3538
Langmuir 2009, 25, 3538-3548
Adsorption/Desorption Kinetics from ATR-IR Spectroscopy. Aqueous Oxalic Acid on Anatase TiO2 Aidan G. Young and A. James McQuillan* Department of Chemistry, UniVersity of Otago, P.O. Box 56, Dunedin, New Zealand ReceiVed September 22, 2008. ReVised Manuscript ReceiVed December 22, 2008 Adsorption and desorption kinetics at the solid/solution interface have been monitored using attenuated total reflection infrared (ATR-IR) spectroscopy to evaluate this approach as an alternative to equilibrium (adsorption isotherm) measurements of adsorption affinity. The adsorption and desorption kinetics of oxalate ion to anatase TiO2 have been measured by using aqueous 1 × 10-4 mol L-1 oxalic acid solutions at pH 4 and thin films of TiO2 particles deposited on an internal reflection prism. The adsorption kinetics were obtained from the absorbance versus time behavior of major adsorbed oxalate infrared absorptions with flow of oxalic acid solution followed by flow of solution not containing oxalic acid to measure the desorption kinetics. Regression analysis of the desorption data based on Langmuir kinetics yielded three distinct pseudo-first-order rate constants with desorption half-lives of 300, 14, and 2 min, indicating the presence of three adsorbed oxalate species of different adsorption affinities. The most slowly desorbing and most strongly bound adsorbate species is likely to be a bidentate chelating oxalate ion from comparisons with the IR spectra of coordination compounds involving oxalate ligands. Regression analysis of the adsorption data was unable to yield the corresponding pseudo-first-order adsorption constants and prevented the calculation from kinetics data of Langmuir adsorption affinity constants. Measurement of adsorption and desorption kinetics by ATR-IR spectroscopy is expected to provide a relatively rapid means of assessing the presence of species of different adsorption affinities in systems in which their spectra are not well differentiated.
Introduction Attenuated total reflection infrared (ATR-IR) spectroscopy with thin deposited particle films has in the past decade become widely used to provide detailed information about wet surface chemistry and adsorption processes.1-4 The high surface area obtained with micrometer thick films of small particles provides good sensitivity for spectra of adsorbed species, even from a single internal reflection. In addition to providing molecular information about the nature of adsorbed species at different pH values, variations of adsorbed species IR peak absorbance (adsorbed amount) with solution concentration can be used to generate adsorption isotherms and to derive adsorption constants (affinities).5 The measurement of adsorption isotherm data by the ATR-IR method typically involves collection of equilibrium adsorbed species spectra for a series of flowing solutions of stepwise increasing concentration. However, this approach suffers from a generally slow approach to adsorption equilibrium and a resulting uncertainty in determining when equilibrium is reached. This limitation is more pronounced and consequently timeconsuming for strongly adsorbed species, which reach adsorption saturation at low solution concentration at which adsorption rates are also low. Furthermore, the longer the duration of the data collection, the greater the need for spectrophotometer temporal stability to preserve data quality. As a result of these factors, the precision of adsorption equilibrium constants from this method is seldom high and has prompted this evaluation of an alternative kinetics approach. * Telephone: +64 3 479 7928; fax: +64 3 479 7906; e-mail:
[email protected]. (1) Hug, S. J.; Sulzberger, B. Langmuir 1994, 10, 3587–3597. (2) McQuillan, A. J. AdV. Mater. 2001, 13, 1034–1038. (3) Lefevre, G. AdV. Colloid Interface Sci. 2004, 107, 109–123. (4) Burgi, T.; Baiker, A. AdV. Catal. 2006, 50, 227–283. (5) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997.
In comparison with other methods for studying adsorption, an advantage of the deposited particle film ATR-IR spectroscopic approach is the facility to readily monitor the kinetics of both adsorption and desorption on the same substrate in the same experiment. Adsorption/desorption kinetics offer the prospect of obtaining adsorption and desorption rate constants to derive adsorption equilibrium constants on a shorter time scale with possibly higher precision than applies to measurements of adsorption constants from equilibrium data. Such an approach has been utilized for some time in metal surface plasmon resonance (SPR) studies of biomolecular interactions,6,7 for which binding constants have been determined from measured adsorption and desorption rate constants. The sensitivity of the SPR method, which is low for the binding of small molecules, has been enhanced by employing colloidal metals.8 The corresponding use of ATR-IR spectroscopy to study adsorption/desorption kinetics of chemical species to solid particles, which often have more than one type of adsorbed species, has been seldom reported. Mendive et al.9 in the study of oxalate adsorption on TiO2 referred qualitatively to a two-stage adsorption followed by an appreciably slower desorption. McComb et al.10 in a study of antimonate ion adsorption on iron oxide particle films showed that the desorption kinetics is strongly dependent on pH. Zhang11 showed that adsorption/desorption kinetics of dicarboxylic acids on hematite particles could be used to distinguish outer-sphere and inner-sphere surface complexation. (6) Karlsson, R.; Michaelsson, A.; Mattsson, L. J. Immunol. Methods 1991, 145, 229–240. (7) O’Shannessy, D. J.; Brigham-Burke, M.; Soneson, K. K.; Hensley, P.; Brooks, I. Anal. Biochem. 1993, 212, 457–468. (8) Englebienne, P.; Van Hoonacker, A.; Verhas, M. Spectroscopy 2003, 17, 255–273. (9) Mendive, C. B.; Bahnemann, D. W.; Blesa, M. A. Catal. Today 2005, 101, 237–244. (10) McComb, K. A.; Craw, D.; McQuillan, A. J. Langmuir 2007, 23, 12125– 12130. (11) Zhang, Y. Adsorption-desorption kinetics of dicarboxylic acids on synthesised iron oxide nano- and mesoporous particles. Master’s Thesis, Lulea University of Technology, 2008.
10.1021/la803116n CCC: $40.75 2009 American Chemical Society Published on Web 02/13/2009
Adsorption/Desorption Kinetics from ATR-IR Spectroscopy
The infrequent use of a kinetic analysis of both adsorption and desorption processes has been partly due to the applicability of only a few analytical methods. One such method is pressure jump relaxation, which was used by Zhang and Sparks12-14 to study the kinetics and mechanism of molybdate, sulfate, selenate, and selenite adsorption on goethite. In these millisecond time scale studies the transformation of outer-sphere adsorbed species into inner-sphere complexes was observed. Other such pressurejump studies have been carried out.15,16 Hansen and Harris17 used total internal reflection fluorescence correlation spectroscopy of fluorescence transients to examine the adsorption and desorption kinetics of the rhodamine 6G cation on a C-18 modified silica. Curwen et al.18,19 have used flow methods combined with ellipsometric detection to study the adsorption and desorption kinetics of cetyl pydridinium chloride on hydrophobic silica surfaces. The adsorption of oxalic acid on anatase TiO2 particles has been chosen for the present adsorption/desorption kinetics ATRIR study. The adsorption behavior of oxalic acid on TiO2 deposited films has been the subject of several ATR-IR studies beginning with the pioneering work of Hug and Sulzberger.1 They investigated the spectra of species adsorbed on Degussa P-25 TiO2 (∼80% anatase, ∼20% rutile) at pH 3 and from singular value decomposition (SVD) and global analysis deduced the presence of up to three inner-sphere adsorbed species. Adsorption constants based on the Langmuir model for these three species were estimated from an apparent adsorption isotherm. However, since this initial work there has been debate about the exact chemical nature of the adsorbed oxalate complexes.9,20-22 These further studies have focused primarily on factor analysis of equilibrium spectra into components from adsorbed species and on computational analysis to deduce lowest energy adsorbed species at the TiO2 surface. In the current work, ATR-IR kinetic measurements were made of the adsorption and desorption of aqueous solution phase oxalic acid on anatase TiO2 particle films. The time evolution of the absorbance of several IR peaks of adsorbed species was monitored and analyzed in terms of a multiple adsorbed species Langmuir model. Different adsorption/desorption kinetics were exhibited by different wavenumber peaks and were correlated to separate adsorbed species of different adsorption affinities, with the desorption kinetics providing clearer distinction between separate species than the adsorption kinetics.
Materials and Methods Materials. Anatase TiO2 was a gift from Dr. Md. K. Nazeeruddin of the Ecole Polytechnique Fe´de´rale de Lausanne and had been prepared from hydrolysis of titanium tetraisopropoxide.23 The crystal (12) Zhang, P. C.; Sparks, D. L. Soil Sci. Soc. Am. J. 1989, 53, 1028–1034. (13) Zhang, P. C.; Sparks, D. L. Soil Sci. Soc. Am. J. 1990, 54, 1266–1273. (14) Zhang, P. C.; Sparks, D. L. EnViron. Sci. Technol. 1990, 24, 1848–1856. (15) Wu, C.-H.; Lin, C.-F.; Lo, S.-L.; Yasunga, T. J. Colloid Interface Sci. 1998, 208, 430–438. (16) Lang, F.; Pohlmeier, A.; Kaupenjohann, M. J. Plant Nutr. Soil Sci. 2000, 163, 571–575. (17) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 4247–4256. (18) Curwen, T. D.; Warner, J. A.; Bain, C. D.; Compton, R. G.; Eve, J. K. J. Phys. Chem. C 2007, 111, 12289–12304. (19) Curwen, T. D.; Bain, C. D.; Eve, J. K. J. Phys. Chem. C 2007, 111, 12305–12314. (20) Weisz, A. D.; Garcia Rodenas, L.; Morando, P. J.; Regazzoni, A. E.; Blesa, M. A. Catal. Today 2002, 76, 103–112. (21) Hug, S. J.; Bahnemann, D. J. Electron Spectrosc. Relat. Phenom. 2006, 150, 208–219. (22) Mendive, C., B.; Bredow, T.; Blesa, M. A.; Bahnemann, D. W. PCCP 2006, 8, 3232–3247. (23) Nazeeruddin, M. K.; Kay, A.; Rodicio, I.; Humphry-Baker, R.; Mueller, E.; Liska, P.; Vlachopoulos, N.; Graetzel, M. J. Am. Chem. Soc. 1993, 115, 6382–6390.
Langmuir, Vol. 25, No. 6, 2009 3539 phase was confirmed by XRD measurements. The BET surface area was measured using a TriStar 3000 N2 adsorption Analyzer at 77 K and was found to be 86 m2 g-1. Oxalic acid, NaCl, and NaOH (Ajax, analytical reagent) were used as received. All water used in experiments was deionized (Millipore, Milli-Q RG, resistivity ) 18 MΩ cm). Solution pH measurements were made with a MettlerToledo MP220 meter to a precision of (0.1. ATR-IR Spectroscopy. A DuraSamplIR triple-reflection 3 mm diameter diamond-faced ZnSe prism (ASI SensIR Technologies) was used to collect spectral data. The diamond surface of the triplereflection prism isolates any potentially corrosive solutions (e.g., pH extremes) from the underlying ZnSe surface. Prior to preparation of the TiO2 films for ATR-IR analysis, the prism surface was cleaned by polishing with 0.015 µm γ-alumina (BDH, polishing grade) on a wet polishing microcloth (Buehler) and then rinsed with water. The TiO2 film was formed by depositing 10 µL of a 1 mg mL-1 suspension in water (pH ∼4) onto the triple-reflection prism. The removal of water using a water pump vacuum (∼50 mbar) for ∼15 min produced a ∼0.25 cm2 film. The triple-reflection prism was interfaced via a rubber O-ring to a plate glass ∼1 mL flow cell of a type previously reported.10 The solutions were delivered to the flow cell using a Masterflex C/L peristaltic pump and Masterflex Tygon tubing at a constant flow rate of 1 mL min-1 unless stated otherwise. IR analysis of the TiO2 films under solution flow was conducted in the absence of laboratory lighting. All films were initially washed with 5 × 10-3 mol L-1 NaOH for 30 min to remove any adsorbed carbonate that may have arisen from traces of dissolved CO2 in the water source. A subsequent wash with 1 × 10-2 mol L-1 NaCl at pH 4 for 15 min was carried out to ensure constant experimental conditions (ionic strength and pH) between the spectra of the background and those of the adsorbed species. A Digilab FTS 4000 infrared spectrometer equipped with a KBr beamsplitter, Peltier cooled DTGS detector, and WinIR Pro version 3.4 software was used to collect and analyze spectra. The optical bench was purged with dried air. ATR-IR spectra were obtained from a variety of spectral resolutions and scan numbers (scan duration 1 s), each of which is given with the relevant data. Spectra were not corrected for dependence of absorbance on wavenumber. Spectra are shown as recorded at room temperature (22 °C), and spectral peak absorbances used in the kinetic analysis were not further modified by baseline correction or subtraction. Apparent adsorption isotherms were determined by flowing stepwise increasing concentrations of aqueous solution species over TiO2 films, at constant pH, with each solution given sufficient time to achieve adsorption equilibrium. Equilibrium was judged by comparison of two successive spectra showing no difference over a 15 min interval. Kinetic experiments were carried out by initially flowing over the film a solution not containing the ligand to obtain a background single-beam spectrum, subsequently flowing the ligand solution to measure the adsorption kinetics, then finally flow of solution without the ligand to obtain the desorption kinetics data. When a solution change was made at the pump, a short time (typically ∼1 min) was required for complete solution change adjacent to the film surface. This was evident in the absorbance data, and such early time data after solution composition changes was not used in the data analysis. For recorded kinetic data, each data point represents an average absorbance over the stated number of scans for the wavenumber chosen to best represent the peak. The time assigned to each data point is the time after the collection of all the scans and subsequent Fourier transformation. Kinetic rate constants were determined by nonlinear regression fitting of functions to absorbance versus time data using Origin Pro version 7.5 software. Uncertainties in rate constants were calculated using a 95% confidence interval based on the nonlinear regression analysis, and coefficient of determination R2 values were listed for the fitted functions. F-test comparisons with associated P values between different functions fitting the same data were carried out to determine the statistically significant better fit.24 An F ratio of near 1.0 indicates the simpler model is correct. (24) Draper, N. R.; Smith, H. Applied Regression Analysis; Wiley: New York, 1990.
3540 Langmuir, Vol. 25, No. 6, 2009
Young and McQuillan
Figure 1. SEM images of a typical TiO2 film deposited on a glass slide from an aqueous suspension showing (a) a cross section through the slide and (b) a higher magnification view showing individual TiO2 particles.
An F ratio of .1.0 indicates either that the more complicated function is correct or that the simpler function is correct but the more complicated function gives a better fit due to random scatter. The P value indicates the likelihood of the latter occurring, and a low P value signals it very unlikely. Scanning Electron Microscopy. SEM imaging was performed with a JEOL 6700F field emission scanning electron microscope (JEOL, Japan). Samples were coated in an Emitech 575X highresolution sputter coater (EM Technologies Ltd., England) with 5 nm of chromium and viewed at a working distance of 3-8 mm with a 3-7 kV range of accelerating voltages. SEM experiments were conducted on films prepared from aqueous suspensions, similarly to those used in the ATR-IR experiments, on glass microscope slides. To provide an estimate of the film thickness from cross-sectional images, the slides were scored on the reverse side using a diamond cutter and then fractured by hand through the film. An average film thickness of ∼1 µm was observed. Figure 1a shows a cross-sectional image of a typical TiO2 film. An average particle diameter of ∼20 nm is observed from the higher magnification SEM image in Figure 1b. From the film thickness and diameter, the volume of a typical deposited TiO2 film such as that shown in Figure 1 can be calculated. From this volume and the mass of TiO2 constituting the film, the porosity of a typical film was estimated to be 0.67. Adsorption Kinetics, Equilibrium, and the Langmuir Isotherm for a Single Site Surface. Adsorption equilibrium and adsorption kinetics theory in relation to the Langmuir adsorption model and the Langmuir adsorption isotherm is outlined in the Supporting Information, which contains more details about the origins of the equations given in this section. Few real particle solid adsorption systems, including the system studied in this work, are expected to strictly adhere to the Langmuir conditions of reversible adsorption/ desorption, monolayer maximum adsorption, all adsorbed species being equivalent, and no interactions between adsorbed species.5 Nevertheless, the adsorption behavior of many systems does not deviate greatly from Langmuir behavior, and the Langmuir isotherm is often used to provide adsorption constants in situations when comparative data are valuable, for example, comparing the adsorption behavior of a series of carboxylic acids on a single solid substrate.25 Furthermore, the adsorption of single solution species at real solid surfaces having several crystal faces usually results in more than one type of adsorbed species, each having a different adsorption affinity. To provide a basis for the analysis of adsorption kinetics with more than one type of adsorbed species, we include here the key relationships from single adsorbed species Langmuir adsorption kinetics theory (see Supporting Information) pertaining to ATR-IR methods for obtaining adsorption equilibrium constants from adsorption kinetics. In general, for ATR-IR particle film spectroscopic experiments, absorbance of a spectral peak due to a single adsorbed species, A, is proportional to surface coverage, that is, θ ) A/Amax. Thus, the time dependence of A may be used to obtain adsorption rate data and rate constants in the circumstances that the adsorption or desorption processes are rate controlling. Absorbance data from an (25) Duffy, N. W.; Dobson, K. D.; Gordon, K. C.; Robinson, B. H.; McQuillan, A. J. Chem. Phys. Lett. 1997, 266, 451–455.
Figure 2. ATR-IR spectra of oxalate adsorbed on anatase TiO2 under equilibrium conditions at pH 4 and I ) 1 × 10-2 mol L-1, for oxalic acid solution concentrations of 1 × 10-6, 5 × 10-6, 1 × 10-5, 5 × 10-5, 1 × 10-4, 5 × 10-4, and 1 × 10-3 mol L-1. Spectra were obtained using a triple-reflection accessory, from 128 scans at 4 cm-1 resolution. Spectra have been slightly offset on the absorbance scale for clarity.
initial experimental period of adsorption from dilute ligand (L) solution with constant concentration can be used to obtain ka′, the pseudo-first-order rate constant for adsorption, using eq 1
θ)
ka′ (1 - e-(ka′+kd′)t) ka′ + kd ′
(1)
where kd′ is the pseudo-first-order rate constant for desorption. If the initial adsorption period is followed by a desorption period into flowed solution not containing the ligand, then kd′ is obtained from the absorbance decay data using eq 2.
θ ) θ0 e-kd′t
(2)
The Langmuir adsorption (affinity) constant KL is then derived from the pseudo-first-order rate constants and the ligand concentration [L] using eq 3.
KL )
ka′ kd′ [L]
(3)
Equation 3 indicates that a more strongly bound adsorbed species is expected to have a larger adsorption rate constant and a smaller desorption rate constant than a more weakly bound adsorbed species.
Results and Discussion (a) Concentration Variation of Spectra of Adsorbed Oxalate. The observed IR absorptions of the different oxalate solution species are relevant to the pH 4 adsorption conditions and so are first considered. Oxalic acid, HOOC-COOH (H2Ox) has carboxylic acid functional groups with pKa1 ) ∼1.5 and pKa2 ) 3.8,1 indicating that Ox2- and HOx- are the predominant solution species at pH 4. IR spectra of 0.1 mol L-1 oxalate solutions under different pH conditions are given in the Supporting Information, Figure S1. The IR spectrum of aqueous solution Ox2- with nonplanar D2d symmetry consists of two strong peaks at 1570 and 1308 cm-1 arising from E and B2 Vas(C-O) modes, respectively.26 In the HOx- species these absorptions shift to 1617 and 1243 cm-1, whereas for aqueous oxalic acid (H2Ox) stretch absorptions are found at 1742 and 1228 cm-1, corresponding to the CdO and CsO bonds, respectively.1,26,27 The IR spectra of oxalate adsorbed to anatase TiO2 under equilibrium conditions at pH 4 are presented in Figure 2. The spectra were recorded with flowing solutions containing 1 × (26) Begun, G. M.; Fletcher, W. H. Spectrochim. Acta 1963, 19, 1343–1349. (27) Degenhardt, J.; McQuillan, A. J. Chem. Phys. Lett. 1999, 311, 179–184.
Adsorption/Desorption Kinetics from ATR-IR Spectroscopy
10-2 mol L-1 NaCl and in order of increasing oxalate concentration ranging from of 1 × 10-6 to 1 × 10-3 mol L-1. A constant salt concentration was utilized to maintain a constant ionic strength influence on the kinetic measurements. The adsorption of oxalic acid on anatase TiO2 has been reported to result in up to three adsorbed species at pH 3.1 More than one adsorbed species are qualitatively evident in the equilibrium spectra presented in Figure 2, where differing IR peak contributions are apparent at different oxalic acid solution concentrations. The spectrum of adsorbed oxalate as shown in Figure 2 is markedly different from that of oxalate species in solution due to the impact of coordinate adsorption on the relatively small molecule. It has generally been agreed in previous studies that oxalate is adsorbed predominantly as the planar bidentate Ox2ion with donor oxygen atoms from both carboxyl groups due to the close similarity of the adsorbed species spectrum with those of such bidentate oxalate ligands in coordination complexes.28 The vibrational modes of bidentate oxalate in coordination complexes are strongly coupled due to the low symmetry of the chelate ring and similarity of bond force constants,29 and this is also expected for adsorbed bidentate oxalate.1,26,30,31 The two most prominent peaks in the Figure 2 spectra occur at about 1719 and 1701-1692 cm-1 and have been assigned to the symmetric and antisymmetric stretch combinations of the two CdO moieties, Vs(CdO) and Vas(CdO), respectively.21,28 The possibility of either of these bands having arisen from an outersphere adsorbed or monodentate coordinated oxalate species can be discounted by comparing these bands with the spectra of oxalate solution species, as given in the Supporting Information. The most striking trend in the Figure 2 spectra with increase in coverage is the change in the relative intensities of the two bands in the 1700 cm-1 region. This has been attributed to the presence of adsorbed oxalate species of different adsorption affinities1 and will be discussed later. The assignments for the next strongest adsorbate peaks at ∼1420 and ∼1270 cm-1 have been largely based on oxalate ligand assignments in coordination compounds.28,29 The ∼1420 cm-1 peak has been assigned to a coupled Vs(CsO) + V(CsC) mode,20,21 whereas the peak at ∼1270 cm-1 has been assigned to both Vas(CsO) + V(CsC)21 and V(CsO) + δ(OsCdC)20 modes. The weak shoulder at ∼1306 cm-1 and the broad illdefined absorption in the 1600 cm-1 region is recognized to arise from an outer-sphere Ox2- adsorbed species on the charged TiO2 surface.20 An enlarged spectral window of the 1500-1200 cm-1 region of Figure 2 is presented in Figure 3. The IR peaks at ∼1420 and ∼1270 cm-1 both show a previously reported clear shift in maxima to lower wavenumber with increasing surface coverage, which may be indicative of contributions from more than one adsorbed species.21 Hug and Sulzberger1 employed singular value decomposition (SVD) and global analysis techniques to separate contributions of three proposed adsorbed species in the IR spectra of oxalate adsorbed on P25 TiO2 (∼80% anatase). The peaks at ∼1420, ∼1270, and ∼1719 cm-1 of adsorbed oxalate were reported to contain contributions from all three proposed adsorbed species.1 The role played by the rutile phase present in the TiO2 substrate was unclear from this early study. The spectrum of adsorbed oxalate on rutile TiO2 has more recently been reported21,22 and shows (28) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds, Part B: Applications in Coordination, Organnometallic, and Bioinorganic Chemistry, 5th ed.; Wiley: New York, 1997. (29) Fujita, J.; Martell, A. E.; Nakamoto, K. J. Chem. Phys. 1962, 36, 324– 331. (30) Cabaniss, S. E.; Leenheer, J. A.; McVey, I. F. Spectrochim. Acta A 1998, 54A, 449–458. (31) Shippey, T. A. J. Mol. Struct. 1980, 67, 223–233.
Langmuir, Vol. 25, No. 6, 2009 3541
Figure 3. ATR-IR spectra of oxalate adsorbed on anatase TiO2 under equilibrium conditions at pH 4 and I ) 1 × 10-2 mol L-1, for oxalic acid solution concentrations of 1 × 10-6, 5 × 10-6, 1 × 10-5, 5 × 10-5, 1 × 10-4, 5 × 10-4, and 1 × 10-3 mol L-1. Spectra were obtained from 128 scans at 4 cm-1 resolution.
Figure 4. Apparent adsorption isotherm of oxalic acid on anatase TiO2, recorded at constant pH 4.0 and 1 × 10-2 mol L-1 NaCl. The Langmuir adsorption isotherm model fitted to the data points (R2 ) 0.76) is also shown.
spectral features similar to those of adsorbed oxalate on anatase TiO2 but with minor peak wavenumber and intensity differences. Despite disagreement regarding some band assignments, there is general agreement that the majority of oxalate adsorbed on anatase TiO2 is in the form of strongly adsorbed surface complexes, which are 5-membered ring chelating and/or 6-membered ring bidentate bridging stuctures.22 An apparent adsorption isotherm shown in Figure 4 was obtained from the absorbance at 1420 cm-1 of the equilibrium spectra shown in Figure 2. A Langmuir isotherm model fitted to the isotherm data points is also shown. A poor fit to the model and thus deviation from Langmuir behavior are evident in a more gradual increase above the initial steep absorbance increase about 1 × 10-4 mol L-1 and is expected if there is more than one adsorbed species with differing adsorption affinities. The corresponding adsorption isotherm data for the other adsorbed oxalate peaks were similarly divergent from Langmuir behavior. The measured apparent isotherm in Figure 4 is similar to that reported in the earlier work by Hug and Sulzberger measured at pH 3.1 They also employed SVD to separate the contributions of the individual adsorbed species in an apparent adsorption isotherm (based on absorbance at 1405 cm-1). The three individual adsorbed oxalate species were estimated to have Langmuir adsorption constants (KL) of approximately 1 × 106, 1 × 105, and 1 × 103 L mol-1, respectively.1 Ligand adsorption experiments in ATR-IR spectroscopic studies are often carried out at adsorbing ligand solution
3542 Langmuir, Vol. 25, No. 6, 2009
Young and McQuillan
Figure 5. ATR-IR spectra of the adsorption of oxalate (at 0, 1, 2, 3, 4, 5, and 20 min) to anatase TiO2 from a 1 × 10-4 mol L-1 solution containing 1 × 10-2 mol L-1 NaCl at pH 4. The arrow indicates evolution of spectra with increasing time. Spectra were obtained using a triplereflection accessory, from 10 scans at 4 cm-1 resolution.
Figure 6. ATR-IR spectra of the desorption of oxalate (at 0, 5, 10, 20, 40, and 100 min) from anatase TiO2 into a solution containing 1 × 10-2 mol L-1 NaCl at pH 4. The arrow indicates evolution of spectra with increasing time. Spectra were obtained using a triple-reflection accessory, from 60 scans at 4 cm-1 resolution.
concentrations of ∼1 × 10-4 mol L-1.10,32,33 At this concentration, negligible solution phase contribution to the measured absorption spectrum is observed. Furthermore, at this concentration close to monolayer coverage is often achieved for coordinatively adsorbed species so that good-quality spectral data of the adsorbed species can be obtained. Thus, from the apparent isotherm data for the 1420 cm-1 peak and the similar isotherm behavior of the other adsorbed oxalate peaks, a kinetic analysis of oxalate adsorption and desorption at 1 × 10-4 mol L-1 is expected to contain contributions from more than one adsorbed species. (b) Adsorption/Desorption Rate Data for 1 × 10-4 mol L-1 Oxalic Acid. The use of a constant flow rate of solution both maintains stable IR spectral cell conditions and facilitates the convenient change of solution composition giving rise to timedependent absorbance difference spectra that exhibit the adsorption and desorption kinetics. Figure 5 shows the time evolution of IR difference spectra resulting from flowing a 1 × 10-4 mol L-1 oxalic acid solution containing 1 × 10-2 mol L-1 NaCl across a typical deposited anatase TiO2 film. Similar spectral data for oxalate adsorption on TiO2 have been reported.21,22 The corresponding time evolution of IR difference spectra obtained during the desorption of oxalate from the same anatase TiO2 film into 1 × 10-2 mol L-1 NaCl solution is shown in Figure 6. Such ATR-IR particle film desorption data have not been previously reported. (32) Young, A. G.; Green, D. P.; McQuillan, A. J. Langmuir 2006, 22, 11106– 11112. (33) Dickie, S. A.; McQuillan, A. J. Langmuir 2004, 20, 11630–11636.
Figure 7. Time dependence of (a) absorbances and (b) normalized absorbances, at pH 4.0 for oxalic acid adsorbed to anatase TiO2 from 1 × 10-4 mol L-1 aqueous solution containing 1 × 10-2 mol L-1 NaCl and the subsequent desorption into aqueous 1 × 10-2 mol L-1 NaCl with a flow rate of 1 mL min-1. Spectra that the adsorption and desorption data points were obtained from were recorded using a triple-reflection accessory at 4 cm-1 resolution from 10 and 60 scans, respectively.
Figures 5 and 6 show different IR peaks evolving on different time scales, indicative of more than one adsorbed species. In particular, the ∼1716 cm-1 peak grows more slowly in adsorption than the peak at about 1695 cm-1 but decays more rapidly in desorption, which suggests from eq 3 that it arises from a less strongly adsorbed species. It is also apparent from Figure 6 that the peak at 1307 cm-1 and unresolved shoulder at ∼1635 cm-1 show similar behaviors with surface coverage. Figure 7 shows the time dependence of absorbances of IR peaks at 1716, 1420, 1307, and 1270 cm-1 observed in Figure 2 at pH 4.0, for oxalic acid adsorbing from a 1 × 10-4 mol L-1 aqueous solution containing 1 × 10-2 mol L-1 NaCl to anatase TiO2 and the subsequent desorption into aqueous 1 × 10-2 mol L-1 NaCl. The strong peak at about 1695 cm-1 was not included due to its greater peak wavenumber shift with absorbance change compared with those of the peaks chosen. Whereas the 1420 and 1270 cm-1 peaks are well isolated from other major absorptions, that is not so for the 1716 and 1307 cm-1 peaks, the absorbances of which will be significantly affected by the tails of the adjacent peaks at ∼1695 and ∼1270 cm-1, respectively. This influence
Adsorption/Desorption Kinetics from ATR-IR Spectroscopy
Langmuir, Vol. 25, No. 6, 2009 3543
is expected to be more pronounced for the low absorbance 1307 cm-1 band, which sits on the tail of the more intense 1270 cm-1 band. Figure 7a shows both the adsorption and desorption stages for the peaks on a single time scale with a rapid initial rise in absorbance tending to a plateau, indicating adsorption saturation, and the slower decay of absorbance once the oxalic acid has been removed from the flow solution. It is noticeable in Figure 7a that the 1420 and 1270 cm-1 peaks more quickly approach adsorption saturation and show slower desorption characteristics than the 1716 and 1307 cm-1 peaks, indicating that these peaks are associated with more strongly bound oxalate. The 1307 cm-1 peak reaches an early absorbance maximum in the adsorption phase and then distinctively decays a little, even while the other peaks are still increasing. Both the 1716 and 1307 cm-1 peaks show more rapid absorbance decay at the early stage of desorption in comparison with the behavior of the 1420 and 1270 cm-1 peaks in the corresponding period. It is qualitatively apparent that none of the peak absorbance decay curves correspond to single-exponential decays, which would be expected for a single adsorbed species when desorption is rate controlling. It is well-known in soil science and other contexts that diffusion can be rate controlling for adsorption in certain systems.34 It is clear from the SEM image presented in Figure 1 and the estimated porosity of 0.67 that the deposited film contains void space between neighboring particles which would allow solution species to diffuse throughout the film. Thus, the possibility of adsorption and desorption rates in the presently reported experiments being diffusion controlled needs to be considered. For diffusion in solution in the absence of adsorption effects the average diffusion distance 〈x〉 and time t are related by
t)
〈x〉2 2D
(4)
where D is the diffusion coefficient. In the current situation 〈x〉 correlates with film thickness.35 The thickness of a typical deposited film used for the kinetic analysis as presented in Figure 7 was ∼1 µm, as shown in the SEM image in Figure 1. The reported diffusion coefficient for oxalic acid36 in a 5 × 10-3 mol L-1 aqueous solution at 25 °C is 1.71 × 10-5 cm2 s-1. Thus, the expected diffusion time, neglecting any adsorption, through a 1 × 10-4 cm thick film would be approximately 0.2 s. Figure 7 shows that the adsorption and desorption processes occur on time scales which are significantly longer than this diffusion time estimate. On this basis the kinetics of the adsorption processes and in particular the desorption processes are therefore not expected to be significantly influenced by diffusion. When the adsorption/desorption experiment was carried out on film of thickness of ∼300 nm, the resulting desorption decay curves showed similar profiles on timescales similar to those presented in Figure 7. On the basis of eq 4, for such a film thickness reduction the time scale of diffusion-limited desorption kinetics would be expected to be reduced by about a factor of ∼10. Lastly, it is well-known that diffusion-controlled adsorption processes obey an approximate t1/2 relationship with θ during the initial phase of adsorption.37-39 In the current work, a plot of (34) Sparks, D. L. Soil Physical Chemistry, 2nd ed.; CRC Press: Boca Raton, FL, 1998. (35) Atkins, P. W. Physical Chemistry, 6th ed.; Oxford University Press: New York, 1998. (36) Sue, K.; Ouchi, F.; Minami, K.; Arai, K. J. Chem. Eng. Data 2004, 49, 1359–1363. (37) Aguilar-Carrillo, J.; Garrido, F.; Barrios, L.; Garcia-Gonzalez, M. T. Chemosphere 2006, 65, 2377–2387. (38) Chen, H.; Wang, A. J. Colloid Interface Sci. 2007, 307, 309–316.
A versus t1/2 showed poor linearization of the initial data points (not shown) and was therefore inconsistent with diffusioncontrolled kinetics. However, the possibility of some influence of diffusion on the kinetics may exist, particularly in the adsorption phase where more rapid chemical reaction occurs. To facilitate qualitative comparisons of the adsorption and desorption rate data for the four peaks, Figure 7b shows the data points on a smaller time scale and with normalized absorbances and an inset box giving a further expansion of the first 4 min of the adsorption phase. For each IR peak, this normalization was based on the maximum absorbance, which was calculated from an average of each data point and its two neighboring data points, in order to mitigate the effect of scattering by background noise. The early part of the desorption phase is more readily analyzed than that of the adsorption phase. In comparison with Figure 7a, it can now be more clearly seen for the desorption phase that the 1420 and 1270 cm-1 peaks have closely similar slow decay behaviors, whereas the 1716 and 1307 cm-1 peaks have faster decay rates, with the 1306 cm-1 peak being associated with the most rapidly desorbing species. It is therefore expected, on the basis of eq 3, that the reverse of this decay rate trend would be observed in the adsorption phase. This prediction is confirmed in Figure 7b for the 1420 and 1270 cm-1 peaks in comparison with the 1716 cm-1 peak data as they approach adsorption saturation after 20 min. However, the 1307 cm-1 peak appears to be anomalous, reaching its maximum absorbance at about 5 min while the other peaks are still increasing in absorbance. The inset expansion of the first 4 min of the adsorption phase in general shows the expected trend in rate of increase of the peak absorbances with the 1420 and 1270 peaks rising at a faster rate than the 1716 cm-1 peak. The 1307 cm-1 peak is initially slowest to develop, but this soon changes, and after about 3 min, the growth rate accelerates to overtake those of the other peaks as their growth rates begin to decline. The apparently anomalous behavior of the 1307 cm-1 peak during the adsorption phase suggests that the nature of the associated adsorbed species is fundamentally different from those of the adsorbed species giving rise to the other peaks. Coordinative (inner-sphere) adsorption of the negatively charged oxalate is known to result in reduction in the net positive charge of TiO2 at this pH.40 If the 1307 cm-1 peak arises from an outer-sphere adsorbed Ox2-, the following processes may occur. First, it is likely that adsorbed outer-sphere Ox2- is an intermediate in the formation of any inner-sphere adsorbed oxalate species,12 and its interfacial concentration may be relatively low while the rate of formation of inner-sphere oxalate is high, which may account for the small 1307 cm-1 peak absorbance during the early stage of the adsorption phase. Second, the acceleration of the 1307 cm-1 peak absorbance after its slow initial increase with time may be partly due to overlap of this peak with the edge of the more rapidly increasing and more intense 1270 cm-1 peak. Third, the observed small decay in the 1307 cm-1 peak absorbance after 5 min may be due to the large extent of coordinative adsorption having reduced the net positive surface charge and hence the capacity of the surface for outer-sphere adsorption. Thus, the assumption of independence of different adsorbed species appears to be questionable, at least for the adsorption phase. (c) Determination of Desorption and Adsorption Rate Constants. According to the Langmuir model of adsorption kinetics, outlined in an earlier section and detailed in the (39) Ho, Y.-S.; Ofomaja, A. E. Process Biochemistry (Oxford, U.K.) 2005, 40, 3455–3461. (40) Dobson, K. D.; Connor, P. A.; McQuillan, A. J. Langmuir 1997, 13, 2614–2616.
3544 Langmuir, Vol. 25, No. 6, 2009
Figure 8. Time dependence of absorbance (at 1420 cm-1) at pH 4.0 for oxalic acid adsorbed to anatase TiO2 from 1 × 10-4 mol L-1 aqueous solution containing 1 × 10-2 mol L-1 NaCl and subsequent desorption into aqueous 1 × 10-2 mol L-1 NaCl. Spectra that the adsorption and desorption data points were obtained from were recorded using a triplereflection accessory at 4 cm-1 resolution from 10 and 60 scans, respectively.
Supporting Information, quantitative analysis of the peak absorbance versus time profiles is expected to yield adsorption and desorption rate constants, provided the adsorption and desorption reactions are rate controlling. However, Langmuir adsorption kinetics theory is strictly for a single adsorbed species system, and it is clear from the adsorption isotherm and adsorption/ desorption kinetics already considered that more than one adsorbed species exists for the oxalate/anatase TiO2 system. We will refer to a multiple adsorbed species (two, three,..., n) Langmuir model as one in which it is assumed that adsorbed species with different adsorption affinities exist, exhibit Langmuir adsorption, and are independent of each other, and thus expressions fitted to the observed absorbance versus time profiles contain sums of contributions from component terms associated with each of the different adsorbed species. The desorption behavior is less complex to analyze than the adsorption behavior. Thus, the desorption behavior of the 1420 cm-1 peak will be considered first to illustrate the procedures utilized to arrive at rate constants. Figure 8 shows the time dependence of absorbance of the 1420 cm-1 peak from the adsorption and desorption data given in Figure 7a. The desorption data points in Figure 8a did not fit well to a single adsorbed species Langmuir model of the type described by eq 2, with the fit resulting in an R2 ) 0.870. Instead, a best fit was obtained to a three adsorbed species Langmuir model of the type A )
Young and McQuillan
A1(e-k1′t) + A2(e-k2′t) + A3(e-k3′t), where A ) absorbance and the kn′ are pseudo-first-order rate constants, with the fitted curve also shown in Figure 8a. There is a very good fit of this function to the data points with R2 ) 0.999. For comparison, a two adsorbed species Langmuir model fitted the desorption data points with R2 ) 0.994. In further support of this conclusion, F-test comparison of the one and two adsorbed species Langmuir fits provided F ) 1687 and P ) 2 × 10-63, indicating the more complex equation provides a significantly better fit. Similarly, F-test comparison of the two and three adsorbed species Langmuir fits provided F ) 252 and P ) 1 × 10-33, but F-test comparison of three and four adsorbed species Langmuir fits provided F ) 1.63 × 10-8 and P ) 1.2, supporting the conclusion that the three adsorbed species Langmuir model provides the best fit. Furthermore, analysis of the desorption data shows that the adsorption is fully reversible, which indicates that equilibrium physical quantities such as equilibrium constants can be employed to describe the system. The obtained desorption rate constants (kd′) for the 1420 cm-1 band and peak absorbance coefficients (A) along with their experimental uncertainties are given in Table 1. The quality of the data fitting appears to confirm the existence of three adsorbed species from which chemical reactions are rate controlling in the desorption process and that desorption appears to occur independently for different adsorbed species. The Table 1 data show that the decay of the 1420 cm-1 peak is dominated (64% of initial peak absorbance) by a slow desorption process, with kd′ of 0.0023 min-1 and half-life of 5 h, and it is this process that is primarily responsible for the long tail in the absorbance decay curve. On the basis of eq 3 this component of the 1420 cm-1 peak corresponds to the most strongly bound adsorbed oxalate. The remaining almost equal minor contributions to the initial absorbance of the 1420 cm-1 peak came from adsorbed species exhibiting much faster desorption (more weakly bound oxalate) with half-lives of 13 and 2 min. As a consequence, the absorbance at 1420 cm-1 after 40 min of desorption is dominated (96%) by the slowest desorbing species. The existence of minor contributions to the 1420 cm-1 peak with different absorbance decay characteristics is at first surprising, considering the isolation of this peak in the spectrum. However, these minor absorbance contributions arise from the nonzero absorbance at 1420 cm-1 in the spectra of two other adsorbed oxalate species present, also seen in the SVD spectra of Hug and Sulzberger.1 Such contributions are also seen in the kinetic analysis of the desorption data for the other major peaks at 1716, 1307, and 1270 cm-1, also shown in Table 1. For all four peaks a three adsorbed species Langmuir model always gave the best fit to the desorption data points as indicated by the R2 values. Furthermore, F tests were carried out for the 1716, 1307, and 1270 cm-1 peaks in a similar manner to that described for the 1420 cm-1 peak. For all four peaks, the F test showed that three adsorbed species provided the best fit to the data. Most importantly, each spectral peak contains absorbance contributions from adsorbed species with the same three kinetic parameters (within experimental error, with one exception) but in different proportions. The recognizable half-lives in common are about 300, 14, and 2 min. From the Table 1 and Figure 7b data it is clear that the absorbance of the 1270 cm-1 peak scales closely with that of the 1420 cm-1 peak, as the desorption kinetic data from these two peaks provide rate constants and relative values of peak absorbance coefficients that are identical within experimental error. This scaling is qualitatively observed in the equilibrium IR spectra of Figures 2 and 3 and in the normalized absorbance
Adsorption/Desorption Kinetics from ATR-IR Spectroscopy
Langmuir, Vol. 25, No. 6, 2009 3545
Table 1. Peak Absorbance Coefficients (A) of Peak Components (n), Percentage of Maximum Absorbance, Desorption Rate Constants, Half-Lives at 22 °C, and Experimental Uncertainties (Calculated from a 95% Confidence Interval) for Major IR Peaks in Kinetics Experiments Carried out with 1 × 10-4 mol L-1 Oxalic Acid Solution at pH 4 R2 peak/cm-1
n
A (%Amax)
kd′/min-1
t1/2/min
n)3
n)2
n)1
1716
1 2 3
0.0069 ( 0.0004 (28%) 0.0052 ( 0.0003 (21%) 0.0125 ( 0.0003 (51%)
0.35 ( 0.04 0.055 ( 0.008 0.0031 ( 0.0003
2.0 ( 0.2 12 ( 2 220 ( 20
0.999
0.994
0.830
1420
1 2 3
0.0016 ( 0.0001 (17%) 0.0017 ( 0.0001 (19%) 0.0059 ( 0.0001 (64%)
0.33 ( 0.04 0.052 ( 0.008 0.0023 ( 0.0002
2.1 ( 0.2 13 ( 2 300 ( 30
0.999
0.994
0.870
1307
1 2 3
0.0010 ( 0.0001 (53%) 0.0004 ( 0.0001 (21%) 0.0005 ( 0.0001 (26%)
0.52 ( 0.08 0.05 ( 0.02 0.003 ( 0.001
1.3 ( 0.2 14 ( 5 230 ( 70
0.986
0.973
0.737
1270
1 2 3
0.0006 ( 0.0001 (18%) 0.0006 ( 0.0001 (18%) 0.0022 ( 0.0002 (64%)
0.28 ( 0.08 0.04 ( 0.01 0.0022 ( 0.0007
2.5 ( 0.7 17 ( 4 300 ( 100
0.996
0.993
0.875
versus time kinetic profiles in Figure 7b. The close correlation between the time dependence of the 1420 and 1270 cm-1 peaks during the desorption suggests these two IR absorptions contain contributions from the same combination of differently adsorbed species with the major initial contribution (64%) coming from the most slowly desorbing species. This most strongly adsorbed species must arise from a bidentate oxalate (Ox2-) ion, which is chelated to surface titanium ions via donor atoms from different carboxylate groups, as in many tris oxalato coordination compounds.28 Compared with the 1420 and 1270 cm-1 peak data, the decay of the dominant spectral peak at 1716 cm-1 yields two rate constants, which are comparable to those of the two faster desorbing species and a slightly higher rate constant for the major slow desorption component (51%) of the peak. It is expected from the spectra of coordination compounds28 that bidentate chelating oxalato ligands that have bands at about 1420 and 1270 cm-1 will be accompanied by a strong absorption around 1700 cm-1. SVD analysis of spectra of oxalate adsorbed on TiO2 has also shown a strong absorption around 1700 cm-1.1 Thus, at least part of the time-dependent behavior of the 1716 cm-1 band will be determined by a contribution from the spectrum of the most strongly adsorbed species. However, the 1716 cm-1 peak will be influenced by the time-dependent behavior of the adjacent ∼1692 cm-1 peak, and the behavior of these peaks cannot be considered in isolation. The peak at ∼1692 cm-1 shows a peak wavenumber that varies over ∼10 cm-1 with changing surface coverage, and therefore a detailed kinetic analysis is not readily carried out. Both peaks at 1716 and ∼1692 cm-1 arise from coupled CdO stretch vibrations, and a possible further complication in their temporal behavior may be the influence of dipolar coupling as surface coverage changes. Thus, the 1716 and ∼1692 cm-1 overlapping peaks appear to contain contributions from closely related adsorbed species, most likely bidentate chelating adsorbed oxalate species on sites having different adsorption affinities. Analysis of the small peak at 1307 cm-1 shows that the major absorbance component (52%) has the highest desorption rate constant, which from eq 3 is indicative of a weakly bound surface species. The present spectral and kinetic data supports previous assignments of this band21,27 to an outer-sphere adsorbed oxalate (Ox2-) ion. An indication of the reproducibility of the desorption data can been seen in the fit parameters obtained for the three adsorbed species from a repeated experiment on a separate anatase film. The data fit with R2 ) 0.998 yielded the following peak ab-
sorbance coefficients and rate constants (A, kd′): 0.0015 (21%), 0.37 ( 0.05 min-1; 0.0015 (21%), 0.052 ( 0.006 min-1; 0.0043 (58%), 0.0016 ( 0.0002 min-1. The agreement between the two sets of data is good and within experimental uncertainty for two of the three rate constants. However, the rate constant of the major absorbance component is a little outside the error limits for agreement. Such discrepancies may be due to experimental factors in the reproducibility of particle film preparation as yet not understood. From the normalized absorbance versus time profiles of the different peaks presented in Figures 7, it is qualitatively apparent that the desorption phase kinetics is more discriminating than the adsorption phase kinetics with respect to the presence of more than one adsorbed species. However, a strongly bound ligand with faster adsorption kinetics is expected to dominate the early stage of adsorption. Figure 8b shows the data points for the 1420 cm-1 peak in the adsorption process. The rate of the adsorption process is approximately 2 orders of magnitude larger than the corresponding initial desorption rate; thus, the adsorption rate components of the different adsorbed species are not readily resolved. Furthermore, the more rapid adsorption reaction rate compared with the desorption rate is expected to give some adsorption-induced temperature increases within the thin particle film. Such influences will be attenuated by the close contact with the flowing solution and are expected to be less significant in the slower reaction rate desorption data. The close adherence to exponential decay behavior in the desorption data appears to provide support for the lack of significant enthalpy change influence in this part of the experiment. After the analysis of the desorption data, the profile of the adsorption kinetics data is expected to contain contributions from three adsorbed species, and eq 1 could be used to describe the contribution from each. However, the fitting of a three adsorbed species version of eq 1 to the adsorption data to allow for each adsorbed species was beyond the capability of the nonlinear regression analysis methods. Even the use of an approximate form of eq 1 (see Supporting Information) to fit a multiple adsorbed species equation of the type A ) A(n)(1 - e-kn′t) + A(n+1)(1 - e-k(n+1)′t) +... resulted in the fitting software being unable to distinguish differing adsorption rate constants for the different adsorbed species. The adsorption data points were able to be fitted to a one adsorbed species Langmuir model of the approximate (1 - e-ka′t) type, with the fitted curve shown in Figure 8b. However, the empirical rate constant resulting from such an analysis bears no
3546 Langmuir, Vol. 25, No. 6, 2009
Young and McQuillan
Table 2. Peak Absorbance Coefficients (A), Empirical Adsorption Rate Constants, Half-Lives at 22 °C, and Experimental Uncertainties (Calculated from a 95% Confidence Interval) for Major IR Peaks in Kinetics Experiments Carried out with 1 × 10-4 mol L-1 Oxalic Acid Solution at pH 4 peak/cm-1
A
ka′/min-1
t1/2/min
R2
1716 1420 1307 1270
0.0218 ( 0.0002 0.0086 ( 0.0002 0.0015 ( 0.0001 0.0031 ( 0.0001
0.41 ( 0.01 0.56 ( 0.01 0.46 ( 0.05 0.52 ( 0.02
1.7 ( 0.1 1.2 ( 0.1 1.5 ( 0.2 1.3 ( 0.1
0.988 0.997 0.910 0.990
simple relationship to the pseudo-first-order adsorption rate constants contributing to the observed behavior. There is a satisfactory fit of the (1 - e-ka′t) function to the data points, and the obtained empirical rate constants with experimental uncertainties are given in Table 2. As expected, the rate constants from the 1420 and 1270 cm-1 peaks are in fairly close agreement. The higher ka′ for the 1306 cm-1 peak compared with that of the 1716 cm-1 peak may be unexpected after earlier comments on the initial rates in the Figure 7 data. However, the later more rapid absorbance increase of the 1306 cm-1 peak produces a higher average adsorption rate. In general, the pseudo-first-order rate constants for adsorption are far larger than the pseudofirst-order desorption rate constants, which reflects the strength of the adsorption interaction (eq 3) considering that the ligand concentration is low and despite the desorption reaction being driven by a high water concentration. The generality of the above analysis of the adsorption/ desorption kinetics observed for the 1 × 10-4 mol L-1 oxalic acid solution using a 1 mL min-1 flow rate was tested from data obtained on the same system using a 2.5 mL min-1 flow rate. As above for the 1420 cm-1 band, a three adsorbed species Langmuir model was found to provide a best fit to the desorption data (R2 ) 0.999) with the following peak absorbance coefficients and rate constants (A, kd′): 0.0031 (28%), 0.49 ( 0.05 min-1; 0.022 (20%), 0.052 ( 0.005 min-1; 0.0056 (51%), 0.0016 ( 0.0002 min-1. The desorption rate constants are expected to be unaffected by flow rate if the desorption is due to ligand exchange by water and there is independence of adsorbed species. By comparison of the data sets for the two flow rates, there is broad agreement in terms of the order of magnitude of the rate constants, although the corresponding component rate constants do not agree in all cases within the errors estimated from the individual data fits. As previously mentioned, these discrepancies may be due to particle film preparation factors. The adsorption phase data fit for the 1420 cm-1 band from the 2.5 mL min-1 flow rate gave ka′ ) 1.2 ( 0.1 min-1 with R2 ) 0.992. The increase in ka′, which is almost in proportion to the flow rate, confirms that the adsorption phase is to a significant extent mass transfer limited at this flow rate, which may account for the poorer quality of the fit. As outlined in an earlier section and detailed in the Supporting Information, the evaluation of ka′ and kd′ for an adsorption/ desorption experiment involving a single adsorbed species yields the Langmuir affinity constant (KL) via eq 3. For a multiple adsorbed species system, assuming that the observed absorbance versus time profiles can be adequately described as the sum of contributions from terms associated with each of the different independent adsorbed species, then eq 3 yields KL for each adsorbed species. In the current study, the desorption data profiles were shown to be described very well by the contributions from three adsorbed species. However, individual peak absorbance components were not able to be resolved from the adsorption data profiles, and there was clear evidence of the influence of mass transfer on the kinetics. Nevertheless, there was qualitative
evidence showing a degree of discrimination between different peaks in initial adsorption rate behavior. Combining pseudofirst-order desorption rate constants kd′ derived from the 1420 cm-1 peak with the single empirical ka′ yields KL values of 2.4 × 106, 1.1 × 105, and 1.7 × 104 L mol-1, which are not too dissimilar from the KL estimates of 1 × 106, 1 × 105, and 1 × 103 L mol-1 for the three adsorbed species given by Hug and Sulzberger from their isotherm data.1 The relative values of the actual pseudo-first-order adsorption rate constants, if measurable, would be expected to further separate the KL values here calculated. In summary, the current desorption kinetics analysis suggests that there are three significant adsorption sites for oxalate adsorbed on anatase TiO2 from 1 × 10-4 mol L-1 oxalate solutions at pH 4. This conclusion is in agreement with previous work for oxalate adsorbed on closely related substrates carried out by Hug and Sulzberger,1 and Mendive et al.22 However, these previous papers suggested all three species were adsorbed via inner-sphere interactions. The current analysis suggests that two adsorbates are likely to be bidentate chelating oxalate species adsorbed via inner-sphere coordinative interactions, whereas the third species displays behavior that is more consistent with an oxalate (Ox2-) ion adsorbed in response to surface charge by outer-sphere interactions. (d) Effect of Ligand Concentration on Adsorption/Desorption Rate Data. It is clear from the concentration variation of adsorbed oxalate spectra in Figure 2 that adsorption at sufficiently low oxalic acid solution concentration will minimize contributions from more weakly adsorbed species. Upon reaching adsorption saturation in an adsorption/desorption experiment at lower oxalic acid solution concentration, it is expected that the desorption data points will fit better to an exponential model with fewer terms than the data in Figure 8a for 1 × 10-4 mol L-1 oxalic acid. Thus, the adsorption kinetics from a 5 × 10-6 mol L-1 aqueous oxalic acid solution and desorption kinetics were investigated under the same experimental conditions as those used for the 1 × 10-4 mol L-1 solution experiment (Figures 7 and 8). Figure 9 shows the time dependence of absorbance at 1420 cm-1 for oxalic acid adsorbing from a 5 × 10-6 mol L-1 aqueous solution containing 1 × 10-2 mol L-1 NaCl at pH 4.0 to anatase TiO2 and the subsequent desorption into aqueous 1 × 10-2 mol L-1 NaCl at pH 4.0. Figure 9a shows both the adsorption and desorption stages on a single time scale, with the separate desorption and adsorption stages shown separately in panels b and c, respectively, of Figure 9. On the basis of the apparent adsorption isotherm given in Figure 4, the 5 × 10-6 mol L-1 oxalic acid concentration corresponds to an equilibrium surface coverage of about 60%. Thus, the data presented in Figure 9 are obtained from spectra with a lower signal-to-noise ratio than those collected at 1 × 10-4 mol L-1 concentration. In contrast to the desorption data points of Figure 8a collected at higher oxalic acid ligand concentration, the data points in Figure 9b do not fit well to a three adsorbed species Langmuir model of the type A ) A1(e-k1′t) + A2(e-k2′t) + A3(e-k3′t). The resulting fit (not shown) gave an R2 ) 0.980, and fitted parameters contained high relative uncertainties. Furthermore, one of the obtained rate constants was approximately 10 orders of magnitude smaller than the other two, which suggests that at 5 × 10-5 mol L-1 oxalic acid concentration the data points collected at 1420 cm-1 contain negligible contribution from a third adsorbed species. Consequently, the desorption data points were fitted to a two adsorbed species Langmuir model of the type A ) A1(e-k1′t) + A2(e-k2′t), with the fitted curve shown in Figure 9b. There is
Adsorption/Desorption Kinetics from ATR-IR Spectroscopy
Langmuir, Vol. 25, No. 6, 2009 3547 Table 4. Absorbance, Adsorption Rate Constant, and Half-Life at 22 °C with Experimental Uncertainty for 1420 cm-1 Peak in Kinetics Experiments Carried out at Oxalic Acid Solution Concentration of 5 × 10-6 mol L-1 A
ka′/min-1
t1/2/min
R2
0.0045 ( 0.0001
0.071 ( 0.001
9.8 ( 0.1
0.992
cm-1 peak at this lower concentration. Further support for this conclusion was obtained from the F test.24 Comparisons between one and two adsorbed species and between two and three adsorbed species Langmuir models gave F ) 554 and P ) 1 × 10-45 and F ) 1.2 and P ) 0.3, respectively. As was observed for the kinetic analysis for 1 × 10-4 mol L-1 oxalic acid solution concentration, the data points for the adsorption process in Figure 9c show a good fit (R2 ) 0.992) to a one adsorbed species Langmuir model of the type A8. The resulting rate constant and Amax coefficient along with their experimental uncertainties are shown in Table 4. For the desorption process the obtained rate constants are similar to those obtained for the two most strongly bound species at higher concentration in Table 1. Specifically, kd2′ ) 0.0019 ( 0.0002 min-1 at 5 × 10-5 mol L-1 is identical to within experimental error to kd3′ ) 0.0023 ( 0.0002 min-1 recorded at 1 × 10-4 mol L-1. Similarly, kd1′ ) 0.10 ( 0.03 min-1 at 5 × 10-5 mol L-1 is slightly outside the experimental error of kd2′ ) 0.052 ( 0.008 min-1 recorded at 1 × 10-4 mol L-1. Whereas the rate of desorption is not influenced by the adsorbing ligand concentration, A site coefficients may vary due to changes in site occupancy. From Table 3 it can be seen that the two adsorbed species show an A coefficient ratio with a larger contribution from the more strongly adsorbed species when compared to the two more strongly adsorbed species in Table 1. This indicates that at 5 × 10-6 mol L-1 solution concentration the most strongly adsorbed species is saturated, whereas the less strongly adsorbed species is only partially saturated. Changing from an adsorbing solution concentration of 1 × 10-4 mol L-1 to 5 × 10-6 mol L-1 constitutes a 20 times decrease in ligand concentration. The adsorption rate constant for 5 × 10-6 mol L-1 oxalic acid was approximately 1 order of magnitude lower than that at higher concentration. The current analysis is based on pseudo-first-order kinetics, in which pseudo-first-order rate constants for adsorption (ka′) are proportional to ligand concentration (see the Supporting Information). The discrepancy between the observed and expected adsorption rate constants for the different concentrations is unexplained to date. Figure 9. Time dependence of absorbance (at 1420 cm-1) at pH 4.0 for oxalic acid adsorbed to anatase TiO2 from 5 × 10-6 mol L-1 aqueous solution containing 1 × 10-2 mol L-1 NaCl and subsequent desorption into aqueous 1 × 10-2 mol L-1 NaCl. Spectra that the adsorption and desorption data points were obtained from were recorded using a triplereflection accessory at 4 cm-1 resolution from 30 and 60 scans, respectively. Table 3. Obtained Desorption Rate Constants at 22 °C and Peak Absorbance Coefficients along with Their Experimental Uncertainties for Kinetics Experiments (from Absorbance at 1420 cm-1) Carried out at Oxalic Acid Solution Concentration of 5 × 10-6 mol L-1. component
A (%Atotal)
kd′/min-1
t1/2/min
R2
1 2
0.0012 ( 0.0001 (25%) 0.0036 ( 0.0001 (75%)
0.10 ( 0.03 0.0019 ( 0.0002
7(2 360 ( 40
0.985
a good fit (R2 ) 0.985) of this function to the data points, and the obtained rate constants and peak absorbance coefficients along with their experimental uncertainties are given in Table 3. The quality of the fit to the data points in Figure 9b supports the conclusion that only two adsorbed species contribute to the 1420
Conclusions 1. ATR-IR spectroscopy with an adsorbate solution flowing over a solid particle film coating an internal reflection prism facilitates the measurement of both adsorption and desorption kinetics on the same film substrate in the same experiment. The reversibility of the adsorption, and hence applicability of equilibrium concepts, is readily determined by this type of experiment. 2. Following adsorption to anatase TiO2 from 1 × 10-4 mol -1 L oxalate solution at pH 4, regression analysis of the desorption absorbance decay yielded three pseudo-first-order rate constants with good precision corresponding to adsorbed species of different adsorption affinities in a multiple adsorbed species Langmuir model. Changing the oxalate concentration gave the expected change in pseudo-first-order adsorption rate constant. 3. The desorption kinetics and IR spectra showed that the most slowly desorbing species with a half-life of about 300 min corresponds to bidentate chelating oxalate adsorbed by inner-
3548 Langmuir, Vol. 25, No. 6, 2009
sphere interactions in comparison with that of about 2 min for the most rapidly desorbing species, which is an oxalate (Ox2-) ion weakly adsorbed by outer-sphere interactions. The latter conclusion is contrary to those from most previous oxalate ATRIR adsorption studies on closely related TiO2 substrates. 4. Regression analysis of the absorbance versus time data for adsorption of oxalate to anatase TiO2 was unable to extract rate constants corresponding to the expected three adsorbed species in the Langmuir model, primarily due to the greater complexity of the analysis. Thus, the calculation of Langmuir adsorption (affinity) constants for the different adsorbed species from the adsorption and desorption rate constants was not achieved for this system. This aim may yet be realized in systems having fewer adsorbed species. 5. A likely utility of the adsorption/desorption ATR-IR kinetics approach shown here is as a relatively rapid means of determining the number of adsorbed species of different adsorption affinity from analysis of absorbance decay curves for desorption. This approach is expected to be more valuable for systems in which
Young and McQuillan
spectra of species from different adsorption affinity sites are less readily distinguished than those of adsorbed oxalate. Acknowledgment. We are grateful to Professor D. D. Do of the Department of Chemical Engineering, University of Queensland, Australia, for discussion of this work and valuable suggestions. We thank Dr. Md. K. Nazeeruddin of the Ecole Polytechnique Fe´de´rale de Lausanne for kindly providing the anatase TiO2, Ron Etzion of the Light Metal Research Centre, University of Auckland, for BET surface area analysis measurements, and Liz Girvan of the Otago Centre for Electron Microscopy, University of Otago, for SEM image collection. This research was funded by the New Zealand Foundation for Research Science and Technology, NERF Grant UOOX0403. Supporting Information Available: Summary of Langmuir adsorption theory including kinetics, equilibrium, and the Langmuir adsorption isotherm as well ATR-IR spectra of oxalate/oxalic acid solutions of different pH values. This information is available free of charge via the Internet at http://pubs.acs.org. LA803116N
