Article pubs.acs.org/JPCC
Hofmeister Effects on Cation Exchange Equilibrium: Quantification of Ion Exchange Selectivity Xinmin Liu, Hang Li,* Wei Du, Rui Tian, Rui Li, and Xianjun Jiang College of Resources and Environment, Southwest University, Chongqing, 400715, P. R. China ABSTRACT: The Hofmeister or specific ion effects are not involved in the existing ion exchange equilibrium theories. In this study, a new cation exchange model considering the specific ion effects was established. The relative adsorption ability was quantified through relative adsorption energy or selectivity coefficients of ions. The quantificational sequence of relative adsorption ratio ((relative adsorption energe for i ion)/(relative adsorption energy for j ion)) calculated from the new model was obtained: Ca > Mg ((Ca2+)/(Mg2+) = 1.407) > K ((Mg2+)/ K2+ = 1.467) > Na (K+/(Na2+) = 1.646) > Li ((Na2+)/(Li2+) = 1.110). It provided a new theory for quantificational description of ionic exchange adsorption selectivity for any ion pairs. The experimental data on various materials (montmorillonite, Illite, and Altamont soil) with very different charge densities agree well with each other. Thus we presume that the new model may apply to all charged surfaces.
1. INTRODUCTION Hofmeister or specific ion effects,1 which depend on system and are the results of pair interactions,2 universally occur in bulk solutions,3,4 at air/water interfaces,4,5 in colloidal and biological systems,3,4,6−8 and even in nonaqueous polar organic solvents.3 Ion exchange equilibrium that occurs at colloidal surfaces was associated with Hofmeister effects.9 The ion exchange selectivity was due to the ionic valence;10−14 however, it has been recognized that ion species with identical valence always exhibits different exchange selectivity.15−20 The ionic hydration14−16,18,21−29 and the ionic dispersion forces7,30 resulted in the Hofmeister effects in ion exchange. The law of matching water affinities (or ion hydration) dependent on ion surface charge density may be a factor that results in Hofmeister effects in free solution.26−28 Both hydration radius and dispersion forces become important only under high electrolyte concentrations,30−33 and the ion valencies are at least two.2 Therefore, with the decrease of electrolyte concentrations, the specific ion effects should decrease correspondingly, and at very low electrolyte concentrations the specific ion effects should disappear. However, Liu et al.15 and Kim et al.34 found that, with the decrease of electrolyte concentration, the specific ion effects sharply increased. In addition, ion specificity occurs at very low salt concentration in adsorption phenomena on solids because of polarizability of ions, ion−water, and ion−ion interactions.35,36 The strong electric field (usually exceeding 108 V/m) from surface charges exists near the charged particle surface and increases at low ion concentration in bulk solution,37 which strongly affects ion exchange equilibrium.15 The strong polarization effects, resulting from coupling between quantum fluctuation of ionic outer shell electrons and the surface electric field, strongly changes the electron cloud configuration of © 2013 American Chemical Society
adsorbed ions on the charged surface. The distance between the charge center of the ion and the surface (the strong electric field existence) will be smaller than the ion radius because the strong electric field repulses electrons and attracts the nucleus. In this study, a new model of ion exchange is established considering the discrepancy of the strong polarization forces of counterions in the adsorbed phase and is used for quantification of the Hofmeister effects on the ion exchange equilibrium. Exchange selectivity of monovalent (Li+, Na+, K+) and bivalent (Ca2+, Mg2+) cations on the negative charge surface is quantified based on the new model. The validity of the new model is verified through comparison ion exchange experiments on montmorillonite with Illite38 and Altamont soil39 in the literature.
2. THEORY 2.1. Selectivity Coefficient. The selectivity coefficient is defined as Ki/j =
ai0
aj0Ni ai0Nj
=
aj0 ∫
1/ κ
Sf (x)dx
i 0 0 1/ κ ai Sf j (x)dx 0
∫
(1)
aj0
where and are the activity of ions i and j species in bulk solution, respectively; Ni and Nj are the adsorption amount of the ith and jth ions; 1/κ is the thickness of the electric double layer; S is the specific surface area of charged particle; and f i(x) and f j(x) are the concentration distributions of the ith and jth ion species. This definition of selectivity has the following characteristics: the exchange adsorption ability of an ion can be Received: December 23, 2012 Revised: February 24, 2013 Published: March 1, 2013 6245
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⎛ ⎞ ⎛ ⎞ Δw̅ Δw̅ ⎜⎜1 + ⎟⎟ZiFφ0 − ⎜⎜1 − ⎟ZjFφ0 (Zi + Zj)Fφ0 ⎠ (Zi + Zj)Fφ0 ⎟⎠ ⎝ ⎝
easily evaluated: if Ki/j > 1, it means the adsorption of the ith ion species is stronger than the jth ion; contrarily, the adsorption of the ith ion species is weaker than the jth ion; it is independent of the valence of ions comparison with other definitions for selectivity.40−42 The defined selectivity coefficient Ki/j is the same with Vanselow coefficient KV for the monovalent ions.41 According to the classical theory, if the Coulomb force between the adsorbed ion and particle surface is the sole source of ion adsorption, we have ⎧ ⎪ wi(x) = ZiFφ(x) ⎨ ⎪ ⎩ wj(x) = ZjFφ(x)
= βi ZiFφ0 − βjZjFφ0
where Δw̅ = w̅ i(add) − w̅ j(add), and w̅ (add) is the average additional energy in the electric field. Thereby ⎧ Δw̅ ⎪ βi = 1 + + ( Z Zj)Fφ0 i ⎪ ⎨ Δw̅ ⎪ ⎪ βj = 1 − (Z + Z )Fφ i j ⎩ 0
(2)
βi + βj = 2
1/ κ −Z Fφ(x)/ RT i
Ki/j = =
e
K i / j = e−(wi̅ (total) − wj̅ (total))/2RT = e−(βiZiFφ0 − βjZjFφ0)/2RT
dx
∫
e
dx
= e−(ZiFφ0 − ZjFφ0)/2RT = e−(wi̅ − wj̅ )/2RT
(4)
where w̅ i = ZiFφ0 and w̅ j = ZiFφ0 are the mean Coulomb interaction energy as taking one mole of i and j cation species from x = 1/κ to x = 0, respectively. Here we suppose the electrolyte concentration in bulk solution is low, thus the effects of ionic hydration volume and dispersion force can be neglected.8,33,45 However, it is wellknown that the surface charges can set up a strong electric field in the space from the surface (usually >108 V/m) extending to a depth of several nanometers in suspension,38,46,47 and this strong electric field might result in strong polarization effects because the electron cloud configuration of ions may be strongly changed under such a strong electric field. Therefore, it will be possible that under low electrolyte concentrations the strong polarization effects may be the real source of the Hofmeister effects, which may profoundly influence cation exchange equilibrium. Taking into account the additional energies that come from the polarization in eq 4, we further suppose ⎧ ⎪ wi̅ (total) = wi̅ + wi̅ (add) = ZiFφ0 + wi̅ (add) ⎨ ⎪ ⎩ wj̅ (total) = wj̅ + wj̅ (add) = ZjFφ0 + wj̅ (add)
(9)
Hofmeister effects refer to the relativeness of anions or cations on a wide range of phenomena.9,30 Therefore, we presume that β values of ions in the new model can reflect the Hofmeister effects in cation exchange equilibrium, resulting from Coulomb and polarization of ions in the electric double layer. The ion with strong quantum fluctuation of outer shell electrons will lead to the strong additional adsorption energy. The water affinity of ions was the controlling factor for their behavior in water rather than polarization for ions.28 However, in the electric double layer, the polarization effects may be the main factor for adsorption on a solid surface. The surface potential increases with a decrease of ionic concentration,11,44,48 thus the selectivity coefficients of ions will increase at very low ion concentrations. 2.2. Calculation of Relative Charge Coefficients β. The average chemical potentials of ith ion species in the diffusion layer and in bulk solution are equal at equilibrium
(3)
1/ κ −Z Fφ(x)/ RT dx e i 0 1/ κ −(Zi − Zj)Fφ(x)/ RT
∫0
(8)
Thus, eq 4 can be modified
where R is the universal gas constant and T is the absolute temperature. Introducing eqs 2 and 3 into eq 1, we get37,44
∫0
(7)
One obtains
where w(x) is the electrostatic adsorption energy, Z the valence of ions, F the Faraday constant, and φ(x) the potential distribution in the electric double layer, and subscripts i and j are the ion species. Taking into account the ionic interaction energy in bulk solution, the Boltzmann equation can be expressed as43 ⎧ f (x) = a 0e−ZiFφ(x)/ RT i ⎪ i ⎨ ⎪ f (x) = aj0e−ZjFφ(x)/ RT ⎩ j
(6)
μi̅ (DL) = μi (Bulk)
(10)
where μ̅i(DL) is the average chemical potential of the ith ion species in the diffuse layer, and μi(Bulk) is the chemical potential of the ith ion species in bulk solution. In the diffuse layer there is μi̅ (DL) = μi0 + RT ln fi ̅ + RT ln γi ̅
(11)
where μi0 is the standard chemical potential of the ith ion species; fi̅ and γi̅ are the average concentration and average activity coefficient of the ith ion species in the diffuse layer, respectively; R is the universal gas constant; and T is the absolute temperature. Considering the ionic interaction (nonideal condition) in the bulk solution there is49 μi (Bulk) = μi0 + RT ln f i0 + RT ln γi
(12)
where f i0 is the concentration of the ith ion species in bulk solution, and γi is the activity coefficient of the ion species. Combining eqs 10−12, one obtains11,37
(5)
ai̅ = ai0
One has 6246
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Table 1. Surface Charge Number of the Used Montmorillonite total Mg2+
a
Mg2+ in interstitial solution
S.C.N.a
average values
volume (L)
conc. (mol/L)
quantity (cmol/kg)
volume (L)
conc. (mol/L)
quantity (cmol/kg)
(cmol(‑)/kg)
(cmol/kg)
0.25 0.25 0.25
0.002302 0.002429 0.002472
56.3 60.4 57.8
0.002125 0.002117 0.002320
0.003105 0.003105 0.003105
0.645 0.654 0.674
111.3 119.5 114.3
115.0
S.C.N.: surface charge number.
where ai0 is the activity of ion i in bulk solution; ai̅ is the mean activity of ion i in EDL; and σκ ai̅ = fi ̅ ·γi ̅ = i e βiZiFφ0 /2RT (14) m
where κ = (8πF I/εRT) ; S is the specific surface area; Nj is the adsorption amount of the jth ion; ε is the dielectric constant of the medium; and I is the ion strength in bulk solution. The selectivity coefficient Kj/i as a function of the ((Sma0j )/(Njκ)) term can be determined through ion exchange experiment, and then the ((βiZi − βjZj)/(βjZj)) value can be obtained.
analyzed for total milliequivilants of Mg2+ in the sample (exchangeable and dissolved in the interstitial solution) by means of an atomic absorption spectrophotometer (HITACHIZ2000). Following the washing with the 0.003 mol/L Mg(NO3)2 solution, the centrifuge tubes and its contents were weighed, and weights of the tube and sample were subtracted from the result to obtain the weight of the interstitial solution. Since the density of a 0.003 mol/L Mg(NO3)2 solution was known (≈1 g/mL), it was possible to convert the latter weight to the corresponding volume and thence to the milliequivalants of Mg2+ in the sample and in the interstitial solution. The difference between the two numbers equaled the exchangeable Mg2+, and the surface charge number can be estimated from the difference divided by the weight of the dry sample. The method was proposed by Low.50 3.2. Different Binary Cation Exchange Experiment. The H+ saturated montmorillonite sample (the ground montmorillonite was treated with 0.1 mol/L HCl and sieved through a 0.25 mm sieve after drying at 70 °C before exchange study) was used in the Li−Na, Li−K, and Na−K exchange experiments under a condition of T = 298 K and pH = 7. The exchange experiments followed the general procedure described in our previous study.15 In the Na−Mg exchange experiment, Na+ saturated montmorillonite was adopted, and the surface charge number was determined by the first experiment. Approximately 1 g of the Na-saturated sample was weighed into a 150 mL triangle bottle, and then standard MgCl2 (0.01 mol/L) solution was added in each triangle bottle (volume 20−60 mL). The suspension sample was allowed to equilibrate for 48 h with continuous shaking at 298 K and then centrifuged. The concentration of Mg2+ was determined by an atomic absorption spectrophotometer (HITACHI-Z2000), and Na+ was determined by a Na+-electrode. The adsorption amount of Mg2+, NMg, is the difference between the milliequivalants of Mg2+ in the sample and in the interstitial solution. The adsorption amount of Na+ was subtracted 2NMg from the surface charge number of montmorillonite determined in the first section, which was given as NNa.
3. EXPERIMENTAL METHODS 3.1. Determination of Surface Charge Number of the Montmorillonite. Purified montmorillonite (from WuHuaTianBao mineral resources Co., Ltd. in Inner Mongolia in China) was used as the experimental material, and its specific surface area (S) is 725 m2/g determined by our combined method.37 The surface charge number of the montmorillonite was determined in triplicate on 1 g samples. Every sample was weighed into a preweighed centrifuge tube (100 mL) and washed successively by dispersion, centrifugation, and decantation with five portions of 0.5 mol/L Mg(NO3)2 solution, five portions of 0.003 mol/L Mg(NO3)2 solution, and five portions of 0.5 mol/L Ca(NO3)2 solution. The washings with 0.5 mol/L Ca(NO3)2 solution were collected (volume 250 mL) and
4. RESULTS AND DISCUSSION 4.1. Surface Charge Number of the Montmorillonite. From Table 1, the surface charge number of montmorillonite is 115 cmol(‑)/kg (an immutable value because the contribution of variable charges was neglected). Low determined that the cation exchange capacity of different montmorillonite with specific surface area >700 m2/g was about 80−114.5 cmol(‑)/ kg.51 The specific surface area of montmorillonite is 725 m2/g determined by Li et al.,37 thus the charge density is 0.1530 C/ m2. 4.2. Relative Charge Coefficient in Different Cation Exchange Medium. The adsorption quantities of the kth ion
where fi̅ and γi̅ the mean activity and activity coefficient of ion i in EDL; σi is the adsorption density of ion i in EDL; the value of m (A−1ij in the literature)11 is 1.856 if the difference of moles of the 1:1 and 2:1 type of electrolytes in the solution mixture were not significant; m = 1.732 if the concentration of the bivalent counterion in bulk solution was much higher than that of the monovalent counterion, and contrarily m = 2, m = 0.5259 × ln( f+0/f++0) + 1.992 in other conditions; κ is the Debye− Hückel parameter; F is the Faraday constant; and φ0 is the surface potential (the potential at the original plane of the diffuse layer). From eqs 13 and 14, the relationships of βi values between the ith and jth counterion can be described as βi Zi ln
maj0 κσj
= βjZj ln
mai0 κσi
(15)
Combining eqs 13 and 14, the following expression can be obtained βjZjFφ0 2RT
= ln
mSaj0 Njκ
(16)
Combining eq 9 with eq 16, there is Kj / i
⎛ Sma 0 ⎞(βiZi − βjZj)/ βjZj j ⎟ = ⎜⎜ ⎟ N κ ⎝ j ⎠ 2
(17)
1/2
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Nk was calculated as: Nk = ( f k − f k0)V/M (f k is the initial concentration of the k ion, f k0 the equilibrium concentration of the k ion, V the volume of the suspension, and M the quality of montmorillonite). Even though the experimental material was prepared as a H+saturated sample in advance, hydroxides were used in the exchange reaction to make the pH = 7 in bulk solution when in equilibrium. The concentrations of cations were much higher than that of H+ in bulk solution (10−7 mol/L); therefore, the equilibrium state was essentially a binary exchange equilibrium between two cation species. At extremely low pH of 1.0 (0.1 mol/L HCl), many clays are unstable and subject to dissolution. However, our preliminary experiments showed that before and after H+ treatment there was no significant change in the montmorillonite structure observed.15 Using the experimental data of ion exchange, the relative charge coefficients of ions in Li−Na, Li−K, and Na−K exchange were determined and the results shown in Figures 1 and 2. The relative charge coefficient is totally independent of the ionic strength, thus the average values of β can be used. The βLi/βNa, βLi/βK, and βNa/βK were calculated in each exchange, βLi = 0.948 ± 0.016 and βNa = 1.052 ± 0.016 in Li−Na exchange (Figure 1a), βLi = 0.741 ± 0.007 and βK = 1.259 ± 0.007 in Li−K exchange (Figure 1b), and βNa = 0.756 ± 0.013 and βK = 1.244 ± 0.013 in Na−K exchange (Figure 1c). In accordance with the above calculations, the β values of different ions can be determined through different binary ion exchange experiments. The βNa (0.906 ± 0.016) and βMg (1.094 ± 0.016) are calculated from the data of Na−Mg exchange equilibrium on montmorillonite (Figure 2a); the βNa (0.741 ± 0.034) and βCa (1.259 ± 0.034) are determined from the Na− Ca exchange experiment on Illite (Figure 2b).52 The βNa/βCa (Figure 2b) and βNa/βMg (Figure 2a) are calculated from the results of exchange experiments on Illite and montmorillonite. The selectivity coefficients in Na−Ca and Na−Mg ion exchange can be described through eq 17, and the prediction curves are shown in Figure 3 (the solid line). On the basis of the classical theory, the βNa = βCa = βMg = 1, the selectivity coefficients are described through eq 17, and the results are shown in Figure 3 (the dashed line). In Na−Ca and Na−Mg exchange, the predicted results of selectivity coefficients for montmorillonite (solid line) based on the new model matched the experimental data for Altamont soil very well39 (Figure 3). If the relative charge coefficients were neglected, one cannot obtain the correct results (dashed lines in Figure 3). The charge density of montmorillonite σmont is 0.1530 C/m2 calculated from the determined specific surface area37 and the surface charge number (Table 1). The charge density of Illite σIllite is 0.2895 C/m238 and of Altamont soil σaltamont soil is 0.6276 C/m2.39,53,54 Although there is considerable difference of charge density among them, it is equivalent for the relative charge coefficients of Na/Ca and Na/Mg calculated from ion exchange on different surfaces. In a word, the new theory describing ion exchange equilibrium may be independent of materials because the main driving force is the strong electrostatic field coming from surface charges, and the intrinsic properties of surface charges on different materials are homogeneous. The origin of Hofmeister series may result from ion correlations that are based on the primitive water model and depends on the surface charge density or result from chemical specific adsorption that is based on short-range hydration phenomena and is independent of surface charge.2
Figure 1. Relative charge coefficients of cations in different binary cation exchange systems on montmorillonite, monomonovalent cations exchange.
However, in the present study, the permanently charged surface (no chemistry adsorption), montmorillonite, was used, and there is no difference by comparison to the ionic selectivity on it with the results on other materials in the literature (Illite and Altamont soil). 4.3. Quantification of Total Adsorption Energy in Different Ion Pair Exchange Equilibrium. The adsorption ability can be quantified based on the determined relative charge coefficients in different ion pairs. The total relative adsorption energy (w̅ i = βiZFφ0) can be quantified through the relative charge coefficient because each ion pair shares the unified surface potential φ0. The relative adsorption ratio, w̅ i/j = w̅ i/w̅ j = βiZi/βjZj, can be calculated, which represents the relative strength of ionic adsorption. According to the above calculations of relative charge coefficients in each ion exchange 6248
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Figure 2. Relative charge coefficients of cations in different binary cation exchange systems on montmorillonite (a) and Illite (b), monobivalent cations exchange.
= 1.699; w̅ K/Na = βK/βNa = 1.244/0.756 = 1.646; w̅ Mg/Na = 2βMg/βNa = 2 × 1.094/0.906 = 2.415; and w̅ Ca/Na = 2βCa/βNa = 2 × 1.259/0.741 = 3.398. From the above results, we can deduce w̅ Ca/Mg = w̅ Ca/Na/w̅ Mg/Na = 1.407 and w̅ Mg/K = w̅ Mg/Na/ w̅ K/Na = 1.467. These results indicate that the Hofmeister effects in ion exchange equilibrium not only are described but also are quantified. Comparing these values with each other, the Hofmeister sequence is: Ca (w̅ Ca/Mg = 1.407) > Mg (w̅ Mg/K =1.467) > K (w̅ K/Na =1.646) > Na (w̅ Na/Li =1.110) > Li. For example, the adsorption ability of Ca2+ is 1.407 times as strong as the one of Mg2+ in Ca−Mg exchange, and the adsorption ability of K+ is 1.646 times as strong as the one of Na+ in K−Na exchange. The essential reason for the difference of exchange adsorption between ions can be explained based on the new theory: not only the ionic valence but also the enhanced polarization of ions in the electric field from the charged particle surface. The selectivity coefficients of ions strongly depend on the relative adsorption energies based on the new model eq 9. On the basis of the new model for cation exchange equilibrium, once the relative charge coefficients β were determined, the selectivity coefficients in different binary exchange equilibrium can be described as a function of surface potential. The selectivity coefficients Ki/j also indeed reflect the adsorption ability; for example, Ki/j > 1 represents that the adsorption of ith ion species is stronger than the one of jth ion species. Moreover, the Ki/j values increase with increasing surface potential, which indicates that the ionic exchange adsorption was strongly affected by surface potential or electric field (Figure 4).
5. CONCLUSIONS The polarization of adsorbed ions in the strong electric field from surface charges may be an important reason for Hofmeister effects in ion cation exchange. A new cation exchange model considering the Hofmeister effects was established in the present study. The force of adsorption on a charged surface is the coupling effects of electrostatic and polarization of ions in the electric field originating from surface charges. The classical model neglecting the specific ion effects cannot obtain the correct results comparison with the experimental data. The Hofmeister sequences in ion exchange equilibrium were quantified based on the new model. The relative adsorption ability of ions was quantified by the total adsorption energy or selectivity coefficients. The sequence of relative adsorption ratio (w̅ i/j = w̅ i/w̅ j) calculated from the new model was obtained: Ca
Figure 3. Selectivity coefficients as a function of x = ((Sma0j )/(Njκ)) (j: Ca2+ in KCa/Na, Mg2+ in KMg/Na, and Ca2+ in KCa/Mg) in different binary ion exchanges. The specific surface area S of Altamont soil is 103 m2/g.53,54 Symbols are the experimental data on Altamont soil;39 the solid line denotes the new model for eq 17 as considering the relative charge coefficients on montmorillonite; and the dashed line represents the classical model for eq 17 as neglecting the difference between relative charge coefficients (β = 1 for all ions).
experiment, a series representing relative adsorption ability of unit charge cations is obtained (Na reference): Ca (βCa/βNa =1.699) > K (βK/βNa =1.646) > Mg (βMg/βNa =1.208) > Na (βNa/βNa =1) > Li (βLi/βNa =0.901). In addition, the w̅ i/j/w̅ Na/Li = βNa/βLi = 1.052/0.948 = 1.110; w̅ K/Li = βK/βLi = 1.259/0.741 6249
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Figure 4. Selectivity coefficients in different ion exchange as a function of surface potential. The minus of surface potential represents the sign of surface charge.
(w̅ Ca/Mg = 1.407) > Mg (w̅ Mg/K = 1.467) > K (w̅ K/Na = 1.646) > Na (w̅ Na/Li = 1.110) > Li. It provided a new theory for quantificational description of ionic adsorption selectivity for any ion pairs. For example, w̅ Mg/K = 1.467 indicated that the adsorption affinity of Mg2+ is 1.467 times as strong as the one of K+ in Mg−K exchange. In the new model, the relative charge coefficient of a given ion pair, reflecting the enhanced polarization in electric field from surface charges, was independent of charged surface. On the basis of the experimental data on various materials (montmorillonite, Illite, and Altamont soil) with very different charge density, we presumed that the new model may apply to all charged surfaces because the strong driving force that comes from surface charges is homogeneous.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: 086-023-68251504. Fax: 086-023-68250444. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (40971146), the National Basic Research Program of China (Grant No. 2010CB134511), Natural Science Foundation Project of CQ CSTC, the Doctor Foundation Program of Southwest University (SWU 111007), and Scientific and Technological Innovation Foundation of Southwest University for Graduates (Grant No. kb2010013).
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