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A Refined Model for the Optimal Metal Content in Semiconductor Photocatalysts Jonathan Zacharias Bloh J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09808 • Publication Date (Web): 21 Dec 2016 Downloaded from http://pubs.acs.org on December 26, 2016

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The Journal of Physical Chemistry

A Rened Model for the Optimal Metal Content in Semiconductor Photocatalysts Jonathan Z. Bloh

∗

DECHEMA Research Institute, Theodor-Heuss-Allee 25, 60486 Frankfurt am Main, Germany E-mail: [email protected]

∗

To whom correspondence should be addressed 1

ACS Paragon Plus Environment


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Abstract Doping with metal ions is a simple and convenient method of improving the photocatalytic activity of semiconducting materials. As revealed previously, the optimal doping ratio is strongly dependent on the particle size and can be predicted with an empirical function. This paper expands on that model, giving a more accurate physical explanation of the observed behaviour. The new model is based on the theory that only the fraction of dopants that is situated on the particle surface have a benecial eect. Analysis of almost 200 data points from the literature revealed that the optimal doping ratio corresponds well to an equivalent of 3.54 surface dopant atoms per particle, apparently independent of other parameters such as material or dopant. With this knowledge, the optimal doping ratio for a given catalyst can be predicted with good precision. The ndings also suggest that doping and grafting essentially cause the same eect, the latter while avoiding detrimental bulk dopants. Hence, bulk doping should be avoided in favour of surface doping or grafting.

Introduction Ever since the rst reports of photocatalytic water splitting in the 1970s, 1 semiconductor photocatalysis has attracted increasing interest as a green and sustainable technology. Briey, semiconducting materials can absorb photons the energy of which exceeds their band-gap. This process leads to the excitation of an electron from the semiconductor's valence band to its conduction band. Simultaneously, a positively charged hole is left behind in the valence band.

These two charge carriers, electron and hole, can subsequently be used to induce

chemical reactions at the semiconductor's surface.

Most applications of this phenomenon

focus on harnessing the formidable oxidative power of the photo-generated holes for the mineralisation of undesired compounds.

This includes waste-water remediation, 2 removal

of air pollutants 3,4 and self-cleaning surfaces 5,6 . More recently, photocatalysis was also explored as a way to produce synthetic fuels such as hydrogen 7 or hydrocarbons 8 and as a

2


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green catalyst in organic synthesis. 9,10 However, one of the major problems impairing widespread application of semiconductor photocatalysis is the rather poor quantum yield of the overall process.

Aside from a few

laboratory studies with articially optimised conditions, the observed quantum yield of the reaction is typically well below ten percent. The majority of the light energy absorbed is not translated into chemical reactions but instead falls victim to recombination. This unproductive process, occurring when electron and hole meet each other again in the semiconductor before reacting with adsorbed molecules, annihilates the photo-generated charge carriers and dissipates their energy as heat or re-emission of a photon. 11 Recombination can best be prevented by introducing an eective means to spatially separate the charge carriers from each other and by keeping the time-span between generation of the charge-carriers and their reaction with adsorbed molecules as short as possible, i.e., give them as little time and opportunity as possible to recombine.

The latter can easily

be arranged by reducing the size of the photocatalyst particles down to a few nanometres. Better charge separation, however, is much harder to achieve. Traditional methods rely on creating an intrinsic electric eld inside the semiconductor to drive the electrons to one and the holes towards the opposite direction. This can be realised by electrically polarising the semiconductor, by constructing a p-n-junction or by utilizing the space-charge-layer formed at the interface with the electrolyte.

However, all of these mechanisms are not readily

applicable when dealing with individual semiconductor particles with dimensions of only a couple nanometres.

An alternative route is to implement charge carrier traps into the

photocatalyst by doping it with atoms of foreign elements. Doping the photocatalyst with metal ions has successfully been explored as a means to reduce recombination rates.

Metal dopants in the semiconductor are thought to be able

to capture the roaming charges inside the semiconductor, trapping them. 12 These trapped charges reduce the amount of free charge carriers and thus their recombination rate. As has been shown by Choi et al.

in 1994, out of 9 dierent metals ions studied as dopants for

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titanium dioxide, 8 signicantly increased the photocatalyst's ecacy. 12 The longer charge carrier lifetime due to reduced recombination could be experimentally veried using laser ash photolysis with transient absorption spectroscopy and correlated well with the increased photocatalytic activity. 12 In the wake of this report, there have been hundreds of publications on metal-doped semiconductors for photocatalytic applications.

Unfortunately, there is a profound lack

of systematic studies on the subject so despite the high number of publications there is little insight into how these systems really work and how to optimise them in terms of photocatalytic activity. In almost all cases, only a few dierent dopant concentrations were studied and often fundamental data such as the particulate size are not available. Moreover, virtually every study used their own non-standardized activity test, further complicating a comparison between dierent studies (or making it almost impossible!). The common consensus amongst all of these studies is that metal-doping can enhance the intrinsic, ultraviolet light induced photocatalytic activity if applied in the right dosage. There is an optimal doping ratio, above which the activity decreases again. The decrease at higher doping ratios can be attributed to the appearance of recombination centres once the average distance between dopants becomes very small. 12,13 The reported optimal doping ratios vary wildly between the dierent studies, even for the same dopant in the same host material.

Many reports, including the abovementioned study by Choi et al.

rather high optimal doping ratio at of magnitude lower in the range of

0.5 at.%

observe a

while others nd that their optimum is orders

0.001 to 0.1 at.%. 1216

This discrepancy was rst analysed

by Zhang et al. who suggested that the optimal doping ratio might be dependent on the particulate size. 17 Recently, we proposed a model explaining this size dependency of the optimal doping ratio. 18 It is based on the assumption that any particle that lacks at least one dopant atom cannot participate from any positive eect the doping might cause. 18 We were then able to calculate the minimum doping level necessary to guarantee at least one dopant per particle as a function of particle size assuming homogeneous distribution of the

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dopants and spherical particle shape. 18 Naturally, this minimum doping level is exponentially higher for smaller sized particles owing to the drastically reduced number of atoms per particle.

Also, at rst glance, this

minimum doping level corresponds very well with the experimentally observed optimal doping ratios, i.e., it seems best to add just enough dopants to guarantee at least one dopant per particle, but no more.

However, upon further analysis it was found that the optimal

number of dopants per particle increased linearly with the particle size, larger photocatalysts seem to favour more dopants per particle. Nevertheless, the data could be used to create a formula to predict the optimal doping ratio molecular mass

M

and density

ρ)

and size

rd,opt =

rd,opt

for a given material (with its parameters

d: 18

6⋅M ⋅ 2.4 nm−1 NA ⋅ ρ ⋅ π ⋅ d2

(1)

Unfortunately, the precision of the prediction is limited at this point since the data points used as a basis for the model are only few and were taken from the literature and were often associated with high uncertainties.

Due to the lack of reported systematic studies it was

not yet possible to properly conrm and rene the model beyond the data samples used to create it and thus to explore the limits of its validity. Also, the aforementioned second order dependency of the optimal doping ratio on the particle size suggests a surface associated eect rather than a bulk one, since the latter would incur a third order dependency. This contradiction with the proposed underlying model is highly unsatisfactory and implies that the model is not entirely accurate. This work will therefore re-evaluate and revise the model by using a surface based approach and also incorporate additional data points that have been published in the meantime.

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Development of a surface based model As described above, the observed second order dependence of the optimal doping ratio on the particle size suggests a surface based eect rather than a bulk one which was the basis for the original model, since the latter would incur a third order dependency. Also, there is good reason to assume that surface metal dopants are more eective than bulk dopants as charge carrier traps since they can release their trapped charges directly onto adsorbed reactants. Charges trapped by bulk dopants, on the other hand, rst have to be de-trapped and brought to the surface before they can react. Additionally, metal-centres on the surface of the semiconductor are reported to enhance charge transfer and multi-electron reactions.

Specically, the very important oxygen re-

duction reaction is enhanced by many metal ions on the photocatalyst surface by allowing multi-electron transfer reactions with more favourable redox potentials. 1922 Since molecular oxygen is the usual electron acceptor for environmental applications of semiconductor photocatalysis and this reaction is often observed to be the rate-limiting step, the improved oxygen reduction properties may also contribute to the increased photocatalytic activity of metal-doped photocatalysts. Therefore, the original model was re-evaluated and it was found that the assumption that only those dopant atoms that happen to be at the surface of the particle contribute to the positive eect results in a model that ts the experimental data even better. The following calculations are based on the assumption that the photocatalyst exhibits ideal spherical shape, since the majority of reports are based on roughly spherical particles. In principle, however, these calculations are also possible for other particle shapes such as rods or discs using geometric principles to take their specic volume and surface into account. For spherical particles, the fraction of dopants that are situated at the surface can be calculated using a simple core-shell model, eq. 2 with surface layer, assuming uniform distribution of the dopants.

6


δ

fs

being the thickness of the

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fs (d) =

d3 − (d − 2δ)3 d3

(2)

Multiplying this equation with the number of dopants per particle number of surface dopants per particle

nd,s ,

nd (rd , d) =

δ

(eq. 3) 18 yields the

eq. 4.

rd ⋅ π ⋅ NA ⋅ ρ ⋅ d3 6⋅M

(3)

rd ⋅ π ⋅ NA ⋅ ρ ⋅ (δd2 − 2δ 2 d + 34 δ 3 ) nd,s (rd , d) = M The thickness of the surface layer

nd

(4)

is a property that is dicult to quantify exactly

for a nanoparticle, since it is dierent for the various crystal faces. As an approximation, we chose to use the nearest neighbour distance ( 304 pm for anatase TiO 2 ) 13 , which is the distance between neighbouring titanium cations. In this context, it can be interpret as the distance of the surface titanium ions to the next ones below the surface and is therefore a rough approximation of the thickness of the surface layer.

Using this approximation, the

optimal doping ratio of all data sets used in the original model falls between the narrow corridor of

1 to 10 surface dopants per particle, cf.

Figure 1. While there is a notable degree

of uncertainty involved, a weighted average calculation yields

3

doped surface atoms per

particle. The resulting modied formula for the optimal doping ratio predicts this state as follows:

rd,opt (d) = with

nd,s,opt = 3.

The number of

3

nd,s,opt ⋅ M π ⋅ NA ⋅ ρ ⋅ (δd2 − 2δ 2 d + 34 δ 3 )

(5)

per particle can be explained through statistical analysis

with Poisson distribution. 18 While for an average of 1 surface dopant per particle, statistical distribution means that only increases to

63 %

of all particles end up having at least one, this coverage

95 % for an average of 3 surface dopants per particle.

So this basically represents

a scenario where there are just enough dopants present to guarantee that just about every

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1 8 1 6 1 4

a v e ra g e n u m b e r o f d o p e d s u r fa c e a to m s p e r p a r tic le

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1 2 1 0 8 6 4 2 0 1

1 0

1 0 0

p a r tic le d ia m e te r / n m

The average number of doped surface atoms per particle as a function of particle size as calculated from eq. 4 for all the data sets used in the original model. Also displayed is the weighted average of 3 as a red solid line and the corridor between 1 and 10 as slashed blue lines.

Figure 1:

18

particle has at least one. As depicted in Figure 2, this rened 'surface model' ts the experimental data points even better than the original 'bulk model'. Also, it oers an explanation for the second order dependency on the particle size, i.e., mainly those dopants that are located on the surface of the particle contribute to the activity enhancing eect. This raises the question whether it is possible to selectively dope the surface of the particle to achieve the same eect. That way, one would avoid the detrimental impact of the bulk dopants at higher concentrations, i.e., recombination centres, and also utilize drastically less mass of the doping element. The benecial eect of surface versus bulk doping has also been highlighted by other authors. 2327 Something very similar to surface doping has been explored by Hashimoto et al. since 2008. 22 The process, described as 'grafting', involves the adsorption of metal-ions onto the surface of the semiconductor photocatalyst. Among other eects such as visible light sensitisation, these metal-grafted materials exhibit enhanced intrinsic photocatalytic activity

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1 0

o r ig in a l " b u lk " m o d e l n e w "s u rfa c e " m o d e l 1

O p tim a l d o p in g r a tio / a t.- %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 .1

0 .0 1

0 .0 0 1 1

1 0

1 0 0

P a r tic le d ia m e te r / n m Figure 2: The predicted optimal doping ratios according to the bulk model (eq. 1, slashed blue line) and the surface model (eq. 5, solid red line) alongside experimentally determined optimal doping ratios (data taken from ref. ). The two data points on the far right are based on zinc oxide, hence the break in the lines is due to dierent material properties. All other data points are based on anatase titanium dioxide. 18

attributed to better charge separation and improved oxygen reduction properties, both of which are observed for the corresponding metal-doped photocatalysts, as well. This raises the question whether the mechanism of grafting is actually identical to that of surface doping, i.e., whether the grafted metal ions are chemically identical to doped metal ions that happen to be located at the surface. In fact, Co(II) ions are reported to adsorb on rutile at sites corresponding to the Ti-equivalent positions in an extension of the rutile structure 28 , i.e., they are acting as if they were dopants in the host material, and there is good reason to assume a similar mechanism for other metals such as Fe(III) or Cu(II). 22 These ndings suggest that the benecial eect of bulk metal doping is purely caused by those few dopants that happen to be on the surface and act as if they were in fact surfacedoped or grafted. If grafting and surface doping are actually identical, grafting metal ions would be superior to doping them since the former achieves the same eect using less resources and also avoiding the detrimental eect of 'useless' bulk dopants.

9


Unfortunately,


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there is not enough data available yet to oer a denite conclusion about this. Also, while some reports tentatively suggest an optimal metal-to-semiconductor concentration ratio for metal-grafted semiconductors there seems to be only little information about its position and whether or not there is a size-dependency as well. 19,20,26,2931 Understanding this correlation will be of paramount importance for the future development and design of optimized photocatalysts. In order to substantiate this theory and also address the second problem of the original model, the limited database, the number of data points used in the model evaluation needs to be drastically increased.

Increasing the database and precision of the model In order to increase the precision of the model recent literature was explored for more examples of metal-doped semiconductors with enough detail to allow being used in the model. While there are hundreds of publications that deal with doped photocatalysts, only few of them are suitable to be included in our model, our selection criteria are outlined below. First of all, the study in question has to evaluate intrinsic, UV-light induced and not visible light photocatalytic activity. Also, since the model assumes spherical particles, only references dealing with roughly spherical primary particles were considered and those dealing with nanorods or mesoporous structures were not included. Also, 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.

In other cases, while the optimal doping ratio is

accurately established, no data on the size of the primary particles are given. Additionally, some sources dealing with iron-doped titania are not included because their proposed optimal doping ratios exceed the solubility limit of iron in anatase and it is thus concluded that not all of the iron atoms are actually incorporated into the host material. To supplement the 19 data sets used in the development of the original model, 1215,17,18,3237

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10 additional data sets of sucient quality and detail were found, 3843 totalling in 177 data points from 29 data sets taken from 17 independent sources. All of the data sets used are listed in Table 1. There is also one dataset from Kuncewicz et al. 44 with rather large particles of

125 nm with sucient detail to be used here.

However, they were investigating visible

light activity and while the behaviour at extremely low doping ratios seems to suggest that the intrinsic activity is also increased, it cannot be said for certain.

Therefore, this data

point is displayed for comparison purposes only and is not used in the actual optimisation. Additionally, the precision could be improved if not just the position of the optimal doping ratio but all data points of a given data set could be used in the model parameter optimization. This would increase the number of data points used from

29 to 177.

However,

to do this, the data rst has to be t to an appropriate model that mimics the doping ratio-activity relationship observed for the samples. In order to facilitate the t to a common model, each data set was rst normalized so that the activity of the undoped sample is equal to 1 while the highest activity at the optimal doping ratio is equal to 2.

The resulting data were then tted to a second order inverse

polynomial with oset origin (Nelder-model function): 45

η(rd ) =

with

η

rd + a b0 + b1 (rd + a) + b2 (rd + a)2

being the normalized activity,

rd

the doping ratio and

a, b 0 , b 1

(6)

and

b2

the parameters

that determine the shape of the function. This type of function is also used in yield-fertilizer models where a small concentration is benecial but a larger detrimental and thus presents a similar case. To t the function to the normalized activity data, the maximum of the function is set to the optimal doping ratio for the respective particle size, the maximum value is normalized to 2 and the activity for pristine samples is set to 1.

b1 =

1 4 and

b2 =

These constraints result in

a = rd,opt

√ 2−1 2 ,

b0 = rd,opt

√ 2+1 16 ,

1√ . As can be seen in Figure 3 for four representative data sets, the 4rd,opt ( 2+1)

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Table 1: The data sets used in the model parameter optimization. Listed are the material (A=anatase, R=rutile) as well as the number of data points N , particle size d, the doping ratios rd studied and the experimentally found optimal doping ratios rd,opt for each data set. *Only used for comparison, not used in the actual optimisation. Material

N

TiO2 (A)/Fe TiO2 (A)/V4+

6

2 - 4

6

2 - 4

TiO2 (A)/Re TiO2 (A)/V3+

7

2 - 4

7

2 - 4

TiO2 (A)/Ru

7

2 - 4

TiO2 (A)/Rh

7

2 - 4

TiO2 (A)/Mn

7

2 - 4

TiO2 (A)/La

6

4

TiO2 (A)/Fe

6

6

TiO2 (A)/Fe

5

TiO2 (A)/Mn

6

TiO2 (A)/Ga

5

TiO2 (A)/Cr

6

TiO2 (A)/Zn

6

TiO2 (A)/Fe TiO2 (A)/V4+

6

TiO2 (A)/Cu

5

TiO2 (A)/Fe

5

TiO2 (R)/Cu

5

TiO2 (R)/Cu

5

TiO2 (A)/Mn

5

TiO2 (A)/Cu

6

TiO2 (A)/W

6

TiO2 (A)/Fe

6

TiO2 (A)/Ru

8

TiO2 (A)/Fe

2

TiO2 (A)/Ru

5

7.3 - 10.6 7.5 9.5 - 12.2 10.2 - 11.56 10.2 - 11.8 11 11.5 - 11.9 11.6 - 12.7 14.5 14.7 13.2 - 15.1 15.54 - 21.42 19 19 19 28.4 - 39.5 30 35.4 - 44.9 45 - 55 45 - 55 125

5

ZnO/Fe

11

ZnO/Ti

10

TiO2 (R)/Rh*

8

d

/ nm

rd / at.% rd,opt / at.% 0.1 - 5 0.5 0.1 - 3 0.5 0.1 - 3 0.5 0.1 - 3 0.5 0.1 - 3 0.5 0.1 - 3 0.5 0.1 - 3 0.5 0.5 - 5 1 0.05 - 1 0.2 0.05 - 2.5 0.25 0.1 - 2 0.2 0.05 - 1 0.1 0.049 - 0.303 0.145 0.05 - 1 0.1 0.02 - 0.2 0.05 0.05 - 1 0.1 0.05 - 1 0.05 0.01 - 0.13 0.05 0.03 - 0.50 0.05 0.042 - 0.46 0.106 0.01 - 0.2 0.02 0.0001 - 10 0.01 0.0001 - 10 0.01 0.0001 - 10 0.01 0.0019 - 0.2878 0.0192 n/a 0.012 0.0004 - 0.0385 0.0019 0.001 - 5 0.005 0.001 - 5 0.002 0.0001 - 0.1 0.0005

12


Reference Choi 12 Choi 12 Choi 12 Choi 12 Choi 12 Choi 12 Choi 12 Liqiang 33 Zhang 17 Zhou 14 Deng 34 Zhou 39 Zhu 35 Chen 37 Zhang 17 Christoforides 40 Christoforides 40 Shokri 43 Shokri 43 Tong 32 Ji 38 Ruggieri 42 Ruggieri 42 Ruggieri 42 Hou²ková 41 Tahiri 15 Hou²ková 36 Bloh 13 Bloh 13 Kuncewicz 44

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selected function ts the observed data points very well.

1 2 5 n m

5 0 n m

1 1 n m

3 n m

2 0 0 %

R e la tiv e n o r m a liz e d a c tiv ity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 5 0 %

1 0 0 %

5 0 %

0 % 0 .0 0 0 1

0 .0 0 1

0 .0 1

0 .1

1

1 0

D o p in g r a tio / %

Representative examples of the normalized photocatalytic activitydoping ratio relationship and their t with the proposed function, eq. 6.

Figure 3:

12,13,35,44

Using this function, a global optimization over all data sets becomes possible. This way, all data points, not just the maxima in activity, are considered in the calculation of the optimal number of surface dopants

nd,s,opt .

An additional dampening factor ( e

−fcr ⋅rd2

) derived

from the cluster probability was used to simulate the drastic decrease in activity observed at very high doping levels due to the sharp increase in recombination centres. 13 The nal equation for the normalized activity therefore:

η

as a function of doping ratio

rd

and particle size

√ 2 8(2rd + rd,opt (d)( 2 − 1)) ⋅ e−fcr rd √ η(rd , d) = √ (2r +r (d)( 2−1))2 √ 4rd + rd,opt (d)(3 2 − 1) + dr d,opt (d)( 2+1)

d

is

(7)

d,opt

with

rd,opt (d)

calculated according to eq. 5 and using Avogadro's constant

rial parameters molecular mass

M,

density

ρ

and nearest neighbour distance

parameters to be optimized, optimal number of surface dopants per particle cluster ratio dampening factor

fcr .

NA ,

the mate-

δ

nd,s,opt

and the and the

The optimization of these parameters was done using a

13



Levenberg-Marquardt algorithm with least squares and yielded a best t for and

fcr = 143.95.

nd,s,opt = 3.54

With these parameters we can calculate a three-dimensional matrix for the

relative photocatalytic activity spanning the whole parameter-space of both, doping ratio and particle size. The resulting plot along with the points used to calculate the parameters can be seen in Figure 4. The plot ts the used data sets very well and almost all experimentally determined optimal doping ratios fall within the corridor of 1 to 10 dopant atoms at the surface, most of them near the calculated optimal line at

1 0 0 0

3.54

per particle.

N o r m a liz e d a c tiv ity 2 0 0 %

P a r tic le d ia m e te r / n m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 0 0 %

0 %

1 0 0

1 0

1 0 .0 0 0 1

0 .0 0 1

0 .0 1

0 .1

1

1 0

D o p in g r a tio / %

The relative normalized activity data as a function of doping ratio and particle size as calculated by eq. 7. All data points are plotted as small black dots with their respective optimal doping ratio marked by a large black circle. The blue solid line represents the calculated optimal doping ratio at nd,s,opt = 3.54 and the slashed blue lines the corridor where there are between 1 and 10 surface dopants present per particle. Figure 4:

Even though this more complicated calculation yielded only a marginally dierent result from the simple approach ( 3.54 versus

3

doped surface atoms per particle), it is now sub-

stantiated by a much larger database and allows predicting the optimal doping ratio with increased certainty for a given material and particle size.

Also, the rened fundamental

model ts the observed behaviour much better than in the original version and is in line with the emerging theory that metal grafting is superior to metal doping in terms of activity

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increase. However, there are still some limitations in the present model.

Due to the scarcity of

comprehensive published data points, this model has not been validated yet for materials other than anatase and rutile titanium dioxide and zinc oxide or for particles smaller than

3 nm

or larger than

55 nm.

The model also does not take into account intrinsic metal

content in the materials originating from impurities in the precursor chemicals. These will undoubtedly have an impact on the actual metal content of the doped or grafted materials, especially at the low levels of metal addition predicted for larger particle size in the ppmregime. Intrinsic defects such as oxygen vacancies that might act as traps, as well, are also ignored in the present model which might lead to inaccuracy at very low doping ratios. It should also be pointed out, that while there are reports of many dierent metal dopants used successfully for increasing the activity, there are also some systems which appear not work.

For instance, in the early study by Choi et al., doping TiO 2 with Fe(III), V(III),

V(IV), Re(V), Mo(V), Ru(III), Mn(III) and Rh(III) all improved the activity (with the same optimal doping ratio in all cases), but doping with Co(III) did not. 12 This means that while many are, not all metal ions are suitable as dopants to increase the activity of the host photocatalysts.

Conclusions The earlier model for the optimal doping ratio was re-evaluated, assuming a surface-based eect rather than a bulk-based one. The new model assumes that only dopants that happen to be situated at the particle surface can contribute a positive eect.

It was found that

the new model ts the experimentally determined data points even better than the original model and can explain the underlying mechanism much better since it is surface based. Also, the database used for the model parameter optimization was extended from 19 to a total of 177 data points from 29 data sets taken from 17 independent publications and ranging from

3

to

55 nm

in particle size and from

0.0019

to

1 at.%

15


in optimal doping ratios.

The


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optimum was found for a case where there are only statistically

Page 16 of 23

3.54 dopant atoms present on

the surface of each spherical particle, just about enough to guarantee every particle ( > has at least one.

97 %)

The doping ratio necessary to achieve this can be calculated with the

model developed here, eq. 5, using

nd,s,opt = 3.54.

The precision is approximately one order

of magnitude for the data evaluated here, representing cases from

1

to

10

surface dopants

per particle.

rd,opt (d) =

nd,s,opt ⋅ M π ⋅ NA ⋅ ρ ⋅ (δd2 − 2δ 2 d + 34 δ 3 )

(5)

The degree of correlation with the model is remarkable given the number of involved parameters (dierent materials, dopants, synthesis methods and activity tests) suggesting that indeed the doping ratio-size-activity relationship is predominantly governed by the number of surface dopants and all the other parameters only seem to play the minor role of ne-tuning the optimal doping ratio within the order of magnitude already set by the former eect. The eect of the surface dopants seems to be similar or even identical to that of grafted metal ions.

They promote the inter-facial charge transfer which reduces the bulk recom-

bination rate in the semiconductor as the charges are more eciently extracted and also enhances the reaction rate with adsorbed molecules. Presumably, this eect is accomplished solely by those few dopants that happen to be situated at the particle surface.

The bulk

dopants, on the other hand, only contribute negative eects such as acting as recombination centres, especially at higher doping ratios which promote cluster formation. Consequently, bulk doping with metal ions for the purpose of increasing the photocatalytic activity should be avoided and only the surface should instead be selectively doped or grafted. That way, less material of potentially rare and expensive metals is needed and also the detrimental eect of higher metal concentrations in the bulk is suppressed. Further studies will be necessary to elucidate whether this model is readily applicable to the case of surface grafting and where the optimal loading is for those materials. Presumably,

16


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the absence of detrimental bulk dopants will allow more exibility in the amount of metal loading in this case, potentially leading to higher numbers of grafted ions per particle at the optimum.

Acknowledgements The author is grateful to D.W. Bahnemann and R. Dillert for fruitful discussions on the subject without which this work would not have been possible.

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Table of Contents entry

23


Refined Model for the Optimal Metal Content in ... - ACS Publications

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