Designing Optimal Metal-Doped Photocatalysts: Correlation between

Article pubs.acs.org/JPCC

Designing Optimal Metal-Doped Photocatalysts: Correlation between Photocatalytic Activity, Doping Ratio, and Particle Size Jonathan Z. Bloh, Ralf Dillert, and Detlef W. Bahnemann* Institut für Technische Chemie, Leibniz Universität Hannover, D-30167 Hannover, Germany ABSTRACT: Semiconductor photocatalysis is an important process for a variety of applications. However, the high recombination rate is still a limiting factor for the photocatalytic activity of the current photocatalysts. Several strategies were employed in an attempt to reduce the recombination rate, including doping with transition metals. While there was some success in increasing the photocatalytic activity, the large discrepancy in the obtained results and the lack of an appropriate model to describe this mechanism are still unsolved problems. In this work, a theoretical model that describes the correlation between photocatalytic activity, doping ratio, and particle size is developed. As a basis for this model, a collection of optimal doping data for different particle sizes of doped titanium dioxide and zinc oxide was used. With this newly developed model it is now possible to predict the optimal dopant concentration for a photocatalyst of a given size.

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INTRODUCTION Semiconductor photocatalysis is the basis for a variety of current and future applications in many different fields, such as surface technology, pollution management, and medicine.1−6 The fundamental principle is the ability of a photocatalyst to absorb photons creating reactive electron−hole pairs which are capable of oxidizing most organic and inorganic compounds. When a photon with sufficient energy is absorbed, an electron is excited from the valence band to the conduction band of the semiconductor. Simultaneously, a positively charged hole is created in the valence band. Recombination of these two species will result in the re-emission of a photon or in the emission of heat.3,7 However, once these two reactive species reach the surface of the semiconductor, they can undergo a variety of reactions with surface-adsorbed molecules.8−12 Unfortunately, photocatalytic reactions often only have quantum yields of a few percent.7,13 Most of the photogenerated charge carriers are recombining before inducing a photocatalytic reaction on the surface of the semiconductor.7 Therefore, this recombination rate has to be reduced in order to improve the activity of the photocatalyst. One way to reduce the recombination rate is by doping the host material with transition metal cations. This is believed to create traps for electrons and/or holes that immobilize the charge carriers and thus reduce the recombination rate.13 Employing this technique, photocatalysts with vastly improved photocatalytic activity have been reported.13−16 Most of these studies focused on titanium dioxide, specifically on iron-doped TiO2.14−16 However, there is a lot of controversy concerning the optimal doping ratio and some researchers even believe cationic doping is detrimental to photocatalytic activity in general.17 This proves that our understanding of the influence of dopants on the photocatalytic activity is still poor at this © 2012 American Chemical Society

point. Obviously, an adequate model explaining the relationship between doping ratio and photocatalytic performance is absolutely essential.

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DATA COLLECTION

As a basis for the model, a sufficiently large sample of data points is required. For this reason, data on the optimal doping ratio of transition metal doped photocatalysts have been collected from different previously published references.13−16,18−37 Only references dealing with roughly spherical primary particles were considered. Those dealing with nanorods or mesoporous structures do not meet the requirements for this model. Many sources are not included in this work because their proposed optimal doping ratio is too undetermined; e.g., the lowest concentration studied had the highest activity but no experiments were done to check if this is actually the lower limit.27−36 In other cases, while the optimal doping ratio is accurately established, no data on the size of the primary particles are given.25,26 Additionally, some sources dealing with iron-doped titania are not included because their proposed optimal doping ratios (>2%) exceed the solubility limit of iron in anatase (about 1 atom %)38−40 and it is thus concluded that not all of the iron atoms are actually incorporated into the host material.33,37 While most of the publications, the data of which are analyzed here, focus on titanium dioxide, specifically on ironReceived: July 24, 2012 Revised: October 6, 2012 Published: November 6, 2012 25558

dx.doi.org/10.1021/jp307313z | J. Phys. Chem. C 2012, 116, 25558−25562

The Journal of Physical Chemistry C

Article

data points. These uncertainties are also listed in Table 1 and are accordingly treated as experimental errors.

doped titanium dioxide, two data points for zinc oxide were also included. Zhang et al. determined the optimal Fe-doping ratio for TiO2 at 0.2 and 0.05 atom % for 6 and 11 nm particles, respectively.14 They also included data from Choi et al. and the well-known Aeroxide TiO2 P25 in their comparison with optimal Fe concentrations of 0.5 and 0.012 atom % for 3 and 30 nm particles, respectively.13,14,18 Choi et al. determined the optimal doping ratio not only for iron but also for manganese, rhenium, rhodium, ruthenium, and vanadium at 0.5 atom %, while their results for cobalt and molybdenum were inconclusive.13 Additionally, data from Tong et al. which set the optimal Fedoping ratio at 0.074 atom % for TiO2 particles with a diameter of 14.5 nm are also included in this work.15 In a similar study done by Zhou et al. with Fe-doped TiO2, an optimal doping ratio of 0.25 atom % was found for particles with a diameter of 9.4.nm.16 To complement the large set of data points for irondoped titania, also results for the optimal doping ratio of chromium-doped (0.094 atom % for 10.2 nm sized particles),22 lanthanum-doped (1.0 atom % for 4 nm sized particles),20 manganese-doped (0.2 atom % for 7.5 nm sized particles),21 ruthenium-doped (0.0192 atom % for 39.3 nm sized particles),24 and zinc-doped (0.1 atom % for 10.9 nm sized particles)23 titania have been considered here. Finally, a previous study of our own is included with large 50 nm Feand Ti-doped zinc oxide particles and corresponding optimal doping ratios of 0.005 and 0.002 atom %, respectively.19 All of the collected data points are summarized in Table 1. It should be noted that usually the experimentally determined optimal doping ratio is subject to a large uncertainty. For instance, Choi et al.13 determined the optimal concentration at 0.5 atom % but only studied 0.1 and 1 atom % as the bordering concentrations. Therefore, the optimal doping ratio might actually be situated somewhere between these two

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MODEL DEVELOPMENT The existence of an optimal doping ratio is usually attributed to the creation of electron/hole traps at lower dopant concentrations and the creation of recombination centers at higher dopant concentrations.13,19 As the former shows a linear dependency and the latter an exponential dependency, the resulting doping ratio vs. photocatalytic activity relationship features a maximum and thus an optimal doping ratio.19,41 In the new model developed here, recombination centers are assumed to be clusters of neighboring dopants. As published elsewhere, the ratio of clusters rc is approximately proportional to the squared doping ratio at low doping ratios for titanium dioxide and zinc oxide:19 rc = rd(1 − (1 − rd)12 ) ≈ 12rd 2

This cluster ratio should be kept as low as possible to avoid creating primarily recombination centers. However, even for the same material such as iron-doped titanium dioxide, the proclaimed optimal doping ratios vary wildly among the different references. For instance, Zhang et al. report an optimal doping ratio of 0.05 atom % for Fe3+-doped titanium dioxide, while the results from Choi et al. indicate an optimal concentration 10 times as high at 0.5 atom %.13,14 A possible explanation for this is that the particles of the latter research group were smaller (2−4 nm) and the optimal doping ratio therefore only corresponds to a value between one and five doping atoms per particle.13 As the particles employed in the study by Zhang et al. have been much bigger (11 nm), their doping ratio can be significantly lower without creating “empty” particles, not containing a single dopant atom.14 This consideration suggests that the optimal doping ratio is dependent not only on the nature of the doping atom but also on the morphology and the size of the particles. This hypothesis was already proposed in 1998 by Zhang et al.14 They concluded that the optimal Fe3+ doping ratio for titanium dioxide is a function of the particle size. However, while the aforementioned study presents results to support this theory, it lacks an adequate model to explain this phenomenon. For this reason, a model is developed here to explain the complex relationship between doping ratio and particle size. This model is based on the assumption that at the optimal doping ratio two different criteria have to be fulfilled. The first criterion is that the doping ratio may not be too high to avoid creating primarily recombination centers. To describe this dependancy, eq 1 is employed. The second criterion is that each individual particle should be doped and thus contain at least one foreign atom as an “empty” particle cannot profit from the positive effect of the doping. Assuming the particles are spherical, the number of doping atoms per particle nd can be calculated using the molar mass M and density ρ of the material, the particle diameter d, the Avogadro number NA, and the doping ratio rd:

Table 1. Experimentally Determined Optimal Doping Ratios rd,opt for Doped Titanium Dioxide and Zinc Oxide with Different Particle Sizes da material

d [nm]

rd,opt [atom %]

uncertainty [atom %]

nd

calcd rd,opt [atom %]

TiO2/Fe, V4+ TiO2/V3+, Re, Ru, Mn, Rh TiO2/La TiO2/Fe TiO2/Mn TiO2/Fe TiO2/Cr TiO2/Zn TiO2/Fe TiO2/Fe TiO2/Fe TiO2/Ru

2−4 2−4

0.5b 0.5b

0.1−1 0.25−1

4 6 7.5 9.4 10.2 10.9 11 14.5 30 39.3

1.0c 0.2d 0.2e 0.25f 0.094g 0.1h 0.05d 0.074i 0.012d,j 0.0192k

9.9 6.6 13.0 31.9 15.4 19.9 10.2 34.6 49.7 179.4

0.97 0.43 0.28 0.18 0.131 0.150 0.129 0.0742 0.0173 0.0101

ZnO/Ti

45− 55 45− 55

0.002l

0.5−1.5 0.1−0.5 0.1−0.5 0.05−0.5 0.053−0.136 0.05−0.3 0.02−0.1 0.042−0.12 − 0.0038− 0.038 0.001−0.01

55.0

0.0044

0.005l

0.001−0.01

137.4

0.0044

ZnO/Fe

2.1 2.1

(1)

1.73 1.73

nd =

a

Also listed are the resulting average number of dopant atoms per particle nd according to eq 2 and the calculated optimal doping ratios according to eq 5. bReference 13. cReference 20. dReference 14. e Reference 21. fReference 16. gReference 22. hReference 23. i Reference 15. jReference 18. kReference 24. lReference 19.

rdd3πNAρ 6M

(2)

For the calculations performed here, density values of 3.9 g cm−3 for titanium dioxide (anatase) and 5.6 g cm−3 for zinc oxide were used, respectively.42 25559



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utilization of such small metal-doped particles seems not to be beneficial. When plotting the reference data points given in Table 1 for the optimal experimentally determined doping ratio into this graph (Figure 1), it is obvious that all the data points are situated near the minimum concentration range necessary to prevent empty particles. This appears to be the limiting factor; once there are enough doping atoms to guarantee at least one dopant per particle, a higher doping ratio is not beneficial anymore. However, when plotting the average number of dopant atoms per particle as a function of the particle size for all the optimal doping ratio data points (see Figure 2), there

In the next step, the number of doping atoms per particle is calculated as a probability density function using the Poisson distribution P(N): P(N ) =

λ N e −λ N!

(3)

This function calculates the probability that the number N is present with an expected value of λ. Transferring this function to the discussed problem, λ becomes the number of doping atoms per particle nd and N is equal to 0 in an empty particle. This results in the probability of an empty particle P(0): ⎛ −r d3πN ρ ⎞ A ⎟ P(0) = exp⎜ d 6M ⎝ ⎠

(4)

This probability is 4.61 and 6.91. This means that nd should be greater than 4.61 to prevent too many particles (i.e., more than 1%) from being empty. For larger particles, this criterion is relatively easy to fulfill: a particle with a diameter of 50 nm still has an average of 272 doping atoms per particle even at a doping ratio of 0.01%. A 5 nm particle, however, needs a doping ratio of at least 0.17% to reach the same number. At a doping ratio of 0.1%, already about 7% of an ensemble of 5 nm particles are empty. Due to the cubic proportionality, an 8-fold doping ratio is needed to maintain a constant P(0) when the particle diameter is halved. This model of empty particles is subsequently combined with the aforementioned cluster ratio. The resulting complex behavior is depicted in Figure 1. As can be seen in Figure 1,

Figure 2. Average number of dopant atoms per particle for the optimal doping ratios plotted as a function of their corresponding particle sizes. The data points include all data from Table 1. Data points corresponding to titanium dioxide and zinc oxide are displayed as filled and empty circles, respectively. Also displayed is the weighted linear regression with a fixed intercept of 0. The scale is doublelogarithmic to better accommodate all data points.

seems to be a linear dependency rather than a fixed number. A weighted linear regression of these data with a fixed intercept at 0 reveals a slope of 2.40 nm−1. This means that, as the particles grow bigger, more than one dopant atom may be present per particle. When assuming that the optimal number of dopants per particle is 2.40 per nm of particle size, as determined by the linear regression, the following formula for the optimal doping ratio rd,opt results: rd,opt ≈ Figure 1. Optimal combinations of particle size and doping ratio, where neither too many recombination centers nor too many empty particles are present. Also displayed are all data points from Table 1.

6M (2.40 nm−1) 2 NAρπd

(5)

The curve calculated for the optimal doping ratio resulting from this formula is displayed in Figure 3 along with the different data points for the optimal doping ratio. As can be seen in Figure 3, this formula yields an excellent fit for the experimental data. For almost all reference data points the calculated optimal doping ratio lies well within the expected range (see Table 1 for comparison), considering the uncertainty. One exception is the data point with 11 nm large iron-doped titania particles for which the model suggests an optimal doping ratio of 0.129 atom % while the experiments resulted in 0.02−0.1 atom %.14 This deviation is, however, only slightly above the expected range. The other observed exception is found for the smallest particles, for which eq 5 predicts an optimal doping ratio of 1.73 atom % while the experimentally observed range is only 0.1−1 atom %. However, as the particle size has such an immense impact and is relatively undefined with 2−4 nm, the resulting calculated optimal doping ratio is actually 0.97−3.90 atom %. Considering this, the

there are basically three different regimes: one where the doping ratio is too low and mainly empty particles are present, one where it is too high and mainly recombination centers are present. This leaves an optimal area with neither many empty particles (P(0) < 1%) nor too many clusters (rc < 0.1 atom %, which is attained at a doping ratio rd of 0.94 atom %). While this optimal corridor is quite wide for larger particles, its gets smaller for smaller particle sizes as the minimum doping ratio to prevent empty particles also rises. When the particles reach a critical size (about 3.2 nm for titanium dioxide and 2.8 nm for zinc oxide), there is no optimal solution. For such small particles, either the cluster ratio is too high or there is a high number of empty particles. According to this model, the 25560



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We strongly suggest that other researchers should critically evaluate this model by utilizing it to predict the optimal doping ratios for other materials and hence validating it experimentally.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the German Federal Ministry of Education and Research (BMBF Project “HelioClean”, Grant 03X0069F) is gratefully acknowledged.

Figure 3. Optimal doping ratios for titanium dioxide (filled circles) and zinc oxide (empty circles) with different particle sizes according to the references listed in Table 1. The calculated optimal doping ratios according to eq 5 for titanium dioxide (solid line) and zinc oxide (dotted line) are also plotted in the graph.

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REFERENCES

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calculated optimal doping ratio might be in the expected range even for this data point, provided that the particle size is in the upper part of the particle size range. However, this data point could also point out the limit of this model, as these particles are partly smaller than the proposed critical size of 3.2 nm and thus violate one of the model’s criteria (too many empty particles). While the precision of this newly developed model is of course limited, the correct order of magnitude for the optimal doping ratio could be predicted in all cases. This model should be applicable to all metal-doped photocatalysts, regardless of the material and metal used. However, due to the lack of data points for other materials and dopants, we could only validate it for titanium dioxide doped with chromium, lanthanum, iron, manganese, rhenium, rhodium, ruthenium, zinc, and vanadium and iron- and titanium-doped zinc oxide.

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CONCLUSIONS Even though different authors have already proposed that the optimal doping ratio is a function of particle size, an adequate model was never developed. In this work, such a model has been proposed to describe the relationship between photocatalytic activity, doping ratio, and particle size. This new model assumes that the optimal doping ratio is a compromise of a sufficient number of dopant atoms, i.e., having at least one dopant per particle and, on the other hand, not too many dopant atoms per particle to avoid recombination centers. A collection of 14 different data points for experimentally determined optimal doping ratios from 11 different authors was used as reference points for the model. The results suggest that the optimal doping ratio is independent of the material and can be calculated using eq 5. This optimal dopant concentration represents a situation where each particle has an average of 2.4 doping atoms per nanometer of particle size. The optimal doping ratios calculated according to this formula are in excellent agreement with the experimentally determined values used as reference points. Using this formula, it is now possible to predict the optimal doping ratio for a given particle size with good precision and thus develop more efficient and custom-tailored photocatalysts. Additionally, it was shown that a lot of the controversy regarding transition metal doping for photocatalysis is not actually a real controversy at all and can instead be described (or should we say: resolved!) by this model. 25561



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Designing Optimal Metal-Doped Photocatalysts: Correlation between

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