New Challenges of Electrokinetic Study in Investigating the Reaction Mechanism of Electrochemical CO 2 Reduction

Transcription

1 Electronic Supplementary Material (ESI) for Journal of Materials Chemistry A. This ournal is The Royal Society of Chemistry 018 Supporting Information New Challenges of Electrokinetic Study in Investigating the Reaction Mechanism of Electrochemical Reduction Chan Woo Lee, ab Nam Heon Cho, a Sang Won Im, a Michael Shincheon Jee, bc Yun Jeong Hwang,* bd Byoung Koun Min,* be and Ki Tae Nam* a a Department of Materials Science and Engineering, Seoul National University, Seoul, , Korea b Clean Energy Research Center, Korea Institute of Science and Technology (KIST), 5 Hwarang-ro 14-gil, Seongbuk-gu, Seoul 079, Republic of Korea c Department of Chemical and Biological Engineering, Korea University, Anam-dong, Seongbuk-gu, Seoul , Republic of Korea d Korea University of Science and Technology, 17 Gaeong-ro, Yuseong-gu, Daeeon 34113, Republic of Korea e Green School, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 0841, Republic of Korea *Correspondence to: nkitae@snu.ac.kr

2 Theoretical Tafel slope and reaction order derivation As mentioned in the main text, derived theoretical Tafel slopes and reaction order could be used to verify the erimentally acquired electrokinetic results and proposed reaction mechanism. Detailed derivations of Tafel slopes and reaction orders respect to possible rate determining steps during electrochemical conversion of to and - are provided. The derivation was accomplished on the basis of previous reports. 1-3 Tafel slope and reaction order derivation for production Potential rate determining steps for electrochemical conversion to has been listed below. (1) () (3) + (aq) + e + H 3 OH + 3 OH + e + H 3 + H O + 3 (4) + Except for a specific rate-limiting step, we assume that all other steps are in quasi-equilibrium as below. K 1 P OH [ 3 ] K [H 3 ] [ K 3 OH [H 3 ] K 4 P 3 ] Each electrochemical equilibrium constants are defined as below. K i ( G i n i (E E i ) or steps (1) and (3), n 1 and n 3 1 because there is one-electron transfer. or steps () and (4), n and n 4 0 because electrons are not involved. During the entire derivation, refers to active site coverage, P is partial pressure of, k i is rate constant, R is the gas constant, T is temperature, and is araday s number. * Reaction (1) as rate determining step Theoretical Tafel slopes could be derived from the rate ression. Tafel slope is defined as shown below. ( E) Tafel slope When, assuming Reaction (1) to be rate-determining steps, the partial current density for production is

3 k 1 P ( βe We begin by taking log of both sides. log log k 1 + log + log P βe.3rt Expressing partial derivative of the rate ression respect to the electrical potential, β log +.3RT If we assume * 1, log 0 β.3rt If we take inverse of the ression shown above, we can acquire theoretical Tafel slope. ( E) Tafel slope.3rt mv dec β Reaction order can be ressed by partial current density respect to [H 3- ] concentration. Temperature, partial pressure, and electrical potential are assumed to be constant. log [H 3 ] 0 Reaction () as rate determining step When, assuming Reaction () to be rate-determining steps, the partial current density for production is k [H 3 ] Assuming reaction step (1) to be in fast equilibrium, following relationship could be shown. k 1 P ( βe k 1 (1 β)e ( rom the relationship shown in equilibrium constant K 1, it is possible to ress current respect to * and

4 assuming * 1, partial current can be ressed as followed. k 1 k P k [H 3 ] 1 ( E RT) Taking log of both sides achieves following term. k 1 log log k + log P k + log [H 3 ] E 1.3RT With temperature, partial pressure, and [H 3- ] concentration remaining constant, Tafel slope can be ressed as shown below..3rt ( E) Tafel slope.3rt mv dec Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Since temperature, partial pressure, and electrical potential remain constant, reaction order could be derived as shown below. log [H 3 ] 1 Reaction (3) as rate determining step When assuming Reaction (3) to be rate-determining steps, the partial current density for production is k 3 OH[H 3 ] ( βe Assuming reaction step (1) and () to be in fast equilibrium, and using equilibrium constant K 1 and K, partial current for production could be shown as followed. k 3 K [H 3 ] [ 3 ] K 1 P ( βe In the limiting case where buffer equilibration and/or mass transport are rapid relative to the rate of catalytic turn-over, the following solution equilibrium can be used in order to ress the partial current in terms of [H 3- ]. 1 + H O + 3 H 3 K buffer [ H 3 ] [ 3 ]P

5 k 3 K [H 3 ] K 1 P ( βe P K Buffer [H 3 ] k 3 K K 1 ( βe P K Buffer Taking log of both sides and differentiating respect to potential, it is possible to achieve following term. Noticeably, as shown on given Equilibrium constant of reactions, only K 1 is dependent to potential as it involves electron during the reaction. log K 1 β.3rt.3rt β.3rt (1 + β).3rt rom above equation, Tafel slope could be ( E) Tafel slope.3rt mv dec (1 + β) Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Considering temperature, partial pressure, and electrical potential to remain constant, reaction order could be shown as below. log [H 3 ] 0 Reaction (4) as rate determining step When assuming Reaction (4) to be rate-determining steps, the partial current density for production is k 4 Assuming reaction step (1), (), and (3) to be in fast equilibrium state, and using equilibrium constant for mentioned reactions, surface coverage of could be ressed as shown below. K 3[H 3 ] [ 3 ] K [H 3 ] [ 3 ] K 1 P K 3 K K 1 P P K Buffer [H 3 ] has been substituted in the partial current term and partial current can been ressed respect to, active site coverage. P k 4 K 3 K K 1 K Buffer P [H 3 ] Taking log of both sides and differentiating respect to potential, it is possible to achieve following term. log K 3 + log K 1.3RT.3RT.3RT rom above equation, Tafel slope could be

6 ( E) Tafel slope.3rt mv dec Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Considering temperature, partial pressure, and electrical potential to remain constant, reaction order could be shown as below. log [H 3 ]

7 Tafel slope and reaction order derivation for - production Potential rate determining steps for electrochemical conversion to - has been listed below. (5) + (aq) + e (6) + H 3 OCHO + 3 (7) OCHO + e (8) + Except for a specific rate-limiting step, we assume that all other steps are in quasi-equilibrium as below. K 5 P OCHO [ 3 ] K 6 [H 3 ] K 7 OCHO K 8 [ ] Each electrochemical equilibrium constants are defined as below. K i ( G i n i (E E i ) or steps (5), (7) and, n 5 and n 7 1 because there is one-electron transfer. or steps () and (4), n 6 and n 8 0 because electrons are not involved. During the entire derivation, refers to active site coverage, P is partial pressure of, k i is rate constant, R is the gas constant, T is temperature, and is araday s number. Reaction (5) as rate determining step When assuming Reaction (5) to be a rate-determining step, the partial current density for - production is k 5 P ( βe We begin by taking log of both sides. * log log k 5 + log + log P βe.3rt Expressing partial derivative of the rate ression respect to the electrical potential,

8 β log +.3RT If we assume * 1 during the reaction, log 0 β.3rt If we take inverse of the ression shown above, we can acquire theoretical Tafel slope. ( E) Tafel slope.3rt mv dec β Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Since temperature, partial pressure, and electrical potential remain constant, reaction order could be derived as shown below. log [H 3 ] 0 Reaction (6) as rate determining step When assuming Reaction (6) to be rate-determining steps, the partial current density for - production is k 6 [H 3 ] Assuming reaction step (5) to be in fast equilibrium, following relationship could be shown. k 5 P ( βe k 5 (1 β)e ( rom the relationship shown in equilibrium constant K 5, it is possible to ress current respect to assuming * 1, partial current can be ressed as followed. * and k k 5 6 P k [H 3 ] 5 ( E RT) Taking log of both sides achieves following term. k 5 log log k 6 + log P k + log [H 3 ] E 5.3RT

9 With temperature, below. P, and [H 3- ] concentration remaining constant, Tafel slope can be ressed as shown.3rt ( E) Tafel slope.3rt mv dec Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Since temperature, partial pressure, and electrical potential remain constant, reaction order could be derived as shown below. log [H 3 ] 1 Reaction (7) as rate determining step When assuming Reaction (7) to be rate-determining steps, the partial current density for - production is k 7 OCHO ( βe Assuming reaction step (5) and (6) to be in fast equilibrium, and using equilibrium constant K 5 and K 6, partial current for - production could be shown as followed. k 7 K 6 K 5 P [ H 3 ] [ 3 ] ( βe In the limiting case where buffer equilibration and/or mass transport are rapid relative to the rate of catalytic turn-over, the following solution equilibrium can be used in order to ress the partial current in terms of [H 3- ]. 1 + H O + 3 H 3 K buffer [ H 3 ] [ 3 ]P P k 7 K 6 K 5 K buffer [H 3 ] ( βe Taking log of both sides and differentiating respect to potential, it is possible to achieve following term. log K 5 β.3rt.3rt β.3rt (1 + β).3rt

10 rom above equation, Tafel slope could be ( E) Tafel slope.3rt mv dec (1 + β) Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Considering temperature, partial pressure, and electrical potential to remain constant, reaction order could be shown as below. log [H 3 ] 1 Reaction (6+7) as rate determining step (6+7) + H 3 + e + 3 Reaction (6+7) indicates simultaneous involvement of both proton and electron during the rate-determining step, which is combination of reaction (6) and reaction (7). When assuming Reaction (6+7) to be ratedetermining steps, the partial current density for - production is written as follows. k [H 3 ] ( βe Assuming reaction step (5) to be in fast equilibrium, following relationship could be shown. rom equilibrium constant K 5, it is possible to ress current respect to *. k K 5 P [H 3 ] ( βe Taking log of both sides and differentiating respect to potential, it is possible to achieve following term. log K 5 β.3rt.3rt β.3rt (1 + β).3rt rom above equation, Tafel slope could be ( E) Tafel slope.3rt mv dec (1 + β) Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Considering temperature, partial pressure, and electrical potential to remain constant, reaction order could be shown as below. log [H 3 ] 1 Reaction (8) as rate determining step When assuming Reaction (8) to be rate-determining steps, the partial current density for - production is

11 k 8 Assuming reaction steps (5) and (6+7) to be in fast equilibrium state, and using equilibrium constant for mentioned reactions, surface coverage of - could be ressed as shown below. K 5 P k (6 + 7) [H 3 ] ( βe k (6 + 7) [ 3 (1 β)e ] ( K 5 P [H 3 ] k (6 + 7) [ 3 ] k (6 + 7) ( E RT) has been substituted in the partial current term and partial current can been ressed respect to, active site coverage. k 8 K 5 P [H 3 ] [ 3 ] k (6 + 7) k (6 + 7) ( E RT) In the limiting case where buffer equilibration and/or mass transport are rapid relative to the rate of catalytic turn-over, the following solution equilibrium can be used in order to ress the partial current in terms of [H 3- ]. 1 + H O + 3 H 3 K buffer [ H 3 ] [ 3 ]P RT) P k 8 K 5 k (6 + 7) k (6 + 7) ( E K Buffer [H 3 ] Taking log of the current term and differentiating respect to potential, it is possible to achieve following term. log K 5.3RT.3RT.3RT.3RT rom above equation, Tafel slope could be ( E) Tafel slope.3rt mv dec Reaction order could be ressed by partial current density respect to [H 3- ] concentration. Considering temperature, partial pressure, and electrical potential to remain constant, reaction order could be shown as below.

12 log [H 3 ] 1 Supplementary References 1 A. Wuttig, Y. Yoon, J. Ryu and Y. Surendranath, J. Am. Chem. Soc., 017, 139, J. Rosen, G. S. Hutchings, Q. Lu, S. Rivera, Y. Zhou, D. G. Vlachos and. Jiao, ACS Catal., 015, 5, S. Gao, Z. Sun, W. Liu, X. Jiao, X. Zu, Q. Hu, Y. Sun, T. Yao, W. Zhang, S. Wei and Y. Xie, Nat. Commun., 017, 8, 1 9.