Experiment and model for the viscosity of carbonated 2-amino-2-methyl-1-propanol-monoethanolamine and 2-amino-2-methyl-1-propanol-diethanolamine aqueous solution

Journal of Molecular Liquids 188 (2013) 37–41

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Experiment and model for the viscosity of carbonated 2-amino-2-methyl-1-propanol-monoethanolamine and 2-amino-2-methyl-1-propanol-diethanolamine aqueous solution Dong Fu ⁎, Huimin Hao, Feng Liu School of Environmental Science and Engineering, North China Electric Power University, Baoding, 071003, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 15 August 2013 Received in revised form 24 September 2013 Accepted 26 September 2013 Available online 9 October 2013 Keywords: AMP–MEA AMP–DEA CO2 loading Viscosity

a b s t r a c t The viscosities of carbonated 2-amino-2-methyl-1-propanol (AMP)–monoethanolamine (MEA) and AMP– diethanolamine (DEA) aqueous solutions were measured by using a NDJ-1 rotational viscometer. The temperature, total mass fractions of amines and CO2 loading respectively ranged from 303.15 K to 323.15 K, 0.3 to 0.4 and 0.1 to 0.5. The experiments were satisfactorily modeled by using a modified Grunberg–Nissan equation. The effects of temperature, mass fractions of amines and CO2 loading on the viscosities of carbonated aqueous solutions were demonstrated on the basic of experiments and calculations. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The greenhouse effect and acid rain caused by the emission of CO2 from industrial processes and coal-fired boilers seriously impacted the sustainable development of the economy. Development of affordable yet technically feasible separation technologies for reducing CO2 emission has attracted global attention. Chemical absorption is one of the most effective approaches for CO2 capture because CO2 can be satisfactorily removed and the absorbents can be well regenerated by heating. Currently, aqueous solutions of alkanol amines have been widely used for the removal of CO2 from a variety of gas streams [1–7]. Among the alkanol amine series, N-methyldiethanolamine (MDEA) takes the advantages of large absorption capacity, high resistance to thermal and chemical degradation, low solution vapor pressure, and low enthalpy of absorption. However, MDEA has a low absorption rate. Adding small amount of primary and secondary amines to an aqueous solution of MDEA has found widespread application in the removal of CO2 [8–18]. Besides MDEA, the sterically hindered amine, e.g., 2-amino-2methyl −1-propanol (AMP), is also considered to be an attractive solvent for the removal of CO2 due to its absorption capacity, absorption rate, selectivity and degradation resistance advantages [19–29]. Compared with MDEA, AMP has the same absorption capacity for CO2 (1 mol of CO2 per mol of amine) but much higher reaction rate [23]. When the aqueous solutions of AMP are used to absorb CO2, as AMP only forms bicarbonate and carbonate ions, the regeneration energy ⁎ Corresponding author. Tel.: +86 312 7522037. E-mail address: [email protected] (D. Fu). 0167-7322/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.molliq.2013.09.014

costs are relatively low. Adding small amount of primary and secondary amines to an aqueous solution of AMP is also helpful to promote the absorption of CO2 [24,25]. For similar relative composition, the rates of absorption of CO2 in AMP–MEA and AMP–DEA aqueous solutions are higher than those in MDEA–MEA and MDEA–DEA aqueous solutions. The viscosities of alkanol amine aqueous solutions are required when designing or simulating an absorption column for CO2 absorption. In particular, solution viscosity is important to the mass transfer rate modeling of absorbers and regenerators because these properties affect the liquid film coefficient for mass transfer. By far, there are some experiments concerning the viscosities of aqueous solutions containing AMP– MEA and AMP–DEA [30–32]. In particular, Mandal et al. [30] measured and modeled the viscosities of both AMP–MEA and AMP–DEA aqueous solutions. However, the experiments and theoretical work for the viscosities of CO2-loaded AMP–MEA and AMP–DEA aqueous solutions are rare. The main purpose of this work is to investigate the viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions experimentally and theoretically, so as to demonstrate the temperature, mass fractions of amines and CO2 loading dependences of the viscosities. To this end,

Table 1 Sample description. Chemical

CAS No.

Purity (in mass fraction %)

Molecular mass

Density (g cm−3)

MEA DEA AMP

141-43-5 111-42-2 124-68-5

99.4 99.4 99.5

61.09 105.14 89.14

1.0003 at 298.15 K [34] 1.0847 at 313.15 K [35] 0.9172 at 313.15 K [35]

38

D. Fu et al. / Journal of Molecular Liquids 188 (2013) 37–41

Table 2 Viscosity of CO2-loaded AMP–MEA aqueous solutions. α

η/(mPa s) 303.15 K

313.15 K

323.15 K

303.15 K

4.83 5.76 6.48 7.10 7.84

4.14 4.70 55.5 66.3 7.45

5.30 5.74 6.38 6.99 7.45

4.83 5.76 6.48 7.10 7.84

4.14 4.70 5.55 6.63 7.45

6.14 6.52 7.00 7.82 8.42

wAMP/wMEA = 0.35/0.05 0.10 0.20 0.30 0.40 0.50

5.45 6.41 7.25 7.91 8.61

5.45 6.41 7.25 7.91 8.61

4.91 5.50 6.09 6.54 6.93

4.69 5.23 5.95 6.60 7.04

4.05 4.73 5.35 6.16 6.65

5.43 5.89 6.34 6.98 7.34

4.61 5.00 5.45 5.90 6.42

6.25 7.00 7.50 8.28 8.75

5.45 6.05 6.77 7.54 7.93

wAMP/wMEA = 0.25/0.10

wAMP/wMEA = 0.25/0.05 0.10 0.20 0.30 0.40 0.50

323.15 K

wAMP/wMEA = 0.20/0.10

wAMP/wMEA = 0.30/0.05 0.10 0.20 0.30 0.40 0.50

313.15 K

wAMP/wMEA = 0.30/0.10 4.17 4.75 5.24 5.98 6.50

3.71 4.24 4.98 5.5 6.12

the viscosities of carbonated AMP–MEA and AMP–DEA were measured at temperatures from 303.15 K to 323.15K, with the total mass fractions of amines and the CO2 loading respectively ranging from 0.3 to 0.4 and 0.1 to 0.5. The modified Grunberg–Nissan equation [33] was used to model the viscosities of carbonated aqueous solutions.

2. Experimental section 2.1. Materials AMP, MEA and DEA were purchased from Huaxin Chemical Co. The sample description is shown in Table 1. They were used without further purification. Aqueous solutions of AMP–MEA and AMP–DEA were prepared by adding doubly distilled water. The uncertainty of the electronic balance is ±0.1 mg.

6.80 7.65 8.03 8.85 9.36

2.2. Apparatus and procedure The carbonated AMP–MEA and AMP–DEA aqueous solutions were prepared according to the methods mentioned in the work of Amundsen et al. [34], Weiland et al. [36] and Fu et al. [37–40]: CO2unloaded AMP–MEA and AMP–DEA aqueous solutions were put into a volumetric flask immersed in the thermostatic bath with a built-in stirrer for uniform temperature distribution. CO2 from a high-pressure tank was introduced into the volumetric flask at certain temperatures (CO2 pressure is 1 atm). Once the carbonated solution was prepared, varying proportions of the unloaded and loaded solutions were mixed together to produce a set of samples having a fixed ratios of AMP/MEA-to-water and AMP/DEA-to-water, but with varying CO2 loading. CO2 loading is defined as α = nCO2 /(nMEA + nAMP) or nCO2 /(nDEA + nAMP), in which nCO2 is the mole of loaded CO2, nMEA, nDEA and nAMP are respectively the moles of MEA, DEA and AMP in the unloaded aqueous solutions.

Table 3 Viscosity of CO2-loaded AMP–DEA aqueous solutions. α

η/(mPa s) 303.15 K

313.15 K

323.15 K

303.15 K

5.06 5.72 6.59 7.39 8.17

4.72 5.30 5.94 6.51 7.60

5.18 5.76 6.10 6.78 7.15

4.07 4.58 4.90 5.50 6.46

3.49 3.84 4.14 4.79 5.56

5.39 5.80 6.35 7.07 7.42

wAMP/wDEA = 0.35/0.05 0.10 0.20 0.30 0.40 0.50

6.10 6.85 7.19 7.83 8.45

4.44 4.94 5.67 6.34 7.30

4.12 4.67 5.30 5.81 6.47

4.16 4.95 5.50 6.00 6.71

3.44 3.95 4.60 5.34 5.99

4.40 4.93 5.50 5.95 6.50

4.19 4.40 4.85 5.27 5.76

4.75 5.44 6.30 6.90 7.43

4.50 5.10 5.93 6.50 7.05

wAMP/wDEA = 0.25/0.10

wAMP/wDEA = 0.25/0.05 0.10 0.20 0.30 0.40 0.50

323.15 K

wAMP/wDEA = 0.20/0.10

wAMP/wDEA = 0.30/0.05 0.10 0.20 0.30 0.40 0.50

313.15 K

wAMP/wDEA = 0.30/0.10 3.45 4.03 4.79 5.30 5.99

3.04 3.44 4.03 4.67 5.35

5.42 5.85 6.64 7.30 7.95

D. Fu et al. / Journal of Molecular Liquids 188 (2013) 37–41

39

Table 4 Model parameters for Grunberg–Nissan equation and the average relative deviation (ARD) between the calculations and experiments. AMP–MEA–water

a b c e f g ARD%

AMP–DEA–water

G12[30]

G13[30]

G23[30]

G12[30]

G13[30]

G23[30]

−20,188.704 567.58227 −1.5818676 −0.06519 1.35366 −0.67553 6.0

−7125.3197 90.102332 −0.1591033

32,9243.12 −1881.0553 2.7614435

18,3225.22 −1239.5022 2.0151020 0.48108 1.78804 −1.06662 10.1

29,0505.08 −1666.1670 2.4645170

31,7856.94 −1806.9045 2.6429190

It is worth noting that CO2 loading is expected to be a major uncertainty in the experiment. In this work, carbonated solution was prepared at non-equilibrium conditions, under which the thermodynamic equilibrium (saturated absorption, corresponding to maximum CO2 loading, αmax) can not be achieved. A certain amount of CO2 escaped when the loaded solution was mixed with unloaded solution and the atmospheric CO2 and humidity have some effects on CO2 loading and solution concentration. To estimate the uncertainty of CO2 loadings, we selected 2 diluted samples (as shown in Table 2, wAMP/wMEA = 0.35/0.05, α = 0.1 and 0.5) and determined the CO2 loadings at 313.15 K using the analysis method based on the precipitation of BaCO3 [34,36]. The obtained CO2 loadings were respectively 0.097 and 0.491, indicating that the real values of CO2 loading may be lower than those listed in Table 2. As documented by Amundsen et al. [34] and Weiland et al. [36], the uncertainty of CO2 loading is less than 2%. The viscosities of the carbonated AMP–MEA and AMP-DEA aqueous solutions were measured from 303.15 to 323.15 K by using an NDJ-1 rotational viscometer produced by Shanghai Hengping Instrument Factory. The measurement ranges for temperature and viscosity are respectively 273.15 to 383.15 K and 0.1 to 100 mPa s. The uncertainties of temperature and viscosity are respectively ± 0.05 K and ± 0.01 mPa s.

3. Results and discussion The viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions at different temperatures, CO2 loadings and amine mass fractions are shown in Tables 2 and 3. Besides experiments, models that can correctly correlate and predict the viscosities are also important. Among the widely used equations [33,36,41], the Eyring [41] equation can only quantitatively describe the temperature dependence of viscosity. The Grunberg–Nissan equation [33] can well describe the temperature and amine concentration dependences, and the Weiland equation [36] can simultaneously describe the temperature, amine concentration and CO2 loading dependences. Comparison shows [37,42] that the Grunberg–Nissan equation is a little more accurate for CO2-unloaded aqueous solutions than the Weiland equation; however, it is inapplicable for CO2-loaded cases because the contribution of CO2 loading has not been taken into account. Fu et al. [37] introduced an empirical expression of the contribution of CO2 loading into the Grunberg–Nissan equation and applied this modified equation to the viscosity of carbonated MDEA–MEA aqueous solutions with success. The modified equation is as following:
 2 ln ηmix ¼ ∑xi ln ηi þ ∑∑xi x j Gij þ e þ fα þ gα

12

12 12

7

6

10

η /(mPa s)

η /(mPa s)

10

10

ð1Þ

8

5

4

3

8

η/(mPa s)

η/(mPa s)

6

4

8

0.1

0.2

0.3

α

0.4

0.5

2 0.1

0.2

0.3

α

0.4

0.5

6

6 4

4 0.1

0.2

0.3

0.4

0.5

α Fig. 1. CO2 loading dependence of the viscosity of AMP–MEA aqueous solutions. Symbols: experimental data from this work, ● T = 303.15 K; ○ T = 313.15 K; ■ T = 323.15 K. Main plot: wAMP = 0.25, wMEA = 0.10; Insert plot: wAMP = 0.30, wMEA = 0.10. Lines: calculated results.

2 0

0

0

α

0

1

Fig. 2. CO2 loading dependence of the viscosity of AMP–DEA aqueous solutions. Symbols: experimental data from this work, ● T = 303.15 K; ○ T = 313.15 K; ■ T = 323.15 K. Main plot: wAMP = 0.25, wDEA = 0.10; Insert plot: wAMP = 0.25, wDEA = 0.05; Lines: calculated results.

D. Fu et al. / Journal of Molecular Liquids 188 (2013) 37–41

Gij ¼ aij þ bij T þ cij T

2

12

ð2Þ

7

where xi and ηi respectively stand for the mole fraction and viscosity of component i. The model parameters aij, bij, cij are directly taken from the work of Mandal et al. [30], as shown in Table 4. The model parameters e, f and g in the modified Grunberg–Nissan equation should be regressed by fitting to the experimental viscosities of carbonated aqueous solutions. The objective function was expressed as: ð3Þ

i¼1

where the superscripts ‘exp’ and ‘cal’ respectively stand for the experimental and calculated data, n is the number of data. The optimized e, f and g are shown in Table 4. Figs. 1 and 2 show the influence of CO2 loading on the viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions. One finds from these figures that at a given temperature and given mass fractions of amines, the viscosities of carbonated aqueous solutions increase monotonically with the increase of CO2 loading. The modified Grunberg–Nissan equation correctly captures the CO2 loading dependence of the viscosities and the calculated results matched the experiments satisfactorily. The corresponding average relative deviations (ARD) between calculations and experiments for carbonated AMP– MEA and AMP–DEA aqueous solutions are respectively 6.0% and 10.1%, as also shown in Table 4. Fig. 3 shows the influence of temperature on the viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions. One finds from these figures that at given CO2 loading and given mass fractions of amines, the viscosities of carbonated aqueous solutions decrease monotonically with the increase of temperature. The temperature dependence of the viscosity can be well described by the exponential relationship. In particular, the Eyring model [41], η = κ1exp(κ2T), can fit the experiments quite well. However, as both κ1 and κ2 are dependent on temperature, too many parameters are needed to model the

12 8

10

6

5

4

η/(mPa s)

n h i X cal exp 1−η =η fs ¼ =n  100%

8

η /(mPa s)

40

3 300

305

310

315

320

325

T/K

8

6

4 300

305

310

315

320

325

T/K Fig. 3. Temperature dependence of the viscosity. wAMP = 0.25. Symbols: experimental data from this work. ● α = 0.1; ○ α = 0. 2; ■ α = 0.3, □α = 0.4, ▲α = 0.5. Main plot: carbonated AMP-–MEA aqueous solutions, wMEA = 0.10; Insert plot: carbonated AMP–DEA aqueous solutions, wDEA = 0.10. Lines: calculated results, —: from the modified Grunberg–Nissan equation; - - -: from the Eyring model.

viscosities when using the Eyring model. Compared with the Eyring model, the modified Grunberg–Nissan equation can simultaneously describe the influence of temperature, mass fractions of amines and CO2 loading on the viscosities with 12 parameters as input. Fig. 4 shows the influence of the mass fraction of AMP on viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions. One finds from this figure that at given temperature, given CO2 loading and given mass fraction of MEA (or DEA), the viscosities of carbonated aqueous solutions increase with the increase of wAMP due to the increase of the solubility of CO2 and the concentration of ions. Similarly, at given temperature, given CO2 loading and given wAMP, the viscosities of carbonated aqueous solutions increase with the increase of wMEA or wDEA, as shown in Fig. 5

η /(mPa s)

6

10

4. Summary The viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions have been measured. The experiments have been satisfactorily modeled by using a modified Grunberg–Nissan equation. The effects of temperature, mass fractions of amines and CO2 loading on the viscosities of carbonated solutions have been demonstrated based on the experiments and calculations. Our results showed that:

η/(mPa s)

4

2

8

0

0

0

α

0

1

6

4

0.1

0.2

0.3

α

0.4

0.5

Fig. 4. Effect of the mass fraction of AMP on viscosity. Symbols: experimental data from this work. Main plot: carbonated AMP–MEA aqueous solutions. T = 313.15 K, wMEA = 0.10; ● wAMP = 0.20; ○ wAMP = 0.25; ■ wAMP = 0.30; Insert plot: carbonated AMP–DEA aqueous solutions. T = 323.15 K, wDEA = 0.05; ● wAMP = 0.25; ○ wAMP = 0.30; ■ wAMP = 0.35. Lines: calculated results.

(1) The modified Grunberg–Nissan equation can correctly describe the viscosities of carbonated AMP–MEA and AMP–DEA aqueous solutions. The agreement with experiments is satisfactory. (2) The increase of CO2 loading tends to increase the viscosity of carbonated AMP–MEA and AMP–DEA aqueous solutions. (3) The increases of the mass fractions of amines and temperature respectively increase and decrease the viscosity of carbonated AMP–MEA and AMP–DEA aqueous solutions. Acknowledgments The authors appreciate the financial support from the National Natural Science Foundation of China (Nos. 21276072 and 21076070),

D. Fu et al. / Journal of Molecular Liquids 188 (2013) 37–41

12 9

10

η /(mPa s)

8

7

6

η/(mPa s)

5

8

4 0.1

0.2

0.3

α

0.4

0.5

6

4 0.1

0.2

0.3

α

0.4

0.5

Fig. 5. Effect of the mass fraction of MEA or DEA on viscosity. T = 313.15 K, wAMP = 0.30. Symbols: experimental data from this work. Main plot: carbonated AMP–MEA aqueous solutions. ● wMEA = 0.05; ○ wMEA = 0.10; Insert plot: carbonated AMP–DEA aqueous solutions. ● wDEA = 0.05; ○ wDEA = 0.10. Lines: calculated results.

the Natural Science Funds for Distinguished Young Scholar of Hebei Province (No. B2012502076), and the Fundamental Research Funds for the Central Universities (No. 13ZD16). References [1] [2] [3] [4] [5]

L. Raynal, P.A. Bouillon, A. Gomez, P. Broutin, J. Chem. Eng. 171 (3) (2011) 742–752. N. Nahicenovic, A. John, Energy 16 (1991) 1347–1377. Y. Maham, A.E. Mather, C. Mathonat, J. Chem. Thermodyn. 32 (2) (2000) 229–236. Y. Maham, A.E. Mather, Fluid Phase Equilib. 182 (1–2) (2001) 325–336. J.M. Navaza, D.G. Diaz, M.D.L. Rubia, J. Chem. Eng. 146 (2009) 184–188.

41

[6] E. Álvarez, R. Rendo, B. Sanjurjo, M. Sanchez-Vilas, J.M. Navaza, J. Chem. Eng. Data 43 (1998) 1027–1029. [7] E. Álvarez, F. Cerdeira, D. Gómez-Diaz, J.M. Navaza, J. Chem. Eng. Data 55 (2) (2010) 994–999. [8] M. Ghulam, M.S. Azmi, K.K. Lau, A.B. Mohamad, J. Chem. Eng. Data 56 (2011) 2660–2663. [9] G. Rochelle, E. Chen, S. Freeman, D.V. Wagener, Q. Xu, A. Voice, J. Chem. Eng. 171 (3) (2011) 725–733. [10] A. Samanta, S.S. Bandyopadhyay, J. Chem. Eng. Data 51 (2006) 467–470. [11] G. Vazquez, E. Alvarez, J.M. Navaza, R. Rendo, E. Romero, J. Chem. Eng. Data 42 (1997) 57–59. [12] S. Kadiwala, A.V. Rayer, A. Henni, Fluid Phase Equilib. 292 (2010) 20–28. [13] P.W.J. Derks, J.A. Hogendoorn, G.F. Versteeg, J. Chem. Thermodyn. 42 (2010) 151–163. [14] P.W.J. Derks, H.B.S. Dijkstra, J.A. Hogendoorn, G.F. Versteeg, AIChE J 51 (2005) 2311–2327. [15] M. Vahidi, N.S. Matin, M. Goharrokhi, M.H. Jenab, J. Chem. Thermodyn. 41 (2009) 1272–1278. [16] B.S. Ali, M.K. Aroua, Int. J. Thermophys. 25 (2004) 1863–1870. [17] P.S. Kamps, AIChE J 49 (2003) 2662–2670. [18] G.W. Xu, C.F. Zhang, A.J. Qin, W.H. Gao, H.B. Liu, Ind. Eng. Chem. Res. 37 (1998) 1473–1477. [19] F.H. Al-Masabi, M. Castier, Int. J. Greenh. Gas Con. 5 (2011) 1478–1488. [20] S. Xu, Y.W. Wang, F.D. Otto, A.E. Mather, Chem. Eng. Sci. 51 (1996) 841–850. [21] Z. Pei, S. Yao, W. Jianwen, Z. Wei, Y. Qing, J. Environ. Sci. 20 (2008) 39–44. [22] J. Xiao, C.W. Li, M.H. Li, Chem. Eng. Sci. 55 (2000) 161–175. [23] G. Sartori, D.W. Savage, Ind. Eng. Chem. Fundam. 22 (1983) 239–249. [24] B.P. Mandal, A.K. Biswas, S.S. Bandyopadhyay, Chem. Eng. Sci. 58 (2003) 4137–4144. [25] B.P. Mandal, S.S. Bandyopadhyay, Chem. Eng. Sci. 61 (2006) 5440–5447. [26] A.K. Saha, S.S. Bandyopadhyay, A.K. Biswas, Chem. Eng. Sci. 50 (1995) 3587–3598. [27] B.P. Mandal, M. Guha, A.K. Biswas, S.S. Bandyopadhyay, Chem. Eng. Sci. 56 (2001) 6217–6224. [28] B.P. Mandal, S.S. Bandyopadhyay, Chem. Eng. Sci. 60 (2005) 6438–6445. [29] B.P. Mandal, M. Kundu, S.S. Bandyopadhyay, J. Chem. Eng. Data 50 (2005) 252–258. [30] B.P. Mandal, M. Kundu, S.S. Bandyopadhyay, J. Chem. Eng. Data 48 (2003) 703–707. [31] C.H. Hsu, M.H. Li, J. Chem. Eng. Data 42 (1997) 714–720. [32] F. Chenlo, R. Moreira, G. Pereira, M.J. Vázquez, E. Santiago, J. Chem. Eng. Data 46 (2001) 276–280. [33] L. Grunberg, A.H. Nissan, Nature 164 (1949) 799–800. [34] T.G. Amundsen, L.E. Oi, D.A. Eimer, J. Chem. Eng. Data 54 (2009) 3096–3100. [35] M.E. Rebolledo-Libreros, A. Trejo, J. Chem. Eng. Data 51 (2006) 702–707. [36] R.H. Weiland, J.C. Dingman, D.B. Cronin, G.J. Browning, J. Chem. Eng. Data 43 (3) (1998) 378–382. [37] D. Fu, L.H. Chen, L.G. Qin, Fluid Phase Equilib. 319 (2012) 42–47. [38] D. Fu, Y.F. Xu, X.Y. Hua, Fluid Phase Equilib. 314 (2012) 121–127. [39] D. Fu, L.G. Qin, H.M. Hao, J. Mol. Liquids 186 (2013) 81–84. [40] D. Fu, H.M. Hao, L.G. Qin, J. Mol. Liquids 181 (2013) 105–109. [41] S. Glasstone, K.J. Laidler, H. Eyring, The theory of rate process, McGraw-Hill, New York, 1941. [42] D. Fu, X.Y. Hua, Y.F. Xu, Acta Chim. Sinica 69 (2011) 772–776.