Basic Electrochemistry

• Electronics: the transport of electrons (or positive holes) Optoelectronics: light + electronics• Electrochemical systems (electrodics + ionics)

  

• Electrochemistry: the coupling of chemical changes to the passage of electricity ionic conduction (flow of ions) + electronic conduction (flow of electrons) Electrochemical devices & electrochemical technologies Materials & devices & processings

What is electrochemistry?

  

 

• Examples of Electrochemical devices/technologies Battery or Fuel cell: chemical state changes(electrochemistry) electric power Photoelectrochemical cell (Solar cell): light + electrochemistry electric power Photocatalysis: light hydrogen or chemical reaction Electrochromic display: chemical state changes by electric signal coloration Sensors: chemical state changes by mass electric signal Electrolysis: electric power chemical species by chemical state changes Electrodeposition: electric power chemical change: thin film, Cu metallization Corrosion: potential difference chemical change Etching • Solid State ElectrochemistrySolid electrolyte: solid substances which can conduct electric current by ionic motion as do electrolyte solutions “solid state electrochemistry” or “solid state ionics” “solid state device” 

 

Several distinct states may correspond to the same energy. That is, each energy level may be degenerate. Three energy levels are shown here, possessing one, three, and five distinct states.

• Basic concepts for electrochemistry

  

 

Electric charge & currentElectric 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 areaAmmeter: measuring current Circuit: electric current flows in a closed path

Electrical potential & electric fieldElectrical potential (unit; volts, V), : the pressure of the electric fluidVoltage: the electrical potential difference ()Voltmeter: measuring an electrical potential difference Electric field strength (unit: V/m) X = -d/dx

Ohm’s law: most conductors obey this lawCurrent density is proportional to the field strength

i X 

i = X = - d/dx 

; electrical conductivity (siemens/m, S = A/V), 1/; resistivity 

= -RIR;resistance (unit of ohm), G; conductance,

G = 1/R = A/L = -I/L; conductor length, A; cross sectionOhm’s law does not have universal validity. It does not apply to electrochemical cells.Resistor: a device that is fabricated to have a stable and known resistance Power (watts) = I2R

 

Electrical quantities & their SI units

Quantity Unit

Current (I)Current density (i)

Charge (Q)Charge density ()

Potential ()Field strength (X)Conductivity ()Resistance (R)

Conductance (G)Permittivity ()

Energy of work (w)Power

Capacitance (C)

Ampere (A)Ampere per square meter (A/m2)

Coulomb (C = As)Coulomb per cubic meter (C/m3)

Volt (V = J/C)Volt per meter (V/m)

Siemens per meter (S/m)Ohm ( =1/S = V/A)Siemens (S = A/V)

Farad per meter (F/m = C/Vm)Joule (J = VC)

Watt (W = J/s = AV)Farad (F = s/ = Ss), F = C/V

Classes of conductorsMaterials 1.Conductors Electronic conductors Ionic conductors 2. Insulators  Conductors: metalsInsulators: plastics, ceramics, gasesNo clear cut distinction between conductor and insulator

Typical value of electrical conductivity

S/m x10-2 for S/cm

  Material /Sm-1

Ionic conductors   Electronic conductors

Ionic crystalsSolid electrolytesStrong(liquid) electrolytes MetalsSemiconductorsInsulators

10-16 – 10-2

10-1 – 103

10-1 – 103

 103 – 107

10-3 – 104

<10-10

Material /Sm-1 Charge carriers

Electron pairsElectronsElectronsElectronsPi electronsPi electronsK+ and Cl-

H+ and HSO4-

Cations & anionsElectrons and holesK+ and Cl-

H+ and OH-

Univalent cations?

 

Electrical conductivity of various materials (most at 298 K)

Superconductors (low temp) AgCuHgC (graphite)Doped polypyrroleMolten KCl (at 1043 K)5.2 M H2SO4 (battery acid)SeawaterGe0.1 M KClH2OTypical glassTeflon, (CF2)nVacuum & most gases

6.3 x 107

6.0 x 107

1.0 x 106

4 x 104

6 x 103

217 82 5.2 2.2 1.3 5.7 x 10-6

3 x 10-10

10-15

0

 

 

 

Electronically conductive polymers

Mobilities: conduction from the standpoint of the charge carriersElectric current = rate at which charge crosses any plane = [number of carriers per unit volume][cross sectional area][charge on each carrier][average carrier speed]

 I = dQ/dt = (NAci)(A)(Qi)(i)

    i: particular charge carrier, ci; concentration, Qi; charge, i; average velocity,

NA; Avogadro’s constant (6.0220 x 1023 mol-1), A; area

zi; charge number = Qi/Qe where Qe (1.6022 x 10-19 C),

e.g., electrons:-1, Mg2+; +2  i fi X d/dx

 fi; force exerted on the charge carrier, X; electric field strength

 

mobility of the carrier, ui (m2s-1V-1 unit) = velocity to field ratio (i / X)

i = uiX = - (zi/zi)uid/dx

zi: absolute value of the charge number

ue- of electrons: 6.7 x 10-3 m2s-1V-1 for Ag, less mobile in other metals

mobility of ions in aqueous solution: smaller than the factor of 105 (factor 105 slower); ucu2+

o = 5.9 x 10-8 m2s-1V-1 in extremely diluted solution

Current I,

I = -A NAQeziuicid/dx

 Faraday constant

F = NAQe = (6.02 x 1023 mol-1)(1.6022 x 10-19 C) = 96485 Cmol-1

 

 

is numerically equal to the charge carried by one mole of univalent cations.(F is large. Small amount of chemicals higher electricity)

If there are several kind of charge carriers, 

I = -AFd/dxziuici

 i = -Fd/dxziuici

Transport number ti; the fraction of the total current carried by one particular

charge carrier  ti = (ziuici )/(ziuici)

  From i = X = -d/dx, conductivity

= Fziuici

 molar ionic conductivity (i); Fui

 

Ion mobilities at extreme dilution in aqueous solution at 298 K

 

Ion uo/m2s-1V-1

H+

K+

Ag+

Cu2+

Na+

Li+

OH-

SO42-

Cl-

ClO4-

C6H5COO-

362.5 x 10-9

76.2 x 10-9

64.2 x 10-9

58.6 x 10-9

51.9 x 10-9

40.1 x 10-9

204.8 x 10-9

82.7 x 10-9

79.1 x 10-9

69.8 x 10-9

33.5 x 10-9

Capacitance parallel conducting plate separated by a narrow gap containing air or insulator

Idt = Q E 

Q = -CEC; capacitance (unit; farads (F) = C/V) 

C = -Q/E = A/LA;cross-section area of the gap, L; width, ; permittivity of the insulator

• Relative permittivity (r) or dielectric constant ( 유전상수 )

air: ~ 1water: 78 Coulomb interaction energy is reduced by two orders of magnitudes from its vacuum valuepolar molecules: rrefractive index: nr = r

1/2 at the frequency

 Capacitor; ; current integrator

 

/0; relative permittivity or dielectric constant

mylar; poly(ethylene glycol terephthalate), (CH2OOCC6H4COOCH2)n

Liquid > solid: large capacitance in electrochemical capacitor (supercapacitor)

 

Material 1012 /Fm-1 Material 1012 /Fm-1

vacuum (0)

N2(g)

Teflon(s), (CF2)n

CCl4(l)

Polyethene (s)Mylar (s)SiO2(s)

Typical glass (s)C6H5Cl(l)

8.854198.859051819.7202838.14449.8

NeopreneClC2H4Cl(l)

CH3OH(l)

C6H5NO2(l)

CH3CN(l)

H2O(l)

HCONH2(l)

TiO2(s)

BaTiO3(s)

5891.7288.9308.3332695.49331500110000

Permittivity of various materials

Electricity flows either by electron motion or ion motionIn both cases, the intensity of the flow (= current density) electric field strength

i = X = -d/dxconductivity

= Fziuici

 determined by the concentration of charge carriers and their mobilities  one form of Ohm’s law

E = -RI

potential difference across resistor to the current flowing through it

Resistor: dissipate energy Capacitor: store energy

 

Summary

. Potential & Thermodynamics

 Introduction

Electrochemistry: chemical change electric forceElectrodics: in which the reactions at electrodes are consideredIonics: in which the properties of electrolytes have the central attention concentration of ions, their mobilities, interactions etc Basic laws were developed in systems with liquid electrolytes “solid state” (same and different features of solid electrolyte system) 

Ionic solutionsMost important ionic conductor e.g., aqueous solution of electrolyteElectrolyte; a substance that produces ions so enhance the electrical conductivity e.g., solid(NaCl), liquid(H2SO4), gas(NH3)

cf) solid electrolyte

ElectrodeThe junction between electronic conductor and ionic conductor that the chemistry of electrochemistry occurs 

Electrochemical cellBasic unit: an ionic conductor sandwiched between two electronic conductorse.g., aqueous solution of electrolyte between two pieces of metal, solid electrolyte between two metals

Cell voltage (E) or emf(electromotive force)electric potential difference between the two electronic conductors voltameter e.g., lead/acid cell (car battery)Electronic conductors: PbO2, Pb

Ionic conductor: concentrated aqueous solution of sulfuric acid 

Electrochemical reactionAnode: Pb(s) + HSO4

-(aq) 2e- + PbSO4(s) + H+(aq)

Cathode: PbO2(s) + HSO4-(aq) + 3H+(aq) + 2e- PbSO4(s) + 2H2O(l)

Cell: PbO2(s) + Pb(s) + 2H+(aq) + 2HSO4-(aq) 2PbSO4(s) + 2H2O(l)

 Right-hand electrode: electrons produced: oxidation, “anode”Left-hand electrode: electrons consumed; reduction, “cathode” Energy is delivered by the cell into the load; ex) car: starting engine, lighting lamps Galvanic cell: a cell which provides energy in this way, “discharge”( 방전 ) 2.0 V without current flow, 1.8 V with current flow (load); “polarization”; voltages decrease in magnitude when energy is taken from them. the effect becomes greater if the current is increased.

“charge” ( 충전 ): current flow in the opposite direction by using an external source (ex. Battery); Electrolytic cell; opposite direction to its spontaneous motionPbO2 : anode, Pb: cathode

  

2.0 V; perfect balance between the applied and cell voltages, no current flow equilibrium cell voltage or reversible cell voltage or null voltage or rest voltage or “open-circuit voltage”(since no current flows, it makes no difference if the circuit is interrupted, as by opening the switch)

VoltammogramPlot of cell currents versus the cell voltages (volt + am(pere) + mogram)

Not linear electrochemical cells do not obey Ohm’s law

 Notation of the structure of cells 

Zn/Zn2+, Cl-/AgCl/AgHg/Hg2Cl2/Cl-(aq)//Zn2+(aq)/Zn

/: phase boundary, “,” or : two components in the same phase, //: liquid junction (a salt bridge)left: oxidation (anode), right: reduction(cathode)

ThermodynamicsWhy is it that chemical reactions in electrochemical cells proceed spontaneously in one direction and furnish current?(thermodynamics: 평형상태에 대한 정보 , kinetics: 전극반응속도에 대한 정보 ):Cell potential of an electrochemical cell 

Ecell = Eright – Eleft

or Ecell = Ecathode – Eanode

 E obtained from the Nernst equation  oO + …+ ne- = rR + …. (reduction)pP + …. = qQ + … + ne- (oxidation)oO + pP + … = qQ + rR + … Ecell (cell reaction)

  

Ecell = E0 – (RT/nF)ln[(aQqaR

r..)/(aOoaP

p..)]

Gibbs free energy, G = -nFEcell

G <0 spontaneous 

E0: standard electrode potential = Eright0 – Eleft

0

Eright

0, Eleft0,,: standard electrode potential of half reactions expresses as reductions

vs. NHE(normal hydrogen electrode) with all species at unit activity (ai =1)

 (see the Table of Standard Potentials)

e.g., MnO2 + 4H+ + 2e- Mn2+ + 2H2O E0 = + 1.23 V

E = E0 –(RT/2F)ln[(aH+

4)/aMn2+], aMnO2, aH2O = unity

G = -nFE cf. RT/2F = [(8.314 JK-1mol-1)(298 K)/2(96485 JV-1mol-1)] = 0.01285 V 

 

Several distinct states may correspond to the same energy. That is, each energy level may be degenerate. Three energy levels are shown here, possessing one, three, and five distinct states.

  

 

 

Several distinct states may correspond to the same energy. That is, each energy level may be degenerate. Three energy levels are shown here, possessing one, three, and five distinct states.

e.g., Zn/Zn2+(aq), Cu2+(aq)/Cu Cell: Zn + Cu2+ Zn2+ + CuRight: Cu2+ + 2e- Cu E0 = +0.34 V Left: Zn2+ + 2e- Zn E0 = -0.76 V  Ecell

0 = +0.34 – (-0.76) = +1.10 V

G0 = -2 x 1.10(V) x 96485 (JV-1mol-1) = -212 kJmol-1

reaction spontaneousEEcell = E0 – (RT/2F)ln(aZn2+/(aCu2+)

 If we assume aZn2+= aCu2+, Ecell = 1.10 V

 ------Hg/Hg2Cl2/Cl-(aq)//Zn2+(aq)/Zn

 2Hg + Cl- + Zn2+ Hg2Cl2 + Zn

right: Zn2+ + 2e- Zn E0 = -0.76 Vleft: Hg2Cl2 + 2e- 2Hg + 2Cl- E0 = +0.27 V

 Ecell

0 = -0.76 –0.27 =-1.03 V, G0 = +199 kJmol-1, should be opposite direction

 

  

 

Measurement of E0: (i)   experiment(ii) E0 = (RT/nF)lnK, K; equilibrium constant of cell K = exp(-G0/RT)(iii) E0 = Eright

0 – Eleft0 or E0 = Ecathode

0 – Eanode0 (from Table)

(iv) E0 = -G0/nF Cell: PbO2(s) + Pb(s) + 2H+(aq) + 2HSO4

-(aq) 2PbSO4(s) + 2H2O(l)

 From thermodynamics Table,Standard Gibbs Energy (kJmol-1): -813.76 (PbSO4(s)), -237.13 (H2O(l)), -218.96

(PbO2(s)), -755.91 (HSO4-(aq)), cf) G0 for element (Pb(s)) and H+(aq) = 0

 G0 = 2G0 (PbSO4(s)) + 2G0 (H2O(l)) – [G0 (PbO2(s)) + 2G0 (HSO4

-(aq))]

= -371 kJmol-1 G0 = -nFE0 E0 = 371000(Jmol-1)/[2 x 96485 (JV-1mol-1)] = 1.923 V battery acid: 5.2 M

Ecell = 1.923 V – (RT/2F)ln[aH2O(l)2/(aH+(aq)

2aHSO4-(aq)2)]

= 1.923 V – 0.01285ln [1/(5.2)2] = 2.008 V

 

activity term: minor contribution to the cell voltageactivity (a) concentration (c); a = c, ; activity coefficientai 1(solvent, pure solid, ideal solution)

(Examples) 1. Indicate in the following reactions which are reductions and which are oxidations:(1) Fe2+ + 2e- Fe (2) Cl- 1/2Cl2 + e- (3) Fe2+ Fe3+ + e-

(4) CrO42- + 3e- Cr3+ (5) O2 + 4e- 2O2- (6) Br2 + 2e- 2Br-

 

2. A Galvanic cell is constructed from a Cu2+/Cu electrode and an Ag+/Ag electrode.(1) Make a schematic drawing of the cell (2) Write the reactions at the electrode  (3) Indicate the anode and the cathode  3. Assuming standard states for all reactants and products, determine the spontaneous direction of the following reactions by calculating the cell potential:(1) Cu + 2HCl = CuCl2 + H2

   (2) Ag + FeCl3 = FeCl2 + AgCl

 

Principles of electrochemistry: Definitions

Two equal electrodes (Lecture #4) interest in one electrode only (Lecture #5)  

ElectrodesWorking electrode(WE): electrode of interestReference electrode(RE): second electrode, measure potential of WE with respect to REElectrode potential E = Ework –Eref

 Reference electrodes

SHE (standard hydrogen electrode) or NHE(normal hydrogen electrode): universally accepted standard

H+(aq, a=1) + e- = 1/2H2(g, 105 Pa) E = 0 V

 SCE (saturated calomel electrode)

Hg2Cl2(s) + 2e- = 2Hg + Cl- Eref = 0.244 V vs. NHE

Ag/AgClAgCl(s) + e- = Ag(s) + Cl-(aq) Eref = 0.199 V with saturated KCl

 

Potentials of reference electrodes E(RHE) = E(NHE) + 0.05916pHE(SCE) = E(NHE) – 0.2444E(Ag/AgCl) = E(NHE) – 0.2223E(Ag/AgCl, sat.KCl) = E(NHE) – 0.196E(Hg/HgO 1M KOH) = E(NHE) – 0.1100 + 0.05946pHE(Hg/Hg2SO4) = E(NHE) – 0.6152

 

  

Potential vs. energy (vs. vacuum)

 

  

예 : Potential vs. energy (vs. vacuum)

 

  

Controlling potential of the working electrode with respect to the reference controlling the energy of the electrons within the working electrode More negitive potential energy of electrons is raised reach a level to occupy vacant states (LUMO) on species in the electrolyte flow of electrons from electrode to solution (a reduction current) More positive potential electron flow from solution (HOMO) to electrode (oxidation current)

Working electrode can act (i) as only a source (for reduction) or a sink (for oxidation) of electrons transferred to or from species in electrolyte (e.g., C, Au, Pt, Hg) or can (ii) take part in the electrode reaction, as in dissolution of a metal M (Zn Zn2+ + 2e-)

 

Applying potential from its equilibrium (or its zero-current)

 PolarizationVoltammogram: historical one vs. new one E > 0 working electrode potential > 0 (positive: right of x-axis)I > 0 oxidation at the working electrode

 

Polarization: the shift in the voltage across a cell caused by the passage of current Departure of the cell potential from the reversible(or equilibrium or nernstian) potential

Ohmic polarizationActivation polarizationConcentration polarization

 Overvoltage (): the voltage shift caused by each kind of polarizationExtent of potential measured by the overpotential: = E - Eeq

E = En + ohm + act + conc

   

   

(i) ohmic polarization 

ohm = IRsol, “IR drop”

Rsol = L/A

If free of activation & concentration polarization, slope = 1/Rsol

  Rsol = L/A

 

   

 If free of activation & concentration polarization, slope = 1/Rsol

Electrochemistry needs to minimize ohm

(conductivity) ohm (by adding extra electrolyte: “supporting electrolyte”)

three-electrode system 

two-electrode cell vs. three-electrode cell 

Eappl = E + iRs = Eeq + + iRs

 IRs: ohmic drop in the solution (ohmic polarization) should be minimized

short distance between working and reference electrode & three-electrode cell Two-electrode cell: iRs problem due to high current flow

Three-electrode cell: current between WE and auxiliary electrode(or counter electrode) Potential measurement between WE and RE almost no current to reference electrode

Potentiostat, etc electrochemical system: three electrode system

 

(ii) activation polarizationslow electrode reaction activation polarization; slow kinetics activation energy This can be overcome by increasing the temperature and by applying extra voltage (activation overvoltage (act))

  

(iii) concentration polarizationfrom difference between the electrode surface and bulk concentration

 R O + ne-

conc = E –En = (RT/nF)ln[(cRbcO

s)/cRscO

b]]

 Limiting currentIdeal polarizable electrode (totally polarized electrode): a very large change in potential upon small currentIdeal nonpolarizable electrode: potential does not change upon passage of current (e.g., reference electrode)

 

Double layerElectrode-solution interface capacitor “double layer”

Same concept as capacitor (two metal sheets separated with q (coulomb)/E = C(farad)) ))

 qM = -qS

qM: charge from electrons in metal electrode, qS: charge from ions in solutioncharge density M =qM/A (C/cm2)double layer capacitance, cd: 10 ~ 40 F/cm2

several models: Helmholtz, Gouy-Chapman, Stern, Grahame model etc

 

)) 

 Same concept as capacitor (two metal sheets separated with q (coulomb)/E = C(farad))

Grahame model: IHP (inner Helmholtz plane, specifically adsorbed anion) + OHP (outer HP, solvated cation) + diffuse layer

  

Electrochemical systems in terms of circuit elements

e.g.,) Hg/K+, Cl-/SCE, Hg: ideal polarized electrode

CSCE, Cd: capacitances of SCE and double layer, Rs: solution resistor

CT = CSCECd/(CSCE + Cd), CSCE Cd CT Cd RC circuit

  e.g.,) applying voltage (or potential) step:potential step: E, EC of capacitor, ER of resistor

q = CdEC

E = ER + EC = iRs + q/Cd

i = dq/dtdq/dt = -q/(RsCd) + E/Rs

q =0 at t = 0 q = ECd[1 – exp(-t/RsCd)]

By differentiating,I = (E/Rs)exp(-t/RsCd)

At time constant = RsCd current for charging the double layer capacitance

drops to 37 % at = t, 5 % at = 3t

 

e.g.,) Rs = 1 , Cd = 20 F, = 20 sec double layer charging is 95 %

complete in 60 sec

Double layer charging process: “non-faradaic process” Cf) oxidation /reduction electron transfer ; governed by Faraday’s law (the amount of chemical reaction caused by the flow of current is proportional to the amount of electricity passed) “faradaic process” or “charge transfer process”

sec Double layer charging pr

sec

 Semiconductor electrodeSemiconductor/electrolyte space charge region due to space charge capacity, Csc, 0.001 ~ 1 Fcm-2, (cf; Cdl = 10 ~ 100 Fcm-2 ) band bending

 n-type SC

when EF of SC lies above that in electrolyte electron flow from SC (positively

charged) to electrolyte (negatively charged) bent upwardby applying potential of bulk = surface, band bending & space charge region

disappear “flat band potential (fb or Efb)”

 

  

space charge capacitance Csc Mott-Schottly equation

 1/Csc

2 = (2/e0N)1/2(- - kT/e)

 : dielectric constant, N: donor or acceptor densities, e: quantity of charge, - = E-Efb

 A plot of 1/Csc

2 vs. potential E should be linear Efb, doping level N

 

 

 

 

 

p-type 

 

p-type