, 193197, 1980.E2070082b = constant, andm = slope (kK)Eq 10 has the form of a straight line y =mx + b, where a plotof t
31、he 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 equal to E/R.5.9 A series of isothermal experiments by Test Method Adescribed in Section 11 at
32、 four or more temperatures, deter-mines the kinetic parameters of activation energy, pre-exponential factor and reaction order. Alternatively, a series ofisothermal experiments by Test Method A described in Section11 at four or more temperatures may be used to determineactivation energy and initial
33、heat flow by test Method Cdescribed in Section 15. Alternatively, the time to a conditionof constant conversion for a series of experiments at four ormore temperatures obtained by this or alternative Test MethodB, described in Section 12, may be used to determine activationenergy only.5.10 A series
34、of not less than four isothermal DSC experi-ments, covering a temperature range of approximately 10 Kand a time less than 100 min (such as those shown in Fig. 1)provides values for da/dt, a,(1a) and T to solve Eq 5, Eq7, and Eq 8.5.11 A series of not less than four isothermal DSC experi-ments coveri
35、ng a temperature range of approximately 10 K anda time less than 100 min provides dH/dt and T to solve Eq 105.12 A variety of time-to-event experiments such as oxida-tion induction time methods (Test Methods D 3350, D 3895,D 4565, D 5483, D 6186, and E 1958) and reaction inductiontime methods (E 204
36、6) provide values for Dt and T to solveequation 5.7.6. Significance and Use6.1 This test method is useful for research and development,quality assurance, regulatory compliance and specificationacceptance purposes.6.2 The determination of the order of a chemical reaction ortransformation at specific
37、temperatures or time conditions isbeyond the scope of this test method.6.3 The activation energy results obtained by this methodmay be compared with those obtained fromTest Method E 698for nth order and autocatalytic reactions. Activation energy,NOTE 1This figure is for a crystallization application
38、 in which the reaction rate increases with decreasing temperature. Chemical reactions show anincrease in reaction rate with increasing temperature.FIG. 1 Heat Flow Curves at a Series of Isothermal TemperaturesE2070083pre-exponential factor and reaction order results by this methodmay be compared to
39、those for Test Method E 2041 for nthorder reactions.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 this test met
40、hod.7.2 This test method is intended for a reaction mechanismthat does not change during the transition. This methodassumes a single reaction mechanism when the shape of thethermal curve is smooth (as in Fig. 2 and Fig. 3) and does notexhibit shoulders, multiple peaks or discontinuation steps.7.3 Me
41、thod precision is enhanced with the selection of theappropriate conversion function f (a) that minimizes thenumber of experimental parameters determined. The shape ofthe thermal curve, as described in Appendix X1, may confirmthe selection of the nth order or autocatalytic models.7.4 Typical nth orde
42、r reactions include those in which allbut one of the participating species are in excess.7.5 Typical autocatalytic reactions include thermoset cure,crystallization and pyrotechnic reactions.7.6 For nth order kinetic reactions, this test method antici-pates that the value of n is small, non-zero inte
43、gers, such as 1or 2. This test method should be used carefully when values ofn are greater than 2 or are not a simple fraction, such as12 =0.5.7.7 Autocatalytic kinetic reactions anticipate that m and nare fractions between 0 and 1 and that their sum (m + n) is lessthan 2.7.8 Since this method uses
44、milligram quantities it is essen-tial that the test specimens are homogeneous and representativeof the larger samples from which they are taken.7.9 Test specimens may release toxic and corrosive effluentsthat may be harmful to personnel or apparatus. Operation witha venting or exhaust system is reco
45、mmended.8. 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 shielding and ventilation of equipment andface and hand protections for users (See
46、Note 7.)9. Apparatus9.1 A differential scanning calorimeter (DSC) that providesthe minimum calorimetric capability for this method includes:9.1.1 A DSC Test Chamber, composed of:FIG. 2 Heat Flow Curve for an nth Order ReactionE20700849.1.1.1 A Furnace(s), that provides uniform controlled heat-ing of
47、 a specimen and reference to constant temperature at aconstant rate within the applicable temperature range of thistest method.9.1.1.2 A Temperature Sensor, that indicates the specimen/furnace temperature to 6 0.01 K.9.1.1.3 A Differential Sensor, that detects heat flow differ-ences between the spec
48、imen and reference equivalent to 1 W.9.1.1.4 Ameans of sustaining a purge gas rate of 10 to 50 6mL/minute in the test chamber.NOTE 4Typically inert purge gases that inhibit sample oxidation are99.9+ % pure nitrogen, helium or argon. Dry gases are recommended forall experiments unless the effect of m
49、oisture is part of the study.9.1.2 A Temperature Controller, for furnace(s) temperatureprograms between selected temperature limits (that is, 300 to900 K) capable of controlling the rate of temperature change ofup to 100 K min1constant to 6 0.1 K min1.9.1.3 A Data Collection Device, to provide a means ofacquiring, storing, and displaying measured or calculatedsignals, or both. The minimum output signals required for DSCare heat flow, temperature and time.9.2 Containers (pans, crucibles, vials, etc. and lids) tha
