Catalysis at the nanoscale may change selectivity Cyrille Costentina,1 and Jean-Michel Savéanta,1 a Laboratoire d’Electrochimie Moléculaire, Université Paris Diderot, Bâtiment Lavoisier, Sorbonne Paris Cité, Unité Mixte de Recherche Université–CNRS 7591, 75205 Paris Cedex 13, France
Among the many virtues ascribed to catalytic nanoparticles, the prospect that the passage from the macro- to the nanoscale may change product selectivity attracts increasing attention. To date, why such effects may exist lacks explanation. Guided by recent experimental reports, we propose that the effects may result from the coupling between the chemical steps in which the reactant, intermediates, and products are involved and transport of these species toward the catalytic surface. Considering as a thought experiment the competitive formation of hydrogen and formate upon reduction of hydrogenocarbonate ions on metals like palladium or platinum, a model is developed that allows one to identify the governing parameters and predict the effect of nanoscaling on selectivity. The model leads to a master equation relating product selectivity and thickness of the diffusion layer. The latter parameter varies considerably upon passing from the macro- to the nanoscale, thus predicting considerable variations of product selectivity. These are subtle effects in the sense that the same mechanism might exhibit a reverse variation of the selectivity if the set of parameter values were different. An expression is given that allows one to predict the direction of the effect. There has been a tendency to assign the catalytic effects of nanoscaling to chemical reactivity changes of the active surface. Such factors might be important in some circumstances. We, however, insist on the likely role of short-distance transport on product selectivity, which could have been thought, at first sight, as the exclusive domain of chemical factors. energy
| nanoparticles | electrocatalysis
N
anoparticles work wonders in many fields of science and technology. This is particularly true in the area of heterogeneous catalysis (1–10). The advantages of ensembles of nanoparticles over foils of the same catalytic material, as well as the role of the particle size, have been frequently recognized with regard to rates. The answer is more elusive as to the possible effect of nanoscaling on product selectivity. It is tempting to attribute such effects to the creation of surface defects that may be triggered by the deposition of the nanoparticles. We, however, explore another type of rationale. The systems where some relevant information is available are few but concern important processes in the area of contemporary energy challenges (11–14), namely the electrochemical hydridation of CO2 into HCO2− versus H2 evolution at a metal electrode in aqueous media (15–19). This is the case when the metal is palladium with which little formate, if any, is generated upon electrolysis on a Pd foil (18, 20), whereas the formate faradaic yield reaches 90–95% with ∼5-nm-diameter Pd nanoparticles dispersed on ∼100-nm carbon particles (18). Very high faradaic yields of formate are similarly found on carbon supported Pt–Pd nanoparticle electrodes in a pH 6.7 phosphate buffer (21, 22). How can such major differences in product selectivity be explained when the catalytic entity is the same in both cases? The information presently available does not allow for the precise delineation of a mechanism for these reactions. The reaction scheme shown in Scheme 1 is only one possible mechanism. We consider this scheme only as an emblematic and, hopefully, www.pnas.org/cgi/doi/10.1073/pnas.1613406113
tutorial example illustrating the general problem of changes of selectivity brought about by passing from macroscopic to nanometric catalytic systems. The scheme possesses two decisive traits that support the possibility of serving this purpose. First, with the scheme being an electrochemical reaction, the pace at which the products are generated, precisely gauged by the current flowing through the electrode, can be accurately controlled by setting the electrode potential. The number of parameters that govern product selection are therefore minimized, allowing easier identification and measurement of the possible role played by nanoscaling. Second, the proposed reaction scheme (Scheme 1) involves competition between steps endowed with different reactions orders, as required for the existence of nanoscaling effects, without being so complicated as to lose track of their physical meaning. The acid, AH, is involved in two different processes at the electrode surface. One is the one electron formation of adsorbed hydrogen atoms (the Volmer step) (23). The other is the Heyrovsky reaction of the acid with the adsorbed hydrogen atom, which takes place in concert with the transfer of a second electron, yielding dihydrogen. CO2 reacts with the adsorbed hydrogen atom concertedly with the transfer of an electron, yielding formate, similarly to the Heyrovsky reaction of the acid in which the latter is simply replaced by CO2 . The irreversibility of the first step is a likely situation since we are interested in fast follow-up reactions. The idea that we are going to develop is that the coupling of these surface reactions of the two reactants with their diffusion toward the reacting surface is different for AH and CO 2. The reactants’ respective concentrations at the electrode surface are, therefore, expected to be influenced by the different conditions in which the reactants’ diffusion comes into play. It is because of these reasons that product selectivity may depend upon the rate of diffusion and, through it, may Significance The benefits of passing from massive catalytic electrodes to a set of nanoparticles of the same material is an issue of considerable current interest. This process relates to the domain of fuels cells and, more generally, to contemporary energy challenges. When several products are concurrently formed, the question arises regarding the possible effect of such nanoscaling on product selectivity. It is tempting to view these effects as relevant to the exclusive domain of purely chemical factors, such as creation of surface defects triggered by nanoparticle deposition. Although such factors might be important in some circumstances, it is shown that product selectivity may well result from the coupling of competitive chemical steps with short-distance transport of the reactants. Author contributions: C.C. and J.-M.S. designed research, performed research, analyzed data, and wrote the paper. Reviewers: R.M.C., The University of Texas at Austin; and P.R.U., University of Warwick. The authors declare no conflict of interest. 1
To whom correspondence may be addressed. Email: [email protected] or [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1613406113/-/DCSupplemental.
PNAS Early Edition | 1 of 3
CHEMISTRY
Contributed by Jean-Michel Savéant, August 12, 2016 (sent for review June 23, 2016; reviewed by Richard M. Crooks and Patrick R. Unwin)
The ratio of a reaction and a diffusion rate constants: ΛVf ðEÞ = Γ 0Hads kVf ðEÞ ðD=δÞ = δ × Γ 0Hads kVf ðEÞ D.
Scheme 1.
Reaction scheme.
depend on nanoscaling (24).* Provided the distance between nanoparticles is large enough (few radii), diffusion around nanoparticles is quasispherical, with diffusion layer thicknesses of the order of the nanoparticle radius (25–28),†,‡ whereas diffusion to planar electrode under moderate stirring or natural convection is of the order of 10−3 cm (29). For nanoparticles of, for example, 10-nm radius, the acceleration of reactant diffusion is thus of the order of 1,000 and able to trigger very substantial changes in product selection, as discussed below. In both cases, the diffusion–reaction coupling takes place under a steady-state regime and may be characterized by a diffusion layer thickness, δ. The reaction diffusion problem may thus be treated in the same way at the macro- and nanoscales, just taking into account that they involve different values of δ (Supporting Information). The analysis of the competition between H2 and HCO2− formation is simplified by the following assumption and approximations. All three electrochemical reactions are assumed to be irreversible. The reactions’ kinetics are thus defined by the three potential (E) dependent rate constants noted in Scheme 1. The diffusion coefficients of AH and CO2 are assumed to be approximately the same (common value: D), and the steady-state approximation is applied to the H ads intermediate (Supporting Information). We may define the selectivity as σ=
2 kCO ðEÞ½CCO2 x=0 f
kH f ðEÞ½CAH x=0
(Supporting Information) (½CAH x=0 and ½CCO2 x=0 are the concentrations of the subscript species at the surface of the planar electrode at which the electrolysis takes place or the nanoparticles are localized), with the faradaic yields being given by HCO−2 % =
ΛVf ðEÞ is the parameter through which nanoscaling may influence product selectivity (Γ 0Hads is the maximal surface concentration of the adsorbed hydrogen atoms). Although individual rate constants CO2 [kVf ðEÞ, kH ðEÞ] may change upon nanoscaling, we f ðEÞ, and kf assume that this change happens at the same pace for all three rate constants, leading to β and χ parameters independent of δ. Product selectivity is then given by (Supporting Information)
σ=
h i 2γ 1 + β + 2ΛVf ðEÞ
( rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ). i2 h i h χð1 + βÞ + ð1 − γÞΛVf ðEÞ − γ + 4γχ 1 + β + 2ΛVf ðEÞ h i + χð1 + βÞ + ð1 − γÞΛVf ðEÞ − γ
Fig. 1 gives an example of the application of this equation to the effect of nanoscaling on product selectivity. The example corresponds to typical conditions for the formate/hydrogen competition in aqueous CO2 reduction (KHCO3 aqueous CO2 saturated solution at pH 7.8, CbCO2 = 0.038 M, CbAH=HCO3 − = 1 M). The analysis of the particular example of Scheme 1 has a more general scope. The analysis shows that large variations of product selectivity in heterogeneous catalysis upon passing from the macro- to the nanoscale may well result from coupling between reactions and transport. It should be noted that, for a given reaction scheme, the very direction in which selectivity varies upon nanoscaling is a function of the values taken by the various parameters. For example, in the case of Scheme 1, the sign of the derivative 2 of the selectivity 3 toward δ: dσ D dσ dδ = Γ 0H kV ðEÞ dΛVf ðEÞ = ½Const > 0 × f
44γ − ðβ + 1Þð1 − 2χÞ5
ads
χ−
hΛV ðEÞ + 1i
has the
f
2
same sign as the expression 4γ − ðβ +h1Þð1 − 2χÞi (Supporting Information). χ−
ΛV ðEÞ + 1 f 2
dσ=dδ < 0 in the case shown in Fig. 1, but the same mechanism
σ 1 , H2 % = . 1+σ 1+σ
As shown in Supporting Information, the selectivity factor, σ, is a function of four parameters, which can be chosen as follows (a glossary of symbols is available in Supporting Information): The ratio of the two bulk concentrations γ = CbCO2 =CbAH. Two reaction rate ratios: CO2 H ðEÞ. β = kVf ðEÞ kH f ðEÞ and χ = kf ðEÞ kf
*It is worth noting that diffusion–reaction coupling has been similarly shown to satisfactorily explain leaving group effects in radical reactions triggered by solvated electron reduction (24). †
The model we discuss applies rigorously when the distance between neighboring nanoparticles is large enough to avoid overlapping of their diffusion layers. In the opposite case, the consequences of increasing overlapping of the diffusion layers (26) will progressively decrease the nanoselectivity effects.
‡
Similar considerations would apply to other nanostructured electrode material, such as carbon nanotubes (27, 28).
2 of 3 | www.pnas.org/cgi/doi/10.1073/pnas.1613406113
Fig. 1. An example of the effect of nanoscaling on product selectivity. Variation of the formate faradaic efficiency with the diffusion layer thickness for the Scheme 1 reduction of CO2 is shown. β = 1, γ = 0.038, χ = 0.005.
Costentin and Savéant
It may also serve to study the variation of selectivity with the nanoparticle size. It can moreover be envisaged to use this type of analysis to investigate the mechanism of the reaction of interest, having in mind that the passage to the nanoscale offers a convenient way of testing the effect of very large diffusion rates, much larger than what can be achieved through force convection at the macroscale. There has been a tendency to ascribe the catalytic effects of nanoscaling to chemical-reactivity changes induced by solid defects of the active surface that might result from the deposition of the nanoparticles. Such factors might be important in some circumstances. We, however, insist on the likely role of short-distance transport on product selectivity, which could, at first blush, have been considered as the exclusive domain of purely chemical factors.
1. Li F, et al. (2008) Scanning electrochemical microscopy of redox-mediated hydrogen evolution catalyzed by two-dimensional assemblies of palladium nanoparticles. J Phys Chem C 112(26):9686–9694. 2. Bard AJ (2010) Inner-sphere heterogeneous electrode reactions. Electrocatalysis and photocatalysis: The challenge. J Am Chem Soc 132(22):7559–7567. 3. Hutton LA, et al. (2011) Electrodeposition of nickel hydroxide nanoparticles on borondoped diamond electrodes for oxidative electrocatalysis. J Phys Chem C 115: 1649–1658. 4. Koper MTM (2011) Structure sensitivity and nanoscale effects in electrocatalysis. Nanoscale 3(5):2054–2073. 5. Ye H, Park HS, Bard AJ (2011) Screening of electrocatalysts for photoelectrochemical water oxidation on W-doped BiVO4 photocatalysts by scanning electrochemical microscopy. J Phys Chem C 115(5):12464–12470. 6. Kleijn SEF, Lai SCS, Koper MTM, Unwin PR (2014) Electrochemistry of nanoparticles. Angew Chem Int Ed Engl 53(14):3558–3586. 7. Zhang ZC, Xu B, Wang X (2014) Engineering nanointerfaces for nanocatalysis. Chem Soc Rev 43(22):7870–7886. 8. Sharma N, Ojha H, Bharadwaj A, Pathak DP, Sharma RK (2015) Preparation and catalytic applications of nanomaterials: A review. RSC Advances 5:53381–53403. 9. Kumar B, et al. (2016) New trends in the development of heterogeneous catalysts for electrochemical CO2 reduction. Catal Today 270:19–30. 10. Lu Q, Jiao F (April 13, 2016) Electrochemical CO2 reduction: Electrocatalyst, reaction mechanism, and process engineering. Nano Energy, 10.1016/j.nanoen.2016.04.009. 11. Lewis NS, Nocera DG (2006) Powering the planet: Chemical challenges in solar energy utilization. Proc Natl Acad Sci USA 103(43):15729–15735. 12. Gray HB (2009) Powering the planet with solar fuel. Nat Chem 1(1):7. 13. Artero V, Fontecave M (2013) Solar fuels generation and molecular systems: Is it homogeneous or heterogeneous catalysis? Chem Soc Rev 42(6):2338–2356. 14. Aresta M, Dibenedetto A, Angelini A (2014) Catalysis for the valorization of exhaust carbon: From CO2 to chemicals, materials, and fuels. technological use of CO2. Chem Rev 114(3):1709–1742. 15. Chen Y, Li CW, Kanan MW (2012) Aqueous CO2 reduction at very low overpotential on oxide-derived Au nanoparticles. J Am Chem Soc 134(49):19969–19972. 16. Li CW, Kanan MW (2012) CO2 reduction at low overpotential on Cu electrodes resulting from the reduction of thick Cu2O films. J Am Chem Soc 134(17):7231–7234.
17. Lee CH, Kanan MW (2015) Controlling H+ vs CO2 reduction selectivity on Pb electrodes. ACS Catal 5:465–469. 18. Min X, Kanan MW (2015) Pd-catalyzed electrohydrogenation of carbon dioxide to formate: High mass activity at low overpotential and identification of the deactivation pathway. J Am Chem Soc 137(14):4701–4708. 19. Zhang S, Kang P, Meyer TJ (2014) Nanostructured tin catalysts for selective electrochemical reduction of carbon dioxide to formate. J Am Chem Soc 136(5):1734–1737. 20. Seshadri G, Lin C, Bocarsly AB (1994) A new homogeneous electrocatalyst for the reduction of carbon dioxide to methanol at low overpotential. J Electroanal Chem 372:145–150. 21. Kortlever R, Peters I, Koper S, Koper MTM (2015) Electrochemical CO2 reduction to formic acid at low overpotential and with high faradaic efficiency on carbon-supported bimetallic Pd–Pt nanoparticles. ACS Catal 5:3916–3923. 22. Kortlever R, Balemans C, Kwon Y, Koper MTM (2015) Electrochemical CO2 reduction to formic acid on a Pd-based formic acid oxidation catalyst. Catal Today 244:58–62. 23. Bockris JO, Reddy AKN (1970) Modern Electrochemistry (Plenum Press, New York), Vol 2, pp 1231–1250. 24. Andrieux CP, Savéant J-M (1993) The origin of leaving group effects in radical reactions triggered by solvated electron reduction. J Am Chem Soc 115:8044–8049. 25. Bard AJ, Faulkner LR (2001) Electrochemical Methods: Fundamental and Applications (John Wiley & Sons, Hoboken, NJ), 2nd Ed, p 360. 26. Amatore C, Savéant J-M, Tessier D (1983) Charge transfer at partially blocked surfaces: A model for the case of microscopic active and inactive sites. J Electroanal Chem 147: 39–51. 27. Bertoncello P, Edgeworth JP, Macpherson JV, Unwin PR (2007) Trace level cyclic voltammetry facilitated by single-walled carbon nanotube network electrodes. J Am Chem Soc 129(36):10982–10983. 28. Dumitrescu I, Dudin PV, Edgeworth JP, Macpherson JV, Unwin PR (2010) Electron transfer kinetics at single-walled carbon nanotube electrodes using scanning electrochemical microscopy. J Phys Chem C 114:2633–2639. 29. Savéant J-M (2006) Elements of Molecular and Biomolecular Electrochemistry: An Electrochemical Approach to Electron Transfer Chemistry (John Wiley & Sons, Hoboken, NJ), p 21.
Costentin and Savéant
PNAS Early Edition | 3 of 3
CHEMISTRY
might exhibit a reverse variation of the selectivity if the set of parameter values were different. Our main conclusion is that variation of product selectivity in heterogeneous catalysis upon passing from the macro- to the nanoscale may well be the result of the coupling between the chemical steps in which the reactant, intermediates, and products are involved and the transport of these species. The example that we have selected indeed shows a huge variation of selectivity upon nanoscaling, directly related to the accompanying span of ∼3 orders of magnitude in diffusion layer thicknesses and, accordingly, in diffusion rates. The method we have develop to identify the governing parameters and analyze the effect of nanoscaling on selectivity can be transposed easily to other reaction schemes.
Among the many virtues ascribed to catalytic nanoparticles, the prospect that the passage from the macro- to the nanoscale may change product selectivity attracts increasing attention. To date, why such effects may exist lacks explanation. Guided by recent experimental reports, we propose that the effects may result from the coupling between the chemical steps in which the reactant, intermediates, and products are involved and transport of these species toward the catalytic surface. Considering as a thought experiment the competitive formation of hydrogen and formate upon reduction of hydrogenocarbonate ions on metals like palladium or platinum, a model is developed that allows one to identify the governing parameters and predict the effect of nanoscaling on selectivity. The model leads to a master equation relating product selectivity and thickness of the diffusion layer. The latter parameter varies considerably upon passing from the macro- to the nanoscale, thus predicting considerable variations of product selectivity. These are subtle effects in the sense that the same mechanism might exhibit a reverse variation of the selectivity if the set of parameter values were different. An expression is given that allows one to predict the direction of the effect. There has been a tendency to assign the catalytic effects of nanoscaling to chemical reactivity changes of the active surface. Such factors might be important in some circumstances. We, however, insist on the likely role of short-distance transport on product selectivity, which could have been thought, at first sight, as the exclusive domain of chemical factors. energy
| nanoparticles | electrocatalysis
N
anoparticles work wonders in many fields of science and technology. This is particularly true in the area of heterogeneous catalysis (1–10). The advantages of ensembles of nanoparticles over foils of the same catalytic material, as well as the role of the particle size, have been frequently recognized with regard to rates. The answer is more elusive as to the possible effect of nanoscaling on product selectivity. It is tempting to attribute such effects to the creation of surface defects that may be triggered by the deposition of the nanoparticles. We, however, explore another type of rationale. The systems where some relevant information is available are few but concern important processes in the area of contemporary energy challenges (11–14), namely the electrochemical hydridation of CO2 into HCO2− versus H2 evolution at a metal electrode in aqueous media (15–19). This is the case when the metal is palladium with which little formate, if any, is generated upon electrolysis on a Pd foil (18, 20), whereas the formate faradaic yield reaches 90–95% with ∼5-nm-diameter Pd nanoparticles dispersed on ∼100-nm carbon particles (18). Very high faradaic yields of formate are similarly found on carbon supported Pt–Pd nanoparticle electrodes in a pH 6.7 phosphate buffer (21, 22). How can such major differences in product selectivity be explained when the catalytic entity is the same in both cases? The information presently available does not allow for the precise delineation of a mechanism for these reactions. The reaction scheme shown in Scheme 1 is only one possible mechanism. We consider this scheme only as an emblematic and, hopefully, www.pnas.org/cgi/doi/10.1073/pnas.1613406113
tutorial example illustrating the general problem of changes of selectivity brought about by passing from macroscopic to nanometric catalytic systems. The scheme possesses two decisive traits that support the possibility of serving this purpose. First, with the scheme being an electrochemical reaction, the pace at which the products are generated, precisely gauged by the current flowing through the electrode, can be accurately controlled by setting the electrode potential. The number of parameters that govern product selection are therefore minimized, allowing easier identification and measurement of the possible role played by nanoscaling. Second, the proposed reaction scheme (Scheme 1) involves competition between steps endowed with different reactions orders, as required for the existence of nanoscaling effects, without being so complicated as to lose track of their physical meaning. The acid, AH, is involved in two different processes at the electrode surface. One is the one electron formation of adsorbed hydrogen atoms (the Volmer step) (23). The other is the Heyrovsky reaction of the acid with the adsorbed hydrogen atom, which takes place in concert with the transfer of a second electron, yielding dihydrogen. CO2 reacts with the adsorbed hydrogen atom concertedly with the transfer of an electron, yielding formate, similarly to the Heyrovsky reaction of the acid in which the latter is simply replaced by CO2 . The irreversibility of the first step is a likely situation since we are interested in fast follow-up reactions. The idea that we are going to develop is that the coupling of these surface reactions of the two reactants with their diffusion toward the reacting surface is different for AH and CO 2. The reactants’ respective concentrations at the electrode surface are, therefore, expected to be influenced by the different conditions in which the reactants’ diffusion comes into play. It is because of these reasons that product selectivity may depend upon the rate of diffusion and, through it, may Significance The benefits of passing from massive catalytic electrodes to a set of nanoparticles of the same material is an issue of considerable current interest. This process relates to the domain of fuels cells and, more generally, to contemporary energy challenges. When several products are concurrently formed, the question arises regarding the possible effect of such nanoscaling on product selectivity. It is tempting to view these effects as relevant to the exclusive domain of purely chemical factors, such as creation of surface defects triggered by nanoparticle deposition. Although such factors might be important in some circumstances, it is shown that product selectivity may well result from the coupling of competitive chemical steps with short-distance transport of the reactants. Author contributions: C.C. and J.-M.S. designed research, performed research, analyzed data, and wrote the paper. Reviewers: R.M.C., The University of Texas at Austin; and P.R.U., University of Warwick. The authors declare no conflict of interest. 1
To whom correspondence may be addressed. Email: [email protected] or [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1613406113/-/DCSupplemental.
PNAS Early Edition | 1 of 3
CHEMISTRY
Contributed by Jean-Michel Savéant, August 12, 2016 (sent for review June 23, 2016; reviewed by Richard M. Crooks and Patrick R. Unwin)
The ratio of a reaction and a diffusion rate constants: ΛVf ðEÞ = Γ 0Hads kVf ðEÞ ðD=δÞ = δ × Γ 0Hads kVf ðEÞ D.
Scheme 1.
Reaction scheme.
depend on nanoscaling (24).* Provided the distance between nanoparticles is large enough (few radii), diffusion around nanoparticles is quasispherical, with diffusion layer thicknesses of the order of the nanoparticle radius (25–28),†,‡ whereas diffusion to planar electrode under moderate stirring or natural convection is of the order of 10−3 cm (29). For nanoparticles of, for example, 10-nm radius, the acceleration of reactant diffusion is thus of the order of 1,000 and able to trigger very substantial changes in product selection, as discussed below. In both cases, the diffusion–reaction coupling takes place under a steady-state regime and may be characterized by a diffusion layer thickness, δ. The reaction diffusion problem may thus be treated in the same way at the macro- and nanoscales, just taking into account that they involve different values of δ (Supporting Information). The analysis of the competition between H2 and HCO2− formation is simplified by the following assumption and approximations. All three electrochemical reactions are assumed to be irreversible. The reactions’ kinetics are thus defined by the three potential (E) dependent rate constants noted in Scheme 1. The diffusion coefficients of AH and CO2 are assumed to be approximately the same (common value: D), and the steady-state approximation is applied to the H ads intermediate (Supporting Information). We may define the selectivity as σ=
2 kCO ðEÞ½CCO2 x=0 f
kH f ðEÞ½CAH x=0
(Supporting Information) (½CAH x=0 and ½CCO2 x=0 are the concentrations of the subscript species at the surface of the planar electrode at which the electrolysis takes place or the nanoparticles are localized), with the faradaic yields being given by HCO−2 % =
ΛVf ðEÞ is the parameter through which nanoscaling may influence product selectivity (Γ 0Hads is the maximal surface concentration of the adsorbed hydrogen atoms). Although individual rate constants CO2 [kVf ðEÞ, kH ðEÞ] may change upon nanoscaling, we f ðEÞ, and kf assume that this change happens at the same pace for all three rate constants, leading to β and χ parameters independent of δ. Product selectivity is then given by (Supporting Information)
σ=
h i 2γ 1 + β + 2ΛVf ðEÞ
( rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ). i2 h i h χð1 + βÞ + ð1 − γÞΛVf ðEÞ − γ + 4γχ 1 + β + 2ΛVf ðEÞ h i + χð1 + βÞ + ð1 − γÞΛVf ðEÞ − γ
Fig. 1 gives an example of the application of this equation to the effect of nanoscaling on product selectivity. The example corresponds to typical conditions for the formate/hydrogen competition in aqueous CO2 reduction (KHCO3 aqueous CO2 saturated solution at pH 7.8, CbCO2 = 0.038 M, CbAH=HCO3 − = 1 M). The analysis of the particular example of Scheme 1 has a more general scope. The analysis shows that large variations of product selectivity in heterogeneous catalysis upon passing from the macro- to the nanoscale may well result from coupling between reactions and transport. It should be noted that, for a given reaction scheme, the very direction in which selectivity varies upon nanoscaling is a function of the values taken by the various parameters. For example, in the case of Scheme 1, the sign of the derivative 2 of the selectivity 3 toward δ: dσ D dσ dδ = Γ 0H kV ðEÞ dΛVf ðEÞ = ½Const > 0 × f
44γ − ðβ + 1Þð1 − 2χÞ5
ads
χ−
hΛV ðEÞ + 1i
has the
f
2
same sign as the expression 4γ − ðβ +h1Þð1 − 2χÞi (Supporting Information). χ−
ΛV ðEÞ + 1 f 2
dσ=dδ < 0 in the case shown in Fig. 1, but the same mechanism
σ 1 , H2 % = . 1+σ 1+σ
As shown in Supporting Information, the selectivity factor, σ, is a function of four parameters, which can be chosen as follows (a glossary of symbols is available in Supporting Information): The ratio of the two bulk concentrations γ = CbCO2 =CbAH. Two reaction rate ratios: CO2 H ðEÞ. β = kVf ðEÞ kH f ðEÞ and χ = kf ðEÞ kf
*It is worth noting that diffusion–reaction coupling has been similarly shown to satisfactorily explain leaving group effects in radical reactions triggered by solvated electron reduction (24). †
The model we discuss applies rigorously when the distance between neighboring nanoparticles is large enough to avoid overlapping of their diffusion layers. In the opposite case, the consequences of increasing overlapping of the diffusion layers (26) will progressively decrease the nanoselectivity effects.
‡
Similar considerations would apply to other nanostructured electrode material, such as carbon nanotubes (27, 28).
2 of 3 | www.pnas.org/cgi/doi/10.1073/pnas.1613406113
Fig. 1. An example of the effect of nanoscaling on product selectivity. Variation of the formate faradaic efficiency with the diffusion layer thickness for the Scheme 1 reduction of CO2 is shown. β = 1, γ = 0.038, χ = 0.005.
Costentin and Savéant
It may also serve to study the variation of selectivity with the nanoparticle size. It can moreover be envisaged to use this type of analysis to investigate the mechanism of the reaction of interest, having in mind that the passage to the nanoscale offers a convenient way of testing the effect of very large diffusion rates, much larger than what can be achieved through force convection at the macroscale. There has been a tendency to ascribe the catalytic effects of nanoscaling to chemical-reactivity changes induced by solid defects of the active surface that might result from the deposition of the nanoparticles. Such factors might be important in some circumstances. We, however, insist on the likely role of short-distance transport on product selectivity, which could, at first blush, have been considered as the exclusive domain of purely chemical factors.
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CHEMISTRY
might exhibit a reverse variation of the selectivity if the set of parameter values were different. Our main conclusion is that variation of product selectivity in heterogeneous catalysis upon passing from the macro- to the nanoscale may well be the result of the coupling between the chemical steps in which the reactant, intermediates, and products are involved and the transport of these species. The example that we have selected indeed shows a huge variation of selectivity upon nanoscaling, directly related to the accompanying span of ∼3 orders of magnitude in diffusion layer thicknesses and, accordingly, in diffusion rates. The method we have develop to identify the governing parameters and analyze the effect of nanoscaling on selectivity can be transposed easily to other reaction schemes.
