Graham J.
Hutchings
Cardiff Catalysis Institute, School of Chemistry, Cardiff University, Cardiff, CF10 3AT, UK. E-mail: hutch@cf.ac.uk
First published on 16th March 2021
Heterogeneous catalysis lies at the heart of the chemical and fuel manufacturing industries and hence is a cornerstone of many economies. Many of the commercially operated heterogeneous catalysts have remained basically unchanged for decades, undergoing small but important optimisation of their formulations. Yet we all acknowledge that there is a continuous drive towards improved catalysts or designing new ones. At the heart of these studies has been the need to gain an improved understanding of the reaction mechanism for these important reactions since this can unlock new ways to improve catalyst design and, of course, the ultimate aim is to design catalysts based on the detailed understanding of the reaction mechanism. These advanced studies have been aided in the last decade by two key factors, namely: (a) access to advanced characterisation techniques based on synchrotron methods and aberration-corrected microscopy that can probe the nature of the active site, and (b) the application of high-level computational methods to understand how the reactants and products interact at the active site. In this paper this theme will be explored using two examples to bring out the complexity in gaining an understanding of a reaction mechanism. Using the zeolite H-ZSM-5 as an example of a single site catalyst, the mechanism of the conversion of methanol to the first hydrocarbon carbon–carbon bond will be discussed. In this section the use of model reactants and reaction probes will be used to try to differentiate between different mechanistic proposals. The second example explores the use of gold catalysts for CO oxidation and acetylene hydrochlorination. In both these examples the importance of advanced characterisation and theory will be highlighted.
At the outset of trying to determine a reaction mechanism it is essential to have some knowledge of the structure of the active site. For some catalysts this is relatively easy, for example the Brønsted acid site of a zeolite1 or well dispersed supported metal atoms or cations.2 The latter have recently been described as single atom catalysts,3 but as the well dispersed single atom is supported on a matrix of atoms, I personally prefer the term single site catalysis,4 although the term single atom catalysis is now very prevalent. For such single site catalysts, the structure of the active site is readily determined and so understanding reaction kinetics is greatly facilitated as turnover frequencies and total turnover numbers are easily determined.
However, for many heterogeneous catalysts the determination of the structure of the active site is more difficult. For example, Co based Fischer–Tropsch synthesis catalysts comprise 20–30% Co by mass and yet the active species is proposed to be Co nanoparticles 6 nm in diameter.5 Why is so much Co required to be present when the active structures are nanoparticles? Cu/ZnO catalysts, which are the active materials for the commercial methanol synthesis and low temperature water–gas shift reactions, comprise 30–50% Cu by mass but in this case the catalyst activity correlates with the Cu surface area of the reduced catalyst6 and again it is proposed that supported Cu nanoparticles are the active species. These are prepared in situ by reduction of a copper zinc hydroxycarbonate prepared by coprecipitation and malachite is the preferred precursor for the current industrial catalyst. Recently, an amorphous copper zinc hydroxycarbonate prepared using supercritical CO2 as an antisolvent7 produced much smaller Cu nanoparticles on reduction which were more disordered, and these have greatly enhanced activity for the low temperature water–gas shift reaction, and this was determined using environmental transmission electron microscopy7 (Fig. 1).
Fig. 1 The microstructures of the reduced georgeite and malachite precursors characterized by ETEM in 2 mbar H2 at 225 °C. Both samples reveal distinct Cu nanoparticles distributed on ZnO as confirmed by FFT analysis. The reduced malachite sample reveals in general larger Cu nanoparticles compared to the georgeite sample. Reproduced with permission from ref. 7. |
In this paper three methods to aid the determination of reaction mechanisms will be described, namely (i) the use of model reagents to probe possible reaction mechanisms, (ii) the use of advanced in situ/operando microscopy and spectroscopy, and (iii) the use of computational methods to probe reaction pathways. Similar approaches can be used for heterogeneous, homogeneous and bio-catalysts, but the discussion in this paper will be restricted to examples of heterogeneous catalysts. The approaches will be illustrated by (i) methanol conversion to hydrocarbons, and (ii) gold catalysis.
Fig. 2 Reaction pathway for methanol conversion to hydrocarbons with H-ZSM-5 at 371 °C. Reproduced with permission from ref. 8. |
The question then remains as to the mechanism by which ethene is formed from methanol/dimethyl ether. In the next sections four of the proposed mechanisms will be discussed focussing on the use of model reagents to probe whether the mechanistic proposal has merit. An important consideration is that if a model mechanism proposes a particular intermediate, then just because these species are adsorbed on the surface of a heterogeneous catalyst it does not mean that basic reactivity patterns can be changed. For example, if a species is nucleophilic it is unlikely to react with itself; i.e. the normal rules for chemical reactions still apply. One proposal for the mechanism of carbon–carbon bond formation in the Fischer–Tropsch reaction was proposed to involve the surface dimerization of two hydroxycarbenes,17 a very unlikely reaction. A more likely pathway would be for the hydroxycarbene to react with an electrophilic species such as a carbene.18 The work presented for the four mechanisms deals with research carried out in the early phase of interest in this reaction mechanism. Interest has grown again in recent years, mainly due to the commercialisation of the MTO process in China,13 and the approach to understanding the mechanism focuses on advanced in situ spectroscopy and computational methods. However, the mechanistic work carried out in the initial phase has laid the foundation on which these subsequent advanced experiments have been based and these will be discussed in a subsequent section.
Fig. 3 Proposed mechanism for the formation of a carbene species from methanol with H-ZSM-5. Redrawn from ref. 8. |
The evidence in favour of this proposal is that CH2N2, a potential source of a carbene, reacts over ZSM-5 to give ethene.19 However, there is a problem with this as CH2N2 can dimerise in the gas phase to give ethene without the intervention of a surface. A further problem is that, as pointed out by Olah,20 in acidic conditions CH2N2 is an electrophilic methylating agent and so with the Brønsted acid form of ZSM-5, CH2N2 would methylate the surface to form a surface methoxyl. Of course, a further carbene could insert into the C–H bond of the methoxyl, leading to carbon–carbon bond formation.
To overcome the problems associated with CH2N2 it is possible to use a substituted carbene CHXN2. We used ethyldiazoacetate and reacted this with both the acidic form H-ZSM-5 and its conjugate base Na-ZSM-5.21 At high temperatures (190–210 °C) and high conversions (20–45%), ethene was observed as the major product. But as these conditions did not mirror those associated with the early stages of the reaction, at lower temperatures (80 °C) and at 0.1% conversion, both ethene and propene were observed. With Na-ZSM-5 at 125 °C and 2% conversion, over 80% propene was formed as the main product. These results were rationalised in a surface catalysed reaction (Fig. 4) in which ethyldiazoacetate adsorbs as surface CHCO2C2H5 which can exist as keto and enol isomers which go on to react to form ethene and propene. The results of this study suggest a surface reaction is involved. The reaction of diazoacetate models C–C bond formation, albeit C1 → C3 and that a C1 intermediate is involved.
Fig. 4 Proposed reaction mechanism for the reaction of ethyldiazoacetate with H-ZSM-5. Reproduced with permission from ref. 21. |
There are two additional problems associated with this mechanism; first, reaction of methanol and H2 over H-ZSM-5 does not lead to methane formation, but if a gas phase carbene species was present, this would lead to methane.22 Secondly, the main problem concerns whether the conjugate base of a strong acid, such as H-ZSM-5, is a sufficiently strong base to deprotonate the methyl group of methanol.
The central question as raised by Rimmelin et al.24 is whether the conjugate base of ZSM-5 is sufficiently strong to enable deprotonation. This is the same question as that raised for the carbene mechanism. However, there is a second piece of evidence that raises concerns for this mechanism. S analogues of trimethyloxonium salts form ylides much more readily than oxonium salts, but CH3SH is a poor substrate for ZSM-5 (ref. 25) and furthermore dimethyl sulfate, a substrate that cannot form a trimethyloxonium intermediate, readily reacts over H-ZSM-5 to form ethene and higher hydrocarbons.25
Fig. 6 Representations of the hydrocarbon pool. (a) Proposal by Mole,28 (b) effect of co-fed alcohols by Langner,29 (c) initial proposal of the hydrocarbon pool by Kolboe,26 (d) pairing mechanism of Sullivan.30 Reproduced with permission from ref. 27. Copyright (2003) American Chemical Society. |
Therefore, the essence of the hydrocarbon pool mechanism is that ethene, the primary product observed with H-ZSM-5 as catalyst, originates from the secondary reactions of this hydrocarbon pool (Scheme 2).
However, this mechanism does not explain the mechanism by which the initial carbon–carbon bonds are formed in the hydrocarbon pool. If we want to understand the mechanism of the methanol to hydrocarbon reaction fully, we need to determine how the initial carbon–carbon bonds are formed. Of course, given the studies of Mole28 and Langer29 these could be introduced in the methanol feed as impurities, but this is not a particularly elegant and satisfying solution to this age-old problem.
The most important evidence in support of this mechanism is that dimethyl sulfate and methyl iodide, both of which are more potent methylating agents than methanol, produce similar product distributions to methanol when used as substrates with H-ZSM-5 (Fig. 7).25,31 Also, it should be noted that neither dimethyl sulfate nor methyl iodide can form trimethyloxonium ions. These findings support the proposal that the initial step in the methanol conversion reaction with H-ZSM-5 is the formation of a surface methoxyl and that methanol is effectively a methylating agent for H-ZSM-5.
Fig. 7 Comparison of the product selectivities for the reaction of methanol and methylating agents over H-ZSM-5 at 250 °C. (a) CH3OH (WHSV 0.005 h−1, 87% conversion), (b) (CH3)2SO4 (WHSV 0.075 h−1, conversion 21%), (c) CH3I (WHSV 0.06 h−1, conversion 0.1%). Reproduced with permission from ref. 25. |
To investigate the role of the conjugate base in methanol conversion, a set of experiments were carried out using a model compound for the conjugate base of the zeolite.32 Reacting LiAl(OiPr)4 with ultra-dry methylating agents led to methylation but no products from ylide formation were observed. Again, this supports methylation as the initial step, but also shows that the conjugate base cannot enable ylide formation with a non-surface bound reaction intermediate. To investigate the methylation mechanism further, methanol was reacted over zeolite β, which interestingly gave very high selectivities for C4 hydrocarbons.33 This was explained mechanistically by initial interaction of a methanol hydrogen bonded to a site adjacent to a surface methoxyl, and the reaction occurs via a concerted electron transfer such that the surface bound methylide is not formally formed (Fig. 8). This proposal may be a viable way for the initial carbon–carbon bond to be formed, as it may involve a cluster of hydrogen bonded methanol molecules within the confined space of the pore structure of H-ZSM-5, since theoretical studies have shown that the direct formation of a surface stabilised carbene species is energetically disfavoured with an energy barrier of 215–232 kJ mol−1.34
Fig. 8 Proposed mechanism for the formation of C4 hydrocarbons for the reaction of methanol with zeolite β. Reproduced with permission from ref. 33. |
Advanced spectroscopy is now extensively used. Wang and Hunger36 reviewed earlier in situ NMR spectroscopy studies discussing the reactions of the surface methoxyl species. More recently, Weckhuysen and co-workers37 have reviewed the recent literature for the use of advanced spectroscopy to study this reaction. For example, Weckhuysen and co-workers38 and Schmidt et al.39 have shown the elegant use of atom probe tomography to map the elements in single crystals of ZSM-5 and follow coke formation. The coke formation, a key aspect of catalyst deactivation for this reaction, is noted to occur in clusters which would be consistent with the formation of the hydrocarbon pool. It was also noted that the aluminium distribution in the large zeolite crystals was not uniform. The question of the role of extra-framework aluminium is an interesting one. Although most samples of H-ZSM-5 contain very little of this species, Wang et al.40 have shown that extra-framework Al can interact with methanol to form a surface methoxy species that is bound to this extra-framework Al.† They used advanced 13C-{27Al} double-resonance solid-state NMR spectroscopy. They proposed that this species was very reactive and could lead to the formation of an ethoxy species. Hence extra-framework Al could play a role in this reaction, although most consider that it is the Brønsted acid site rather than a Lewis acid site that dominates the formation of the surface methoxyl species.
Howe and co-workers,41 following up on their earlier in situ infra-red spectroscopy studies of this reaction,42 have used operando synchrotron infrared microspectroscopy with high temporal resolution (down to 0.25 s) to identify the initial events occurring when methanol vapor is in contact with a crystal of zeolite H-ZSM-5 (Fig. 9). They were able to follow the formation of dimethyl ether and hydrocarbons in the initial period of the reaction that establishes the hydrocarbon pool. In addition, they indicated the possibility of a CH2 species being involved. Subsequently,43 they studied the effects of crystal size on methanol to hydrocarbon conversion over single crystals of ZSM-5 using operando synchrotron infrared microspectroscopy. They studied methanol conversion with coffin-shaped H-ZSM-5 crystals of different sizes: large (∼250 × 80 × 85 μm3), medium (∼160 × 60 × 60 μm3) and small (∼55 × 30 × 30 μm3). The induction period, for direct alkene formation by deprotonation of surface methoxy groups, was found to decrease with decreasing crystal size and with increasing reaction temperature. Experiments with a continuous flow of dimethyl ether showed that evolution of the hydrocarbon pool and indirect alkene formation are also strongly dependent on crystal size.
Fig. 9 (a) Time course of the ν(OH) 3600 cm−1 band intensity relative to an activated crystal recorded at 2 s intervals during the first 8 μL methanol pulse injected into a N2 flow of 100 mL min−1 over an H-ZSM-5 crystal at 300 °C. (b) MS traces recorded during this experiment: m/z = 31 measures methanol, m/z = 45 DME, m/z = 41 propene (with a contribution from DME fragmentation), and m/z = 55 butene. (c) Evolution of the CH stretching region between 186 and 190 s. (d) The same experiment performed with 0.25 s time resolution during a 4 μL methanol pulse over a crystal from the same batch at 300 °C, (e) the corresponding MS traces and (f) evolution of the CH stretching region between 87.2 and 88.2 s after injection. Reproduced with permission from ref. 41. Copyright (2019) American Chemical Society. |
It is clear that advanced spectroscopies, especially those using synchrotron techniques, coupled with computational methods will in the future be able to give much more valuable insights into this fascinating reaction mechanism. At present it is clear that the initial interaction of methanol or dimethyl ether with H-ZSM-5 leads to the formation of a surface methoxyl species as initially proposed based on experimental evidence with methylating agents as model reactants.25 How this surface methoxyl is then involved in carbon–carbon bond formation continues to be a matter of debate. Certainly, the formation of an isolated carbene species is not energetically possible.34 However, perhaps the possibility that the formation of the surface associated carbene species involves a concerted electron transfer with a cluster of hydrogen bonded methanol molecules could be explored computationally.
Fig. 10 Conversion of CO as a function of temperature. (1) Au/α-Fe2O3 (Au:Fe = 1:9, coprecipitation, 400 °C), (2) 0.5 wt% Pd/γ-Al2O3 (impregnation, 300 °C), (3) Au fine powder, (4) Co3O4 (carbonate, 400 °C), (5) NiO (hydrate, 200 °C), (6) α-Fe2O3 (hydrate, 400 °C), (7) 5 wt% Au/α-Fe2O3 (impregnation, 200 °C), (8) 5 wt% Au/γ-Al2O3 (impregnation, 200 °C). Reproduced with permission from ref. 45. |
Fig. 11 CO oxidation over model catalysts comprising monolayers and bilayers of Au. Reproduced with permission from ref. 47. |
An interesting observation was made by Herzing et al.,49 in which two Au/FeOx catalysts were prepared by coprecipitation and dried in different ways. Both were dried at 120 °C for 16 h, but the one dried in flowing air was exceptionally active for CO oxidation at 25 °C, whereas the material dried in static air was inactive. According to conventional HRTEM, the two materials showed near identical populations of gold nanoparticles. However, according to AC-STEM, the sample calcined in flowing air had bilayer clusters that were not present in the sample prepared by calcination in static air (Fig. 12). This prompted a study where the highly active material was further calcined at a range of higher temperatures49 to prepare a set of Au/FeOx materials that exhibited a range of decreasing activities. Examination by AC-STEM showed that the samples contained well dispersed gold atoms in addition to monolayer and bilayer clusters as well as gold nanoparticles, but the activity mapped the population density of the bilayer Au clusters (Fig. 13). If the activity of this catalyst was solely due to the bilayer clusters, then the activity of this Au/FeOx catalyst was determined to be 3.5 s−1 (ref. 50) which is very similar to the value reported by Chen and Goodman47 in their model studies on the activity of extended Au bilayers. These two studies therefore provide a basis for theoretical studies to investigate the reaction mechanism.
Fig. 12 High-magnification aberration-corrected STEM-HAADF images of (A and B) the inactive and (C and D) the active Au/FeOx catalysts acquired with AC-STEM. The white circles indicate the presence of individual Au atoms, whereas the black circles indicate sub-nanometer Au clusters consisting of only a few atoms. Reproduced with permission from ref. 49. |
Fig. 13 Relative populations of (i) dispersed Au atoms, (ii) 0.2 to 0.3 nm monolayer Au clusters, (iii) 0.5 nm bilayer Au clusters, and (iv) Au nanoparticles > 1 nm in diameter, as a function of the catalyst calcination temperature and measured CO conversion. The error bars correspond to two standard deviations on the size measurements. Reproduced with permission from ref. 49. |
The origin of the high activity of FeOx catalysts was explored in a joint study by Haruta, Hutchings and co-workers.51 It was noted that the two groups had been using very different approaches to the coprecipitation method. Haruta and co-workers used a method in which the acidic solution (Fe(NO3)3 + HAuCl4 in water) was added to the base (Na2CO3 in water) rapidly, whereas Hutchings and co-workers added the acidic solution slowly to the basic solution. Two sets of materials were prepared using these methods, with both being dried at 120 °C (denoted by CP-1 for adding the acid into the base and CP-2 for adding the base into the acid) and then calcined at 300 °C (denoted by CP-3 for adding the acid into the base and CP-4 for adding the base into the acid), giving four samples in all. The catalysts were then tested for CO oxidation, and the effect of reaction temperature on CO conversion is shown in Fig. 14. The two catalysts dried at 120 °C gave, within experimental error, identical CO conversion versus time profiles. However, the two catalysts calcined at 300 °C behaved very differently. CP-3 improved in activity, whereas CP-4 displayed a markedly poorer catalytic activity (Fig. 14). Detailed examination of the catalysts with electron microscopy using a new counting algorithm showed that the two dried catalysts had very different populations of gold species present on the support surface, yet their activity was almost identical. It was concluded that it was not possible to assign just one type of Au species as being active, while the others are inactive, in order to explain all the sets of data. Instead, it was proposed that an activity hierarchy for the different Au species was present. This readily explains the observed behavior since the co-existence of a wide range of Au nanostructures each having a different intrinsic activity needs to be considered (Fig. 15). Hence the final reported activities of these catalysts should be the weighted sums of the activities of each of the different species present, combined with their relative population densities (i.e. total activity , where ρi and εi represent the population fraction and intrinsic activity, respectively, for the ith active species). This hierarchy of activities can then be used to explain the observed activities for the wide range of gold catalyst preparation methods. It is noted that bilayer clusters have a higher intrinsic activity than nanoparticles which in turn have a higher intrinsic activity than gold atoms. The reason for the enhancement in activity for CP-3 was also explained.51 As precipitation is rapid, the FeOx particles that are formed contain embedded Au species which on calcination migrate to the surface of the support particles, and these newly formed Au species are highly active. The FeOx formed by the slow precipitation method does not have such an Au reservoir and so there is no replenishment of active Au species and the Au species present on the surface are sintered into larger inactive nanoparticles.
Fig. 14 (a) CO conversion at various temperatures. Catalyst mass 150 mg, gas flow 50 mL min−1 1 vol% CO in air; (b) Arrhenius plots obtained under low conversion conditions showing that the catalysts all exhibit similar activation energies. Empty circles ○ (CP-1, dried, 6 wt% Au by ICP), filled circles ● (CP-3, calcined, 6 wt% Au by ICP), empty squares □ (CP-2, dried, 3.5 wt% Au by ICP), filled squares ■ (CP-4, calcined, 3.5 wt% Au by ICP). The arrows shown in (a) represent the thermal activation behaviour (black arrow) of the CP-3 catalyst and the thermal deactivation behaviour (white arrow) of the CP-4 catalyst. Reproduced with permission from ref. 51. |
Fig. 15 Representative HAADF-STEM images of CP-1 and CP-3 catalysts (acid-into-base). Images from ‘dried-only’ (a and b) and ‘calcined’ catalysts (c and d) showed the co-existence of nanoparticles of various sizes, sub-nm clusters and isolated atoms. Au nanoparticles – white arrows; sub-nm Au clusters – yellow circles; and isolated Au atoms – white circles. The scale bars in (a) and (c) represent 10 nm. The scale bars in (b) and (d) represent 1 nm. Reproduced with permission from ref. 51. |
The mechanism of low temperature CO oxidation with supported Au has been widely studied, but a proposal made by Bond and Thompson52 in 2000, based on all the information to hand at that time, can be considered to be a representative model (Fig. 16). The surface atoms of the Au nanostructure at the periphery in contact with the support carry a net positive charge. CO adsorbs on a low coordinate Au0 atom on the upper layer while a hydroxyl formed from water adsorption at a defect site adjacent to the gold nanoparticle transfers to the cationic Au peripheral site, creating an anion vacancy on the surface of the support. The CO and OH− form a carboxylate group, and an oxygen molecule occupies the anion vacancy as O2−. This then oxidizes the carboxylate group by abstracting a H atom, forming CO2, and the resulting hydroperoxide ion HO2− then oxidizes a further carboxylate species, forming another CO2 and restoring two hydroxyl ions to the support surface, completing the catalytic cycle.
Fig. 16 Schematic representation of the mechanism of CO oxidation on a supported gold catalyst. Reproduced with permission from ref. 52. |
Fig. 17 Correlation of the activity of carbon-supported metal chloride catalysts for acetylene hydrochlorination. Reproduced with permission from ref. 53. |
While the correlation predicts that Au cations are the active species, early microscopy and XPS ex situ investigations showed the presence of Au metal nanoparticles and so for many years the active sites were considered to be Au cations located at the periphery of the nanoparticle and the support. However, with the advent of AC-STEM and the use of synchrotron XAS and XANES it has been possible to show that in situ the Au is present as wholly dispersed cations and no nanoparticles are present (Fig. 18).2 There is a correlation between the white line height in the L3 edge XAFS and the catalyst productivity, showing that the higher the concentration of Au+ in the catalyst, the higher the activity, and the catalyst cycle involves Au+ and Au3+. These findings therefore confirm the original prediction based on the standard electrode potential.53 Based on this knowledge the mechanism of the hydrochlorination reaction was investigated.57 The role of Au(I) was studied with density functional theory (Fig. 19). The interaction of HCl with supported Au+ was studied using AuCl and the energetics of its interaction with HCl to form AuCl2H, which has more Au3+ character as determined by the Hirshfeld charge. The formation of vinyl chloride then occurs via the interaction of the surface AuCl2H with acetylene, and this represents a facile low energy pathway for the reaction.
Fig. 18 Characterization of a freshly prepared 1 wt% Au/C catalyst prepared from aqua regia solvent. (a) Representative HAADF-STEM image showing isolated Au species. (b) Powder X-ray diffraction data for this catalyst. (c) Fourier transform of k3 weighted χ EXAFS ex situ data for the sample and a gold foil reference. The variation in the magnitude of the Fourier transform is plotted against the distance R from the Au absorber. (d) Ex situ Au L3-edge normalised XANES spectra of the sample and a gold foil reference material. Reproduced with permission from ref. 2. |
Fig. 19 Mechanism for the transformation of AuCl to AuCl2H and the formation of vinyl chloride, reproducing AuCl. Key: Au atoms (gold), Cl atoms (green), H atoms (white), C atoms (grey) and O atoms (red). Energies are referenced to the geometry optimized configuration of AuCl on the carbon support and gas phase acetylene and HCl. Binding energies for each energy minimum and the Hirshfeld charge on each Au atom are shown for each step. Reproduced with permission from ref. 2. |
Looking to the future, where can we expect further advances? There is a great need for improved time resolution for the in situ techniques that are available to us. Inroads into this have been made, for example with the use of synchrotron infrared microspectroscopy where a time resolution of 0.25 s has been achieved,41,43 but we can expect further advances in this area. For example, it can be expected for oxidation reactions that EPR spectroscopy will play an enhanced role in the future since radical species are often involved in oxidations. It would be ideal to be able to combine techniques in such a way that the bulk and surface structure of a catalyst can be investigated in real time as the products are being analysed. It is clear that many are trying to make these advances. Indeed, the use of in situ techniques coupled with high level computational modelling is a major theme of the Faraday Discussion on reaction mechanisms in catalysis.
Footnote |
† When Dr D. J. Willock asked a question relating to the role of extra-framework Al, this made me consider this matter and ref. 39 has now been included in this paper, but it was not part of the opening lecture or the subsequent discussion. |
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