Cooperative Surface‐Particle Catalysis: The Role of the “Active Doughnut” in Catalytic Oxidation

Abstract We consider the factors that govern the activity of bifunctional catalysts comprised of active particles supported on active surfaces. Such catalysts are interesting because the adsorption and diffusion steps, which are often discounted in “conventional” catalytic scenarios, play a key role here. We present an intuitive model, the so‐called “active doughnut” concept, defining an active catalytic region around the supported particles. This simple model explains the role of adsorption and diffusion steps in cascade catalytic cycles for active particles supported on active surfaces. The concept has two important practical implications. First, the reaction rate is no longer proportional to the number of active sites, but rather to the number of “communicative” active sites—those available to the reaction intermediates during their respective lifetimes. Second, it generates an important testable prediction concerning the dependence of the total reaction rate on the particle size. With these tools at hand, we examine six experimental examples of catalytic oxidation from the literature, and show that the active doughnut concept gives valuable insight even when detailed mechanistic information is hard to come by.


Introduction
Ta ndemr eactions, in which two or more catalytic cycles are combinedi nto one synthetic operation, have gained much attention recently. [1][2][3] This reflects as hifti ns ynthetic chemistry towardsm ore complex systems, where elements of classic organic synthesis, biosynthesis, homogeneous catalysis and heterogeneous catalysis are combined into efficient one-pot processes. [2,4] The increased complexity mimics natural systems, with the ultimate goal of combining the benefits of classical solid catalysts (easy separation and high stability)w ith those of biocatalysis and homogeneous catalysis (high product selectivity and mild reaction conditions). [5][6][7] Designing such tandem catalysts is challenging, because per definition they musti nclude at ransition step between the two catalytic sites. This can complicate things compared to the classic Langmuir-Hinshelwood model,w here the steps of diffusion and adsorption/desorption are often discounted, especially in cases where the chemical reaction at the active site is rate-determining. If at andem system comprises two separate cycles (for example an acid-catalysed reaction at one site followed by ab ase-catalysed reaction at another [8] ), then the classical model suffices. But when ac atalytic cycle requires both sites, the diffusiono fs hort-lived intermediates between these sites cannot be ignored. [9] The simplest configuration of such acatalystisanactive particle on an active surface. The particle and the surface are each responsible forap art of the catalytic cycle, and active intermediates must travel between the two "sites". The best way to illustratet his is by looking at an experimental example: Figure1shows the catalytic oxidation of alcohols with molecular oxygen in the presence of metal oxide particles on nitrogen-doped carbon. [10] Here, the nitrogen-doped carbon surface activates incoming dioxygen molecules. These short-lived active oxygen species then diffuse to the metal oxide particles, which catalyse the subsequento xidationo fa lcohols. Common sense tells us that there must be av olumea round each cata-We considert he factorst hat govern the activity of bifunctional catalysts comprised of active particles supported on active surfaces. Such catalysts are interesting because the adsorption and diffusion steps, which are often discounted in "conventional" catalytic scenarios, play ak ey role here. We present an intuitive model, the so-called "active doughnut" concept, defining an active catalytic region aroundt he supported particles. This simple model explains the role of adsorption and diffusion steps in cascade catalytic cycles for active particles supported on active surfaces. The concept has two important practical implications. First, the reaction rate is no longer proportional to the number of active sites, but rather to the number of "communicative" active sites-those availablet ot he reactioni ntermediates during their respective lifetimes. Second,i tg enerates an importantt estable prediction concerning the dependence of the total reaction rate on the particle size. With these tools at hand, we examine six experimental exampleso fc atalytic oxidationf rom the literature, and show that the active doughnut concept gives valuable insight even when detailed mechanistic information is hard to come by. Figure 1. Cartoon of the cooperative actionb etween ap article and asurface illustrating the "active doughnut" concept. Dioxygeni sactivateda tt he nitrogen-doped carbon surface, and the activatedoxygen species then travels to the metal oxide particle and reacts with an alcohol that has adsorbed there. Reactionconditions KGaA. This is an openaccessarticleunder the termsoft he Creative Commons AttributionL icense, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. lytic particle where the majority of the reactions occur.W ec all this toroidal volume the "active doughnut".
In this concept paper,w ep roposeatheoretical framework for describing the physical space in which two catalytic sites communicate. In particular,w efocus on catalytically active particles dispersed on ac atalytically active surface. The volume of interaction in such systems is toroidal,s ow ed ub it the "active doughnut". We first developt he concept based on theoretical considerations, highlighting the implications of the size and shape of the active doughnut for different types of supported catalysts. Subsequently,w ee xamine six experimental case studies of catalytic oxidation reactions. These cases satisfyt wo criteria:1 )Atl east one of the reaction steps is catalysed by the particlea nd another step is catalysed by the surface, and 2) the catalytic particlesa re homogeneously dispersed on the surface. Note that this definition excludes catalysis at the particle-surface interface,f or example dual perimeter sites, [11] which are effectively as ingle catalyst.

Active site or active volume?
When ac atalysti sc omprised of activep articles on an active surface, the classic "active site" concept becomes too simplistic. Instead, different steps of the catalytic cycle occur at different sites. Therefore, we musta lso consider the interaction between the sites. This interaction can be via chemical communication (exchange of reaction intermediates) and/orv ia electronic communication (electron transfer between sites in redox catalysis). Thus, the real active site is actually an active volume, its bordersd efinedb yt he intermediates' lifetime and mobility. Mobility can refer to both mass-ande lectron-transfer,s ince active sites may communicate chemically and/ore lectronically.
The shape of the active volume depends on two sets of parameters.F irst, it depends on the physicalc haracteristics of the catalyst: particles ize, shape and dispersion on the surface. For example, if ac atalytic particlei slarge compared with its active volume, this volume is merely at orus at the base of the particle. Conversely,i ft he particle is small, the active volume may cover it completely,r esulting in ah emisphere ( Figure 2a). Second, the dimensions of the active volumea re determined by the reactivity,d iffusion and sorption of the intermediates. The size of the active volumei sd irectly correlated to the diffusivity and lifetimeso fa ctive species. Furthermore, distortions from toroidal/ hemispherical symmetry result from differences in reactivity and sorption betweenp article and surface.

Practicalimplications of the active doughnut concept
The actived oughnutc oncept has two important practical implications. First, the reactionr ate is no longer proportional to the number of active sites, but rather to the number of "communicative" active sites-those availablet oi ntermediates during their lifetime. Active sites at the top of al arge particle, for example, or at the surfacef ar away from ap article, would be useless for tandem catalysis. If ap article is too large, much of its surface area will go unused. Furthermore, if particles are bunched together,t heir active volumes overlap,a nd the catalytic surface is under-utilized. This has important implications for reporting turnover numbers (TONs), whose values are underestimated when determined in either of theses ituations. Practically speaking,t he most efficient particle-surface tandem catalysts are those where both particles ize and inter-particle distance are of the same order of magnitude as the active doughnutthickness (r AD ).
Second, the concept generates an important testable prediction, concerning the dependence of the reactionr ate (v)o n the particles ize (R). In most catalytic systems, the total surface area of particlesi sm uch smaller than the surfacea rea of the support. This turns particle surfacea rea into al imiting factor in tandemc atalysis, yielding an interesting opportunity for testing the "active doughnut" concept experimentally.C onsider the following two extreme cases,w ith particles either much smaller or much larger than their active volumes (as in Figure 2b). If the particle is small, intermediates can diffuse to its entire surface. In this case the reaction rate (v)w ill dependo n the surfacea rea of a hemisphere (given by Equation (1), where A is the area of the particle that participates in catalysis). Thus, the rate of this reaction step will have a quadratic relationt o the particle radius: v / R 2 .I nc ontrast,i fp articles are too large, only abelt-shaped region surrounding the particlebase participates in catalysis, with its area given in Equation (2). In this case, the reaction rate becomes linearly dependent on particle radius: v / R.N ote that this behaviour is very similar to that observed for dual perimeter site catalysts, where the activity depends linearly on the particlesize. [12,13] Hence, when gradually increasing particle size, there will be ap oint where the dependence of vv s. R will shift from quadratic to linear.T his point can be determined experimentally,a nd used as an estimate for the effective size of the active doughnut. a) The relative size of the active doughnutv olume( green) varies with particle size. b) In the case of large particles, the catalytically active surface is abelt circling their base. Thus, the active doughnut radius (r AD )isproportionalt op article radius, and the reactionr ate correlates linearly to particle size (R). On small particles, however,the active surface is hemispherical, leadingtoaquadratic correlation.

Case Studies
The "active doughnut" idea was first presented in our preliminary communication on catalytic oxidative dehydrogenation of alcohols with molecular oxygen using metal oxide particles on nitrogen-doped carbon. [10] In that example, particles were ca. 200 nm in diameter,a nd spaceda bout 500 nm apart. The catalyst fulfils both conditions for "active volumes": the surfacea nd the particlesc atalyse different reaction steps and the particles are homogeneously dispersed. [10] Oxidation of alcohols requires the transfer of two protons from the alcohol to the activated oxygen in order to complete the catalytic cycle, forming an aldehyde/ketonea nd water.T his means that both reactions must take place in closep roximity,i no ther words within the active volume.
Here we extend the concept to five additional case studies of different catalytic cycles.T hese are nickel-aluminium-doped hydrotalcite, gold on chromium-doped hydrotalcite, silver on alumina,p latinum on alumina and silver on zinc oxide. They all catalyset he oxidative dehydrogenation of alcohols, either with or without molecular oxygen. Botht he particle and the surface (i.e.,t he support) are catalytically active. The cases are organized by particle size, examining two limiting cases of R/r AD . We start with small particles ( % 0.8-3 nm) and then move to large particles(40-200 nm).
Both particle and surfacea re catalytically active, yet not every communication betweent he two creates an active doughnut. For example, the HT-bound alkoxide is not expected to diffuse through the solution bulk, but rather along the surface, hopping between M n + ÀOH groups. Thus, its reaction will be limited to the surface, rather than av olume. Conversely, when as urfacep rotonr ecombines with the Au-boundh ydride and the active oxygen species (O*) at the Au-HT interface ring, it can easily diffuse through the solution.
Since the particlesa re small ( % 2.5 nm) andp rotons diffuse quickly,w ee xpect the active doughnut to cover the particles entirely.I ts size will depend on the protond iffusivity in the specific reactione nvironment-in this case, toluenea t1 00 8C. Thus, if two of these particles are too close to each other,t heir active doughnuts will overlap, loweringt he effective reaction volume. Thise mphasises the importance of sufficient particle dispersion.
Hensen et al. studied the same reaction, but using aC rdoped hydrotalcite as ac atalytic surfacef or supporting gold nanoparticles (d % 0.7-1.3 nm, dispersion 20-50 nm, Figure 4). [14] Cr doping makes the HT surface redox-active, allowing it to reduce O 2 with ah elping hand from the Au particle. This occurs by electron transfer from Cr 3 + ÀOH to the Au, yieldingC r 6 + =Oa nd af ree activated oxygen species (OH*). [14] This species could be ah ydroxyl radical or hydroxide anion. Then, benzyl alcohola dsorbs at the gold particle,w hich acti-  [18] c) The "active doughnut step": diffusion of ap roton from the surface, to recombinewith ah ydride and an active oxygen species at the particle.  [14] c) The "active doughnut step":OH* producedb yO 2 reductionatt he surface, diffuse to the particle-bounds ubstrate, and dehydrogenate the particle-bound substrate. vates its hydroxyl group, helped by OH* coming from the surface O 2 reduction. [41] The next step is b-hydride elimination: the aldehyde product desorbs, andahydride is produced at the Au particle.F inally,t he hydride recombines with the Crbound oxygen to form Cr 3 + ÀOH. The exact mechanism of this recombination is still under debate.
The diffusion of the OH* speciesf rom the surfacea nd its recombination at the particle is ar eaction stept hat involves an active doughnut ( Figure 4c). However,i ft he OH* travels mainly by surface diffusion, the active doughnut will be thin and close to the surface. This situation is probable, since such oxygen species can coordinate easily with surface metal ions. On the other hand, the size of the active doughnut also depends on the electrical conductivity of the support. Since O 2 activation involves ar edox step (oxidation of Cr III by the Au particle), am ore conductives ubstrate could allow this step to occur farther away from the particle. Overall, lacking data on the OH* species ando nC r:HT conductivity, it'sh ard to estimate the magnitude of theseo pposing effects-andt hus the size of this step's active doughnut.
Interestingly,a nother reaction step may involvea na ctive doughnut reactive volume. It is the recombination of ap article-bound hydride with the Cr=Oa tt he surface. However,a hydride adsorbed on ag old surfaceh as am uch longer lifetime than one in solution,e specially that the solvent( toluene) is apolar.T herefore, bulk diffusioni sn ot expected in this case. In more polar solvents, however,b ulkd iffusion could be more pronounced, leadingt oa ni nteraction volume, rather than area.
Zhao et al. have also reported the oxidative dehydrogenation of benzyl alcohol, [42] this time using Ni-Al-layered double hydroxides (Ni-Al-LDH) as ac atalytic surface, and Au as small (% 5nm) catalytic nanoparticles.T hree separate catalytic regions were proposed:t he Ni-Al-LDH surface, the Au particle and the interface between Au and the NiO 6 octahedra. The mechanism is similar to Hensen's: the LDH surface binds the substrate, the Au particle promotes b-H elimination and the interface layer activates oxygen because of its unique local electronic structure. In contrastt oH ensen's hypotheses, these authors suggest that the OH* does not diffuse at all-ruling out an active doughnut scenario.
All of the above cases involved alcohol dehydrogenation, with oxygen as an electron acceptor. All may involve an active doughnut step. The particle sizes are similar ( % 1-5 nm), so these cases are still in the "hemisphere"-type reactionv olume (Figure 2a). The main differenceb etween the cases is in the diffusing species: H + and OH À have different diffusivitiesa nd differents orptions trengthst ot he metal hydroxide surface. Thus, the active doughnuts are expected to have different sizes despite the similarities between the systems.
Further differences between the cases stem from the chemical properties of hydrotalcite, which contains many OHbetween the HT layers. This renders it basic, and OH À -conductive. Tuning the basicity and OH À conductivityo fH Tm aterials may allow changing the active doughnuts ize. For example, doping may introduce more surface acidic sites, promoting sorption of OH* species( as in Hensen's mechanism). This would reduce surface-diffusivity and enlarge the active doughnut. However, the electronic conductivity of hydrotalcites is not expected to affect the active doughnut dimensions. Since it requires an activation barrier of 0.5-0.7 eV, [43] it is only expected to play a role at higher temperatures.
The particles are spacedt ens of nanometres apart, so each particlec an accommodate multiple substrate molecules. Both the metal particles and the acid-base sites on alumina are crucial for high catalytic activity. [44][45][46] Thus, we may test for active doughnut reaction steps. Shimizu andc o-workers reported quantitative TOF data for different particles izes. [16] We then replottedt his data based on the total TOF per particle (see Figure S1). While more points are required for ac onfident conclusion, this data indicates aq uadratic relationf or small particles and al inear relation for larger particles (assuming this reaction step is slow enought oaffect the overall rate).
On both catalysts (Ag/Al 2 O 3 and Pt/Al 2 O 3 ), the alcohols ubstrate is first deprotonated by the basic, hydroxylated alumina surface. The metal particle then oxidizes this surface-bound alkoxide to yield an aldehyde product (whichd esorbs) and a particle-bound hydride. Finally,aprotond iffuses from the surface and recombines with the particle-bound hydride, and H 2 desorption completes the catalytic cycle. Thel ast step (H À /H + recombination) is expected to occur in the active doughnut volume. The protons are more likely than hydrides to diffuse through solution.T herefore, the acidity of the surface is critical in determining the dimensions of the active doughnut, whereas the nature of the catalytic particle (Ag vs. Pt) is unimportant. Practically speaking, since the actived oughnuts on Ag and Pt are similarly sized, switching between the two will not require adjustments regarding particle dispersion.

Large-particle catalysts
The second category covers those cases where large catalytic particles (R @ r AD )a re supported on catalytic surfaces. Hosseini-Sarvari and co-workersp repared Ag/ZnO catalysts for the oxidant-free dehydrogenation of alcohols ( Figure 5). [47] While this materialcatalyses the same reaction reported by Shimizu et al., the particles herea re much larger (40-50 nm). Moreover,t he catalytic substrate is different (ZnO rather than Al 2 O 3 ), and a base (KOH) is added to deprotonatet he benzyl alcohol substrate. Similarly to Shimizu's catalysts, the active doughnut step here also involves the recombination of proton and hydride. However,t he higher R/r AD ratio determines that most of the particles' surface area remains unused. This is in contrast with Shimizu's materials, where activity is limited by unused surfaceo ft he substrate. Metal particlesb yt hemselves are also knownt oc atalyse dehydrogenation reactions. [48][49][50] Yetw hen For even larger particles( > 100 nm), as in the case of our metal oxide on nitrogen-doped carbon catalysts, [10] the active doughnut volume is smaller still, relative to the particle. Here, the nitrogen-doped carbons urfacei sr esponsible for oxygen activation, [51][52][53] whilem etal oxide particles (such as CoO x and CuO x )c atalyset he alcohol oxidation (see illustration in Figure 1). This reaction requires the transfer of two protons from the alcohol to the oxygen. However,a st he alcoholi s bound on the particle and the oxygen is activated at the surface, the two must be close enough to reactw ithin the short life-span of the active oxygen species. Thus, owing to the large size of the metal oxide particles ( % 200 nm), catalysis will occur within ar elatively small active doughnut volumea tt he base of the metal oxide particles.
In summary,w eh ave identified six cases of catalytic oxidation of alcohols where the active doughnut concept applies. These case studies are grouped based on particle size:s mall (0.8-3 nm), and large (> 10 nm). The small-particle catalysts (Au/Ni-Al-HT,A u/Cr-HT,P t/Al 2 O 3 ,A g/Al 2 O 3 ,) have either alumina or hydrotalcite catalytic surfaces, that contribute acid-base or redox reactivity.O nt hese supports, the surface active sites are well-dispersed and activev olumei sm ost likely hemispherical. The large-size category includes the Ag/ZnOc atalystw ith a particles ize of 30-60 nm on as urfacew ith particle spacingo f % 400 nm andt he metal-oxide particleso nn itrogen-doped carbon catalyst with very large particles, spaced micrometres apart. Here the active doughnut volume is much smaller relative to the particles, rendering most of the particles' surfacei nactive.
Interestingly,t he active doughnut concept could be applied to different reactionm echanisms. Twod ifferent mechanisms were proposed for oxidative dehydrogenation with molecular oxygen. In the case of Au/Ni-Al-HT,t he alcohol is first fixed on the catalytic surface and then reacts on the particle. [42] Oxygen activation happens at the particle/surface interface. Conversely, in the case of Au/Cr-HT,t he proposed mechanism is that the surfacea ctivates oxygen to generate an OH* intermediate that reacts with the substrate which is bound to the particle. [26] Yet in both cases an activated oxygen species diffusesa nd recombines with ah ydride, creating an active doughnut reaction volume. In acceptorless dehydrogenation, the active doughnut step involves the diffusion of ap roton from the catalytic surface to recombine with ah ydride on the metal particle.

Conclusion
When both the particle and substrate are catalytically active, there exists ad efined "active doughnut" volume, where most of the catalytic action takes place. Its size and shape can be estimated from the particles' size and their spatial distribution, as well as from the lifetime, absorption, and diffusivity of the reaction intermediates. The active doughnut concept offersa usefulf ramework for planning anda nalysing the optimal size of catalytically active particles, and their distribution on the surface. It suggestst hat calculated turnover frequencies may be underestimated when the particles are too large, or when the particles' surface concentration is too low.F urthermore, it offers predictive tools:F or small particles (R ! r AD ), the reaction rate for the 'active doughnut" step will have aq uadratic dependence on the particler adius, since the whole particle can be utilized. For larger particles, especiallyw hen the active doughnut radius is smaller than the particle size (R @ r AD )t his dependence will be linear.T he transition pointb etween these two correlations (roughlyw hen R % 2r AD )m ay offer an ew tool for estimating the size of these active doughnuts without the ap riori requirement of af ull mechanistic picture. We hope that the framework presented here will cast an ew light on the least-studied reaction steps in catalytic cycles (the fast steps), and ultimately help chemists to design better bifunctional cascade catalysts.