**6. pH dependence of metastable-equilibrium adsorption**

According to MEA theory, both adsorbent/particle concentration (i.e., Cp) and adsorbate concentration could fundamentally affect equilibrium adsorption constants or isotherms when a change in the concentration of reactants (adsorbent or adsorbate) alters the reaction irreversibility or the MEA states of the apparent equilibrium. On the other hand, a general theory should be able to predict and interpret more phenomena. To test new phenomenon predicted by MEA theory can not only cross-confirm the theory itself but also provide new insights/applications in broadly related fields. The influence of adsorbate concentration on adsorption isotherms and equilibrium constants at different pH conditions was therefore studied in As(V)-anatase system using macroscopic thermodynamics and microscopic spectral and computational methods.14, 31, 32

The thermodynamic results14 showed that, when the total mass of arsenate was added to the TiO2 suspension by multiple batches, the adsorption isotherms declined as the multi-batch increased, and the extent of the decline decreased gradually as pH decreased from 7.0 to 5.5 (Figure 16). This result provided a direct evidence for the influence of adsorption kinetics (1 batch/multi-batch) on adsorption isotherm and equilibrium constant, and indicated that the influence varied with pH.

According to MEA theory, for a given batch adsorption reaction under the same thermodynamic conditions, when the reaction is conducted through different kinetic pathways (1-batch/multi-batch), different MEA states (rather than a unique ideal equilibrium state) could be reached when the reaction reaches an apparent equilibrium (within the experimental time such as days).14 Equilibrium constants or adsorption isotherms, which are defined by adsorption density, are inevitably affected by the reactant concentration when they alter the final MEA states.11, 12

Advances in Interfacial Adsorption Thermodynamics:

Metastable-Equilibrium Adsorption (MEA) Theory 537

Fig. 17. DFT calculated structure of inner-sphere and H-bond adsorption products of arsenate on TiO2: (a) monodentate mononuclear arsenate H-bonded to a H2O surface functional group occupying the adjacent surface site (MM1); (b) monodentate mononuclear arsenate H-bonded to a -OH surface functional group occupying the adjacent surface site (MM2); (c) bidentate binuclear (BB) complex; (d) H-bonded complex. Red, big gray, small gray, purple circles

The EXAFS coordination number of *CN*1 and *CN*2 represented statistically the average number of nearest Ti atoms around the As atom corresponding to a specific interatomic distance. We used the coordination number ratio of *CN*1/*CN*2 to describe the relative proportion of BB mode to MM mode in adsorption samples. The *CN*1/*CN*2 was 1.6 and 2.2 for 1-batch and 3-batch adsorption samples at pH 7.0, respectively (Table 1),14 indicating that 3-batch adsorption samples contained more BB adsorbed arsenate than that of 1-batch adsorption samples. This result was cross-confirmed by measuring the spectral shift of X-ray absorption near edge structure (XANES) and Fourier transform infrared spectroscopy

denote O, Ti, H, As atoms, respectively. Distances are shown in angstroms.

(FTIR).

Fig. 16. Adsorption isotherms of As (V) on TiO2 in 0.01mol/L NaNO3 solution at 25 °C under different pH. TiO2 particle concentration is 1g/L. 1-batch stands for a series of total arsenate being added to TiO2 suspension in one time, and 3-batch stands for the total arsenate being added averagely to TiO2 suspension in 3 times every 4 hours. EXAFS samples were marked by ellipse, in which the initial total As (V) concentration is 0.80 mmol/L.


Table 1. Summary of As(V) K-edge EXAFS results for 1-batch and 3-batch adsorption samples at pH 5.5, 6.2 and 7.0.

The comparison of EXAFS measured and DFT calculated results indicated that arsenate mainly formed inner-sphere bidentate binuclear (BB) and monodentate mononuclear (MM) surface complexes on TiO2, where EXAFS measured two As-Ti distances of 3.20±0.05 and 3.60±0.02 Å (Table 1) corresponded to the DFT calculated values of BB (3.25 Å) and MM (3.52 Å) complexes (Figure 17), respectively.14

Fig. 16. Adsorption isotherms of As (V) on TiO2 in 0.01mol/L NaNO3 solution at 25 °C under different pH. TiO2 particle concentration is 1g/L. 1-batch stands for a series of total arsenate being added to TiO2 suspension in one time, and 3-batch stands for the total

As-O

Sample

samples at pH 5.5, 6.2 and 7.0.

(3.52 Å) complexes (Figure 17), respectively.14

arsenate being added averagely to TiO2 suspension in 3 times every 4 hours. EXAFS samples were marked by ellipse, in which the initial total As (V) concentration is 0.80 mmol/L.

CN R(Å) σ2 CN1 R1(Å) σ2 CN2 R2(Å) σ<sup>2</sup> 1-batch pH5.5 3.9 1.68 0.002 1.9 3.17 0.008 1.1 3.60 0.01 8.6 1.8 3-batch pH5.5 4.0 1.68 0.002 2.2 3.26 0.01 0.9 3.61 0.008 14.2 2.4 1-batch pH6.2 4.0 1.68 0.002 1.8 3.16 0.007 1.0 3.59 0.006 11.0 1.7 3-batch pH6.2 3.9 1.68 0.002 2.1 3.19 0.008 0.8 3.59 0.01 9.0 2.5 1-batch pH7.0 4.1 1.69 0.002 1.8 3.17 0.007 1.1 3.59 0.001 13.2 1.6 3-batch pH7.0 4.1 1.68 0.002 2.2 3.22 0.004 1.0 3.60 0.001 10.9 2.2

As(V)-pH5.5 4.1 1.68 0.004 6.7 As(V)-pH7.0 4.1 1.69 0.003 5.3

Table 1. Summary of As(V) K-edge EXAFS results for 1-batch and 3-batch adsorption

The comparison of EXAFS measured and DFT calculated results indicated that arsenate mainly formed inner-sphere bidentate binuclear (BB) and monodentate mononuclear (MM) surface complexes on TiO2, where EXAFS measured two As-Ti distances of 3.20±0.05 and 3.60±0.02 Å (Table 1) corresponded to the DFT calculated values of BB (3.25 Å) and MM

Calculated values 4.0 1.70 2.0 3.25 1.0 3.52

As-Ti

BB MM Res. CN1/CN2

Fig. 17. DFT calculated structure of inner-sphere and H-bond adsorption products of arsenate on TiO2: (a) monodentate mononuclear arsenate H-bonded to a H2O surface functional group occupying the adjacent surface site (MM1); (b) monodentate mononuclear arsenate H-bonded to a -OH surface functional group occupying the adjacent surface site (MM2); (c) bidentate binuclear (BB) complex; (d) H-bonded complex. Red, big gray, small gray, purple circles denote O, Ti, H, As atoms, respectively. Distances are shown in angstroms.

The EXAFS coordination number of *CN*1 and *CN*2 represented statistically the average number of nearest Ti atoms around the As atom corresponding to a specific interatomic distance. We used the coordination number ratio of *CN*1/*CN*2 to describe the relative proportion of BB mode to MM mode in adsorption samples. The *CN*1/*CN*2 was 1.6 and 2.2 for 1-batch and 3-batch adsorption samples at pH 7.0, respectively (Table 1),14 indicating that 3-batch adsorption samples contained more BB adsorbed arsenate than that of 1-batch adsorption samples. This result was cross-confirmed by measuring the spectral shift of X-ray absorption near edge structure (XANES) and Fourier transform infrared spectroscopy (FTIR).

Advances in Interfacial Adsorption Thermodynamics:

adsorbed As(V)-1 batch

adsorbed As(V)-3 batches

**963**

**963**

TiO2

dissolved arsenate

**Absorbance**

dissolved arsenate, and TiO2 at pH 7.0.

complexes in real equilibrium adsorption.

Metastable-Equilibrium Adsorption (MEA) Theory 539

1000 950 900 850 800 750

**wavenumber(cm-1**

Theoretical equilibrium adsorption constant (*K*) of calculated surface complexes (BB, MM and H-bonded complexes in this adsorption system) that constructed real equilibrium adsorption constant were significantly different in the order of magnitude under the same thermodynamic conditions (Table 2). The theoretical *K* were in the order of BB (6.80×1042) >MM (3.13×1039) >H-bonded complex (3.91×1035) under low pH condition, and in the order of MM (1.54×10-5) > BB (8.72×10-38) >H-bonded complex (5.01×10-45) under high pH condition. Therefore, even under the same thermodynamic conditions, the real equilibrium adsorption constant would vary with the change of the proportion of different surface

DFT results (Table 2) showed that H-bond adsorption became thermodynamically favorable (-203.1 kJ/mol) as pH decreased. H-boned adsorption is an outer-sphere electrostatic attraction essentially (see Figure 17d), so it was hardly influenced by reactant concentration (multi-batch addition mode).14 Therefore, as the proportion of outer-sphere adsorption complex increased under low pH condition, the influence of adsorption kinetics (1-

Both the macroscopic adsorption data and the microscopic spectral and computational results indicated that the real equilibrium adsorption state of As(V) on anatase surfaces is generally a mixture of various outer-sphere and inner-sphere metastable-equilibrium states. The coexistence and interaction of outer-sphere and inner-sphere adsorptions caused the extreme complicacy of real adsorption reaction at solid-liquid interface, which was not taken into account in traditional thermodynamic adsorption theories for describing the macroscopic relationship between equilibrium concentrations in solution and on solid surfaces. The reasoning behind the adsorbent and adsorbate concentration effects is that the conventional adsorption thermodynamic methods such as adsorption isotherms, which are

batch/multi-batch) on adsorption isotherm would weaken (Figure 16).

Fig. 19. ATR-FTIR spectra of adsorbed As(V) of 1-batch and 3-batch adsorption samples,

**868**

**873**

**873**

**771**

**786**

**786**

**803**

**818**

**835**

**)**

**849**

**822**

**803**

**778**

**903**

**903**

**903**

DFT calculation showed that the theoretical XANES transition energy of BB complex was 0.62eV higher than that of MM complex. Therefore, the blue-shift of As (V) K-absorption edge observed from 1-batch to 3-batch adsorption samples suggested a structural evolution from MM to BB adsorption as the multi-batch increased (Figure 18).31

Fig. 18. The first derivative K-edge XANES spectra of As (V) adsorption on anatase.

The DFT calculated frequency analysis showed that the As-OTi asymmetric stretching vibration (υas) of MM and BB complexes located at 855 and 835 cm-1, respectively. On the basis of this theoretical analysis, the FTIR measured red-shift of As-OTi υas vibration from 1 batch sample (849 cm-1) to 3-batch sample (835 cm-1) suggested that the ratio of BB/MM in 3-batch sample was higher than that in 1-batch sample (Figure 19).32

The good agreement of EXAFS results of *CN*1/*CN*2 with XANES and FTIR analysis also validated the reliability of the CN ratio used as an index to approximate the proportion change of surface complexation modes. BB complex occupies two active sites on adsorbent surface whereas MM occupies only one. For monolayer chemiadsorption, a unit surface area of a given adsorbent can contain more arsenate molecules adsorbed in MM mode than that in BB mode. Therefore, the increase of the proportion of BB complex from 1-batch to 3-batch addition mode was shown as the decrease of adsorption density in 3-batch isotherm (Figure 16).

Table 1 showed that the relative proportion of BB and MM complex was rarely affected by pH change from 5.5 to 7.0, indicating that the pH dependence for the influence of adsorption kinetics (1-batch/multi-batch) on adsorption isotherm was not due to inner-sphere chemiadsorption.14 The influence of pH on adsorption was simulated by DFT theory through changing the number of H+ in model clusters. Calculation of adsorption energy showed that the thermodynamic favorability of inner-sphere and outer-sphere adsorption was directly related to pH (Table 2).14 As pH decreased, the thermodynamic favorability of inner-sphere and outer-sphere arsenate adsorption on Ti-(hydr)oxides increased. This DFT result explained why the adsorption densities of arsenate (Figure 16) and equilibrium adsorption constant (Table 2) increased with the decrease of pH.

DFT calculation showed that the theoretical XANES transition energy of BB complex was 0.62eV higher than that of MM complex. Therefore, the blue-shift of As (V) K-absorption edge observed from 1-batch to 3-batch adsorption samples suggested a structural evolution

Fig. 18. The first derivative K-edge XANES spectra of As (V) adsorption on anatase.

3-batch sample was higher than that in 1-batch sample (Figure 19).32

adsorption constant (Table 2) increased with the decrease of pH.

(Figure 16).

The DFT calculated frequency analysis showed that the As-OTi asymmetric stretching vibration (υas) of MM and BB complexes located at 855 and 835 cm-1, respectively. On the basis of this theoretical analysis, the FTIR measured red-shift of As-OTi υas vibration from 1 batch sample (849 cm-1) to 3-batch sample (835 cm-1) suggested that the ratio of BB/MM in

The good agreement of EXAFS results of *CN*1/*CN*2 with XANES and FTIR analysis also validated the reliability of the CN ratio used as an index to approximate the proportion change of surface complexation modes. BB complex occupies two active sites on adsorbent surface whereas MM occupies only one. For monolayer chemiadsorption, a unit surface area of a given adsorbent can contain more arsenate molecules adsorbed in MM mode than that in BB mode. Therefore, the increase of the proportion of BB complex from 1-batch to 3-batch addition mode was shown as the decrease of adsorption density in 3-batch isotherm

Table 1 showed that the relative proportion of BB and MM complex was rarely affected by pH change from 5.5 to 7.0, indicating that the pH dependence for the influence of adsorption kinetics (1-batch/multi-batch) on adsorption isotherm was not due to inner-sphere chemiadsorption.14 The influence of pH on adsorption was simulated by DFT theory through changing the number of H+ in model clusters. Calculation of adsorption energy showed that the thermodynamic favorability of inner-sphere and outer-sphere adsorption was directly related to pH (Table 2).14 As pH decreased, the thermodynamic favorability of inner-sphere and outer-sphere arsenate adsorption on Ti-(hydr)oxides increased. This DFT result explained why the adsorption densities of arsenate (Figure 16) and equilibrium

from MM to BB adsorption as the multi-batch increased (Figure 18).31

Fig. 19. ATR-FTIR spectra of adsorbed As(V) of 1-batch and 3-batch adsorption samples, dissolved arsenate, and TiO2 at pH 7.0.

Theoretical equilibrium adsorption constant (*K*) of calculated surface complexes (BB, MM and H-bonded complexes in this adsorption system) that constructed real equilibrium adsorption constant were significantly different in the order of magnitude under the same thermodynamic conditions (Table 2). The theoretical *K* were in the order of BB (6.80×1042) >MM (3.13×1039) >H-bonded complex (3.91×1035) under low pH condition, and in the order of MM (1.54×10-5) > BB (8.72×10-38) >H-bonded complex (5.01×10-45) under high pH condition. Therefore, even under the same thermodynamic conditions, the real equilibrium adsorption constant would vary with the change of the proportion of different surface complexes in real equilibrium adsorption.

DFT results (Table 2) showed that H-bond adsorption became thermodynamically favorable (-203.1 kJ/mol) as pH decreased. H-boned adsorption is an outer-sphere electrostatic attraction essentially (see Figure 17d), so it was hardly influenced by reactant concentration (multi-batch addition mode).14 Therefore, as the proportion of outer-sphere adsorption complex increased under low pH condition, the influence of adsorption kinetics (1 batch/multi-batch) on adsorption isotherm would weaken (Figure 16).

Both the macroscopic adsorption data and the microscopic spectral and computational results indicated that the real equilibrium adsorption state of As(V) on anatase surfaces is generally a mixture of various outer-sphere and inner-sphere metastable-equilibrium states. The coexistence and interaction of outer-sphere and inner-sphere adsorptions caused the extreme complicacy of real adsorption reaction at solid-liquid interface, which was not taken into account in traditional thermodynamic adsorption theories for describing the macroscopic relationship between equilibrium concentrations in solution and on solid surfaces. The reasoning behind the adsorbent and adsorbate concentration effects is that the conventional adsorption thermodynamic methods such as adsorption isotherms, which are

Advances in Interfacial Adsorption Thermodynamics:

[2] Sverjensky, D. A., *Nature* 1993, 364 (6440), 776-780.

**7. Acknowledgment** 

Oxford, 2006.

3247.

1873-1879.

271 (1), 35-40.

271 (1), 28-34.

1522.

961.

**8. References** 

Metastable-Equilibrium Adsorption (MEA) Theory 541

The study was supported by NNSF of China (20073060, 20777090, 20921063) and the Hundred Talent Program of the Chinese Academy of Science. We thank BSRF (Beijing),

[1] Atkins , P. W.; Paula, J. d., *Physical Chemistry, 8th edition*. Oxford University Press:

[8] Cheng, T.; Barnett, M. O.; Roden, E. E.; Zhuang, J. L., *Environ. Sci. Technol.* 2006, 40, 3243-

[13] He, G. Z.; Pan, G.; Zhang, M. Y.; Waychunas, G. A., *Environ. Sci. Technol.* 2011, 45 (5),

[15] Nyffeler, U. P.; Li, Y. H.; Santschi, P. H., *Geochim. Cosmochim. Acta* 1984, 48 (7), 1513-

[19] Li, X. L.; Pan, G.; Qin, Y. W.; Hu, T. D.; Wu, Z. Y.; Xie, Y. N., *J. Colloid Interface Sci.* 2004,

[20] Pan, G.; Qin, Y. W.; Li, X. L.; Hu, T. D.; Wu, Z. Y.; Xie, Y. N., *J. Colloid Interface Sci.* 2004,

[23] Drits, V. A.; Silvester, E.; Gorshkov, A. I.; Manceau, A., *Am. Mineral.* 1997, 82 (9-10), 946-

[25] Manceau, A.; Lanson, B.; Drits, V. A., *Geochim. Cosmochim. Acta* 2002, 66 (15), 2639-2663.

[29] Li, W.; Pan, G.; Zhang, M. Y.; Zhao, D. Y.; Yang, Y. H.; Chen, H.; He, G. Z., *J. Colloid* 

[30] Sander, M.; Lu, Y.; Pignatello, J. J. *A thermodynamically based method to quantify true* 

[22] Bochatay, L.; Persson, P.; Sjoberg, S., *J. Colloid Interface Sci.* 2000, 229 (2), 584-592.

[26] Silvester, E.; Manceau, A.; Drits, V. A., *Am. Mineral.* 1997, 82 (9-10), 962-978.

SSRF (Shanghai), and KEK (Japan) for supplying synchrotron beam time.

[3] O'Connor, D. J.; Connolly, J. P., *Water Res.* 1980, 14 (10), 1517-1523. [4] Voice, T. C.; Weber, W. J., *Environ. Sci. Technol.* 1985, 19 (9), 789-796.

[6] Benoit, G., *Geochim. Cosmochim. Acta* 1995, 59 (13), 2677-2687.

[11] Pan, G.; Liss, P. S., *J. Colloid Interface Sci.* 1998, 201 (1), 77-85. [12] Pan, G.; Liss, P. S., *J. Colloid Interface Sci.* 1998, 201 (1), 71-76.

[5] Honeyman, B. D.; Santschi, P. H., *Environ. Sci. Technol.* 1988, 22 (8), 862-871.

[7] Benoit, G.; Rozan, T. F., *Geochim. Cosmochim. Acta* 1999, 63 (1), 113-127.

[9] McKinley, J. P.; Jenne, E. A., *Environ. Sci. Technol.* 1991, 25 (12), 2082-2087. [10] Higgo, J. J. W.; Rees, L. V. C., *Environ. Sci. Technol.* 1986, 20 (5), 483-490.

[14] He, G. Z.; Zhang, M. Y.; Pan, G., *J. Phys. Chem. C* 2009, 113, 21679-21686.

[21] Bochatay, L.; Persson, P., *J. Colloid Interface Sci.* 2000, 229 (2), 593-599.

[28] Post, J. E.; Appleman, D. E., *Am. Mineral.* 1988, 73 (11-12), 1401-1404.

*sorption hysteresis*; Am Soc Agronom: 2005; pp 1063-1072.

[24] Post, J. E.; Veblen, D. R., *Am. Mineral.* 1990, 75 (5-6), 477-489.

[27] Wadsley, A. D., *Acta Crystallographica* 1955, 8 (3), 165-172.

*Interface Sci.* 2008, 319 (2), 385-391.

[16] Dzombak, D. A.; Morel, F. M. M., *J. Colloid Interface Sci.* 1986, 112 (2), 588-598. [17] Pan, G.; Liss, P. S.; Krom, M. D., *Colloids Surf., A* 1999, 151 (1-2), 127-133. [18] Pan, G., *Acta Scientiae Circumstantia* 2003, 23 (2), 156-173(in Chinese).

defined by the macroscopic parameter of adsorption density (mol/m2), can be inevitably ambiguous, because the chemical potential of mixed microscopic MEA states cannot be unambiguously described by the macroscopic parameter of adsorption density. Failure in recognizing this theoretical gap has greatly hindered our understanding on many adsorption related issues especially in applied science and technology fields where the use of surface concentration (mol/m2) is common or inevitable.


Table 2. Calculated Δ*G*ads (kJ/mol) and equilibrium adsorption constant *K* at 25 °C of arsenate on various protonated Ti-(hydr)oxide surfaces.

Metastable-equilibrium adsorption (MEA) theory pointed out that adsorbate would exist on solid surfaces in different forms (i.e. MEA states) and recognized the influence of adsorption reaction kinetics and reactant concentrations on the final MEA states (various outer-sphere and inner-sphere complexes) that construct real adsorption equilibrium state. Therefore, traditional thermodynamic adsorption theories need to be further developed by taking metastable-equilibrium adsorption into account in order to accurately describe real equilibrium properties of surface adsorption.
