1237 Lecture #17 of 18

Transcription

1 Lecture #17 of

2 1238 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

3 But wait! You told us that Marcus Theory led to an inverted region where is evidence for the inverted region by electrochemistry? 1239 Three regions of electron transfer (I) Normal, (II) Barrierless, (III) Inverted ΔG 0 < λ ΔG 0 = λ ΔG 0 > λ and you told us that this had a Gaussian shape

4 There is no inverted region! Thank you, Fermi, Marcus & Gerischer! 1240 Physicist from Wiki and pc/pchistory.html Enrico Fermi ( ) Electrochemist E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states Heinz Gerischer ( )

5 There is no inverted region! Thank you, Fermi, Marcus & Gerischer! 1241 ρ has units of cm -2 ev -1 Physicist from Wiki and pc/pchistory.html Enrico Fermi ( ) Electrochemist E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states Heinz Gerischer ( )

6 There is no inverted region! Thank you, Fermi, Marcus & Gerischer! 1242 ρ has units of cm -2 ev -1 and has units of cm -3 ev -1 E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states & molecule states

7 There is no inverted region! Thank you, Fermi, Marcus & Gerischer! 1243 ρ has units of cm -2 ev -1 and has units of cm -3 ev -1 it s that Gaussian term! E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states & molecule states

8 the rate of electron transfer is dictated by the law of mass action 1244 constant (cm 3 ev) area (cm 2 ) E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states & molecule states

9 the rate of electron transfer is dictated by the law of mass action 1245 constant (cm 3 ev) area (cm 2 ) E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states & molecule states

10 the rate of electron transfer is dictated by the law of mass action E bias varies the probability function (0, 1) resulting in (D)istributions of occupied metal states & molecule states

11 experimental validation of the theory and lack of inverted region 1247 Sikes, Smalley, Dudek, Cook, Newton, Chidsey & Feldberg, Science, 2001, 291, 1519 Chidsey, Science, 1991, 251, 919

12 experimental validation of the theory and lack of inverted region 1248 λ λ λ = 0.85 ev RC double layer charging 1 st order electron-transfer kinetics Chidsey, Science, 1991, 251, 919

13 experimental validation of the theory and lack of inverted region 1249 λ λ E bias λ = 0.85 ev and there was no inverted region because at large driving forces there was always a state in the metal that overlapped the most probable D O Chidsey, Science, 1991, 251, 919

14 experimental validation of the theory and lack of inverted region 1250 λ λ E bias λ = 0.85 ev and there was no inverted region because at large driving forces there was always a state in the metal that overlapped the most probable D O Chidsey, Science, 1991, 251, 919

15 experimental validation of the theory and lack of inverted region 1251 λ λ E bias λ = 0.85 ev and there was no inverted region because at large driving forces there was always a state in the metal that overlapped the most probable D O Chidsey, Science, 1991, 251, 919

16 Well, that was disappointing when is there an inverted region? at semiconductors! 1252 but how? bandgap Hamann, Gstrein, Brunschwig & Lewis, JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

17 Well, that was disappointing when is there an inverted region? at semiconductors! 1253 but how? inverted E bias bandgap Hamann, Gstrein, Brunschwig & Lewis, JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

18 Well, that was disappointing when is there an inverted region? at semiconductors! 1254 but how? Vary the molecule, not the bias! but λ must be the same for each! barrierless E bias bandgap Hamann, Gstrein, Brunschwig & Lewis, JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

19 Well, that was disappointing when is there an inverted region? at semiconductors! 1255 normal E bias bandgap Hamann, Gstrein, Brunschwig & Lewis, JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

20 Well, that was disappointing when is there an inverted region? at semiconductors! 1256 λ = 0.67 ev cm 4 s -1 a second order rate constant ( x concentration 2 ) E bias bandgap Hamann, Gstrein, Brunschwig & Lewis, JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

21 Well, that was disappointing when is there an inverted region? at semiconductors! 1257 λ = 0.67 ev E bias bandgap cm 4 s -1 a second order rate constant ( x concentration 2 ) but more work is still needed in order to nail this! Hamann, Gstrein, Brunschwig & Lewis, JACS, 2005, 127, 7815 and JACS, 2005, 127, 13949

22 1258 Q: What was 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, DONE!

23 Let s summarize the steady-state behavior from the entire course 1259 by looking at data on stirred (non-hysteretic) I E (J E) curves and at each location, let s think about what resistance is limiting the observed behavior R ET R DL R MT R u Circuit representation of electrochemical cell

24 RECALL: Let s compare total capacitance (C) and differential capacitance (C d ) as follows: 1260 E z = pzc

25 Let s summarize the steady-state behavior from the entire course 1261 by looking at data on stirred (non-hysteretic) I E (J E) curves and at each location, let s think about what resistance is limiting the observed behavior so, we want to know what dictates R = I E 1 at each E Fe 3+/2+ and H + electrocatalysis H + /H 2 electrocatalysis

26 Let s summarize the steady-state behavior from the entire course 1262 by looking at data on stirred (non-hysteretic) I E (J E) curves and at each location, let s think about what resistance is limiting the observed behavior so, we want to know what dictates R = at each E but this will be hard because we have several convoluting factors I E 1 R ET R DL R MT R u Circuit representation of electrochemical cell what are the limiting behaviors of each major resistance and can we even begin to piece out which component is responsible, while recalling that the total E app (I) = E ET (I) + E DL (I) + E MT (I) + E u (I) +?

27 what are the limiting behaviors of each major resistance and can 1263 we even begin to piece out which component is responsible? electro catalysis mass transport resistance (ir drop)

28 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

29 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

30 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

31 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

32 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

33 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

34 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

35 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

36 Let s try some examples EXAMPLE # electro catalysis mass transport resistance (ir drop)

37 Let s try some examples EXAMPLE #5 You get the idea! 1273 and what does E LJ or E Donnan do to these plots? Shifts them left/right electro catalysis mass transport resistance (ir drop)

38 1274 Q: What s in this set of lectures? A: B&F Chapters 9, 10, and 6 main concepts: Sections : Sections : Rotating (Ring-)Disk Electrochemistry Electrochemical Impedance Spectroscopy Sections , 11.7, 14.3: Linear Sweep Voltammetry (LSV), Cyclic Voltammetry (CV), Thin-Layer Electrochemistry To really learn about your laboratory systems move beyond steady-state conditions!

39 RDE is also a steady-state technique (slide 1 of 3) 1275 B&F B&F Levich Equation (term) At high rotation rates, C(0,t) = C* and then series current limited by electron-transfer at electrode (i K )

40 RDE is also a steady-state technique (slide 2 of 3) 1276 By doing this as a function of potential, one can determine k 0 and α kinetic parameters without dealing with trying to stir perfectly as required for B V kinetics Levich Equation (term) At high rotation rates, C(0,t) = C* and then series current limited by electron-transfer at electrode (i K )

41 and RRDE is very useful, too! (slide 3 of 3) 1277 * Chemistry at disk can be confirmed at ring if ω is fast enough

42 How do we learn anything from complex systems? 1278 Steady-state reactions and processes can be amazingly complex (e.g. see everything we have covered thus far) ideally, we need to piece out each mechanistic component from interrelated processes we do this by performing studies over various time regimes thus, we need to change the temporal response of our measurements! R(R)DE: stirring removes mass-transport limits, which is nice rotating the electrode does the same thing so precisely change the rotation rate we can also surround the disk/button by a second ring electrode to observe products of electron transfer EIS: sweep/scan potentials over very small range but then change the region (DC) and also change the scan rate (AC)? CV: change the scan rate mechanisms by Saveant s Foot of the Wave (e.g. ECE, etc.) modeling using BASi DigiSim, EC Lab, etc. UME: sweep/scan VERY fast forward and backward

43 a few words about electrochemical impedance spectroscopy (EIS) 1279 capacitor only: capacitor & resistor in series: What is the resistance?

44 a few words about electrochemical impedance spectroscopy (EIS) 1280 capacitor only: capacitor & resistor in series: What is the resistance? R Et () It ()

45 we need a compact way to represent this impedance Z = R + ix

46 a complex plane representation of the total electrical impedance It s called a Nyquist plot. Z = R + ix 1282 the capacitive component of the impedance (reactance) the total impedance the resistive component of the impedance

47 Z im (x 10 6 ) let s look at Nyquist plots for a few simple circuits: 1283

48 Z im (x 10 6 ) first, a series RC circuit like with double-layer charging X = Z im = 1 ωc = F = 107 Ω = 10 MΩ 1284

49 Z im (x 10 6 ) first, a series RC circuit like with double-layer charging X = Z im = 1 ωc = F = 107 Ω = 10 MΩ 1285 for a capacitor, as frequency increases (max ~1 MHz), Z Im decreases until you hit the x- axis, which is the uncompensated resistance in the cell

50 what about a parallel RC circuit? 1286

51 a semi-circle does this make sense? 1287 at low frequency, Z im << Z Re (= R), and the circuit behaves like there is no capacitor, and just a resistor

52 a semi-circle does this make sense? 1288 at high frequency, Z im = 0, and the circuit behaves like there is no capacitor and no resistor so here, R u = 0

53 a semi-circle does this make sense? 1289 in between these limits, the circuit has both capacitive and resistive behavior maximum phase angle

54 1290 to an electrical engineer, an electrochemical cell looks like this: Z f is the Faradaic impedance called the Randles equivalent circuit

55 1291 Here is the Nyquist plot for the full Randles equivalent circuit: Angle is theoretically 45 for a Warburg impedance, Z W Finally, a simple way to measure R u assuming our potentiostat can do it

56 that was a brief primer on EIS, where S is for spectroscopy? 1292 FOR YOUR REFERENCE For example, from Wiki, one type of IS is dielectric spectroscopy which monitors the screening (permittivity) of systems as a function of the frequency of light (which is an EM wave and is related to wavelength by the speed (of light)) Our data was based on EM AC signals as a function of frequency too Also, impedance is the opposition to the flow of alternating current (AC) in a complex system and so EI"S" is appropriate (but confusing).

57 1293 Q: What s in this set of lectures? A: B&F Chapters 9, 10, and 6 main concepts: Sections : Sections : Rotating (Ring-)Disk Electrochemistry Electrochemical Impedance Spectroscopy Sections , 11.7, 14.3: Linear Sweep Voltammetry (LSV), Cyclic Voltammetry (CV), Thin-Layer Electrochemistry To really learn about your laboratory systems move beyond steady-state conditions!