Zhijuan Sun ,Xiao Wang ,Fei Guo ,Chunyue Jiang *,Qinmin Pan

1 The Zhejiang Province Key Laboratory of Biofuel,Ocean College,Zhejiang University of Technology,Hangzhou 310014,China

2 The Zhejiang Province Key Laboratory of Biofuel,College of Chemical Engineering,Zhejiang University of Technology,Hangzhou 310014,China

3 Department of Polymer Science and Engineering,Soochow University,Suzhou 215123,China

A B S T R A C T Bio-sourced nylon 69,one of promising engineering plastics,has a great potential in developing sustainable technology and various commercial applications.Isothermal and nonisothermal crystallization kinetics of nylon 69 is a base to optimize the process conditions and establish the structure-property correlations for nylon 69,and it is also highly beneficial for successful applications of nylon products in industry.Isothermal and nonisothermal crystallization kinetics has been investigated by differential scanning calorimetry for nylon 69,bio-sourced even-odd nylon.The isothermal crystallization kinetics has been analyzed by the Avrami equation,the calculated Avrami exponent at various crystallization temperatures falls into the range of 2.28 and 2.86.In addition,the Avrami equation modified by Jeziorny and the equation suggested by Mo have been adopted to study the nonisothermal crystallization.The activation energies for isothermal and nonisothermal crystallization have also been determined.The study demonstrates that the crystallization model of nylon 69 might be a two-dimensional(circular)growth at both isothermal and nonisothermal crystallization conditions.Furthermore,the value of the crystallization rate parameter(K)decreases significantly but the crystallization half-time(t1/2)increases with the increase of the isothermal crystallization temperature.To nonisothermal crystallization,the crystallization rate increases as the cooling rate increases according to the analysis of Jeziorny's theory.The results of Mo's theory suggest that a faster cooling rate is required to reach a higher relative degree of crystallinity in a unit of time,and crystallization rate decreases when the relative degree of crystallinity increases at nonisothermal crystallization conditions.

?2015 The Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

1.Introduction

Nylons(polyamides)are important commercial engineering plastic materials used widely in a variety of applications for their excellent overall properties,such as eminent toughness,high modulus,good temperature and corrosion resistance,shockproof,antifatigue,and oil proof[1,2].The preparation of nylon has relied on crude oil as a major feedstock for more than half a century,but now the threat of an oil shortage has stimulated the investigation for alternative chemical feed stocks,for which bio-mass and its derivatives are,for example,recently investigated to prepare bio-sourced materials.Bio-sourced nylon 69,a type of medium and long chain nylon with characteristic properties,is particularly suitable for numerous commercial applications including compact disks,automotive parts,and other goods[3,4].Azelaic acid is an important raw material to synthesize bio-sourced nylon 69 and can

☆Supported by the Natural Science Foundation of Zhejiang Province(LY15B060006),the National Natural Science Foundation of China(21104066)and the Zhejiang Province Public Technology Research and Industrial Grant(2012C21078).

*Corresponding author.

E-mail address:sunzj@zjut.edu.cn(C.Jiang).be obtained from the byproduct of biodiesel,which can be prepared by renewable resource,for example,Chinese tallow tree seeds[5].

The properties of crystalline polymer materials are dependent not only on their macromolecular chain structures,but also,in a great degree,on their morphologies,crystalline structure and degree of crystallization,which in turn is significantly controlled by the crystallization process during the polymer molding process[6].Furthermore,polymer molding technologies including extrusion-molding and film-forming are often performed under the isothermal or nonisothermal conditions in practical applications.In previous works[7-9],crystallization kinetics of various nylons have been described by applying different processing conditions such as isothermal annealing,cooling from the melt,or solvent-induced crystallization.It has been demonstrated that there are different morphologies and crystalline structures for different types of nylon,which is strongly dependent on the orientation of amide group and parity characteristic of carbon number in nylon.For example,Cui and his group[7,8]investigated the crystallization kinetics of polyamide 911 and the polyamide 1011,and the results showed that the spherulite growth mode of the two polyamides is mainly in a three-dimensional orientation with thermal nucleation.On the other hand,the effect of crystallization temperature on the formation of crystal structure is very important.Song et al.[9]observed the α-form of nylon 1212 at above 150°C,and the γ-form at90°C.It is surprising that the α form and the γ-form could transform to each other under specific conditions.Furthermore,the crystallization behavior of nylon-based nanocomposites has also been reported to explore the effect of nanofillers on the macroscopic performance of nanocomposites[10,11].Although the nylon 69 products can be widely used,quite a few investigations on nylon 69 have been reported.

In this study,the sample of nylon 69 was prepared by a melt polycondensation technique,the main objective of this article is to investigate the isothermal and nonisothermal crystallization kinetics of nylon 69 by differential scanning calorimetry(DSC),using the Avrami equation and the two theories of Jeziorny[12]and Mo[13],respectively.Furthermore,the crystallization kinetics parameters and the activation energies of isothermal and nonisothermal crystallization of nylon 69 were also determined according to classical theories.

2.Experimental

2.1.Materials

Azelaic acid and hexane diamine with purity of 99%were purchased from Aladdin and used without further purification.Analytical grade ethanol without water and concentrated sulfuric acid were supplied by Zhejiang Juhua Co.,Ltd.Nitrogen with a minimum purity of 0.9999 was purchased from Hangzhou Jingong Industrial Gas Co.Ltd.

2.2.Synthesis of nylon 69

Nylon 69 was synthesized here by a melt polycondensation technique with the reaction principle shown in Fig.1,including two steps:preparation of salt of nylon 69 and melt polycondensation reaction.

2.2.1.Preparation of salt of nylon 69

Firstly,the monomers of azelaic acid(14.13 g)and hexane diamine(8.80 g)were dissolved by ethanol in a thermostat water bath with 60°C,respectively,and the mass ratio of the monomer/ethanol was set to 1:4.Secondly,the solution of azelaic acid was added slowly to the solution of hexane diamine under stirring,and then the white crystal(salt of nylon 69)was produced.Finally,the crystal of nylon 69 salt was washed by ethanol without water at least three times and dried at 50°C in a vacuum oven for over 12 h before polycondensation.

2.2.2.Melt polycondensation

Firstly,nylon 69 salt(5 g)and hexane diamine(8.80 g)were added into a round-bottomed flask connected with an inert gas joint,and then the fl ask was placed in a thermostat oil bath.Oxygen and volatile were removed by using nitrogen with the speed of 0.6 L·min-1,and the whole process of polymerization was carried with a continuing nitrogen purge.

Secondly,the system of reaction was heated to 190°C and the mixture of salt of nylon 69 and hexane diamine melted for 1 h,and then the polymerization was started by increasing the temperature of the reaction system to 210°C,and the reaction was carried out for 2 h.The reaction system was then heated to 250°C and the polymerization was kept for 2-3 h;at the same time,the speed of nitrogen was increased to 3 L·min-1to keep the polymerization continuing for the step-growth polymerization.

Finally,when the polymerization was completed,the sample of melted nylon 69 was taken from the flask rapidly by a preheated glass rod,and the sample was transferred rapidly to a film form and cooled to room temperature with the sweep fluid of nitrogen,and then the production of nylon 69 was obtained after drying at50°C in a vacuum oven for over 12 h.

2.3.Characterization

2.3.1.The molecular weight of the nylon 69

The molecular weight of the nylon 69 sample was tested by the Ubbelohde viscosity method,the solvent was concentrated sulfuric acid.Efflux times were recorded as the mean value by three times.The relative viscosity(ηr)and intrinsic viscosity of the nylon 69 were 1.63 and 0.72 dl·g-1in concentrated sulfuric acid(96%),respectively.

2.3.2.The melt temperature of the nylon 69

The nylon 69 sample without heat treatment was heated to melt from 25 to 260°C at a heating rate of 10°C·min-1by differential scanning calorimetry(DSC),and then cooled at the cooling rate of 10°C·min-1,thus the melting and crystallization curves were obtained and shown in Fig.2.Only one melting peak was observed at 213.17°C and an exothermal peak was examined at around 181°C during the crystallization process,which suggested that the melt temperature of nylon 69 was 213.17°C.2.3.3.Isothermal and nonisothermal crystallization process by DSC

Fig.2.DSC thermograms(heating scan and cooling scan)of nylon 69.

Fig.1.Schematic representation of the polymerization of nylon 69.

For the DSC analyses,all the thermal treatment was performed in a TA Instruments Q-100 using aluminum pans.All DSC experiments were performed under a nitrogen purge at a constant flowrate and the sample weights were between 5 and 8 mg.

The DSC experiments of isothermal crystallization of a nylon 69 sample comprised two stages:(1)the sample was heated to 260°C at a rate of 20°C·min-1and maintained for 3 min to eliminate any previous thermal history and(2)the sample was cooled at a rate of 40°C·min-1to the predetermined crystallization temperature(Tc)and was maintained at Tcfor 60 min.The Tcwas set for T1(200°C),T2(202°C),T3(204°C),T4(206°C)and T5(208°C).

The nonisothermal crystallization procedure also comprised two stages:(1)the first stage was the same as that of the above isothermal crystallization and(2)the sample was cooled from 260 to 25°C at four different rates of 5,10,20,and 25°C·min-1,respectively,so the four DSC thermograms of nonisothermal crystallization processes were obtained.

3.Results and Discussion

3.1.Isothermal crystallization

3.1.1.Isothermal crystallization behavior

The isothermal crystallization behavior of the nylon 69 samples was carefully investigated by DSC.Fig.3 shows the DSC thermograms of the nylon 69 samples at various isothermal crystallization temperatures.As can be seen,the crystallization peaks shift toward the right and become broader with increasing crystallization temperature.It implies that the crystallization time of the nylon 69 samples increased as the crystallization temperature increased,and that is to say that the crystallization rate decreases with the increasing crystallization temperature.This is because the bulk crystallization rate becomes more slow and the crystallites within the spherulites become more regular(growing in radial direction)as the isothermal crystallization temperature increases[14].

Fig.3.DSC traces of nylon 69 isothermally crystallized at the indicated temperatures.

3.1.2.Isothermal crystallization kinetics analysis

The isothermal crystallization kinetics was usually analyzed by the relative crystallinity(Xt)at different crystallization times and the Avrami equation.The relative crystallinity at different crystallization times can be calculated according to the following equation[15].

where Xc(t)and Xc(t=∞)are the relative crystallinity at time t and infinite time,respectively,and d Hc(t)/d t is the heating flow per gram of the sample.The plot of X(t)as a function of time t for the nylon 69 undergoing the isothermal crystallization process at various Tcis shown typically in Fig.3.The curves all have characteristic sigmoid isotherms and shift to the right with increasing isothermal crystallization temperature.The results show that completion time of crystallization becomes longer and the crystallization rate decreases as the isothermal crystallization temperature increases.The Avrami equation(Eqs.(2)and(3))is commonly used not only to determine the growing rate of a metal crystal but also to analyze the crystallization rate of polymer[16-18].In this work,the Avrami equations are adopted to analyze the isothermal crystallization process of nylon 69.

where K is the crystallization rate constant and n is the Avrami exponent whose value is related to the mechanism of nucleation and the form of crystal growth,respectively.According to the isothermal crystallization data from DSC,the relation between lg[-ln(1-X(t))]and lg t for the nylon 69 at various isothermal crystallization temperatures(T1-T5)was shown in Fig.5.

All the curves in Fig.5 were linear from beginner to 70%in the complete regions,but the curves deviated from the linear relation at longer crystallization time.This was presumably because the nylon 69 sample turns into the secondary crystallization at the end of the isothermal crystallization process;just like most semicrystalline polymers,the spherulites could colloid each other in the secondary crystallization and the deviation occurs under experimental conditions.

For comparison,the regime of about 10%-70%conversion in the curves for the samples is chosen to determine the exponent n and K according to Eq.(3).Applying the least square theory to the linearrange in Fig.5,the values of n and K(Table 1)are obtained from the slope and intercept of the fitted curves,respectively.The Avrami exponent(n)represents the dimensionality of crystal growth for different crystallization mechanisms;for example,crystal forms spherulite growth when n equals to 3-4,while crystal forms circular disk shape growth when n equals to 2-3[19].

Fig.4.Relative crystallinity versus different crystallization times in the isothermal crystallization process for nylon 69 sample.

Fig.5.Typical plots of lg[-ln(1-X(t))]versus lg(t)of the nylon 69 isothermally crystallized at the predetermined temperatures.

Table 1 Parameters of the isothermal crystallization for nylon 69

As shown in Table 1,all the obtained values of n for the nylon 69 sample at various crystallization temperatures fall into the range of 2.28 and 2.86,indicating that the crystallization model of nylon 69 might be a two-dimensional(circular)growth with thermal nucleation[20].In addition,the values of the crystallization rate parameter K for nylon 69 decreased significantly with the increasing isothermal crystallization temperature,suggesting that the crystallization rate decreased as the crystallization temperature increased.That is because the crystallization rate is determined by the nucleation rate of crystallization,and a larger k value is corresponding to a higher rate of crystallization.This finding was consistent with the result of the crystallization time,which was involved in the isothermal crystallization behavior analysis.

Moreover,some other important parameters have also been used to analyze the crystallization kinetics,such as the crystallization half-time,rate of crystallization,and time for maximum crystallization[21].The crystallization half-time(t1/2)is defined as the time at which the relative degree of crystallinity reaches 50%and can be found in Fig.4,and the rate of crystallization(G)is defined as the reciprocal of t1/2and can be calculated from Eq.(4).Therefore,the crystallization half-time is used to characterize the crystallization rate directly,it can be said that the longer the crystallization half-time,the slower the rate of crystallization.Fig.6 shows the t1/2values of nylon 69 versus the isothermal crystallization temperature(T1-T5),it is found that the t1/2increases with increasing crystallization temperature,that is to say,the rate of crystallization of nylon 69 decreases with the increase in the crystallization temperature.

Fig.6.The crystallization half-time(t1/2)as a function of crystallization time(T c)for nylon 69.

For the crystallization process of the polymers,there are two stages including the crystal nucleation stage and the crystal growth stage.The former belongs to thermodynamics process,and the crystal nucleus is more easily destroyed by molecular thermal motion when the crystallization temperature is closer to the melt point of polymers,and then the rate of nucleation is slower;furthermore,the nucleation stage is the control step for the rate of crystallization.As discussed above,the crystallization temperatures are close to the melt point of the nylon 69 sample in this investigation.Therefore,the rate of crystallization is mainly controlled by the crystal nucleation stage;when the crystallization temperature increases,the rate of nucleation decreases resulting in the decrease in the rate of crystallization.

In addition,the time to reach the maximum rate of crystallization(tmax)can also be used to characterize the rate of crystallization,and it corresponds to the point at which the second derivative of X(t)versus t equals 0[22].Thus tmaxcan be determined from Eq.(5).The calculated values of tmaxare also listed in Table 1,and the results in Table 1 are in accordance with those deduced from the Avrami integral curves(Fig.5).

3.1.3.Activation energy of isothermal crystallization

Assuming that the crystallization of the nylon 69 sample in this investigation is a thermal activation process,the crystallization rate constant(K)can be described by the Arrhenius equation as follows[23]:

where k0and ΔE are the front factor independent of temperature and the activation energy of isothermal crystallization,respectively;R is the gas constant(8.3144 J·mol-1·K-1).According to Eq.(7),the plot of(1/n)ln K versus 1000/Tcfor nylon 69 is illustrated in Fig.7,and the R-square of the fitting line is 0.97.The value of ΔE can be determined as the slope of the obtained line in Fig.7,which equals to-100.72 kJ·mol-1.

3.2.Nonisothermal crystallization

3.2.1.Nonisothermal crystallization behavior

Fig.7.A typical plot of(1/n)ln K versus 1000/T c of the nylon 69 isothermally crystallized.

The nonisothermal crystallization process is more complicated than the isothermal crystallization process based on the comprehensive consideration of the crystallization temperature and crystallization time;however the nonisothermal crystallization process is close to polymer molding processes,such as extrusion,stretching,and blow molding.Therefore,the investigation of the nonisothermal crystallization is very important for practical applications.

Fig.8 is the DSC thermograms of the nylon 69 sample at various cooling rates under nonisothermal crystallization conditions.It is obvious that all cooling curves include one crystallization peak and the location of the crystallization peak is shifted from high temperature to low temperature with the increasing cooling rate.Moreover,the shape of the crystallization peak is gradually widened when the cooling rate is increased,which means that the range of crystallization temperature is gradually broad,and the crystallization peak temperature(Tp)decreases form 184.33°C to 176.38°C when the cooling rate increases from 5°C·min-1to 25°C·min-1.This is because it needs to take some time to finish the polymer chain rearrangement and enter into crystal lattices;thus there is a delay period of the crystallization at the cooling process.Furthermore,the delay period increases with the increase in the cooling rate,so the crystallization peak is shifted to low temperature and the Tpdecreases with increasing cooling rate.These results reveal that the rearrangement capacity of polymer chains to regular crystal is poor at a fast cooling rate,and then the nucleation and the beginning of crystallization are delayed,and the beginning crystallization temperature and the crystallization peak temperature are shifted to low temperature.On the contrary,when the cooling rate is slow,the mobile capacity of polymer chains is improved to facilitate the formation of crystal nuclei and the regular arrangement time is short,and then the crystallization can begin at high temperature.

Fig.8.DSC traces of nylon 69 nonisothermally crystallized at various cooling rates.

3.2.2.Nonisothermal crystallization kinetics analysis

As the nonisothermal crystallization process is complicated,a variety of theories which are used to analyze the nonisothermal crystallization kinetics have been developed by Ozawa,Jeriorny,Mo et al.[24,25].In this work,the nonisothermal crystallization kinetics of nylon 69 is investigated by the relative crystallinity(Xt)at different crystallization times and the two theories of Jeriorny and Mo were applied.The relative crystallinity under nonisothermal crystallization conditions can be calculated according to the following equation:

where t0and tEare the crystallinity times at the beginning and end,respectively.Plotting Xtversus the crystallinity time t at various cooling rates therefore yields S-like curves(seen in Fig.9).Based on these curves,the relation of the crystallinity time(t)and the crystallinity temperature(T)can be calculated by the following equation(Eq.(9)):

where T0and Φ are the temperature at the beginning(t=0)and the cooling rate,respectively.Plotting Xtversus the crystallinity temperature(T)at various cooling rates,reverse S-like curves were obtained(seen in Fig.10).As shown in Figs.9 and 10,the tail of all curves becomes flat,which means that the crystallization rate becomes slow.This is because the spherocrystals collide with and squeeze each other at the end of nonisothermal crystallization process.

The results of Tp,t1/2and the total enthalpies of crystallization(ΔHc)of nonisothermal crystallization at various cooling rates(shown in Table 2)are in accordance with those deduced from the curves in Figs.8 and 9 and Eq.(10).From Table 2,itis observed that Tpand t1/2decrease with the increase in the cooling rate,that is to say the crystallization rate increases with increasing cooling rate.

In order to analyze the nonisothermal crystallization kinetics,Jeziorny extended the classical Avrami equation from the isothermal crystallization to the nonisothermal crystallization.Firstly the nonisothermal crystallization is regarded as the isothermal crystallization in order to get the crystallization rate constant(K)and Avrami exponent(n)from the relation between lg[-ln(1-X(t))]and lg t(seen in Fig.11),and then the K is corrected by the cooling rate as follows:

Fig.9.The relative crystallinity versus crystallization time in the nonisothermal crystallization process for nylon 69 at various cooling rates.

Fig.10.The relative crystallinity versus crystallization temperature in the nonisothermal crystallization process for nylon 69 at various cooling rates.

Table 2 Parameters of the nonisothermal crystallization of nylon 69 at various cooling rates

where Kcis the corrected crystallization rate constant of the nonisothermal crystallization by Jeziorny's theory.

In Fig.11,all the curves contain the linear part and non-linear part,and these two parts are corresponding to the primary crystallization period and the secondary crystallization period,respectively.The parameters of the nonisothermal crystallization kinetics at the main crystallization period are shown in Table 3.It can be found that the values of n of nylon 69 at various cooling rates fall into the range of 2.13 and 2.46,indicating that the crystallization model of nylon 69 at nonisothermal crystallization conditions might be a two-dimensional(circular)growth.Nevertheless,the crystallization model becomes more sophisticated by including the crystal growing in the secondary crystallization period.Furthermore,the corrected crystallization rate parameter Kcof nylon 69 increased significantly with increasing cooling rate,suggesting that the crystallization rate increased as the cooling rate increased.

Fig.11.A typical plot of lg[-ln(1-X(t))]versus lg t of the nylon 69 nonisothermally crystallized at various cooling rates.

Table 3 Parameters of the nonisothermal crystallization of nylon 69 according to Jeziorny's theory(the primary crystallization period)

For Jeziorny's theory is only suitable for the main crystallization period at nonisothermal crystallization conditions,Mo combined the Avrami equation with the Ozawa equation and developed a new theory to analyze the nonisothermal crystallization kinetics of polymers,and the new equation is described as follows[7,9]:

where α is the ratio of the Avrami exponent(n)to the Ozawa exponent(m),and F(T)is a characteristic of crystallization rate with unit of K·mina-1,which means a requirement cooling rate to reach a defined degree of crystallinity in a unit of time,that is to say,the bigger the value of F(T),the slower the crystallization rate.The values of F(T)can be obtained by plotting lgΦ versus lg t at the same relative degree of crystallinity.

Fig.12 shows the plot of lgΦversus lg t at various degrees of crystallinity and the values of a and F(T)are listed in Table 4.As shown in Fig.12 and Table 4,the value of F(T)increases with increasing relative degree of crystallinity,which suggests that a faster cooling rate is required to reach a higher relative degree of crystallinity in a unit of time.Moreover,the crystallization rate decreases when the relative degree of crystallinity increases at nonisothermal crystallization conditions.

3.2.3.Activation energy of nonisothermal crystallization

Fig.12.A plot of lgΦ versus lg t at various degrees of crystallinity.

Table 4 The values of α and F(T)at various relative crystallinity

The activation energy of nonisothermal crystallization for polymers is usually calculated by the Kissinger equation as follows[26]:where ΔE is the activation energy of nonisothermal crystallization for nylon 69,and the meanings of other parameters are the same as above.According to Eq.(12),the plot ofversus 1/Tpis illustrated in Fig.13,and the R-square of the fitting line is 0.99.The value of ΔE can be determined from the slope of the obtained line in Fig.13,which equals to-146.95 kJ·mol-1.

Fig.13.A typical plot ofversus 1000/T p of the nylon 69 nonisothermally crystallized.

4.Conclusions

Nylon 69 with an intrinsic viscosity of 0.72 dl·g-1in concentrated sulfuric acid was prepared by a melt polycondensation technique.The isothermal crystallization at various temperatures(T1-T5)and the nonisothermal crystallization at various cooling rates have been investigated by DSC.

For the isothermal crystallization,the analysis results of Avrami's theory indicate that the Avrami equation is only applicable for isothermal crystallization from beginning to 70%in the plots of relative crystallinity versus different crystallization times.This is because there is the secondary crystallization of nylon 69 at the end of the isothermal crystallization process.Based on the Avrami equation,the Avrami exponent(n),crystallization rate constant(k),crystallization half-time(t1/2)and rate of crystallization(τ1/2)are determined,and the results show that the crystallization model of nylon 69 should be a two-dimensional(circular)growth with thermal nucleation,and the values of the K for nylon 69 decrease significantly but the t1/2increases with increasing isothermal crystallization temperature,suggesting that the crystallization rate decreases as the crystallization temperature increases.

For the nonisothermal crystallization,it is observed that all DSC thermograms at various cooling rates have one crystallization peak and the location of crystallization peak is shifted from high temperature to low temperature with increasing cooling rate.The results reveal that the nucleation and the beginning of crystallization are delayed when the cooling rate is turned to fast,and the delay period increases with the increase in the cooling rate.Furthermore,the two theories of Jeziorny and Mo have been adopted to study the nonisothermal crystallization kinetics of nylon 69.The analysis of Jeziorny's theory shows that the values of the n for nylon 69 at various cooling rates fall into the range of 2.13 and 2.46,which mean that the crystallization model of nylon 69 at nonisothermal crystallization conditions might be a two-dimensional(circular)growth,but the crystallization process with the growing crystal becomes complicated in the secondary crystallization period.It is also found that the corrected crystallization rate parameter Kcof nylon 69 increases significantly with increasing cooling rate,suggesting that the crystallization rate increases as the cooling rate increases.The analysis of Mo's theory shows that the value of F(T)increases with increasing relative degree of crystallinity,which suggests that a faster cooling rate is required to reach a higher relative degree of crystallinity in a unit of time,and crystallization rate decreases when the relative degree of crystallinity increases at nonisothermal crystallization conditions.

In addition,the activation energies for isothermal and nonisothermal crystallization have been determined as-100.72 kJ·mol-1and-146.95 kJ·mol-1according to the Arrhenius and Kissinger theories,respectively.

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