Electronic Supplementary Information. Low-cost industrially available molybdenum boride and carbide as platinum-like catalysts

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1 Electrnic Supplementary Infrmatin Lw-cst industrially available mlybdenum bride and carbide as platinum-like catalysts fr the hydrgen evlutin reactin in biphasic liquid systems Micheál D. Scanln, a Xiajun Bian, b Hern Vrubel, c Vérnique Amstutz, a Kurt Schenk, d Xile Hu, c BaHng Liu b and Hubert H. Girault* a a Labratire d Electrchimie Physique et Analytique (LEPA), Ecle Plytechnique Fédérale de Lausanne (EPFL), Statin 6, CH-1015 Lausanne, Switzerland. Hubert.Girault@epfl.ch; Fax: ; Tel: b Department f Chemistry, Institute f Bimedical Sciences, Fudan University, Shanghai, , P.R. China. c Labratry f Inrganic Synthesis and Catalysis (LSIC), Ecle Plytechnique Fédérale de Lausanne (EPFL), BCH-3305, CH-1015 Lausanne, Switzerland. d Institut des Sciences et Ingénierie Chimiques (ISIC) and Institut de Physique des Systèmes Bilgiques (IPSB), EPFL, CH-1015, Lausanne, Switzerland. 1

2 Table S1. Calculated equilibrium cncentratins (mm) f each f the cnstituent ins fr the shakeflask utlined in Scheme 1, main text, (aqueus phase f 100 mm HCl; rganic phase f 10 mm LiTB and 2.5 mm DMFc in 1,2-DCE) fr the initial partitin f the electrlyte ins and at a time (t = x) when full cnversin f DMFc t DMFc (and cncmitant cnsumptin f prtns) has taken place. [A] Partitining in 0, w ΔG tr,i (kj ml -1 ) 0 Δ w φ tr,i V Aqueus Initial 1,2-DCE Initial Aqueus (t = x) 1,2-DCE (t = x) [H ] eq / mm [Li ] eq / mm [TB - ] eq / mm [Cl - ] eq / mm [DMFc ] eq / mm [A] The Galvani ptential difference ( Δ w φ ) is calculated as V fr the initial partitin f the electrlyte ins and V at a time when full cnversin f DMFc t DMFc has taken place. The Gibbs energy f transfer ( ΔG 0, w tr,i ), and cnsequently the standard in transfer ptential ( ΔG 0, w tr,i = z i FΔφ 0, w tr,i ), fr each electrlyte in and DMFc were btained frm references (s1) and (s2), respectively. 2

3 Optimisatin f the quantities f catalytic micrparticles required fr biphasic HER kinetics studies Fig. S1. Optimisatin f the quantity f catalyst required fr bservatin f the maximum biphasic HER rates fr (A) M 2 C and (B) MB. The kinetics f the biphasic HER with chemically cntrlled plarizatin, see Scheme 1, fr each cncentratin f catalyst were fllwed by mnitring changes in the UV/Vis absrbance (λ max = 779 nm) f rganic slublised DMFc. 3

4 Determinatin f the reactin rder with respect t prtn cncentratin fr biphasic reactins in the presence f each catalytic micrparticle The rate f reactin fr the catalyzed biphasic HER by can be written as a v = k DMFc H b (S1) where a and b are the reactin rders fr [DMFc] and [H ], respectively. The rate f reactin with respect t [DMFc] was fund t be first rder in the presence f M 2 C and MB micrparticles and zer rder with Pt, W 2 C and WC micrparticles present (Fig. 5(A), main text). Thus, t determine the reactin rder with respect t prtns fr M 2 C and MB micrparticles the lgarithm f the rate f reactin is ln(v) ln( DMFc )= ln(k) bln H ( ) (S2) whereas, fr Pt, W 2 C and WC micrparticles the lgarithm f the rate f reactin reads ln(v) = ln(k) bln H ( ) (S3) Thus, the reactin rder with respect t prtn cncentratin (b) fr each catalytic micrparticle was determined by pltting ln(v)-ln([dmfc]) vs. ln([h ]) fr M 2 C and MB micrparticles and by pltting ln(v) vs. ln ([H ]) fr Pt, W 2 C and WC micrparticles. Zer rder kinetics with respect t prtn cncentratin fr each catalyst was bserved, see Fig. S2. 4

5 Fig. S2. Rate rder determinatin with respect t prtns: Fr Pt, W 2 C and WC the natural lgarithm f the reactin rate, ln (ν), estimated frm the slpe f the plynmial fit t the experimental data, was pltted as a functin f the natural lgarithm f prtn cncentratin, ln ([H ]). Fr M 2 C and MB, ln (ν)-ln ([DMFc]) was pltted as a functin ln ([H ]). 5

6 Cyclic vltammetry cntrl experiments Fig. S3. Cyclic vltammgrams fr electrchemical cells (see Scheme 2, main text) cmparing the baseline respnse (x = 0, y = 0, z = 5; dtted line) t that (A) in the presence f rganic slubilised DMFc but absence f M 2 C (x = 2.5, y = 0, z = 5; slid line), in the presence f bth M 2 C and rganic slubilised DMFc (x = 2.5, y = 0.5, z = 5; dashed line) and (B) in the presence f M 2 C but absence f rganic slubilised DMFc (x = 0, y = 0.5, z = 5; red slid line). Scan rate: 50 mv s -1. 6

7 Derivatin f the Nernst equatin fr the biphasic hydrgen evlutin reactin The glbal reactin fr biphasic hydrgen evlutin reads DMFc H,w catalyst DMFc, 1 2 H (S4) 2 where w and dente the aqueus and rganic phases, respectively. Frm a thermdynamic viewpint, the wrk required t transfer a mle f ins, such as DMFc r prtns, frm a vacuum t a liquid phase, α (i.e. w r ), is defined as the electrchemical ptential, μ i α, where μ i α = μ i α z i Fφ α (S5) The z i Fφ α term is the electrical wrk required t transfer the charge that the in pssesses int phase α. An in in slutin will have shrt-distance interactins with its envirnment, fr example in-diple interactins, dispersin frces, and hydratin t sme extent will ccur. Thus, the energy level f the in in a phase clearly depends n its chemical envirnment. This is represented by μ i α, the chemical ptential f in i in phase α. Fr an uncharged species, such as DMFc, the electrchemical ptential is slely dependent n this chemical cntributin such that μ i α = μ i α. In slutin, μ i α is represented by μ i α = μ i α,0 RT ln a i α (S6) α where μ,0 i is the standard chemical ptential and a α i is the activity f the in i. The activity is a measure f the effective cncentratin f species i in slutin. Activity depends n temperature, pressure and cmpsitin f the slutin, amng ther factrs. Fr a real gas, such as H 2, the chemical ptential fr a given pressure may be expressed with regard t a standard pressure value, p 0, f 1 bar as (s3) μ α α i = μ,0 i RT ln f p 0 (S7) 7

8 where f is the fugacity, a term that takes int accunt the partial pressure f the real gas and deviatins f its behaviur with respect t an ideal gas. When an electrchemical cell is balanced against an external surce f ptential, and the entire system is at equilibrium, then the Gibbs energy ( ΔG) fr a reactin is zer and ΔG = n i ΔG Prducts i n j ΔG Reactants j = 0 (S8) where n i and n j and the stichimetric cefficients fr the prduct and reactant species, respectively. Thus, the Gibbs energy f the PCET reactin utlined in eqn (S4) at equilibrium can be expressed in terms f the electrchemical ptentials f each f the reactant and prduct species and is In turn, eqn (S9) leads directly t ΔG = μ DMFc 1 2 μ μ H 2 DMFc w μ H = 0 (S9) 0, ΔG = μ DMFc RT ln 0, μ DMFc RT ln z DMFc Fφ 1 2 μ 0 H 2 μ 0,w H RT ln a w H RT ln f 1 2 H 2 p 0 z H Fφ w = 0 (S10) Rearranging eqn (S10) we get 0, ΔG = (μ DMFc 0, μ DMFc ) ( 1 2 μ 0 μ 0,w H 2 H ) RT ln w a H 1 f 2 H2 p 0 z Fφ z DMFc H Fφ w = 0 (S11) The fllwing factrs are taken int cnsideratin: (1) z DMFc = z H = 1, 0, (2) (μ DMFc 0, μ DMFc ) ( 1 2 μ 0 μ 0,w 0 H 2 H ) = E DMFc /DMFc SHE i.e. the standard redx ptential f the DMFc /DMFc cuple in 1,2-DCE with respect t the aqueus standard hydrgen electrde (SHE), (3) RT ln w a H 1 f 2 H2 p 0 = RT ln a DMFc 1 a DMFc 2 RT ln f H 2 w p 0 RT ln a H ( ) 8

9 At atmspheric pressure and under bubbling cnditins we may neglect the term 1 2 RT ln f H 2 p 0 and, additinally, RT ln a w ( H ) ln10 w = RTLg a H w ( )= RTpH, therefre RT ln( a H )= ln10rtph. Thus, re-arranging with the abve factrs taken int accunt and subsequently dividing each term by Faraday s cnstant yields φ w φ = E 0 DMFc/DMFc F SHE RT F ln a DMFc RT ln10ph (S12) F Finally, the Nernst equatin fr the biphasic hydrgen evlutin reactin reads 0 Δ w φ HER =Δ w φ HER RT F ln a DMFc RT F ln10ph (S13) 0 where Δ w φ HER = E 0 DMFc/DMFc F SHE and Δ w φ HER = φ w φ, termed the redx Galvani ptential difference f the hydrgen evlutin reactin. References ( s1) A. J. Olaya, M. A. Méndez, F. Crtes-Salazar and H. H. Girault, J. Electranal. Chem., 2010, 644, (s2) B. Su, I. Hatay, F. Li, R. Partvi-Nia, M. A. Méndez, Z. Samec, M. Ersz and H. H. Girault, J. Electranal. Chem., 2010, 639, (s3) H. H. Girault, Analytical and Physical Electrchemistry, EPFL Press: Lausanne, Switzerland,

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