Supplementary material Hetergeneus versus Hmgeneus electrn transfer reactins at liquid-liquid interfaces: The rng questin? Pekka Pelj*, Evgeny Smirnv, and Hubert. H. Girault Labratire d Electrchimie Physique et Analytique, Écle Plytechnique Fédérale de Lausanne, EPFL Valais Wallis, Rue de l'industrie 17, Case Pstale 44, CH-1951 Sin, Sitzerland 1
S1. Mdel fr the hetergeneus and hmgeneus electrn transfer The mdel f the electrn transfer acrss the liquid-liquid interface as built in 1D utilizing COMSOL Multiphysics 4.4 and 5.2. Effects f migratin ere assumed negligible, s t Transprt f Diluted Species physics ere utilized fr diffusin f all the species, ne in aqueus phase and the ther in il phase. The ptential ramp as dne using a tringle functin ith 5 mv transitin zne and t cntinuus derivatives. The general diffusin equatin fr a species i is: ci ( Di ci) = Ri t (S1) here c is cncentratin, t is time, D is the diffusin cefficient and R is the reactin term fr the species i. The species in the mdel are Fc, Fc, (present in bth phases) and 3 Fe(CN) 6 and 4 Fe(CN) 6 present nly in the aqueus phase. Additinally, e have the ptassium catin K in bth phases. There are n reactins in the rganic phase. Fc can partitin int the aqueus phase, here it ill react hmgeneusly by the flling reactin: Fc() () k 1 Fc 4 () () k 1 (S2) This reactin is described as a bimlecular reactin R Fc = R Fc = R 4 Fe(CN)6 = R Fe(CN)6 = c Fc t = k 1 Fc k Fc 1 Fe(CN) 4 6 (S3) The equilibrium cnstant K hm = k 1 /k 1 can be evaluated hen the redx ptentials f bth redx cuples are knn. E Fc /Fc =.381 V vs. SHE [1] and the frmal ptential fr ferrferricyanide E 4 Fe(CN)6 /Fe(CN) as evaluated as.467 V vs. SHE in 1 mm LiCl [2] and as 6.4445 V vs. SHE in 1 mm Li 2 SO 4 in this rk. The equilibrium cnstant fr the reactin (S2) can be calculated as K hm = exp ΔG RT = exp F RT E 4 Fe(CN)6 / E Fc /Fc = 3.1 (LiCl) 2
r 12.4 (Li 2 SO 4 ) (S4) k 1 as varied t match the simulatins and experimental data The cncentratin bundary cnditins ere used at uter bundaries f the phases (c i = bulk cncentratin). The bundary cnditins at the liquid-liquid interface ere set as inard fluxes (N i ) accrding t the flling reactins: k ET,f Fc() () Fc 4 () () (hetergeneus ET) (S5) k ET,b k P,f Fc() Fc() (partitin f ferrcene) (S6) k P,b k IT,f Fc () Fc () (IT f ferrcenium) (S7) k IT,b k IT2,f K (aq) K () (IT f K catin) (S8) k IT2,b In the aqueus phase, the inard fluxes are N, 4 Fe(CN)6 = N, Fe(CN)6 = k ET,f Fc() Fe(CN) 6 () k ET,b Fc () Fe(CN) 4 () 6 (S9) N, Fc = k IT,f Fc () k Fc () IT,b N, K = k IT2,f K () k K () IT2,b (S1) (S11) N, Fc = k P,f Fc() k P,b Fc() (S12) In the TFT phase, the inard fluxes include bth cntributins frm reactins (S5) and (S6) r (S7): N, Fc = k ET,f Fc() Fe(CN) 6 () k Fc () ET,b Fe(CN) 4 () 6 (S13) k P,f Fc() k P,b Fc() 3
N, Fc = k ET,f Fc() Fe(CN) 6 () k ET,b k IT,f Fc () k Fc () IT,b N, K = k IT2,f K () k M () IT2,b Fc () Fe(CN) 4 () 6 (S14) (S15) Here the bimlecular rate cnstants ket,f and ket,band unimlecular rate cnstants fr in transfer reactins (k IT and k IT2 ) are Butler-Vlmer type rate cnstants depending n the Galvani ptential difference Δ φ ith the expressins: k ET,b = k ET exp α 1 ( f ( Δ φ Δ φ ET )) ( ) f ( Δ φ Δ φ Fc ) f ( Δ φ Δ φ K ) k ET,f = k ET exp α f Δ φ Δ φ ET k IT,b = k IT exp α 1 k IT,f = k IT exp α f Δ φ Δ φ Fc k IT2,b = k IT2 k IT2,f = k IT2 exp α 1 exp α f Δ φ Δ φ K (S16) here f = F/RT. The α fr all the in transfer reactins as set t.5, and as varied beteen and 1 fr electrn transfer reactins. The unimlecular standard rate cnstants fr in transfer ( kit and k IT2 ) ere set t.1 cm s 1, as the in transfer acrss the liquid-liquid interface is fast and reversible. Similar values fr nrmal in transfer reactins have been reprted in the literature, [3], and the bimlecular standard rate cefficient fr the ET reactin k ET as varied in the simulatins. The kinetics fr partitin f neutral ferrcene ere emplyed by calculating the partitin cefficient f Fc, K p, setting k P,b as.1 cm s 1 and calculating the frard rate cnstant k P,f = K k. Partitin cefficient f Fc beteen TFT and ater as calculated frm the p P,b thermdynamic cycle as described by Fermin and Lahtinen [4]. Standard ptential f a redx cuple in rganic slvent can be expressed ith the help as the redx ptential in ater and the Gibbs energies f transfer f reduced and xidized species frm ater t il: 4
E x/red = E x/red ΔG,, ΔG x red F (S17) Hence, the redx ptential f Fc in TFT can be expressed as E Fc /Fc = E Fc /Fc Δ φ Fc ΔG, Fc F (S18) This equatin can be used t calculate the transfer energy and als partitin cefficient f Fc frm ater t TFT (standard redx ptentials f Fc in ater ( E Fc /Fc =.381 V vs. SHE [1]) and TFT ( E Fc /Fc =.736 V vs. SHE as btained in this rk) are knn, and Δ φ Fc as taken as the half-ave ptential f Δ φ =.115 V 1/2, Fc [2]) as, ΔG Fc K p,fc = exp = 113373 (S19) RT The standard electrn transfer ptential as evaluated by Δ φ ET = E Fc /Fc E 4 Fe(CN)6 / (S2) S2. Mdel fr the NP catalyzed interfacial electrn transfer Anther apprach as used t cnsider the metal particle as a biplar electrde in beteen the t phases. In this case, the mdel as cnstructed ith t Transprt f Dilluted Species physics and Electric Currents physics t accunt fr the current thrugh the biplar electrde. Fr simplicity, nly electrn transfer as cnsidered (Reactin S5). N, the xidatin f Fc as cnsidered t take place at the il side f AuNP, and reductin f Fe(III) in the aqueus phase. k,x Fc() Fc () e (S21) k,red 5
k,x 4 Fe(CN) 6 () () e (S22) k, red N, the inard fluxes at the aqueus and il side are N, 4 Fe(CN)6 = N, Fe(CN)6 = k,x Fe(CN) 4 6 () k Fe(CN),red 6 () (S23) N, Fc = N, Fc = k,x Fc() k,red Fc () (S24) here the rate cnstants fr xidatin and reductin are expressed as k,red = k aq exp α 1 f E NP E 4 FeCN6 /FeCN 6 Δ φ k,x = k aq exp α f E NP E 4 FeCN6 Δ /FeCN 6 φ k,red = k exp α 1 ( f ( E NP E Fc /Fc )) ( ( )) k,x = k exp α f E NP E Fc /Fc (S25) Nte that in Eq. (S23) the directin f flux is reversed, as in reactins (S21-22) the electrns are fling frm il t metal t aqueus phase, and current is fling the ppsite ay (xidative current is psitive as defined by IUPAC). The effect f the Galvani ptential difference included in the expnents f the rate cnstants f the aqueus phase. k as set as.4 cm s 1 [5], and all values f α ere set t.5. experimental CVs. k as varied t btain satisfactry crrespndence ith the The gverning equatins f the Electric Currents physics in the metal phase are: J= σe = σ (S26) E NP here J and E are current density and electric field (bth are vectr variables), σ is cnductivity and E NP is the nanparticle ptential. This equatin is Ohm s la fr the current and the ptential. The bundary cnditins ere set utilizing the inard current density: J = FN, Fe(CN)6 4 (S27) 6
J = FN, Fc (S28) When slving the system, the NP ptential E NP is flating s that bth J and J have the same magnitude. In this case, simulatins ere perfrmed in cnditins here aqueus redx cuple as alays in hundred-fld excess. Hence the Fermi level f the NP as fixed by the ferrferricyanide redx cuple ( E NP E 4 FeCN6 /FeCN 6 φ ), and the ver ptential as mstly n the il side. Fr example, the ver-ptential ith the Fe(II)/Fe(III) rati f 1/1 in the aqueus phase as nly.4 mv at the psitive ptential limit f the scan. S3. Cyclic vltammetry f ferr/ferricyanide cuple Figure S-1 shs the cncentratin nrmalized CVs btained ith Pt and Gc disk electrdes, shing decreased reversibility fr 1/1 mm Fe 2 /Fe 3 cncentratin in 1 mm Li 2 SO 4 electrlyte. 7
Figure S-1. CVs f the ferr/ferricyanide cuple btained ith Pt and Gc disk electrdes. The current density as nrmalized by the ttal irn cncentratin, 1 mm Li 2 SO 4 electrlyte, scan rate 1 mv s 1. S4. Reactin layer thickness in the pre-partitining mechanims Figure S-2 shs the reactin rate f xidatin f Fc ( R Fc = k 1 Fc k Fc 1 Fe(CN) 4 6 frm Eq. S3, xidatin reactin shn as psitive) in the aqueus side f the interface, nrmalized by the initial cncentratin f ttal irn in the aqueus phase, as a functin f distance frm the liquid-liquid interface, fr different amunt f ttal irn at the scan rates f 1 (S-2a) and 1 mv s 1 (S-2b) at different Galvani ptential differences. The results shn that the reactin layer thickness increases frm 1 t 1 nm ith decreasing initial ttal irn cncentratin in the aqueus phase. 8
Figure S-2. Reactin layer thicknesses ith different ferr/ferricyanide cncentratins. The nrmalized hmgeneus reactin rate in the aqueus phase as a functin f distance frm the interface, scan rate 1 mv s 1 (a) and 1 mv s 1. Fe(II)/Fe(III) rati f 1:1. Simulatins dne as in Figure 3 a-c). Supplementary References [1] S. Daniele, M.A. Bald, C. Bragat, A steady-state vltammetric investigatin n the xidatin f ferrcene in ethanl ater mixtures, Electrchem. Cmmun. 1 (1999) 37 41. di:1.116/s1388-2481(98)11-3. [2] E. Smirnv, P. Pelj, M.D. Scanln, H.H. Girault, Interfacial Redx Catalysis n Gld Nanfilms at Sft Interfaces, ACS Nan 9 (215) 6565 6575. di:1.121/acsnan.5b2547. [3] Z. Samec, Dynamic electrchemistry at the interface beteen t immiscible electrlytes, Electrchim. Acta. 84 (212) 21 28. di:1.116/j.electacta.212.3.118. [4] D.J. Fermin, R. Lahtinen, Dynamic Aspects f Hetergeneus Electrn-Transfer Reactins at Liquid Liquid Interfaces, in: A.G. Vlkv (Ed.), Liquid Interfaces in Chemical, Bilgical, and Pharmaceutical Applicatins, Marcel Dekker Inc., Ne Yrk, 21: pp. 179 227. [5] V. Mareček, Z. Samec, J. Weber, The dependence f the electrchemical charge-transfer cefficient n the electrde ptential, J. Electranal. Chem. Interfacial Electrchem. 94 (1978) 169 185. di:1.116/s22-728(78)8312-x. 9