Article pubs.acs.org/jced
Activity Coefficients for CsBr + MeOH/EtOH + H2O Ternary Systems Using Potentiometric Measurements at 298.15 K Yanping Du,†,‡ Jing Tang,† Shu’ni Li,*,† Quanguo Zhai,† Yucheng Jiang,† and Mancheng Hu*,† †
Key Laboratory of Macromolecular Science of Shaanxi Province, School of Chemistry and Chemical Engineering, Shaanxi Normal University, Xi’an, Shaanxi, 710062, P. R. China ‡ School of Environment and Chemical Engineering, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, P. R. China
ABSTRACT: In this paper, the mean activity coefficients for CsBr, as well as the osmotic coefficients, the excess Gibbs free energies, the Gibbs energies of transference, and the primary hydration in different MeOH−water and EtOH−water mixtures at 298.15 K are calculated by potentiometric measurements. The cell used in this work contains two ion selective electrodes (ISEs): Cs-ISE|CsBr(m), ROH(w), H2O(1 − w)|Br-ISE (R = Me and Et), and the mass fraction of ROH in the mixture (w) was varied between 0 and 0.3 in 0.1 unit steps. The experimental data were correlated very well by the thermodynamics equations of Pitzer, modified Pitzer, and Debye−Hückel models.
1. INTRODUCTION
presented, while the mass fraction of alcohol in the mixture (w) was varied between 0 and 0.3.
It is well-known that the determination of activity coefficients of electrolytes in water−organic solvents is very important in many fields, especially for separation processes. Activity coefficients have been also reported for a wide variety of alkali metal chlorides in MeOH−water and EtOH−water mixtures by potentiometric measurements. For example, Gupta1 used the Pitzer’s equation for the activity coefficient of HCl, NaCl, and KCl in MeOH−water mixtures. Khoo et al.2 obtained the activity coefficients of LiCl, NaCl, KCl, RbCl, CsCl, and HCl in MeOH−water mixtures at 298.15 K. Yao et al.3 determined the activity coefficients of NaCl in MeOH−water at 308.15 K and 318.15 K. Hernández-Luis et al.4 and Hu et al.5 obtained the activity coefficients of LiCl in EtOH−water at 298.15 K. Moreover, there are many potentiometric studies of NaBr in mixtures with cosolvent.6−9 In the previous study, we reported the activity coefficients of LiCl, RbCl, CsCl, RbF, and CsF in alcohol−water mixtures.5,10−13 As an extension of our work, the ternary systems CsBr−MeOH−water and CsBr−EtOH−water at 298.15 K were studied in this paper. The activity coefficients (γ±), osmotic coefficients (Φ), excess Gibbs free energies (GE), and standard Gibbs energies of transference (ΔGt0) for CsBr in MeOH−water and EtOH−water mixed solvent systems are © 2012 American Chemical Society
2. EXPERIMENTAL SECTION Cesium bromide (A.R. purity > 0.9950) was purchased from Shanghai China Lithium Industrial Co., Ltd., and dried in an oven at 383 K for overnight before use. Analytical grade methanol and ethanol were obtained from Sinopharm Chemical Reagent Co., Ltd., and all of them were analytical grade with purity greater than 0.9950 and were used without further purification. Double-distilled water was used in all of the experiments whose specific conductance was approximately (1.0 to 1.2)·10−4 S·m−1. Mean ion activity coefficients of CsBr in alcohol−water mixed solvents have been obtained at 298.15 K from the potentiometric measurements of a bi-ion selective electrode (ISE) cell Cs‐ISE|CsBr(m), ROH(w), water(1 − w)|Br‐ISE (R = Me, Et)
(1)
Received: June 20, 2012 Accepted: August 20, 2012 Published: August 27, 2012 2603
dx.doi.org/10.1021/je300671y | J. Chem. Eng. Data 2012, 57, 2603−2609
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Table 1. Experimental Electromotive Force, E, Mean Activity Coefficients, γ±, and Osmotic Coefficient, Φ, at the Different CsBr Molalities and Weight Percent of MeOH/EtOH in the MeOH/EtOH−Water System at 298.15 K m/mol·kg−1
−E/mV
γ±
0.0040 0.0094 0.0173 0.0266 0.0399 0.0550 0.0943 0.1572
−12.0 30.6 60.7 81.4 101.1 116.3 141.1 164.3
0.9160 0.8931 0.8718 0.8483 0.8298 0.8092 0.7648 0.7206
0.0023 0.0073 0.0143 0.0227 0.0330 0.0473 0.0648 0.0954 0.1431 0.1957
−30.2 27.1 60.2 82.4 100.8 117.7 132.4 149.5 167.2 180.6
0.9310 0.8947 0.8699 0.8441 0.8307 0.8053 0.7825 0.7414 0.6975 0.6620
0.0031 0.0068 0.0126 0.0200 0.0288 0.0415 0.0636 0.0863 0.1187
−2.5 35.6 65.8 87.7 104.9 121.8 140.8 154.0 167.4
0.9339 0.8938 0.8682 0.8377 0.8130 0.7840 0.7404 0.7055 0.6658
0.0013 0.0110 0.0154 0.0219 0.0299 0.0394 0.0520 0.0786 0.1039
−35.5 69.2 84.8 101.4 115.5 127.9 140.1 157.3 168.2
0.9385 0.8511 0.8236 0.8000 0.7710 0.7448 0.7156 0.6616 0.6188
0.0049 0.0118 0.0180 0.0267 0.0372 0.0493 0.0657 0.0883 0.1169 0.1482
10.9 54.0 74.5 93.4 109.0 122.2 135.5 148.7 161.0 171.2
0.9084 0.8728 0.8527 0.8305 0.8075 0.7878 0.7658 0.7367 0.7070 0.6801
0.0012 0.0059 0.0094 0.0143 0.0202 0.0288 0.0376 0.0656
−45.7 35.3 57.6 77.7 94.0 110.5 122.8 147.5
0.9117 0.8971 0.8691 0.8448 0.8214 0.7943 0.7729 0.7165
m/mol·kg−1
Φ
w = 0.00 Pure Water 0.9741 0.2303 0.9589 0.3146 0.9425 0.4086 0.9268 0.5341 0.9073 0.6718 0.8879 0.8186 0.8435 0.9718 0.7816 1.1219 w = 0.10 MeOH−Water 0.9791 0.2514 0.9616 0.3096 0.9444 0.3746 0.9279 0.4488 0.9102 0.5369 0.8886 0.6399 0.8646 0.7452 0.8262 0.8600 0.7714 0.9716 0.7149 1.0803 w = 0.20 MeOH−Water 0.9727 0.1486 0.9583 0.1991 0.9409 0.2541 0.9228 0.3232 0.9041 0.3915 0.8800 0.4652 0.8423 0.5398 0.8070 0.6154 0.7598 0.6921 w = 0.30 MeOH−Water 0.9807 0.1351 0.9354 0.2300 0.9211 0.2929 0.9020 0.3571 0.8809 0.4262 0.8580 0.5007 0.8298 0.5756 0.7754 0.6479 0.7278 w = 0.10 EtOH−Water 0.9677 0.2105 0.9479 0.2876 0.9338 0.3867 0.9168 0.4780 0.8989 0.5715 0.8798 0.6741 0.8560 0.7864 0.8258 0.9043 0.7898 1.0225 0.7526 w = 0.20 EtOH−Water 0.9825 0.2080 0.9581 0.2775 0.9455 0.3543 0.9308 0.4306 0.9150 0.5096 0.8946 0.5932 0.8755 0.6781 0.8215 0.7598 2604
−E/mV
γ±
Φ
180.9 194.5 205.9 217.3 227.0 234.9 242.0 247.8
0.6795 0.6481 0.6230 0.5950 0.5713 0.5468 0.5289 0.5129
0.7165 0.6465 0.5721 0.4770 0.3763 0.2721 0.1660 0.0640
191.1 199.6 207.0 213.9 220.6 226.5 231.4 235.3 239.2 242.2
0.6322 0.6057 0.5782 0.5519 0.5256 0.4947 0.4673 0.4369 0.4172 0.3978
0.6576 0.5996 0.5366 0.4661 0.3842 0.2901 0.1955 0.0938 −0.0039 −0.0981
176.7 187.8 197.0 205.5 211.8 217.1 221.0 224.3 226.5
0.6373 0.5904 0.5533 0.5133 0.4790 0.4469 0.4155 0.3887 0.3607
0.7186 0.6521 0.5826 0.4982 0.4171 0.3314 0.2461 0.1610 0.0757
177.9 195.2 202.2 207.2 211.3 214.4 216.1 218.0
0.5748 0.4728 0.4255 0.3846 0.3490 0.3156 0.2838 0.2616
0.6868 0.5403 0.4493 0.3550 0.2580 0.1560 0.0534 −0.0452
185.8 198.2 209.5 217.1 223.1 228.3 232.9 236.8 240.0
0.6362 0.5927 0.5493 0.5152 0.4843 0.4543 0.4259 0.3996 0.3761
0.6825 0.6001 0.4986 0.4081 0.3173 0.2195 0.1143 0.0054 −0.1023
192.7 202.5 209.3 215.0 219.0 222.1 224.1 225.8
0.5446 0.4940 0.4417 0.4060 0.3709 0.3384 0.3078 0.2839
0.5982 0.5004 0.3962 0.2954 0.1933 0.0870 −0.0193 −0.1204
dx.doi.org/10.1021/je300671y | J. Chem. Eng. Data 2012, 57, 2603−2609
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Table 1. continued m/mol·kg−1
−E/mV
γ±
0.1015 0.1519
165.8 181.6
0.6612 0.6009
0.0005 0.0019 0.0043 0.0085 0.0131 0.0189 0.0305 0.0569 0.0914 0.1176
−78.3 −10.2 29.5 62.5 82.8 99.9 121.5 147.8 166.1 174.9
0.9330 0.9241 0.8842 0.8502 0.8190 0.7918 0.7471 0.6681 0.5939 0.5478
m/mol·kg−1
Φ
w = 0.20 EtOH−Water 0.7602 0.8351 0.6809 w = 0.30 EtOH−Water 0.9871 0.1385 0.9732 0.1654 0.9578 0.1944 0.9372 0.2219 0.9188 0.2753 0.8980 0.3358 0.8617 0.3993 0.7913 0.4768 0.7101 0.5532 0.6530
−E/mV
γ±
Φ
226.8
0.2634
−0.2126
180.2 185.6 190.0 193.2 198.1 201.9 204.5 206.6 207.7
0.5157 0.4797 0.4446 0.4145 0.3676 0.3245 0.2870 0.2504 0.2205
0.6094 0.5548 0.4978 0.4452 0.3458 0.2366 0.1252 −0.0079 −0.1363
where m is the molality of CsBr in the solvents and w the mass fraction of MeOH or EtOH in the mixed solvent. The measurement procedure applied in the experiment has been described in previous studies.10,11 The Cs-ISE was prepared by ourselves.14 The Br-ISE (model 302) was obtained from Jiangsu Electroanalytic Instrument Factory.
3. RESULTS The cell potential E is given by: E = E 0* − 2k ln(mγ±)
(2)
where γ± is the mean ion activity coefficient of electrolyte, k = RT/F, and R, T, and F have their usual meanings. E0* is the apparent standard potential of the cell which includes the asymmetry potential of both ISE electrodes.15 The molalities m and emf readings E are given in Table 1 for each MeOH−water and EtOH−water mixture, respectively. First of all, the activity coefficients of the CsBr in aqueous solutions were measured with molality between (0.0040 and 1.1219) mol·kg−1 for calibrating the electrode system and compared with the literature value.16 After the calculation of γ± at 25 °C, the Pitzer equation was employed for this system. When the obtained potentials were plotted against ln(mγ±), a good linear correlation is obtained with the values of E0*, k, and a correlation coefficient were 276.2 mV, (25.67 ± 0.02) mV (theoretical Nernst slope: 25.69 mV), and 0.9999, respectively. As it can be observed in Figure 1, two results are in good agreement. So the system containing bi-ISEs is enough for our study. The potentiometric data were correlated by the extended Debye−Hückel,17 Pitzer,18 and the modified Pitzer19 approaches. For a MX electrolyte, these equations are presented as follows: The extended Debye−Hückel equations:17
Figure 1. Plot of ln γ± vs m1/2 for CsBr in MeOH + H2O (top) and EtOH + H2O (bottom) at 298.15 K for different mass fractions: ○, 0, reference data;16 ●, 0; ▲, 0.10; ▼, 0.20; ◆, 0.30.
By fitting eqs 2 and 3, the results for E0*, a (the ion size parameter), c (the ion-interaction parameters), and d (the same as c) can be optimized. M and Ext are the average molecular mass of mixed and the contribution of the extended terms. The values of a, c, d, E0*, and the standard deviations are listed in Table 2. Based on the Pitzer equations,18 the excess Gibbs free energy (GE) can be written as:
log γ± = −Am1/2 /(1 + Bam1/2) + cm + dm2 − log(1 + 0.02mM ) + Ext
(3)
A = 1.8274·106ρ1/2 /(εT )3/2 kg1/2·mol−1/2
(3a)
where
B = 50.2901ρ1/2 /(εT )1/2 kg1/2·mol−1/2·Å−1
GE /(n w RT ) = f Gx + 2m2BGx + 2m3C Gx
(4)
where f Gx = −AφI ln(1 + b I )/b
(3b) 2605
(4a)
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Table 2. Values of E0* and the Debye−Hückel Parameters for CsBr in the Different (MeOH + Water and EtOH + Water) Mixtures at 298.15 K a w
c
Å
0.00 0.10 0.20 0.30
E0*
d −1
−2
g ·mol 2
kg·mol
CsBr + MeOH + Water −0.0350 0.00029 −0.0344 −0.1549 0.00024 −0.1544 −0.2755 −0.00008 −0.2756 −0.3534 0.00043 −0.3527
3.71 3.70 4.61 4.60 3.74 3.74 1.82 1.81
a
mV
SD
c
Å
E0*
d −1
−2
g ·mol 2
kg·mol
mV
SD
−289.2 −289.2 −304.8 −304.8 −316.1 −316.1
0.17 0.17 0.25 0.25 0.37 0.37
CsBr + EtOH + Water −276.2 −276.2 −285.7 −285.7 −298.0 −298.0 −309.4 −309.4
0.32 0.32 0.27 0.27 0.17 0.17 0.28 0.30
−0.1721 −0.1716 −0.3449 −0.3443 −0.5297 −0.5274
4.18 4.17 3.36 3.35 1.84 1.83
0.00029 0.00041 0.0014
Table 3. Values of Average Molecular Mass M, Dielectric Constant ε, Density d, Debye−Hückel Constants A and B, Pitzer Constants (Aφ), and the Bjerrum Parameter q for (MeOH + Water and EtOH + Water) Mixtures at 298.15 K M
d −1
w
ε
g·mol
Aφ
q
kg ·mol−1/2
Å
0.3285 0.3347 0.3419 0.3504
0.3921 0.4214 0.4562 0.5007
3.57 3.77 4.00 4.27
0.3380 0.3498 0.3635
0.4337 0.4877 0.5564
3.84 4.18 4.58
A −3
g·m
0.00 0.10 0.20 0.30
18.02 18.84 19.74 20.74
78.38 74.20 70.00 65.56
0.9971 0.9799 0.9645 0.9489
0.10 0.20 0.30
19.19 20.52 22.05
72.80 67.00 61.02
0.9804 0.9664 0.9505
B −1/2
−1/2
kg ·mol 1/2
mol
MeOH + Water 0.5100 0.5489 0.5944 0.6504 EtOH + Water 0.5650 0.6353 0.7249
−1
·Å
1/2
Table 4. Values of E0* and the Pitzer and Modified Pitzer Parameters of CsBr in the Different (MeOH or EtOH + Water) Mixtures at 298.15 K Pitzer β w
β
0 −1
kg·mol
modified Pitzer φ
1
−E * 0
C −1
kg·mol
−2
k ·mol 2
0.00 0.10 0.20 0.30
−0.0172 −0.1521 −0.2927 −0.4236
0.1933 0.3714 0.2806 −0.0829
0.0003 0.0003 −0.0001 0.0008
0.10 0.20 0.30
−0.1719 −0.3714 −0.6226
0.3231 0.2351 −0.0749
0.0004 0.0006 0.0025
mV
SD
C Gx = 1/2C φ ln γ± = f γ + mBγ + m2C γ ⎤ ⎡ I 2 f γ = −Aφ⎢ + ln(1 + b I )⎥ ⎦ ⎣1 + b I b
(4b)
C = 1.5C
φ
−2
kg·mol
k ·mol
−0.0345 −0.1754 −0.3093 −0.4112 −0.1943 −0.3916 −0.6126
2
mV
SD
0.0002 0.0002 −0.0001 0.0004
276.1 285.4 297.7 309.2
0.24 0.26 0.17 0.29
0.0002 0.0003 0.0013
288.9 304.5 315.9
0.15 0.25 0.37
(6)
where
(4c)
f φ = −Aφ
(5)
I 1+b I
Bφ = β 0 + β1e−α
I
(6a) (6b)
In these equations, the mean ionic activity coefficient (γ±) on the molality scale and osmotic coefficient (Φ) can be calculated. nw refers to the number of kilograms of solvent. m and I indicate the molality (mol·kg−1) and the total ionic strength. The parameters of a and b with constants are 2.0 and 1.2 kg1/2·mol−1/2. β0, β1, and Cφ are the interaction parameters. Aφ (kg1/2·mol−1/2) is defined by:
(5a)
2β1 [1 − e−α I (1 + α I − (1/2)α 2I )] α 2I (5b)
γ
kg ·mol
−E0*
CMX −1
Φ − 1 = f φ + mBφ + m2C φ
where
Bγ = 2β 0 +
BMX −1/2
CsBr + MeOH + Water 276.2 0.25 1.9040 285.6 0.29 2.5788 297.8 0.17 2.0355 309.2 0.29 0.9958 CsBr + EtOH + Water 289.1 0.18 2.3211 304.6 0.26 1.8737 315.8 0.37 1.0369
2β (1) [1 − e−α I (1 + α I )] α 2I
BGx = β (0) +
bMX 1/2
Aφ = 1.4006·106d1/2(ε /T )3/2
(5c) 2606
(7)
dx.doi.org/10.1021/je300671y | J. Chem. Eng. Data 2012, 57, 2603−2609
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The values of d, ε, M, A, B, Aφ, and q (Bjerrum parameter) are listed in Table 3, where the density and the dielectric constant are taken from the literature.10,15 By introducing eq 5 into eq 2, the values for E0*, β0, β1, and Cφ at each MeOH−water and EtOH−water mixture studied can be optimized. Table 4 shows the above values together with the corresponding standard deviation of the fit. According to the modified Pitzer equation:19 ln γ± = −Aφ[I1/2/(1 + bMX I1/2) + (2 + bMX I1/2) ln(1 + bMX I1/2) + 2m]BMX + 3m2C
(8)
By fitting eqs 2 and 8, the parameters of bMX, BMX, and CMX as well as the corresponding standard deviation are obtained and shown in Table 4.
4. DISCUSSION As shown in Tables 2 and 4, the results of E0* obtained in the fit using the Debye−Hückel, the Pitzer, and the modified Pitzer models are very close, and the standard deviations were found to be less than 0.40 mV. Moreover, for both mixed solvents, almost the same results are observed by the extended Debye− Hückel model with d = 0 or not. Therefore, from these three equations, the mean E0* values could be obtained for each solution. The average values listed in Table 5 were used to calculate the mean ionic activity coefficients, which are summarized in Table 1. Table 5. Average Values of Standard Potential E0* from Three Equations and Standard Gibbs Energy of Transference ΔGt0 of CsBr for MeOH + Water and EtOH + Water Mixtures at 298.15 K w 0.00 0.10 0.20 0.30
(−E0*)/mV
ΔGt0/kJ·mol−1
CsBr + MeOH + Water 276.2 ± 0.10 0.00 285.6 ± 0.15 0.91 297.8 ± 0.17 2.08 309.3 ± 0.20 3.19
(−E0*)/mV
Figure 2. Excess Gibbs free energy GE with molality of CsBr in MeOH−water (top) and EtOH−water (bottom) solvents at 298.15 K.
ΔGt0/kJ·mol−1
CsBr + EtOH + Water 289.1 ± 0.13 304.6 ± 0.21 315.9 ± 0.27
model. These profiles were observed in many similar systems.7,23 The averages of the E0* obtained by the three models are listed in Table 5. The standard free energy of transference, ΔGt0, which can be calculated from the average of E0* using the following equation:24
1.24 2.74 3.83
The values of a (ion size parameter) are almost constants with 3.47 Å and 3.27 Å for MeOH−water and EtOH−water mixtures. The average of a is less than the radii of ions in crystals Cs+ and Br− (3.63 Å),20 which can be explained by the ionic association or other reasons.21 In the CsBr + MeOH + water and CsBr + EtOH + water systems, (a − q) become negative with the mass fraction of alcohol increasing, as the same as the NaF15 in MeOH + water and EtOH + water, NaCl21 and NaF22 in ethylene carbonate + water mixtures, which indicate that the ionic association increased. Figure 1 shows the ln γ± vs m1/2 in different mass fractions of MeOH and EtOH in water at 298.15 K. The values of excess Gibbs free energies (GE) and osmotic coefficients (Φ) for all of the series were calculated by using the Pitzer ion-interaction parameters (see Table 4) into eqs 4 and 6. Figure 2 shows the calculated excess Gibbs free energies GE versus the molality of CsBr in different mass fractions of MeOH and EtOH in water. It can be observed from Figures 1 and 2, the values of mean activity coefficient and the excess Gibbs free energy decrease by increasing the molality of CsBr. The values of mean activity coefficients decrease with increasing the mass fraction of MeOH or EtOH content at a fixed molality of CsBr. This can be explained by the interaction
ΔGt 0 = −zF(Es 0 − Ew 0) = − zF(Es 0* − Ew 0*) − (Es asym − Ew asym)
(9)
where “w” and “s” refer to the pure water and the solvent mixture, respectively. Other symbols have their usual meaning. Equation 9 may be used without any problems when (Esasym − Ewasym) is insignificant compared to (E0s * − E0w*)4. The values of ΔGt0 appear in Table 5 for both the MeOH−water and the EtOH−water mixtures. It can be observed that the values of the standard Gibbs energy of transfer become more positive with the increase of the mass fraction of MeOH and EtOH in the mixture, which show the transference is not spontaneous and a decrease in solvation of CsBr in both alcohol−water systems. For MeOH−water and EtOH−water systems, the differences of the values of ΔGt0 mainly depend on the solvent properties (dielectric constant, polarizability, ability donation electron, etc). An important correlation was found by Feakins and French,25 which made a calculation of the primary hydration (nhydr) for 1:1-valent electrolyte, according to the following equation 2607
dx.doi.org/10.1021/je300671y | J. Chem. Eng. Data 2012, 57, 2603−2609
Journal of Chemical & Engineering Data ΔEc 0 = Ecs 0 − Ecw 0 = nhydr(RT /F )ln φw
■
(10)
(10a)
φw = (ww /d w )/(ww /d w + wo/do)
(10b)
where Em0 is the standard potential difference in molal scale and can be abbreviated as E0. φw is the volume fraction of water in the solvent mixture. Subscript “s”, “w” and “o” stand for mixed solvent, water, and organic component, respectively. Figure 3 is
Figure 3. Plot of ΔEc0 vs a function of the water volume fraction for MeOH−water (■) and ethanol−water (●) mixtures at 298.15 K.
the relationship between ΔEc0 vs (RT/F)ln φw for the two electrolytes. The values of nhydr obtained were 3.3 (r = 0.999) and 3.8 (r = 0.997) for CsBr in MeOH−water and EtOH− water mixtures.
5. CONCLUSION Using the galvanic cell Cs-ISE|CsBr(m), alcohol(w), water(1 − w)|Br-ISE, the mean ionic activity coefficients of CsBr in the MeOH−water and EtOH−water mixtures was obtained. The experimental data were correlated very well by Debye−Hückel, Pitzer, and modified Pitzer equations. Moreover, osmotic coefficients, excess Gibbs free energies, and the primary hydration were calculated along with the corresponding parameters. The Gibbs energies of transfer of the CsBr from the water to the MeOH + water and EtOH + water mixture were estimated. The results show that CsBr in the MeOH− water mixtures are more solvated than in the EtOH−water mixtures.
■
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being Ec 0 = Em 0 + 2k log ds
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This work was supported by the National Natural Science Foundation of China (No. 21171111) and the Fundamental Research Funds for the Central Universities (Program No. 2010ZYGX027). Notes
The authors declare no competing financial interest. 2608
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