1、Designation: E 2041 081Standard Test 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
2、or, in the 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.1NOTEMinor editorial corrections were made in April 2009.1. Scope1.1 This test method des
3、cribes the determination of thekinetic parameters of activation 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 to 870 K (100 to
4、 600 C).1.2 This treatment is applicable only to smooth exothermicreactions 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 determinati
5、on of kineticparameters for most thermoset curing reactions or to crystalli-zation reactions.1.3 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.4 This test method is similar, but not equivalent to, ISOMethod 11357, Part 5, th
6、at contains provisions for additionalinformation not supplied by this test method.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 and health practices and d
7、etermine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3E 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 Kineti
8、c Constants forThermally 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 Cal
9、orimetersE 1142 Terminology Relating to Thermophysical PropertiesE 1445 Terminology Relating to Hazard Potential ofChemicalsE 1641 Test Method for Decomposition Kinetics by Ther-mogravimetryE 1970 Practice for Statistical Treatment of Thermoanalyti-cal Data2.2 ISO Standards:ISO 11357 Part 5: Determi
10、nation 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 1445.4. Summary of Test Method4.1 Atest specimen is heated at a linear rate in a differentialscanning calor
11、imeter 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. Integration of the heat flow as a function oftime yields the total heat of a reaction.1This test method is under
12、the jurisdiction ofASTM Committee E37 on ThermalMeasurements and the direct responsibility of Subcommittee E37.01 on Calorimetryand Mass Loss.Current edition approved Sept. 1, 2008. Published October 2008. Originallyapproved in 1999. Last previous edition approved in 2003 as E 2041 03.2Borchardt, H.
13、J., Daniels, F., J. Amer. Chem. Soc. Vol 79, pp.4146 (1957).3For 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.4
14、Available from American National Standards Institute, 11 W. 42nd St., 13thFloor, New York, NY 10036.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.4.2 The Borchardt and Daniels2data treatment is used toderive the kinetic parameters
15、of activation energy, Arrheniuspre-exponential factor, and reaction order from the heat flowand total heat of reaction information obtained in 4.1 (seeSection 5).5. Basis of Methodology5.1 Kinetic reactions may be modeled with a number ofsuitable equations. The Borchardt and Daniels2method makesuse
16、of the general rate equation to describe the dependence ofthe rate of reaction 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 rea
17、ction conducted at temperature (T), the rateequation of Eq 1, may be cast in 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 yi
18、eldsa straight line, the slope of which is equal to n and the interceptis equal 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)
19、,E = Activation energy (J mol1),T = Absolute temperature (K), andR = Gas constant (= 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
20、 plot of the logarithm of the reaction rate constant (lnk(T)versus the reciprocal 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
21、its logarithmic form:lnda/dt 5 lnZ 1 nln1 2a 2 E/RT (5)The resultant equation has 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, ar
22、e experimental parameters obtained froma single linear heating rate DSC experiment 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 metho
23、d is useful in research and development.6.2 The determination of the appropriate 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, h
24、owever, is not described in this test method.7. Interferences7.1 Because of its 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 eval
25、uatekinetic parameters, is not applicable to all cases. The user ofthis test method 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
26、-tions.NOTE 1Endothermic reactions are controlled by the kinetics of theheat transfer 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
27、 upon heating must besmooth, well shaped (as in Fig. 1) with no shoulders, multiplepeaks 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 no
28、t nth order and to whichBorchardt and Daniels kinetic may not be applied for predic-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
29、n greater than 2 or that are not simple fractions, suchas12 = 0.5, are highly 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 size
30、s ( 5 mg) and highly conductive sealed speci-men containers, for example, aluminum, 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 cor
31、rosive effluents, or both, may be releasedwhen heating the test specimen and may be harmful topersonnel or to the apparatus. Operating with a venting orexhaust system is recommended.E204108128. Apparatus8.1 Differential Scanning Calorimeter (DSC)The instru-mentation required to provide the minimum d
32、ifferential scan-ning calorimetric capability for this method includes thefollowing: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 ran
33、ge of thistest method.8.1.1.2 Temperature Sensor, to provide an indication of 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 g
34、as at a rate of 10 to 50 mL/min.NOTE 2Typically, 99.9+% pure nitrogen, helium, 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 furna
35、ce(s) betweenselected temperature limits, that is, 170 to 870 K, at a rate oftemperature change of up to 10 K/min constant to 6 0.1 K/min.8.1.3 Data Collection Device, to provide a means of acquir-ing, storing, and displaying measured or calculated signals, orboth. The minimum output signals require
36、d for DSC are heatflow, temperature, and time.8.2 Containers (pans, crucibles, vials, etc.), that are 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 me
37、thod.8.3 While not required, the user will find useful calculator orcomputer and data analysis software 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 ca
38、pacity of at least 100 mg.9. Calibration9.1 Perform any calibration procedures recommended bythe apparatus 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 Meth
39、odE 968.10. Procedure10.1 Weigh 1 to 10 mg of test specimen to a precision of6 10 g into a sample container 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
40、 DSC samplechamber and prepare the apparatus for an experimental run.FIG. 1 Idealized DSC CurveE20410813NOTE 3This 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
41、erroneousresults. Small specimen sizes may be used to obtain this critical non-selfheating assumption.10.2 Equilibrate the specimen at a temperature 40 K belowthe first exothermic behavior.NOTE 4This temperature may be determined from a previouslyrecorded exploratory run using Test Method E 537.10.3
42、 Heat the test specimen at a rate of 5 K/min to atemperature 10 K higher than the completion of the exothermicreaction as indicated by the return to baseline. Record the heatflow and sample temperature throughout this region.NOTE 5Other heating rates ( 10 K/min) may be used but shall beindicated in
43、the report.Agreement of results undertaken at several heatingrates will provide confidence in the method 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 rea
44、ction order (n), activation energy (E), andArrhenius pre-exponential factor (Z) according to the proce-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 perpendicu
45、lar line from the baseline to thepeak of the thermal curve and record this value in mW. Onlyresults 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
46、heating rate and rerun theexperiment (see Note 3).11.3 Integrate the total peak area bounded by the peak itselfand the constructed baseline to obtain the heat of the reaction(DH)inmJ.11.4 Identify the temperatures which correspond approxi-mately to 10 and 90 % of the peak area obtained in 11.3.11.5
47、Select a temperature interval which provides a mini-mum of ten equally-spaced values between the temperaturelimits 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 ill
48、ustrated inFig. 1.NOTE 6It is convenient to prepare a table of these values.11.7 For each of the fractional 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 7In this and
49、 all subsequent calculations, retain all availablesignificant figures rounding only the final result to the number ofsignificant figures described in Section 13.NOTE 8The 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 7).NOTE 9Often, it is convenient to report the value of reciprocaltemperature in units of kK1.11.9 Calculate
