866
Langmuir 1994,10,855-860
Chromatographic Charge Density Determination of Materials with Low Surface Area Christa S. Burgisser, Andre M. Scheidegger,t Michal Borkovec,*and Hans Sticher Institute of Terrestrial Ecology, Federal Institute of Technology (ETH), Grabenstrasse 3, 8952 Schlieren, Switzerland Received August 30,1993. In Final Form: November 29,1993@ A new method is presented for the determination of the charge density as a function of pH for oxides. From measured pH-breakthrough curves through a chromatographic column filled with the sorbent, one can obtain the charge density by a simple integration. This method is specially interesting when classical titration experiments cannot be applied, for example, if the sorbent has a low surface area with not enough sites to be detected by common potentiometric titrations. The feasibility of the technique is demonstrated by measuring charge densities of silica and iron oxides and comparing with known data.
Introduction Important characteristics of sorbents in aqueous media are their number of sites and the charge densities in dependence on pH and on ionic strength. Usually, this information is obtained by classical potentiometric titration experiments and many results of this kind can be found in the 1iterature.l However, such titration experiments are limited to materials with sufficiently high surface area. The number of sites must typically exceed 1W mol/L solution so that they can be detected in this fashion. Therefore, materials of low surface area are hardly possible to analyze with this titration technique. For minerals with a typical number of sites of around 10-8 mol/m2the surface area should be roughly larger than 1 m2/g in order to obtain a reasonable solid-liquid ratio. For materials with a lower surface area the classical titration procedure becomes extremelydifficult. Very few results of this kind have been reported where a special mass titration technique has been employed.2 Nevertheless, sorption processes can be studied in several different ways. Beside the batch procedure, alternative techniques rely on the use of flow-through ~ ~this reactorsa or on chromatographic e ~ p e r i m e n t s .In article we show how the chromatographic method can be used for the determination of the charge density at different pH values. The charge density as a function of pH can be viewed as an adsorption isotherm of the socalled acidity. This isotherm has a S-shaped or sigmoidal form. Nonlinear chromatography literature shows how such an isotherm can be extracted from the breakthrough
* To whom correspondence should be addressed. 'Present address: Department of Plant and Soil Sciences, University of Delaware, Newark, DE 19717-1303. a Abstractpublishedin Aduance ACSAbstracts, February 1,1994. (1) Stu", W. Aquatic Surface Chemistry; John Wiley & Sons: New York, 1987. Bolt, G. H.; De Boodt, M. F.; Hayes, M. H. B.; McBride, M. B. Interactions at the Soil Colloid-Soil Solution Interface; NATO ASI, Series E Applied Sciences, Vol. 190, Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991. (2)Ahmed, S.M. Can. J. Chem. 1966,44, 1663. (3) Caraki, T. H.; Sparks, D. L. Soil Sei. SOC.Am. J. 1985,49, 1114. Miller, D. M.; Sumner, M. E.; Miller, W. P. Soil Sci. SOC. Am. J. 1989, 53, 373. (4) DeVault, D. J. Am. Chem. SOC.1943,65,532. (5) Glueckauf, E. J. Chem. SOC.1947,149, 1302. (6) Helfferich,F.;Klein,G.MulticomponentChromatography: Theory of Interference; Marcel Dekker: New York, 1970. (7) Schweich, D.; Sardin, M. J. Hydrol. 1981, 60, 1. (8) Griffioen, J.; Appelo, C. A. J.; Van Veldhuizen, M. Soil Sci. SOC. Am. J. 1992.66.1429. (9) Birrgikr; C. S.; Cemik, M.; Borkovec, M.; Sticher, H. Environ. Sci. Technol. 1993, 27 (5), 943.
curves. This method can also be applied for the charge density determination of materials with surface areas well below 1 m2/g, and one can investigate a wide variety of materials which are essentially inaccessible by classical potentiometric titration. As will be discussed later, not all materials can be analyzed with the same ease. The practicability of the method depends particularly on the surface charge density and the slope of the charging curve. The main disadvantage of this method is that it is hardly possible to obtain charge densities around pH 7. Depending on the time scale of the experiment, the dissolution of the material may pose problems. As proton adsorption is usually a fast process the chromatographicexperiments can be performed at high flow rate, where dissolution processes can be neglected.
Concepts NonlinearChromatography. The behavior of a single component in local equilibrium has been described in the nonlinear chromatography literature.6JJ0 The concentration c(x,t) of a sorbing chemical per unit volume of the mobile phase (being a function of location x and time t) is described by the convection-dispersion equation
where v is the travel velocity, D the dispersion coefficient, q the amount of the sorbed species per unit mass of sorbent, and p the mass of sorbent per unit pore volume. For a nonsorbing chemical, a so-called conservative tracer, eq 1 can be solved analytically.11 The response of a dirac-pulse of this tracer at the outlet of the column of length L has a Gaussian shape with the average time t o = L/u and a standard deviation u. The relative width of the pulse u2/ to2 = 2/Pe can be related to the column Peclet number Pe = Lv/D. For adsorbing species the response of the chromatographic column can be directly expressed in terms of the adsorption is~therm.~J*~JO For the case of a linear adsorption isotherm (q = KDC,where KD is the partition coefficient), the breakthrough curve has the same shape as a conservative tracer but is delayed in time by the retention factor R = 1+ ~ K D In . the case of a chemical ~
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(10) Aris, R.; Amundson, N. R. Mathematical Methods in Chemical Engineering, 2. First-Order Partial Differential Equations with Applications; Prentice-Hak Englewood Cliffs, NJ, 1973. (11) For a review see: Villermaux, J. In Percolation Roces8e8; Rodriguea, A. E., Tondeur, D., Eds.; Sijthoff L Noordhofi Alphen aan den Rijn, T h e Netherlands, 1981; p 83.
0743-7463/94/2410-0855$04.50/0 0 1994 American Chemical Society
Biirgisser et al.
856 Langmuir, Vol. 10, No. 3, 1994
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Figure 1. Schematic representation of the response of a chromatographic column to a sigmoidal isotherm (a). Below, the column breakthrough of a step concentration change without dispersion effectsie shown: (b) change from c1 to C5 and back; (c) change from c1 to cg (I) and from c6 to cg (11). obeying a convex adsorption isotherm (e.g. Langmuir isotherm) a self-sharpening adsorption front and a diffuse desorption front develop. For a concave isotherm the reverse is true. Neglecting dispersion effects (D= 0) the shape of the diffuse front can be calculated from eq 1.The concentration c moves with a velocity10
The concentration-dependent retention time t ( c ) is related to the derivative of the adsorption isotherm (3)
Furthermore, the experimental record of the retention time t ( c ) can be integrated to obtain the adsorption isotherm by q ( c ) = q(co)
+P
( y-
1) dc'
(4)
The value of the overall retention factor R, which represents the area of the normalized breakthrough curve, is given by
The influence of the dispersion onto the diffuse part of the isotherm can be considereds as negligibly small for column Peclet numbers Pe > 50. In the case of sigmoidal isotherms the presence of combined fronts complicates the situation somewhat. Breakthrough fronts may contain diffuse and sharp ~ a r t a . ~Let J us consider the breakthrough of a chemical which obeys a sigmoidal isotherm, shown in Figure la. For an input step change in concentrations from c1 to c6 the column response is shown in Figure lb. Both, the adsorption and desorption front start with a diffuse part which is followed by a sharp part. The concentrations where these changes happen (namely at c2 and c4) can be obtained according to the Golden rule or string rule.7112 At (12)Golden, F. M. PhD. Dissertation, University of California a t Berkeley, CA, 1969.
Figure 2. (a)Schematicrepresentation of the chargingbehavior of silica (I)and goethite (11) plotted as surface charge density IJ versus pH. (b) Schematic acidity adsorption isotherm for silica or goethiteplotted as adsorbedacidityq versus acidity in solution c. (c) Response of a chromatographic column with a step input from a low acidity concentration (high pH, where c < 0) to a high one (low pH, where c > 0) and back. (d) Same column response as shown in (c), but in pH units. the concentration c2 the tangent drawn from the point cg touches the adsorption isotherm (similarlyat c4 the tangent goes from c1). Note that the breakthrough curve shown in Figure l b contains no information on the isotherm between concentration c2 and c4. Therefore, in the case of a sigmoidal isotherm, it is not possible to calculate the entire adsorption isotherm from a single chromatographic experiment. Fronts covering the whole concentration range can, however, be obtained6 by performing two experiments to the point of inflection c3. The first experiment goes from concentration c1 to c3 (Figure IC, curve I). The column must be preequilibrated with a solution of concentration c1. The experiment starts by flushing a solution of concentration c3 through the column. The formed diffuse front of this experiment can be integrated from c1 to cg according eq 4 to obtain the lower branch of the adsorption isotherm. The isotherm must then be shifted by q(c1) in order to take the amount already adsorbed on the surface at concentration c1 into account. In a second experiment the column must be first saturated with solute of the concentration cg before eluting with a solution of concentration c3 (Figure IC,curve 11). The integration of the diffuse front according to eq 4 from cg to cg yields the upper branch of the adsorption isotherm. A shift of q(c3) which is known from the first experiment must be included. Charge Densities. In Figure 2a charge densities of silica (curve I) and goethite (curve 11)as a function of the pH are plotted schematically. The proton adsorption reactions on the oxide surfaces can be described by a twopK model which involves the following reactions
S-O-+ H+ + S-OH S-OH + H+ + S-OH2+
K,
(6)
K2 (7) For silica log K1 around 7 and log K2 near -2 were reported.lSl6 The charging behavior is fully dominated by the protonation of oxo groups (eq 6). Due to the very low log K2 the proton adsorption on SiOH surface groups (eq 7)can be neglected. For the point of zero charge (pzc) of silica, values between pH 1 and 3.7 have beenreported.l6 (13)Schindler,P.;Kamber, H. R.Helu. Chim. Acta 1968,61(7),1781. (14)Manrhall, K.;Ridgewell, G. L.;Rochester,C. H.;Simpeon, J. Chem. Ind. (London) 1974.19.775. (16)Hiemsba, T.;De Wit, J. C. M.; Van Riemdijk, W. H. J. Colloid Interface Sci. 1989,133 (l), 105. (16)Parks, G. A. Chem. Rev. 1966,66,177.
Charge Density Determination The protonation of goethite can also be described by a two-pK model.l7-l9 The two-pK model has been questioned by Hiemstra et al.,m who have introduced a multisite complexation model. The pzc value of goethite presented varies from pH 7 to 10. in the literature15~17~l*~21~22 In our context, molecular interpretation of the titration curve is not important. Rather we have to know the charge densities as a function of pH. Due to the different protonation behavior of the two oxides the charge density curves have completely different shapes.15 The development of charge densities with pH can also be viewed as adsorption of the so-called acidity. Thus the charge density curve can be transformed into an acidity adsorption isotherm. The fundamental quantity, which we shall call the acidity defined with respect to pure water,23is the difference between the total proton and hydroxyl concentration. In the case of no other protonation reactions in solution this concentration c is given by
which can be calculated from the pH of the solution (pH = -log [H+l) and the ion product of water Kw= W4M2 at 25 OC. The amount of sorbed acidity q is proportional to the charge density Q and can be calculated from
= uA/F (9) where A is the specific surface area of the material per unit mass and F the Faraday constant. Since the concentrations of H+ and OH- are always related by the constant ion product of water, we can consider the acidity as a single component, obeying the convection-dispersion equation (eq 1). Note that c and q can also have negative values. In Figure 2b we plot the charging curve as an acidity adsorption isotherm. The isotherm appears Sshaped, in the case of silica as well as in the case of goethite. Based on the reasoning presented previously one can directly predict the breakthrough curves from the acidity isotherms. The point of inflection lies near pH = 7 where c = 0. Applying the Golden rule to the isotherm shown in Figure 2b, we obtain the column response presented in Figure 2c. One obtains this result for a step input from a low acidity concentration to a high one and back. The same breakthrough,but in more familiar pH units is shown in Figure 2d. To evaluate the charging curve from the column experiment, one has to perform breakthrough step experiments between solutionsof different pH. The column must be preequilibrated with an unbuffered inert-electrolyte solution of an adjusted pH and then flushed with a solution of a pH near 7. After recording the breakthrough of the solution one changes back to the preequilibration solution. To obtain the acidity adsorption isotherm over the whole pH range, two such experiments must be performed (as schematically represented in Figure IC), q
(17) Balistrieri, L.;Murray, J. W. In Chemical Modeling in Aqueous System; Jenne, E. A,, Ed.; American Chemical Society: Washington, DC, 1979; p 275. (18) Sigg, L.;Stumm, W. Colloids Surf. 1980, 2, 101. (19) Hayen, K.F.;Papelis, C.; Leckie, J. 0. J. Colloid Interface Sci. 1988,125 (2), 717. (20) Hie",T.;VanRiemdjk, W. H.;Bolt,G.H.J. Colloidlnterface Sci. 1989, 133 (l),91. (21) Hingeton, F.J.; Po", A. M.; Quirk, J. P. J. Soil Sci. 1972,23, 177. (22) Bloeech, P.M.;Bell, L. C.; Hughes, J. D. Aust. J. Soil Res. 1987, 25,377. (23) Stumm, W.; Morgan, J. J. Aqwtic Chemistry; John Wiley & Sons: New York, 1981. Morel, F. M.M.; Hering, J. G. Principles and Applications of Aquatic Chemistry; John Wiley & Sons: New York, 1993.
Langmuir, Vol. 10, No. 3, 1994 857 first with a preequilibrating solution of a high pH (ci for experiment I), second with a low pH (cg for experiment 11). For both experiments the breakthrough curves of the solution of pH near 7 (c3) show a diffuse front. By integratingthese two diffuse fronts (using eq 4), one obtains the two branches of the acidity adsorption isotherm as discussed above. If the two experiments are performed to the same pH near 7, the two branches can be combined to obtain the whole sigmoidal adsorption isotherm. By use of eqs 8 and 9 this isotherm can then be transformed to the charge density curve. Note that since unbuffered electrolyte solutions of adjusted pH are used in these experiments,we obtain a proton adsorption density curve which depends on the used electrolyte and is commonly referred to as the charge density curve. The integration of the diffuse front yields the shape and the relative position of the isotherm up to an additive constant (q(c0) in eq 4). This constant can be obtained, for example, by performing an experiment down to the pzc where there is no overall charge by definition. The column must therefore be preequilibrated with a solution of known pH and then flushed with a solution with the pH of the pzc. The retention of this breakthrough gives directly the charge density at the pH of the preequilibrating solution. Since the breakthrough curve is given by the derivative of the isotherm only, the method will yield no information about the location of the pzc. (Onefaces a similar problem in the potentiometric batch titration as the protonation state of the sorbent must be known in advance.) Therefore, in order to calculate absolute charging curves with the present method, one has to know the pzc from an independent experiment. This information can be also obtained from column experiments. Severalmethods can be applied. (1)One can determine the pzc by the adhesion method which is described by Kallay et a1.N The procedure consists of measuring the rate of the uptake of charged latex particles on solid surfaces as a function of the pH. (2) Conventional streaming potential measurement can be used for this purpose.26 (3)An interesting option is to perform similar pH-breakthrough experiments by varying the ionic strength. Since the magnitude of the charge density decreases with decreasing concentration of the inert electrolyte, one can determine the position of the pzc by performing a column experiment by changing the ionic strength of the input solution of a given pH. The breakthrough curve shows pH-change after one pore volume which returns to the original value at some later time. The sign of the observed pH-change at the outflow will change as one scans different pH values of the input solutions past the pzc. If the pH of the input solution equals the pzc, there is no effect of the ionic strength on the charge and no pH-change is observed.
Experiments Materials. T w o different sorbents were used in this study. One was a white, calcined silica sand (Seesand, Siegfried), which was sieved down to a size fraction of 126-250 pm, washed with dilute nitric acid and distilled water, and oven dried at 110 "C before use. The sand contains 99% SiOr, with traces of Na, Al, Fe, and Ca as determined by X-ray fluorescence spectroscopy. It consists mainly of cristobalite as identified by X-ray powder diffraction. A BET surface area of 0.08 ma/g was measured by a surface area analyzer (Micromeritics, Gemini 2360). The material density amounts to 2.31 g/cma, which was determined by an air pycnometer (Micromeritica, 1305). (24) Kallay, N.;Torbic, 2.; Golic, M.; Matijevic, E. J. Phys. Chem. 1991, 95 (l8), 7028. (25) Hunter. R. J. Zeta Potential in Colloid Science. Principles and Applications; Academic Preee: London, 1981.
Bfirgisser et ai.
858 Langmuir, Vol. 10, No. 3, 1994 The other sorbent was goethite-coated sand. The goethite, a commercial product (Fe-52,0rganic/InorganicChemical Corp., CA) was freed from impurities by washing, then freeze-dried and coated on the above described silica sand. The coating reaction is described by Scheideggeret The crystallographicallypure goethite with a BET surface area of 24 m2/gadheres very strongly and irreversibly to the silica surface. The BET surface area of the goethite-coated silica sand was determined to be 0.25 m2/g. The coated sand consistsof 0.65 5% (w/w)goethite. Batch titration data are availablefor this goethiteF7 The pzc for the pure goethite is 7.9. At the pzc the slope of the titration curve du/dpH in 0.1 M NaNOs is about 4.5 pC/cm2. This number is well comparable with literature results,lSJ7J8where values of 3.5-6.5 pC/cm2were reported. Solutions. All chemicals were of highly purified quality. Sodium nitrate (Suprapur, Merck) and nitric acid (Titrisol, Merck) were used. COz-free sodium hydroxide was prepared as described by Vogel." The water used was obtained from a Nanopure apparatus. COz-free water was prepared by boiling and cooling under Nz. Sodium nitrate was added (in a glovebox under Nz) to adjust the ionic strength. For the experiments with cristobalite we have used an ionic strength of 0.01 M, while for experiment with goethite-coated silica sand 0.1 M was chosen. The pH was adjusted by adding nitric acid or sodium hydroxide. The solutions where kept COz free by connecting a tube filled with sodium hydroxide on granulated support (Merck). Chromatographic Techniques. The sorbents suspended in water were packed into glass chromatography columns of 1 cm diameter and 15-40 cm lengths. The feeding solutions were passed through a degasser (Erma) and were pumped using HPLC pumps (Sykam) at flow rates between 1and 6 mL/min through the thermostated column (25 "C) past an injector (for pulse experiments) and two-wayvalve (for step experiments). For the tracer experiments the outflow of the column has been monitored with an UV/VIS flow-throughdetector (Linear UVIS 204),which was connected to a PC for data accumulation. The pH was measured by a flow-throughpH electrode (Ingold)and monitored by a pH meter (Orion, Model SA 720). For the calibration of the electrode, buffer solutions (Orion) at the same flow rates were used. In order to correct the small time-dependent drift of the electrode, calibrations were performed before and after the experiment and interpolated linearly in between. The flow rate has been determined by a flow meter (Humonics Optiflow 1000). Pore volume and Peclet numbers of the columns used were determined by means of pulse experiments with conservative tracers. The column was preequilibrated with 0.01 M sodium perchlorate (p.a. Merck). Solutions of potassium bromide and sodium nitrate (p.a. Merck) were injected from a sample loop of 25-300 p L and measured on-line, bromide at 215 nm and nitrate at 220 nm. By fitting the pulse response data to the analytical solution of the convection dispersion equation (eq 1) using a nonlinear least-squares procedure, the average travel time to and the standard deviation u of the pulse were determined. These results were in good agreement with calculations based on the first and second moment of the column output. The columns were carefully packed in order to achieve Peclet numbers as high as possible (Pe > 500). Since protonation reactions are usually fast, reasonably high travel velocities between u = 1 X l(r m/s and u = 24 X 1o-L m/s (corresponding to flow rates of 1 to 6 mL/min) were used. We have observed kinematic porosities of 0.50 f 0.01 which leads to p of 2580 f 50 g/L (see eq 1). The observed dispersivities were independent of flow velocity and in the range of D / v = 0.5 f 0.1 mm. The influence of the dissolution of the silica was estimated by measuring the solution concentration of dissolved Si in the outlet of the column at different pH and flow rates. The concentration of solublesilicawasdetermined by ICP-AES spectroscopy (Varian). Silica dissolves at 25 "C with the following dissolution rates: 1 X 10-" mol m-2 s-l (pH = 6),3 X 10-11 mol m-* s-1 (pH = 8), 8 X 1W1 mol m-2 s-1 (pH = 9.5), and 17 X 10-11 mol m-2 s-l (pH = 10.2). These dissolution (26) Scheidegger, A.;Borkovec, M.; Sticher, H. Geoderma 1993,58,43. (27) Hoins, U.;Charlet, L.; Sticher, H. Water, Air, Soil Pollut. 1993, 68,241. (28) Vogel, A. 1. A Text-Book of Quantitative Inorganic Analysis; Longmans: London, 1961; p 241.
IO
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t/to Figure 3. Breakthrough curve through a column packed with silica sand of acidity step input for 0 It/to < 7.5 (arrow) at feed concentrations of pH = 9.52 and pH = 3.98. Note the similarity with Figure 2d.
rates compare well with results for quartz of Wollast and Chou" which have been reviewed by Hiemstra and Van Riemsdijk-w Depending on the flow rate and the pH of the performed experiments, the consumption of OH- due to the dissolution of silica may have to be taken into account.
Results Silica Sand. First a breakthrough experiment from pH = 9.52 to pH = 3.98 has been performed. The result is shown in Figure 3. One observes the fronts expected from the isotherm for this pH range (see Figure 2d). The adsorption as well as the desorption front starts with a diffuse part and ends with a sharp part. The calculated overall retention from the second front represents the difference of acidity adsorbed between pH = 9.52 and pH = 3.98 and amounts to 9.9 f 0.5 pC/cm2. Since at pH = 4 the charge density is negligibly small compared to the charge at pH = 9.5, the obtained amount of adsorbed acidity can be assumed to be proportional to the absolute charge of the silica sand at pH = 9.5. The overall charge density calculated from the first front (in Figure 3) is around 30% higher. This difference arises from the consumption of OH- by the deprotonation of dissolved silicic acid with log K1 around -9.7.31 In this first part of the breakthrough the column is saturated with a solution of high pH for a longer time than in the second part where dissolution effects can be neglected. For the same reason experiments performed with smaller flow rates show higher retention factors. Figure 4 shows an experiment performed from pH = 9.77 to pH = 8.30. One observes first a diffuse front which is followed by a sharp front that is typical for a sorbate obeying a concave isotherm. From the overall retention one calculates a charge density difference of 5.3 f 0.3 pC/ cm2 between the two p H values. The experimental data points of the diffuse front were interpolated using a leastsquares spline fit.s2 Using eq 4this interpolating function has been integrated numerically to obtain the adsorption isotherm. Several experiments were performed in the pH region of 6.5 to 10.2, and the resulting charging curves were reproducible within 10%. The average isotherm was ~~
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(29) W o h t , R . ; Chou, L. In Transactions,XZZZCongreaaoftheZS~~ Hamburg, 1987; Vol. V, p 127. (30) Hiemstra, T.;Van Riemsdijk, W. H. J. Colloid ZnterfaceSci. 1990, 136 (l),132. (31) Baas, C. F., Jr.; Mesmer, R. E. The Hydrolysis ofcations;Krieger Publishing Co.: Malabar, FL, 1976. (32) DeBoor, C. A Practical Guide to Splines; Spinger: New York, 1978.
Charge Density Determination 10.0
Langmuir, Vol. 10, No. 3, 1994 859
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Figure 6. Surface charge density of goethite-coatedsilica sand in 0.1 M NaN03. Solid lines are calculated from the diffuse fronts of two column breakthrough experiments (lower branch from pH = 9.61to pH = 7.50,upper branch from pH = 3.62to pH = 7.50). Data points are calculated from batch titrations of
6. The data points also shown in Figure 6 represent results of independent classical acid-base titration experiments performed by Hoins et al.27 with the pure goethite, corrected by the charges of silica where data by B o l P were used. We observe good agreement between the data obtained from the column breakthrough curves and the titration experiments.
-5
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Figure 4. Breakthrough curve through a column packed with silica sand of acidity step input for 0 5 t/to < 30 (arrow)at feed concentrations of pH = 9.77 and pH = 8.30.
-
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Figure 5. Surface charge densityof silica sand in 0.01 M NaN03.
Solid line is calculated from the diffuse front of a breakthrough curve (used shift Bee text). Data points represent results of silica titration results of (0)Boltsain 0.01 M NaCl, (0) Abendroth% in 0.01 M KCl, and (A)Tadros and Lyklemas in 0.01 M KCl. shifted in such a way that the isotherm crossed the charge density of -9.9 pC/cm2 at pH = 9.5 as determined above. The result is compared in Figure 5 (solid line) with literature batch titration results for silica. Goethite-Coated Sand. The procedure is similar as described above with the difference that two experiments were performed in order to obtain both branches of the acidity adsorption isotherm below and above pH = 7. The first experiment was done from pH = 9.61 to pH = 7.50. From the retention of the front, one calculates a charge density of 6.5 0.5 pC/cm2between these two pH values. The point of zero charge of the used goethite was measured27to be at pH = 7.9 and, taking into account the contribution of silica to the charge according to the data by Bolt,33the pzc of the goethite-coated sand amounts to approximately 7.5. Therefore, the obtained charge density of -6.5 pC/cm2represents the absolute charge at pH = 9.5. The evaluation of eq 4 using the least-squares spline integration procedure for the diffuse adsorption front, taking into consideration the required shift of 6.5 pC/cm2, yields the lower branch of the charging curve in Figure 6. A second experiment was performed from pH = 3.62 to pH = 7.50. A charge density of 10.8 f 1 pC/cm2 can be calculated from the retention of the fronts, which corresponds to the charge density at pH = 3.6. The acidity adsorption isotherm between these two pH values was again calculated by integration of the diffuse front and is shown as the upper branch of the charging curve in Figure (33) Bolt, G.H.J . Phys. Chem. 1957, 61, 1166.
Discussion In the present paper a chromatographic method for the measurement of charge densities as a function of pH for oxides in column experiments is introduced. The procedure consists of packing the sorbent in question into a chromatographic column of a high Peclet number which is eluted with unbuffered solutions of varying pH. From the retention of the breakthrough curves one can calculate the charge densities. By preequilibrating the column with a solution of either high or low pH which is followed by a step change to an unbuffered solution of pH around 7, charge density curves can be directly obtained. The charge density curve as a function of pH must be viewed as an adsorption isotherm of the so-called acidity. This method is specially interesting when classicaltitration experiments are no longer sensitive enough for the measurement of charge densities. For example, this is usually the case for minerals with specific surface area below 1 m2/g. With the present method charge densities of such materials can be measured quite easily, as shown, for example, in this paper for a silica sand with a surface area of 0.08 m2/gand a goethite-coated sand with 0.25 m2/g. One of the disadvantages of this method is that it is necessary to flush the column with an unbuffered solution of pH around 7 in order to obtain the whole acidity isotherm. For experimental reasons it is difficult to prepare such a solution. Usually the actual pH value of this solution is somewhat different and experiments turn out to be performed beyond the point of inflection of the isotherm. However, only diffuse parts of the breakthrough curve can be used to calculate the isotherm and as a consequence it is hardly possible to evaluate the acidity isotherm at pH values near 7. The usefulness of the present procedure depends very strongly on the properties of the oxides used, particularly on the surface charge density and the slope of the charge density curve. In the present paper we have shown that the procedure works well in the case of a silica sand and a goethite-coated sand. Let us discuss these results in some more detail.
860 Langmuir, Vol. 10, No. 3, 1994
With the present method the charge density of a silica sand was measured in the pH range of 7.5-10.2. The determination of the charge density of this material is very difficult with any other technique. Possibly, the mass titration method may represent an alternative2but it seems to pose much more stringent conditions on the accuracy of the pH measurement than the technique presented here. With the present method the shape of the charge density curve can be reproduced within f5%. The absolute position of the isotherm is obtained from the retention of a breakthrough curve in an experiment down to the pzc. Due to silica dissolution effects the retention depends somewhat on the pH and the flow rate. Therefore, the relative accuracy of the measured relative position is around 10%. As the pzc of silica is around pH = 2, it would be desirable to perform this experiment down to this pH. However, acidity at pH = 2 is too high to get a measurable high retention of the front, and the experiment can only be performed down to a pH of around 4, where the surface charge is very low already. For this silica sand it is not possible to get the branch of the acidity adsorption isotherm at pH below 7. Experiments in this pH range would show fronts with very small retentions, caused by the low charge densities. In Figure 5 the charge densities for cristobalite in 0.01 M NaNO3 solution determined by the present method are compared to some results from the literature determined by potentiomeric titrations. Depending on the silica used different charge densities have been reported. Bolt33has used an amorphous silica (180 m2/g) in 0.01 M NaC1, A b e n d r ~ t ha~nonporous ~ pyrogenic silica (170 m2/g)in 0.01 M KC1, and Tadros and L ~ k l e m aa microporous ~~ silica (56 m2/g) in 0.01 M KC1. The number of charges per unit area of silica surface has been shown to be independent of particle size.36 The results of A b e n d r ~ t hin~1~M KC1 can be well compared with the ones from Ahmed? who used quartz (0.043 m2/g) in a 1M KNO3 solution and from Schindler et al.,37who used a silica gel (160 m2/g) in 1 M NaC104. The charge densities found in this study compare best with the ones found by Bolt.33 For microporous silica as Tadros and LyklemaN used, much higher charge densities were found. These higher charges have been attributed to the presence (34) Abendroth, R. P. J. Colloid Interface Sci. 1970,34 (4), 591. (35) Tadros, T. F.; Lyklema, J. J . Electroanal. Chem. 1968, 17, 267. (36) Heston, W. M., Jr.; Iler, R. K.; Sears, G. W., Jr. J. Phys. Chem. 1960,64, 147. (37) Schindler,P. W.;Fht,B.;Dick,R.;Wolf,P.U. J.CoZloidInterface Sci. 1976, 55 (2), 469.
Biirgisser et al. of internal hydroxyl or hydrogen ions. Perram3*proposed that the silica surface is coated with a gel layer which provides a microporosity for ions but not for nitrogen or other molecules when the silica surface is dried. Therefore, microporoussilica can act quite differently from nonporous particles. Yates and HealY9 have shown that nonporous silica with a smaller charge density can be obtained by heating precipitated silica. Silica used in this study was processed at high temperature and therefore one would expect its surface to be quite nonporous. For this reason the observed charge densities are reasonable indeed. Charge densities of a goethite-coated sand could be evaluated by column experiments in the pH range of 3.7-6 and from 7.5to 9.5. Two experiments had to be performed, each to a pH close to the pzc of 7.5. The needed shift to take into account the charge density at the pH where the experiment starts, could directly be calculated out of the retention of the fronts. The accuracy of this shift is about 10%. The upper branch of the charge density curve (at low pH) is the same for different flow rates. This is not astonishing since in the chosen pH ranges dissolution of silica is small and has no effect. The dissolution of goethite can be neglected anykay over the whole pH range. The pzc of the used goethite coated sand is 7.5, which is very close to the point of inflection of the acidity isotherm. Therefore it is possible to obtain the two branches of the isotherm from two breakthrough experiments only. In Figure 6 the charge densities of the goethite-coated sand obtained from column experiments and from classical titration experiments are compared. We observed good agreement between the two methods, which demonstrates the feasibility of the column procedure. The results are comparable to other goethite titration data found in the literature.16J7J8 This method of performing breakthrough experiments with protons can be used to measure charge densities of many different materials. It is especially interesting when the surface area of the charge density is very small, for example, for materials like metals, glass beads, and latex particles. For smaller particles HPLC techniques with higher pressure can be applied. Acknowledgment. We thank J. C. Westall for initiating the proper interpretation of the experiments and Ph. Behra for the careful reading of the manuscript. (38) Perram, J. W. J . Chem. SOC.,Faraday Trans. 2 1973,69 (I),993. (39) Yates, D.E.;Healy, T. W. J. Colloid Interface Sci. 1976,M (l), 9.
