239 Lecture #4 of 18
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- Roy Stephens
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1 Lecture #4 of
2 240 Q: What s in this set of lectures? A: Introduction, Review, and B&F Chapter 1, 15 & 4 main concepts: Section 1.1: Redox reactions Chapter 15: Electrochemical instrumentation Section 1.2: Charging interfaces Section 1.3: Overview of electrochemical experiments Section 1.4: Mass transfer and Semi-empirical treatment of electrochemical observations Chapter 4: Mass transfer
3 241 Looking forward Section 1.1 (and some of Chapter 15) 2-electrode versus 3-electrode measurements Reference electrodes Potentiostats Compliance voltage/current J E and I E curves Kinetic overpotential Faradaic reactions
4 Potentiostat summary 242 The potentiostat does not control the potential of the working electrode! The potentiostat controls the potential of the counter electrode only (relative to the working electrode) The counter electrode is the most important electrode, followed by the reference electrode Compliance voltage limits are very important in the choice of the potentiostat / application With a few components you can build your own potentiostat for < $100! Passive potentiostats do not hold the WE at earth ground, but can measure potentials across electrolyte interfaces Rowe,..., Plaxco, PLoS One, 2011, 6, e23783 Mott,..., Sykes, J. Chem. Educ., 2014, 91, 1028
5 and that is why we use a 3-electrode potentiostat 243 WE = working electrode CE = counter (or auxiliary) electrode RE = reference electrode Out of sight, out of mind is a bad motto!
6 244 An example of two RE scales You re welcome! B&F back inside
7 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). 245 Let s suppose that this WE is platinum, and that all three electrodes are immersed in 1.0 M HCl
8 ... okay, now let s measure the current that flows as we change the potential of 246 the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). What is the starting potential for this experiment? That is, what is the open-circuit potential? an oxidation: 2Cl (aq) Cl 2 (g) + 2e in 1.0 M HCl SHE a reduction: 2H + (aq) + 2e H 2 (g)
9 ... okay, now let s measure the current that flows as we change the potential of 247 the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). What is the starting potential for this experiment? That is, what is the open-circuit potential? an oxidation: 2Cl (aq) Cl 2 (g) + 2e in 1.0 M HCl Somewhere in here but not sure where no half-reaction is dominant SHE a reduction: 2H + (aq) + 2e H 2 (g)
10 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). i Current flow is proportional to rate, so let s write this like chemists: an oxidation: 2Cl (aq) Cl 2 (g) + 2e Rate mol s SHE = dn dt = i nf 248 but for electrochemists, this is less useful because it depends on the experimental set-up (i.e. electrode area)! a reduction: 2H + (aq) + 2e H 2 (g)
11 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). i Current flow is proportional to rate, so let s write this like chemists: an oxidation: 2Cl (aq) Cl 2 (g) + 2e Rate mol s SHE = dn dt = i nf 249 but for electrochemists, this is less useful because it depends on the experimental set-up (i.e. electrode area)! a reduction: 2H + (aq) + 2e H 2 (g) Rate mol s cm 2 = i nfa = j nf this is much better! Can we define each of these variables by name and unit?
12 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). i an oxidation: 2Cl (aq) Cl 2 (g) + 2e SHE 250 Given that the reactions shown here occur in a single cell (no salt bridge), when this E is applied to the WE and current flows at this I, what current flows at a large Pt CE and where on this plot would you put a point to show its response? a reduction: 2H + (aq) + 2e H 2 (g)
13 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). an oxidation: 2Cl (aq) Cl 2 (g) + 2e 251 Given that the reactions shown here occur in a single cell (no salt bridge), when this E is applied to the WE and current flows at this I, what current flows at a large Pt CE and where on this plot would you put a point to show its response? SHE Psssst! Don t forget me! I m still here! a reduction: 2H + (aq) + 2e H 2 (g)
14 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). an oxidation: 2Cl (aq) Cl 2 (g) + 2e 252 Given that the reactions shown here occur in a single cell (no salt bridge), when this E is applied to the WE and current flows at this I, what current flows at a large Pt CE and where on this plot would you put a point to show its response? SHE a reduction: 2H + (aq) + 2e H 2 (g) Current matching equal and opposite the current at the WE is the same as that at the CE Kirchhoff s Current Law
15 ... okay, now let s measure the current that flows as we change the potential of the platinum working electrode (imagine that we have a potentiostat here that allows us to do that). an oxidation: 2Cl (aq) Cl 2 (g) + 2e 253 Given that the reactions shown here occur in a single cell (no salt bridge), when this E is applied to the WE and current flows at this I, what current flows at a large Pt CE and where on this plot would you put a point to show its response? SHE a reduction: 2H + (aq) + 2e H 2 (g) Current matching equal and opposite the current at the WE is the same as that at the CE Kirchhoff s Current Law okay, but what if protons could not be reduced so easily? An overpotential is required!
16 Now, pretend this experimental I E curve (from my labs; in fact, measured by your trusty TA!) was measured when the Pt WE was switched with a Hg WE why does little current flow until ~ -1 V? 254 vs. SHE
17 Now, pretend this experimental I E curve was measured when the Pt WE was switched with a Hg WE why does little current flow until ~ -1 V? 255 Overpotential! which is present due to kinetic/rate/current limitations η = E app E Eq vs. SHE
18 Now, pretend this experimental I E curve was measured when the Pt WE was switched with a Hg WE why does little current flow until ~ -1 V? 256 Overpotential! which is present due to kinetic/rate/current limitations η = E app E Eq What if you dump in Cd 2+, whose E 0 (Cd 2+ /Cd 0 ) -0.4 V vs. SHE? vs. SHE
19 Now, pretend this experimental I E curve was measured when the Pt WE was switched with a Hg WE why does little current flow until ~ -1 V? 257 Overpotential! which is present due to kinetic/rate/current limitations η = E app E Eq What if you dump in Cd 2+, whose E 0 (Cd 2+ /Cd 0 ) -0.4 V vs. SHE? Current response will be kinetically determined and current will start to pass at about -0.4 V vs. SHE vs. SHE
20 Now, pretend this experimental I E curve was measured when the Pt WE was switched with a Hg WE why does little current flow until ~ -1 V? 258 Overpotential! which is present due to kinetic/rate/current limitations η = E app E Eq What if you dump in Cd 2+, whose E 0 (Cd 2+ /Cd 0 ) -0.4 V vs. SHE? Current response will be kinetically determined and current will start to pass at about -0.4 V vs. SHE vs. SHE
21 Also, don t forget about possible compliance voltage issues (maximum voltage to CE) and compliance current too! under conditions of steady-state current flow, we are concerned with matched (equal and opposite) currents at the WE and CE 259 WE vs. RE CE vs. RE vs. SHE
22 more terminology 260 supporting electrolyte an inert salt added to impart ionic conductivity to the solution (e.g. 1 M HCl, in this case) background limits the two potential limits at which the pure solvent + supporting electrolyte begin to react at the working electrode
23 261 Electrochemical window (Potential range) all acid (1) If you wanted an aqueous battery with a large voltage, which electrode is best? (2) Between aqueous and non-aqueous batteries, which can generate the largest potential? B&F back inside cover
24 262 Electrochemical window (Potential range) all acid (1) If you wanted an aqueous battery with a large voltage, which electrode is best? Hg (in 0.1 M Et 4 NOH) or C (in 0.1 M KCl) (2) Between aqueous and non-aqueous batteries, which can generate the largest potential? Non-aqueous!... much larger solvent window B&F back inside cover
25 more terminology 263 supporting electrolyte an inert salt added to impart ionic conductivity to the solution (e.g. 1 M HCl, in this case) background limits the two potential limits at which the pure solvent + supporting electrolyte begin to react at the working electrode polarizable electrode an electrode operated within a potential range in which no Faradaic electrochemistry occurs Scientist Faraday s law The amount of chemical reaction caused by the flow of current is proportional to the amount of electricity passed. (B&F) an oxidation: 2Cl (aq) Cl 2 (g) + 2e solvent window SHE Michael Faraday ( ) from Wiki a reduction: 2H + (aq) + 2e H 2 (g)
26 more terminology 264 supporting electrolyte an inert salt added to impart ionic conductivity to the solution (e.g. 1 M HCl, in this case) background limits the two potential limits at which the pure solvent + supporting electrolyte begin to react at the working electrode polarizable electrode an electrode operated within a potential range in which no Faradaic electrochemistry occurs Scientist Faraday s law The amount of chemical reaction caused by the flow of current is proportional to the amount of electricity passed. (B&F) an oxidation: 2Cl (aq) Cl 2 (g) + 2e solvent window SHE Michael Faraday ( ) from Wiki Typically, chemical reaction is measured by mass (g) and electricity passed is measured by charge (C) don t forget z in the math! a reduction: 2H + (aq) + 2e H 2 (g)
27 and, even more terminology 265 Faradaic electrochemistry electrochemistry characterized by the flow of current to/from electron donor/acceptor species present at the electrode surface Non-Faradaic electrochemistry electrochemistry characterized by the flow of current to/from an electrode surface in the absence of donor/acceptor species, typically dominated by capacitive charging of the electrode or adsorption/desorption phenomena Scientist Faraday s law The amount of chemical reaction caused by the flow of current is proportional to the amount of electricity passed. (B&F) an oxidation: 2Cl (aq) Cl 2 (g) + 2e solvent window SHE Michael Faraday ( ) from Wiki Typically, chemical reaction is measured by mass (g) and electricity passed is measured by charge (C) don t forget z in the math! a reduction: 2H + (aq) + 2e H 2 (g)
28 and lastly, typical WE ranges for EChem experiments/technologies 266 J 3E-y 2E-y 1E-y -2.0E-x -1.5E-x -1.0E-x -0.5E-x -1E-y 0.5E-x 1.0E-x 1.5E-x 2.0E-x E, vs. SHE -2E-y -3E-y Cyclic voltammogram: x = 1, y = 4 5 ΔE = 500 mv J = ±100 μa/cm 2 Nanopore: x = -1, y = 9 E = ±10 V J = ±1 na/cm 2 Photoelectrochemistry: x = 0 1, y = 2 E = E oc = ±700 mv J = J sc = ±30 ma/cm 2 Fuel Cell / Battery: x = 0, y = 0 E = 1 3 V J = 1 2 A/cm 2
29 267 A review of Section 1.1 (and some of Chapter 15) 2-electrode versus 3-electrode measurements Reference electrodes Potentiostats Compliance voltage/current J E and I E curves Kinetic overpotential Faradaic reactions
30 268 Q: What s in this set of lectures? A: Introduction, Review, and B&F Chapter 1, 15 & 4 main concepts: Section 1.1: Redox reactions Chapter 15: Electrochemical instrumentation Section 1.2: Charging interfaces Section 1.3: Overview of electrochemical experiments Section 1.4: Mass transfer and Semi-empirical treatment of electrochemical observations Chapter 4: Mass transfer
31 269 Looking forward Sections 1.2 and 1.3 RC circuits (~90% of slides) Electrochemically active surface area Uncompensated resistance Placement of electrodes, and other properties
32 270 our Pt WE is polarizable within this potential range SHE a polarizable electrode that has been polarized imposes a background electric response an added current in a voltammetric experiment, for example (not observable on this scale) that is transient (e.g. a blip) and is observed in all electrochemical experiments We need to understand this background current!
33 The electrical response of a polarizable electrode is approximated by a series resistor and capacitor (a series RC circuit) 271 Power Supply E (T)otal resistor = solution R capacitor = WE interface C E T = E R + E cap +
34 The electrical response of a polarizable electrode is approximated by a series resistor and capacitor (a series RC circuit) Power Supply R = the solution resistance (between the WE and RE) resistor = solution capacitor = WE interface R C
35 The electrical response of a polarizable electrode is approximated by a series resistor and capacitor (a series RC circuit) 273 Power Supply R = the solution resistance (between the WE and RE) C = the net capacitance (of the WE and the CE), C(T)otal 1 C T = 1 C C 2 resistor = solution capacitor = WE interface R C to measure C 2(WE), make C 1(CE) large or use a three-electrode setup and a pstat
36 First, what are approximate values for R (S) and C (d)? 274 Power Supply R = the solution resistance (between the WE and RE) In aqueous solutions containing 0.1 M supporting electrolyte, R = a few ohms; for non-aq., R > 100 Ω C = the net capacitance (of the WE and the RE), C(T)otal ~20 µf/cm 2 of electrode area for gold or platinum; 2-5 µf/cm 2 for carbon, typically (but these change slightly with potential) resistor = solution capacitor = WE interface (Farad is C/V, where V is J/C) R C
37 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
38 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC Could there be a problem with an instantaneous 6 V potential step, for example? Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
39 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC Could there be a problem with an instantaneous 6 V potential step, for example? Compliance current! (at t = 0, E = ir (Ohm s law)) Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
40 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC What is the potential drop at the WE interface due to this charging current at t = 0? E (app) What portion of E app is actually felt by the WE at t = 0? Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
41 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC What is the potential drop at the WE interface due to this charging current at t = 0? E (app) What portion of E app is actually felt by the WE at t = 0? Little of it! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
42 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): NOTE: Electronics can limit the observation of rapid chemical kinetics (i.e. RDS is charging and not electron transfer) E E WE vs. RE t What is the potential drop at the WE interface due to this charging current at t = 0? E (app) What portion of E app is actually felt by the WE at t = 0? Little of it! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
43 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC but where did this equation for current come from? who s comfortable with me just giving you this equation? Let s manipulate units! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
44 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): B&F eqn. (1.2.8) E = E R + E C = ir s + q C d R E T = E R + E cap + C
45 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): B&F eqn. (1.2.8) E = E R + E C = ir s + q C d Units: C Units: C/V R C
46 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): B&F eqn. (1.2.8) E = E R + E C = ir s + q C d B&F eqn. (1.2.9) i = 1 R s E q C d = dq dt Units: C Units: C/V R C Units: C/s
47 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): B&F eqn. (1.2.8) E = E R + E C = ir s + q C d B&F eqn. (1.2.9) i = 1 R s E q C d = dq dt Units: C Units: C/V R C Units: C/s Need to integrate!
48 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): B&F eqn. (1.2.8) E = E R + E C = ir s + q C d B&F eqn. (1.2.9) i = 1 R s E q C d = dq dt Units: C Units: C/V R C Units: C/s Need to integrate! 1 dt = 1 R s E q dq = C d C d EC d +q dq
49 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): B&F eqn. (1.2.8) E = E R + E C = ir s + q C d B&F eqn. (1.2.9) i = 1 R s E q C d = dq dt Units: C Units: C/V R C Units: C/s Need to integrate! 1 dt = 1 R s E q dq = C d C d EC d +q dq 1 t = ln EC d + q ln EC d (assuming that at t = 0, q = 0) = ln EC d + q EC d Integrated!
50 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): 1 t = ln EC d + q ln EC d = ln EC d + q EC d Integrated!
51 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): 1 t = ln EC d + q ln EC d = ln EC d + q EC d Integrated! t EC d e = EC d + q
52 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): 1 t = ln EC d + q ln EC d = ln EC d + q EC d Integrated! t EC d e = EC d + q q = EC d 1 e t q B&F eqn. (1.2.10) t
53 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): 1 t = ln EC d + q ln EC d = ln EC d + q EC d Integrated! t EC d e = EC d + q q = EC d 1 e t B&F eqn. (1.2.10) Need to differentiate! dq dt = EC d 1 e t
54 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): 1 t = ln EC d + q ln EC d = ln EC d + q EC d Integrated! t EC d e = EC d + q q = EC d 1 e t Need to differentiate! dq dt = EC d 1 e t = E e t = I R s Done! B&F eqn. (1.2.10) B&F eqn. (1.2.6)
55 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC What are the units of RC? R (Ω) x Cap (F) R (V / C/s) x Cap (C/V) R Cap (V-s/C x C/V) R Cap (s)! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
56 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC What are the units of RC? R (Ω) x Cap (F) R (V / C/s) x Cap (C/V) R Cap (V-s/C x C/V) R Cap (s)! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
57 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC What are the units of RC? R (Ω) x Cap (F) R (V / C/s) x Cap (C/V) R Cap (V-s/C x C/V) R Cap (s)! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
58 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC Why is 37% of the initial signal noteworthy? What are the units of RC? R (Ω) x Cap (F) R (V / C/s) x Cap (C/V) R Cap (V-s/C x C/V) R Cap (s)! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
59 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Voltage step (that is, increment the potential by an amount, E): i = E R exp t RC Why is 37% of the initial signal noteworthy? Plug in t = RC! Ah ha! What are the units of RC? R (Ω) x Cap (F) R (V / C/s) x Cap (C/V) R Cap (V-s/C x C/V) R Cap (s)! Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.7
60 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity?
61 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? q = EC d 1 e t B&F eqn. (1.2.10) q t
62 Now, what response is obtained for various inputs to this circuit? Potential-step potentiostatic chronoamperometry (chronocoulometry) Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? q = EC d 1 e t q t = EC d B&F eqn. (1.2.10) q t
63 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 301 q = EC d 1 e t q t = EC d B&F eqn. (1.2.10) q q = 1 e q t t t
64 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 302 q = EC d 1 e t q t = EC d B&F eqn. (1.2.10) q q = 1 e q t t 0.95 = 1 e t = e t 0.95 t
65 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 303 q = EC d 1 e t q t = EC d B&F eqn. (1.2.10) q q = 1 e q t t 0.95 = 1 e t = e t 0.95 ln 0.05 = t 0.95 t
66 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 304 q = EC d 1 e t q t = EC d B&F eqn. (1.2.10) q q = 1 e q t t 0.95 = 1 e t = e t 0.95 assuming 1 cm 2 ln 0.05 = t 0.95 t 0.95 = 1Ω 20μF ln = 60μs t
67 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 305 q = EC d 1 e t q t = EC d q = 1 e q t t 0.95 = 1 e t = e t 0.95 ln 0.05 = t 0.95 B&F eqn. (1.2.10) assuming 1 cm 2 t 0.95 = 1Ω = 60μs As above, assuming a 6 V potential step, now what is the average current that flows up to t 0.95? 20μF ln 0. 05
68 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 306 q = EC d 1 e t q t = EC d q = 1 e q t t 0.95 = 1 e t = e t 0.95 ln 0.05 = t 0.95 B&F eqn. (1.2.10) assuming 1 cm 2 t 0.95 = 1Ω = 60μs As above, assuming a 6 V potential step, now what is the average current that flows up to t 0.95? I avg = C / s = (C/V x V) / s 20μF ln 0. 05
69 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 307 q = EC d 1 e t q t = EC d q = 1 e q t t 0.95 = 1 e t = e t 0.95 ln 0.05 = t 0.95 B&F eqn. (1.2.10) assuming 1 cm 2 t 0.95 = 1Ω = 60μs As above, assuming a 6 V potential step, now what is the average current that flows up to t 0.95? I avg = C / s = (C/V x V) / s = 20 μf x 6 V / 60 μs 20μF ln 0. 05
70 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 308 q = EC d 1 e t q t = EC d q = 1 e q t t 0.95 = 1 e t = e t 0.95 ln 0.05 = t 0.95 B&F eqn. (1.2.10) assuming 1 cm 2 t 0.95 = 1Ω = 60μs As above, assuming a 6 V potential step, now what is the average current that flows up to t 0.95? I avg = C / s = (C/V x V) / s = 20 μf x 6 V / 60 μs = 120 μc / 60 μs 20μF ln 0. 05
71 Example: Consider the case where R = 1 Ω and C = 20 µf/cm 2. How long will it take to charge C to 95% of its maximum capacity? 309 q = EC d 1 e t q t = EC d q = 1 e q t t 0.95 = 1 e t = e t 0.95 ln 0.05 = t 0.95 B&F eqn. (1.2.10) assuming 1 cm 2 t 0.95 = 1Ω = 60μs As above, assuming a 6 V potential step, now what is the average current that flows up to t 0.95? I avg = C / s = (C/V x V) / s = 20 μf x 6 V / 60 μs = 120 μc / 60 μs = 2 A! Compliance? 20μF ln 0. 05
72 Now, what response is obtained for various inputs to this circuit? Current-step galvanostatic chronopotentiometry Current step (that is, increment the current by an amount, i): E = i R + t C B&F eqn. (1.2.12) Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.9
73 Now, what response is obtained for various inputs to this circuit? Current-step galvanostatic chronopotentiometry Current step (that is, increment the current by an amount, i): E = i R + t C B&F eqn. (1.2.12) So, a constant applied current results in a linear sweep of the potential thus, what if we instead applied the potential sweep? Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure 1.2.9
74 Now, what response is obtained for various inputs to this circuit? Linear-sweep voltammetry cyclic voltammetry Potential scan (that is, ramp the applied potential, E(t) = vt for one direction): i = vc d scan rate 1 exp t R S C d B&F eqn. (1.2.15) Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure
75 Now, what response is obtained for various inputs to this circuit? Linear-sweep voltammetry cyclic voltammetry Potential scan (that is, ramp the applied potential, E(t) = vt for one direction): i = vc d scan rate 1 exp t R S C d B&F eqn. (1.2.15) ASIDE: Recall, for a potential step, the same shape q q = EC d 1 e t B&F eqn. (1.2.10) Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure t
76 Now, what response is obtained for various inputs to this circuit? Linear-sweep voltammetry cyclic voltammetry Potential scan (that is, ramp the applied potential, E(t) = vt for one direction): i = vc d scan rate 1 exp t R S C d B&F eqn. (1.2.15) So the total current envelope at any potential that is well-removed from the switching potential will be: i = 2Cv, with v s units being V/s i = 2Cv Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure
77 Now, what response is obtained for various inputs to this circuit? Linear-sweep voltammetry cyclic voltammetry This is an example of a cyclic voltammogram with clear RC charging /thesuiteworld.com*wp-includes*theme-compat*dallas-texas-scenery-5417.jpg/ i = 2Cv Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure
78 Now, what response is obtained for various inputs to this circuit? Linear-sweep voltammetry cyclic voltammetry Yuck! What can we alter experimentally to change the magnitude of the resulting capacitive current signal? /thesuiteworld.com*wp-includes*theme-compat*dallas-texas-scenery-5417.jpg/ i = 2Cv Bard & Faulkner, 2nd Ed., Wiley, 2001, Figure
79 Slow capacitive charging/discharging can convolute data/kinetics think RC Thus, minimize R u(ncompensated), R s(eries), and C d(ouble layer) by doing the following: 1. Decrease the series resistance (between the WE and RE) by a) increasing the concentration of supporting electrolyte b) increasing the polarity of solvent c) decreasing the viscosity of solvent d) increasing the temperature Move the RE tip as close as possible to the WE so that R u (between the WE and RE) is a smaller fraction of R s (between the WE and CE) 3. Decrease the electrochemically active area of the WE to decrease C d proportionally
80 Real electrochemical surface area can be approximated or taken as a ratio with the true geometric-area electrode 318 Prof. Sergio Trasatti (Università de Milano, Italy) Prof. Oleg Petrii (Moscow State University, Russia) Trasatti and Petrii, Pure & Appl. Chem., 1991, 63, 711
81 Real electrochemical surface area can be approximated or taken as a ratio with the true geometric-area electrode 319 Trasatti and Petrii, Pure & Appl. Chem., 1991, 63, 711
82 SUMMARY Properties of electrodes WE Ideally polarizable (horizontal line on J E plot), i.e. does not drive redox chemistry of/by itself (i.e. when no redox-active molecules are added) Well-defined size so that you can convert I (A) to J (A/cm 2 geom) 320 J, A non-polarizable (RE) 3E-3 2E-3 1E-3 polarizable (WE) E E, V vs. SHE -2E-3-3E-3
83 SUMMARY Properties of electrodes WE Ideally polarizable (horizontal line on J E plot), i.e. does not drive redox chemistry of/by itself (i.e. when no redox-active molecules are added) Well-defined size so that you can convert I (A) to J (A/cm 2 geom) 321 CE Polarizable and non-polarizable both have advantages and disadvantages Large why? Far from WE why? Another compartment? R Ω
84 SUMMARY Properties of electrodes WE Ideally polarizable (horizontal line on J E plot), i.e. does not drive redox chemistry of/by itself (i.e. when no redox-active molecules are added) Well-defined size so that you can convert I (A) to J (A/cm 2 geom) 322 CE Polarizable and non-polarizable both have advantages and disadvantages Large why? Far from WE why? Another compartment? RE Ideally non-polarizable Close to WE, but not too close why? Minimize ir u potential drop/loss between WE and RE Luggin Haber capillary about ~2 diameters away Correct for ir u drop electronically or manually files/e-luggin%20agcl.htm
85 Geometry and uncompensated resistance models 323 * Numbers are Ru / Ru(CE far) Myland and Oldham, Anal. Chem., 2000, 72, 3972
86 Geometry and uncompensated resistance models 324 * Numbers are Ru / Ru(CE far) Myland and Oldham, Anal. Chem., 2000, 72, 3972
87 Geometry and uncompensated resistance models 325 Myland and Oldham, Anal. Chem., 2000, 72, 3972
88 326 A review of Sections 1.2 and 1.3 RC circuits Electrochemically active surface area Uncompensated resistance Placement of electrodes, and other properties
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