Bright T.
Kusema
and
Dmitry Yu.
Murzin
*
Laboratory of Industrial Chemistry and Reaction Engineering, Process Chemistry Centre, Department of Chemical Engineering, Åbo Akademi University, FI-20500 Åbo/Turku, Finland. E-mail: dmurzin@abo.fi; Fax: +358 2 215 4479; Tel: +358 2 215 4985
First published on 31st July 2012
This minireview presents an overview on the recent developments for the heterogeneous catalytic aerobic oxidation of rare sugars over supported gold catalysts. The selective oxidation of several rare sugars; L-arabinose, D-galactose and D-lactose representing pentoses, hexoses and disaccharides, respectively, is reviewed. The critical evaluation of the aerobic oxidation of the different sugars presents a great opportunity to understand the fundamentals of the surprising reactivity and extraordinary properties of gold. This in turn can open up the possibilities for industrial exploitation of sustainable and green processes. Emphasis was put on catalysis, kinetics and mechanistic studies based on understanding of the fundamental reaction engineering.
![]() Bright T. Kusema | Dr. Bright T. Kusema studied and received his B.Sc. and M.Sc. degree in Chemical Engineering and Biotechnology at the D. I. Mendeleev University of Chemical Technology of Russia in Moscow (2001-2007). He obtained his PhD in Chemical Engineering at the Åbo Akademi Univesity in Åbo/Turku, Finland (2011) under the guidance of Prof. Dmitry Yu. Murzin and Prof. Tapio Salmi. He continues working as a post-doc researcher in the field of heterogeneous catalysis for the synthesis of fine chemicals. |
![]() Dmitry Yu. Murzin | Prof. Dmitry Yu. Murzin studied chemical technology at the Mendeleev University of Chemical Technology in Moscow (1980–1986). He obtained his PhD in 1989 and his DSc (1999) at Karpov Institute of Physical Chemistry, Moscow. He worked at the Universite Louis Pasteur, Strasbourg and Åbo Akademi University as a post-doc (1992–1994). Between 1995–2000 he was associated with BASF. Since 2000 he holds the Chair of Chemical Technology at Åbo Akademi University. He serves on several catalysis and chemical engineering editorial boards. He is co-author of a monograph, holds 3 patents and is a co-author of ca. 530 publications. |
The sugar platform of the biorefinery system is based on (bio-) chemical conversion processes of biomass to sugar feedstocks. Woody biomass consists of lignocellulosic material, which is made up of three primary fractions: hemicellulose, cellulose, and lignin.7,8 Extraction of hemicelluloses and the rare and specialty sugars they contain can be easily achieved in water at moderate temperatures. The sugar feedstocks of mainly pentoses, hexoses and di-saccharides, such as L-arabinose, D-galactose and D-lactose, respectively, are considered in this work. These specialty or rare sugars are obtained from hemicelluloses, such as arabinogalactan, which account for 20–35% of lignocellulosic biomass.9,10D-Lactose is a disaccharide which consists of D-glucose and D-galactose moieties, and it is a by-product of the dairy industry.11,12 This makes them prime candidates for sustainable feedstocks for fine chemicals.
The important parameters for the (bio-) chemical processes of the sugar platform are temperature, pH, pressure, reaction time, substrate concentration, added reactants or catalysts. Catalysis and innovative process design will play an important role in the transformation of the sugar feedstocks into chemicals, materials and fuels. The immense importance of catalysis in the chemical industry is manifested by the fact that roughly 85–90% of all chemical products have undergone catalytic transformation during the course of production.13,14 The aldonic acids produced from L-arabinose, D-galactose and D-lactose as well as their derivatives have many applications in the food, pharmaceutical and cosmetic industries. Thus, the carbohydrates, a single class of natural products can be a major bio-feedstock and platform chemicals, from which it would be possible to develop both industrially and economically viable routes for the synthesis of fine chemicals.15
The application of heterogeneous catalysis for lignocellulosic biomass processing, which involves the transformation of carbohydrates to give products of greater value is a very promising field of research and in the past years the attention has intensified towards selective oxidation over noble-metal catalysts.16 Moreover, the major advantage of employing heterogeneous catalysts is the ease of separation and recycle, no waste or toxic material is generated and amenable to continuous processing. The development of an aerobic inorganic catalyst for the title reaction and related processes with an inexpensive oxidant, such as air or molecular oxygen and an aqueous solution, is a clean and elegant route employing mild reaction conditions, under which high activity and selectivity can be obtained. In addition, carbohydrate-based products have advantageous biodegradability and biocompatibility properties. Selective oxidation of carbohydrates over gold catalysts towards valuable sugar acids featured in this minireview is therefore a promising field of application.
In many cases, Au doped with other noble metals such as Pd and Pt shows an extra-high activity and a high resistance to deactivation due to synergetic effects. It has previously been demonstrated that bimetallic catalysts based on Au, Pd and Pt metals and supported on activated carbon are much more active in the liquid phase oxidation than monometallic ones.33,34 The properties of bimetallic Au–Pd catalysts depend strongly on the nature of the support used, catalyst preparation and treatments.35 Different materials, such as ceria, alumina, titania and activated carbon, were used as the supports for catalysts in selective oxidation of various alcohols and sugars. Among the reducible oxides, ceria is one of the most efficient supports, because of its capability to store oxygen and become reduced.36 Au nanoparticles supported on nanocrystalline cerium oxide were shown to be extremely effective in the oxidation of aldehydes to acids and also in the oxidation of allylic alcohols.37,38
It has been observed that the oxidation reactions exhibit structure sensitivity, i.e. the catalyst activity is influenced by the size of the gold nanoparticles.17,28 The Au nanoparticles can be prepared by using different methods and treatments that allow a wide range of particle diameters. It is well known that the preparation method is crucial in controlling the catalyst activity. Generally, an impregnation method tends to produce rather large particles (>10 nm) that may be undesirable for oxidation reactions, whereas deposition–precipitation and direct ion exchange methods result in small gold nanocrystals deposited on the surface of the support.39 The preparation methods can produce a wide range of materials, depending on the special needs as these methods involve the close control of a wide range of experimental variables which affect the nature of the Au species.40
There has been much debate concerning the nature of the active sites of Au catalysts. The active catalysts are typically found to comprise of small Au nanocrystallites of diameter 2–4 nm, supported on an oxide material. It has been proposed that Au atoms at the interface between the Au cluster and the oxide support material together with the availability of the defect sites at this interface are probably the important features of the active oxidation centers.41,42 Several research groups have proposed and reassessed the oxidation mechanism on the basis of the model that the substrate is activated by the adsorption on to Au0 on the surface of the Au nanoparticle, and that the O2 is activated by the Au atoms at the boundary between the support material and the Au nanocrystals. The Au atoms at the boundary have been proposed to be cationic in nature, possibly Au+ or Au3+.43–45
It is generally accepted that liquid-phase oxidation on noble metal catalysts takes place via an oxidative dehydrogenation mechanism which, in fact can be split into several steps according to Mallat and Baiker.46–49 It is believed that the first step is the dehydrogenation and oxidation of the hydrogen bound to the hemiacetal carbon atom which leads to the formation of the lactone. Hydrolysis of the lactone gives the aldonic acid. An alkaline pH is favorable for the saponification of the lactone.50 Alternative mechanisms such as the direct involvement of the oxidizing species in the rate determining step of dehydrogenation,51 and oxygen assisted dehydrogenation mechanisms,52 and the involvement of peroxidic intermediates have also been proposed.53 However, the exact reaction sequence through which the dehydrogenation mechanism occurs is still under dispute, due to the complex nature of the adsorbed species on the metal surface, the debated origin of the adsorbed oxygen species, and the roles played by the gold species.19,54 The understanding of the mechanism is far from complete as there is no consensus on the nature of the adsorbed intermediates and the reacting species. The nature of the adsorbed species mainly depends on the pH value of the reaction medium, the concentration of the oxidizing agent and the acidity of the catalyst.
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Fig. 1 Structure of arabinogalactan. |
Lactose is a disaccharide consisting of D-glucose and D-galactose moieties joined by a β-1 → 4-glycosidic linkage (Fig. 2). Several million tons of lactose are produced annually as a by-product of the dairy industry, therefore it has a potential for the production of fine chemicals.11,12 Lactose can be hydrolyzed to the monosaccharides, D-glucose and D-galactose. Furthermore, isomerization in alkaline solution to lactulose, catalytic hydrogenation or oxidation to the corresponding polyhydric alcohol and acid, respectively, are industrially viable processes. The selective oxidation of a D-glucose moiety of D-lactose produces the corresponding aldonic acid, lactobionic acid.61
Sugars readily form cyclic hemiacetals, which in the aqueous solutions are in equilibrium with the open chain forms. The open-chain aldehydo-form could ring close and from this, different forms with furanose and pyranose rings are formed, which in addition can have either an α or a β anomeric conformation. The final proportions of these forms depend on the sugar molecule and type of solvent. In an aqueous solution, the cyclic aldehydo-form and pyranose ring are heavily favoured because of the relative thermodynamic stability.62 Therefore, it can be supposed that the predominant form of sugars under the mild reaction conditions is the hemiacetal pyranose. In the cyclic form, the hydroxyl group to be oxidized might be part of the hemiacetal, which is oxidatively dehydrogenated to the intermediate lactone with the subsequent transformation into the corresponding carboxylic acid.
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Fig. 2 Structure of D-lactose. |
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Scheme 1 Selective oxidation of L-arabinose to arabinolactone and arabinonic acid by molecular oxygen over gold catalysts. |
Slightly alkaline conditions were favorable for high initial rates, catalyst activity and product selectivity, attaining a complete conversion and total selectivity towards arabinonic acid at both pH values 8 and 9 within 200 min. The acidic conditions retarded the sugar oxidation, due to the catalyst deactivation by the lactone and aldonic acid strongly adsorbed on the metal surface. At low pH values, product adsorption on the catalyst strongly inhibits the reaction (Fig. 3). A lower conversion of 23% and as well as a lower selectivity of 46% were achieved at pH value 6. Accordingly, the optimum conditions for the selective oxidation of arabinose were 60 °C, pH 8 and oxygen flow rate of 2.5 ml min−1, which are rather mild operation conditions achieving high selectivity >99% towards the desired product. Furthermore, under these conditions, the catalyst was demonstrated to be stable and it was reused at least 3 times with no loss of activity, Au particle sintering or leaching of the metal. In situ catalyst potential measurements during arabinose oxidation gave information about the extent of the oxygen accumulation on the metal surface from the reduced to the oxidized state and a correlation to activity was obtained (Fig. 4). The main driving forces for the catalyst potential changes are the rates of oxygen adsorption and oxygen consumption in the chemical reaction on the catalyst surface. The apparent activation energy Ea for the selective oxidation of arabinose was 23.8 kJ mol−1. This was close to the Ea found in ref. 28 for the oxidation of D-glucose over Au catalysts. However, it has been reported that different aldoses did not have the same reactivity because of their different configurations.64–66 The aldopentoses have equal rates of oxidation to the corresponding aldonic acids, whereas the rates of the consecutive oxidation to the aldaric acids follow the order xylo, arabino > lyxo, ribo.64 It is likely that a certain configuration of the substrate (axial OH 2 or 4) is more favorable with regard to the adsorption on the catalytic surface, as well as the reactivity, which may lead to higher catalytic activity.
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Fig. 3 Selectivity to arabinonic acid as a function of L-arabinose conversion at different pH values over Au/Al2O3 catalysts at 60 °C and oxygen flow rate of 2.5 ml min−1. |
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Fig. 4 Catalyst potential for L-arabinose oxidation over Au/Al2O3 catalysts at 60 °C, pH 8 and oxygen flow rate 2.5 ml min−1. |
Selective oxidation of L-arabinose was further investigated over bimetallic Pd–Au catalysts supported on alumina and ceria.67 The catalysts were treated in hydrogen or oxygen at 300 °C, or by aqueous solution of formaldehyde at room temperature. Improvements in the catalyst activity, selectivity and stability can be achieved by using bi- and to some extent tri-metallic catalysts.33–35 Moreover, it has been pointed out that by alloying Au to Pt or Pd, the leaching of metals was avoided and the catalyst life was improved.68 The bimetallic Au–Pd catalysts demonstrated higher activity and selectivity in comparison with the monometallic Au and Pd catalysts. Thus, the presence of mixed Au–Pd species is a key factor for higher activity of these catalysts in oxidation of arabinose, similar to oxidation of different alcohols and other saccharides also described elsewhere in the literature.18 Activity and selectivity of catalysts were dependent on the catalyst treatment and the nature of the support used. The Au–Pd/CeO2 catalyst reduced by formaldehyde manifests the highest activity and selectivity demonstrated by a TOF value of 0.275 s−1 and 90% selectivity to arabinonic acid (Table 1).
Support | Catalyst | |||
---|---|---|---|---|
Au | Au–Pd | |||
TOF (s−1) | Selectivitya (%) | TOF (s−1) | Selectivitya (%) | |
a Selectivity to arabinonic acid at 50% L-arabinose conversion. b FMD – formaldehyde. | ||||
Al2O3–O2 | 0.093 | 80 | 0.149 | 81 |
Al2O3–H2 | 0.094 | 86 | 0.122 | 85 |
Al2O3–FMDb | 0.027 | 86 | 0.094 | 90 |
CeO2–O2 | 0.092 | 82 | 0.171 | 75 |
CeO2–H2 | 0.101 | 78 | 0.143 | 77 |
CeO2–FMDb | 0.090 | 86 | 0.275 | 90 |
Because of the observed TOF values for bimetallic Au–Pd exceeding that of the monometallic Au catalysts, it can be inferred that the synergetic effect of the two metals contributed to the higher activity of the bimetallic catalysts. Mutual interactions of supported Au and Pd species depending on the support nature and catalyst treatment were observed. A more pronounced interaction between Au and Pd species was observed for Au–Pd/Al2O3 catalysts, while interactions of Au and Pd with reducible ceria coexist with the mutual interaction between these metals. Au metallic species seem to be responsible for the activation of arabinose while an easy redox transformation of Pd species can revoke oxygen activation. Thus, core–shell structures formed by Au species or Au–Pd alloy covered with thin PdO film manifest a synergetic effect on the selective arabinose oxidation by molecular oxygen.
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Scheme 2 Selective oxidation of D-galactose to galactonolactone and galactonic acid by molecular oxygen over gold catalysts. |
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Fig. 5 Selectivity to galactonic acid as a function of D-galactose conversion at different pH values over Au/Al2O3 catalysts at 60 °C and oxygen flow rate of 2.5 ml min−1. |
Comparative studies for the selective oxidation of hexoses such as D-glucose, D-galactose and D-mannose between Au and Pd and Pt derived catalysts also revealed the superiority of Au by a substantial margin.64,65 It was however revealed that Au displayed a higher activity in D-glucose compared to D-galactose or other glucose derivatives with a protective group such as acetyl or amine. The presence of these groups probably constricts the access of the catalyst to the carbon with the anomeric hydroxyl of the substrate.70,71 It appears that the structure of the sugars influences the activity of the Au catalyst. Nevertheless, Au catalysts in all the cases showed the highest catalytic activity and a permanently high selectivity towards the aldonic acid was found independent of the substrate investigated.
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Scheme 3 Reaction scheme for D-lactose oxidation by molecular oxygen. |
Among the supported metals tested, Au supported on alumina and ceria demonstrated high activity and selectivity to lactobionic acid. Pd catalysts resulted in the consecutive oxidation step to 2-keto-lactobionic acid. It was also found that Pd is more prone to deactivation due to over-oxidation and self-poisoning.73,74 Both the Au and Pd catalysts were, however, deactivated under conditions of high pH and high temperature. The influence of surface acidity on lactose oxidation over Pd supported on beta and MCM-22 zeolites was investigated.75 It was observed that Pd supported on MCM-22 zeolites were the most active catalysts. The acidity of the support as well as the method of Pd incorporation had a strong influence on the catalytic activity and selectivity. The surface acidity had a positive influence on the metal dispersion beneficial for the catalyst activity. However, the acidity has a negative effect on lactose oxidation reaction to lactobionic acid. Therefore, a compromise between the support porosity, acidity and metal loading is required to achieve both high activity and selectivity towards the desired product.
Various supported Au catalysts on metal oxides were utilized in the aerobic oxidation of D-lactose.74 Very high selectivity to D-lactobionic acid was achieved for all the Au catalysts which seems to be intrinsic characteristics of the Au catalysts. The catalyst activity was evidently dependent on the type and nature of support. Among the catalysts investigated, Au on alumina was the most active catalyst for the oxidation of D-lactose to the corresponding aldonic acid, analogous to pentoses and hexoses.63,64,69 The other Au catalysts were characterized with lower activity and higher rates of deactivation at prolonged reaction times. In some cases, the application of bimetallic catalysts and the addition of promoters were also demonstrated to increase the activity and selectivity of Pd and Pt based catalysts in the oxidation of D-lactose to lactobionic acid.76–78
A comparison on the aerobic oxidation of different disaccharides of various substrate configurations has also been reported.64,71 Maltose and cellobiose are composed of two units of D-glucose, whereas lactose and melibiose comprise D-galactose and D-glucose units. It was pointed out that the D-glucose presents a more preferential configuration than D-galactose, hence maltose and cellobiose possess a more beneficial configuration during the oxidation over Au catalysts. The presence of D-galactose in the structure of lactose and melibiose might induce a slower adsorption of the disaccharide on the catalyst surface, and implicitly, a lower catalytic activity. However, all the different disaccharides showed the same high selectivity towards the corresponding aldonic acids, similar to what was also observed for the oxidation of pentoses and hexoses over Au catalysts.63,69
Different reaction parameters, such as temperature and oxygen flow rates, were investigated and it was concluded that the moderate and optimized conditions of 60 °C, oxygen flow rate of 2.5 ml min−1 and pH 8 were sufficient to have a complete conversion of the sugars without further degradation of the products at prolonged reaction times. The above-mentioned reaction conditions were applied for L-arabinose, D-galactose and D-lactose oxidation. The same experimental conditions facilitate a direct comparison of the sugar structures, the monosaccharides, i.e. pentose in L-arabinose vs. hexose in D-galactose, and a disaccharide such as D-lactose, to the catalytic activity and selectivity. By using the same Au/Al2O3 and similar reaction conditions of 60 °C, pH 8 and oxygen flow rate of 2.5 ml min−1, high catalytic activity and a total selectivity with respect to the formed aldonic acids for all the sugars were found. The catalytic activity was 0.53, 0.34 and 0.67 mmol s−1 gAu−1 for L-arabinose, D-galactose and D-lactose, respectively.63,69,74 These values are in the same order of magnitude to other major works on selective catalytic oxidation of the corresponding sugars previously reported in the literature.
The analysis of the structure sensitivity follows a classical approach based on the average values, obtained by using high resolution TEM. The calculations of the Au dispersions were based on the assumption that Au particles are cubooctahedral, even though particles around 1 nm have also icosahedral structures and above 1 nm decahedral crystals may appear. The influence of different Au particle sizes in the selective oxidation of L-arabinose and D-galactose on the catalyst activity is demonstrated in Fig. 6. A volcano-type relationship between the catalyst activity and the Au particle size demonstrated by the catalyst activity passing through maximum was deduced. The catalysts with an average particle diameter of around 2 nm were the most active in the L-arabinose and D-galactose oxidation. This result is explained as follows: carbohydrates are adsorbed on the gold atoms with low coordination numbers, i.e. corners, edges, steps, via the carbonyl group. The number of low-coordinated atoms has a maximum value around 2 nm. Below this size, there is efficient contact of Au nanoclusters with the support, whereas for the particles above 2 nm the number of these low-coordinated sites decreases. It can therefore be assumed that the catalyst with a diameter of 2.0 nm and 2.6 nm had the maximum number of these active sites for the adsorption of L-arabinose and D-galactose, respectively, and oxygen activation. However, the selectivity towards the aldonic acids of L-arabinose and D-galactose was not influenced by the different gold particle sizes. Similar observations were also revealed that there is an optimal metal particle size in a range of 3–10 nm giving the highest initial rates for the oxidation of D-glucose, D-lactose and rhamnose over supported metal catalysts.28,78,85,86 However, in all the cases, a deviation of the catalytic activity for particles larger than 6 nm has been detected, as well as an almost complete inactiveness for particles larger than 10 nm.
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Fig. 6 Dependence of catalyst activity on gold particle size of Au/Al2O3 in (a) L-arabinose and (b) D-galactose selective oxidation, respectively, at 60 °C, pH 8 and oxygen flow rate 2.5 ml min−1. |
A quantitative thermodynamic approach of the cluster size effect was used to describe the size-dependent Langmuir–Hinshelwood mechanism and the two-step catalytic cycle.80,81 The general treatment took the surface energy excess into account because of an intrinsic increase in the chemical potential with a decrease in size, as well as the changes in the chemical potential upon adsorption. An expression for the Langmuir–Hinshelwood mechanism was obtained from ref. 80 and 81 which could be modified and simplified leading to a four-parameter dependence for L-arabinose and D-galactose oxidation in the following way;
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Comparison between the experimental and calculated data performed in ref. 69 and 84 demonstrated the applicability of the kinetic equations to treat the experimental data as a function of Au cluster size. Results of the calculations along with the values of parameters for L-arabinose and D-galactose are illustrated in Fig. 6, demonstrating that the reaction rates are passing through the maximum, confirming a good correspondence between the calculations and the model. The metal particle size is an important factor in the catalytic activity in sugar oxidation.
An oxidative dehydrogenation mechanism was proposed (Table 2) and a kinetic model taking into account the changes in the catalyst potential was developed for the selective oxidation of the sugars, L-arabinose and D-lactose.95,96 It is suggested that the sugars are activated by adsorption onto Au0 on the surface of the Au nanoparticles and that the dioxygen is activated by the atoms at the boundary between the support and the gold nanocrystals. The interface between the small Au particles and the support, together with the availability of defect sites at this interface are probably the important features of the active centers.41–45 This effect is thought to be highly significant for Au particles with diameter around 2 nm, which coincides with a dramatic enhancement in activity. The proposed oxidative dehydrogenation mechanism suggests that the reaction proceeds via the dehydrogenation of the adsorbed hydrogen atom bound to the hemiacetal carbon atom of sugars in the cyclic aldehydo-form, into the lactone, followed by the oxidation of the adsorbed hydrogen atom with dissociatively adsorbed oxygen. In a pure dehydrogenation mechanism, the rate determining step is considered to be the dehydrogenation of the hydroxyl group to the lactone species with its subsequent saponification favored by the alkaline pH into the acid product.
Step | Reaction | N(1) | N(2) | N(3) | N(4) |
---|---|---|---|---|---|
N(1): 2A + O2 = 2B + 2H2O, N(2): B + H2O = C, N(3): O = O, N(4): 2H2O = 2OH− + 2H+. | |||||
1 | A + * ≡ A* | 0 | 0 | 0 | 0 |
2 | A + *′ ≡ A*′ | 2 | 0 | 0 | 0 |
3 | O2 + 2* ≡ 2O* | 1 | 0 | 0 | 0 |
4 | O* + *′ ≡ O*′ + * | 2 | 1 | 1 | 1 |
5 | A*′ + O*′ → B*′ + H2O + *′ | 2 | 0 | 0 | 0 |
6 | B*′ + OH−*′ → D*′ + *′ | 0 | 1 | 0 | 0 |
6a | D*′ + H+ → (fast) C + *′ | 0 | 1 | 0 | 0 |
7 | O*′ + H2O + 2e− → 2OH− + * | 0 | 0 | −1 | 1 |
8 | OH− + * → O* + H+ + 2e− | 0 | 1 | 0 | 2 |
9 | O*′ + H2O + 2e− → 2OH− + *′ | 0 | 1 | 1 | 1 |
10 | OH− + * ≡ OH−* | 0 | 0 | 0 | 0 |
11 | OH− + *′ ≡ OH−*′ | 0 | 1 | 0 | 0 |
12 | B*′ ≡ B + *′ | 2 | −1 | 0 | 0 |
A mechanistic kinetic model was used to describe the experimental data of L-arabinose and D-lactose oxidation over Au/Al2O3 taking into account the catalyst electrochemical changes.97–99 The model was based on the physico-chemical explanations of the observed phenomenon. The oxidative dehydrogenation mechanism was adopted and the following sequence of stages was suggested showing the selective oxidation pathway (Table 2).
It is assumed that the sugars, L-arabinose or D-lactose, can adsorb on both the faces and the edges of the Au clusters (steps 1 and 2, respectively). Oxygen is adsorbed on the edges with dissociation (step 3), thereafter migrating to the faces (step 4). The sugar oxidation involves dehydrogenation of the adsorbed hydroxyl of the hemiacetal to the lactone and oxygen reduction in step 5. The product, aldonic acid, is formed in steps 6 and 6a via the intermediate species, while steps 7 and 8 account for electron transfer, which involves oxygen adsorbed on the edges. Finally, as the oxidation rate was found to be dependent on pH, the adsorption of OH− on faces was also included in the model (step 11). Electron transfer involving adsorption of OH− on the edges was also included in the model (step 9). In addition, step 10 accounts for direct adsorption of OH− on the edges without electron transfer. Based on the suggested reaction mechanism and steps, kinetic equations were derived for the oxidation reaction rates along the first route N(1) and the second route N(2), respectively, in the following ways:
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