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Corresponding author: Lianying Wang

State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Box 98, 15 Beisanhuan Dong Lu, Beijing, 100029, China. Fax: +8610-64425385; Tel: +8610-64451027 E-mail: [email protected]

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S1:

S1. Molecular structures for [Eu(EDTA)]- and [Eu(NTA)2]3- complexes.

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S2 Kinetics Study The kinetic equation for a solid state reaction can be expressed in the general form f(%) = kt,

(1)

where % is the extent of reaction and the nature of the differential function f(%) varies according to the model. The commonly used expressions for f(%) and their corresponding integrated forms g(%) are listed in Table 1.1, 2 There are two methods which can be used to analyze the kinetics of solid state reactions: in the isothermal method, the extent of reaction % is measured as a function of time at constant temperature, whereas in the non-isothermal method the value of % is measured as the sample is heated at a controlled rate.3 In this work, the equations of Satava-Sestak 4 and Coats-Redfern 5 were employed to study the kinetics of the structural transformation of ZnAl-Eu(EDTA) LDH under non-isothermal conditions.

The Satava-Sestak equation, lg g (%) = lg

AEa (R

0.4567Ea RT

2.315

(2)

and the Coats-Redfern equation, ln ( g (%)/T 2) = ln AR (1 (Ea

2RT ) Ea

Ea RT

(3)

allow the activation energy Ea and pre-exponential factor A to be calculated. In these equations, the parameter ( is the heating rate. As shown in Fig. 9a, the basal spacing, d, of ZnAl-Eu(EDTA) LDH initially decreases with increasing temperature up to 150 oC (423 K), where it essentially reaches an equilibrium plateau. Hence the extent of reaction % as a function of calcination temperature is defined as: %(T) = ( dT – d303) / ( dT – d423). The value of % therefore varies from 0 at the start of the reaction to 1 at equilibrium. The resulting plot of % versus temperature is shown in Fig. 11. The I-T data shown in Fig. 11 were compared by least-squares analysis with the calculated values for every commonly used kinetic model (Table 1) using both the Satava-Sestak and the Coats-Redfern equations. The following criteria were employed to find the best fit to the experimental data: 3

(i)

the correlation coefficient R should be greater than 0.98, and the closer the value of R to unity, the more suitable the model, and

(ii)

the standard deviation should be less than 0.1, and

(iii)

there should be a high degree of consistency with the state of the reaction system.

The results of the statistical analyses are shown in Table 2. Using either the Satava-Sestak or the Coats-Redfern equation, the best fitting kinetic model for the structural transformation of ZnAl-Eu(EDTA) LDH is the A2 mechanism, corresponding to the second-order Avrami-Erofe’ev equation which may be written as g (I) = [-ln(1-%)]1/2

(4).

Table 1 The commonly used kinetic models. Mechanism One-dimensional diffusion Two-dimensional diffusion (Valensi eq.) Three-dimensional diffusion (sphere, Jander eq.) Three-dimensional diffusion (cylinder, G–B eq.a) Two-dimensional phase boundary reaction Three-dimensional phase boundary reaction Nucleation and nuclei growth (A–E eq.b, n=1) Nucleation and nuclei growth (A–E eq., n=1.5) Nucleation and nuclei growth (A–E eq., n=2) Nucleation and nuclei growth (A–E eq., n=3) Exponential nucleation (Mample eq.) Exponential nucleation (Mample eq.) Exponential nucleation (Mample eq.) Exponential nucleation (Mample eq.) Power law (n=1.5) Power law (n=2) a

Symbol D1 D2 D3

f(%) 0.5/% [-ln(1-%)]-1 1.5(1-%)2/3[1-(1-%)1/3]-1

g(%) %2 %+(1-%)ln(1-%) [1-(1-%)1/3]2

D4

1.5[(1-%)1/3-1]-1

(1-2%/3)-(1-%)2/3

R2

2(1-%)1/2

1-(1-%)1/2

R3

3(1-%)2/3

1-(1-%)1/3

A1

1-%

-ln(1-%)

A1.5

1.5(1-%)[-ln(1-%)]1/3

[-ln(1-%)]2/3

A2

2(1-%)[-ln(1-%)]1/2

[-ln(1-%)]1/2

A3

3(1-%)[-ln(1-%)]2/3

[-ln(1-%)]1/3

P1 P2 P3 P4 C1.5 C2

1 2%1/2 3%2/3 4%3/4 (1-I)1.5 (1-I)2

% %1/2 %1/3 %1/4 (1-I)-1/2 (1-I)-1

Ginstling-Brounstein Equation.

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b

Avrami-Erofe’ev Equation.

c

Prout-Tompkins Equation.

Table 2 Fitting results for the commonly used kinetic models obtained form different methods. No.

E, kJmol–1

Satava-Sestak equation D1 85.16 D2 94.18 D3 106.09 D4 98.08 R2 50.12 R3 53.05 A1 59.58 A1.5 39.72 A2 29.79 A3 19.86 P1 42.58 P2 21.29 P3 14.19 P4 10.65 C1.5 20.99 C2 41.97 Coats-Redfern equation D1 D2 D3 D4 R2 R3 A1 A1.5 A2 A3 P1 P2 P3 P4 C1.5 C2

83.78 93.24 105.74 97.33 47.14 50.19 57.00 36.36 26.22 16.59 39.31 17.91 11.97 9.89 17.62 38.68

Log A, min–1

R

S.D.

14.39 15.53 16.76 15.49 9.51 9.78 11.27 8.51 7.17 5.87 8.65 5.93 5.10 4.72 6.32 9.42

0.9654 0.9746 0.9844 0.9783 0.9802 0.9844 0.9912 0.9912 0.9912 0.9912 0.9654 0.9654 0.9654 0.9654 0.9465 0.9465

0.2332 0.2196 0.1921 0.2107 0.1026 0.0961 0.0806 0.0538 0.0403 0.0269 0.1166 0.0583 0.0389 0.0291 0.0725 0.1450

11.17 12.39 13.72 12.39 5.87 6.18 7.76 4.70 3.16 1.70 4.88 1.77 0.93 0.69 2.15 5.64

0.9603 0.9711 0.9825 0.9754 0.9749 0.9804 0.9891 0.9880 0.9870 0.9858 0.9549 0.9465 0.9496 0.9635 0.9207 0.933

0.5400 0.5087 0.4453 0.4882 0.2390 0.2239 0.1882 0.1260 0.0947 0.0627 0.2712 0.1355 0.0877 0.0610 0.1658 0.3312

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Literature Cited (1) Conesa, J. A.; Marcilla, A.; Caballero, J.A.; Font, R. Comments on the validity and utility of the different methods for kinetic analysis of thermogravimetric data. J. Anal. Appl. Pyrol. 2001, 58-59, 617-633. (2) Dollimore, D.; Tong, P.; Alexander, K. S. The kinetic interpretation of the decomposition of calcium carbonate by use of relationships other than the Arrhenius equation. Thermochim. Acta 1996, 282/283, 13-27. (3) Halikia, I.; Neou-Syngouna, P.; Kolitsa, D. Isothermal kinetic analysis of the thermal decomposition of magnesium hydroxide using thermogravimetric data. Thermochim. Acta 1998, 320, 75-88. (4) Satava, V.; Sestak, J. Computer calculation of the mechanism and associated kinetic data using a non-isothermal integral method. J. Therm. Anal. Calorim. 1975, 8, 477-489. (5) Coats A. W.; Redfern J. P. Kinetic parameters from thermogravimetric data. Nature, 1964, 201, 68-69.

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