Jurnal 4

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Effect of inorganic salt on the thermal degradation of nitrocellulose and reaction mechanism of its mixture

Guo-zhong Xu, Xu Gao, Mi Li, Zhong-xuan Han, Lin Jiang

^*

School of Mechanical Engineering, Nanjing University of Science and Technology, China

a r t i c l e i n f o

Article history:

Received 7 September 2022 Received in revised form 20 October 2022

Accepted 14 November 2022 Available online xxx

Keywords:

Thermal analysis

Thermal decomposition mechanism Malek method

Nitrocellulose Inorganic salt

a b s t r a c t

In this study, to better understand the reaction mechanism between inorganic salts and nitrocellulose, CaCO3and Li2CO3were evaluated with respect to their effects on the thermal degradation of NC in nitrogen atmosphere using TG/DSC at three different heating rates (2, 5, 10 K/min). The numerical relationship between activation energy (E) and conversion rate was obtained by FWO and KAS method, and it was discovered that CaCO3could improve the thermal stability of NC. Activation energy values were calculated by Kissinger method, and it was found that NC that contain Li2CO3had the highest activation energy while NC containing CaCO3had the lowestEvalue. By combining the thermal analysis data with Malek method, the most probable mechanism model of thermal degradation is obtained asSestak- Berggren model, which expression isf(a)¼a^m(1 -a)ⁿ. As a result of this study, there are certain guiding principles that can be applied to the pyrolysis reaction model and to the actual production process of nitrocellulose.

licenses/by-nc-nd/4.0/).

1. Introduction

Nitrocellulose (NC) is a typical ﬂammable and explosive sub- stance, which is not only an important component of propellants and high explosive, but also widely used as additives in paints and varnishes [1]. In the military and civil industries, spontaneous combustion is one of the problems faced because of NC’sﬂammable and explosive properties.

Studies have been conducted on the mechanism of NC spontaneous combustion. Historically, nitrogen oxides, primarily NO2, have been known to reduce the induction period of NC, and the presence of oxygen increases the heatﬂow during NC pyrolysis. In the previous studies, it had been pointed out that the stability of NC was affected by nitrogen dioxide, therefore, the initial stage of thermal degradation of NC was affected by nitrogen dioxide [2].

Based on this ﬁnding, the commonly stabilizers of NC, tereph- thalic(TPA), N,N⁰-Dimethyl-N,N⁰-diphenylurea(C2), Akardite-II(A- KII), andN-Methyl-4-nitroaniline(MNA), can capture the nitrogen oxides released during NC pyrolysis to improve thermal stability

[3]. For these typical stabilizers, scholars have recently conducted the following studies. Wei et al. studied the effect of plasticizer DPA on the thermal decomposition of NC and it was found that at lower temperatures, DPA improved the thermal stability of NC, but no improvement was observed at higher temperature [4]. Zhao Yang et al. [5] investigated the effects of four typical stabilizers (DPA, AKII, MNA, C2) on the thermal decomposition of NC by Adiabatic acceleration calorimeter (ARC) apparatus, and found that the addition of stabilizers would change the autocatalytic reaction mechanism of NC, and the reaction mechanism of NC might become biased from Bna autocatalytic reaction mechanism to n- level reaction mechanism; MNA had the most signiﬁcant effect on the autocatalytic reaction characteristics of NC. Cieslak et al. [6]

investigated the effect of stabilizers (C1, C2, AKII and TPA) on the thermal stability of nitrocellulose with different nitrogen contents and found that TPA had the best stabilization effect and prolonged the induction period of the autocatalytic reaction compared to other stabilizers. In addition, scholars have also devoted themselves to exploring new, environmentally friendly stabilizers [7e9] and studying the effect of two-component stabilizers on the thermal degradation of NC [10e12].

In 2010, due to the fact that industrial water would be used at the factory to clean NC, and industrial water contains a wide range of inorganic salts. Thus Katoh et al. studied and found that

*Corresponding author.

E-mail address:ljiang@njust.edu.cn(L. Jiang).

Peer review under responsibility of China Ordnance Society

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Defence Technology

j o u r n a l h o m e p a g e :w w w . k e a i p u b l i s h i n g . c o m / e n / j o u r n a l s / d e f e n c e - t e c h n o l o g y

https://doi.org/10.1016/j.dt.2022.11.010

2214-9147/©2022 China Ordnance Society. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC- ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: G.-z. Xu, X. Gao, M. Liet al., Effect of inorganic salt on the thermal degradation of nitrocellulose and reaction mechanism of its mixture, Defence Technology, https://doi.org/10.1016/j.dt.2022.11.010

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induction periods for NC containing 2% CaCO3 under isothermal storage at 120C were about 15 h longer than those for NC containing CaSO4, CaCl2, ZnSO4, and CuCl2were about 4e5 h shorter than those for pure NC under the condition of isothermal storage at 120C. Therefore, it was considered that when components of industrial water were accumulated in NC, the stability and instability of inorganic salts cancelled each other [13]. Katoh et al. selected 17 kinds of weakly basic salts and hydroxides and studied their effects on the thermal stability of NC. It was pointed out that the effect of inorganic salts on the thermal stability of NC could be divided by its acidity and alkalinity: strong alkaline solution (pH>13) contracted the induction period, alkaline saturated solution (pH ¼ 10e12) prolonged the induction period, and neutral solution accelerated the hydrolysis of NC [14]. It was found that the effect of Li₂CO₃on the thermal stability of NC was about the same as that of conventional stabilizers, and the thermal stability increased with the increase of the amount of inorganic salt under the condition of 120C isothermal experimental [15]. In 2018, Wei et al. analyzed the thermal behavior of NC with different aging periods. Results showed that NC had the worst thermal stability when they were stored at 90C for 24 days, and the thermal stability of NC could signiﬁcantly increase when the storage time exceed 32 days [16].

Most of the aforementioned work focused on the effect of ad- ditive on NC and it was found that the alkaline environment of NC could inhabit the occurrence of thermal spontaneous combustion.

In practice, inorganic salts are usually added to NC- humectant systems, and the reactions between NC and humectant [17e20]

have been studied deeply, but the reactions between NC and inorganic salts are less studied and not mathematically expressed.

The focus of this paper is to study the reaction mechanism of the mixture, NC contains Li₂CO₃or CaCO₃, which was analyzed using a Thermogravimetry/Differential Scanning Calorimetry (TG/DSC) analyzer to obtain the TG-DTG-DSC curves and thus calculate the kinetic parameters.

2. Experiment

The experiment used a NC, and CaCO3, Li2CO3were produced by Sinopharm Chemical Reagent Co., Ltd. and Shanghai Aladdin Biochemical Technology Co., Ltd., respectively. The purity of these inorganic salts reached to 99%, and 99.99% respectively. The mixture was prepared according to the principle that the inorganic salt mass was 5% of the total mass.Fig. 1shows that the preparation process of the samples: the inorganic salts were added to the corresponding mass of NC, soaked in anhydrous ethanol, stirred and then baked in an oven at 45C for 9 h. The samples were turned and baked in the oven for another 4.5 h. There are 3 kinds of samples, 2 of which are the mixture of NC and inorganic salt. NC samples containing CaCO3, Li2CO3were named as NC-C, NC-L, respectively.

The 3rd kind of samples is the pure NC (NCeP) that is used for

comparison (shown inTable 1).

The instrument type used in this research is METTLER TOLEDO TG/DSC 3þ made in Switzerland, which has a heating rate of 0.02e150 K/min, and the sensitivity of balance is 0.1mg. The heating rates of experiments were 2, 5, 10 K/min, respectively. Nitrogen was selected as theﬂowing gas under theﬂow rate of 30mL/min¹; the sample mass of each experiment was 1 mg and the initial mass error of the sample should not exceed 0.1 mg; the temperature range for all samples was set as 25e450C.

3. Calculation methods

For the decomposition process of NC, the chemical reaction rate can be described by Eq.(1)according to Arrhenius equation d

a

dt¼

b

^d

a

dT¼kðTÞfð

a

Þ (1)

whereT is the temperature in absolute temperature,K; b^{is the} constant heating rate, K/min, and its expression isb¼dT/dt; k(T) is the chemical reaction rate constant, s¹; f(a) is the reaction mechanism function, dimensionless; the conversion rate,a^{, is the} ratio of the instant mass loss of the sample to the total mass loss in a certain temperature range. The conversion rate can be calculated using Eq.(2)

a

¼ mom

m_om_f (2)

Here,mo,mandmfare the initial mass, the mass at timet, and the residual mass of the sample at the end, respectively, all samples in this paper are in milligram.

k(T) can be expressed by Arrhenius equation as follows:

kðTÞ ¼Aexp

E RT

(3) whereAis the pre-exponential factor, min¹;Eis the activation energy, J/mol;Ris the gas constant, and its value equals to 8.314 J/

(mol$K).

Based on the above equation, Eq.(1)can be described by the following equation:

d

a

dt¼Aexp

E

RT

(4) Among the above parameters, the activation energy E, pre- exponential factor A and reaction mechanism function f(a^{) are} combined into a deﬁnition of kinetic triplet. It can be obtained that the relevant conclusions of the thermal stability and thermal decomposition mechanism of the sample through the calculation and analysis of the kinetic triplet during the pyrolysis of NC and

Fig. 1.A brief process of samples processing is shown.

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mixture samples.

Activation energyErepresents the minimum energy required for reactant molecules to reach the active molecules. In other words, low activation energy represents a high risk of materials.

The TG curves is obtained under non-isothermal conditions, and the activation energy can be calculated by the iso-conversional rate method. The typical iso-conversional rate methods include Kissinger-Akahira-Sunose (KAS) [21,22], Flynn-Wall-Ozawa (FWO) [23,24] and Friedman [25] for calculations. The expressions of the calculation methods are as follows:

ln

b

i

T_a²_;i¼ln A_aR

EGð

a

Þ

E

RT_a_;i (5)

ln

b

i¼ln A_aR

EGð

a

Þ

5:33051:052 E

RT_a_;i (6)

ln

b

i

d

a

dt

a;i

!

¼lnðA

a

^fð

a

Þ Þ E

RT_a_;i (7)

whereT_a,i,A_a, are the absolute temperature, pre-exponential factor at the extent of conversiona, respectively.biis the heating rate.G(a) is the integral form of the reaction mechanism function. The subscriptiindicates different heating rate. By plotting lnbi/T_a,i2, lnbi, and ln[bi(da^/dt)a,i] against 1/T for the whole range of conversion (0e1), the activation energy can be obtained according to the corresponding slopes from Eqs.(5)e(7).

Currently, a number of methods exist for determining the reaction mechanism function, including Satva method, Bagchi method, the double extrapolation method, Malek method, Dolli- more method, CRTA method, etc. [26e28]. It should be noted that the formal assumptions and approximations of the mechanism function leads to systematic errors in all of these methods. Pro- fessor J. M. Criado and the International Society of Thermal Analysis have proposed that the Malek method can signiﬁcantly reduce the range of kinetic mechanism function, because there are no assumptions and approximate conditions in this method, so the ac- curacy of the mechanism function is effectively improved [28e32].

In this paper, the Malek method was employed to determine the thermal decomposition mechanism function of NC and mixture samples. The detail derivation process of Malek method is as follows:

Reaction rate equation and the Coats-Redfern equation are shown in Eqs.(4) and (8)

Gð

a

Þ ¼ ð^a

0

d

a

fð

a

^Þ^¼

ART² E

b

^exp

E

RT

(8)

According to Eqs.(4) and (8), it can be deduced that

Gð

a

^{Þ ¼}^ART_E

b

²^d

a

dt

1

fð

a

Þ (9)

whenaequals to 0.5, Eq.(9)can be written as

Gð0:5Þ ¼ART_0:5² E

b

d

a

dt

0:5

1

fð0:5Þ (10)

where T_0.5 and(da^/dt)0.5 are the temperature and reaction rate whenais 0.5, respectively.

Dividing Eq.(9)by Eq.(10)gives the expression fory(a⁾ yð

a

^{Þ ¼}_T^T

0:5

2 da dt

da dt

0:5

¼ fð

a

ÞGð

a

Þ

fð0:5ÞGð0:5Þ (11)

Here,y(a) is the deﬁnition function. There are 19 commonly used kinetic mechanism functions, corresponding to different mechanism model [33]. The mechanism function is shown in Table 2.

3.1. The most probable f(a) using the y(a^{) -}astandard curve The standard data consisting of ai,f(ai) (i ¼ 1,2,3,…, j) and a¼0.5,f(0.5) were substituted into Eq.(11). And it was obtained that the relationship curve between y(a^{) against} a^{, which is} regarded as the standard curve [33].

The experimental data consisting ofai,T_i, (da^/dt)I(i¼1,2,3,…,j) anda0.5,T0.5, (da^/dt)0.5were substituted into Eq.(11). It was gained that the relationship curvey(a^{) against}a, which is regarded as the experimental curve.

3.2. The most probable f(a) using the Z(a^{) -}astandard curve In non-isothermal experiment, the relationship between sample temperature and experimental time is as follows:

T¼T₀þ

b

^t ⁽¹²⁾

whereT0is the initial temperature of sample,K;tis experimental time, min.

As shown in Eq. (13), E/RT, which is common in Arrhenius equation, has deﬁned asu

u¼E=RT (13)

The temperature integral equation ð^T

0

e^udT¼E

RPðuÞ ¼E R

e^u

u

p

ðuÞ (14)

According to Eqs.(4) and (12)e(14), it is known that

Gð

a

Þ ¼ ð^a

0

d

a

fð

a

^Þ^¼

A

b

ð^T

0

e^RT^EdT¼AE

b

^R

ð^u

∞

e^u

u² du¼ AE

b

^R^PðuÞ

¼AE

b

^R

e^u

u

p

ðuÞ (15)

Table 1

Samples nomenclature and inorganic salt content in the samples.

Samples Additives The purity of additives/% The concentration of additives/%

NC-P None None None

NC-C CaCO3 99.0% 5.0

NC-L Li2CO3 99.99% 5.0

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d

a

dt¼

b

T

p

^ðuÞ^f^ð

a

ÞGð

a

Þ (16)

wherep(u) is the rational function in the temperature integral Eq.

(14), and its expression isp^(u)¼1/(uþ2).

According to Eq.(16), the expression ofZ(a^{) is}

Zð

a

^{Þ ¼}

p

^ðuÞ^d_dt^a^T

b

^¼^f^ð

a

^ÞGð

a

^Þ ⁽¹⁷⁾

The standard data that the data areai,Z(ai) (i¼1,2,3,…,j) are substituted into Eq. (17)and the graph is made to obtain in the Z(a⁾earelationship curve, which is regarded as the standard curve to obtain the standard proﬁle [33].

The experimental data that the data are b^, aⁱ^, ^Tⁱ^{, (d}a^/dt)ⁱ (i¼1,2,3,…,j) and theEvalue that obtained by FWO method are substituted into Eq.(17)for theZ(a⁾earelationship curve, which is the experimental curve [33].

4. Results and discussion

4.1. TG/DSC analysis

FromFigs. 2-4, it is shown that the thermal degradation pro- cesses of NC and its mixtures have a main peak, and the temperature of the main peak increases with the increase of heating rate.

For example, the temperature corresponding to the maximum exothermic rate of NC-P are 193.98, 204.00 and 211.02C, respectively. It can be seen fromFig. 5that the heatflow of NC-P pyrolysis increases with the increase of heating rate, and the values are in turn: 2.45, 7.09, 13.85 W/g. CombiningFigs. 5and6andTable 3, it is found that with the increasing of heating rate, CaCO3has more and more obvious influence on the thermal degradation of NC. Com- binedFigs. 5-8andTable 3, it is found that Li2CO3 has a certain inhibitory effect on the heatflow during NC pyrolyzes at all heating rates, the heat releases during NC-L thermolysis are 1 time, 0.735 times and 0.896 times of those of NC-P, respectively. At the same heating rate, the TG curves of these samples are similar, but the DSC curves of these samples are not similar. When the heating rate is 2 K/min, the peak values of DSC curves of NC-C are much higher than those of NC-P and NC-L, and the curves of the latter two are relatively similar; when the heating rate is increased, the peak Table 2

Commonly used reaction models describing the pyrolysis process of matters.

Reaction model Model code f(a) G(a)

P1 Power law 4a^3/4 a^1/4

P4 Power law 2/3a^1/2 a^3/2

R1 Zero-order 1 А

R2 Phase-boundary controlled reaction 2(1-a)^1/2 [1-(1-a)^1/2]

R3 Phase-boundary controlled reaction 3(1-a)^2/3 [1-(1-a)^1/3]

F1 First order (1-a⁾ ^-ln(1-a⁾

F3/2 Three-halves order (1-a)^3/2 2[(1-a)^1/2e1]

F2 Second order (1-a)² (1-a)¹-1

F3 Third-order (1-a)³ (1/2)[ (1-a)²-1]

A3/2 Avrami‒Erofeev (n¼1.5) (3/2) (1-a)[-ln(1-a)]^1/3 [-ln(1-a)]^2/3

A2 Avrami‒Erofeev (n¼2) 2(1-a)[-ln(1-a)]^1/2 [-ln(1-a)]^1/2

A3 Avrami‒Erofeev(n¼3) 3(1-a^)[-ln(1-a^)]^2/3 ^[-ln(1-a^)]^1/3

A4 Avrami‒Erofeev (n¼4) 4(1-a)[-ln(1-a)]^3/4 [-ln(1-a)]^1/4

D1 One-dimensional diffusion 1/2a a²

D2 Two-dimensional diffusion 1/[-ln(1-a)] (1-a) ln(1-a)þa

D3 Three-dimensional diffusion 3(1-a)^1/3/2[(1-a)^1/3e1] [1-(1-a)^1/3]²

D4 Four-dimensional diffusion 3/2[(1-a)^1/3e1] (1-2a/3) - (1-a)^2/3

Fig. 2.The TG and DTG curves of NC-P at different heating rates were compared. Fig. 3.The TG and DTG curves of NC-C at different heating rates were compared.

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values of DSC curve of NC-L are much smaller than those of the other two, and the heat releases during NC-C pyrolyzes are always higher than that of NC-P. To sum up, it can be presumed that in the case of non-isothermal condition, CaCO3 can catalyze the exothermic of NC and Li2CO3 can hinder the heat release of NC thermolysis.

It can be found fromTable 3that the presence of inorganic salts can change the onset temperature of the thermal degradation process of NC, such as the presence of CaCO3 makes the onset degradation temperature of NC decreases at all heating rates (see Fig. 6). On the other hand, Li2CO3makes that the onset degradation temperature of NC descends at a lower heating rate; whenb¼5 or 10 K/min, the onset degradation temperature is increased, which contributed to the thermal stability of NC. This is because Li2CO3

can effectively inhibit NOxreleased from NC by neutralizing the acids that accelerates the thermal degradation of OeNO₂bond (as shown in R1eR3) [15]. It's important to point out that the amount of NOxreleased from NC is independent of the thermal behavior of NC.

Li2CO3þH2O/2Li^þþHCO3þOH (R1)

HCO3þH2O/H2CO3þOH (R2)

RONO₂þH₂O/ROHþHNO₃ (R3)

Two iso-conversional methods, including KAS, FWO methods, were applied to calculate the thermal kinetics of sample pyrolysis.

The relationship between the activation energy (E) and the conversion rate (a) can be obtained by applying aforementioned kinetic methods. It can be seen fromFig. 9that the activation energy of NC-P increases with the growth of conversion, and the activation energy of NC-C decreases initially, and then remains roughly constant; and whena<0.68, the activation energy of NC-C is higher than that of NC-P, it is caused by that CaCO3stabilized by neutralizing acids. As compared to the previous samples, NC-L shows different patterns ofE-arelationship: with the growth of conversion, the activation energy of NC-L increasesﬁrstly, and then decreases; whena0.22, the values are smaller than that of NC-P;

whena>0.24, the activation energy value of NC-L is signiﬁcantly larger than that of NC-P. It indicates that Li2CO3 can reduce the thermal stability of NC.

As shown inTable 4, activation energy is calculated using the Kissinger method for each sample atTp, the peak temperature of the DTG curves, it is found that NC-L exhibits the highest activation energy, with a value of 261.14 kJ/mol; NC-C exhibits the lowest activation energy, with a value of 162.33 kJ/mol. Despite the fact Fig. 4.The TG and DTG curves of NC-L at different heating rates were compared.

Fig. 5.The DSC curves of NC-P at different heating rates were compared.

Fig. 6.The DSC curves of NC-C at different heating rates were compared.

Table 3

The characteristic temperatures and heatﬂow of the decomposition process obtained at different heating rates.

Samples To/C Tp/C Tf/C Heatﬂow/(W$g¹)

NC-P-2K 182.29 193.98 208.13 2.45

NC-P-5K 187.53 204.00 220.29 7.09

NC-P-10K 191.59 211.02 229.20 13.85

NC-C-2K 179.26 193.61 204.46 2.92

NC-C-5K 185.42 202.96 216.08 7.31

NC-C-10K 178.77 211.41 229.54 14.90

NC-L-2K 181.86 191.22 204.49 2.45

NC-L-5K 189.78 198.60 211.35 5.21

NC-L-10K 204.43 206.73 215.49 12.41

Note:To,Tp,Tfare the onset temperature of experiment starting, the temperature corresponding to the maximum reaction rate, theﬁnal temperature of experiment end, respectively.

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that the values of activation energy are different from those shown inFig. 9, it can be pointed out that the sample containing Li2CO3has the largest value of activation energy in the whole process.

4.2. Determination of mechanism function of thermal decomposition

4.2.1. Determination of the most probable mechanism function of thermal decomposition

The Malek method can be used to determine the category by comparing they(a⁾ea^and^Z(a⁾eaof the experimental data with the standard curve, or they(a) shape and eigenvalues can be used to infer the most probablef(a). In this paper, the latter approach is taken.

The FWO method was applied to calculate theEvalues of each sample. Based on the TG data, the reaction rate da^/dt,^y(a^{) and the} corresponding temperatureTwere calculated byEq. (11) andZ(a⁾ was obtained by Eq.(17). The experimental curves ofy(a⁾ea^and Z(a⁾eaat various heating rates are shown inFig. 10.

The curves obtained from the experimental data are used toﬁnd

the eigenvaluesaManda^∞P, both of which are the correspondinga at the peak of they(a⁾ea^and^Z(a⁾eacurves, respectively,apis thea at the peak of the DSC curve. The most probable mechanismf(a⁾ can be inferred from these parameters.Table 5presents the characteristic parameters derived from theﬁtted curves.

Based on the criterion in Ref. [33] combined with the data in Table 5, it can be inferred that the decomposition of these samples conforms to the Sestak-Berggern mechanism model, which indicates that the decomposition of these samplesﬁts the autocatalytic pyrolysis model. The mechanism function of the S.B. model can be described asf(a⁾¼a^m^(1-a⁾ⁿ^.

4.2.2. Determination of the kinetic parameters m, n

The parameters,mandn, can be determined by the following equation

ln d

a

dte^u

¼lnAþnln½

a

^sð1

a

Þ (18) Here, the parameters,nandm, can be obtained by plotting lnh

da dte^ui against ln½a^sð1aÞ; the parameter,s, can be described by Eq.(19) s¼m

n¼

a

M

1

a

M

(19) The result is shown inTable 6.

Therefore, the thermal decomposition mechanism of NC-P, NC- C, NC-L are.

fð

a

Þ ¼

a

^1:42501ð1

a

Þ^1:81018 (20)

fð

a

Þ ¼

a

^1:31036ð1

a

Þ^1:79515 (21)

fð

a

Þ

a

^1:27651¼ ð1

a

Þ^1:80185 (22)

Fig. 7.The DSC curves of NC-L at different heating rates were compared.

Fig. 8.Whenb¼2K/min, the TG and DSC curves of samples were compared.

Fig. 9.TheE-arelation of each sample was calculated by FWO and KAS method.

Table 4

Activation energy for each sample was calculated by the Kissinger method [22].

Samples NC-P NC-C NC-L

E/(kJ$mol¹) 169.04 162.33 261.47

R² 0.99892 0.99822 0.97672

Note: R²is the degree of linearﬁtting.

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Fig. 10illustrates the comparison of they(a⁾eacurves obtained from Eqs. (20)-(22) with those obtained from the experimental data.

4.3. The limitation of the research

Although the Malek method has the advantages of avoiding the

trouble of tryingf(a) one by one and the effect of KCE whenE,Aand f(a⁾are obtained simultaneously, the limitations of this paper are respectively.

Firstly, in the previous study, the scholars found that the pyrolysis of NC was affected by the n-order model, the autocatalytic reaction model [34e38] and the modulation function [39,40].

However, both thenth-order model and the autocatalytic model are not represented in this paper, this may be due to the fact that the addition of inorganic salts may lead to the ratio of nth-order model and the autocatalytic model. This paper assumes in the theoretical part only for the autocatalytic model, which is the main problem.

Secondly, in the actual storage, inorganic salts are usually added to NC-humectants system to achieve a better stable effect. In this paper, the authors only consider the reaction between inorganic salts and NC and ignore the situation in the actual storage. The authors plan to investigate the mechanism and decoupling analysis of inorganic salt in NC-humectants in the next experiment to explore the optimal ratio of inorganic salt in this system.

5. Conclusions

The thermal stability, reaction mechanism of NC with different inorganic salts and pure NC were investigated using a TG/DSC apparatus. The main conclusions from the analysis can be sum- marized as follows:

(1) The characteristic temperatures of NC and its mixtures indicate that the presence of inorganic salt can have some effect on the thermal degradation of NC. The TG curves of samples heated at different heating rates were analyzed using the FWO and KAS method, and it was found that: the activation energy value of NC-L increasedﬁrst, followed by a decline, and whena<0.24, the values are less than that of NC-P. In other words, with the presence of Li₂CO₃, the thermal stability of NC was reduced. The activation energy values of NC-C declined and then enhanced with the growth ofa

Fig. 10.Curves obtained by Malek method of all samples. Note: Theﬁgures in the left row show they(a)eacurves obtained from experimental data and theoretical formulas, and theﬁgures in the right row show theZ(a)eacurves; from top to bottom, the pictures in each row are the experimental curves of NC-P, NC-C, NC-L respectively.

Table 5

Characteristic parameters of each sample.

Samples b/(K$min¹) aM a^∞P ap

NC-P 2 0.46 0.40 0.37

5 0.42 0.42 0.46

10 0.44 0.44 0.57

NC-C 2 0.40 0.40 0.41

5 0.44 0.44 0.52

10 0.42 0.42 0.47

NC-L 2 0.38 0.38 0.47

5 0.44 0.44 0.48

10 0.42 0.42 0.38

Table 6

Kinetic parameters were calculated at different heating rates.

Samples b/(K$min¹) n m R²

NC-P 2 1.80693 1.53924 0.89476

5 1.80804 1.30927 0.92524

10 1.81557 1.42652 0.93881

average 1.81018 1.42501 \

NC-C 2 1.53782 1.02521 0.60325

5 1.94303 1.52667 0.93157

10 1.90460 1.37919 0.88691

average 1.79515 1.31036 \

NC-L 2 1.76610 1.08245 0.93353

5 1.81271 1.42427 0.94040

10 1.82674 1.32281 0.94253

average 1.80185 1.27651 \

(8)

and was higher than that of NC-P whena<0.68. Based on the Kissinger method, it was found that NC-L had the highest activation energy, while NC-C had the lowest.

(2) The kinetics of the exothermic decomposition of NC-P, NC-C, NC-L were studied using DSC and TG data using the Malek method, which revealed theSestak-Berggren model to be the most appropriate model for describing the pyrolysis process of these samples, and reaction mechanism equations for each sample are as follows: f(a⁾ ¼ a^1.425009^(1-a⁾^1.81018^, f(a⁾ ¼ a^1.31036^(1-a⁾^1.79515^, ^f(a⁾ ¼ a^1.29633^(1- a⁾^1.32289,respectively.

Declaration of competing interest

The authors declare that they have no known competing ﬁnancial interests or personal relationships that could have appeared to inﬂuence the work reported in this paper.

Acknowledgments

The authors would like to thank the National Natural Science Foundation of China (NSFC, Grants No. 52176114 and 52111530091) and Jiangsu Funding Program for Excellent Postdoctoral Talent.

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