Nanoscale Spatial Distribution of Supported Nanoparticles Controls Activity and Stability in Powder Catalysts

Abstract

Supported metal nanoparticles are essential components of high-performing catalysts, and their structures are intensely researched. In comparison, nanoparticle spatial distribution in powder catalysts is conventionally not quantified, and the influence of this collective property on catalyst performance remains poorly investigated. Here, we demonstrate a general colloidal self-assembly method to control uniformity of nanoparticle spatial distribution on common industrial powder supports. We quantify distributions on the nanoscale using image statistics and show that the type of nanospatial distribution determines not only the stability, but also the activity of heterogeneous catalysts. Widely investigated systems (Au-TiO₂ for CO oxidation thermocatalysis and Pd-TiO₂ for H₂ evolution photocatalysis) were used to showcase the universal importance of nanoparticle spatial organization. Spatially and temporally resolved microkinetic modelling revealed that non-uniformly distributed Au nanoparticles suffer from local depletion of surface oxygen—and therefore lower CO oxidation activity—compared to uniformly distributed nanoparticles. Nanoparticle spatial distribution also determines stability of Pd-TiO₂ photocatalysts, because non-uniformly distributed nanoparticles sinter while uniformly distributed nanoparticles do not. This work introduces new tools to evaluate and understand catalyst collective (ensemble) properties in powder catalysts, thereby paving way to more active and stable heterogeneous catalysts.

Graphical Abstract

INTRODUCTION

Nanoparticles (NPs) are key components in heterogeneous catalysts, owing to properties that differ from bulk materials such as quantum effects and high numbers of undercoordinated atoms.^1,2 These properties stem from unique NP structural features such as tunable size, shape and composition.^3,4 However, some important NP properties arise not from their individual structure but from their collective behavior, which is determined by the NP spatial organization.⁵ As an example, spectroscopic signals from surface plasmon resonance or Raman scattering are greatly modified when NPs in solution aggregate and the spectra are dependent on the NP spatial organization in the aggregates, opening many new characterization opportunities.^6,7 Collective behavior also appears in two-dimensional films of ferromagnetic NPs where the magnetic field of each NP becomes weaker as the assemblies become denser.⁸ Thus, NP collective properties are pervasive in seemingly disparate disciplines, with further examples being mechanical behavior of NP-polymer composites⁹ and exciton coupling in NP superstructures.¹⁰ Although established in nanoscience, NP collective properties in heterogeneous catalysts have received little attention.

Heterogeneous catalysts are usually developed with focus on the supported NP structure.^11–15 This is reasonable, since the NP and/or NP-support interface provides active sites where reactants interact to lower the reaction activation energy.¹⁵ However, because heterogeneous catalysts consist of enormous ensembles of individual NPs, collective properties could also influence catalyst performance. It was recently shown in model planar systems that the distance between supported NPs can influence the local microkinetics through effects such as hydrogen spillover.¹⁶ Thus, NP spatial distribution may influence activity in realistic (powder) catalysts because different NP spatial distributions should give different distributions of local microkinetics, in turn giving different overall catalytic rates. In addition, particle growth^17–19 and atomic redispersion²⁰ are also strongly dependent on the interparticle distance so the type of NP spatial distribution may also impact catalyst stability.¹⁷ The influence of NP spatial distribution on catalyst performance in powder catalysts remains essentially unexplored because conventional catalyst preparation has not allowed varying spatial distribution of supported NPs without simultaneously changing their size distribution.^17,21–23 Thus, because NP size strongly influences both activity^24–27 and stability, ^28–30 it has been challenging to deconvolute NP distribution effects from NP size effects.^17,23 Still, there has been a small number of studies attempting to correlate NP spatial distribution to stability of thermocatalysts. Unfortunately, the catalysts in these studies had both different spatial and size distribution of NPs,^17,23 which makes elucidation of correlation between NP spatial distribution and catalyst stability difficult (since NPs of different size distributions also sinter at different rates^28–30).

To accurately study the influence of NP spatial distribution on catalysis, realistic catalysts must be prepared that have different distributions, but are otherwise identical. Here we present a colloidal self-assembly method to change NP spatial distribution on common industrial supports (such as TiO₂ and Al₂O₃) without changing weight loading, NP size distribution or other NP structural properties. Using this novel approach, we demonstrate that NP spatial distribution strongly influences both activity and stability in heterogeneous thermo- and photocatalysis. Moreover, we show that non-uniform distributions—distinguished by log-normally distributed NPs—commonly found in heterogeneous catalysts are not optimal, but that uniform distributions—distinguished by normally distributed NPs—give better catalytic performance. Because NP spatial distribution scarcely has been investigated, new quantities must be introduced to characterize this collective property. We introduce NP number-density as an easily measured quantity with predictive power for catalyst performance.

RESULTS AND DISCUSSION

Control and Characterization of NP Spatial Distributions.

The most common catalyst preparation techniques, impregnation-drying and coprecipitation are cheap and versatile and therefore used across industry and academia.³ In impregnation-drying, supports are impregnated with a metal salt solution and then dried to form the catalyst, while in coprecipitation separate salt solutions of metal and support are mixed with ensuing precipitation of solid catalyst.³ Unfortunately, these techniques frequently result in NP spatial distributions that are non-uniform and uncontrolled on the nanoscale.^{3,17,21–23,31–40} As an example, industrially relevant cobalt Fischer–Tropsch catalysts prepared by impregnation-drying exhibit significant nanoscale clustering with many NPs in some regions, but few in others.^36,37 More uniform NP spatial distributions have been achieved by judiciously modifying the drying atmosphere, but NP size distributions were not conserved.^17,21 To isolate the influence of NP spatial distribution from size distribution, we propose an alternative approach, using pre-synthesized NPs to generate different spatial distributions. In this work, we used colloidal methods to prepare catalysts with varied nanoparticle spatial distributions that led to different catalytic properties (Figure 1). Colloidal Au NPs (3.2 nm +/− 0.5 nm, Figure 1 A) and Pd NPs (3.8 nm +/− 0.2 nm, Figure 1 B) were synthesized in organic solvents (Experimental Section) with oleylamine as a stabilizing ligand. As is conventional,^3,20,41–43 the NPs were then deposited onto TiO₂ by direct addition to the support grains, also in organic solvent. This protocol, similarly to what is frequently observed with impregnation-drying or coprecipitation,^{3,17,21–23,31–40} gave non-uniform distribution on supports with some regions having many, and others few NPs (Figure 2 summarizes particle distributions for the samples shown in Figure 1; more below). Because of their non-uniform distributions, the conventionally impregnated samples, labelled Au-TiO₂-C and Pd-TiO₂-C, represent conditions typically observed in heterogeneous catalysts (Figure 2 B,D,H,J).^{3,17,21–23,31–40}

Figure 1. Conventional and surfactant-assisted deposition of NPs onto TiO_2.

(A) TEM micrograph of Au NPs and (B) of Pd NPs. NP size distributions are included in Figure S1. (C) Schematic illustration of conventional impregnation and (D) surfactant-assisted impregnation of NPs on metal oxide support grains. (E) DLS size distribution of TiO₂ grains in hexanes with surfactant. DLS measurement of TiO₂ in pure hexanes was not possible due to fast agglomeration and sedimentation of grains. (F) Photographs of TiO₂ dispersion in hexanes with surfactant (left) and in pure hexanes (right) at different times, 3 min and 30 min, after sonication.

Figure 2. Statistics of NP spatial distributions.

(A, C) Typical TEM micrographs of Au-TiO₂-SA and (B, D) Au-TiO₂-C exemplifying regions with low and high NP number-density. (E) NP number-density distributions of Au NPs on TiO₂ grains. Au-TiO₂-C has non-uniform, log-normal distribution (red curve), and Au-TiO₂-SA has uniform, normal distribution (blue, dashed curve). (F) Cumulative fractions of Au NPs vs NP number-density on Au-TiO₂-C, red curve and Au-TiO₂-SA, blue dashed curve. (G, I) Typical TEM micrographs of Pd-TiO₂-SA and (H,J) Pd-TiO₂-C exemplifying regions with low and high NP number-density. (K) NP number-density distributions of Pd NPs on TiO₂ grains. Pd-TiO₂-C has non-uniform, log-normal distribution (red curve), while Pd-TiO₂-SA has uniform, normal distribution (blue, dashed curve). (L) Cumulative fractions of Pd NPs vs NP number-density on Pd-TiO₂-C, red curve and Pd-TiO₂-SA, blue dashed curve. The statistical parameters describing the normal, ρ_# ~ N(μ, δ²) and log-normal, ln(ρ_#) ~ N(μ, δ²), distributions in (E,K) are given in Table S1.

It is commonly thought that an optimal catalyst should consist of monodisperse, size-, shape- and composition-tunable NPs deposited on porous powder supports.^14,44,45 It is further thought, but rarely studied, that uniform NP spatial distributions are needed for optimal performance.^17,23 Colloidal synthesis affords monodisperse size-, shape- and composition-tunable NPs from a wide range of metals and is therefore ideally suited to produce catalysts.^4,44 However, the final step for obtaining optimal catalysts, namely a general method for uniform deposition of colloidal NPs is, until now, lacking. We hypothesized that the non-uniform NP distribution obtained by adding pre-synthesized NPs to support grains results from poor dispersion of the hydrophilic grains in organic solvent, such that large areas of the grains were not exposed to the solvent during impregnation (Figure 1 C). Consequently, we sought a method to better disperse the grains for more uniform NP deposition. Surfactants can be used to render hydrophilic mineral grains hydrophobic, a property frequently used to recover minerals by froth flotation in the mining industry.⁴⁶ We discovered that the appropriate choice of surfactant also makes common support grains (TiO₂ and Al₂O₃) hydrophobic and therefore dispersible in organic solvents, allowing uniform NP impregnations.

We used the surfactant sodium hexadecane sulfonate (NaHDS) to better disperse supports (Figure 1 D), which resulted in visually slowed sedimentation (Figure 1 F). Dynamic light scattering (DLS) measurements (Figure 1 E) further showed that the average size (≈130 nm) of TiO₂ grains suspended with surfactant was similar to the size of single grains observed by transmission electron microscopy (TEM) (Figure S2), suggesting that grain agglomeration was negligible. Here, we define a TiO₂ grain as a cluster of irreversibly fused primary TiO₂ nanoparticles. As hypothesized, addition of metal NPs to the suspension of surfactant stabilized TiO₂ resulted in more uniform NP spatial distributions (Figure 2 A,C,G,I). Surfactant-assisted impregnations, labelled Au-TiO₂-SA and Pd-TiO₂-SA, and conventional impregnations were made from the same NP stocks—Au and Pd respectively—such that catalysts only differed in NP spatial distribution and not in NP structural properties. After impregnation, all catalysts were thoroughly washed to remove surfactant (Experimental Section).

Spatial distribution of Cu/Zn NPs on porous silica has previously been quantified by measuring the distribution of nearest neighbor distances between particles using electron tomography which is time-consuming to implement.¹⁷ However, although this quantity may be relevant for particle growth,¹⁷ it fails to provide information on the local NP surface concentration in different spatial regions of catalyst and may therefore be less effective in rationalizing microkinetic effects. Moreover, to determine nearest neighbor distributions, distances must be measured for each particle. The time-consuming effort of image acquisition and analysis meant that only one support grain was evaluated,¹⁷ which, considering statistical variance between grains, likely is not representative of the entire catalyst sample. Here we instead propose a novel quantitative description of NP spatial distributions that is more representative of the entire sample and that can be obtained from simple TEM images. Images of many individual support grains were acquired, the number of NPs on each grain counted and the projected grain area measured (Experimental Section). The NP number-density, ρ_#, was then defined:

$${\rho }_{\#}=\frac{\mathit{Number}\mathit{of}\mathit{NPs}}{\mathit{Projected}\mathit{grain}\mathit{area}\left(\mathrm{\mu }{\text{m}}^2\right)}$$ (eqn. 1)

This quantity captures both the local average interparticle distance, which is relevant for NP growth, and the local NP surface concentration, which is relevant for the microkinetic environment. NP spatial distributions were then described by mapping the NP number-densities across many TiO₂ support grains (Figure 2 E,K). A detailed discussion regarding the appropriateness of NP number-density for describing NP spatial distribution is given in the Supporting Section S1.

In the literature, electron microscopy is often used to support notions such as “uniform” or “non-uniform” NP spatial distributions without substantiating the terms with image statistics or other means.^{3,33,43,47,48} Here, using the NP number-density distributions generated by image analysis, these qualitative notions could be quantified. The NP number-density in the uniform samples, Au-TiO₂-SA and Pd-TiO₂-SA, was normally distributed (eqn. 2 and Figure 2 E,K, blue curves) —while the NP number-density in the conventional samples, Au-TiO₂-C and Pd-TiO₂-C, was log-normally distributed (eqn. 3 and Figure 2 E,K, red curves).

$${\mathit{\rho }}_{\#}~\mathit{N}\left(\mu ,{\mathit{\sigma }}^2\right)$$ (eqn. 2)

$$\mathit{ln}\left({\mathit{\rho }}_{\#}\right)~\mathit{N}\left(\mu ,{\mathit{\sigma }}^2\right)$$ (eqn. 3)

Where ρ_# is the NP number-density, μ is the mean and σ is the standard deviation. In the case of uniform, normally distributed samples the average NP number-density, 〈ρ_#〉, is identical to μ:⁴⁹

$$\langle {\mathit{\rho }}_{\#}\rangle =\mu$$ (eqn. 4)

while in the case of non-uniform, log-normally distributed samples 〈ρ_#〉 is given by:⁴⁹

$$\langle {\mathit{\rho }}_{\#}\rangle =\mathit{exp}\left(\mu +\frac{{\mathit{\sigma }}^2}{2}\right)$$ (eqn. 5)

The average NP number-density in conventional and surfactant-assisted catalysts differed by less than 10 %, confirming that the catalysts only differed in NP spatial organization, not in number of NPs, which was also confirmed by inductively coupled plasma – mass spectrometry (ICP-MS) measurements. NP number-density averages, ICP-MS results and statistical parameters describing all samples are given in Table S1.

Thus, even though the catalysts were macroscopically identical, their nanoscale NP spatial distributions were strikingly different. To illustrate the difference between uniform, normal and non-uniform, log-normal distributions, the fractions of NPs residing in high NP number-density regions can be extracted from Figure 2 F and L. In Au-TiO₂-SA, only 1 % of NPs are in regions with more than 2000 NPs μm⁻², while 23 % of NPs are in such regions in Au-TiO₂-C. In Pd-TiO₂-SA, 1 % of NPs are in regions with more than 3800 NPs μm⁻², while 54 % of NPs are in such regions in Pd-TiO₂-C.

The normal distribution achieved by surfactant-assisted impregnation is a distinguishing feature of NP depositions with maximized interparticle spacing, because it suggests (by the central value theorem⁴⁹, see also Supporting Section S1) that NPs were equally probable to deposit on each support grain. The normal distribution of NP number-density thus corroborates that support grains were fully dispersed and exposed to solvent in the presence of NaHDS surfactant. In contrast, the log-normal distribution observed in the conventional samples indicates unequal probability⁴⁹ for NPs to deposit on different support grains, showing that grains were agglomerated in the impregnation solvent such that some grains were exposed, having high probability of NP attachment, while most grains were not exposed, having low probability of NP attachment.

Distribution-Dependent CO Oxidation Catalysis on Au-TiO₂.

CO oxidation rates were measured at atmospheric pressure in a conventional quartz microreactor at 80 °C. The Au-TiO₂ catalysts were diluted with inert silicon carbide and high space velocities were used to eliminate heat and mass transfer limitations (Experimental Section). Interestingly, while oxidation rates, O₂ rate orders and activation energies were comparable to previous reports,^50–60 Au-TiO₂-SA showed substantially higher rate (≈ 2 x) than Au-TiO₂-C (Figure 3 A,B,C). Both catalysts deactivated to stable rates over time which is commonly observed with Au-TiO₂ catalysts,^{51,55–57,61} but the relative rate enhancement remained (Figure 3 A). Deactivation of Au-TiO₂ during CO oxidation usually cannot be ascribed to particle growth, but to blocking of active sites by chemical species such as carbonates.^55,61 TEM image analysis demonstrated that NP size distributions also in our catalysts were identical before and after catalytic activity (Figure 3 D) and different activity between the samples due to Au NP size can thus be ruled out. Because catalysts differed only in their NP spatial distribution (Figure 2 E,F) the difference in rates can only be due to this collective property. Thus, our results establish the crucial importance of NP spatial distribution for optimizing not only stability,¹⁷ but also activity of heterogeneous catalysts.

Figure 3. Distribution-Dependent CO Oxidation Catalysis on Au-TiO₂.

(A) Transient CO oxidation rates on Au-TiO₂-SA, upper curve and Au-TiO₂-C, lower curve. Additional repeat measurements (Figure S3) show high reproducibility. (B) O₂ reaction orders measured after reaction rate stabilization on Au-TiO₂-SA, upper curve and Au-TiO₂-C, lower curve. (C) Arrhenius plots collected after reaction rate stabilization on Au-TiO₂-SA, upper curve and Au-TiO₂-C, lower curve. The apparent activation energy of CO oxidation on Au-TiO₂-C (37.1 ± 0.9 kJ mol⁻¹) is higher than on Au-TiO₂-SA (29.7 ± 1.5 kJ mol⁻¹) with a 99.993 % confidence level (see Supporting Section S2). (D) Particle size distributions before and after catalytic activity for Au-TiO₂-SA and Au-TiO₂-C. Typical TEM images before and after catalytic activity are given in Figure S4.

To elucidate the experimentally observed rate dependence on NP spatial distribution, reaction mechanisms must be considered. Substantial evidence suggests that CO oxidation on Au-TiO₂ in dry conditions and slightly elevated temperatures (T ≥ 80 °C) occurs through the Au-assisted Mars-van Krevelen mechanism.^{50,57,62–68} The full mechanism (Supporting Section S3) can be reduced to two steps, reduction and oxidation of the TiO₂ support:^64,68

$$\mathit{CO}(\mathit{g})+{\mathit{O}}_{\mathit{act}}\stackrel{{\mathit{k}}_{\mathit{red}}^{\mathit{eff}}}{\to }\mathit{C}{\mathit{O}}_2(\mathit{g})+\square {\mathit{o}}_{\mathit{act}}$$ (eqn. 6)

$${\mathit{O}}_2(\mathit{g})+2{\square }_{{\mathit{o}}_{\mathit{act}}}\stackrel{{\mathit{k}}_{\mathit{ox}}^{\mathit{eff}}}{\to }2{\mathit{O}}_{\mathit{act}}$$ (eqn. 7)

Equation (6) describes reduction of the TiO₂ surface by abstraction of surface lattice oxygen (O_act) with Au-adsorbed CO to form CO₂ and surface lattice oxygen vacancies (□_Oact). Equation (7) describes re-oxidation of the TiO₂ surface by reaction of newly formed □_Oact and gaseous O₂. At 80° C, □_Oact diffusion rate is significantly smaller compared to O_act abstraction rate,⁵⁰ meaning that the surface coverage of □_Oact will be higher and O_act coverage lower in regions with high Au NP number-density than in regions with low NP number-density (Figure 4 A). A lower O_act coverage (a more reduced TiO₂ surface) is expected to result in higher activation energy for the CO₂ production step (eqn. 6).⁶⁹ A significantly larger fraction of NPs resides in high number-density regions in Au-TiO₂-C compared to in Au-TiO₂-SA (Figure 2 F). Thus, we propose that compared to Au-TiO2-SA, Au-TiO2-C has a larger fraction of NPs in regions with low O_act coverage under reaction conditions at steady-state, causing the experimentally observed (Figure 3 A, C) higher activation energy and lower overall catalytic rate.

Figure 4. Spatially and temporally resolved microkinetic model of CO oxidation on Au-TiO₂.

(A) Schematic illustration of reaction zones, illustrated in semi-transparent red, around NPs in a low NP number-density region (top) and high NP number-density region (bottom). Surface coverage of O_act is lower in the high NP number-density region because the reaction zones around individual NPs overlap to a larger degree than in low NP number-density regions. (B) Illustration of model used for computational treatment. Our model consists of two Au regions, separated by a variable distance of TiO₂ surface. High NP number-density regions are thus represented by short distances between the gold regions, while lower NP number-density regions are represented by larger distances. (C) Surface coverage of O_act as a function of position between Au regions during steady-state CO oxidation. Plots were generated for different separations between Au regions ranging from 0.5 nm to 20 nm. (D) Steady-state CO oxidation rates (per meter of Au/TiO₂ perimeter) as a function of separation between Au regions.

To further unveil the role of O_act depletion on CO oxidation rates, we developed a spatially and temporally resolved microkinetic model for the Mars-van Krevelen mechanism. This mechanism has previously been microkinetically modelled, but without considering spatial variation of local microkinetics (i.e. without considering surface concentration gradients of reaction intermediates).⁶⁹ Here we developed a spatially resolved model by adding surface diffusion of reaction intermediates to the previously proposed elementary steps⁶⁴ (see Supporting Section S3 for details).

Our model consists of two gold NPs, separated by a variable distance of TiO₂ surface (Figure 4 B). High NP number-density regions in the real catalysts are then represented by short distances between the gold regions in the model, while low NP number-density regions are represented by larger distances. NP separation in the model was varied between 0.5 nm and 20 nm, a range which at the low end represents high NP number-density regions in Au-TiO₂-C (Figure 2 D), and at the high end represents high NP number-density regions in Au-TiO₂-SA (Figure 2 C). The surface coverage of O_act during steady-state operation of the catalyst was then computed as a function of position between the Au regions (Figure 4 C). For larger Au separation (10 nm and 20 nm), the TiO₂ surface at the midpoint between the Au regions had identical O_act coverage (i.e. ≈ 100 %) under steady-state operation as during rest. However, O_act coverage at the Au-TiO₂ perimeter was decreased to ≈ 90 % during steady-state operation. More interestingly, at shorter Au separation, O_act coverage was further decreased, both at the perimeter and between the Au regions. The effect is seen already at an Au separation of 5 nm, after which the O_act steady-state coverage monotonically decreases with decreasing NP separation (Figure 4 C). Because O_act is a reacting species in the CO₂ production step (eqn. 6), lower O_act coverage near the Au-TiO₂ perimeter leads to lower CO oxidation rates. Moreover, a lower O_act coverage (a more reduced TiO₂ surface) leads to a higher activation barrier for the CO₂ production step,⁶⁹ further lowering CO oxidation rates (see Supporting Section S3 for details). Thus, at small Au separation the overall reaction rate is reduced ≈ 4-fold compared to larger Au separation (Figure 4 D).

The computational results are robust, as demonstrated by exploring a wide range of reaction barriers reported in the literature, with qualitatively similar results (Supporting Section S3). The results therefore support our hypothesis that local depletion of O_act in Au-TiO₂-C compared to in Au-TiO₂-SA causes lower overall CO oxidation rates. Our results suggest that discrepancy in the literature regarding CO oxidation activity over Au-TiO₂ may in part be due to differences in hierarchical organization of nanoparticles, with clustered Au NPs leading to lower CO oxidation rates. Moreover, this result is generalizable to many oxidation reactions proceeding by the Mars-van Krevelen mechanism, which includes oxidation over metal NPs on reducible supports (e.g. CeO₂, Fe_xO_y and ZrO₂).

In fact, all catalytic reactions where intermediates transport across the NP/support boundary potentially could exhibit a rate dependence on the NP spatial distribution. This is because in such reactions, different NP spatial distributions may give rise to different distributions of local microkinetics, and therefore different catalytic rates. Reactions where intermediates transport or react across the NP/support boundary include not only those of Mars-van-Krevelen type, but also all reactions involving spillover of adsorbed intermediates. The importance of such reactions is enormous and include for example hydrogenation, Fisher-Tropsch, ammonia and methanol synthesis.^70–73

Distribution-Dependent H₂ Evolution Photocatalysis on Pd-TiO₂.

Photocatalytic measurements were carried out using a quartz photoreactor (Figures S5 and S6) irradiated with collimated light of wavelength 337 nm. Pd-TiO₂ photocatalysts were dispersed in 1:1 water:ethanol and transient H₂ evolution quantum efficiencies (QEs) were determined using an online gas-chromatograph (Experimental Section). No H₂ evolution was observed from Pd-TiO₂ in the dark, and no H₂ evolution was observed in irradiated suspensions of TiO₂ without Pd NPs. Thus, both light and Pd NPs are necessary for H₂ generation. Initial QEs were the same for Pd-TiO₂-C and Pd-TiO₂-SA (≈ 50 %) and similar to previous reports,^74–76 but Pd-TiO₂-C deactivated substantially quicker than Pd-TiO₂-SA such that after 20 h irradiation, QE was ≈ 30 % in the former and ≈ 40 % in the latter (Figure 5 A). Thus, our results underline that control of nanoscale NP spatial distribution is crucial not only in thermocatalysis, but also in photocatalysis.

Figure 5. Distribution-Dependent H₂ Evolution Photocatalysis on Pd-TiO₂.

(A) Transient H₂ production QEs with Pd-TiO₂-SA, upper curve and Pd-TiO₂-C, lower curve. Additional repeat measurements (Figure S7) show high reproducibility. (B) Transient absorption measured at 770 nm in 1:1 water:ethanol of pure TiO₂, Pd-TiO₂-SA and Pd-TiO₂-C before and after photocatalysis. Full spectra at 50 ps delay time are given in Figure S8. (C) Size distributions of Pd NPs on Pd-TiO₂-SA before (blue) and after (brown) catalysis. (D) TEM micrograph of high NP number-density region on Pd-TiO₂-SA before and (E) after catalysis. (F) Size distributions of Pd NPs on Pd-TiO₂-C before (blue) and after (brown) catalysis. (G) TEM micrograph of high NP number-density region on Pd-TiO₂-C before and (H) after catalysis. Boxed sections in the size distributions (C, F) are used to highlight the difference in particle growth between Pd-TiO₂-SA and Pd-TiO₂-C.

It is usually assumed that enhanced QEs with metal NPs on semiconductors result from improved charge separation via electron injection from semiconductor to metal.^74,77–80 This mechanism implies there is an optimal NP number-density,^77,79 in turn suggesting that uniform NP spatial distributions should result in higher QEs than non-uniform distributions. Thus, it is surprising that NP spatial distribution (Figure 2 K,L) does not influence initial activity (Figure 5), suggesting that electrons may not transfer to the NPs. To further investigate charge separation, we used transient absorption (TA) spectroscopy. A broad photoinduced absorption at 770 nm has been assigned to trapped electrons at the TiO₂ surface,⁸¹ and if excited electrons are injected from TiO₂ to Pd, both a decrease in initial absorption and more rapid decay is expected with Pd-TiO₂ compared to pure TiO₂. However, catalysts both before and after photocatalytic activity and irrespective of NP spatial distribution showed similar initial absorption and decay transients as pure TiO₂ (Figure 5 B), similar to observations recently made on Au-TiO₂ and Pt-TiO₂ with TA and time-resolved fluorescence spectroscopies.⁸⁰ The result suggests that electrons are not injected into Pd NPs.

Our results suggest that for Pd-TiO₂, electron injection into the metal is not necessary for high QEs. Instead the results suggest that the role of Pd is purely catalytic. In heterogeneous photocatalysis both photoinduced charge separation and surface catalysis are needed to carry out complete catalytic cycles. Photoinduced charge separation occurs in the semiconductor (TiO₂). However, although broadly assumed, but rarely shown, there is no inherent need for electrons to separate into the metallic NPs for catalysis to occur. An alternative mechanism, where intermediates are photogenerated on the semiconductor surface and then, catalyzed by the metal NPs, form products have been previously proposed,⁸² and recently garnered strong experimental evidence.⁸⁰ Our results support this interpretation, rather than the paradigm that electron injection into the metal is necessary for photocatalysis to proceed.

Although initial activity was similar irrespective of NP spatial distribution, Pd-TiO₂-C showed markedly lower stability compared to Pd-TiO₂-SA (Figure 5 A). Commonly, particle growth is a major cause for catalyst deactivation.^17,83 To elucidate if growth differed depending on NP spatial distribution, we quantified NP size distributions by TEM image analysis (Experimental Section) before and after catalytic activity (Figure 5 C,F). In contrast to the case of Au-TiO₂ for CO oxidation, with no reaction-induced particle growth (Figure 3 D and Figure S4), significant NP distribution-dependent growth was observed in Pd-TiO₂ for H₂ generation photocatalysis. In fact, Pd-TiO₂-SA showed negligible, and Pd-TiO₂-C substantial growth (Figure 5 C-H). Because the particle growth was very severe in regions of high NP number-density, it can be concluded that the more severe particle growth in Pd-TiO₂-C compared to Pd-TiO₂-SA was due to the substantially higher fraction of NPs residing in high number-density regions in Pd-TiO₂-C (Figure 2 L). One of two mechanisms, particle migration and coalescence or Ostwald ripening is usually invoked to rationalize particle growth during catalysis. In the first mechanism, individual particles move on the support surface until they meet and coalesce. In the second mechanism, atomic or molecular species eject from smaller particles, migrate on the support surface and incorporate into larger particles.⁸³ Both mechanisms imply more severe sintering in high NP number density regions.¹⁷ However, further study is needed to elucidate which of these mechanisms cause sintering of Pd NPs in Pd-TiO₂ during photocatalysis.

Using the measured change in NP size (Figure 5 C,F) and simple geometric arguments, the reaction-induced loss of active sites in Pd-TiO₂-C compared to Pd-TiO₂-SA could be estimated (Supporting Section S4). The analysis suggests that after deactivation, Pd-TiO₂-SA had ≈ 31 % more perimeter sites and ≈ 14 % more surface sites than Pd-TiO₂-C. Interestingly, the final difference (≈ 31 %) in perimeter sites between Pd-TiO₂-SA and Pd-TiO₂-C scales closely with the activity difference (≈ 33 %) between the catalysts after deactivation (Figure 5 A). In the absence of other plausible catalyst differences—the NPs were initially identical—our results show that NP distribution-dependent particle growth is the main cause for faster deactivation in Pd-TiO₂-C compared to Pd-TiO₂-SA. The results also give support for a rate-determining step at the Pd NP/TiO₂ perimeter, which was previously proposed by some authors.⁸²

CONCLUSIONS

We have shown that NP spatial distributions profoundly influence catalyst performance. Moreover, distributions affect different systems in different ways—activity in Au-TiO₂ for CO oxidation and stability in Pd-TiO₂ for H₂ generation photocatalysis—that may be difficult to predict a priori. Consequently, the mode of influence—activity, stability or both—must be evaluated and explained (depletion of reaction intermediates, particle growth, etc.) on a system-by-system basis. Our approach provides means to do this, because NP spatial distribution can be tuned while keeping weight loading, size distribution and other structural properties constant, and many NPs and supports can be combined, e.g. Pd-Al₂O₃ is demonstrated in Figure S9. We expect knowledge of how NP spatial distribution influences catalyst performance will pave way to more rational catalyst design, since such knowledge can inform when spatial distributions must be controlled for optimal performance. Also important, our method can show when control over NP spatial distribution is not necessary, such that simpler preparation techniques can be used.

The possible impact of controlling NP spatial distribution is enormous. This is because activity in all reactions involving spillover of reaction intermediates could potentially be improved by optimizing NP spatial distribution. Such reactions include, but are not limited to hydrogenation, Fisher Tropsch, ammonia and methanol synthesis and many oxidation reactions.^70–73 Finally, our results show that it is important to control and quantify NP spatial distribution before studying other NP structural effects, because changing NP structural properties frequently changes spatial distributions, which may then convolute effects stemming from the NP structural properties.

EXPERIMENTAL SECTION

Chemicals.

Isopropyl alcohol (IPA), ethanol, methanol, hexanes, potassium hydroxide (KOH), conc. hydrochloric acid (HCl), concentrated nitric acid (HNO₃) were purchased from Fisher Scientific. Sodium hexadecane sulfonate (NaHDS), CAS 15015–81-3 was purchased from TCI chemicals. P25 TiO₂ (Aeroxide), HAuCl₄•3H₂O (ACS reagent grade), tetralin (1,2,3,4-tetrahydronaphthalene), Palladium (II) acetylacetonate (Pd(acac)₂), 0.35 mass fraction Pd, 1-dodecene (DDE, 93–95 %), 1-octadecene (ODE, 90 %) were purchased from Acros Organics. tert-butylamine borane (TBAB, 97 %) 1-oleylamine (OLAM, 70 %), oleic acid (OLAC, 90 %), trioctylphosphine (TOP, 97 %) were purchased from Sigma-Aldrich. 1-tetradecene (TDE, 94 %) was purchased from Alfa Aesar. High purity gases (> 99.999 % purity) from Airgas were used for all experiments, giving a water content below 10 ppm. All reagents and solvents were used as received.

Cleaning procedures.

A base bath (8 L isopropyl alcohol, 2 L deionized (DI) water and 500 g KOH) was used to clean all glassware. After immersion for at least 1 h in the base bath, the glassware was rinsed copiously in DI water, and then in Milli-Q water. The glassware was then washed with aqua regia (0.66 : 0.71 volume HCl (conc.) : volume HNO₃ (conc.)) and rinsed copiously with Milli-Q water before drying in a clean oven at 120 °C.

Preparation of colloidal Au NPs.

Au NPs were synthesized using a modification of previously reported protocols.^84,85 First, 20 mL tetralin and 20 mL OLAM were mixed in a 125 mL 3-neck reaction flask, stirred with a magnetic stir bar and brought to 42 °C in an oil-bath. A glass-coated thermocouple inside the 3-neck flask was used to control the temperature via feedback control. After the reaction temperature (42 °C) was reached, 200 mg of HAuCl₄•3H₂O was added. Note: a Teflon-coated spatula should be used for handling the HAuCl₄•3H₂O. Immediately after HAuCl₄•3H₂O dissolved, a reducing solution (88.7 mg of TBAB dissolved in a mixture of 2 mL OLAM and 2 mL tetralin) was quickly injected. The reaction mixture was then stirred for 60 min. To remove reaction by-products and excess OLAM, the reaction mixture was washed by repeated (3 times) precipitation with addition of anti-solvents (IPA and ethanol), collection of NPs by centrifugation (discarding the supernatant) and redispersion of NPs in solvent (hexanes). Concentration of the final dispersion of Au NPs in hexanes (typically 0.05 mg mL⁻¹ to 0.25 mg mL⁻¹) was measured by UV-Vis absorption spectroscopy calibrated with ICP-MS.

Preparation of colloidal Pd NPs.

Pd NPs were synthesized using a modification of previously reported protocols.⁸⁶ First, 305 mg of Pd(acac)₂ was added to a 125 mL 3-neck reaction flask, then 19 mL TDE and 21 mL ODE were added followed by 0.82 mL OLAM and 1.58 mL OLAC, and the mixture was stirred with a magnetic stir bar. The flask was then closed with septa, connected to a Schlenk line and degassed under vacuum at room temperature for 50 min. After the initial degassing, 1.12 mL TOP (stored and handled in a glovebox) was added to the reaction mixture. The reaction mixture was then brought to 50 °C using feedback control from a thermocouple to a heating mantle, and the mixture was degassed for another 60 min. The reaction mixture was then put under N₂ gas and heated to 280 °C at a ramp rate of ≈ 40 °C min⁻¹. After reaching the reaction temperature (+/− 5 °C), the mixture was held for 15 min before removing the heating mantle, allowing the reaction mixture to cool down to room temperature. To remove reaction by-products, the reaction mixture was washed by repeated (3 times) precipitation with addition of anti-solvents (IPA, methanol and Milli-Q water), collection of NPs by centrifugation (discarding the supernatant) and redispersion of NPs in solvent (hexanes). Concentration of the final stock dispersions of Pd NPs in hexanes (typically 0.05 mg mL⁻¹ to 0.25 mg mL⁻¹) was measured by UV-Vis calibrated with ICP-MS.

Preparation of supported NPs by conventional impregnation.

Conventional impregnation was carried out similarly to previously reported protocols.^41,84,86 In a 500 mL reaction flask, 160 mg of P25 TiO₂ was mixed with 240 mL hexanes, and the dispersion was sonicated for 15 min. An appropriate volume (5 mL to 15 mL) of NP stock solution needed to reach the desired weight loading (0.0035 mass fraction Au for Au-TiO₂ and 0.01 mass fraction Pd for Pd-TiO₂) was then fed into the P25 TiO₂ dispersion (stirred by magnetic stir bar) with a syringe pump at a rate of 0.5 mL min⁻¹. After NP adsorption, catalysts (Au-TiO₂-C or Pd-TiO₂-C) were collected by centrifugation. To mimic the washing of samples produced by surfactant-assisted impregnation (see below), the catalysts were further washed by repeated (2 times) dispersion (with sonication) into 40 mL methanol followed by collection of the catalyst with centrifugation, discarding the supernatant. Finally, the samples were dried under vacuum. In the case of Au-TiO₂-C, ligands on the Au NPs were removed by a previously reported fast annealing protocol.⁸⁷ To avoid oxidation of the Pd NPs, in the case of Pd-TiO₂-C, ligands on the Pd NPs were instead removed with dilute acid, similarly to what has been previously reported.⁸⁸ The Pd-TiO₂-C catalyst was washed by dispersion of the catalyst in weakly acidified methanol (0.02 mol HCl L⁻¹), followed by collection of the catalyst by centrifugation (discarding the supernatant). The procedure was then repeated in weakly acidified ethanol (0.02 mol HCl L⁻¹) followed by pure ethanol (2 times) to remove acid. The Pd-TiO₂-C catalyst was then dried under vacuum. The methods for removing capping agents have been previously validated.^87,88 However, in the unlikely case that capping agents are still present, they are the same on the pairwise compared catalysts and the catalyst washing and pretreatment procedure is also identical between the samples, so any unlikely influence of the capping agents will be the same for both catalysts. Finally, the surfactant that is added to disperse TiO₂ is highly soluble in methanol, and it is therefore highly unlikely that any remains after extensive washing.

Preparation of supported NPs by surfactant-assisted impregnation.

First, a NaHDS stock solution (5 mg mL⁻¹) was prepared by dissolving 50 mg of NaHDS in 10 mL of methanol with sonication. In a 500 mL reaction flask, 160 mg P25 TiO₂ was then mixed with 240 mL hexanes, 0.96 mL of IPA and 2 mL of the NaHDS stock solution, and the dispersion was sonicated for 15 min. An appropriate volume (5 mL to 15 mL) of NP stock solution needed to reach the desired weight loading (0.0035 mass fraction Au for Au-TiO₂ and 0.01 mass fraction Pd for Pd-TiO₂) was then fed into the P25 TiO₂ dispersion (stirred by magnetic stir bar) with a syringe pump at a rate of 0.5 mL min⁻¹. After NP adsorption, catalysts (Au-TiO₂-SA or Pd-TiO₂-SA) were collected by centrifugation. The catalysts were further washed by repeated (2 times) dispersion (with sonication) into 40 mL methanol followed by collection of the catalyst with centrifugation, discarding the supernatant. Finally, the samples were dried under vacuum. In the case of Au-TiO₂-SA, as for Au-TiO₂-C, ligands on the Au NPs were removed by a previously reported fast annealing protocol.⁸⁷ Ligands on the Pd-TiO₂-SA catalyst were removed as described above for the Pd-TiO₂-C catalyst.

Characterization Techniques.

Transmission electron microscopy (TEM) images were acquired on a FEI Tecnai operating at 200 kV. The powder samples were deposited on lacey C/Cu grids by first gently sonicating in ethanol and then immediately drop-casted onto the grid.

Transient absorption spectroscopy was performed using a chopped 1 kHz 325 nm pump excitation generated from an optical parametric amplifier using 35 fs amplified Ti: sapphire laser (SpectraPhysics). The pump power used for experiments was 200 μJ/cm². A 2 kHz probe beam was generated by focusing the 800 nm Ti: sapphire fundamental through a sapphire plate to produce a supercontinuum. Samples were prepared by dispersing dried photocatalyst powder in 1:1 water:ethanol mixtures by sonication and measured in 2 mm cuvettes in transmission geometry. Data was collected and analyzed with Ultrafast Systems software.

UV-Vis spectroscopy for concentration determination of NP stock solutions was carried out on an Agilent Cary 300 UV-Vis system. DLS measurements were carried out on a Brookhaven instrument, Nanobrook Omni. NaHDS stock solution (5 mg mL⁻¹) was prepared by dissolving 50 mg of NaHDS in 10 mL of methanol with sonication. In a 500 mL reaction flask, 160 mg P25 TiO₂ was then mixed with 240 mL hexanes, 0.96 mL of IPA and 2 mL of the NaHDS stock solution, and the dispersion was sonicated for 15 min just before the DLS measurement. Samples were prepared for ICP-MS by digestion in aqua regia and analyzed on a Thermo Scientific XSERIES 2 Quadrupole instrument.

Image analysis for NP size distributions.

The freely available, open source image processing tool ImageJ⁸⁹ was used for image analysis. Size distributions of colloidal and supported NPs were estimated from TEM images. To reduce observer bias, the longest dimension across the particles was always measured. At least 100 particles were measured to generate distributions.

Image analysis for NP number-density distributions on supports.

ImageJ⁸⁹ was used for image analysis. An estimate of the number-density of NPs on a TiO₂ grain was found by dividing the number of NPs observed on the grain with the projected area of the grain. To capture spatial variation of number-density within a grain, each micrograph of a grain was tiled into 16 sub-images before NPs were counted. The workflow was:

1. One micrograph per grain was acquired. (280 nm x 280 nm, 1024 pixels x 1024 pixels for Au-TiO₂-C and Au-TiO₂-SA and 312 nm x 312 nm, 1024 pixels x 1024 pixels for Pd-TiO₂-C and Pd-TiO₂-SA).

2. Each micrograph was split into 16 tiles.

3. The number of NPs were counted in each tile.

4. The projected area of the TiO₂ grain in each tile was measured.

5. The ratio number of NPs / projected grain area was calculated. This is the NP number-density.

6. Histograms of grain count (or region count) vs NP number-density were created. For each sample, 43 grains were used for generation of histograms.

The workflow described here is exemplified with TEM micrographs in the Supporting Information, Figure S10 and Figure S11. A detailed discussion regarding the image statistics is given in Supporting Section S1.

CO oxidation rate measurements.

Catalytic rate measurements were conducted using a plug flow reactor (quartz U-tube, 1 cm inner diameter). The catalyst bed consisted of 10 mg catalyst (Au-TiO₂-SA or Au-TiO₂-C) diluted and thoroughly mixed (using mortar and pestle) with 490 mg silicon carbide (1:49 dilution ratio). To ensure reproducible mass-loading of catalyst, at least 30 mg of catalyst was measured for each experiment and diluted with silicon carbide to a 1:49 ratio. In the quartz U-tube reactor, the reaction bed was sandwiched between two layers of granular acid-washed quartz (900 mg bottom layer, 800 mg top layer). It was checked that the silicon carbide and quartz, in absence of catalyst, was not active for CO oxidation under the reaction conditions used. The catalyst bed was heated using a Micromeritics Eurotherm 2416 furnace, and the temperature was measured with a thermocouple inserted in the catalyst bed.

Gas flows for CO oxidation rate measurements (transient rates, apparent activation energies and O₂ reaction orders) were prepared by combining 5 % O₂ in Ar (certified standard, Airgas), 5 % CO in Ar (certified standard, Airgas) and Ar (99.999 %, Airgas). The gases were mixed using electronic thermal mass-flow controllers (Brooks SLA5850). In all experiments, the total gas flow was 88 mL min⁻¹, giving a space velocity of 528000 mL h⁻¹ g⁻¹_cat. The gas composition in the feed and reactor effluent was determined using an online gas chromatograph (Buck Scientific Model 910, Ar carrier gas) with a Hayesep D column, a thermal conductivity detector and a flame ionization detector. The reactor effluent was sampled by the gas chromatograph every 456 s.

Before starting the experiment, it was checked that the reaction lines were gas-tight by flowing pure argon over the catalyst bed to confirm no contaminant gases were observed. Before measuring catalytic rates, the catalysts were pretreated. First, 5 % O₂ in Ar was passed over the catalyst bed while it was heated (25 °C min⁻¹) to 330 °C (+/− 3 °C) and then held for 120 min, then the reaction gas (0.23 %_vol CO, 4.77 %_vol O₂, balance Ar) was passed (88 mL min⁻¹) over the catalyst bed (also at 330 °C) for 30 min. The purpose of the pre-treatment is to remove any organic contamination and/or oxide that may have formed on the catalyst surface during storage and handling. The motivation for passing the reaction gas over the catalyst at 330 °C during pre-treatment, while data is recorded at 80 °C, is to avoid temperature- or reaction-induced structural changes of the catalyst during data collection, which may be difficult to elucidate. After the pre-treatment, Ar was passed over the catalyst bed and it was cooled to reaction temperature (80 °C +/− 2 °C) while under Ar. Once the reaction temperature was stable at 80 °C +/− 2 °C, the flow of Ar was replaced by the reaction mixture (0.23 %_vol CO, 4.77 %_vol O₂, balance Ar, 88 mL min⁻¹), and the CO oxidation rate was measured for 20 h. Arrhenius plots for determination of apparent activation energies were the collected.

O₂ reaction orders were measured after measuring the transient CO oxidation rate for 20 h, at which time the CO oxidation rate was stable (Figure 3). The kinetic dependence on O₂ was measured using 5 different O₂ concentrations in the reaction stream (4.77, 3.86, 2.95, 2.05, 1.14) %_vol, with the CO concentration held constant at 0.23 %_vol and with balance of Ar. The gas flow was 88 mL min⁻¹ in all measurements.

The above reaction conditions were chosen to ensure differential conditions, i.e. conversion < 20 %,⁵³ such that rates and rate orders could be accurately extracted. Conversion after rate stabilization was below 5 % for all samples in this study.

Photoreactor.

The photoreactor consists of a custom-made quartz beaker in a gas-tight stainless-steel encasing with quartz windows both at the top and bottom of the reactor (Figure S5). The photoreactor is connected to argon gas lines and inserted in a custom-made stage in a solar simulator while the reactor effluent is continuously measured by a Buck Scientific Model 910 gas chromatograph (Figure S6). When the light is turned on, the entire surface area (19 cm²) of the liquid sample in the quartz beaker is illuminated with collimated light with a wavelength of 337 nm. Collimated white light is generated by a 150 W xenon lamp in an Oriel® Sol1A™ solar simulator (model 94201A). A band pass filter (337 nm, 10 nm FWHM, Edmund Optics, 50 mm diameter) was used to pass only light with a wavelength of 337 nm. A UV-VIS spectrum of the bandpass filter is presented in Figure S12. The intensity of light exiting the photoreactor was measured with a thermopile light sensor (Newport, model 919P-003–10) connected to a power meter (Newport, 843-R). Because the catalyst suspension absorbs 100% of light (optical Density > 10 by UV-Vis absorption spectroscopy with 0.35 mg mL⁻¹ catalyst in 25 mL 1:1 water:ethanol), the intensity of light absorbed by catalyst was determined by measuring the light exiting the photoreactor when 25 mL of pure 1:1 water:ethanol was in the photoreactor. The intensity of light absorbed by the catalyst was thus determined to be 7.9 W m⁻². Note that part of this light may have been scattered rather than absorbed by the catalyst, but such scattering leads to an underestimation of the true QE, such that the reported QE represents a lower bound. Also note that because both Pd-TiO₂-C and Pd-TiO₂-SA are made from the same batch of P25 TiO₂, the scattering component in both catalyst suspensions should be identical. Measurements of the intensity of light exiting the reactor when filled with 25 mL 1:1 water:ethanol gave identical results before and after the photocatalytic reaction, ensuring stable operation of the lamp during the photocatalytic measurement.

Photocatalysis measurements.

The catalyst (Pd-TiO₂-C or Pd-TiO₂-SA) was dispersed by sonication (15 min) in 1:1 water:ethanol at a concentration of 0.35 mg mL⁻¹. At this catalyst concentration the reaction rate does not change significantly with concentration (Figure S13), a condition which is desirable for QE measurements according to IUPAC guidelines.⁹⁰ The photoreactor was then filled with 25 mL of this suspension, a stir bar was added, and the suspension was stirred vigorously. The photoreactor was then connected to the argon line (Figure S6) and the headspace of the reactor was purged (in the dark) with argon (40 mL min⁻¹) until no O₂/N₂ peak could be observed in the reactor effluent. After the photoreactor was fully purged of O₂/N₂, the light was turned on and the suspension was irradiated for 20 h, during which time the effluent gas (40 mL min⁻¹) was analyzed by the gas chromatograph (Buck Scientific Model 910, Ar carrier gas) every 24.5 min.

Quantum efficiency calculation.

The photon flux absorbed by the catalyst is calculated from the intensity absorbed by the catalyst (7.9 W m⁻², see above) and the irradiated area (19 cm²) of the photocatalytic suspension. Given that the incident light has a wavelength of 337 nm, the photon flux then becomes:

$$\mathit{Photon}\mathit{Flux}=7.9\left(\frac{\mathit{J}}{\mathit{s}\ast {\mathit{m}}^2}\right)\ast 0.0019\left({\mathit{m}}^2\right)\ast \frac{337\ast {10}^{-9}}{\mathit{h}\ast \mathit{c}}\left(\frac{\mathit{m}}{\mathit{J}\ast \mathit{s}\ast \frac{m}{s}}\right)=2.55\ast {10}^{16}\frac{\mathit{photons}}{\mathit{s}}$$

Where h is Planck’s constant and c is the speed of light.

The quantum efficiency is then calculated by the following formula:^78,90,91

$$\mathit{QE}(\mathit{\%})=\frac{2\ast {\mathit{H}}_2\mathit{production}\mathit{rate}}{\mathit{Photon}\mathit{Flux}}\ast 100$$

Microkinetic modelling.

The microkinetic model was constructed and solved using python and the numpy package. It simulates the spatial and temporal variations in the O_act and O_ad coverage over a rectangular TiO₂ (101) surface lattice that is periodic in the y-direction and with Au at the two boundaries in the x-direction. The distance between the Au particles was varied (0.5 nm to 20 nm) to simulate different Au distributions in the real catalysts. The kinetics of CO oxidation, TiO₂ re-oxidation and surface oxygen (O_act and O_ad) diffusion was accounted for as specified in Supporting Section S3.

Complementary DFT calculations were conducted to study the □_Oact formation energy as a function of i) distance from the Au particles, and ii) O_act coverage at the Au-TiO₂ perimeter. All calculations where performed at the at the PBE-D3(BJ)^92–94 level of theory using the parameters in reference⁶⁸ with the VASP package^95–98 on a periodic (4×5) model of the TiO₂ (101) surface including a 2 nm thick and tall Au-nanorod. See Supporting Section S3 for further details.