1、Designation: E 2041 03Standard Method forEstimating Kinetic Parameters by Differential ScanningCalorimeter Using the Borchardt and Daniels Method1This standard is issued under the fixed designation E 2041; the number immediately following the designation indicates the year oforiginal adoption or, in
2、 the case of revision, 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 This test method describes the determination of thekinetic parameters of activatio
3、n energy, Arrhenius pre-exponential factor, and reaction order using the Borchardt andDaniels2treatment of data obtained by differential scanningcalorimetry. This test method is applicable to the temperaturerange from 170 to870 K (100 to 600C).1.2 This treatment is applicable only to smooth exotherm
4、icreactions with no shoulders, discontinuous changes, or shifts inbaseline. It is applicable only to reactions with reaction ordern # 2. It is not applicable to autocatalyzed reactions and,therefore, is not applicable to the determination of kineticparameters for most thermoset curing reactions or t
5、o crystalli-zation reactions.1.3 Electronic instrumentation or automated data analysissystems or treatments equivalent to this test method may beused.NOTE 1The user is advised that all electronic data treatment may notbe equivalent. It is the responsibility of the user of such electronic datatreatme
6、nt to verify applicability to this test method.1.4 SI values are the standard.1.5 This test method is similar, but not equivalent to, ISOMethod 11357, Part 5, which contains provisions for additionalinformation not supplied by this test method.1.6 This standard does not purport to address all of the
7、safety 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 regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:E 473 Terminology Relating to
8、 Thermal Analysis3E 537 Test Method for Assessing the Thermal Stability ofChemicals by Methods of Differential Thermal Analysis3E 698 Test Method for Arrhenius Kinetic Constants forThermally Unstable Materials3E 967 Practice for Temperature Calibration of DifferentialScanning Calorimeters and Differ
9、ential Thermal Analyz-ers3E 968 Practice for Heat Flow Calibration of DifferentialScanning Calorimeters3E 1142 Terminology Relating to Thermophysical Proper-ties3E 1145 Terminology Relating to Hazardous Properties ofChemicals3E 1641 Test Method for Decomposition Kinetics by Ther-mogravimetry3E 1970
10、Practice for Statistical Treatment of Thermoanalyti-cal Data32.2 ISO Standards:ISO 11357 Part 5: Determination of Temperature and/orTime of Reaction and Reaction Kinetics43. Terminology3.1 DefinitionsSpecific technical terms used in this testmethod are defined in Terminologies E 473, E 1142 andE 144
11、5.4. Summary of Test Method4.1 A test specimen is heated at a linear rate in a differentialscanning calorimeter or other suitable calorimeter through aregion of exothermic reaction behavior. The rate of heatevolution, developed by a chemical reaction, is proportional tothe rate of reaction. Integrat
12、ion of the heat flow as a function oftime yields the total heat of a reaction.4.2 The Borchardt and Daniels2data treatment is used toderive the kinetic parameters of activation energy, Arrheniuspre-exponential factor, and reaction order from the heat flowand total heat of reaction information obtain
13、ed in 4.1 (seeSection 5).1This test method is under the jurisdiction of ASTM Committee E37 on ThermalMeasurements and the direct responsibility of Subcommittee E37.01 on TestMethods and Recommended Practices.Current edition approved Oct. 1, 2003. Published November 2003. Originallyap-proved in 1999.
14、 Last previous edition approved in 2001 as E 2041 01.2Borchardt, H.J., Daniels, F., J. Amer. Chem. Soc. Vol 79, pp.4146 (1957).3Annual Book of ASTM Standards, Vol 14.02.4Available from American National Standards Institute, 11 W. 42nd St., 13thFloor, New York, NY 10036.1Copyright ASTM International,
15、 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5. Basis of Methodology5.1 Kinetic reactions may be modeled with a number ofsuitable equations. The Borchardt and Daniels2method makesuse of the general rate equation to describe the dependence ofthe rate of reactio
16、n on the amount of material present.da/dt 5 kT! 12a!n(1)where:da/dt = reaction rate (min1)a = fraction reacted (dimensionless),k(T) = rate constant at temperature T (min1), andn = reaction order (dimensionless)5.2 For a reaction conducted at temperature (T), the rateequation of Eq 1, may be cast in
17、its logarithmic form:lnda/dt 5 lnkT!# 1 nln1 2a (2)This equation has the form of a straight line, y = mx+b,where a plot of the logarithm of the reaction rate (lnda/dt)versus the logarithm of the fraction remaining ln1a yieldsa straight line, the slope of which is equal to n and the interceptis equal
18、 to lnk(T).5.3 The Borchardt and Daniels model also makes use of theArrhenius equation to describe how the reaction rate changesas a function of temperature:kT! 5 ZeE/RT(3)where:Z = Arrhenius pre-exponential factor (min1),E = Activation energy (J mol1),T = Absolute temperature (K), andR = Gas consta
19、nt (= 8.314 J mol1K1).5.4 The Arrhenius equation Eq 3 also may be cast in itslogarithmic form:lnkT!# 5 lnZ 2 E/RT (4)The equation has the form of a straight line, y = mx + b,(where y lnk(T), m E/R, x 1/T and b lnZ) wherea plot of the logarithm of the reaction rate constant (lnk(T)versus the reciproc
20、al of absolute temperature (l/T) produces astraight line, the slope of which is equal to E/R and theintercept of which is lnZ.5.5 As an alternate to Eq 2 and 4, the rate and Arrheniusequations may be combined and cast in its logarithmic form:lnda/dt 5 lnZ 1 nln1 2a 2 E/RT (5)The resultant equation h
21、as the form z = a + bx + cy (wherez lnda/dt, lnZ a, b n, x ln1a, c E/R, andy l/T) and may be solved using multiple linear regressiondata treatment.5.6 The values for da/dt,(1a) and T needed to solve Eq2, Eq 4 and Eq 5, are experimental parameters obtained froma single linear heating rate DSC experim
22、ent scanning throughthe temperature region of the reaction exotherm as shown inFig. 1.5.7 Kinetic results obtained by this test method may becompared with those obtained by E 698.6. Significance and Use6.1 This test method is useful in research and development.,6.2 The determination of the appropria
23、te model for a chemi-cal reaction or transformation and the values associated with itskinetic parameters may be used in the estimation of reactionperformance at temperatures or time conditions not easilytested. This use, however, is not described in this test method.7. Interferences7.1 Because of it
24、s simplicity and ease of use, the Borchardtand Daniels method is often the method of choice for charac-terization of the kinetic parameters of a reaction system. TheBorchardt and Daniels method, like all tools used to evaluatekinetic parameters, is not applicable to all cases. The user ofthis test m
25、ethod is expressly advised to use this test method andits results with caution.7.2 Tabulated below are some guidelines for the use of theBorchardt and Daniels method.7.2.1 The approach is applicable only to exothermic reac-tions.NOTE 2Endothermic reactions are controlled by the kinetics of theheat t
26、ransfer of the apparatus and not by the kinetics of the reaction.7.2.2 The reaction under investigation must have a constantmechanism throughout the whole reaction process. In practice,this means that the reaction exotherm upon heating must besmooth, well shaped (as in Fig. 1) with no shoulders, mul
27、tiplepeaks or discontinuous steps.7.2.3 The reaction must be nth order. Confirmation of an nthorder reaction may be made by an isothermal experiment suchas that described in Appendix X1.7.2.4 Typical reactions which are not nth order and to whichBorchardt and Daniels kinetic may not be applied for p
28、redic-tive purposes include many thermoset curing reactions andcrystallization transformations.7.2.5 The nth order kinetic reactions anticipate that thevalue of n will be small, non-zero integers, such as 1 or 2.Values of n greater than 2 or which are not simple fractions,such as12 = 0.5, are highly
29、 unlikely and shall be viewed withcaution.7.2.6 The Borchardt and Daniels method assumes tempera-ture equilibrium throughout the whole test specimen. Thismeans that low heating rates, (that is, 10 K/min), smallspecimen sizes ( 5 mg) and highly conductive sealed speci-men containers, for example, alu
30、minum, gold, platinum, etc.,should be used.7.3 Since milligram quantities of specimen are used, it isessential that the specimen be homogeneous and representativeof the test sample from which they are taken.7.4 Toxic or corrosive effluents, or both, may be releasedwhen heating the test specimen and
31、may be harmful topersonnel or to the apparatus. Operating with a venting orexhaust system is recommended.E20410328. Apparatus8.1 Differential Scanning Calorimeter (DSC)The instru-mentation required to provide the minimum differential scan-ning calorimetric capability for this method includes thefoll
32、owing:8.1.1 DSC Test Chamber, composed of the following:8.1.1.1 Furnace(s), to provide uniform controlled heating ofa specimen and reference to a constant temperature at aconstant rate within the applicable temperature range of thistest method.8.1.1.2 Temperature Sensor, to provide an indication of
33、thespecimen/furnace temperature to 6 0.01 K.8.1.1.3 Differential Sensor, to detect heat flow differencebetween the specimen and reference equivalent to 1 W.8.1.1.4 A means of sustaining a test chamber environmentof purge gas at a rate of 10 to 50 6 mL/min.NOTE 3Typically, 99.9+% pure nitrogen, heliu
34、m, or argon is em-ployed. Use of dry purge gas is recommended and is essential foroperation at subambient temperatures.8.1.2 Temperature Controller, capable of executing a spe-cific temperature program by operating the furnace(s) betweenselected temperature limits, that is, 170 to 870 K, at a rate o
35、ftemperature change of up to 10 K/min constant to 6 0.1 K/min.8.1.3 Recording Device, capable of recording and display-ing any fraction of the heat flow signal (DSC curve), includingthe signal noise, on the Y-axis versus temperature on theX-axis.8.2 Containers (pans, crucibles, vials, etc.), that ar
36、e inert tothe specimen and reference materials, and which are of suitablestructural shape and integrity to contain the specimen andreference in accordance with the specific requirements of thistest method.8.3 While not required, the user will find useful calculator orcomputer and data analysis softw
37、are to perform the necessaryleast squares best fit or multiple linear regression data treat-ments required by this test method.8.4 Balanceto weigh specimens, or containers, or both, to6 10 g with a capacity of at least 100 mg.9. Calibration9.1 Perform any calibration procedures recommended bythe app
38、aratus manufacturer in the instrument operatorsmanual.9.2 Calibrate the DSC temperature signal over the range ofthe reaction using Practice E 967.9.3 Calibrate the DSC heat flow signal using Test MethodE 968.10. Procedure10.1 Weigh 1 to 10 mg of test specimen to a precision of6 10 g into a sample co
39、ntainer and hermetically seal thecontainer. Weigh the specimen and container to 6 10 g. Loadthe test specimen into the apparatus using an equivalent emptyspecimen container as the reference. Close the DSC samplechamber and prepare the apparatus for an experimental run.FIG. 1 Idealized DSC CurveE2041
40、033NOTE 4This test method is based upon a “non-self heating” assump-tion. Combinations of specimen size and reaction kinetics that produceheat flow greater than 8 mW fail this assumption and produce erroneousresults. Small specimen sizes may be used to obtain this critical non-selfheating assumption
41、.10.2 Equilibrate the specimen at a temperature 40 K belowthe first exothermic behavior.NOTE 5This temperature may be determined from a previouslyrecorded exploratory run using Test Method E 537.10.3 Heat the test specimen at a rate of 5 K/min to atemperature 10 K higher than the completion of the e
42、xothermicreaction as indicated by the return to baseline. Record the heatflow and sample temperature throughout this region.NOTE 6Other heating rates ( 10 K/min) may be used but shall beindicated in the report. Agreement of results undertaken at several heatingrates will provide confidence in the me
43、thod and efficacy of the results.10.4 Cool the specimen container to ambient temperatureand reweigh. Record and report any change in mass from thatobserved in 10.1 prior to the test.10.5 Calculate reaction order (n), activation energy (E), andArrhenius pre-exponential factor (Z) according to the pro
44、ce-dures in Section 11.11. Calculation11.1 Construct a linear baseline from a point on the baselinebefore the reaction exotherm to a point on the baseline after thereaction.11.2 Construct a perpendicular line from the baseline to thepeak of the thermal curve and record this value in mW. Onlyresults
45、for which the maximum heat flow (as expressed by thisline) are less than 8 mW shall be used in these calculations. Ifthe heat flow at the peak maximum is greater than 8 mW,reduce the specimen size or heating rate and rerun theexperiment (see Note 4).11.3 Integrate the total peak area bounded by the
46、peak itselfand the constructed baseline to obtain the heat of the reaction(DH) in mJ.11.4 Identify the temperatures which correspond approxi-mately to 10 and 90 % of the peak area obtained in 11.3.11.5 Select a temperature interval which provides a mini-mum of ten equally-spaced values between the t
47、emperaturelimits determined in 11.4.11.6 At each of the ten temperatures identified in 11.5,record the rate of reaction (dH/dt) in mW, temperature (T)inKand heat of reaction remaining (DHT) in mJ as illustrated inFig. 1.NOTE 7It is convenient to prepare a table of these values.11.7 For each of the f
48、ractional areas obtained in 11.6,determine the fraction remaining (1 a) and the fractional rateof reaction (da/dt) using the following equation:1 2a! 5DHT/ DH (6)da/dt 5 dH/dt! / DH (7)NOTE 8In this and all subsequent calculations, retain all availablesignificant figures rounding only the final resu
49、lt to the number ofsignificant figures described in Section 13.NOTE 9The values for (1 a) should range between 0.9 and 0.1depending upon the values selected in 11.4 and 11.511.8 Calculate the reciprocal of absolute temperature foreach value determined in 11.6 and 11.7 (see Note 8).NOTE 10Often, it is convenient to report the value of reciprocaltemperature in units of kK1.11.9 Calculate the natural logarithm of the rate of reaction(lnda/dt) for each of the values determined in 11.6 and 1
