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The Surface Charging at Low Density of Protonatable Surface Sites Marek Kosmulski Lublin University of Technology, Lublin, Poland Received April 15, 2005. In Final Form: June 9, 2005 The point of zero charge (PZC) of a sparingly soluble metal oxide depends on the density of protonatable surface oxygen atoms. The shift in the PZC is due to protonation/deprotonation of water in the regions free of protonatable surface oxygen atoms originating from the solid. The PZC of alumina increases when the density of protonatable surface oxygen atoms increases. In contrast, the PZC of titania is rather insensitive to the density of protonatable surface oxygen atoms. In surfaces of many materials the regions free of protonatable surface oxygen atoms dominate. These materials have a PZC at pH about 4.
1. Introduction 1
Yang et al. found the IEP of gas bubbles (hydrogen, oxygen) at pH about 4. Similar values of IEP were observed for ice2-4 and for several organic polymers.5 The coincidence of these IEP is probably due to a similar mechanism of surface charging in the above systems.6 In the case of the gas-water interface, and most likely also for ice-water and certain organic polymer-water interfaces, the dispersed phase does not provide protonatable oxygen atoms. We will term such systems nonprotonatable surfaces, to distinguish them from dispersed phases which expose protonatable surface groups, e.g., sparingly soluble metal oxides. Most experimental work has been carried out for protonatable surfaces, and most theoretical studies assume that the surface is protonatable. Namely, the surface charge of a sparingly soluble metal (hydr)oxide in contact with aqueous solution of 1:1 inert electrolyte (e.g., alkali metal nitrate V, chlorate VII, or halide) is attributed to protonation and deprotonation of surface sites, which are identified with protonatable surface oxygen atoms. The protonation and deprotonation of the surface sites can be induced by adjustment of the pH of the solution. At low pH, the reaction7
≡SO1/2- + H+ ) ≡SOH1/2
(1)
where S≡ denotes a surface atom, is shifted to the right, i.e., most surface sites are protonated, and the surface carries a positive charge. At high pH, reaction 1 is shifted to the left, most surface sites are deprotonated, and the surface carries a negative charge. Finally at pH equal to log K of reaction 1, the net surface charge density σ0 equals zero.5 Such a pH value can be determined experimentally as the point of zero charge (PZC), and it depends on the nature of the metal oxide. A few metal oxides, e.g., titania, produce a PZC that is rather insensitive to the experimental conditions, method, or specific sample of the solid. (1) Yang, C.; Dabros, T.; Li, D.; Czarnecki, J.; Masliyah, J. H. J. Colloid Interface Sci. 2001, 243, 128. (2) Drzymala, J.; Sadowski, Z.; Holysz, L.; Chibowski, E. J. Colloid Interface Sci. 1999, 220, 229. (3) Kallay, N.; Cakara, D. J. Colloid Interface Sci. 2000, 232, 81. (4) Kallay, N.; Cop, A.; Chibowski, E.; Holysz, L. J. Colloid Interface Sci. 2003, 259, 89. (5) Kosmulski, M. Chemical Properties of Material Surfaces; Marcel Dekker: New York, 2001. (6) Drzymała, J. Private communication, 2001. (7) Bolt, G. H.; van Riemsdijk, W. H. In Soil Chemistry B. PhysicoChemical Models, 2nd ed.; Bolt, G. H., Ed.; Elsevier: Amsterdam, 1982; p 459.
Reaction 1 combined with certain electrostatic models (diffuse layer, Stern) can be used to obtain model curves of surface charging. Specialized computer programs, e.g., ref 8, are available to adjust the model parameters to experimental data. In model calculations at least one adjustable parameter is required, namely, the concentration of the surface sites (surface oxygen atoms protonatable according to reaction 1). The literature reports the site densities found by numerical adjustment from the surface charging data, as well as from independent measurements (crystallographic data, IR spectra, tritium exchange9,10). In both categories, the values reported by different authors for the same metal oxide, and even for the same specimen, are rather scattered, and most reported values fall in the range5,9,10 from 1 to 30 sites nm-2. Site densities above 30 nm-2 were also reported, but very seldom. Very seldom a simple model based on reaction 1 properly reproduces the experimental results. Even when the dependence of the effect of the pH and ionic strength on σ0 is properly reflected, a simple model does not explain the discrepancies in the PZC between various specimens representing the same chemical compound. Namely, there is no apparent reason for a difference in K of reaction 1 between various samples of, e.g., hematite. More complex models make it possible to achieve a better match between calculated and measured charging curves. Actually the surface is heterogeneous, and there is a distribution of site density as a function of K rather than a constant K of reaction 1 for all surface sites. In the models taking into account the surface heterogeneity, different functions (discrete11 or continuous12) are used to represent such a distribution. For example, in the MUSIC model,11 the distribution function is based on the analysis of the crystal structure and contribution of particular faces to the total surface area. The sum (integral) of densities of all types of surface sites (over K) in the models taking into account the surface heterogeneity is up to about 30 sites nm-2, and the nonprotonatable portion of the surface does not contribute to the surface charge. The models taking into account the surface heterogeneity can be used to (8) Herbelin, A.; Westall, J. FITEQL, ver. 3.1; Oregon State University: Corvallis, OR, 1994. (9) Koretsky, C. K.; Sverjensky, D. A.; Sahai, N. Am. J. Sci. 1998, 298, 349. (10) James, R. O.; Parks, G. A. Surf. Colloid Sci. 1982, 12, 119. (11) Hiemstra, T.; van Riemsdijk, W. H.; Bolt, G. H. J. Colloid Interface Sci. 1989, 133, 91. (12) Rudzinski, W.; Charmas, R.; Piasecki, W.; Cases, J. M.; Francois, M.; Villieras, F.; Michot, L. J. Colloids Surf. A 1998, 137, 57.
10.1021/la051019o CCC: $30.25 © 2005 American Chemical Society Published on Web 07/06/2005
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explain the discrepancies in the PZC of various specimens representing apparently the same material. Namely, the effective PZC of a material depends on the contributions of particular types of surface sites, which have different acidities. When surface sites of low PZC prevail, the effective PZC of the surface is lower and vice versa. However, the practical success of the above approach in preparation of materials of preassumed PZC by adjustment of the morphology of the crystals is limited. Here we offer an alternative approach. In our model, nonprotonatable surfaces gain their surface charge due to protonation and deprotonation of the surface layer of water. As we show later, the nonprotonatable surfaces demonstrate a broad pH range where the σ0 is negligibly low in absolute value. Thus it is practically impossible to detect the PZC by potentiometric titration. On the other hand, the electrokinetic potential is high enough to precisely determine the IEP, which for pristine surface is assumed to be equal to PZC. When the surface is not protonatable (i.e., the dispersed phase does not provide protonatable oxygen atoms), proton affinity of the surface layer of water is independent of the nature of the dispersed phase (cf. results discussed above for air bubbles, etc.). Also in other systems with nonprotonatable surfaces, the IEP is at pH about 4. On the other hand, an experimentally found IEP at pH about 4 may suggest that the surface is not protonatable, although the same value of IEP may be produced by protonatable surfaces as well. The importance of protonation and deprotonation of the surface water is not limited to the systems with fully nonprotonatable surfaces. At sufficiently low concentration of protonatable surface groups originating from the dispersed phase, the nonprotonatable portion of the surface significantly affects the surface charging. Only at very high concentrations of protonatable surface groups originating from the dispersed phase, the classical models are satisfactory. In the present model calculations we are particularly interested in mixed (protonatable + nonprotonatable) surfaces, when both mechanisms of the surface charging (reaction and protonation/deprotonation of surface water) have to be taken into acount. 2. Model Calculations The surface density of proton charge was calculated for preassumed values of model parameters. No attempt was made to adjust the model parameters to a specific set of experimental data. The present model is not aimed at modeling of a single set of surface charging curves obtained for a certain sample at 3 or more different ionic strengths. This can be equally well done by means of the existing models. The present model qualitatively explains the trends in the PZC and in numerical values of surface charge density reported for different samples having the same formal chemical structure, but various densities of surface sites. The model parameters were adjusted to produce σ0 in the range of about 0.1 C m-2 in the presence of 0.1 mol dm-3 inert electrolyte, 3 pH units from the PZC (metal oxides) or at pH 7 (silica). The temperature was always 25 °C. The concentration of inert electrolyte (1:1 electrolyte, the nature of the anion and of the cation is immaterial) was 0.001, 0.01, 0.1, and 1 mol dm-3. The studied pH range was 3-11 (air, metal oxides) or 2-9 (silica). The effect of the concentration of 1:1 electrolyte on the activity of protons and of hydroxyl anions in solution was neglected (their activity was assumed to be equal to their molarity). The capacitance C of the Stern layer was assumed to be 1 F m-2. The relationship between the surface charge and
Kosmulski Table 1. The Stoichiometric Coefficients log K
ψ
≡SOH1/20 -0.5 ≡SOH21/2+ 6 0.5 H+ 0 nonprotonatable 0 surface + -3 1 excessive H on nonprotonatable surface missing H+ on -11 -1 nonprotonatable surface
≡SOH1/2-
nonprotonatable surface H+
1 1
1 1 1 1
1
1
-1
the surface potential in the Stern model is discussed in detail in refs 5, 13, and 14. The surface charging of four types of interfaces was studied. 2.1. Air-Water. The surface charging is due to the high field strength around the proton, which makes the proton more hydrophilic than the hydroxyl anion. According to Marcus15 the absolute Gibbs energy of proton hydration is -1056 kJ mol-1 while for the hydroxyl anion it is -439 kJ mol-1. Therefore, in a neutral solution (pH 7) there is an excess of hydroxyl anions and deficit of protons on the surface (with respect to the bulk composition), and the surface carries a negative charge. However, the sign of the surface charge can be reversed at sufficiently low pH, when the activity of protons in solution is higher than the activity of the hydroxyl anions by many orders of magnitude. In order to quantify this effect, the activity coefficients of the proton and of the hydroxyl anion in the interfacial layer were assumed to be equal to 103 and 10-3, respectively. These activity coefficients refer only to the transfer of proton from and to the nonprotonatable portion of the surface, and they do not apply to the surface charging reaction according to the 1 - pK model (reaction 1). The difference in the activity coefficients in the interfacial layer between proton and hydroxyl ions by a factor of 1 000 000 corresponds to a difference in Gibbs transfer energy by 34 kJ mol-1, i.e., by 1/18 of the difference in the bulk hydration energy quoted above. At pH 4 the concentrations of protons and hydroxyl anions in the interfacial layer are both equal to 10-7 mol dm-3, and the surface is electroneutral. The above value of the PZC corresponds to the IEP of gas bubbles reported in the literature.1 At pH below 4 the surface carries a positive charge. The interfacial region consists of a monomolecular layer of water molecules (30 molecules nm-2), which can be neutral (most of them), protonated (positively charged), or deprotonated (negatively charged). The ions of inert electrolyte do not have access to the surface, and they do not contribute to the surface charge. The ions of inert electrolyte contribute to the Stern layer (C ) 1 F m-2) and to the diffuse layer. In the basic version of the present model the effect of the nature of the 1:1 inert electrolyte on the surface charging is neglected (constant C), but the model can be refined to produce anionand cation-specific charging curves by allowing cationand anion-dependent C. The stoichiometric coefficients representing the chemical equilibrium problem of interest and the equilibrium constants are shown in Table 1. The columns represent the components, and the rows represent species. The approach to the chemical equilibrium problem used in (13) Westall, J.; Hohl, H. Adv. Colloid Interface Sci. 1980, 12, 265. (14) Lutzenkirchen, J. In Adsorption: Theory, Modeling and Analysis; Toth, J., Ed.; Marcel Dekker: New York, 2002; p 631. (15) Marcus, Y. Ion solvation; Wiley: New York, 1985; pp 107, 108.
Surface Charging of Protonatable Surface Sites
Figure 1. The surface charge density at the air-water interface.
the present paper was explained in detail, e.g., in ref 13. The empty cells are zeros. For an entirely nonprotonatable surface, the two first rows are not applicable. 2.2. Alumina-Water and Titania-Water. The protonatable surface sites, which belong to the solid (alumina or titania), react according to the equations (1 - pK model)
≡AlO1/2- + H+ ) ≡AlOH1/2+
log K ) 10 (2)
≡TiO1/2- + H+ ) ≡TiOH1/2+
log K ) 6 (3)
where ≡Al and ≡Ti denote surface atoms, and the log K values are taken from refs 5 and 11. The density of surface sites depends on a specific sample of alumina or titania, and it ranges from 2 to 30 sites nm-2. With a high site density (30 nm-2), protonation/deprotonation of the surface according to eq 2 or 3 is the only charging mechanism. With lower site density, the proton charge is due to two effects. The surface sites react according to eq 2 or 3. The nonprotonatable fraction of the interface reacts as described in section 2.1 (air-water interface). The surface density of water molecules which contribute to the surface charge according to the mechanism described in section 2.1 equals 30 nm-2 minus the density of the surface sites. The model calculations were carried out for site densities of 30, 20, 10, 5, and 2 nm-2. 2.3. Silica-Water. The surface sites of silica are neutral at low pH, and at high pH they gain negative charge according to the following reaction:
≡SiOH ) ≡SiO- + H+
log K ) -7 (ref 5) (4)
Similarly as described in section 2.2, the model calculations were carried out for a combination of charging mechanism due to reaction 4 with that discussed in section 2.1, and the sum of site density on one hand and surface concentration of water molecules on the other was 30 nm-2. The model calculations were carried out for site densities of 30, 20, 10, 5, and 2 nm-2. 3. Results and Discussion The σ0 as the function of pH and ionic strength is presented in Figures 1-4. The charging curves in Figures 1-3 representing four ionic strengths have a common intersection point at PZC (σ0 ) 0). In Figure 4, the charging curves representing four ionic strengths merge at low pH. The absolute value of σ0 increases when the ionic strength increases, and the four curves in each graph correspond
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to inert electrolyte concentrations of 0.001 (closest to the pH axis), 0.01, 0.1, and 1 mol dm-3 (most remote from the pH axis). The surface charging of the air-water interface is presented in Figure 1. The PZC is at pH 4, although very low absolute values of σ0 at pH < 7 do not allow to read the PZC from the graph. The shape of the charging curves of nonprotonatable surfaces shown in Figure 1 is significantly different from the shape of the charging curves of protonatable amphoteric surfaces (high slope of the charging curves near the PZC, cf. Figures 2a and 3a), and this difference makes it possible to distinguish between protonatable and nonprotonatable surfaces. Charging curves with a very low slope and with a very low absolute value of σ0 over a broad pH range (3 pH units or more) have been reported in the literature, chiefly for silica, but also for other materials.5 Very low absolute values of σ0 do not imply low absolute values of ζ potentials. For example, the σ0 of silica at pH 5 and at low ionic strength is negligibly low in absolute value, but the ζ potential is as high as about -50 mV for the same conditions.16,17 Thus, the PZC, which cannot be determined by surface titration, can be determined by electrokinetic methods (assuming that the IEP and PZC match) when the charging curve is similar to that shown in Figure 1. The surface charging of the alumina-water interface calculated for five different densities of surface sites is presented in Figure 2. The difference in the course between the charging curves obtained for 30 and 20 sites nm-2 is insignificant. Further decrease in the site density to 10 sites nm-2 induces a shift in the charging curves to the left by about 0.2 pH unit, and a decrease in the absolute value of σ0. Further decrease in the site density to 5 sites nm-2 induces a further shift in the charging curves to the left by about 0.2 pH unit, and a further decrease in the absolute value of σ0. Finally, a decrease in the site density to 2 sites nm-2 induces a shift in the PZC to pH 9.4, and a decrease in the absolute value of σ0 to up to 1/2 of the value obtained for 30 sites nm-2. On the positive branch of the charging curves, the most substantial decrease in the σ0 (by a factor of 2) is observed for 1 mol dm-3 inert electrolyte at pH about 3, and for lower ionic strengths and at higher pH the effect of the site density on the σ0 is less significant. Our results are very different from a classical model (neglecting the surface charging in nonprotonatable regions), in which the PZC is independent of the site density, and the absolute value of σ0 at given pH and ionic strength is nearly proportional to the site density. Thus, in a classical model, the absolute value of σ0 for 2 sites nm-2 would be lower by a factor of 15 than for 30 sites nm-2. On the negative branch of charging curves shown in Figure 2, the absolute value of σ0 at given pH and ionic strength increases when the site density decreases. This effect is due to a shift in the PZC to low pH. The surface charging of the titania-water interface calculated for five different densities of surface sites is presented in Figure 3. The difference in the course of the charging curves induced by a decrease in the site density is even less significant than that shown in Figure 2 (alumina). The PZC is rather insensitive to the site density. The absolute value of σ0 decreases as the site density decreases from 30 to 2 sites nm-2 by up to 1/3 at high pH (negative branch of charging curves) and by 1/5 at low pH (positive branch). The surface charging of the silica-water interface calculated for five different densities of surface sites is (16) Kosmulski, M.; Matijevic, E. Langmuir 1992, 8, 1060. (17) Hartley, P. G.; Larson, I.; Scales, P. J. Langmuir 1997, 13, 2207.
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Figure 2. The surface charge density at the alumina-water interface: (a) 30 sites nm-2, (b) 20 sites nm-2, (c) 10 sites nm-2, (d) 5 sites nm-2, (e) 2 sites nm-2.
presented in Figure 4. There is no PZC for 30 sites nm-2, and the surface is negatively charged over the entire pH range, but at lower site densities, the surface assumes a positive charge at very low pH. The PZC is at pH 2 for site density above 10 sites nm-2, and for 10, 5, and 2 sites nm-2 the PZC is at pH 2.1, 2.3, and 2.5, respectively, and it further shifts to high pH when the site density decreases. Thus, the scatter in the IEP of silica reported in the literature (from below 2 if any to about 45) can be due to the difference in the site density between various specimens. The relative effect of the site density on the σ0 of silica is the most significant at pH about 4. With high site densities, the negative σ0 is substantial at pH as low as 4, and with lower site densities, the σ0 is negligibly low at pH 4 or even higher. For all systems studied with 5 or more sites nm-2, the contribution of the nonprotonatable portion of the surface
to the total surface charge is negligible, irrespective of the ionic strength and the nature of protonatable sites. With 2 sites nm-2, the contribution of the nonprotonatable portion of the surface is as low as a few percent. Thus, almost the entire surface charge is located on the protonatable sites, and the effect of the nonprotonatable portion of the surface is indirect, via its effect on the surface potential. The results shown in Figures 2-4 comply with the experimentally observed trend5 that the PZC of different titanias reported in the literature are relatively consistent, and the PZC of different aluminas and iron (hyrd)oxides are less consistent. Figure 2 also explains why aluminum and iron hydroxides (high density of protonatable surface hydroxyl groups) have usually a higher PZC than anhydrous oxides of the same metals (high fraction of nonprotonatable surface).
Surface Charging of Protonatable Surface Sites
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Figure 3. The surface charge density at the titania-water interface: (a) 30 sites nm-2, (b) 20 sites nm-2, (c) 10 sites nm-2, (d) 5 sites nm-2, (e) 2 sites nm-2.
4. Possible Refinement of the Model The above presentation is limited to a combination of the model for nonprotonatable surface (with preassumed activity coefficients of proton and of hydroxyl anion in the surface layer) with a 1 - pK model (reaction 1) for protonatable surface and with the Stern electrostatic model (preassumed Stern layer capacitance of 1 F m-2). The model for nonprotonatable surface can be modified by changing (1) the activity coefficients of proton and of hydroxyl anion in the surface layer; (2) the density of protonatable water molecules (present value: 30 nm-2). The model for protonatable surface can be modified by (1) changing K of reactions 2-4; (2) switching from 1 pK to 2 - pK or to the triple layer18 model (TLM) (18) Davis, J. A.; James, R. O.; Leckie, J. O. J. Colloid Interface Sci. 1978, 63, 480.
(comparison of 1 - pK, 2 - pK, and triple layer models is presented in many reviews, e.g., refs 5 and 14); and (3) taking into account the surface heterogeneity within either of the above three models. The electrostatic model can be modified by (1) changing the Stern layer capacitance (for positive and for negative branch of charging curves); (2) switching from the Stern model to the diffuse layer or to the triple layer model. Moreover, the effect of the ionic strength on the activity coefficients of proton and of hydroxyl anion in solution can be taken into account. The above modifications make it possible to adjust the model curves to a specific set of experimental charging curves. The above modifications do not change the general trends observed in the present study, i.e., the shift in the PZC of alumina to low pH and the shift in the PZC of silica to high pH when the site density decreases. In other words,
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Figure 4. The surface charge density at the silica-water interface: (a) 30 sites nm-2, (b) 20 sites nm-2, (c) 10 sites nm-2, (d) 5 sites nm-2, (e) 2 sites nm-2.
the limited number of results shown in the paper is representative of an extensive modeling study involving hundreds of model curves, and study of the effect of all possible parameters. The present model can solve only a few problems encountered with surface charge modeling, and many problems persist. It is not a mechanistic model: attempts of derivation of the model parameters from the fundamental physical constants will be presented in a further paper. The present model inherited many problems from the original 1 - pK, 2 - pK, and TLM models. One problem is that models with few parameters are not able to reproduce the data, and with a higher number of model parameters, many sets of parameters produce practically identical model curves.19,20 (19) Katz, L. E.; Hayes, K. F. J. Colloid Interface Sci. 1995, 170, 477. (20) Kosmulski, M. Colloids Surf. A 1996, 117, 201.
5. Conclusions Our model explains the following effects observed experimentally, which are not reflected in classical models. 1. Relatively consistent absolute values of σ0 in a series of specimens representing the same chemical formula (in spite of various site densities). 2. Relatively consistent PZC of various titanias. 3. Discrepancies in the PZC between various aluminas (and other materials of high PZC) and between various silicas (and other materials of low PZC). 4. IEP at pH about 4 for many dissimilar materials. Acknowledgment. The author expresses his deep gratitude to Professor Jan Drzymała of Wrocław University of Technology, Wrocław, Poland, for fruitful discussions. LA051019O
