Resolving the Controversy about the Band Alignment between Rutile

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Resolving the Controversy About the Band Alignment Between Rutile and Anatase: the Role of OH–/H+ Adsorption. Jolla Per Kullgren, Bálint Aradi, Thomas Frauenheim, Ladislav Kavan, and Peter Deak J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b04821 • Publication Date (Web): 09 Sep 2015 Downloaded from http://pubs.acs.org on September 13, 2015

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The Journal of Physical Chemistry

Resolving the Controversy About the Band Alignment Between Rutile and Anatase: the Role of OH–/H+ Adsorption. Jolla Kullgren,1)* Bálint Aradi,1) Thomas Frauenheim,1) Ladislav Kavan,2) and Peter Deák1)* 1) Bremen Center for Computational Materials Science, University of Bremen, P.o.B. 330440, D28334 Bremen, Germany 2) J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, CZ-18223 Prague 8, Czech Republic

ABSTRACT: The synergic effect of mixing rutile (R) and anatase (A) crystals in photocatalysis is often attributed to a staggered alignment of the band structures, but it is widely disputed whether the conduction band edge of rutile or that of anatase is higher. Photoelectron spectroscopy (PES) supports the former, flat-band potential (FBP) measurements the latter. Theoretical alignment of the bulk band structures, as well as calculated offsets across actual interfaces support the PES data. The theoretical study presented here shows that the FBP data can be explained by taking into account the adsorption of OH– and H+ ions in the electrolyte solution. We conclude that in case of nanopowders, applied in photocatalysis, the dipole layer created by surface adsorption and the one at the R/A interface both have an influence on the alignment, and the end result may change from experiment to experiment. I. INTRODUCTION The two most important forms of titania (TiO2), rutile (R) and anatase (A), find applications in many areas, like in gas sensors, fuel cells, memristors, optoelectronics, photovoltaics, Li-ion batteries, or catalysis- and photo-catalysis. Anatase is generally considered to be the more photoactive, but rutile/anatase mixtures exhibit an even higher photocatalytic activity. The effect has been linked to the separation of photo-excited charge carriers, driven by the band offset at the R/A interface.1,2,3,4,5,6,7 (Here and in the following band offset will refer to the difference in the position of the band edges, with respect to a common reference.) The magnitude and direction of the R/A band offset are, however, subject of strong debate, and all possible arrangements of the band edges have been proposed in the literature (see, e.g. Refs. [8,9,10,11,12]). Some studies8,9,13,14,15,16,17 suggest that electron transfer from rutile to anatase is the key to the synergy, while others10,11,18,19,20,21,22,23

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conclude that the charge transfer is in the opposite direction. It should be noted, however, that few of the studies have actually measured the band offset directly. Quite often, the proposed alignment scheme is just an assumption to explain observations which might have had other reasons too. In the following, we will limit our discussion to those experiments that directly measure the R/A band offset. One such type of experiment is X-ray photoelectron spectroscopy (XPS), in vacuum environment, and all such studies so far have predicted a staggered alignment with both the valence and conduction band of rutile above the anatase counterparts.8,16,17 In Refs.[8,16], A and R parts in direct contact have been measured with respect to a common reference. In Ref.[17] the transitivity rule was invoked after separately measuring R and A in contact with the same conducting oxide. XPS measures the energy of occupied states, and can establish the offset between the valence band maxima (VBM). This ∆EVBM can be converted into the difference between the conduction band minima, ∆ECBM, by using the well-known difference of the band gaps: Eg(A) – Eg(R) = 0.2 eV

(1)

(at room temperature),24 yielding the values shown in Table 1. It is known, that the work function of a material depends on the surface orientation. (For example, it is higher for the R(110) surface than for R(100) by ~0.1 eV.25) This variation shows up in the morphology/orientation dependence of the XPS results on ∆ECBM, too. The other type of experiment is flat-band potential (FBP) measurement with respect to a reference electrode, in an aqueous or aprotic electrolyte solutions, in separate measurements on R and A surfaces. Many such measurements have been carried out on nanocrystalline samples,26,27,28 where quantum confinement effects might have interfered. Here we discuss results for well defined A(101) and A(001) surfaces,22,29 as well as for the R(001),22 R(100) and R(110) surfaces.23 Relating the published results to the reversible hydrogen electrode (RHE) erases the pH-dependence of FBPs, and the actual values are: -0.156, -0.216, +0.044, -0.083, +0.007 V vs. RHE, respectively. (For further discussion and compilation of experimental FBPs see Supporting Info). The FBP reflects the position of the Fermi-level EF, and it is usually assumed in the literature that EF is very close to the CBM in both polymorphs. Therefore, a CBM-offset of -0.200, -0.073, and -0.163 eV was predicted for R(001), R(100) and R(110) with respect to A(101). These CBM-offsets of the rutile surfaces shift by -0.06 eV with respect to the A(001) surface. The prediction, that the CBM of rutile is lying lower than that of anatase, appears to be in sharp contrast to the XPS results. We note, however, that EF actually does not necessarily have the same position with respect to the CBM in the two polymorphs. ACS Paragon Plus Environment

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Table 1. Conduction band offset ∆ECBM = ECBM(R) – ECBM(A) in eV. (Positive values mean that rutile lies higher.) For the deduction of the FBP values, see the text. The notation “/” means an actual interface with electrical contact between rutile (R) and anatase (A), while “;” denotes separate measurements with respect to a common reference. Note that the error margin of the FBP values indicate the uncertainty in the difference of the Fermi-level position w.r. to the CBM in rutile and anatase. Expt.

System

∆ECBM

Theoretical alignment

System

∆ECBM

XPS [8]

R(100) / A(001)

+0.07

intrinsic Fermi-levels [36]

R-bulk ; A-bulk

0.35

XPS [16]

R-poly / A-poly

+0.22

ionization potentials [16]

R-bulk ; A-bulk

0.30

XPS [17]

R(001) ; A-poly

+0.5±0.1

potential at Ti atom [17]

R-bulk ; A-bulk

0.39

interface pot. jump [38]

R(001)/A(100)

0.21


R(100)/A(100)

0.65


R(110)/A(101)

0.69

R(110) ; A(101)

-0.14±0.29

FBP [22,29]

R(001) ; A(001)

–0.010±0.150

FBP [23,29]

R(100) ; A(001)

+0.115±0.150

FBP [23,29]

R(110) ; A(001)

+0.025±0.150

FBP [22]

R(001) ; A(101)

+0.050±0.150

FBP [22,23]

R(100) ; A(101)

+0.175±0.150

potential with respect to

FBP [22, 23]

R(110) ; A(101)

+0.085±0.150

vacuum (present work)

The Fermi-level is pinned by the charge transition level of the majority dopant, which is typically the oxygen vacancy (VO) in TiO2.30 It has been established theoretically, that the level positions of VO are different in bulk rutile and anatase.31 In rutile, at moderate concentration, VO is in the 2+ charge state but binds two self-trapped electrons on nearby (but not first neighbor) Ti(3+) sites. The corresponding adiabatic (+/0) charge transition level was calculated, in excellent agreement with experiment,32 to be at CBM-0.4 eV. At high concentrations, VO retains its electrons and the (+/0) level is at CBM-0.1 eV. In contrast, theory predicts VO to be very shallow in anatase (independent of the concentration),31 with an experimentally measured (+/0) level at CBM-0.004 eV.33 (We note that a similar difference, can be seen between the positions of the adiabatic (+/0) levels in R and in A also for Nb doping. 34,35 ) Therefore, depending on the VO concentration, the published FBP differences have to be shifted by 0.1-0.4 eV, yielding the CBM-offsets shown in Table 1. Since the VO concentrations are usually unknown from the source references, we put the uncertainty scale to the upper limit, which is ± 0.15 eV. As can be seen, this brings the FBP results nearer to the XPS ones but, within the given uncertainty, the FBP results still indicate the possibility of a slightly negative ∆ECBM, i.e., a possible flow of electrons from anatase to rutile, while the unambiguously positive XPS values mean electron flow in the opposite direction. It is the purpose of this paper to address this contradiction by theoretical modeling. The R/A band alignment has also been addressed theoretically in the past. Our group has calculated



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the band offsets by aligning the bulk band structures at the intrinsic Fermi-level, 36 while the ionization potentials of R and A, or the electrostatic potential around Ti atoms in the two polymorphs were used for the same purpose in Refs.[16,17], respectively. The results, also shown in Table 1, are very close to each other and appear to be in line with the XPS data. However, these values could be modified substantially by a dipole layer formed at the interface between well defined surfaces of R and A. Earlier, we have investigated this effect by establishing an actual interface between the most reactive and the most common surfaces, R(100)/A(100) and R(110)/A(101), respectively, by simulated annealing.37 A very recent similar study has considered the R(001)/A(100) interface. 38 Aligning the bulk band structures based on the jump of the electrostatic potential at the interface has given ∆ECBM > 0 values for all three interfaces (see Table 1), i.e., the CBM of rutile higher than that of anatase. The FBP values of Table 1 deviate from that. Under specific conditions (e.g., in case of strongly reduced material) the CBM of rutile could lie below that of anatase and – in any event – the FBP offsets are smaller than the ones obtained in XPS. This difference can very well originate from the fact that XPS is carried out on solid heterostructures in vacuum (with no or little interference from contaminants on samples with well defined free surfaces), while FBP in an aqueous environment (containing all sorts of ions and so adsorbates on the surface). In the latter case, specific interface structures at the H2O/TiO2 interface may give rise to an additional dipole layer and modify the work function. It has been shown experimentally that the work function of the R(110) surface changes from 5.5 eV to 4.9 eV between a quasi-stoichiometric and a hydroxylated state.39 Such an effect will obviously be sensitive to the specific R or A surface considered. To the best of our knowledge no theoretical estimate for the R/A band offset has been presented so far in the presence of water. In the following, we will describe our density functional theory (DFT) investigation to clarify the issue. We will provide an estimate for the water induced shifts in the band offset between rutile and anatase particles, predominantly exposing their thermodynamically most stable surface facets, namely R(110) and A(101). We will provide evidence that, indeed, the difference between XPS and FBP can be explained by the presence of H+ and OH– adsorbates. At the end of the paper we will also discuss, why charge transfer between R and A particles, in direct electric contact, is possible in the direction opposite to the one following from the band alignment. II. METHODS The terms potential, potential offset and band offset will be used throughout the text and we define these quantities in this paragraph. Unless explicitly stated otherwise, potential will refer to the local electrostatic potential inside a rutile or anatase particle, with respect to vacuum. Potential offset and


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band offset will be used to refer to the difference in potential or band edge position between rutile and anatase. We will determine the valence band offset ∆EVBM, and the potential offset, ∆Φ, which are related to each other through the following relation (see Fig.1): R A ∆EVBM = EVBM − EVBM = ∆Φ + ∆Erel

(2)

R A Here EVBM and EVBM refer to the valence band maximum, with respect to vacuum, and ∆Erel is

defined through: R A ∆Erel = Erel − Erel

(3)

R A where Erel and Erel are the positions of the VBM relative to the average potential in bulk rutile and

anatase, respectively. Note that with the convention used here, positive values in the band offset means that the valence band of rutile is located above the anatase counterpart. The CBM offset will be obtained from ∆EVBM using Eq.(1).40

Figure. 1: The relationship between the potential offset (∆Φ) and valence band offset (∆EVBM), as used throughout the text.

Fig. 1 illustrates the relationship between the terms in Eq.(2-3), and how band offsets are calculated in the current investigation. We consider water adsorption on R and A slabs separately, and calculate the potential profile across the slab/vacuum region, to determine Φ with respect to vacuum. Potential profiles along the surface normal of R(110) and A(101) have been obtained from the spatially resolved potential by taking a planar average perpendicular to the surface normal. The potential profiles were further processed by applying a Gaussian smearing to obtain a smooth curve with plateaus from which the potential relative to vacuum can be easily obtained. In order to assess the difference between the effect of a monolayer (ML) and liquid water, we have carried out density-functional-based tight-binding molecular dynamics (MD) simulations for rutile and anatase slabs, consisting of about 20 Å of TiO2 and 25 Å of liquid water.41 From the MD ACS Paragon Plus Environment


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trajectories over a time span of 25 ps, 250 snap-shots (after every 0.1 ps) have been evaluated, calculating the planar averaged local potential perpendicular to the interface, at the DFT level. The average obtained for ∆Φ was within 0.1 eV of the value for the corresponding slabs with ML water adsorption. The potential profile across a liquid-H2O/R(110) interface was also determined earlier from molecular dynamics (MD) simulation, using classical potentials in Ref. [42]. The calculated planar averaged potential in the rutile slab was about 2 eV below that in the water region. The liquidH2O/A(101) interface was investigated using a combination of force field MD and density functional theory in Ref. [43]. The potential of an A(101) slab covered with 16 ML of water was determined to be -10 eV with respect to the water region. The large difference in the potential offset in these two studies is not a reflection of the surfaces being that different but rather a consequence of using classical and quantum mechanical descriptions. In order to make a comparison, we need to simulate the two surfaces with the same technique. Therefore, we compare here potential offsets ∆Φ obtained from DFT calculations in the generalized gradient (GGA) approximation. The exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE) has been used.44 Although DFT-GGA underestimates the band gap, the difference between R and A (see Eq.(1)) is well reproduced, and we can expect the same accuracy for the potential difference between the two polymorphs as well. We have calculated Erel both with PBE and with the screened hybrid functional R A of Heyd, Scuseria and Ernzerhof (HSE06).45 The former resulted in Erel = 2.96 eV and Erel = 1.66

eV, i.e., ∆Erel =1.29 eV. The ∆Erel value obtained by HSE06 was within 0.1 eV of this. All calculations were performed with the Vienna ab-initio simulation package (VASP 5.2),46,47,48,49 using dispersion correction. 50 , 51 , 52 A cutoff of 420 eV was used for the plane-wave basis-set describing the valence electrons (10 for titanium and 6 for oxygen). Core electrons were treated by the Projector Augmented Wave (PAW) method.53,54 The investigated slabs included 10 TiO2 layers (periodic in 2D), repeated along the surface normal, with at least 25 Å of vacuum between the repeated images. The surface cell parameters were a = 3.823 Å, b = 5.551 Å, and γ = 69.9° for A(101) and a = 5.968 Å, b = 6.587 Å, and γ = 90° for R(110). We have used (1x1) bulk terminations with oxygen ion furthest out. These surface models are well established in both the experimental and theoretical literature (see, e.g., Ref. [55] and references therein). A 4×4×1 Monkhorst-Pack set56 was used in all systems. Dipole correction was employed where applicable.


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III. RESULTS We have investigated the effect of water on the CBM-offset by considering the adsorption superstructures shown in Figs.2-3. ML structures of molecular water were obtained by placing H2O molecules atop the 5-fold coordinated Ti atoms (Ti5c) on both surfaces, with one of the hydrogen atoms pointing towards a neighboring 2-fold coordinated oxygen atom (O2c). Fully dissociated ML structures were constructed by transferring all hydrogen atoms pointing towards an O2c atom to that oxygen atom. In this way pairs of terminal and bridging hydroxyl groups (OH) were formed. Terminal OH groups arise through OH– adsorption on Ti5c sites, while bridging OH groups arise through H+ adsorption on O2C sites. These groups act as Brønsted acids and bases, as summarized in Fig. 4.

Figure 2: Side- and top-view of the topmost layer of the R(110) surface at ML water coverage. The most stable configurations for molecular, mixed and dissociative water adsorption on the pristine surface are shown in (a)-(c), respectively. The most stable configuration for the hydrogenated and water covered surface is shown in (d). See text for more details.

Figure 3: Side- and top-view of the topmost layer of the A(101) layer after water adsorption. The most stable configurations for molecular (a) and dissociative (b) adsorption of 1 ML, as well as the molecular configuration for a water bi-layer (c) are shown. The most stable configuration for the hydrogenated and water covered surface is shown in



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(d).

Figure 4: Schematic illustration of acidic and basic sites at a TiO2 surface. Hydroxyl ions (OH–) are attracted by undercoordinated Ti5c sites while protons (H+) are attracted by undercoordinated O2c sites (middle part of the figure). Terminal OH groups are colored blue and the hydrogen in the bridging OH groups are colored red. (Note that OH– and H+ may originate from the same water molecule corresponding to water dissociation.) Surfaces with purely terminal or purely bridging OH groups are depicted on the left and on the right, respectively.

Alternating rows of molecular and dissociated water molecules along the [100] direction of the R(110) surface lead to a so called mixed water ML. For the R(110) surface we adopt the p(2×1) arrangement of a mixed water ML, as described by Kowalski et al.57 In agreement with that work, we find a preference for molecular water adsorption on R(110), as shown by the water adsorption energies in Table 2. Table 2. Adsorption energy per water molecule Eads, VBM position with respect to vacuum EVBM, and CBM-offset ∆ECBM, for the R(110) and A(101) surfaces (all in eV). The systems are described in Figs. 2 and 3. EVBM was obtained A R from the calculated ∆Φ values and with Erel = 1.66 eV; Erel = 2.96 eV from bulk PBE calculations.

Eads (eV)

System

R(110)

A(101)

Pristine surface

EVBM (eV)

∆ECBM (eV)

R(110)

A(101)

-7.53

-7.78

+0.05

with 1 ML H2O (molecular)

1.07

0.98

-6.24

-6.55

+0.12

with 1 ML H2O (dissociated)

0.87

0.90

-6.87

-6.63

–0.44

with 1 ML H2O (mixed)

0.99

with Bilayer H2O (molecular)

-6.62 0.91

Hydrogenated surface + 1 ML H2O (molecular)

1.09

0.76

-6.73 -5.15

-5.51

+0.16

The structure of water on the A(101) surface has been studied by Selloni et al,58,59,60,61 and we adopt their water structures here (see Fig. 3), including the stable water bi-layers (BLs) suggested in Ref. [59]. (We emphasize here that in contrast to the A(101) surface, multi-layer adsorption at the R(110) surface, appears to be unfavorable.62) In agreement with the results of the Selloni et al., we find that ML molecular adsorption is energetically favored also on the A(101) surface. While the case of dissociative water adsorption corresponds to an equal amount of terminal and bridging OH groups on the surface, we have also considered surfaces with only bridging OH groups below the monolayer of water. Actually, one expects the adsorbtion of H+ onto the bridging oxygen atom, however, since the FBP measurements22,23,29 have been carried out on reduced or Nb-doped ACS Paragon Plus Environment

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n-type samples, we expect that the positive charge on the bridging OH group will be screened by the free carriers or compensated by small electron polarons trapped near the adsorption site. This is simulated by adding, besides H+, also an electron e– to the (originally nominally undoped and stoichiometric) model (i.e., adding, in effect, a neutral H atom). As expected, this electron ends up mostly on surface Ti atoms. The results for the CBM-offsets are shown in Table 2. As can be seen, ∆ECBM between the free R(110) and A(101) surfaces is substantially lower than what we have obtained for the R(110)/A(101) interface, and even lower than the generic off-set between bulk crystals (see the theory column of Table 1). This emphasizes the importance of the dipole layer on the surface or at the interface. In agreement with earlier calculations on rutile,63 adding a ML of molecular water to the pristine surfaces shifts EVBM significantly but in a similar manner for R(110) and A(101), therefore does not affect ∆ECBM much, increasing it slightly. Bridging OH groups (H+ adsorbed on O2c) on the surface increase ∆ECBM further. Our result for the dissociated ML of water, however, indicates that the increase in the number of terminal OH groups (OH– adsorbed on Ti5c) can tune the CBM offset between the extreme values of +0.16 and -0.44 eV, to be compared with the range of [+0.25 ; -0.065 eV] deduced from actually observed FBP data for R(110) and A(101) (see Table 1).

IV. DISCUSSIONS Table 1 proves that theory is able to reproduce both the XPS and FBP data on the R/A band alignment at a semi-quantitative level. The variation of the observed band offsets can generally be understood in terms of the different dipole layers, forming on free surfaces or at the interface of rutile and anatase, which shift the generic band offset between the bulk crystals. The main difference between XPS and FBP results comes from the fact that the former is carried out in vacuum and the latter in an aqueous electrolyte solution, containing OH– and H+ ions. R A R A Adsorption of OH– and H+ ions can shift the CBM-offset from ECBM to ECBM , with > ECBM < ECBM

increasing [OH–]/[H+] ratio. Therefore, in all applications where TiO2 serves as an electrode, the relevant information on the R/A band alignment comes from FBP measurements. However, the FBP result will strongly depend on both the ratio of adsorbed [OH–]/[H+], and on the difference in the Fermi-level positions (w.r. to CBM) in the two polymorphs (determined, in the case of selfdoping, by the VO concentration in rutile). In contrast, both XPS and the theoretical investigation of R/A interfaces always provide ACS Paragon Plus Environment


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R A . We believe that this is the relevant alignment for R and A layers in direct contact. In ECBM > ECBM

such cases the band alignment calls for electrons flowing from rutile to anatase and holes from anatase to rutile (see green arrows in Fig.5). This kind of charge separation is also promoted by the existence of Ti(4+/3+) electron traps in rutile and of O(2-/1-) hole traps in anatase,31,34 which lead to the dominance of mobile holes in bulk rutile and to the dominance of mobile electrons in anatase, upon excitation in the bulk (see black arrows in Fig.5).37 It should be noted however, that the R/A interface contains undercoordinated sites which act as amphoteric traps.38 These can act as recombination centers or channels for electron transfer from anatase to rutile,21 (see red arrows in Fig.5). A high concentration of such coordination defect can effectively quench the charge separation.

Figure. 5: Schematic representation of the charge transfer processes which may occur between R and A layers in contact, after photo-generation of electron-hole pairs (dashed vertical lines) in the bulk or near the surface. Dashed black lines indicate the charge transition levels of trapping sites. (In case of Ti(4+/3+) the vicinity of a VO(+) is assumed.) Green arrows show the direction of charge transfer due to the band alignment between R/A layers. Black arrows show the trapping process of electrons in bulk rutile and holes in bulk anatase. Red arrows indicates the role of interface traps (IT): recombination and back-channeling of electrons.

Experiments, however, are often carried out on mixed-phase nanoparticles in a humid environment. In such systems, grains of the size of ca. 20-40 nm are connected through small “necks”, 10 nm in diameter or less.11,64,65 The band alignment will be influenced both by the interface dipole across the neck and by the dipole layers due to OH–/H+ adsorption on the surface. The actual band offset will depend on particle size and OH/H coverage, as well as on size and structure of the interface region. It should also be noted that, due to the difference in the position of the pinned Fermi-levels with respect to the CBM in R (0.1 – 0.4 eV) and in A (0.004 eV), the relative position of the band edges will shift, if oxygen-deficient, sufficiently “macroscopic” R and A particles are brought into contact. Models based on ideal material do not account for this. Still, as long as before contacting ECBM(R) - ECBM(A) > -0.096 eV, this shift will not reverse the electron current predicted by the relative position of the band edges in ideal material. (This is definitely the case for all the ACS Paragon Plus Environment

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investigated layer structures.) In case of mixed, sintered powders applied in an electrolyte solution, however, if ECBM(R) - ECBM(A) < -0.096 eV in the ideal model, this shift could still lead to an R A flow of electrons. (We note, however, that at the typical size of particles in these powders, it is difficult to estimate in what extent Fermi-level pinning plays a role.) In summary, all these possible effects explain the different outcome of experiments on mixed nanopowders. Direct theoretical modeling by first-principles methods in this size range is not yet feasible. However, from many experiments on mixed nanopowders in humid environment, it appears likely that a flow of electrons in the A R direction is possible.

IV. CONCLUSIONS We have investigated the band alignment between the R(110) and A(101) surfaces in humid R A band offset between the free, pristine surfaces, +0.05 eV, environment. The calculated ECBM − ECBM

is substantially smaller than in the case of actual R/A interfaces, but still in line with XPS experiments on the latter. Molecular adsorption of water is energetically preferred on both surfaces, and the shift of the band edges is nearly identical, preserving the direction of the band offset between the pristine surfaces. This situation does not change if the ML of water molecules is replaced by liquid water. In contrast, considering the adsorption of OH– and H+ ions, the R A band offset can be tuned into the negative range with increasing OH/H ratio on the ECBM − ECBM

surface, as indicated by FBP measurements. We emphasize that electron self-trapping in rutile and its absence in bulk anatase, lead to different Fermi-level positions in the two polymorph (depending on the nature and concentration of the dopants), and this has to be taken into account in evaluating FBP data, which are the relevant ones in case of applying TiO2 as an electrode. We also note that our model does not include the electrolyte solution itself, and the only effect considered is the OH– /H+ ratio, which tunes the band alignment between R and A from positive to negative. Our results unambiguously predict the flow of electrons from rutile to anatase (and of holes in the opposite direction) for R/A layers in electrical contact. The resulting charge separation is reinforced by the aforementioned self-trapping effects but weakened by interface traps. In case of mixed-phase nanoparticles in humid environment, the actual alignment is determined by both the interface dipole and the surface OH/H coverage, and will be strongly dependent on the particular experimental conditions. This explains the observed controversies in the literature.



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V. AUTHOR INFORMATION Corresponding Authors *

E-mail: [email protected] ; [email protected]

PHONE: +46(18)471-3721; +49(421)218-62353

VI. ACKNOWLEDGEMENTS This work has been supported by the Grant HHB15 at the Julich Supercomputer Centre (JSC). JK acknowledges the Hanse-Wissenschaftskolleg (HWK) for support and Matthew Wolf for useful discussions. LK acknowledges the support from Grant Agency of the Czech Republic (contract No. 13-07724S). Supporting Information Available A compilation of experimental FBPs and their discussion is provided. This information is available free of charge via the Internet at http://pubs.acs.org .

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Resolving the Controversy about the Band Alignment between Rutile

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