Electrode kinetics, finally!

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Aileen Brown
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1 1183 Q: What s in this set of lectures? A: B&F Chapter 3 main concepts: Sections 3.1 & 3.6: Homogeneous Electron-Transfer (ET) (Arrhenius, Eyring, TST (ACT), Marcus Theory) Sections 3.2, 3.3, 3.4 & 3.6: Heterogeneous ET (Butler Volmer Eq, Tafel Eq, Volcano Plot, Gerischer Theory, Quantum Mechanical Tunneling) Section 3.5: Multistep ET Mechanisms Electrode kinetics, finally!

2 Marcus Theory the idea Minor assumptions to go from internal (potential) energy to free energy (ΔG = ΔH TΔS) Three regions of electron transfer (I) Normal, (II) Barrierless, (III) Inverted 1184 The nuclear reorganization energy, λ, is the free energy required to reorganize the solvent (outer) and bonds (inner) when the electron moves from the reactant to product energy potential energy well but at the nuclear arrangement of the reactant and for ΔG 0 = 0 ΔG 0 < λ ΔG 0 = λ ΔG 0 > λ

3 here s a thought experiment that gets us an expression for k f : What happens to ΔG cǂ and ΔG aǂ when the potential is changed by E? * assume E eq = E * Linearized Marcus Theory 1) O is stabilized (i.e. lowered) by F(E E 0 ) 2) and the barrier height decreased by (1 α)f(e E 0 ) 3) the net change in the cathodic barrier is the difference: F(E E 0 ) (1 α)f(e E 0 ) = αf(e E 0 ) NOTE: It s positive; the cathodic barrier became larger. 4) and the anodic barrier just decreased by (1 α)f(e E 0 )

4 now plug these into our expression for the current: 1186 replace (E E 0 ') with η = (E E eq ) and i 0 (B&F, pp ) Butler Volmer Equation: eliminate effects due to mass transfer stir well or pass a small current or use surfaceadsorbed species!

5 What do these equations predict? (-) * Note: These quadrants are flipped 1187 but at least they are (-, -) and (+, +)... now that I edited them (+) the Current Overpotential Equation

6 What do these equations predict? (-) * Note: These quadrants are flipped 1188 but at least they are (-, -) and (+, +)... now that I edited them the exponential increase of i c the exponential increase of i a (+) the Current Overpotential Equation

7 What do these equations predict? (-) * Note: These quadrants are flipped 1189 but at least they are (-, -) and (+, +)... now that I edited them i 0 i 0 (+) the Current Overpotential Equation

8 if mass transport effects can be neglected (by rapidly stirring the solution, for example), then the Butler-Volmer Eq. is valid: 1190 (-) (+) * Note: These quadrants are flipped but at least they are (-, -) and (+, +) now

9 if mass transport effects can be neglected (by rapidly stirring the solution, for example), then the Butler-Volmer Eq. is valid: (-) 1191 i 0 (j 0 ) is called the exchange current (density) and is the current that is equal and opposite at an electrode at equilibrium (think microscopic reversibility) (+) * Note: These quadrants are flipped but at least they are (-, -) and (+, +) now it is the most convenient indicator of the kinetic facility of an electrochemical reaction

10 a challenge in all types of kinetic analyses is making the mass-transfer-limited current, i l, high enough so that a kinetically-controlled reaction rate is observed 1192 (-) (+) * Note: These quadrants are flipped but at least they are (-, -) and (+, +)

11 j 0 can vary over twenty orders of magnitude! Consider just one reaction: proton reduction (H 2 evolution) !

12 j 0 can vary over twenty orders of magnitude! Consider just one reaction: proton reduction (H 2 evolution) ! To test the materials below Pt, don t use a CE made of Pt as in acid it dissolves!

13 Sabatier Principle and Volcano plots for, for example, proton reduction (H 2 evolution) 1195 Parsons, Trans. Faraday Soc., 1958, 54, 1053 Trasatti, Electroanal. Chem. Interfac. Electrochem., 1972, 39, 163

14 Sabatier Principle and Volcano plots for, for example, proton reduction (H 2 evolution) 1196 Spillover (synergism) H H H H H H H H + Ni Mo e Parsons, Trans. Faraday Soc., 1958, 54, 1053 Trasatti, Electroanal. Chem. Interfac. Electrochem., 1972, 39, 163

15 Simple, multistep electron-transfer mechanisms 1197

16 Simple, multistep electron-transfer mechanisms 1198

17 Simple, multistep electron-transfer mechanisms 1199

18 Simple, multistep electron-transfer mechanisms 1200 Tafel slope depends on rate-determining step fun kinetics!

19 Simple, multistep electron-transfer mechanisms 1201 are not so simple imagine CO 2 + 8e + 8H + CH 4 + 2H 2 O

20 and where α introduces asymmetry into this J E curve 1202 the Butler Volmer Equation * Note: These quadrants are flipped but at least they are (-, -) and (+, +)

21 note that when α < 1 / 2, at any η value, oxidation is preferentially accelerated * Note: These quadrants are flipped but at least they are (-, -) and (+, +)

22 note that when α > 1 / 2, at any η value, reduction is preferentially accelerated * Note: These quadrants are flipped but at least they are (-, -) and (+, +)

23 now, more specifically, α is related to the symmetry of the barrier in the vicinity of the crossing point 1205 tan = opposite / adjacent derive this by applying TOA to the two right triangles on the right tan θ = αfe/x tan ϕ = (1 α)fe/x Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 3.3.3

24 if the barrier is symmetrical 1206 this means that the cathodic and anodic barriers are affected equally by the change in potential. Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure 3.3.4

25 if the R side is steeper than the O side 1207 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure this means that a change in the electrode potential affects the anodic barrier more than the cathodic barrier. Note that in the limit of a vertical potential-energy curve for R at the crossing point, α = 0 and 100% of the potential change accelerates oxidation.

26 if the R side is more shallow than the O side 1208 Bard & Faulkner, 2 nd Ed., Wiley, 2001, Figure this means that a change in the electrode potential affects the cathodic barrier more than the anodic barrier. Note that in the limit of a vertical potential-energy curve for O at the crossing point, α = 1 and 100% of the potential change accelerates reduction.

27 two limiting cases for the B-V Eq. are important 1209 first, if η is small, then exp(x) can be approximated by a Taylor/ Maclaurin series expansion as 1 + x i = i αfη α fη = +i 0 fη

28 two limiting cases for the B-V Eq. are important 1210 first, if η is small, then exp(x) can be approximated by a Taylor/ Maclaurin series expansion as 1 + x i = i αfη α fη What s small? exp(0) = = 1 (error = 0%) exp(1) = = 2 (error = -26%) so small means η < 30 mv (αfη = (0.5)(1 / 26 mv)(30 mv) = 0.58) exp(0.58) = = 1.58 = +i 0 fη (error = -11%)

29 two limiting cases for the B-V Eq. are important 1211 first, if η is small, then exp(x) can be approximated by a Taylor/ Maclaurin series expansion as 1 + x i = i αfη α fη = +i 0 fη Note: no α! and ohmic

30 two limiting cases for the B-V Eq. are important 1212 if, instead, η is large, then either i c or i a can be neglected and we obtain the famous Tafel Eq. which has two versions: for η << 0: (current negative, or reducing/cathodic) i = i 0 exp αfη... ln i = ln i 0 αfη for η >> 0: (current positive, or oxidizing/anodic) i = +i 0 exp 1 α fη ln i = ln i α fη

31 1213 both α and i 0 (and thus k 0 ) and are obtained from a J E curve in one direction * Note: The x axis is flipped; sorry. Slope -1 = Tafel Slope ( mv per decade )

32 note: η is large means > 120 mv or so 1214 * Note: The x axis is flipped; sorry. Slope -1 = Tafel Slope ( mv per decade )

33 note: η is large means > 120 mv or so 1215 Which catalyst is best? (A) j o = 10-4 A cm -2 and 120 mv decade -1 (B) j o = 10-7 A cm -2 and 60 mv decade -1 * Note: The x axis is flipped; sorry.

34 note: η is large means > 120 mv or so 1216 Which catalyst is best? (A) j o = 10-4 A cm -2 and 120 mv decade -1 (B) j o = 10-7 A cm -2 and 60 mv decade -1 It depends on the desired j * Note: The x axis is flipped; sorry.

35 note: η is large means > 120 mv or so 1217 Which catalyst is best? (A) j o = 10-4 A cm -2 and 120 mv decade -1 (B) j o = 10-7 A cm -2 and 60 mv decade -1 It depends on the desired j For 1 ma cm -2, (A) is best but * Note: The x axis is flipped; sorry.

36 note: η is large means > 120 mv or so 1218 Which catalyst is best? (A) j o = 10-4 A cm -2 and 120 mv decade -1 (B) j o = 10-7 A cm -2 and 60 mv decade -1 It depends on the desired j For 1 ma cm -2, (A) is best but for 1 A cm -2, (B) is best * Note: The x axis is flipped; sorry. where catalyst (A) requires η = 480 mv, while catalyst (B) requires η = 420 mv!

37 Laboratory #7 Wrap-Up will be held right now Discuss the activity Provide feedback Recommend other activities Fe 3+/2+ and H + electrocatalysis y-axis: current y-axis: log current (care of Sunny, Mackenzie, & Kyle)

38 Laboratory #7 Wrap-Up will be held right now Discuss the activity Provide feedback Recommend other activities OH /H 2 O electrocatalysis RHE V (care of Simon, Peter, & Hong) Trotochaud, Young, Ranney, and Boettcher, JACS, 2014, 136, 6744

39 What does real data look like? 1221 wait, what is E 0 (O 2,H + /H 2 O)?

40 What does real data look like? 1222 wait, what is E 0 (O 2,H + /H 2 O)? 1.23 V vs. SHE Huh?

41 What does real data look like? 1223 wait, what is E 0 (O 2,H + /H 2 O)? 1.23 V vs. SHE Huh? Oh, this is in base? Gotcha! Now I see why RHE is a nice RE for these systems

42 wait, the Tafel Slope (in units of mv/decade) changes? 1224 Yup! this is a consequence of a change in the mechanism of the reaction, resulting from a change in the chemical state of the catalyst, for example.

43 Recall (and for clarity) that we have already encountered the overpotential, and seen a case where it is important 1225 O + ne - R n- (insoluble)

44 Recall (and for clarity) that we have already encountered the overpotential, and seen a case where it is important 1226 O + ne - R n- (insoluble) C * R = 0 C * O = the bulk concentration of O e.g. Ag + + e - Ag 0

45 Recall (and for clarity) that we have already encountered the overpotential, and seen a case where it is important 1227 O + ne - R n- (insoluble) C * R = 0 C * O = the bulk concentration of O e.g. Ag + + e - Ag 0 Repeating a derivation akin to one we did in Chapter 1 E = E 0 + RT nf ln C O + RT nf ln i l i i l

46 Recall (and for clarity) that we have already encountered the overpotential, and seen a case where it is important 1228 O + ne - R n- (insoluble) Repeating a derivation akin to one we did in Chapter 1 E = E 0 + RT nf ln C O + RT nf ln i l i i l E eq E E eq = η conc = RT nf ln i l i i l

47 Recall (and for clarity) that we have already encountered the overpotential, and seen a case where it is important 1229 O + ne - R n- (insoluble) Repeating a derivation akin to one we did in Chapter 1 E = E 0 + RT nf ln C O + RT nf ln i l i i l E eq E E eq = η conc = RT nf ln i l i i l Interpretation: An extra voltage, beyond the E eq, is required to drive mass transport of species to the electrode surface.

48 Recall (and for clarity) that we have already encountered the overpotential, and seen a case where it is important 1230 η conc = RT nf ln i l i i l Interpretation: An extra voltage, beyond the E eq, is required to drive mass transport of species to the electrode surface.

49 What s happening here (not electrocatalysis)? 1231 O + ne - R n- (insoluble)

50 1232 An overpotential that is derived from rate-limiting mass transport alone is called a concentration overpotential, η conc. It s also called: concentration polarization. Kinetic overpotential is often just called overpotential, but can also be called activation overpotential. we are almost finished this topic

surface c, c. Concentrations in bulk s b s b red red ox red

surface c, c. Concentrations in bulk s b s b red red ox red CHEM465/865, 26-3, Lecture 16, Oct. 13, 26 compact layer S c ox,red b c ox,red Note, that we explicitly distinguish concentrations at surface bulk b red c, c from those in s red b ox s ox c, c. Concentrations