The kinetic of mass loss of grades A and B of melted TNT by isothermal and non-isothermal gravimetric methods

1.Introduction

There are several advantages for TNT(2,4,6-trinitrotoluene)as a common bulk explosive.These advantages are low cost,safety in handling,fairly high explosive power,good chemical and thermal stability,compatibility with other explosives,a low melting point favorable for melt casting operations and moderate toxicity[1,2].TNT is a crystalline substance.The importance of TNT as a military explosive is based upon its relative safety in manufacture,loading,transportation,and stowage,and upon its explosive properties.Manufacturing yields are high and production relatively economical.However,TNT is toxic,odorless,comparatively stable,nonhygroscopic,and relatively insensitive[3].

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When TNT is pure,it is known as grade A of TNTand varies from white to pale yellow.When the proportion of impurities is much greater,the color is darker,often brown,and the chemical is known as grade B of TNT.It may be ignited by impact,Friction,spark,shock,or heat.The freezing point varies between 80.6°C for grade A(re fined TNT)to 76°C for grade B(crude TNT).The freezing point of grade B depends on the kind and amounts of impurities[4].

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With respect to the importance and applications of TNT as a familiar explosive,the study of kinetic of mass loss of it can be a valuable study for producers and consumers of this explosive.In the present work,the kinetic of mass loss of grade A of TNT and grade B of TNT was studied by methods of isothermal and nonisothermal gravimetric methods.

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The kinetics of mass loss is studied generally using isothermal and non-isothermalmethods.The isothermalgravimetric methodhaveseveraladvantagesincludes:(i)detection of changes in the mechanism because decomposition rates are obtained for a single temperature;(ii)the rate can be obtained by solving analytically an equation;and(iii)homogeneous temperature for sample is reached after attaining the isothermal temperature.However,the isothermal measurements have also show the disadvantages such as:the need to several experiments at different temperatures,requiring a larger amount of sample and the reaction takes place to a certain extent before the sample attains the desired constant temperature[5,6].

The rate of a decomposition reaction is expressed as a function of the fraction reacted,as determined using mass loss data.The kinetic equation for mass loss in isothermal method is as

The higher kinetic of mass loss of melted TNT samples in aluminum container can be related to the ease of heat transfer,especially,and the catalytic effect of metals[15].Also,the presence of impurities such as dinitro toluene(DNT)and mononitro toluene(MNT)in the grade B of TNTsample is due to increasing of mass loss kinetic.Because,the impurities are more volatile in compare to pure TNT.The grade B of TNT is a heterogeneous composition and thus it has the lower freezing point and the less thermal stability[16-18].

The aim of kinetic studies is to obtain the activation energy of thermal decomposition of samples through comparison of a series of measured values(α,t).

With m0being the initial mass,mtthe mass at time t and mfthe final mass.The rate constant k is expressed as an Arrhenius-type temperature dependence

A thermobalance of DuPont 951 thermogravimetric analyser was used in thermogravimetric experiments under N2gas atmosphere.The samples with initial mass of 1.0000 g were taken in an open container of glass and aluminum.Isothermal thermogravimetric measurements were carried out at temperatures of 80,90 and 100°C.

The kinetic of mass loss in isothermal conditions can be calculated by pseudo-zero order

2.Experimental

The grades A and B of TNT were used in this research.The freezing points of 80.57 and 78.15°C,and purity of 99.8 and 98.2%,respectively,were obtained for grades A and B of TNT.The standard method of Mil-DTL-248D was used for determination of freezing points[13].The purity of samples was determined by using GC-ECD(gas chromatography-electron capture detector)method based on the Standard Method 8095[14].

The kinetic equation for non-isothermal methods is[9].

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A Mettler Toledo AG TGA/SDTA851e was used to record of TG/DTG analysis curves of TNT samples.Non-isothermal thermogravimetic measurements were carried out from 30 to 330°C at heating rates of 10,15 and 20 °C·min-1.The initial mass of samples was 1 mg.Continuous recordings of sample temperature and mass loss and its first derivatives were taken.Alumina sample containers were used(70μL volume)with alumina powder as the reference material.Nitrogen atmosphere was applied during the analysis( flow rate of 50 mL·min-1).The precision of temperature was within ±0.1 °C.

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3.Results and discussion

3.1.The kinetic of mass loss of TNT samples in isothermal method

Based on the freezing points of TNT samples,the temperatures of 80,90 and 100°C were used for mass loss of melted TNTsamples.The variations ofα(the degree of conversion)versus time for mass loss of melted TNT samples in two containers of glass(Gl)and aluminum(Al)in isothermal method are given in Figs.1 and 2,respectively.As it is seen,the mass loss of TNTsamples is completed in times of 70 and 90 h,respectively for grades of B and A in aluminum container and at isothermal temperature of 100°C.While,α=1 is observed at times of 480 and 560 h,respectively for grades of B and A of TNT in glass container and at this temperature.In the other words,in aluminum container,grade B of TNT shows the mass loss of 37.9%in time of 200 h at temperature of 100°C while in these temperature and time,a mass loss of 17.1%is seen for grade A of TNT.Also,in these conditions(temperature and time)and in glass container,the mass loss of melted TNT is observed 6.6%and 0.65%,respectively,for grades of B and A.Therefore,the kinetic of mass loss are resulted as:grade B of TNT-Al＞grade A of TNTAl＞ grade B of TNT-Gl＞ grade A of TNT-Gl.

Whereαis the degree of conversion,t is the time,k is the temperature-dependent rate constant and f(α)is a function that represents the reaction model[7,8].Theαvalues are obtained as

Whereβ=dT/dt.There are several methods for deriving kinetic parameters from Eq.(4),such as(i)the differential method,i.e.direct application of Eq.(4);(ii)the difference-differential method,i.e.the Freeman and Carroll method;(iii)the integral method using a simple approximation of the exponential temperature integral,i.e.the Coats-Redfern method;and(iv)modelindependent methods,i.e.isoconversional methods based on heating rate such as the Ozawa-Flynn-Wall(OFW)method,the Friedman method or the Kissinger method[10,11].The derivate data from measured mass-temperature curve is used in differentialmethodswhiletheintegralmethodsovercomethis disadvantage using the measured thermogravimetric data without differentiation[12].

上文例(1)这样的句子属于典型的叙事语体句，符合上面列出的要求；而在《骆驼祥子》中的另一段，则属于非典型的叙事语体句：

Where mi,mt,x,k and t are the initial mass of sample,the mass of sample at time t,the reduced mass,the kinetic constant and time,respectively[19,20].After the calculation of kinetic constants in each temperature,the activation energy of mass loss process is calculated by using the Arrhenius equation(Eq.(3)).The obtained data are collected in Table 1.

The DTG curves of TNT samples at heating rates of 10,15 and 20 K·min-1are shown in Fig.3.Theα -Tcurves of DTG data(based on the surface area of DTG curves)are also presented in Fig.4.

The kinetic of mass loss of a chemical compound caused by degradation,sublimation and or vaporization that can be used for study the aging of it.The accelerated aging in high temperatures(in isothermal conditions)is used for obtaining the kinetic parameters and then the prediction of lifetime of sample in usual temperature such as temperature of 25°C.For chemically caused ageing processes,the formula of Eq.(6)has been proved by experience to be suitable.This formulation is based on the van't Hoff rule[22].

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Fig.1.The variations ofα-time for mass loss of melted TNT samples(grades of A and B)in isothermal temperatures(oC)and in container of glass(Gl).

Fig.2.The variations ofα-time for mass loss of melted TNT samples(grades of A and B)in isothermal temperatures(oC)and in container of aluminum(Al).

Table 1 The kinetic constant(h-1)and activation energy(kJ·mol-1)of mass loss of melted TNT in isothermal conditions.

Temperature/oC Grade A of TNT Grade B of TNT Glass Aluminum Glass Aluminum k×10-3 Ea k×10-3 Ea k×10-3 Ea k×10-3 Ea 80 0.2 1.9 0.6 6.3 90 0.7 114.1 5.2 95.3 1.2 68.7 12.6 60.0 100 1.6 10.8 2.1 18.8

In Eq.(6),tEis the in-service time inyears at temperature TE,tTis the test time in days at ageing temperature TT,F is the reaction rate change factor per 10°C temperature change,TTis the ageing temperature inoC,TEis the in-use temperature inoC andΔTFis the temperature interval for actual value of F;here,ΔTFis always 10 °C.The F factor is determined by the use of the Arrhenius equation[23].This factor(Eq.(7))was deduced from the work of van't Hoff,who compiled and compared reaction rates obtained at different temperatures.The range often met for this factor is between 2 and 4,and higher values are possible,up to 6[23].

Here,Eais the activation energy in kJ·mol-1,and R is the ideal gas constant.The time prediction of mass loss of used samples at temperature of 25°C is given in Table 2.The obtained results show that the mass loss of 100%is occurred in 477 and 646 days for grade A of TNT in containers of aluminum and glass,respectively,at temperature of 25°C.While,for grade B of TNT,the lifetime of 50 and 84 days is seen in containers of aluminum and glass,respectively,at this temperature for to complete of mass loss.

3.2.The kinetic of mass loss of TNT samples under non-isothermal conditions

The obtained results show that the activation energy of mass lossprocessofmelted TNT isin range of60-69 and 95-114 kJ mol-1for grades of B and A,respectively.As mentioned,the decreasing of Eavalues for grade B can be related to the impurities and thus this type of TNTshows the lower thermal stability.Also,ease the heat transfer and the catalytic effect of aluminum container is due to the decreasing of activation energy of mass loss process of melted TNT samples[21].

The maximum of peaks in DTG curves are seen at temperatures of 190.0,220.0 and 238.6°C for grade A of TNTand 180.0,207.9 and 230.0°C for grade B of TNT at heating rates of 10,15 and 20 K·min-1,respectively.As it is seen,the peak temperatures in DTG thermograms are shifted to the higher temperatures with increasing of heating rate[24].Also,the initial temperatures ofmass loss of grades of A and B of TNT are observed at temperatures of 128.6,138.6 and 148.6 °C and 100.0,110.9 and 130.0 °C,respectively,at heating rates of 10,15 and 20 K·min-1.As similar to the results of isothermal method,the decreasing of temperatures(initial and maximum)of mass loss for grade B of TNT versus grade A can be related to impurities of grade B.However,the mass loss is completed for both samples at temperature of 210°C.The DTG curves of grade B of TNT,especially at heating rate of 10 K·min-1,indicate a pre-peak for mass loss at temperature of 120°C that can be assigned for impurities.

Table 2 The prediction of lifetime(day)of TNT samples for mass loss at temperature of 25°C by using isothermal method.

mass loss/% Grade A of TNT Grade B of TNT Aluminum container Glass container Aluminum container Glass container 10 47.7 64.6 5.0 8.4 20 95.4 129.2 10.1 16.8 30 143.1 193.8 15.0 25.2 40 190.8 258.4 20.2 33.6 50 238.5 322.9 25.1 41.9 60 286.2 387.6 30.0 50.4 70 333.9 452.2 35.1 58.8 80 381.7 516.8 40.2 67.2 90 429.4 581.4 45.0 75.6 100 477.1 645.9 50.1 83.9

Fig.3.The DTG curves of grades of A and B of TNT at heating rates of 10,15 and 20 K·min-1.

Fig.4.Theα -T curves of DTG data of grades of A and B of TNT at heating rates of 10,15 and 20 K·min-1.

The model-free methods[25,26]of Ozawa(Eq.(8)),Kissinger(Eq.(9)),Ozawa-Flynn-Wall(OFW,Eq.(10))and modified Kissinger-Akahira-Sunose(KAS,Eq.(11)),are used for calculation of the activation energies of decomposition reactions of TNT samples based on DTG data.

Table 3 The Eavalues(kJ·mol-1)of TNT samples by the model-free methods.

Method Grade A of TNT R2value Grade B of TNT R2value Ozawa 101.6 0.994 70.2 0.987 Kissinger 99.1 0.946 66.2 0.954 Ozawa-Flynn-Wall 101.6 0.955 70.2 0.963

Table 4 The Eavalues(kJ·mol-1)of TNT samples by using KAS method.

Conversion fraction(α) Grade A of TNT Grade B of TNT Ea R2 Ea R2 0.10 117.6 0.889 60.9 0.835 0.20 116.5 0.972 62.6 0.921 0.30 122.1 0.879 65.0 0.939 0.40 121.7 0.859 66.4 0.932 0.50 119.1 0.896 67.3 0.945 0.60 118.8 0.935 67.9 0.943 0.70 118.3 0.952 68.6 0.940 0.80 119.0 0.974 71.7 0.927 0.90 121.6 0.980 74.1 0.943 Average=119.4±1.9 Average=67.2±4.1

In these equations,β is heating rate(K·min-1),Eais activation energy(kJ·mol-1),Tmor Tpare the maximum temperature or peak temperature of DTG curves,A is Arrhenius constant and T is temperature(K).The activation energy(Ea)can be evaluated from the slope of the straight line which gives the best regression coefficients(R2)[27].The obtained results using methods of Ozawa,Kissinger and OFW are collected in Table 3.

The obtained Eavalues show that the activation energy of grade B of TNT is in range of 66-70 kJ mol-1.While,the activation energy is obtained in amplitude of 99-101 kJ mol-1for grade A of TNT[28-30].The presence of impurities in grade B is due to reduction of activation energy of mass loss process.Also,the Eavalues and regression coefficients of the curves by using KAS method in conversion fraction(α)of 0.10-0.90 are collected in Table 4.The average of Eavalues are obtained 119.4±1.9 and 67.2±4.1 kJ mol-1 for grades A and B of TNT,respectively.The results obtained from different methods con firm each other.

Kinetic predictions are the most important practical application of kinetic analysis.The predictive equation was originally proposed in the following form of Vyazovkin[5,6]:

The respective prediction is called model-free predictions,because it eliminates the reaction model.The model-free predictions are not limited to a given model[31,32].It is applicable to the processes for which Eαvaries withαand theygenerally produce more reliable estimates for the lifetime,tα.

However,the predicted life times of isothermal and nonisothermal methods are different(Tables 2 and 5),and the obtained values of non-isothermal method show the more life times.The reasons for these issues can be expressed in a few ways.The mass loss of samples was studied in temperatures(80-100°C)nearto normal temperatures,while,the mass loss is seen at temperatures 180-230°C in non-isothermal conditions.Outsourcing over more distances can lead to more errors.On the other hand,the main phenomenon in the isothermal method can be due to sublimation and evaporation of melted TNT samples.But,in nonisothermalmethod,degradation ofsamples is dominant phenomenon.

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Table 5 Thelifetime(day)of TNTsamples for mass loss at temperature of 25°C by using nonisothermal method.

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4.Conclusions

The isothermal and non-isothermal methods could be used as useful methods for study the mass loss of energetic materials such as TNT samples.The obtained kinetic constants could be used for prediction of life times of samples.

The mass loss of grade A of TNT(pure TNT)and grade B of TNT(impure TNT)is investigated by using isothermal and nonisothermal methods.The variations of mass versus time are used for calculation of kinetic constants and activation energies.The obtained k and Eavalues showed that the impurities is due increasing of kinetic of mass loss and decreasing of activation energy,thermal stability and life time of samples.Also,the material of the sample container is very in fluential on kinetic parameters.So that the kinetic of mass loss of samples in metallic container are increased and the activation energy,thermal stability and life time of samples are decreased.

Acknowledgement

We would like to thank the research committee of Malek-ashtar University of Technology(MUT)for supporting this work.

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