Report

Potential Sweep Methods 2-25-2014 Linear Potential Sweep Voltammetry Ox + ne– ⇄ Red E (V) (-) E(t) = Ei – vt At Ei nonfaradaic current COx , CRed (M) COx* Increasing time at |E| < |E0'| More negative E at |E| > |E0'| t (s) i (A) - Supporting electrolyte present in excess to minimize migration. - Solution unstirred to min. convection. - O2 is removed by bubbling N2. - Stationary electrodes: HDME, graphite, Pt, etc. Distance from Electrode (cm) (+) v ranges from 10 mV s-1 to ~1000 V s-1 for conventional electrodes; up to 106 V s-1 for UMEs. ip ip/2 E (V) Ep/2 Ep (-) Cyclic Voltammetry COx* E (V) (-) Distance from Electrode (cm) (+) Distance from Electrode (cm) El Ox + ne– Red ip,c Ox – ne– Red ip,a i (A) COx , CRed (M) COx , CRed (M) COx* DEp E (V) E0' (-) Ei 0 t (s) l - Reversal technique analogous to double-potential step methods. - Experiment time scale: 103 s to 10-5 s. - For reversible electron transfer: - DE = |Ep,a – Ep,c| = 59 mV/n - |Ep – Ep/2| = 57 mV/n - ip,a/ip,c = 1 El Derivation of i-E relationship: Description of system and conditions O + ne– ⇄ R (Assume semi-inf linear diff & only O initially present at potential Ei where no faradaic reaction occurs, rapid electron transfer) CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] E(t) = Ei – vt Time dependence makes Laplace transform complicated. Rewrite boundary condition (Nicholson & Shain): CO(0,t) / CR(0,t) = q e –st = q S(t) We want to determine the i-E relationship. Since E is linearly related to t, we first find the i-t relationship. Recall that current is proportional to flux at the electrode surface. Review of i-t derivation strategy O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) Recall Fick’s 2nd Law: CR(x,t) / t = DR 2CR(x,t) / x2 CO(x,t) / t = DO 2CO (x,t) / x2 CO(x,0) = CO* CR(x,0) = 0 limx CO(x,t) = CO* limx CR(x,t) = 0 Recall Laplace Transform: () = ∞ − 0 ∞ () = ′() = − = / = = (s) 0 ∞ − ′ 0 = − 0 + (s) 2 () 2 = − ′ 0 − 0 + 2 (s) L{CO(x,t) / t} = L{DO 2CO(x,t) / x2} − (, 0) + , = 2 (, ) 2 Solving Laplace transform differential equation for concentration profile O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) − ∗ 2 (, ) − , 0 − , = = 2 − (, 0) + , = 2 (, ) 2 To solve, consider the analogous equation: 2 () − 2 = − 2 2 ′ 2 − 0 − 0 − = −/ − + 2 0 + ′(0) ′ ′ ′ = = + + ( + )( − ) + − Find C(x) by inverse Laplace Notice D’ = b/a2 ′ − = ∞ − ′ − = 0 −1 () = = −1 ∞ 0 ′ − + ′ = + ′ ′ ′ −1 −1 + + = ′ − + ′ + /2 + − Application of boundary conditions O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) − ∗ 2 (, ) − , 0 − , = = 2 CO(x,t) / t = DO 2CO (x,t) / x2 2 () − + 2 0 + ′(0) ′ ′ ′ 2 − = − = = + + ( + )( − ) + − 2 −1 () = = ′ − + ′ + /2 , = ′ − / + ′ Recall Boundary conditions: CO(x,0) = CO* limx CO(x,t) = CO* , = ′ − lim , = ∗ / →∞ / + ∗ / / + ∗ / CR(x,0) = 0 limx CR(x,t) = 0 , = ′ − / Determining coefficients for concentration profile O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) Flux balance: (, ) , = ′ − ′ − 1 1 2 2 − ′ , = ′ − / + =0 + ∗ / 1 1 2 2 / (, ) =0 =0 , = ′ − / B’ = –A’x ; x = (DO/DR)(1/2) =0 + ∗ / , = ′ − / For any i-E experiment For reversible system (potential step): q = CO(0,t) / CR(0,t) = exp[n F (E – E0’) / (R T)] ∗ + ′ = −′ 0, = 0, Current-time function for potential step O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) , = ′ − ∗ / + , = ′ − For reversible system: ∗ ′ = − (1 + ) ∗ + ′ = −′ q = CO(0,t) / CR(0,t) = exp[n F (E – E0’) / (R T)] ∗ , = − − (1 + ) ∗ / + Consider Flux: (, ) − 0, = = x = (DO/DR)(1/2) ∗ , = − (1 + ) = =0 / 1/2 ∗ 1 2 (1 + ) = / 1/2 ∗ 1 1 2 2 (1 + ) Concentration profile coefficients for potential sweep O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) , = ′ − ∗ / + , = ′ − / For reversible system (Potential Sweep): CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] CO(0,t) / CR(0,t) = q e –st = q S(t) s = n F v/ (R T) q = exp[n F (E – E0’) / (R T)] Consider Flux: (, ) − 0, = = = 1 1 ′ − 2 2 =0 (, ) = =0 ′ = − −′ 1/2 1/2 1 1 2 2 Concentration-time function at electrode surface for potential sweep O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) For Potential Sweep: ∗ , = ′ − / + ∗ 0, = − 1 1+ 2 2 −1 Convolution integral: ′ 0, − 0 0, = − −1 1 1 2 2 ∗ − 1 1 2 −1 −1 () = F t ∗ G(t) = ∗ = 0, = =− 1 1 2 2 () = f t ∗ g(t) = − 0 −1 1 2 ∗ = − 1 1 2 0 1 −2 − 1 −2 Application of boundary conditions to general concentration integral equations for potential sweep O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) For Potential Sweep: ∗ 0, = − 0, = ∗ 1 1 1 2 2 0 −1/2 − ( ) − − − 1 2 1 − 2 0 f(t) = i(t) / (n F A) −1/2 0, = ( ) − − 1 2 0 General equations for potential sweep (electrode kinetics/boundary conditions not yet considered) For reversible system (Potential Sweep): CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] q = exp[n F (E – E0’) / (R T)] CO(0,t) / CR(0,t) = q e –st = q S(t) s = n F v/ (R T) Using boundary conditions to find i-t relationship (reversible systems) O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) 0, = ∗ −1/2 − ( ) − − 1 2 0 −1/2 0, = ( ) − − 1 2 0 f(t) = i(t) / (n F A) For reversible system (Potential Sweep): CO(0,t) / CR(0,t) = q e –st = q S(t) CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] s = n F v/ (R T) q = exp[n F (E – E0’) / (R T)] − 0 ( )−1/2 − 1 2 0, = = ( )−1/2 0, = 1 −2 () 0, − 1 2 () = ∗ − 0, ( )−1/2 ∗ − 0, 0, = ∗ ∗ 1 −2 1 −2 () + ∗ 1 −2 () Using boundary conditions to find i-t relationship (reversible systems) O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) For reversible system (Potential Sweep): CO(0,t) / CR(0,t) = q e –st = q S(t) CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] − − 1 2 0 0, = ∗ 1 −2 − 0 0, = = ( )−1/2 1 −2 () + 1 −2 1 −2 () 0, − 1 2 () − = 1 −2 0 ∗ 1/2 1/2 = + 1 Solution gives i(t) i(E). Closed-form solution cannot be obtained, must use numerical methods. ∗ − 0, ( )−1/2 ∗ = 1 −2 + x = (DO/DR)(1/2) f(t) = i(t) / (n F A) 1 −2 () i(t) to i(E) (reversible systems) O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) For reversible system (Potential Sweep): − 1 −2 0 ∗ 1/2 = + 1 x = (DO/DR)(1/2) 1/2 s t = n F v t/(R T) = n F (Ei – E)/(RT) f(t) = i(t) / (n F A) q = exp[n F (E – E0’) / (R T)] Change from i(t) i(E). − 1 −2 = 0 0 − 0 1 −2 −1/2 − 1 − 2 ∗ 1/2 1/2 = + 1 f(t) = g(st); z = st 0 () − 1 = 2 1 + 1 i(E) in sweep experiments (reversible system) O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) For reversible system (Potential Sweep): − 1 − 2 −1/2 0 ∗ 1/2 1/2 = + 1 q = exp[n F (E – E0’) / (R T)] f(t) = i(t) / (n F A) = x = (DO/DR)(1/2) () 1 1 = + 1 2 f(t) = g(st); z = st 0 − ∗ () () = ( )1/2 ∗ ( )1/2 i = n F A CO* (p DO s)1/2 c(s t) (6.2.17) s t = n F v t/(R T) = n F (Ei – E)/(RT) c(st) is a pure number for any given t. Equations for peak current i = n F A CO* (p DO s)1/2 c(s t) (6.2.17) s t = n F v t/(R T) = n F (Ei – E)/(RT) For reversible charge transfer at 25o C: p 1/2c (st) reaches maximum of 0.4463 when n (E – E1/2) is –28.5 mV (Table 6.2.1). Randles–Sevčik Eqn (6.2.19): ip = (2.69 x 105) n3/2 A DO1/2 CO* v1/2 E1/2 = E0’ + (R T) ln(DR/DO)1/2/ (nF) ip / (CO* v1/2) = constant (current function) ip (A) (+) Steady-state current (e.g. RDV) i (A) v v1/2 (V1/2 s-1/2) E1/2 E (V) (-) Depletion of O near electrode More on peak shape (reversible systems) Depletion of O near electrode v i (A) i (A) (+) Equal O, R: i ~0.852ip Recall Cottrell Eqn for E-step (5.2.11): i(t) = n F A DO1/2 CO* / (p t)1/2 E1/2 E (V) t (s) (-) (+) Ep = E1/2 – 28.5/n mV Ep/2 = E1/2 + 28.0/n mV i (A) For reversible charge transfer at 25o C: ip ip/2 E (V) Ep/2 Ep (-) LSV with spherical electrodes and UMEs i = n F A CO* (p DO s)1/2 c(s t) + n F A DO CO* f(s t) / r0 i (spherical correction) i (plane) s t = n F v t/(R T) = n F (Ei – E)/(RT) i (A) (+) Spherical term dominates if v << R T D / (n F r02) If 0.5 mm radius, D = 10-5 cm2/s, T = 298 K, steady state up to 10 V/s. v E (V) (-) Double-layer C and uncompensated R During potential step experiment (stationary, constant A electrode), charging current disappears after few RuCd (time constant). In potential sweep, ich always flows. ℎ = + − − Section 1.2.4. in B&F Recall Randles–Sevčik Eqn (6.2.19): ip = (2.69 x 105) n3/2 A DO1/2 CO* v1/2 |ich| = A Cd v Limit for max useful scan rate and min concentration Also: EWE = Eapp + iR ich more important at high v. v = 100a i (A) i (A) ip ich E (V) (-) ich E (V) v = 900a ip ip i (A) v=a (+) x 40 (+) x 20 (+) x 1 |ich| / ip = Cd v1/2 (10-5) / (2.69 n3/2 DO1/2 CO*) (-) ich E (V) (-) Irreversible e– transfer (boundary condition) O + ne– ⇄ R (Assume semi-inf linear diff, only O initially present, and rapid charge-transfer kinetics) Recall boundary condition for reversible system (Potential Sweep): CO(0,t) / CR(0,t) = q e –st = q S(t) CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] And the general concentration equations: 0, = ∗ −1/2 − ( ) − − 1 2 0 −1/2 0, = ( ) − − 1 2 0 f(t) = i(t) / (n F A) Led to: i = n F A CO* (p DO s)1/2 c(s t) (6.2.17) kf O + R (Assume semi-inf linear diff, only O initially present, and totally irreversible, one-electron, one-step) The corresponding boundary condition is: e– (, ) − 0, = = =0 = () (0, ) Sec. 5.5 in B&F = 0 − −0′ Irreversible e– transfer i(E) kf O + R (Assume semi-inf linear diff, only O initially present, and totally irreversible, one-electron, one-step) The corresponding boundary condition is: e– (, ) − 0, = = = () (0, ) = 0 − =0 f = F / (R T) And the general concentration equations: 0, = ∗ −1/2 − ( ) − 0 − 1 2 −0′ −1/2 0, = ( ) − − 1 2 0 f(t) = i(t) / (n F A) Leads to: i = F A CO* (p DO v)1/2 [(a F) / (R T)]1/2 c(bt) Compare to Reversible: i = n F A CO* (p DO s)1/2 c(s t) (6.3.6) (6.2.17) b=afv a transfer coefficient Equations for peak current (irreversible) i = F A CO* (p DO v)1/2 [(a F) / (R T)]1/2 c(bt) One-step, one-electron (6.3.6) For irreversible charge transfer at 25o C: p 1/2c (bt) reaches maximum of 0.4958 (Table 6.3.1). Peak current (6.3.8): ip = (2.99 x 105) n (ana)1/2 A DO1/2 CO* v1/2 Compare to (6.2.19): ip = (2.69 x 105) n3/2 A DO1/2 CO* v1/2 0<a<1 (+) Since ana always < n, ip, irrev smaller than ip, rev. Don’t forget: EWE = Eapp + iR Reversible reaction can appear irreversible if iR drop not compensated! Min by using 3electrode cell, positive feedback compensation at v > 1 V/s, consider UME i (A) na is the number of electrons involved in the rate-limiting step. E (V) E0' (-) Peak shape for irreversible system i = n F A CO* (p DO v)1/2 [(a F) / (R T)]1/2 c(bt) (6.3.6) Peak current (6.3.8): ip = (2.99 x 105) n (ana)1/2 A DO1/2 CO* v1/2 Compare to (6.2.19): ip = (2.69 x 105) n3/2 A DO1/2 CO* v1/2 |Ep – Ep/2| = 48/(a na ) mV 0<a<1 |Ep – Ep/2| = 57/n mV Irreversible peak is broader and smaller than reversible peak. As a decreases, peak widens and decreases in magnitude. 1/2 0′ = − 0.78 + ln 0 + ln 1/2 i (A) (+) Compare to reversible: Unlike reversible, Ep is a function of scan rate for irreversible. Ep shifts more negative for reduction by 30/(a na) m V at 25oC for each 10-fold increase in scan rate. E (V) E0' (-) Quasireversible e– transfer (boundary condition) Recall boundary condition and i(E) relationship for reversible system (Potential Sweep): CO(0,t) / CR(0,t) = q e –st = q S(t) CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] i = n F A CO* (p DO s)1/2 c(s t) (6.2.17) And the boundary condition and i(E) relationship for the totally irreversible system: − 0, = (, ) = = () (0, ) =0 i = F A CO* (p DO v)1/2 [(a F) / (R T)]1/2 c(bt) = 0 − − 0′ f = F / (R T) (6.3.6) Now consider reactions where electron transfer limitations make consideration of the reverse reaction necessary (quasireversible – Matsuda and Ayabe): kf – O + e ⇄ R (Assume semi-inf linear diff, only O initially present, one-electron, one-step) The corresponding boundary condition is: kb (, ) − 0, = = = 0 − =0 − 0′ 0, − (0, ) − 0′ Quasireversible e– transfer equations Now consider reactions where electron transfer limitations make consideration of the reverse reaction necessary (quasireversible – Matsuda and Ayabe): kf – O + e ⇄ R (Assume semi-inf linear diff, only O initially present, one-electron, one-step) kb The corresponding boundary condition is: (, ) − 0, = = 0, = ∗ −1/2 − ( ) = 0 − 0, − (0, ) − 0′ =0 − 0 − 0′ − 1 2 −1/2 0, = ( ) − − 1 2 0 Matsuda and Ayabe showed peak shape and characteristics to be function of a and parameter L: Λ= i = F A CO* (DO v)1/2 [F/ (R T)]1/2 Y(E) 0 1− 1/2 (6.4.5) Quasireversible, reversible, irreversible Now consider reactions where electron transfer limitations make consideration of the reverse reaction necessary (quasireversible – Matsuda and Ayabe): Matsuda and Ayabe showed peak shape and characteristics to be function of a and parameter L: 0 Λ= 1/2 1− i = F A CO* (DO v)1/2 [F/ (R T)]1/2 Y(E) (6.4.5) kf O + e– ⇄ R kb i = n F A CO* (p DO s)1/2 c(s t) (6.2.17) i = F A CO* (p DO v)1/2 [(a F) / (R T)]1/2 c(bt) (6.3.6) Y(E) is shown in Fig. 6.4.1. L > 10, behavior of Y(E) approaches that of reversible system. System |Ep – Ep/2|at 25oC (mV) Reversible 57/n Irreversible 48/(a na ) Quasireversible 26D(L, a) L ≥ 10, D(L, a) ≈ 2.2 |Ep – Ep/2| ≈ 57 L < 10-2 & a = 0.5, D(L, a) ≈ 3.7 |Ep – Ep/2| ≈ 96 Scan rate and kinetics System |Ep – Ep/2|at 25oC (mV) Reversible 57/n Irreversible 48/(a na ) Quasireversible 26D(L, a) L ≥ 10, D(L, a) ≈ 2.2 |Ep – Ep/2| ≈ 57 L < 10-2 & a = 0.5, D(L, a) ≈ 3.7 |Ep – Ep/2| ≈ 96 Depending on L (v), a system may show rev, quasirev or irrev behavior. Appearance of kinetic effects depends on time window of experiment. At small v (long t) rev, while at large v (short t) irrev. For n = 1, a = 0.5, T = 25oC, and D = 10-5 cm2/s with L ≈ k0/(39 D v)1/2 Matsuda and Ayabe suggested Reversible: L ≥ 15 ; k0 ≥ 0.3v1/2 cm/s Quasireversible: 15 ≥ L ≥ 10 –2(1+a) ; 0.3v1/2 cm/s ≥ k0 ≥ 2 x 10-5 v1/2 cm/s Totally irreversible: L ≤ 10 –2(1+a) ; k0 ≤ 2 x 10-5 v1/2 cm/s Increased v makes rxn more difficult (broader wave, shifted negatively for reduction) Also need fast recorder < 0.5 V s-1 ; computer or oscilloscope > 0.5 V s-1 iR compensation as iR drop distorts linear input ramp of potential sweep EWE = Eapp + iR Cyclic Voltammetry COx* E (V) (-) Distance from Electrode (cm) (+) Distance from Electrode (cm) El Ox + ne– Red ip,c Ox – ne– Red ip,a i (A) COx , CRed (M) COx , CRed (M) COx* DEp E (V) E0' (-) Ei 0 t (s) l - Reversal technique analogous to double-potential step methods. - Experiment time scale: 103 s to 10-5 s. - For reversible electron transfer: - DE = |Ep,a – Ep,c| = 59 mV/n - |Ep – Ep/2| = 57 mV/n - ip,a/ip,c = 1 El (-) Cyclic Voltammetry (boundary value problem) El E (V) 0, = ∗ − ( ) Ei 0 t (s) −1/2 0, = ( ) l −1/2 − − 1 2 0 − − 1 2 0 f(t) = i(t) / (n F A) (0 < t ≤ l) E = Ei – vt (t > l) E = Ei – 2vl + vt (0 < t ≤ l) CO(0,t) / CR(0,t) = exp[n F (Ei – vt – E0’) / (R T)] q = exp[n F (E – E0’) / (R T)] CO(0,t) / CR(0,t) = q e –st = q S(t) s = n F v/ (R T) (t > l) CO(0,t) / CR(0,t) = exp[n F (Ei – 2vl + vt – E0’) / (R T)] CO(0,t) / CR(0,t) = q e st – 2sl = q S(t) Shape of curve on reversal segment dependent on El! (+) ip,c El1 CV curve shape El2 Shape of curve on reversal segment dependent on El! (isp)0 ip,a i (A) (ip,a)0 El E (V) , , = , , 0 + - For reversible electron transfer: ip,a/ip,c = 1 - regardless of v and El if El > 35/n mV past Ep,c and D, but must measure ip,a from decaying cathodic current. (-) 0.485 , If El is > 35/n mV beyond Ep,c, peak shape generally the same, like forward segment but plotted in opposite direction. 0 + 0.086 Suggestion by Nicholson if actual baseline for measuring ip,a cannot be determined. Also consider: allowing current to decay to nearly zero then performing reverse sweep. Don’t forget charging current: peak must be measured from proper baseline. |ich| = A Cd v Real experiments: ip measurement imprecise due to uncertainty in correction for charging current, definition of baseline. CV not ideal for quantitative properties reliant on ip (concentration, rate constants), but offers ease of interpreting qual and semi-quan behavior. CV curve shape (+) ip,c El1 ip,a El2 (isp)0 i (A) (ip,a)0 El E (V) (-) Shape of curve on reversal segment dependent on El! If El is > 35/n mV beyond Ep,c, peak shape generally the same, like forward segment but plotted in opposite direction. DEp is a slight function of El, but always close to 59/n mV (25oC). Repeated cycling steady state (decreased ip,c and increased ip,a) DEp = 58/n mV (25oC). CV curve shape (quasirev) Recall for quasirev: = 0 1− = −1/2 1/2 /2 0 = 1/2 y (at 25oC) DEp (mV) 20 61 5 65 2 72 0.5 105 0.25 141 DEp is a function of v, k0, a, and El. If El is 90/n mV beyond peak, El effect is small. 0.3 < a < 0.7, DEp nearly ind of a, only depends on y (Nicholson method) Variation of DEp with v y estimate k0 Beware of uncomp R: ipRu must be small. Effect of Ru most important when currents large and k0 rev limit (DEp only slightly diff from rev value) Multicomponent or multistep charge transfer (-) (+) Other strategies: O' + n'e- (-) Notice i’p must be measured from decaying current of first wave. i (A) Assume current decays as t-1/2 to get baseline. Recall Cottrell Eqn for E-step (5.2.11): i(t) = n F A DO1/2 CO* / (p t)1/2 t (s) (-) E (V) R' E (V) i'p E (V) R i (A) O + ne- Reestablish init. cond. then go through with full scan Hold E ~60/n mV beyond Ep to get more accurate baseline t (s) Stop scan for 20-50 seconds, allow current to decay. Requires convection-free conditions. t (s) Consider difference between CV and steady-state voltammetry, pulse voltammetry methods. Multistep charge transfer and wave order problem (+) Mulitstep (O + n1e R1, then R1 + n2e R2) similar to two component, but shape depends on DE0 = E20 – E10, reversibility of each step, n1 and n2. R i (A) O + ne- i'p O' + n'e- E (V) R' (-) -100 mV < DE0 < 0 single broad wave Ep ind of scan rate DE0 = 0 single peak with ip between ip(1e), ip(2e) and Ep – Ep/2 = 21 mV DE0 > 180 mV, 2nd easier than 1st single wave characteristic of 2e reduction DE0 = –(2RT/F)ln2 = –35.6 mV (25oC), no interaction between R and O observed wave has shape of one-e transfer (consider redox polymer with k noninteracting centers: –(2RT/F)ln k) DE0 more positive than –(2RT/F)ln2 2nd e transfer assisted by first (+) Coupled chemical reactions and CV shape O + ne ⇄ R k i (A) R + Z R-Z (not electroactive) E (V) (+) (-) O + ne ⇄ R k i (A) R+ZO+P E (V) (-) Cases involving adsorption See Wopschall & Shain Anal. Chem. 1967, 39: 1514-1542 O+eR Osoln I Rsoln Rads I Oads G Rxn coord O weakly adsorbed V Post-wave DG = -nFE R weakly adsorbed Adsorption stabilizes species (lower G), otherwise wouldn’t occur spontaneously V Pre-wave Osoln G O strongly adsorbed Oads Rsoln Rads Rxn coord R strongly adsorbed Variation of CV shape w/ scan rate (V) (single charge-transfer events) I. II. Reversible charge transfer (er): O + ne- ⇄ R − Irreversible charge transfer (ei): + → III. Rev Chem rxn preceding rev ct (crer): ⇄ ; + − ⇄ − IV. Rev Chem Rxn preceding irrev ct (crei): ⇄ ; + → V. Rev ct followed by rev chem rxn (ercr): + − ⇄; ⇄ − VI. Rev ct followed by irrev chem rxn (erci): + ⇄; → ′ VII. Catalytic rxn w/ rev ct (erci’): + ⇄; + → − ′ VIII. Catalytic rxn w/ irrev ct (eici’): + → ; + → − Reprinted with permission from Nicholson & Shain, Anal. Chem. 1964, 36: 706-723. Copyright 1964 American Chemical Society. Linear sweep methods • Signal shape can depend on electrode size, v, k0, a, El • Good for qualitative or semi-quantitative description of system based on ip, DEp • Experimental data compared to mathematical models • ip measurement complicated by baseline correction – ich, iR drop, reversal baseline – mathematical corrections, additional experiments • High scan rates: quasireversible behavior, large iR effect • Detection limit ~10-6 or 10-7 M at best