View
130
Download
2
Category
Tags:
Preview:
DESCRIPTION
Characterization Technique: Voltammetry. Reading : Bard & Faulkner 1 st week: ch. 1 & ch. 2 (pp. 44-54) 2 nd week: ch. 1, ch. 3 (pp. 87-107), & ch. 6 (pp. 226-236) 3rd week: ch. 1 & ch. 13 Or the topics in any electrochemistry textbook. Current vs. reaction rate i (A) = dQ/dt (C/s) - PowerPoint PPT Presentation
Citation preview
Characterization Technique: Voltammetry
Reading: Bard & Faulkner 1st week: ch. 1 & ch. 2 (pp. 44-54)2nd week: ch. 1, ch. 3 (pp. 87-107), & ch. 6 (pp. 226-236)3rd week: ch. 1 & ch. 13
Or the topics in any electrochemistry textbook
Current vs. reaction ratei (A) = dQ/dt (C/s)Q/nF = N (mol)
n: # of electrons in reaction (2 for reduction of Cd2+)
Rate (mol/s) = dN/dt = i/nFElectrode process: heterogeneous reaction
Rate (mols-1cm-2) = i/nFA = j/nFj: current density (A/cm2)
Electrode reaction: i-E curvesPolarization: departure of the cell potential from the equilibrium potentialExtent of potential measured by the overpotential: = E - Eeq
Factors affecting electrode reaction rate and current1. Mass transfer2. Electron transfer at the electrode surface3. Chemical reactions4. Other surface reactions: adsorption, desorption, electrodeposition
Review of homogeneous kineticsDynamic equilibrium kf
O + e = R kb
Rate of the forward process vf (M/s) = kfCA
Rate of the reverse reaction vb = kbCB
Rate const, kf, kb: s-1
Net conversion rate of A & B vnet = kfCA – kbCB
At equilibrium, vnet = 0 kf/kb = K = CB/CA
*kinetic theory predicts a const conc ratio at equilibrium, just as thermodynamicsAt equilibrium, kinetic equations → thermodynamic ones→ dynamic equilibrium (equilibrium: nonzero rates of kf & kb, but equal)
Exchange velocity v0 = kf(CA)eq = kb(CB)eq
Arrhenius equation & potential energy surfaces
k = Ae–EA/RT
EA: activation energy, A: frequency factor
Transition state or activated complex→ Standard internal E of activation: ΔE‡ Standard enthalpy of activation: ΔH‡
ΔH‡ = ΔE‡ + Δ(PV)‡ ~ ΔE‡
k = Aexp(-ΔH‡/RT)
A = A′exp(ΔS‡/RT) ΔS‡: standard entropy of activation
k = A′exp[-(ΔH‡ - TΔS‡)/RT] = A′exp(-ΔG‡/RT)
ΔG‡: standard free energy of activation
Transition state theory (absolute rate theory, activated complex theory)
General theory to predict the values of A and EA
Rate constants k = κ(kT/h)e-ΔG‡/RT
κ: transmission coefficient, k: Boltzmann const, h: Planck const
Essentials of electrode reactions *accurate kinetic picture of any dynamic process must yield an equation of the thermodynamic form in the limit of equilibrium kf
O + ne = R kb
Equilibrium is characterized by the Nernst equation
E = E0′ + (RT/nF)ln(Co*/CR
*) bulk concKinetic: dependence of current on potential Overpotential η = a + blogi Tafel equation
Forward reaction rate vf = kfCO(0,t) = ic/nFACO(0,t): surface concentration. Reduction → cathodic current (ic)Backward reaction rate vb = kbCR(0,t) = ia/nFA
Net reaction rate vnet = vf – vb = kfCO(0,t) – kbCR(0,t) = i/nFA
i = ic – ia = nFA[kfCO(0,t) – kbCR(0,t)]
Butler-Volmer model of electrode kinetics Effects of potential on energy barriers Hg Na+ + e = Na(Hg)
Equilibrium → Eeq
positive potential than equilibrium
negative potential than equilibrium
One-step, one-electron process kf
O + e = R kb
Potential change from E0′ to E → energy change –FΔE = -F(E – E0′)
ΔG‡ change: α term (transfer coefficient)
ΔGa‡ = ΔG0a
‡ – (1 – α)F(E – E0′)ΔGc
‡ = ΔG0c‡ + αF(E – E0′)
kf = Afexp(-ΔGc‡/RT)
kb = Abexp(-ΔGa‡/RT)
kf = Afexp(-ΔG0c‡/RT)exp[-αf(E – E0′)]
kb = Abexp(-ΔG0a‡/RT)exp[(1 – α)f(E – E0′)]
f = F/RT
At CO* = CR
*, E = E0′
kfCO* = kbCR
* → kf = kb; standard rate constant, k0
At other potential E
kf = k0exp[-αf(E – E0′)]kb = k0exp[(1 – α)f(E – E0′)]
Put to i = ic – ia = nFA[kfCO(0,t) – kbCR(0,t)]
Butler-Volmer formulation of electrode kinetics
i = FAk0[CO(0,t)e-αf(E – E0′) - CR(0,t)e(1 – α)f(E – E0′)
k0: large k0 → equilibrium on a short time, small k0 → sluggish (e.g., 1 ~ 10 cm/s) (e.g., 10-9 cm/s)
kf or kb can be large, even if small k0, by a sufficient high potential
The transfer coefficient (α)α: a measure of the symmetry of the energy barrier
tanθ = αFE/xtanφ = (1 – α)FE/x
→α = tanθ/(tanφ + tanθ)
Φ = θ & α = ½ → symmetrical
In most systems α: 0.3 ~ 0.7
Implications of Butler-Volmer model for 1-step, 1-electron processEquilibrium conditions. The exchange currentAt equilibrium, net current is zero
i = 0 = FAk0[CO(0,t)e-αf(Eeq – E0′) - CR(0,t)e(1 – α)f(Eeq – E0′)
→ ef(Eeq – E0′) = CO*/CR
* (bulk concentration are found at the surface)
This is same as Nernst equation!! (Eeq = E0′ + (RT/nF)ln(CO*/CR
*))“Accurate kinetic picture of any dynamic process must yield an equation of thethermodynamic form in the limit of equilibrium”
At equilibrium, net current is zero, but faradaic activity! (only ia = ic)→ exchange current (i0)
i0 = FAk0CO*e-αf(Eeq – E0′) = FAk0CO
*(CO*/CR
*)-α
i0 = FAk0CO*(1 – α) CR
*α
i0 is proportional to k0, exchange current density j0 = i0/A
Current-overpotential equationDividing
i = FAk0[CO(0,t)e-αf(E – E0′) - CR(0,t)e(1 – α)f(E – E0′)]
By i0 = FAk0CO*(1 – α) CR
*α
→ current-overpotential equation i = i0[(CO(0,t)/CO
*)e-αfη – (CR(0,t)/CR*)e(1 – α)fη]
cathodic term anodic termwhere η = E - Eeq
Approximate forms of the i-η equation(a) No mass-transfer effectsIf the solution is well stirred, or low current for similar surface conc as bulk
i = i0[e-αfη – e(1 – α)fη] Butler-Volmer equation
*good approximation when i is <10% of il,c or il,a (CO(0,t)/CO* = 1 – i/il,c = 0.9)
For different j0 (α = 0.5): (a) 10-3 A/cm2, (b) 10-6 A/cm2, (c) 10-9 A/cm2 → the lower i0, the more sluggish kinetics → the larger “activation
overpotential”((a): very large i0 → engligible activation overpotential)
(a): very large i0 → engligible activation overpotential → any overpotential:“concentration overpotential”(changing surface conc. of O and R)
i0 → 10 A/cm2 ~ < pA/cm2
The effect of α
(b) Linear characteristic at small ηFor small value of x → ex ~ 1+ x i = i0[e-αfη – e(1 – α)fη] = -i0fη
Net current is linearly related to overpotential in a narrow potential range near Eeq
-η/i has resistance unit: “charge-transfer resistance (Rct)”
Rct = RT/Fi0
(c) Tafel behavior at large η i = i0[e-αfη – e(1 – α)fη] For large η (positive or negative), one of term becomes negligiblee.g., at large negative η, exp(-αfη) >> exp[(1 - α)fη]
i = i0e–αfη
η = (RT/αF)lni0 – (RT/αF)lni = a + blogi Tafel equation
a = (2.3RT/αF)logi0, b = -(2.3RT/αF)
(d) Tafel plots (i vs. η) → evaluating kinetic parameters (e.g., i0, α)
anodic cathodic
Effects of mass transferPut CO(0,t)/CO
* = 1 – i/il,c and CR(0,t)/CR* = 1 – i/il,a
to i = i0[(CO(0,t)/CO*)e-αfη – (CR(0,t)/CR
*)e(1 – α)fη]
i/i0 = (1 – i/il,c)e-αfη – (1 – i/il,a)e(1 – α)fη
i-η curves for several ratios of i0/il
Multistep mechanismsRate-determining electron transfer- In electrode process, rate-determining step (RDS) can be a heterogeneous to electron-transfer reaction→ n-electrons process: n distinct electron-transfer steps → RDS is always a one-electron process!! one-step, one-electron process 적용 가능 !!
O + ne = R→ mechanism: O + n′e = O′ (net result of steps preceding RDS) kf
O′ + e = R′ (RDS) kb
R′ + n˝e = R (net result of steps following RDS)n′ + 1 + n˝ = n
Current-potential characteristics
i = nFAkrds0[CO′(0,t)e-αf(E – Erds 0′) – CR′(0,t)e(1 – α)f(E –Erds 0′)]
krds0, α, Erds
0′ apply to the RDS
Multistep processes at equilibriumAt equilibrium, overall reaction → Nernst equation
Eeq = E0′ + (RT/nF)ln(CO*/CR
*)
Nernst multistep processesKinetically facile & nernstian (reversible) for all steps
E = E0′ + (RT/nF)ln[CO(0,t)/CR(0,t)]
→ E is related to surface conc of initial reactant and final product regardless ofthe details of the mechanism
Mass transport-controlled reactionsModes of mass transferElectrochemical reaction at electrode/solution interface: molecules in bulk solution must be transported to the electrode surface “mass transfer”Mass transfer-controlled reaction
vrxn = vmt = i/nFA Modes for mass transport: (a) Migration: movement of a charged body under the influence of an electric field (a gradient of electric potential)(b) Diffusion: movement of species under the influence of gradient of chemical potential (i.e., a concentration gradient)(c) Convection: stirring or hydrodynamic transport
Nernst-Planck equation (diffusion + migration + convection)
Ji(x) = -Di(Ci(x)/x) –(ziF/RT)DiCi((x)/x) + Civ(x)
Where Ji(x); the flux of species i (molsec-1cm-2) at distance x from the surface,
Di; the diffusion coefficient (cm2/sec), Ci(x)/x; the concentration gradient at
distance x, (x)/x; the potential gradient, zi and Ci; the charge and
concentration of species i, v(x); the velocity (cm/sec) Steady state mass transfersteady state, (C/t) = 0; the rate of transport of electroactive species is equal to the rate of their reaction on the electrode surface In the absence of migration (excess supporting electrolyte),
O + ne- = RThe rate of mass transfer,
vmt (CO(x)/x)x=0 = DO(COb – CO
s)/where x is distance from the electrode surface & : diffusion layer
vmt = mO[COb – CO
s]
where COb is the concentration of O in the bulk solution, CO
s is the
concentration at the electrod surfacemO is “mass transfer coefficient (cm/s)” (mO = DO/δ)
i = nFAmO[COb – CO
s]
i = -nFAmR[CRb – CR
s]
largest rate of mass transfer of O when COs = 0 “limiting current”
il,c = nFAmOCOb
Maximum rate when limiting current flows
COs/CO
b = 1 – (i/il,c)
COs = [1 – (i/il,c)] [ il,c/nFAmO] = (il,c – i)/(nFAmO)
COs varies from CO
b at i = 0 to negligible value at i = il
If kinetics of electron transfer are rapid, the concentrations of O and R at the electrode surface are at equilibrium with the electrode potential, as governed by the Nernst equation for the half-reaction
E = E0´+ (RT/nF)ln(COs/CR
s)E0´: formal potential (activity coeff.), cf. E0 (standard potential)
(a) R initially absentWhen CR
b = 0, CRs = i/nFAmR
COs = (il,c – i)/(nFAmO)
E = E0´- (RT/nF)ln(mO/mR) + (RT/nF)ln(il,c – i/i)i-E plotWhen i = il,c/2, E = E1/2 = E0´- (RT/nF)ln(mO/mR)E1/2 is independent of concentration & characteristic of O/R system
E = E1/2 + (RT/nF)ln(il,c – i/i)
(b) Both O and R initially presentSame method,
CRs/CR
b = 1 – (i/il,a)
il,a = -nFAmRCRb
CRs = -[1 – (i/il,a)] [ il,a/nFAmR] = -(il,a – i)/(nFAmR)
Put these equations to E = E0´+ (RT/nF)ln(COs/CR
s)
E = E0´ – (RT/nF)ln(mO/mR) + (RT/nF)ln[(il,c – i)/(i - il,a)]
When i = 0, E = Eeq and the system is at equilibriumDeviation from Eeq: concentration overpotential
Electrochemical techniques
Potential step experimentTypes of techniquesPotentiostat: control of potential
Basic potential step experiment: O + e → R (unstirred solution, E2: mass-transfer (diffusion)-limited value (rapid kinetics → no O on surface))
chronoamperometry (i vs. t)
-Series of step experiments (between each step: stirring for same initial condition)
4, 5: mass-transfer (diffusion)-limited (no O on electrode surface)) sampled-current voltammetry (i(τ) vs. E)
Potential step: E1 → E2 → E1 (reversal technique) double potential step chronoamperometry
IntroductionMost widely used technique Applying a continuously time-varying potential working electrode -oxidation/reduction reactions of electroactive species-adsorption of species-capacitive current due to double layer charging-mechanisms of reactions-identification of species-quantitative analysis of reaction rates-determination of rate constants Two forms: linear sweep voltammetry(LSV) & cyclic voltammetry(CV)
Voltammetry
Potential Sweep Methods
IntroductionLinear sweep voltammetry (LSV)
Cyclic voltammetry (CV)
Nernstian (reversible) systemsSolution of the boundary value problemO + ne = R (semi-infinite linear diffusion, initially O present) E(t) = Ei – vt Sweep rate (or scan rate): v (V/s)Rapid e-transfer rate at the electrode surface
CO(0, t)/CR(0, t) = f(t) = exp[nF (Ei - vt - E0′)/RT]
i = nFACO*(πDOσ)1/2χ(σt)σ = (nF/RT)v
Peak current and potentialPeak current: π1/2χ(σt) = 0.4463
ip = 0.4463(F3/RT)1/2n3/2ADO1/2CO*v1/2
At 25°C, for A in cm2, DO in cm2/s, CO* in mol/cm3, v in V/s → ip in amperes
ip = (2.69 x 105)n3/2ADO1/2CO*v1/2
Peak potential, Ep
Ep = E1/2 – 1.109(RT/nF) = E1/2 – 28.5/n mV at 25°C
Half-peak potential, Ep/2
Ep/2 = E1/2 + 1.09(RT/nF) = E1/2 + 28.0/n mV at 25°C
E1/2 is located between Ep and Ep/2
|Ep – Ep/2| = 2.20(RT/nF) = 56.5/n mV at °C
For reversible wave, Ep is independent of scan rate, ip is proportional to v1/2
Spherical electrodes and UMEsSpherical electrode (e.g., a hanging mercury drop)
i = i(plane) + nFADOCO*φ(σt)/r0
φ(σt): tabulated function (Table 6.2.1)
For large v in conventional-sized electrode → i(plane) >> 2nd termSame for hemispherical & UME at fast scan rate
For UME at very small v: r0 is small → i(plane) << 2nd term→ voltammogram is a steady-state response independent of v→ v << RTD/nFr0
2
r0 = 5 μm, D = 10-5 cm2/s, T = 298 K → steady-state voltammogram at v < 1 V/s r0 = 0.5 μm → steady-state behavior up to 10 V/s
Transition from typical peak-shaped voltammograms at fast v to steady-statevoltammograms at small v
cf. For potential sweep (Ch.1)Linear potential sweep with a sweep rate v (in V/s) E = vtE = ER + EC = iRs + q/Cd
vt = Rs(dq/dt) + q/Cd
If q = 0 at t = 0, i = vCd[1 – exp(-t/RsCd)]
- Current rises from 0 and attains a steady-state value (vCd): measure Cd
Effect of double-layer capacitance & uncompensated resistanceCharging current at potential sweep
|ic| = ACdv
Faradaic current measured with baseline of ic
ip varies with v1/2, ic varies with v → ic more important at faster v
|ic|/ip = [Cdv1/2(10-5)]/[2.69n3/2DO1/2CO
*]
At high v & low CO* → severe distortion of the LSV wave
Ru cause Ep to be a function of v
Totally irreversible systemsSolution of the boundary value problem kf
Totally irreversible one-step, one-electron reaction: O + e → R
i = FACO*DO1/2v1/2(αF/RT)1/2χ(bt)
χ(bt) (Table 6.3.1). i varies with v1/2 and CO*
i/FA = DO(∂CO(x, t)/∂x)x=0 = kf(t)CO(0, t)
Where kf = k0e–αf(E(t) – E0′), E(t) = Ei – vt
→ kf(t)CO(0, t) = kfiCO(0, t)ebt
Where b = αfv & kfi = k0exp[-αf(Ei – E0′)]
For spherical electrodesi = i(plane) + FADOCO*φ(bt)/r0
Peak current and potentialMaximum χ(bt) at π1/2χ(bt) = 0.4958Peak current
ip = (2.99 x 105)α1/2ACO*DO
1/2v1/2
n-electron process with RDS: n in right side
Peak potentialα(Ep – E0′) + (RT/F)ln[(πDOb)1/2/k0] = -0.21(RT/F) = -5.34 mV at 25°C
Or Ep = E0′ - (RT/αF)[0.780 + ln(DO
1/2/k0) + ln(αFv/RT)1/2]|Ep – Ep/2| = 1.857RT/αF = 47.7/α mV at 25°C
Ep: ftn of v → for reduction, 1.15RT/αF (or 30/α mV at 25°C) negative shift for tenfold increase in v
ip = 0.227FACO*k0exp[-αf(EP – E0′)]
→ ip vs. Ep – E0′ plot at different v: slope of –αf and intercept proportional to k0
n-electron process with RDS: n in right side
i-E curve (CV) at different Eλ
(1) Eλ (1) E1/2 – 90/n, (2) E1/2 – 130/n, (3) E1/2 – 200/n mV, (4) after ipc → 0
ipa/ipc = 1 for nernstian regardless of scan rate, Eλ (> 35/n mV past Epc), D
ipa/ipc → kinetic informationIf actual baseline cannot be determined,
ipa/ipc = (ipa)0/ipc + 0.485(isp)0/ipc + 0.086
Reversal charging current is same as forward scan, but opposite sign
ΔEp = Epa – Epc ~ 2.3RT/nF (or 59/n mV at 25°C)
Quasi-reversible system
Kinetics +oxidation/reduction
v irreversibility , peak current , separation anodic and cathodic peaks
Adsorbed species
Adsorption of reagent or product on electrode voltammetric wave modified
Reversible reaction of adsorbed species O and R
Ip,c = (-n2F2vAO,i/4RT)
where O,i is surface concentration of adsorbed O. the same Ip magnitude for
oxidation
Ep = E0’ – (RT/nF)ln(bO/bR)
bO and bR: the adsorption energy of O and R
The value of Ep is the same for oxidation and reduction
Cyclic voltammogram for a reversible system of species adsorbed on the electrode
Multi component systemsVarious voltammetric waves appear
Cyclic votammogram in the investigation of systems of more than one component
Thin layer cellReversible: peak current v, no separation between anodic and cathodic peaks, total symmetric Ep
Irreversible:
Shape of the cyclic voltammogram obtained in a thin-layer cell for a reversible system
Electric charge (=amount of electricity) Q (unit: Coulomb, C), time tElectric current (unit: ampere (A)):
I = dQ/dt
Q = Idt
Current density (unit: A/m2): i = I/A,
A: surface of area
Charge calculation
Hads → H+ + e-
Effect of adsorption of electroinactive species→ such adsorption inhibit (or poison) an electrode reaction or accelerate the
electrode reaction (e.g., hydrogen or oxygen)k0 = kθ=0
0(1 – θ) + kc0θ
Where kθ=00 is the standard rate const at the bare surface & kc
0 that at the filmed portions
For completer blockage by the film, kc0 = 0
For catalysis by the filmed area, kc0 > kθ=0
0
Effect of adsorbed substancesHydrogen & oxygenCO & organics
CV of Pt Single Crystals
Current – potential curves for a Ta/Ta2O5 electrode in 0.1M TBAP/MeCN
Electronic Structure using CV
CV of Au (111) CV of Pt (111) in H2SO4
0.1 mM H2SO4 (10 mV/S)
1.0 mM CuSO4/0.1 mM H2SO4 ( 2 mV/s)
Cu electrodeposition
Cyclic Voltammograms of 316 SS
-1.25 V : Fe reduction (Fe3+ to Fe2+)-0.6 V : Cr reduction (Cr6+ to Cr3+) -0.8 V : Fe oxide formation (active to passive transition)0 V : Trnspassive behavior of SS0.3 V : Cr oxidation to Cr6+
In vivo applications of CVe.g., rat brain
ascorbic acid oxidation in rat brain
Recommended