Electrochemistry Lecture 2 Voltammetry CHE 729

Voltammetry

Dr. Wujian Miao

Reference Books

Electrochemical Cell

 Working electrode: place where redox occurs, surface area few mm2 to limit current flow.  Reference electrode: constant potential reference  Counter (Auxiliary) •Supporting electrolyte: electrode: inert alkali metal salt does not material, plays no part react with electrodes but in redox but completes has conductivity circuit

1 Electrochemical Instrumentation

Voltammetry

 Electrochemistry techniques based on current (i) measurement as function of

voltage (Eappl)  Voltammetry — Usually when the working electrode is solid, e.g., Pt, Au, GC.  Polarograph — A special term used for the voltammetry carried out with a (liquid) MURCURY electrode.  Voltammogram — The plot of the electrode current as a function of potential.

Linear sweep voltammetry

 The potential is varied linearly with time with sweep rates v ranging from 10 mV/s to about 1000 V/s with conventional electrodes and up to 106 V/s with ultramicroelectrodes (UMEs).

 It is customary to record the current as a function of potential, which is equivalent to recording current versus time.

 Linear sweep voltammetry, linear scan voltammetry (LSV), or linear potential sweep chronoamperometry.

2 X = 0 x = 0

x = ∞ (“bulk”)

(Ox + ne  Red) (reversible)

Linear Sweep/Scan Voltammetry

Peak-shaped i~E profile

For A + e = A- reversible reaction, E0(A/A-) = E0 (1) E >> E0, i ~ 0 (2) E = E0 + dE, i >> 0, increases (3) E = E0, i >> 0, [A] = [A-] =[A*]/2

0 (4) E = E - 28.5 mV, i  maximum, [A]x =0 ~ 0.25[A*] (5) E << E0, i >> 0, decreases, as the depletion effect

AAe  RT [A] EE0 ln nF [A ] 0  where EE , [A] = [A ]x0

DigiSim demonstration

3 Cyclic Voltammetry （CV）

 Potential: E(t) = Ei - t (V), 0 < t 

E(t) = Ei -2 + t (V), t > 

 CV is not an ideal method for quantitative evaluation of system properties. It is powerful in qualitative and semi- quantitative reaction behavior. DigiSim demonstration 10

Cyclic Voltammetry- i vs time

DigiSim demonstration 11

NERNSTIAN (REVERSIBLE) SYSTEMS

Semi-infinite linear diffusion, only O exist initially LSV: potential changes linearly at a sweep rate of v (\//s)

 Nernst equation nF Ct(0, )  Et() E0' ln O RT CR (0, t ) Ct(0, ) nF O 0'   exp (EtEi  ) St ( ) CtR (0, )  RT t 0' St() e ,  =( nFRTv / ); exp( nFRTE / )(i E )

4 Mass Transfer/Transport

For a Nernst process:

vvinFArxnmt/ flux () J

vrxn : net rate of electrode reaction

vmt : rate of mass transfer iA: current; : area of electrode J unit : mole cm-2 s-1

iiiitotald m c

If use short times ( < 10 s) and don’t stir (quiescent),

then itotal = id + im

Nernst-Planck Equation (governing the mass transport to an electrode)

 x F x x   C i  zi   x J i Di x RT Di C i x C i

Diffusion Migration Convection

-2 -1 Ji(x) = flux of species i at distance x from electrode (mole cm s ) 2 Di = diffusion coefficient (cm /s) Ci(x)/x = concentration gradient at distance x from electrode (x)/x = potential gradient at distance x from electrode (x) = velocity at which species i moves (cm/s)

“-”: flux direction opposites the concentration gradient change

5 If We Use High Concentration of Good Electrolyte in Quiescent Solution...

Nernst-Planck Equation reduces to... Fick’s First Law

• Flux of substance is proportional to its concentration gradient:

  xt,  i xt, C o  J 0 D o x nFA

i.e., flux  concentration gradient

LSV Reversible System

After the Laplace transformation and a series of mathematical treatments of the diffusion equations:

((/))  nF RT 

where  ( t ) is a pure number at any given point and can be solved numerically. 𝜒 [“kai”]

Excel Calculation of t

My Excel calculation 0.446295

6 0.5

t) 0.45 0.4 

 0.35  0.3 0.25 0.2 0.15 0.1 0.05 0 200 100 0 -100 -200

n(E-E1/2) (mV)

Reversible system

0 { ( tnEEmV )}max  0.4463 when ( - ) 28.5

Peak current and potential

 Peak current ip 3 F 1/2 3/2 * 1/2 1/2 inACDp  0.4463( ) OO 1/2 RT ivp 5 3/2 * 1/2 1/2  = (2.69 10 )nACDOO at 25 C. Units: Amperes, cm^2, cm^2/s, mol/cm^3, V/s

 Peak potential Ep

EEp1/228.5 / n (mV) atC 25 

0' 1/2 EERTnFDD1/2 (/)ln(/)RO

 Ep is independent of scan rate.

7 E0’ oR ne  (A) i  EEp1/21.109 RTnF /  28.5/ n mV@ 25 C  EEp/2 1/21.109 RTnFE /  1/2 28.5/ n mV@ 25 C Current

0'RT DR 1/2 0' EE1/2 ln( )  E nF Do

E (mV, vs. ref electrode)

 |EEpp/2 | 2.22 RTnF /  57.0/ n mV@ 25 C 1/2 Efvifvpp( ) ( )

Cyclic Voltammetry

Cyclic Voltammograms for a Reversible Reaction

 iipc/ pa 1.0 RT  (EE  )  2(1.109 ) pa pc nF  57 mV/n at 25o C (independent of the scan rate) 0'  EEE = (pa pc )/2 3/2 1/2 * 1/2  inADcvp = constant oo (at 25o5 C, constant = 2.69 10 )

8 Diffusion Controlled Reversible Process

For electrode adsorption process

ivp 

Peak separation potentials, although close to 57 mV, are slightly a function of switching potentials.

Reversibility of Electrochemical System Can be Changed via the Change of Scan Rate

/lamda At small v (or long times), systems may yield reversible waves, while at large v (or short times), irreversible behavior is observed.

f = nF/RT

9 Electron Transfer Rate k 0 0 kEi , pp ,

Totally Irreversible System

(NO Reversal Peak)

CV Applications in Diagnosing Chemical Reaction Mechanisms

EC Reaction (Electron Transfer followed by A Chemical Reaction

10 EC Reaction: Scan Rate Dependent

(a) At Fast Scan Rate (b) At Slow scan Rate

ECE Process

OR ST OR

(2nd ST)

(ST)

 T S TS

(a) S is more difficult to reduce (b) S is easier to reduce than O (i.e., E0’ < E0’ ) 0 0 S O than O (i.e., E ’S > E ’O) 32

Multi-step Systems

 0  O+n1e  R1 (E1 )  0 R1 +n2e  R2 (E2 ) 0 0 0  E =E2 -E1

E 0 (2RT / F )ln2  36 mV The CV looks the same as one electron-transfer process.

E0: (a) -180 mV; (b) -90 mV; (c) 0 mV; (d) 180 mV.

11 Ohmic Potential, IR Drop

• Potential change (drop) due to electrochemical solution resistance

• Eir = IR I—current of the electrochemical cell, R—resistance of the electrolyte solution.

•Ecell = Ecathode-Eanode-IR

• Question: In electrochemical study, an inert electrolyte is always added to the analyte solution. Why?

A + e = B A R = 10 Ohm R = 0 Ep = 100 mV Ep = 58 mV

cA =1 mM 50 mV/s Area = 1 cm2

Faradaic and Nonfaradaic Processes Faradaic • Charges or electrons are transferred across the electrode|electrolyte interface as a result of electrochemical reactions • Governed by Faraday’s law

QnFN A where n = # of e transfered F = Faraday constant (96, 485 C/mol)

NA = # of moles of electroactive species dQ dN inF A dt dt

12 Nonfaradaic Process • Charges associated with movement of electrolyte ions, reorientation of solvent dipoles, adsorption/desorption of species, etc. at the electrode|electrolyte interface. • Changes with changing potential and solution composition • Charges do not cross the interface but external currents can still flow • Regarded as “background current”

Nonfaradaic Processes and the nature of electrode|electrolyte interface; the Double layer diffuse layer compact inner layer layer compact inner

• Electrons transferred at electrode surface by redox reactions occur at liquid/solid interface (heterogeneous)

• (1) A compact inner layer (d0  d1) • (2) a diffuse layer (d1 –d2)

Charging current ic

10-40 F/cm2 Potential dependent

13 Equivalent Circuits of Electrochemical Cell

CSCE >> Cd

RC Circuit-Voltage Ramp (Potential Sweep)

ic = f(v)

EvtE  E RCSd

vt Rsd(/) dq dt q / C if qt 0 at 0

ivCdsd[1 exp( tRC / )] 41

General Equivalent Circuit

Overall current I  iicf i Signal-to-noise ratio (SNR) = f ic SNR , limit of detection (LOD)

14 iCv [1 exp( tRC / )] Cyclic Voltammetry cd sd

(iticcv ; , ) inADCpc 2.69 10 5 3/2 1/2 v1/2 f Ox Ox (ipc  v1/2 ) f

if 1 v = dE/t SNR1/2 ic v  small at fast vC and low LOD of CV ~ 10-5 -10 -6 M

Itotal

How do we eliminate the charging current so that electrochemical techniques could be used in quantifying low concentrations of redox species?

(Pulse Voltammetry)

RC Circuit-Potential Step

I = 5% (E/Rs) at t = 3

RsCd time constant in s

15 (A-)

(A)

- A is reduced to A at potential E2

This kind of experiment is called chronoamperometry, because current is recorded as a function of time.

Cottrell Equation i cc DD(oo ) ( ) , δ   Dt nFAox x 00 oδ x ccDc***00 D (oooo )D ( ) oo δ  Dt D c*1/2* nFAD c inFA oo o o  Dt  1/2t 1/2

Curves 1, 2, 3, Co(0, t) not 0 -not diffusion controlled (electrode reaction-controlled)

16 Sampled Current Voltammetry (Normal Pulse Voltammetry)

Eliminating ic: Potential Step/Pulse Voltammetry

Staircase Voltammetry E if When applying E : ic E  E t t itRCiecsdcexp( / ) Rs * nFADOx C Ox 1/2 Potential it() i t fft sample point at  , ic  0, so SNR (LOD~10-8 M) Time

Normal Pulse Voltammetry Differential Pulse Voltammetry

Additive Cyclic Square Wave Voltammetry (ACSWV)

2H+1 F fa fc ic  iicc R rarc ic  iicc j j' F R Total additive I ic ic c 4H+1 FR Ic iic  c 0

ifa :forward anodic i fa cc ic fc icc: forward cathodic i ira : reverse anodic i  cc rc fc icc: reverse cathodic i ic 51

17 52

Pulse Voltammetric Techniques

• All pulse techniques are based on the difference in the rate of the decay of the charging and the faradaic currents following a potential step (or "pulse").

* Et nFA DCo iiCottrellEqchexp( ); f  ( .) RRCssd t

• The rate of decay: ich much faster than if.-- ich is negligible at a time of 5RsCd (time constant, ~µs to ms) after the potential step.

• The sampled i consists solely of the faradaic current.

Important parameters Pulse amplitude: the height of the potential pulse. This may or may not be constant depending upon the technique. Pulse width: the duration of the potential pulse. Sample period: the time at the end of the pulse during which the current is measured.

18 Staircase Polarography/Voltammetry

Digital potentiostats use a staircase wave form as an approximation to a linear wave form. This approximation is only valid when E is small (< =0.26 mV) and analog current integration filtering is used.

Normal Pulse Polarography/Voltammetry

19 58

Differential Pulse Voltammetry (DPV)

20 Square Wave Voltammetry (SWV)

Peak Current:

=1 for large pulse amplitudes

Charging current (smaller more than an order of magnitude than that of NPV) with LOD 10 nM.

C60 reductions

21 Square Wave Voltammetry (SWV)

22 SWV Response

23 Comparison between SWV and CV

SWV Strengths CV Strengths • Low electrochemical • More intuitively in background. chemical terms for most • Much low detection practitioners. limit. • Reversal of CV covers • Much less distortion a large span of E— of voltammogram- more readily highlights easy to fit theoretical linkages b/w processes data. occurring at widely • Better for evaluating separated potentials. quantitative • Wider range of time parameters. scales.

Applications of Voltammetry

• Dopamine detection • Au or Si NPs redox in mice brains behavior •…… •……

Anodic Striping Voltammetry (ASV)

Principle of anodic stripping. (a) Preelectrolysis at Ed; stirred solution, (b) Rest period; stirrer off. (c) Anodic scan.

24 ASV-Electrode Dependence

Pyrolytic graphite

HMDE

Polished GC

Unpolished GC

Sensitivity and Limit Detection