# ASTM E1231-15

Designation: E1231 − 15Standard Practice forCalculation of Hazard Potential Figures of Merit forThermally Unstable Materials1This standard is issued under the fixed designation E1231; the number immediately following the designation indicates the year oforiginal adoption 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.1. Scope1.1 This practice covers the calculation of hazard potentialfigures of merit for exothermic reactions, including:(1) Time-to-thermal-runaway,(2) Time-to-maximum-rate,(3) Critical half thickness,(4) Critical temperature,(5) Adiabatic decomposition temperature rise,(6) Explosion potential,(7) Shock sensitivity,(8) Instantaneous power density, and(9) NFPA instability rating.1.2 The kinetic parameters needed in this calculation maybe obtained from differential scanning calorimetry (DSC)curves by methods described in other documents.1.3 This technique is the best applicable to simple, singlereactions whose behavior can be described by the Arrheniusequation and the general rate law. For reactions which do notmeet these conditions, this technique may, with caution, serveas an approximation.1.4 The calculations and results of this practice might beused to estimate the relative degree of hazard for experimentaland research quantities of thermally unstable materials forwhich little experience and few data are available. Comparablecalculations and results performed with data developed for wellcharacterized materials in identical equipment, environment,and geometry are key to the ability to estimate relative hazard.1.5 The figures of merit calculated as described in thispractice are intended to be used only as a guide for theestimation of the relative thermal hazard potential of a system(materials, container, and surroundings). They are not intendedto predict actual thermokinetic performance. The calculatederrors for these parameters are an intimate part of this practiceand must be provided to stress this. It is strongly recommendedthat those using the data provided by this practice seek theconsultation of qualified personnel for proper interpretation.1.6 The values stated in SI units are to be regarded asstandard. No other units of measurement are included in thisstandard.1.7 There is no ISO standard equivalent to this practice.1.8 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 regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2C177 Test Method for Steady-State Heat Flux Measure-ments and Thermal Transmission Properties by Means ofthe Guarded-Hot-Plate ApparatusC518 Test Method for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter ApparatusE473 Terminology Relating to Thermal Analysis and Rhe-ologyE537 Test Method for The Thermal Stability of Chemicalsby Differential Scanning CalorimetryE698 Test Method for Kinetic Parameters for ThermallyUnstable Materials Using Differential Scanning Calorim-etry and the Flynn/Wall/Ozawa MethodE793 Test Method for Enthalpies of Fusion and Crystalliza-tion by Differential Scanning CalorimetryE1269 Test Method for Determining Specific Heat Capacityby Differential Scanning CalorimetryE1952 Test Method for Thermal Conductivity and ThermalDiffusivity by Modulated Temperature Differential Scan-ning CalorimetryE2041 Test Method for Estimating Kinetic Parameters byDifferential Scanning Calorimeter Using the Borchardtand Daniels Method1This practice is under the jurisdiction of ASTM Committee E27 on HazardPotential of Chemicals and is the direct responsibility of Subcommittee E27.02 onThermal Stability and Condensed Phases.Current edition approved Nov. 1, 2015. Published January 2016. Originallyapproved in 1988. Last previous edition approved in 2010 as E1231 – 10. DOI:10.1520/E1231-15.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1E2070 Test Method for Kinetic Parameters by DifferentialScanning Calorimetry Using Isothermal MethodsE2716 Test Method for Determining Specific Heat Capacityby Sinusoidal Modulated Temperature Differential Scan-ning CalorimetryE2890 Test Method for Kinetic Parameters for ThermallyUnstable Materials by Differential Scanning CalorimetryUsing the Kissinger Method2.2 Other Standards:NFPA 704 Identification of the Hazards of Materials forEmergency Response, 201233. Terminology3.1 Definitions:3.1.1 The definitions relating to thermal analysis appearingin Terminology E473 shall be considered applicable to thispractice.3.2 Definitions of Terms Specific to This Standard:3.2.1 adiabatic decomposition temperature rise, Td—an es-timation of the computed temperature which a specimen wouldattain if all of the enthalpy (heat) of decomposition reactionwere to be absorbed by the sample itself, expressed by Eq 5.High values represent high hazard potential.3.2.2 critical half thickness, a—an estimation of the halfthickness of a sample in an unstirred container, in which theheat losses to the environment are less than the retained heat.This buildup of internal temperature leads to a thermal-runaway reaction, expressed by Eq 3.3.2.2.1 Discussion—This description assumes perfect heatremoval at the reaction boundary. This condition is not met ifthe reaction takes place in an insulated container such as whenseveral containers are stacked together or when a container isboxed for shipment. These figures of merit underestimate thehazard as a result of this underestimation of thermal conduc-tivity.3.2.3 critical temperature, Tc—an estimation of the lowesttemperature of an unstirred container at which the heat lossesto the environment are less than the retained heat leading to abuildup of internal temperature expressed by Eq 4. Thistemperature buildup leads to a thermal-runaway reaction. (SeeNote 3.)3.2.4 explosion potential, EP—an index value, the magni-tude and sign of which may be used to estimate the potentialfor a rapid energy release that may result in an explosion.Positive values indicate likelihood. Negative values indicateunlikelihood. The reliability of this go-no-go indication isprovided by the magnitude of the numerical value. The greaterthe magnitude, the more reliable the go-no-go indication.3.2.5 instantaneous power density, IPD—the amount ofenergy per unit time per unit volume initially released by anexothermic reaction.3.2.5.1 Discussion—This practice calculates the IPD at250°C (482°F, 523 K).3.2.6 NFPA instability rating, IR—an index value forranking, on a scale of 0 to 4, the instantaneous power densityof materials. The greater the value, the more unstable thematerial.3.2.7 shock sensitivity, SS—an estimation of the sensitivityof a material to shock induced reaction relative tom-dinitrobenzene reference material.Apositive value indicatesgreater sensitivity; a negative value less sensitivity. The reli-ability of this go-no-go indication is provided by the magnitudeof the numerical value. The greater the magnitude, the morereliable the go-no-go indication.3.2.8 time-to-maximum-rate, TMR—an estimate of the timerequired for an exothermic reaction, in an adiabatic container(that is, no heat gain or loss to the environment), to reach themaximum rate of reaction, expressed by Eq 2.3.2.9 time-to-thermal-runaway, tc—an estimation of thetime required for an exothermic reaction, in an adiabaticcontainer (that is, no heat gain or loss to the environment), toreach the point of thermal runaway, expressed by Eq 1.4. Summary of Practice4.1 This practice describes the calculation of nine figures ofmerit used to estimate the relative thermal hazard potential ofthermally unstable materials. These figures of merit includetime-to-thermal-runaway (tc), time-to-maximum-rate (TMR),critical half thickness (a), critical temperature (Tc), adiabaticdecomposition temperature rise (Td), explosion potential (EP),shock sensitivity (SS), instantaneous power density (IPD), andinstability rating (IR). These calculations are based upon thedetermined or assumed values for activation energy (E),pre-exponential factor (Z), specific heat capacity (Cp), thermalconductivity (λ), heat of reaction (H), heat flow rate (q) anddensity or concentration (ρ). The activation energy and pre-exponential factor may be calculated using Test Methods E698,E2041, E2070,orE2890. The specific heat capacity may beobtained from Test Methods E1269 or E2716. Thermal con-ductivity may be obtained from Test Methods C177, C518,orE1952. Heat of reaction may be obtained from Test MethodE793. Heat flow rate may be obtained from Test MethodE2070, 13.5, where it is called dH/dt. Values for concentrationor density may be estimated from known values of modelmaterials or through actual measurement. In addition, certainassumptions, such as initial temperature and containergeometries, must be supplied.5. Significance and Use5.1 This practice provides nine figures of merit which maybe used to estimate the relative thermal hazard of thermallyunstable materials. Since numerous assumptions must be madein order to obtain these figures of merit, care must be exercisedto avoid too rigorous interpretation (or even misapplication) ofthe results.5.2 This practice may be used for comparative purposes,specification acceptance, and research. It should not be used topredict actual performance.3Available from National Fire Protection Association (NFPA), 1 BatterymarchPark, Quincy, MA 02269, http://www.nfpa.org.E1231 − 1526. Interferences6.1 Since the calculations described in this practice arebased upon assumptions and physical measurements whichmay not always be precise, care must be used in the interpre-tation of the results. These results should be taken as relativefigures of merit and not as absolute values.6.2 The values for time-to-thermal-runaway, critical halfthickness, and critical temperature are exponentially dependentupon the value of activation energy. This means that smallimprecisions in activation energy may produce large impreci-sions in the calculated figures of merit. Therefore, activationenergy of the highest precision available should be used (1).46.3 Many energetic materials show complex decomposi-tions with important induction processes. Many materials areused or shipped as an inhibited or stabilized composition,ensuring an induction process. In such cases, time-to-thermal-runaway will be determined largely by the induction processwhile critical temperature will be determined by the maximum-rate process. These two processes typically have very differentkinetic parameters and follow different rate-law expressions.6.4 It is believed that critical temperature, using the samesize and shape container, provides the best estimate of relativethermal hazard potential for different materials (see Section10).6.5 Extrapolation of TMR to temperatures below thoseactually measured shall be done only with caution due to thepotential changes in kinetics (activation energy), the potentialfor autocatalysis, and the propagation of errors.7. Apparatus7.1 No special apparatus is required for this calculation.8. Calculation8.1 Time-to-thermal-runaway from sample initial tempera-ture T is defined by (see Ref (2)):tc5CpRT2eE/RTEZH(1)where:tc= time-to-thermal-runaway, s,Cp= specific heat capacity, J/(g K),R = gas constant = 8.314 J⁄(K mol),E = activation energy, J/mol,Z = pre-exponential factor, s−1,H = enthalpy (heat) of reaction, J/g, andT = initial temperature, K.NOTE 1—Time-to-thermal-runaway is related to time-to-maximum-ratebut assumes a first order reaction.8.2 Time-to-maximum-rate, TMR, is defined by (see Refs(1) and (3)):TMR 5 CpRT12⁄Eq (2)where:T1= initial temperature, K (that is, the temperature at whichTMR is to be estimated), andq = mass normalized heat flow rate at (T1), W/g.NOTE 2—Time-to-maximum-rate is related to time-to-thermal-runawaybut assumes a zeroth order reaction.8.3 Critical half thickness at environmental temperature Tois defined by (see Ref (4)):a 5SδλRTo2eE/RToHZEρD12(3)where:a = critical half-thickness, cm;λ = thermal conductivity, W/(cm K);To= environment temperature, K;ρ = density or concentration, g/cm3; andδ = form factor (dimensionless) (4, 5):0.88 for infinite slab,2.00 for infinite cylinder,2.53 for a cube,2.78 for a square cylinder, and3.32 for sphere.8.4 Critical temperature Tcis defined by (see Refs (1) and(6)):Tc5SRElnSd2ρ HZET2cλδRDD21(4)where:Tc= critical temperature, K, andd = shortest semi-thickness, cm.8.5 Adiabatic decomposition temperature rise Tdis definedby:Td5HCp(5)where:Td= adiabatic decomposition temperature rise, K.8.6 Explosion potential EP is defined by (7, 8):EP 5 log@H# 2 0.38log@Tonset2 298 K# 2 2.29 (6)where:EP = explosion potential, andTonset= onset temperature by DSC, K.8.7 Shock sensitivity SS is defined by (7):SS 5 log@H# 2 0.72log@Tonset2 298 K# 2 1.60 (7)where:SS = shock sensitivity relative to m-dinitrobenzene.8.8 Instantaneous power density at 250°C is defined by(NFPA 704):5IPD 5 HZρexp@2E/523 K R# (8)4The boldface numbers in parentheses refer to the list of references at the end ofthis standard.5Reprinted with permission from NFPA 704 – 1996, “Identification of theHazards of Materials for Emergency Response,” copyright 1996, National FireProtectionAssociation, Quincy, MA. This reprinted material is not the complete andofficial position of the NFPAon the referenced subject which is represented only bythe standard in its entirety.E1231 − 1538.9 Instability rating is defined by Table 1 (NFPA 704).8.10 Methods of Obtaining Parameters:8.10.1 The activation energy E and frequency factor Z maybe obtained by Test Methods E698, E2041,orE2070. Othermethods may be used but shall be reported.NOTE 3—In Test Methods E698 and E2041, the activation energy andpre-exponential are mathematically related and must be determined fromthe same experimental study.8.10.2 The enthalpy (heat) of reaction H may be obtained byTest Methods E793 or E537. Other methods may be used butshall be reported.8.10.3 Room temperature specific heat capacity, Cp, may beobtained by Test Method E1269.8.10.4 Environment temperature Tois taken to be thetemperature of the air space surrounding the unstirred con-tainer.8.10.5 Concentration or density of material ρ is the amountof reactive material per unit volume. The value of 1.28 g/cm3may be assumed for many organic materials.8.10.6 The form factor δ is a dimensionless unit used tocorrect for the type of geometry for the unstirred container.Five cases are ordinarily us