Environ. Sci. Technol. 2007, 41, 303-308
Photocatalytic Degradation Characteristics of Different Organic Compounds at TiO2 Nanoporous Film Electrodes with Mixed Anatase/ Rutile Phases DIANLU JIANG,† SHANQING ZHANG, AND HUIJUN ZHAO* Centre for Aquatic Processes and Pollution (CAPP) and School of Environmental and Applied Sciences Gold Coast Campus, Griffith University PMB 50, Gold Coast Mail Center, Queensland 9726 Australia
Nanoporous TiO2 film electrodes with a mixed anatase/ rutile phase were prepared by dip-coating TiO2 nanoparticle colloid onto Indium Tin Oxide (ITO) conducting glass substrates and a subsequent calcination process at 700 °C for 16 h. The photocatalytic oxidation of a wide range of organic compounds has been studied using the photoelectrochemical method under the conditions that the photohole capturing step controls the overall photocatalytic processes. The characteristics of the mixed anatase/ rutile phase TiO2 film electrodes were compared with pure anatase phase TiO2 film electrodes to identify the key differences between them. The results revealed that different organic compounds, despite their difference in chemical entities, can be stoichiometrically mineralized at the mixedphase TiO2 electrode under diffusion-controlled conditions, which is in great contrast to the situation at the pure anatase phase TiO2 electrode. The exceptional ability of the mixed-phase TiO2 electrodes for mineralization of organic compounds and their remarkable resistance to the inhibition by aromatic compounds at higher concentration has been explained by the synergetic effect of the rutile and anatase phases. For this type of mixed phase electrodes, upon absorption of UV light, the electron-transfer pathway from anatase phase to rutile phase facilitates the separation of photoelectron and photohole, extending the lifetime of the photoelectron and photohole.
Introduction In recent years, TiO2 photocatalysis has drawn a great deal of attention, largely because of its superior ability for destruction of organic contaminants, which can be potentially used for water and air pollution control (1, 2). At present, two different photocatalytic systems are commonly used for oxidative degradation of organics. These are particle suspension and immobilized TiO2 photocatalytic systems (2, 3). The most notable advantage of the TiO2 particle suspension system is its suitability for large scale applications (4). Nevertheless, the reuse of photocatalyst presents a great * Corresponding author phone: +61-7-5552 8261; fax: +61-75552 8067; e-mail:
[email protected]. † Current address: Department of Chemistry and Biochemistry California State University, Los Angeles, California 90032. 10.1021/es061509i CCC: $37.00 Published on Web 11/23/2006
2007 American Chemical Society
challenge for the commercialization of the technology (5). This is because the process of photocatalyst reuse involves the separation of TiO2 particle from the reaction solution and economically viable separation technology is not currently available. From a fundamental research point of view, despite enormous efforts, the current understanding on the kinetic properties of such photocatalytic system is still far from satisfaction. To date, most published kinetic data tend to be apparent rather than inherent (3). To our knowledge, current research methods employed are only capable of obtaining apparent kinetic parameters due to the complexity involved in the particle suspension systems. In fact, for a particle suspension photocatalytic system, experimental conditions can be controlled only before the reaction commences. Once the reaction begins, it is extremely difficult to control the experiment under desired conditions, at the time the measurement is made (6). This often results in the published data not being comparable. Immobilization of TiO2 particles eliminates the need for separation of photocatalyst from the solution suspension. From a fundamental research point of view, immobilizing TiO2 particles onto a conducting substrate provides additional advantages. First, it enables the use of electrochemical techniques to study photocatalytic processes. A photocatalytic process is essentially a redox process that involves electron transfer. Therefore, the introduction of electrochemical techniques allows in situ measuring of the electron transfer, and as a result, the behavior of the electron transfer can be used to represent the kinetic characteristics of a photocatalytic process (6, 7). Second, the introduction of electrochemical techniques provides us with a new means to inject energy into the system, which can be used to manipulate the system to our advantage. For example, applying a potential bias suppresses the recombination of photogenerated electrons and holes, hence, it enhances the rate of the photocatalytic reaction (8, 9). Third, the introduction of electrochemical techniques makes it possible to physically separate the oxidation half reaction from the reduction half reaction, which greatly simplifies the system. This permits us to study the photocatalytic oxidation of organic compounds alone (10) without the influence from the removal of photoelectrons by electron acceptors (at the auxiliary electrode) (6, 11-13). Furthermore, electrochemical techniques can also be used to modulate the rate-limiting step of the overall photocatalytic process, allowing a targeted process to be quantitatively studied (6, 12, 13). Finally, the rapidity and highly sensitive nature of the electrochemical technique allow real-time acquisition of kinetic data, while still maintaining large solution volume to electrode area ratio, when a small size electrode is employed. The later is of particular importance for fundamental studies, since it ensures the preservation of the desired experimental conditions, i.e., the consistent composition of the bulk solution throughout the measurement process (6, 12, 13). In our previous study, a photoelectrochemical method was employed to obtain the photocatalytic degradation characteristics of different organic compounds at TiO2 nanoporous film electrodes with a pure anatase phase (referred as the anatase TiO2 electrodes) (11). In this work, we employed the same method to obtain the photocatalytic degradation characteristics of organic compounds at the TiO2 nanoporous film electrodes with a mixed anatase/rutile phases (referred as the mixed-phase TiO2 electrodes). Such mixed-phase TiO2 electrodes were used for the determination of chemical oxygen demand in wastewater (14, 15). The focus of this study is to identify the major differences between the VOL. 41, NO. 1, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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two different types of TiO2 photocatalysts (i.e., anatase and mix-phased) by quantitatively comparing their photocatalytic degradation characteristics, and to understand the causes. In order to achieve these, all experiments were carried out using the same group of organic compounds, under identical experimental conditions that were employed in the previous study (11).
Experimental Section Materials. Indium Tin Oxide (ITO) conducting glass sheets (8-10Ω/square, Delta Technologies Limited) were used as substrates for TiO2 film coating. All chemicals were of analytical grade and purchased from Sigma-Aldrich unless otherwise stated. All solutions were prepared using high purity deionized water (Millipore Corp., 18MΩcm). Preparation of the nanoporous TiO2 film electrode. Aqueous TiO2 colloid was prepared by hydrolysis of titanium butoxide according to the method described by Nazeeruddin et.al (16). The resultant colloidal solution contained 60 g dm-3 of TiO2 solid with particle size ranging from 8 to 10 nm. The ITO slide was used as the electrode substrate and was pretreated before use. After the pretreatment, the ITO slide was dip-coated with the TiO2 colloidal solution. The coated electrodes were ambient dried, and then calcined in a muffle furnace at 700 °C temperature for 16h in air. The thickness of TiO2 porous films was 1 µm as measured with a surface profilometer (Alpha-step 200, Tencor Instrument). Apparatus and Methods. The crystalline phase of TiO2 films were characterized by X-ray diffraction (XRD). XRD patterns were obtained with a diffractometer (Philips PW1050) using Cu-KR radiation at a scan rate of 0.2° min-1 in 2θ. The surface roughness and morphology of the porous TiO2 films was characterized by using a scanning electron microscope (SEM) (JSM-6400F, JEOL). All photoelectrochemical experiments were performed using the same system set up as previously described (11).
Results and Discussion Structural Characteristics of the Electrode. X-ray diffraction analysis (XRD) was carried out to identify the crystalline phase of the TiO2 film. The XRD patterns of TiO2 nanoporous films calcined at different temperatures were obtained. The ratio of the two different crystal forms was calculated according to the peak intensity ratio of IA(101)/IR (110) with SiroQuant, a commercial quantitative powder XRD phase analysis software. It revealed that the electrodes contained 100% anatase TiO2 when the film was calcined below 500 °C. In contrast, a mixture of anatase and rutile was obtained when the film was thermally treated at a temperature above 650 °C. A TiO2 film containing 96.8% of anatase and 3.2% of rutile was obtained when the film was calcined at 700 °C for 16h. It was found that the ratio between anatase and rutile phases increased as the treatment temperature increased. The average crystallite size of the mixed-phase film calcined at 700 °C for 16 h was ca. 33 nm, which was also calculated from the X-ray diffraction peak broadening of the anatase (101) plane using the Scherrer equation (17). The surface morphology of the film was examined by SEM. The film surface was found to be rough and porous. The crystallite size within the range of 30-50 nm was observed, indicating the particles are sintered aggregates from primary nanoparticles (8 nm). Characteristics of Potential/Photocurrent Curves. The linear voltammetry technique was employed to study the effect of potential bias on the photocurrent response. Shown in Figure 1 is a set of typical voltammograms for the mixed phase TiO2 electrode obtained under illumination in the blank solution (0.1 M NaNO3) and the solutions containing different concentrations of glucose. All other organic compounds 304
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FIGURE 1. Voltammograms of a mixed phase TiO2 electrode in 0.1 M NaNO3 solution containing glucose of different concentrations under illumination at pH 4.0. (a) 0, (b) 0.1 mM, (c) 0.5 mM, (d) 0.1M, (e) 0.5M. investigated exhibit similar voltammograms to those shown in Figure 1. It must be noted that all TiO2 nanoporous film coated ITO conducting glass electrodes give similar voltammograms in either the presence or absence of organic compounds. In all cases, the photocurrents increase as the applied potential bias increases within the low potential range, which can be attributed to the limitation of free electron transport in the film (6). The photocurrents saturate at higher potentials due to the limitation of the photohole capture process at the TiO2 surface (6). The magnitude of the saturated photocurrents depends on the concentration of organic compounds and their chemical identities. For a given light intensity (results in same photohole density at the electrode surface), the magnitude of saturated photocurrents is determined by the availability of organic compounds at the electrode surface and the photohole capture ability of electron donors (i.e., organic compounds). Comparison of these voltammograms with those obtained at the anatase TiO2 electrodes (11) reveals that the photocurrent-potential (Iph/E) relationship for each case in the low potential range is markedly different. The Iph/E relationship obtained at low potentials for the anatase TiO2 electrode was linear (6), while for the mixed-phase TiO2 electrode this relationship was not linear, particularly, at low concentrations. The coexistence of rutile phase in the higher temperature treated electrode is responsible for the difference. This is because the band gaps (Eg) for anatase phase and rutile phase TiO2 are slightly different. The Eg for anatase (3.2 eV) is 0.2 eV more positive than that of rutile (3.0 eV), which results in the photoelectrons generated at the anatase phase being transferred to rutile phase (18). Due to the differences in band gap potentials between anatase and rutile phases, when the applied potential is swept between the conduction band potentials of anatase and rutile TiO2, only those electrons sitting on anatase particles can be drawn out. When the applied potential is more positive than the conduction potential of rutile TiO2, those electrons sitting on both anatase and rutile particles can be drawn out. This causes the nonlinear Iph/E at low potentials, in particular, at low organic compound concentrations. The change of Iph/E characteristics at low potentials with glucose concentration supports this argument. Saturated Photocurrent/Concentration (Isph/C). As discussed above, the saturated photocurrent measured here reflects the kinetics of the photohole capture process at the electrode surface, which is related to the photohole capture ability of electron donors, as well as the competition between the kinetics of photohole seizure and that of the photoelectron/photohole recombination. To study the effect of concentration and the chemical structure of organic compounds on the kinetics of photohole capture, the steady-state
FIGURE 2. Isph/C plots of different organic compounds, (a) nonaromatic of large concentration range, (b) nonaromatic of low concentration range, (c) aromatic organic compounds. photocurrent values were measured at +0.30 V, at different concentrations for each compound. Figure 2 shows the Isph/C relationships of different organic compounds under the illumination of the same light intensity (6.6 mW/cm-2) at the same applied potential bias (+0.30 V) and pH (4.0). Figure 2a shows the Isph/C plot for nonaromatic organic compounds. For all nonaromatic compounds investigated, Isph increased linearly with concentration in the low concentration range (see Figure 2b) and reached saturation at high organic concentrations. For strong adsorbate molecules such as glutamic acid, malonic acid, succinic acid, glutaric acid and glycine (19, 20), the maximum Isph obtained at high concentrations was almost constant with a value around 0.40 mA. This contrasts with the kinetic characteristics of photocatalytic degradation of these compounds at the anatase TiO2 electrodes where the maximum Isph values were markedly different among these compounds (11). Similar trends were observed for the smaller strong adsorbate molecules such as formic acid and oxalic acid that involves the least number of transferred electrons and least number of reaction steps during their mineralization. However, the magnitude of the maximum Isph at high concentrations was much higher. This is probably due to the current doubling effect in which weak adsorbent molecules are different from strong ones. Whereas, for weakly adsorbate molecules such as glucose and methanol, after the initial linear increase of Isph with concentration, Isph keeps increasing at a slower pace and the
maximum Isph was attained at much higher organic concentration. The maximum Isph values situate between the maximum Isph values for the simplest strong adsorbate molecules and those for other strong adsorbate molecules. Comparison of Figure 2a and b with the corresponding Isph/C curves obtained at the anatase TiO2 electrodes (11) also reveals that the linear concentration ranges were much larger at the mixed-phase TiO2 electrode. Figure 2c shows the plot of Isph-C for different aromatic organic compounds. At low concentrations, linear Isph-C relationships were observed. At higher concentrations, the Isph decreased slightly after reaching the maximum indicating slight electrode deactivation by these aromatic compounds. This is in sharp contrast to the results obtained from the anatase TiO2 electrodes, where a significant inhibition effect was observed for the aromatic compounds (11). In addition, the linear ranges observed using the mixed phase TiO2 nanoporous film electrode were more than 6 times larger than those using the anatase TiO2 electrodes (11). The Saturation Photocurrent and Equivalent Concentration. Under the experimental conditions employed, the magnitude of the Isph represents the photohole capture rate by electron donors at the electrode surface. This rate is determined by factors such as the availability of organic compounds at the TiO2 surface, the rate of photohole generation, the lifetime of photoholes and the interaction of the organic compounds and TiO2 surface. For a given TiO2 electrode the intrinsic lifetime of photoholes is fixed, and under illumination of a given light intensity, the rate of photohole generation is also fixed. Therefore, the value of Isph is mainly determined by the availability of organic compounds at the electrode surface and their interaction with the TiO2 surface. As presented above, for all the compounds studied, the linear increase of Isph in low molar concentration range indicates that the overall photocatalytic oxidation process is controlled by the availability of organic compounds at the electrode surface, i.e., controlled by the diffusion process. For the organic compounds investigated, the number of electrons required for complete mineralization of these compounds varies from 2 e- for formic acid and oxalic acid to 30 e- for phthalic acid. Since elementary reactions involving more than two electrons rarely occur, the photocatalytic degradation of large organic molecules must undergo many elementary reactions. The photocatalytic mineralization of different organic compounds can be noticeably different from one to another because of the differences in their chemical structures, the number of electrons required for the mineralization, the number of steps and intermediates, and the chemical properties of these intermediates. A question is raised: Under the diffusion control conditions, are the organic molecules diffused to the electrode surface completely mineralized? This needs to be addressed first. According to the semiempirical treatment of steady-state mass transfer method (11), under the diffusion control condition, the limiting photocurrent can be given by the following:
Isph )
nFADC δ
(1)
where, n is the number of electrons transferred for the complete mineralization of organic compounds, F is the Faraday constant, A is the apparent surface area of the electrode, D and δ refer to the diffusion coefficient of an organic compound and the thickness of the effective diffusion layer respectively, and C is the bulk concentration of the organic compounds. Equation 1 predicts that, under diffusion-controlled conditions, if all organic molecules reaching the electrode VOL. 41, NO. 1, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Plot of Isph against Fluxin for different dicarboxylic acids at pH 4.0. Fluxin values were calculated using D ) 9.78 × 10-6 cm2/s for hydrogen oxalate, D ) 8.45 × 10-6 cm2/s for hydrogen malonate, D ) 7.83 × 10-6 cm2/s for hydrogen succinate, and D ) 7.0 × 10-6 cm2/s for hydrogen glutarate. surface are stoichiometrically mineralized a linear Isph-Ceq relationship with a slope of FDA/δ would be held for all organic compounds. If we define an arbitrary flux index as Fluxin) nADC ) ADCeq, then eq 1 can be written as follows:
Isph )
F × Fluxin ) kFluxin δ
(2)
Under diffusion-controlled conditions, if we assume δ is same for all compounds at different Fluxin (this is reasonable due to Fluxin is a normalized parameter) and the reaction takes place stoichiometrically, then for a given electrode k ) F/δ is a constant regardless of chemical identities of the organic compounds. Under these conditions, eq 2 predicts a linear relationship between the Iphs and Fluxin, and a unity slope, k ) F/δ, should be obtained for all compounds. The diffusion coefficients of most organic compounds in 0.1 M NaNO3 are not available but the diffusion coefficients of some dicarboxylic acids in water are available from literature (11). These dicarboxylic acids were subsequently selected as model compounds. Figure 3 shows the Isph-Fluxin curves of these model compounds. It was found that Isph responded linearly to the change of Fluxin at the low equivalent flux and then saturated at high Fluxin. The slopes for the linear part of the curves were almost identical for all dicarboxylic acids investigated. The linear parts of all curves can be fitted by the linear equation of Isph ) 0.00365Fluxin + 0.101 (mA), with R2 of 0.998. The intercept of 0.101 mA is the background photocurrent resulting from the photocatalytic oxidation of water. The results obtained are the same as those predicted by eq 2, which confirms that all assumptions made for eq 2 have been met and all dicarboxylic acids under diffusion-controlled conditions were stoichiometrically mineralized regardless of their chemical identities. The results also reveal that, except for oxalic acid, the maximum Isph observed at high Fluxin were very similar for all other dicarboxylic acids investigated, indicating the indiscriminate mineralization of different organic compounds. These results contrast with the photocatalytic oxidation of the same group of compounds at the anatase TiO2 electrode, where the maximum Isph varied significantly for different compounds due to the accumulation of intermediates or incomplete mineralization of organic compounds (11). The extraordinarily high maximum Isph observed for oxalic acid at high Fluxin and the upward deviation of Isph at medium Fluxin can be attributed to the current doubling effect resulting from the additional electrons injection by radical intermediates (21, 22). For other dicarboxylic acids the current doubling effect cannot be observed probably due to the unfavorable spatial orientation of radical intermediates. 306
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FIGURE 4. Isph/Ceq relationships for different organic compounds, (a) nonaromatic of larger equivalent concentration range (for data point denotation see Figure 4b), (b) same nonaromatic of low equivalent concentration range, and (c) aromatic organic compounds. The number of electrons transferred for the mineralization of organic compounds are as follows: two for oxalic and formic acids, six for methanol and glycin, eight for malonic acid, 14 for succinic acid, 20 for glutaric acid, 24 for glucose, 26 for o,m,pchlorophenol, 28 for phenol and salicylic acid, and 30 for phthalic acid. For most organic compounds the diffusion coefficients are not available. In order to obtain the similar kinetic information as described above for a wider spectrum of organic compounds, a new term, equivalent concentration (Ceq ) nC), is employed to replace the molar concentration. By converting the molar concentration into Ceq, we effectively normalized molar concentrations of different organic compounds into the same measurement scale in term of photohole demand (the photoholes required for the mineralization of a molecule) (7). Hence, the photohole demand for all compounds with the same Ceq is the same. Isph-Ceq relationships of nonaromatic compounds are plotted in Figure 4a. Linear Isph-Ceq relationships were obtained for all compounds investigated at low Ceq values (see Figure 4b). Small differences in the slopes of these linear curves can be attributed to the differences in diffusion coefficients of the organic compounds. At high Ceq values, the deviation of Isph from linearity for all compounds was
due to incomplete mineralization. Under such conditions, the availability of organic compounds at the electrode surface is not the limiting factor. For formic acid and oxalic acid, at medium Ceq values, the upward deviation from linearity was due to the current doubling effect, which can only be observed at higher concentrations where the accumulation of organic compounds at the TiO2 surface occurs. In addition, the Isph values at high Ceq values observed for all compounds, except formic acid and oxalic acid, were similar indicating indiscriminate mineralization of different organic compounds. Isph-Ceq curves obtained from photooxidation of aromatic compounds are shown in Figure 4c. The slopes of the linear part of the Isph-Ceq curves were very close for all aromatic compounds investigated. Moreover, the slopes of these straight lines are close to those of the nonaromatic compounds shown in Figure 4b. At high Ceq values, the Isph values reached a maximum and then decreased slightly perhaps due to the inhibition effect of benzene ring intermediates (11). This is different from the case of photooxidation of nonaromatic compounds as shown in Figure 4a, where no inhibition effect was observed at high Ceq values. Although the electrode inhibition effect of aromatic compounds is still observable at high Ceq values, the degree of the inhibition is much less severe, compared to the inhibition effect occurring at the anatase TiO2 electrode (11). Furthermore, the linear range observed at the mixed-phase TiO2 electrode is much larger than that at the anatase TiO2 electrode, indicating enhanced oxidation efficiency (11). Further Discussion. It is generally accepted that the photocatalytic degradation of strong adsorbate molecules takes place via inner-sphere charge-transfer mechanism, whereas the photocatalytic degradation of weak adsorbate molecules occurs via outer-sphere charge-transfer mechanism (23). The organic compounds investigated here include both strong and weak adsorbate molecules. The affinity of these organic compounds to TiO2 surface is expected to differ significantly. It was demonstrated that the adsorption behavior of strong adsorbate molecules for the hightemperature calcined electrodes was very similar to that of the low-temperature calcined electrodes. However, differences in the maximum Isph for different compounds at the mixed-phase TiO2 electrode are much less obvious than the differences at the anatase TiO2 electrodes. This implies that the differences in the interaction between the organic molecules and TiO2 surface, the nature of intermediates, and the distribution characteristics of photohole demand on the TiO2 surface (7). This is because different organic compounds have much less influence on the overall photohole capture process at the mixed-phase TiO2 electrode than that of at the anatase TiO2 electrodes. This demonstrates that the exceptional photocatalytic activity of the mixed-phase TiO2 electrode is due largely to the long lifetime of photoholes, prolonged by the electron transfer between rutile and anatase phases. At the mixed-phase TiO2 electrode surface, the differences in Isph at high concentrations for different compounds probably result mainly from the difference in their current doubling effect. For the current doubling effect to occur, the relative steric position of intermediate radical to the valence band is very important (24). Because of this, for the larger strong adsorbate molecules and their partially degraded radical intermediates (anchored to certain sites) may be not sterically favored for electron injection. In contrast, small strong adsorbate molecules (e.g., formic acid and oxalic acid) undergo only one radical intermediate in their mineralization therefore the radical intermediate tends to be free to find the right sites to inject electrons. The exceptionally high Isph at high concentrations for small strong adsorbate molecules may suggest that the corresponding radical intermediates are in a favored steric position to inject electrons. The maximum Isph values for nonspecific adsorbate
molecules, such as methanol and glucose at high concentrations, range between those for small strong adsorbate molecules and those for larger strong adsorbate molecules supports the above arguments. Overall, the above results demonstrate that when mixedphase TiO2 electrodes are used, all organic compounds, irrespective of their chemical identities, undergo stoichiometric degradation under diffusion controlled conditions, as indicated by their linear photocurrent responses. More importantly, the linear concentration ranges on an equivalent concentration scale for different organic compounds are very similar, which is in great contrast to the case of the anatase TiO2 electrode where the linear range is largely dependent on the chemical identities of organic compounds (11). This is a remarkable finding, given the enormous differences in their chemical configurations, the number of electrons transferred, and number of elementary steps and intermediates involved during their mineralization. From the results obtained in this study, there are three major differences between the mixed-phase TiO2 electrode and the anatase TiO2 electrode. One is that the linear ranges of Isph/Ceq for different organic compounds obtained from the mixed-phase TiO2 electrode, in particular for aromatic compounds, are significantly extended. Another is that the photocatalytic oxidation occurring at the mixed-phase TiO2 electrode tends to be indiscriminate in regard to the type of organic compounds compared to anatase TiO2. The third difference is the inhibition effect by aromatic compounds observed at the high-temperature treated electrode is much less significant for mixed-phase TiO2. These major differences can all be attributed to the coexistence of anatase and rutile phases in the high-temperature treated electrode. The coupling of these two phases allows the vectorial displacement of electrons from the anatase phase to the rutile phase that inhibits the photoelectrons/hole recombination. In effect, the spatial separation of photoelectrons from photoholes is realized, which in turn, prolongs the lifetime of photoelectrons and photoholes (25). Owing to the longer lifetime of photoholes, the mixed-phase TiO2 electrode can photocatalytically oxidize a wide spectrum of organic compounds in a more effective and indiscriminate manner (10, 15).
Acknowledgments We appreciate Australian Research Council and Aqua Diagnostic Pty Ltd. for the financial support of the work.
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Received for review June 26, 2006. Revised manuscript received October 11, 2006. Accepted October 12, 2006. ES061509I
