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Size-dependent decomposition temperature of nanoparticles: A theoretical and experimental study
Physica B 454 (2014) 175–178
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Size-dependent decomposition temperature of nanoparticles: A theoretical and experimental study Shanshan Wang, Zixiang Cui, Xiaoyan Xia, Yongqiang Xue n Department of Applied Chemistry, Taiyuan University of Technology, Taiyuan 030024, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 25 May 2014 Received in revised form 17 July 2014 Accepted 19 July 2014 Available online 12 August 2014
Thermal decomposition of nanomaterials is often involved in the preparation and applications of nanomaterials, of which decomposition temperature can be surprisingly different from corresponding bulk materials. However, there is a lack of theoretical and experimental investigation on the relationship between the decomposition temperature and nanoparticle size. In present study, the relation between the decomposition temperature and the size of nanoparticles was derived theoretically, which indicates that the decomposition temperature decreases with the size of the nanoparticles decreasing, and there is a linear relationship between the decomposition temperature and the reciprocal of the particle size when the radius is bigger than 10 nm. Thermal decomposition experiments of nano-calcium carbonate with different sizes were carried out by thermo-gravimetric (TG), the onset decomposition temperatures (Tonset) and the temperature of the DTG peaks (Tmax) were measured and both of them present well liner relationship with the reciprocal of the particle size. The depress regularity of the onset decomposition temperature of nanocalcium carbonate agrees with the derived thermodynamic relationship. This thermodynamic theory provides a quantitative description for the decomposition temperature of nanoparticles, also it can be used to predict and explain the thermal decomposition behavior of nanomaterials. & 2014 Elsevier B.V. All rights reserved.
Keywords: Nanoparticles Particle sizes Decomposition temperature Size effect Thermodynamics
1. Introduction At the present, nano-sized materials have been widely used in many areas due to their outstanding properties. During the preparation and applications of nanomaterials, thermal decomposition is often involved, such as the thermal decomposition of nano-sized energetic materials [1,2], chromium(III) carboxylates catalyst [3], polymers [4,5] and drug delivery material [6]. Also it is involved in the calcination of precursors for preparing superconductors [7]. Due to the surface effect is so great that the decomposition temperature of the nanoparticles has largely changed compared with the corresponding bulk material. So far, much attention has been paid to the effect of particle size on the decomposition temperature. Mulokozi et al. [8] studied the influence of sample size on the thermal decomposition of K2C2O4, and their work showed that the characteristic temperatures (the reaction start, peak and end temperatures) are markedly reduced by fine grinding. Markmaitree et al. [9] investigated the decomposition of lithium amide (LiNH2) with and without high-energy ball milling and obtained that when the particle size decreased from block to the scale of n Correspondence to: Department of Applied Chemistry, Taiyuan University of Technology, 79 YingZe West Street, Wanbailin District, Taiyuan 030024, PR China, Tel./fax.: þ86 351 6014476. E-mail address: [email protected] (Y. Xue).
http://dx.doi.org/10.1016/j.physb.2014.07.058 0921-4526/& 2014 Elsevier B.V. All rights reserved.
500 nm to 8 mm the onset temperature for the decomposition of LiNH2 reduced from 120 1C to room temperature. Tan et al. [10] investigated the thermal decomposition of nano-TATB ranging from 18 nm to 50 nm by TG and DSC, their study indicated that the thermal decomposition occurred in the range of 361.5– 385.0 1C and its peak temperature was 373.7 1C with a decrease of approximately 7 1C compared with original TATB. Sovizi et al. [11] investigated the thermal stability of nano-sized and micronsized nitrocellulose samples by TG–DTG analysis, which showed that the decomposition temperature of the nano-sized samples is lower than that of micron-sized samples and it decreases with the reduction of the particle size. Song et al. [12] studied the thermal decomposition of nano-RDX, the results indicated that the peak temperature for thermal decomposition of nano-RDX decreased by 10.74 1C compared with those of the raw RDX. Fathollahi et al. [13] investigated the particle size effect on the decomposition of energetic materials by DSC, their work showed that the decomposition temperatures of the smaller particles were lower than those of the larger ones, and as the particle size of HMX increased the thermal decomposition temperature of HMX enhanced. The thermal decomposition of nano-sized calcium carbonate had been studied [14–18], and the thermal analyses indicated that the decomposition temperature of nano-calcium carbonate was lower than that reported for bulk carbonate and the decomposition temperature decreases gently in the scope of micron-sized
176
S. Wang et al. / Physica B 454 (2014) 175–178
diameter, but decreases sharply when the average diameter decreases from micron to nanometer region. From all the study results mentioned above, it is obvious that particle size has remarkable effect on the decomposition temperature. However, there is a lack of theoretical and experimental investigation on the relationship between decomposition temperature and nanoparticle size. In the present paper, the relation between the decomposition temperature and the nanoparticle size is derived by thermodynamic theory; furthermore, the decomposition temperatures of nano-calcium carbonates with different sizes are investigated experimentally; then the regularity and the extent about the size influence on the decomposition temperature is discussed.
2. Theoretic analysis for decomposition temperature of nanoparticles For a dispersed system consisting of N components with B ¼1, 2,…, N, the molar Gibbs free energy change for a chemical reaction in dispersed system is made of bulk phase Δr Gbm (the superscript b denotes bulk quantities) and surface phase Δr Gsm [19] (the superscript s denotes surface quantities),
Δr G m ¼ Δ
b r Gm þ
Δ
s r Gm :
Δr Gbm ¼ Δr Hbm T Δr Sbm ;
ð2Þ
and
B
2νB σ B M B 2νB σ B V mB ¼∑ ; ρB rB rB B
ð3Þ
where Δr H bm and Δr Sbm are the molar reaction enthalpy and molar reaction entropy corresponding to the bulk phase in reaction systems respectively, νB , σ B , M B , V mB , ρB and r B denote the stoichiometric number, surface tension, molar mass, molar volume, density and radius of component B, respectively. Substituting Eqs. (2) and (3) into Eq. (1), it becomes 2ν σ V Δr Gm ¼ Δr Hbm T Δr Sbm þ ∑ B B mB : rB B
ð4Þ
For a decomposition reaction of nanoparticles, the nanoparticles can be decomposed only when Δr Gm r 0 under the conditions of constant temperature and pressure. Thus the lowest decomposition temperature appears when Δr Gm ¼ 0 and Eq. (5) is obtained
Δr H bm T Δr Sbm þ ∑ B
2νB σ B V mB ¼ 0; rB
ð5Þ
As the product formed at the very beginning of the decomposition reaction was so little that it can be neglected. Thus, only the items of the reactants are left in the sum of Eq. (5). Therefore, Eq. (5) can be simplified as
Δr Hbm T Δr Sbm þ
2νσ V m ¼ 0: r
ð6Þ
As we know Δr H bm , Δr Sbm and V m are functions of T, and σ is a function of T and r, namely σ ðT; rÞ, if T is regarded as an intermediate variable, the relation between the decomposition temperature and the radius of nanoparticles can be derived from the partial derivative of Eq. (6) against r, as follows ∂Δr H bm ∂T
! p
∂T ∂r
p
Δr Sbm
∂Δr H bm ∂T ∂Δr Sbm ∂T
∂T ∂r
T p
∂Δr Sbm ∂T
! p
∂T ∂r
p
þ 2ν
∂ σV m ¼ 0; r ∂r p
ð7Þ
! ¼ ΔC p;m ;
ð8Þ
p
! ¼
ΔC p;m T
p
;
ð9Þ
and
h ∂σ ∂V ∂T i ∂σ ∂T m ∂T p ∂r p V m þ ∂r p V m þ ∂T p ∂r σ r σ V m ∂ σV m ¼ ; ∂r r r2 p ð10Þ
where ΔC p;m is the difference between the molar heat capacities of the product and reactant at a constant pressure. Eqs. (7)–(10) can be combined into h i 2νV m σ r ∂∂rσ p ∂T ¼ ; ð11Þ ∂r p rF r 2 Δr Sbm where " F ¼ 2ν
ð1Þ
In Eq. (1),
Δr Gsm ¼ ∑
since
∂σ ∂T
Vm þ p
# ∂V m σ : ∂T p
ð12Þ
Eq. (11) is the exact differential relation between the decomposition temperature and the radius of the particle, which can be solved by numerical differentiation. According to the Tolman equation σ ¼ σ 1 =ð1 þ 2δ=rÞ (σ 1 is surface tension of the corresponding bulk substance, δ is the Tolman parameter which is on the order of 10 10 m) [20], the size effect of surface tension becomes notable only when the size is less than 10 nm [21]. Thus, the effect of the radius on the surface tension can be neglected when the particle size is more than 10 nm. Then, Eq. (11) can be approximated as ∂T 2νσ V m ¼ : ð13Þ ∂r p rF r 2 Δr Sbm Integrating Eq. (13) with radius of particle from 1 to r and temperature from T b decomposition temperature of the block particle to T decomposition temperature of the nanoparticles, one gets ! 2νσ V m F b T T ¼ ln 1 : ð14Þ F r Δr Sbm From Eq. (12), we can estimate the order of magnitudes for F with ð∂σ =∂TÞp is on the order of 10 4 [22], Vm 10 5 [23], ð∂σ =∂TÞp 10 9 to 10 10 [23] and σ 100 [24] for general solid. As a result, the order of magnitude for F is approximate to 10 9. In addition, the order of magnitudes for Δr Sbm in Eq. (14) is 102 (on the premise of v¼ 1) [25]. Therefore, for a nanoparticle (r is on the order of 10 8) the value of F=ðr Δr Sbm Þ in Eq. (14) is approximate to 0. Consequently, according to the expression of equivalent infinitesimal, Eq. (14) can be simplified to T Tb ¼
2νσ V m r Δr Sbm
:
ð15Þ
It can be seen from the above formula that the decomposition temperature of nanoparticles depends on not only the properties of the bulk phase (Tb, Δr Sbm ) but also the particle radius and the surface tension. From what had been mentioned above that when the radius is more than 10 nm, effect of the radius on the surface tension can be ignored. And since the stoichiometric number v for reactant is negative, so νσ V m =ðr Δr Sbm Þ o0 one can educe from Eq. (15) that the decomposition temperature of nanoparticle is lower than that of the block substance, and that the decomposition
S. Wang et al. / Physica B 454 (2014) 175–178
temperature drops with the particle radius decreasing. There is an approximate linear relationship between the decomposition temperature and reciprocal of the radius. We can estimate the order of magnitude for ΔT (ΔT ¼ T T b ) of nano-carbonate. Based on the order of magnitudes V m , σ and Δr Sbm , when r is on the order of 10 6 m, ΔT is on the order of 10 1 K, in other words, the effect of particle size on decomposition temperature can be neglected; when r is on the order of 10 8 m and 10 9 m, ΔT is on the order of 101 K to 102 K, namely, the effect of particle size on the decomposition temperature becomes obvious.
3. Experimental 3.1. Preparation of nano-CaCO3 The nano-calcium carbonates were prepared by double decomposition method. Dissoluble calcium salt was mixed with ammonium hydroxide by adding dispersing agent, and reacted under CO2 flow at certain rate (2–8 mL/min) at 20 1C. Samples obtained were filtrated and washed with distilled water, and then dried under vacuum.
(JCPDS Card NO. 5-586). The main characteristic peaks at 23.11, 29.41, 36.21, 39.61, 43.21, 47.51 and 48.51 can be assigned to the (0 1 2), (1 0 4), (1 1 0), (1 1 3), (2 0 2), (0 1 8) and (1 1 6) planes of crystal structure, respectively. In addition, no other peak observed suggest that the samples were pure. The average diameters of the nanoparticles were calculated by the Scherrer formula. 4.2. Decomposition temperature of nano-CaCO3 The TG and DTG curves of the nano-calcium carbonate with different sizes measured by thermogravimetry are presented in Figs. 2 and 3. The TG and DTG curves show that the thermal decomposition of nano-calcium carbonate occurred at the temperature ranging from 650 1C to 800 1C. The onset decomposition temperature and the temperature of the DTG peaks of nano-calcium carbonate with different size were obtained after the analysis of the TG and DTG
3.2. Characterization of nano-CaCO3 The as-prepared samples were examined using a Germany Bluker D8 Advance Powder diffractometer (Cu Ka, λ ¼0.154178 nm). Particles sizes of samples were calculated by Scherrer formula based on the half peak width of characteristic diffraction peaks. 3.3. Thermal measurement Thermogravimetric analysis (TG and DTG) of the nano-CaCO3 were carried out using a thermal analysis system (WACT-2A). The rate of heating of the samples was kept at 15 1C/min under N2 flow at 60 mL/ min. CuSO4 5H2O was used as the calibrating standard material.
4. Results and discussion 4.1. Average size of nano-CaCO3
Fig. 2. TG curves of nano-CaCO3 with different radii.
Fig. 1 shows the XRD patterns of the nano-CaCO3 (a, b, c, d and e). The XRD patterns indicate that all samples exhibit a calcite structure
Fig. 1. XRD patterns of the as-synthesized nano-CaCO3 with different sizes: (a) 18.1 nm, (b) 22.4 nm, (c) 26.2 nm, (d) 33.5 nm, and (e) 44.1 nm.
177
Fig. 3. DTG curves of nano-CaCO3 with different radii.
178
S. Wang et al. / Physica B 454 (2014) 175–178
Table 1 The decomposition temperatures of nano-calcium carbonate with different radii. r/nm
18.1
22.4
26.2
33.5
44.1
r 1/nm 1 T onset /1C T max /1C
0.055 658.5 683.1
0.045 678.2 707.0
0.038 685.5 734.9
0.030 714.6 789.3
0.023 725.0 796.7
Table 2 The extrapolated values for nano-calcium carbonate and the literature values for block calcium carbonate. Extrapolated values/1C
The literature value (T onset )/1C
T onset
T max
773.0
888.9
825
5. Conclusions This study reveals that the size of nanoparticles has significant effect on the onset decomposition temperature and the peak temperature. With the size of the nanoparticles decreasing, the onset decomposition temperature and the peak temperature drop, and there is a linear relationship between them and the reciprocal of particle size. The experimental results are consistent with this thermodynamic theory for decomposition of nanoparticles. The thermodynamic theory provides a quantitative description for the decomposition temperature of nanoparticles, also it can be used to predict and explain the thermal decomposition behavior of nanomaterials.
Acknowledgements
Fig. 4. The relation between the decomposition temperatures (T onset and T max ) and the reciprocal of particle radii of nano-CaCO3.
curves. The onset decomposition temperature (T onset ) of nanoparticles was selected at a constant weight loss of 5% [26]. The temperatures of the DTG peaks (T max ) refer to that the decomposition rate reached the maximum value. The data of T onset and T max are listed in Table 1. It can be seen from Table 1 that the effect of particle size on the decomposition temperature is noticeable and the decomposition temperature drops with the radius decreasing, which is consistent with the literatures reported [14–18]. If one plot the decomposition temperatures (T onset and T max ) against the reciprocal of particle radius, Fig. 4 will be obtained. Fig. 4 indicates that the particle size has significant influence to the onset decomposition temperature and the peak temperature, both of them reduce with the radius decreasing and there is a well linear relationship between them and the reciprocal of radius. The depress regularity of the onset decomposition temperature is consistent with the derived thermodynamic equation ahead. We can educe from Eq. (15) that the decomposition temperature T is equal to T b when the size approaches infinity. That is to say, the decomposition temperature of the block calcium carbonate can be obtained by extrapolating the radius to infinity (r-1), namely, r 1 ¼ 0. The extrapolated results and the literature value of decomposition temperatures [27] are given in Table 2. It can be seen from Table 2 that the experimental onset temperature for block calcium carbonate obtained by extrapolating is close to the literature value, and it is indicated that the regularity of the linear relation between the decomposition temperature and the reciprocal of radius is reliable.
This work was supported by the National Natural Science Foundation of China (no. 21373147) and by the Program for the Top Science and Technology Innovation Teams of Higher Learning Institutions of Shanxi Province of China. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
[27]
Y. Bayat, V. Zeynali, J. Energetic Mater. 29 (2011) 281. G. Yang, F. Nie, H. Huang, Propellants Explos. Pyrotech. 31 (2006) 390. B.P. Baranwal, T. Fatma, A. Varma, Asian J. Chem. 22 (2010) 5865. L. Aboutorabi, A. Morsali, Inorg. Chim. Acta 363 (2010) 2506. B.P. Baranwal, T. Fatma, A. Varma, J. Mol. Struct. 920 (2009) 472. J. Wang, J. Sun, F. Wang, Appl. Surf. Sci. 274 (2013) 314. N.R.M. Suib, P.N. S.M. Mahmud, S.Y.S. Yahya, M.M. Jusoh, I. Hamadneh, Adv. Mater. Res. 832 (2014) 195. M. Mulokozi, E. Lugwisha, Therm. Anal. 37 (1991) 583. T. Markmaitree, R. Ren, L.L. Shaw, J. Phys. Chem. B 110 (2006) 20710. X.R. Tan, X.H. Duan, C.H. Pei, Nano 8 (2013) (1350055/1-1350055/). M.R. Sovizi, S.S. Hajimirsadeghi, B. Naderizadeh, J. Hazard. Mater. 168 (2009) 1134. X. Song, F. Li, J. Zhang, Chin. J. Explos. Propellants 6 (2008) 001. M. Fathollahi, S.M. Pourmortazavi, S.G. Hosseini, J. Energetic Mater. 26 (2008) 52. D.X. Li, H.Y. Shi, J. Deng, Y.Z. Xu, J. Zhejiang Univ. Sci. A 4 (2003) 363. Y. Tang, Y. Li, J. Song, Z. Pan, Acta Phys. Chim. Sin. 23 (2007) 717. J.M. Criado, A. Ortega, Thermochim. Acta 195 (1992) 163. R.J. Liu, J.F. Chen, F. Guo, J. Yun, Z.G. Shen, Chin. J. Chem. Eng. 11 (2003) 302. J.F. Chen, Z.Q. Jia, Y.H. Wang, C. Zheng, Chin. J. Chem. Phys. 10 (1997) 457. Y.Q. Xue, B.J. Gao, J.F. Gao, J. Colloid Interface Sci. 191 (1997) 81. V.M. Fokin, E.D. Zanotto, J. Non-Cryst. Solids 265 (2000) 105. Y.Q. Xue, X.C. Yang, Z.X. Cui, W.P. Lai, J. Phys. Chem. B 115 (2010) 109. Z.H. Jiang, D.Z. Sun, X.J. Deng, The Applied Surface Chemistry Technology, Harbin Industry University Press, Harbin (2000) 30–31. H.P. Robert, Perry’s Chemical Engineering’s Handbook, sixth ed., Chemical Engineering Press, 1992 (14,148). X.C. Fu, W.X. Shen, T.Y. Yao, Physical Chemistry, Higher Education Press, Beijing (1990) 164–165 (888–889). A. Peter, Physical Chemistry, Oxford press, New York, 1994 (Chapter10). X. Shen, The Differential Thermal and Thermogravimetry Analysis and the Nonisothermal Kinetic of Solid State Reaction, Metallurgy Industry Press, Beijing (1995) 75–76. J.A. Dean, Lange’s Handbook of Chemistry, McGraw-Hill Co., New York (1999) 9.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Size-dependent decomposition temperature of nanoparticles: A theoretical and experimental study Shanshan Wang, Zixiang Cui, Xiaoyan Xia, Yongqiang Xue n Department of Applied Chemistry, Taiyuan University of Technology, Taiyuan 030024, PR China
art ic l e i nf o
a b s t r a c t
Article history: Received 25 May 2014 Received in revised form 17 July 2014 Accepted 19 July 2014 Available online 12 August 2014
Thermal decomposition of nanomaterials is often involved in the preparation and applications of nanomaterials, of which decomposition temperature can be surprisingly different from corresponding bulk materials. However, there is a lack of theoretical and experimental investigation on the relationship between the decomposition temperature and nanoparticle size. In present study, the relation between the decomposition temperature and the size of nanoparticles was derived theoretically, which indicates that the decomposition temperature decreases with the size of the nanoparticles decreasing, and there is a linear relationship between the decomposition temperature and the reciprocal of the particle size when the radius is bigger than 10 nm. Thermal decomposition experiments of nano-calcium carbonate with different sizes were carried out by thermo-gravimetric (TG), the onset decomposition temperatures (Tonset) and the temperature of the DTG peaks (Tmax) were measured and both of them present well liner relationship with the reciprocal of the particle size. The depress regularity of the onset decomposition temperature of nanocalcium carbonate agrees with the derived thermodynamic relationship. This thermodynamic theory provides a quantitative description for the decomposition temperature of nanoparticles, also it can be used to predict and explain the thermal decomposition behavior of nanomaterials. & 2014 Elsevier B.V. All rights reserved.
Keywords: Nanoparticles Particle sizes Decomposition temperature Size effect Thermodynamics
1. Introduction At the present, nano-sized materials have been widely used in many areas due to their outstanding properties. During the preparation and applications of nanomaterials, thermal decomposition is often involved, such as the thermal decomposition of nano-sized energetic materials [1,2], chromium(III) carboxylates catalyst [3], polymers [4,5] and drug delivery material [6]. Also it is involved in the calcination of precursors for preparing superconductors [7]. Due to the surface effect is so great that the decomposition temperature of the nanoparticles has largely changed compared with the corresponding bulk material. So far, much attention has been paid to the effect of particle size on the decomposition temperature. Mulokozi et al. [8] studied the influence of sample size on the thermal decomposition of K2C2O4, and their work showed that the characteristic temperatures (the reaction start, peak and end temperatures) are markedly reduced by fine grinding. Markmaitree et al. [9] investigated the decomposition of lithium amide (LiNH2) with and without high-energy ball milling and obtained that when the particle size decreased from block to the scale of n Correspondence to: Department of Applied Chemistry, Taiyuan University of Technology, 79 YingZe West Street, Wanbailin District, Taiyuan 030024, PR China, Tel./fax.: þ86 351 6014476. E-mail address: [email protected] (Y. Xue).
http://dx.doi.org/10.1016/j.physb.2014.07.058 0921-4526/& 2014 Elsevier B.V. All rights reserved.
500 nm to 8 mm the onset temperature for the decomposition of LiNH2 reduced from 120 1C to room temperature. Tan et al. [10] investigated the thermal decomposition of nano-TATB ranging from 18 nm to 50 nm by TG and DSC, their study indicated that the thermal decomposition occurred in the range of 361.5– 385.0 1C and its peak temperature was 373.7 1C with a decrease of approximately 7 1C compared with original TATB. Sovizi et al. [11] investigated the thermal stability of nano-sized and micronsized nitrocellulose samples by TG–DTG analysis, which showed that the decomposition temperature of the nano-sized samples is lower than that of micron-sized samples and it decreases with the reduction of the particle size. Song et al. [12] studied the thermal decomposition of nano-RDX, the results indicated that the peak temperature for thermal decomposition of nano-RDX decreased by 10.74 1C compared with those of the raw RDX. Fathollahi et al. [13] investigated the particle size effect on the decomposition of energetic materials by DSC, their work showed that the decomposition temperatures of the smaller particles were lower than those of the larger ones, and as the particle size of HMX increased the thermal decomposition temperature of HMX enhanced. The thermal decomposition of nano-sized calcium carbonate had been studied [14–18], and the thermal analyses indicated that the decomposition temperature of nano-calcium carbonate was lower than that reported for bulk carbonate and the decomposition temperature decreases gently in the scope of micron-sized
176
S. Wang et al. / Physica B 454 (2014) 175–178
diameter, but decreases sharply when the average diameter decreases from micron to nanometer region. From all the study results mentioned above, it is obvious that particle size has remarkable effect on the decomposition temperature. However, there is a lack of theoretical and experimental investigation on the relationship between decomposition temperature and nanoparticle size. In the present paper, the relation between the decomposition temperature and the nanoparticle size is derived by thermodynamic theory; furthermore, the decomposition temperatures of nano-calcium carbonates with different sizes are investigated experimentally; then the regularity and the extent about the size influence on the decomposition temperature is discussed.
2. Theoretic analysis for decomposition temperature of nanoparticles For a dispersed system consisting of N components with B ¼1, 2,…, N, the molar Gibbs free energy change for a chemical reaction in dispersed system is made of bulk phase Δr Gbm (the superscript b denotes bulk quantities) and surface phase Δr Gsm [19] (the superscript s denotes surface quantities),
Δr G m ¼ Δ
b r Gm þ
Δ
s r Gm :
Δr Gbm ¼ Δr Hbm T Δr Sbm ;
ð2Þ
and
B
2νB σ B M B 2νB σ B V mB ¼∑ ; ρB rB rB B
ð3Þ
where Δr H bm and Δr Sbm are the molar reaction enthalpy and molar reaction entropy corresponding to the bulk phase in reaction systems respectively, νB , σ B , M B , V mB , ρB and r B denote the stoichiometric number, surface tension, molar mass, molar volume, density and radius of component B, respectively. Substituting Eqs. (2) and (3) into Eq. (1), it becomes 2ν σ V Δr Gm ¼ Δr Hbm T Δr Sbm þ ∑ B B mB : rB B
ð4Þ
For a decomposition reaction of nanoparticles, the nanoparticles can be decomposed only when Δr Gm r 0 under the conditions of constant temperature and pressure. Thus the lowest decomposition temperature appears when Δr Gm ¼ 0 and Eq. (5) is obtained
Δr H bm T Δr Sbm þ ∑ B
2νB σ B V mB ¼ 0; rB
ð5Þ
As the product formed at the very beginning of the decomposition reaction was so little that it can be neglected. Thus, only the items of the reactants are left in the sum of Eq. (5). Therefore, Eq. (5) can be simplified as
Δr Hbm T Δr Sbm þ
2νσ V m ¼ 0: r
ð6Þ
As we know Δr H bm , Δr Sbm and V m are functions of T, and σ is a function of T and r, namely σ ðT; rÞ, if T is regarded as an intermediate variable, the relation between the decomposition temperature and the radius of nanoparticles can be derived from the partial derivative of Eq. (6) against r, as follows ∂Δr H bm ∂T
! p
∂T ∂r
p
Δr Sbm
∂Δr H bm ∂T ∂Δr Sbm ∂T
∂T ∂r
T p
∂Δr Sbm ∂T
! p
∂T ∂r
p
þ 2ν
∂ σV m ¼ 0; r ∂r p
ð7Þ
! ¼ ΔC p;m ;
ð8Þ
p
! ¼
ΔC p;m T
p
;
ð9Þ
and
h ∂σ ∂V ∂T i ∂σ ∂T m ∂T p ∂r p V m þ ∂r p V m þ ∂T p ∂r σ r σ V m ∂ σV m ¼ ; ∂r r r2 p ð10Þ
where ΔC p;m is the difference between the molar heat capacities of the product and reactant at a constant pressure. Eqs. (7)–(10) can be combined into h i 2νV m σ r ∂∂rσ p ∂T ¼ ; ð11Þ ∂r p rF r 2 Δr Sbm where " F ¼ 2ν
ð1Þ
In Eq. (1),
Δr Gsm ¼ ∑
since
∂σ ∂T
Vm þ p
# ∂V m σ : ∂T p
ð12Þ
Eq. (11) is the exact differential relation between the decomposition temperature and the radius of the particle, which can be solved by numerical differentiation. According to the Tolman equation σ ¼ σ 1 =ð1 þ 2δ=rÞ (σ 1 is surface tension of the corresponding bulk substance, δ is the Tolman parameter which is on the order of 10 10 m) [20], the size effect of surface tension becomes notable only when the size is less than 10 nm [21]. Thus, the effect of the radius on the surface tension can be neglected when the particle size is more than 10 nm. Then, Eq. (11) can be approximated as ∂T 2νσ V m ¼ : ð13Þ ∂r p rF r 2 Δr Sbm Integrating Eq. (13) with radius of particle from 1 to r and temperature from T b decomposition temperature of the block particle to T decomposition temperature of the nanoparticles, one gets ! 2νσ V m F b T T ¼ ln 1 : ð14Þ F r Δr Sbm From Eq. (12), we can estimate the order of magnitudes for F with ð∂σ =∂TÞp is on the order of 10 4 [22], Vm 10 5 [23], ð∂σ =∂TÞp 10 9 to 10 10 [23] and σ 100 [24] for general solid. As a result, the order of magnitude for F is approximate to 10 9. In addition, the order of magnitudes for Δr Sbm in Eq. (14) is 102 (on the premise of v¼ 1) [25]. Therefore, for a nanoparticle (r is on the order of 10 8) the value of F=ðr Δr Sbm Þ in Eq. (14) is approximate to 0. Consequently, according to the expression of equivalent infinitesimal, Eq. (14) can be simplified to T Tb ¼
2νσ V m r Δr Sbm
:
ð15Þ
It can be seen from the above formula that the decomposition temperature of nanoparticles depends on not only the properties of the bulk phase (Tb, Δr Sbm ) but also the particle radius and the surface tension. From what had been mentioned above that when the radius is more than 10 nm, effect of the radius on the surface tension can be ignored. And since the stoichiometric number v for reactant is negative, so νσ V m =ðr Δr Sbm Þ o0 one can educe from Eq. (15) that the decomposition temperature of nanoparticle is lower than that of the block substance, and that the decomposition
S. Wang et al. / Physica B 454 (2014) 175–178
temperature drops with the particle radius decreasing. There is an approximate linear relationship between the decomposition temperature and reciprocal of the radius. We can estimate the order of magnitude for ΔT (ΔT ¼ T T b ) of nano-carbonate. Based on the order of magnitudes V m , σ and Δr Sbm , when r is on the order of 10 6 m, ΔT is on the order of 10 1 K, in other words, the effect of particle size on decomposition temperature can be neglected; when r is on the order of 10 8 m and 10 9 m, ΔT is on the order of 101 K to 102 K, namely, the effect of particle size on the decomposition temperature becomes obvious.
3. Experimental 3.1. Preparation of nano-CaCO3 The nano-calcium carbonates were prepared by double decomposition method. Dissoluble calcium salt was mixed with ammonium hydroxide by adding dispersing agent, and reacted under CO2 flow at certain rate (2–8 mL/min) at 20 1C. Samples obtained were filtrated and washed with distilled water, and then dried under vacuum.
(JCPDS Card NO. 5-586). The main characteristic peaks at 23.11, 29.41, 36.21, 39.61, 43.21, 47.51 and 48.51 can be assigned to the (0 1 2), (1 0 4), (1 1 0), (1 1 3), (2 0 2), (0 1 8) and (1 1 6) planes of crystal structure, respectively. In addition, no other peak observed suggest that the samples were pure. The average diameters of the nanoparticles were calculated by the Scherrer formula. 4.2. Decomposition temperature of nano-CaCO3 The TG and DTG curves of the nano-calcium carbonate with different sizes measured by thermogravimetry are presented in Figs. 2 and 3. The TG and DTG curves show that the thermal decomposition of nano-calcium carbonate occurred at the temperature ranging from 650 1C to 800 1C. The onset decomposition temperature and the temperature of the DTG peaks of nano-calcium carbonate with different size were obtained after the analysis of the TG and DTG
3.2. Characterization of nano-CaCO3 The as-prepared samples were examined using a Germany Bluker D8 Advance Powder diffractometer (Cu Ka, λ ¼0.154178 nm). Particles sizes of samples were calculated by Scherrer formula based on the half peak width of characteristic diffraction peaks. 3.3. Thermal measurement Thermogravimetric analysis (TG and DTG) of the nano-CaCO3 were carried out using a thermal analysis system (WACT-2A). The rate of heating of the samples was kept at 15 1C/min under N2 flow at 60 mL/ min. CuSO4 5H2O was used as the calibrating standard material.
4. Results and discussion 4.1. Average size of nano-CaCO3
Fig. 2. TG curves of nano-CaCO3 with different radii.
Fig. 1 shows the XRD patterns of the nano-CaCO3 (a, b, c, d and e). The XRD patterns indicate that all samples exhibit a calcite structure
Fig. 1. XRD patterns of the as-synthesized nano-CaCO3 with different sizes: (a) 18.1 nm, (b) 22.4 nm, (c) 26.2 nm, (d) 33.5 nm, and (e) 44.1 nm.
177
Fig. 3. DTG curves of nano-CaCO3 with different radii.
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Table 1 The decomposition temperatures of nano-calcium carbonate with different radii. r/nm
18.1
22.4
26.2
33.5
44.1
r 1/nm 1 T onset /1C T max /1C
0.055 658.5 683.1
0.045 678.2 707.0
0.038 685.5 734.9
0.030 714.6 789.3
0.023 725.0 796.7
Table 2 The extrapolated values for nano-calcium carbonate and the literature values for block calcium carbonate. Extrapolated values/1C
The literature value (T onset )/1C
T onset
T max
773.0
888.9
825
5. Conclusions This study reveals that the size of nanoparticles has significant effect on the onset decomposition temperature and the peak temperature. With the size of the nanoparticles decreasing, the onset decomposition temperature and the peak temperature drop, and there is a linear relationship between them and the reciprocal of particle size. The experimental results are consistent with this thermodynamic theory for decomposition of nanoparticles. The thermodynamic theory provides a quantitative description for the decomposition temperature of nanoparticles, also it can be used to predict and explain the thermal decomposition behavior of nanomaterials.
Acknowledgements
Fig. 4. The relation between the decomposition temperatures (T onset and T max ) and the reciprocal of particle radii of nano-CaCO3.
curves. The onset decomposition temperature (T onset ) of nanoparticles was selected at a constant weight loss of 5% [26]. The temperatures of the DTG peaks (T max ) refer to that the decomposition rate reached the maximum value. The data of T onset and T max are listed in Table 1. It can be seen from Table 1 that the effect of particle size on the decomposition temperature is noticeable and the decomposition temperature drops with the radius decreasing, which is consistent with the literatures reported [14–18]. If one plot the decomposition temperatures (T onset and T max ) against the reciprocal of particle radius, Fig. 4 will be obtained. Fig. 4 indicates that the particle size has significant influence to the onset decomposition temperature and the peak temperature, both of them reduce with the radius decreasing and there is a well linear relationship between them and the reciprocal of radius. The depress regularity of the onset decomposition temperature is consistent with the derived thermodynamic equation ahead. We can educe from Eq. (15) that the decomposition temperature T is equal to T b when the size approaches infinity. That is to say, the decomposition temperature of the block calcium carbonate can be obtained by extrapolating the radius to infinity (r-1), namely, r 1 ¼ 0. The extrapolated results and the literature value of decomposition temperatures [27] are given in Table 2. It can be seen from Table 2 that the experimental onset temperature for block calcium carbonate obtained by extrapolating is close to the literature value, and it is indicated that the regularity of the linear relation between the decomposition temperature and the reciprocal of radius is reliable.
This work was supported by the National Natural Science Foundation of China (no. 21373147) and by the Program for the Top Science and Technology Innovation Teams of Higher Learning Institutions of Shanxi Province of China. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
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