'ro Palfiela, HeatLet xzd S:eS/ec; Gill, Linda and Ian

Industrial Electrochemistry

.

SECOND EDITION

Derek Pletcher Deparrmenf of Chemistry, University of Southampron

and

Frank C. Walsh Deparrmenr of Chemistry, Portmouth Polytechnic

L o n d o n New York CHAPMAN AND HALL

Fwst publtrhed in 1981 by Chapman and l lal t Ltd I I Ncw Feller t anc, London EC4P 4EE Publ#rhcd ~n Ihc USA by Chapman and Hall 29 Well 15th Strcct. New Yort NY lmOl Pap.rb.ck cd%t\on first pubbrhd 1984 b n d cdlt~on IW

Q 1982. 1984. 1990 Dcrck Plctcher and Frank C. Walsh

Typcm in lOj12 Times by Mmcmillan India Lld. Bansalore 560025 ., . . mI4 i2 Great Etinir ct th: U n i m i t y Prcrr, Csrnb~idge

ISBN 0 412 3WIO 4

All rights rc rved . No pan of this book may br reprinted or reproducrd. or utilized in any form or by any dccrronic. mechanical or othcr mranr, now known or hcreaker invented, including phorncngyin~ i n d recording, or in any information storage and retrieval system. withour pcrmirrion in writing lrnm the publisher.

B d l U Ubnry Cmlmlo~ulng in PuMicstion Dnts

Plctchcr, Derek Induslrial c\ec1rochcmirrry. - 2nd ed. I . lnduptrial clrctrcxhcmtnry I Title 11. Walrh, Frank. C. 1932- 660.2'97 ISBN 0 412 30410 4

Pletckr. Dcrck. Industrial elcclrochcmistrylDerct Plctchcr and Frank C. Wslsh- 2nd cd. p. cm. BiMiopaphy: p. Indudn indcr. ISBN 0 412 30410 4. 1. Elcctrochrmistry. Indllrtrial. 1. Wslsh, Frank. C. 1952- 11. Title.

TP2SS.PJ7 1989 6 6 0 . 2 ' 9 7 4 ~ 19

Contents

Prefoce Symbols

I Fundamenlal concepts 1 .I Electron transfer 1.2 M a s transport 1.3 The in1crpla)i of electron transfcr'and maw lnnspor l conlrol 1.4 Adsurption , 1.5 Electrocatalyiir 1.6 Phase formalion in clectrodc reactions I.? Chemical reactions 1.8 The properties or electralylc solutions 1.9 The assessment o f all voltage 1.10 Elalrochcmirtry at surfaces on open circuit Furthcr reading

2 E lahahemiea l engineering 2.1 General considerarions 2.2 Costing an cltctrolytic pra7ss 2.3 Pcdormana and figurn or merit 2.4 Electrolysis p,amrncters 2.5 Principles o f cell design 2.6 Thc additional tahnology o fe la t ro ly t i c p r w w 2.7 T y p i d p l l designs 2.8 b b o r a l o r y data and scale-up F u r t h u reading

3 7he cblor-8lki1li lndmtry 3.1 Gcncral conap ls 01 brine cleclrolysis 3.2 Modern technological dcvclopmcnls 3.3 Chlorine all ~echnologies

viii xi

v i Contents

3.4 T te production d potauium hydroxide Further rcad iy

4 nlbr extradlom, d d n p a d production of metal ' *'- I 4 I Electrowinning 4.2 Cmenlation 4.3 Elatrorrfining 8 4.4 Eloctro&po~ition 01 metal powdcrs I Further rcadipg

I 5 Olhcr lrorganlc dstrolytic prrnscr

5.1 Fluorine 1 5.2 Watcr datrolysis I 5.3 Sodium chlorste and sodium bromalc I 5.4 Peracidr and their salts 5.5 Potassium pcrrnanqanate 5.6 Potwrium dichromatc and chromic acid 5.7 Hydrogen pcroxidc 5.8 0mm 5.9 Manganese dioxide 5.10 Cuprous oxide 5.1 I Synlhuis or metal salts via anodic dissolution Furlhcr reading

I 6 Orgenic elmhmynthrsls

6.1 Thc hydrodimerization or acrylonitrile 6.2 Othcr commercial clcclrorynthetic promscs 6.3 Indirect eloctroaynrhesis 6.4 The luturc 01 clectrosynthcsis Further reading

7 Wmter purlfkarlon, etRpmt trcstment and recycling or Indwhlml pmcce aue rm 7.1 Metal ion removal and metal recovery 7.2 Hypochlorite and low-tonnage chlorine clcclrolysers 7.3 Ekctrod~alyais 7.4 Tho tmtment 01 liquors containing dissolved chromium 7.5 Rlcctrolytic methods of phase separation 7.6 Fluc-pas desulphurization 7.7 Other electrochemical proasses Further recdlnp

8 Metal llnllhln[ 8.1 Bloclmplrtinp 8.2 Elcclrtrler8 plat in^

8.3 Conversion coatings 8.4 Eleclraphorctic painting 8.5 0 t h rcbtcd aurfacc-finiahing techniques Further md ing

9 Metals a d nutmiah p r a a i q 9.1 Electrolonning 9.2 Ela t ro~hemiu l machining 9.3 Electrochemical etching Further reading

10 Corr4aa a d lh eatmi 10.1 Fundapenrelr or mrroaion 10.2 The Ulcrmodynamia 01 corrorinn 10.3 The k i m t i a 01 wrrosion reactions 10.4 Corrosion pmblemr in p n c t i a * 10.5 Corrorion pmvcntion and control 10.6 Corrosion pmblcmr in clatrolytic promsing 10.7 Corrosion mmuremeat and monitor in^ Further m d i n g

I 1 8 . i i s b a n d f d c d b 11.1 Batlcry chmctmisticr 11.2 Battery sp&ifications 11.3 Evaluation 01 battery perlormanu 11.4 Ballcry wmponenls 11.5 Prcscnt battery ryscems 11.6 Batteries under dcvclopmcnt 11.7 Fucl a l l a Furlhcr reading

I1 Ekhoebanlal umn and d i o r i q i s k n l q m 12.1 Elat rochemid pmadurer 12.2 Polarography to anodic stripping volLammetry 12.3 I on -~ek t i r e elcctmdea 12.4 Porbbk and o n - l k & v i m 12.5 Elatrochemial biolcnmra 12.6 E la l r ochnn id detector cells lor high-perlormanu

liquid chromatography (HPLC) 12.7 Misccllaneour Furthcr reading

Contents v i i

Index

Preface

The objcctivc of this xcond edition remains thediscussion olthe many diverse roles o l electrochemical technology in industry. Throughbut the book, the intention i s to cn~phasizc that the applications, though extremely diverse, all are based on the sdmc principles o l clcctrochcmistry and clslrochcmical engineer- ing. Tho% lamiliar with the first edition will note a significant inerease in the number or pages. Thc most obvious addition is the scparatr chapter on clectrochcmical sensors but, i n lact, all chapters have been revicwcd thoroughly and many have h e n altered substantially. Theoe changes to the book partly rcflect the difkrcnl view ofa second auuthor as well as comments from students and friends. Also. they arise inevitably from the vitality and strength of elcctr~chcmical technology; in addition l o important improvcmcnts in tcch- nology. new electrolytic processes and electrochemical devices continue to be reported.

I n the prelace to the first edition i t was stated: . . . the future for clcclrochemical technology i s bright and there is a general expctation that nclu applications of clcctrochemistry will becmc economic as the world responds to the challcngc o l more cxpcnsivc energy. o l the need to develop new materials md to exploit diflerent chemical lcedstocks and of the nmcssity to protect the cnvironmcnt. Thc preparation of this second edition, seven years after these words were wriltcn, provided an occasion l o review thc p r o m o l industrial electro- chemistry. To our great pleasure. the conclusion i a that despite the fact that cmray has not become more expensive. the progrcra in terms o l both improved technology and completely new procrsscs and dcvias i s very substantial. Improved membrane cell technology for the chlor-alkali industry, new processes lor the manulacturc of low-tonnage organic and inorganic chemicals, thc appcarancz on thc market o l new lithium batteries and avaricty olstnsors, the coming o l a le of cathodic clcctropainting many electrolytic proasses lor emucnt treatment. the commercial availability o l ncvcrsl lamilies o l electro- chemical tells, etc. arc a l l symptoms of a healthy technology.

Less satislactory arc the status o l clcctrochmistry and ckclnxhcmicnl enginaring as acadcmic disciplines. They remain insuRricntly taught at both undcrgraduatc arid postgraduak Icvds. Morcovn. cvm when they appur within the syllabur, a l l t m lrequently one aspcct olthc subjects i s oovcd l o the exclusion of all othcn. I t is a prime hope o l both authors that Lbis book will encouragemany more teachers lo takeup lhechalkngcoltcachioganintcgralcd applied electrochcmistry course.

Following the two introductory chaplcrs, wc havc lricd to w 4 similar approach lor the discussion o l the various groups of applications. We have sough1 to relate the technology to the underlying principlcr and lo discuss current thinking and practiu within thc industricr as well as to comment on likely fulu;.e tret,ds. We would wish to emphasiy howevcr, that it ir never our purpose to compare the technologies, mlls or deviar available from competing companies; the cxample~ sclectcd arc based on our pcnonal cxpcricnm and ere in the text lor illustrqtion. We havc also sought to dercribc only technology which has already reached industrial usagc.Hcncc, we have alwaystrid to avoid the temptation to outline t l~e many othcr processes which havc only been demonstrated in the laboratory or on a small pilot sfale (otherwix the b w k would bc in many voldmes). We have attcmpted thcreby, lo produx r readable account o l real industrial electrochemistry, useful to both students and (how already cngagcd in the investigation or some aspcd of thc subjnc.

I n writing this book, many compromises had to be made. Therc have bccn many livcly (but friendly) dcbatcs between the two authors and topicrdiscurrcd have included the depth o l treatment, the balance between fundamental and applied aspects and the choice of illustrative material. By lar thc most vexed topics wcrc, howevcr, more relating to signs, symbols and othcr wnvenlions; throughout wc wcrc aware that the established pract im of clectrochcmists, cleetroplaters, corrosion enginars, materials technologists and chemical cn- einecrs wcrc quite diHcrmr and thcy also dcpnded on the country olorigin. I n these very unlortunatccircumstances, authom arc bound to oRendmoct readcrs. In some desperation wc decided to lollow a system which will bc m a t readily acceptable to elc~trochcmists sin- wc cxpccl thcm to bc our largest group of readers. Mort of a l l we havc endeavoured io achieve uniformity.

Finally, i t is a pleasum lo thank thc many who havc helped us in the preparation of lhis book. The most obvious are those who have kindly persuaded their organizations to rclcaw the photographs which ilhulratc the teat. There are, however, many othcr industrialists and academics who have provided sour- material. We also la1 that we owc much gratitude to the many who have stimulated our inlerest in applied ckctrochemistry. I n the case o l one of us (D.P.) special mcntion should bc made of Professor Martin Flcischmann (University of Southampton) and D r Gordon L m i s (associate and guide during a survcy o l industrial elutrochcmistry carried odt in 1979). The other (F.C.W.) would wish to single out D r Des Barker (Portsmouth Polytechnic),

x Preface

D r David Gabe (University 01 Loughborough) and Prolersor Martin Fleisch- mann, as particulnrly strong influences in his training. W t arc both also aware olour deb1 lo several companies who have givcn us practical training in the most amptable way - they have paid us as consullanls! Thanks are due to Susan Neale and David Jackson o l the Frewen Library, Portsmouth Polytechnic who checked the listsollurther reading at iheend oleach chapter. Our typists are also remembered with many thanks. Lastly. we wish to acknowledge the debt to our families, especially our wives who have suRcrcd extra duties to allow the completion ollhis book, but also our parentsand childrenior their contributions to our contented writing.

Derek i't~tchel Frank Walsh

Symbols

Symbol a + a -

a * A As A, h I3 CI cp c;

Definilion Activity 01 cation Activity o l anion Mean ionic activity Elcclrode area Eleclrosctive area per unit reactor volume Ueclrorctive area pcr unit elcclrodc volumc Cosl or a unit 01 electrical power Width 01 flow channel Concentration 01 species i Conmntration o l species i in the bulk solution Concenlralion 01 s p i e s i at the electrode

surface lnilial conocnlration 01 rzsctant Concenlralion 01 reactant at time r Concentration 01 reactant at inlel to reactor Concentration 01 reactant at oullct 01 reactor Capilal inverted Capacitance Capacity 01 a battery electrode Electrolysis power cost Fixed capital Variable reactor investment cost Land capital Cosl 01 electrolyte agitation Working capital Total scrap value 01 plan1 Heat capacity at oonstanl pressure Equivalent diameter o l a flow channel Depreciation

Typical unlrs Dimensionless Dimcnsionlcss Dimcnsionlcss m1 ,-I

m ' t W - ' s - ' m molm-' molm-' molm- '

xii Symbols

Symbol Definition Dl DiKusion coefficienl of swies i E Measured or applied electrode potential E. Equilibrium electrode potential E: Standard electrode potcntial E f Equilibrium calhodc potential E: Equilibrium anode potcntial .@ Cathodc potential EA Anodc potcntial E L Equilibrium all potential ( c E:) FCC,, Crll pot?ntiat (6- F A ! EM Membrane porential E,. Corrosion potential En,, Potential at which transpassivity first occurs E . . Point of zero charge potcntial t,. Thermoneulral all potential F Farnday constan0 9 Ambrat ion due to gravity Gi Total Gihbs free energy lor species i G; Gibbs free cncrgy for speFics i i n thc absence

of a potential field dG Gibbs free cnergy change AC;m Standard Gibbs free cncrgy of adsorpiion ZG, Gibbs free cnergy ofaetivation lor thc

lonvnrd process h H ~ a t transkr wefficicnt H Enthalpy i Current 6 Exchange current for the cathodic proass 1: Cxchangc current for the mctal dissolution

reaction , Critical current for thc onset of passivation I,, Current in the passive range i~ Mass transpon wntrollcd limiting current I Current density: I=i /A 10 Exchange current density 4 Exchnngc current dcnsity for thc hydrogen

evolution reacllon 1: Eachangc current density for the rnctal

dissolution rcac6on 1 Reduclion (cathodic) partial current density f Oxidation (anodic) partial current density IL Limiting current density (under mars transport

control due to diKusion or convective dinusion)

Typicol vnils m's-' v v v v v v v v v v v v v v A srnol-I ms-' Jrnol-' Jmol- '

Jmol" Jmol-' Jmol-'

W m - ' K - I J m ~ l - ~ A A A

A Am-' Am- ' Am- '

Am-'

Am-' Am-' Am- '

Syrnbol Dejniricn I,, Optimum currcnt density 1. Current dcnaity at a dislana x alosg thc

electrode k Rate constant lor first ordcr chemical proass i; Ralc constant for thc forward (cathodic) process L Ratc constant for the rcvcrsc (anodic) process ko Ratc mnslanl for an electron transfer proass at

E=O V vs. thc rcferena electrode k' Standard rate urnstant for an clcctrodc proars k, Mass transport coeRkient k . Avelagtd. overall heat transter coelfic~cn[ K' Kohlrausch constant KO Selectivity constant for species i I Characteristic length L Length of a plate electrode m, Molality of cation m . Molality of anion m Number of moles of clcclroactivc spcicr me Initial molar amount of mclant m, Molar amount o l ructant at timc t rn,,,,, Molar amount of reactant st the inlel to a

reactor m,,,,, Molar amount of reactant at thc outlet of a

reaztor m, Molar amount of product M Molar mass n Number of elatrons "P Number of molcs of product N Projected lifetime of plant Nc Chromatographic plate number N, Mass flow 4 Elcclricel charge Q Volumetric flow mtc Q Charge density Q, Heat Row r Radius of disc or cylinder electrode R Gas constant R Elcdr ic~ l roislancc R,,,, Cell mistancs ROnc-,, Rcsistanoe olclectrical circuit, including busbsrs R, Linear polaritation nsinlana s Spaa-vdocity 3. Normalized spacc-velocity

Symbols aiii

Typical unifr Am-' Am-'

s - ' ms-' ms- ' rns '

ma-' m s - I m's '

rno l 11' Dirncnrionlna rn m mol kg- l molkg-' mol mol mol rnol

mol

mol kgmol-' Dimensionless Dirncnsionlm ycars Dimcnsionlers kgs" A s m3a-' Asm-' W m J K ~ ' m o l " ohm ohm ohm ohm - ' s - a

i 1 xiv Symbols Symhnl Definilior~ S Entropy 5 Separation of electrodes s* Oscrall selecrivily t Time 1' Time to discharge hatlcry I' Critical time in hatch processing 11 Relention time

i l+ Tranaporl numhcr orcallon I 1 - Transport number or anion

T Te~pcrs tu r? I "I Mobility 01 species i 1 V t Number 01 positive ions I v - Number 01 negative ions

u Velocily 01 elcclrolyle flow 1'1 Solution vcloci[y in the x direction

I u Mean Row velocity V Volume v, Reactor volume V, Reservoir volume I:, Molar volume VE Electrode volume w Mass of material W Power required lor clec~rodc;clectrolyte

movcmcnt W,,, Electrolylic power requirement x Distance. thickness or penetration x A F- - -. , - - - a ,,,,:,,,..! ::anversion 21 Electrical charge on spcics i Z Frequency lactor lor an aclivalion controlled

prooess

Din~ensiunless Groups

BAPL' Gr Grashol Number: Gr I.= p '11

Re Rcynolds Numher: R e = - I v

Sr Schmidt Number: ~ r = ; D

I Sh k,' Shcrwood Number: SIX= -- D

Tjpiral units JK ' - ! m Dimensionlcss S S 5

S Dimensionlcss Dimensionless K m's-' V - ' Dimensionless Dimensionless m s - ' m s - I m s - ' m3 my m3 m3mol - ' m '

W m Dimensionless Dimensionless m s - '

Dimcnsionless

Dimensionless

Dimensionless

Dimensionlcss

E

'I 'I' 'Ic 'I* H RP K

Definition Greek

Transfer coefficient Anodic iransfer coefficient Cathodic lransler coefficient Inverse or the slope o l a logli l vs. E (or logl i l

vs. q plot) Energy yield Thermal energy yield Effectivyless factor for mass transport control Activity ~ R ~ ~ c c I of cation Activity coefficient or anion Mean ionic activity cafficient Stefan-Boltzmann wnslant =5.67 x lo-# Nernstian, conantration boundary layer

thickness Emissivity Overpolential ( E - E , ) Polarization ( E - Em,,) Overpotenlial at cathode Overpotential at anode Surfaa coverage Material yield Electrolytic conduc~ivity lonic wnductivity or cation at infinite dilution lonic wnductivity 01 anion at infinite dilution Thermal wnductivity Mclar wnductivity cf elec!rc!;.!e Molar conductivity or electrolyte at infinite

dilution Dynamic viscosity Kinematic visoosity; (p lp) Density Difference in density between solution at

elalrodc sur(aa and bulk Spacetime yield Normalized spacetime yield f ~ a k variance %lector lime constant Rs idena timc Space-time Peak fidelity

Symbols xv

Typical units

Dimensionless Dimensionless Dimensionless v

Dimr.lsi~nlcss Dimensionlcss Dimcnsionless Dimensionless Dimcnsionless Dimensionless Wm- 'K - ' m

Dimensionless v v v v Dimensionless Dimensionless ohm- 'm- ' ohm-' mlmol-' ohm-' m'mol-' W r n - ' K - ' ohm-' m'mol-' o h m i m'mol-'

kgm-Is ' ' m2s - ' kgm-' k8m-'

kgm- ' r - ' kgm-'s- ' Dimensionless Dimcnsionless s S Dimensionlcss

xvi Symbols

Symbol Definilion 4 ~ u r r c n t cficiency 4 Absolute potential at the electrode surlace d. Overall conversion related yield . . dl Absolute potential o l lhc bulk solulion phase 4, Absolute polential at the plane olclosest

approach of cations $ Potential field strength w Rotation rate

Dimensionless v Dimcnsionlcss v v

1 Fundarnelrtal concepts

An clcctrochemical rcaclion i s a hclcrogencous chemical process involving the lransfcr of chargc to or from an clectrodc, gcncrally a metal, carbon or a ;cmiconduc~or. The chargc transfer may be a cathodic proass in which nn

I olherwise stable species is reduced by the transfer ofelnlrons from an clcctrodc. Examples of such reactions which arc important in clntrochcmical technology include:

H

N a + + e- + Hg- NaHg (1.3) 2CH, = CHCN + 2H,0 + 2e-(CH,CH,CN), + 2 O H 11.41 IJbO, + 4Ht +SO:- + 2c--PbSO, + 2H,O (1 .5 )

Conversely, the charge transfer may be an anodic process wherc an otherwise stable species i s oxidized by the removal of clectrons to the clcctrode and relevant examples would be.

Some typical cathodic s"d anodic processes arc also shown in Fig. 1.1. O lcourx , clcctrochcmistry is only possiblc i n a all which contalns bolh an

anode and a cathode and, to avoid the accumulation of net positivc or ncl

i

Fundarnenral concepts 3 2 f ~ l n d a ~ n r ~ ~ r a l concepts

- -

Electrode colutlon Electrade Loyer Soluhon

(0) s~mple electron transfer. ( b ) Metal aeposnt+r e g Fc3'+ e-- Fe" e g CU" t 2e -Cu

Elecrroac Solution Pb electrode Pornus b02 Solution layer

I c I Gas evolu~ion._ ( d l surface film tmnslormo!io~ =.g ZCI -2e - C I ~ e g P~O~*IH*+ 5o:t ~ ~ U D S O , , ' H ~ U

Fa electrode Solution ng electrode Oxide layer Soluliom (n;,o! (e) Anodic dissoluhm

eg. Fe-zeLFc,+ LllOxide formation c g 2Ag-2e-+ 20H--bg10 + H1O

l Inrenneaiates

b

Porous electrode Solution E l ~ h o d e kIu!ion

l g ) Gas raduction in pornus gas Lnl Electron tronsler wim coupled chernehy, diffusion electmde. eg . 2Cy-CHCN + 2H20 + 2e- c Q. 0 1 t 4 ~ ' t 4e'+ 2H,O -tCH,CH,CN), + 20H-

Fin. 1.1 Some common types of clcclrodc proccsscs For simplicity. ions 01 thc back- ~rotdnd r l t i l rolylr (nalncrically in largc crccsr) and rtrunlcr lolls arc not shown

negative charge somewhcrc i n the all. the amounl 01 reduction at the cathode and oxidation at the anode must beequal. Moreover. Ihc neassity to mainlain charge balance throughoul the cell system has olher important conscquencrs:

I . Fo r electrolysis to occur, electrons must pass l rom the anode l o the cathode through an external, electrical circuit inlerwnnccting the two electrodes.

2. There must he a mechanism lor charge transport between thc electrodes within the cell.

I n fact, the movement 01 ions lhrough the solution and any separator between the electrode is responsible lor maintaining charge neutrality within the electro- lyte solution; anions move towards the anode and/or cations towards the cachouc in sulcicn: q9anli;g l o ,r.ain;ain a c : ~ z ~ g e t s : ~ n c s i n p:;ctir:, t:,s charge may not be carried by the same ions throughout the interelectrode gap. The charge transporl pr- essential l o electrolysis are illustrated in Fig. 1.2 lor the case o l a cell wi th a cation selective membrane as described i n Chapter 3, (section 3.2.2).

The equality of dlectrons passing across each electrode surlace and through the external circuit largely determines the way i n which we seek t o undcrsland or t o study electrode reactions and electrolysis cells. The current i is i n fact the rate at which clcc::ons move lhrough the external circuit. I t is also a very

Anolyre Cation Catholyte selective membrone

Fig. 1.2 Charee lranspan prazsxs csscntial toelectrolysis in a m l l containin8 a cation- sclectivc mcmbranc as a wpantor.

4 Flrndornentol concepts

convcnirnt measure of the rate of tile clcctrode reactions and also 01 the overall chemical change i n thc cell. Moreover. the chargcq passing through thc external circuit tells one the extent o f chemical change at each electrode. Thc charge required to convert m rnol of starting material to product i n an nc- electrode reaction is readily calculated using Faraday's laws o f electrolysis, ie.:

q = [idr = mnF (1.12)

where F i s (he Faraoay constant (96485C mol- ') . The total chemical change in thc cell is found by adding the anode and

qathode reactions; thus the chemical change i n a lead-acid battcry during discharge is obtained by adding rcactions (1.5) and (1.9, ic.:

PbO, + P b + ZSO:' + 4H' --A 2PbS0. + 2H,O (1.13) and that i n a water elcctrolyser by adding reactions (1.1) and (1.6), i e.:

2H,O---.2H, + 0, (1 14) The thermodynamics cf electrochemical cells is treated i n all textbooks of physical chemistry as are the conventions. The discharging lcad-acid battery would commonly be written as the cell.

Pbl PbSO. laqucous FI,SO.I PbO, IPbSO. IPb (1.15) where phase boundaries are denoted by vertical lines. The cquillhrium (or reversible) cell potential is obtained by subtracting thc equilibrium potential of the anode (left-hand elcctrode i n reaction (1.1 5)) from that of the cathode (right- hand electrode i n reaction (1.15)) and this i s related to thc rrce energv of the overall ccll reaction (as written in reaction (1.13)) by the well known equation:

AG = -IIFE;I,,, = - n F ( c - : I (1.16)

Experimentally, the equilibrium cell potential for the lead-acid bauery i s found t o be + 2.05V and, hence. the free energy change associated with the rcdox reaction between Pb and PbO, is - 394 kJ mo l - ' . Clearly, thermodynamics is telling us that the reaction is very favourable (or strictly that the position of equilibrium lies strongly t o the side of conversion o f the PbO, and Pb to PbSO,) as i s to he expc ted lor a system which is used to supply cnergy, ie . a battery. Equally, t l~ecalculat ion is confirming that the conversion o f PbSO. ta Pb and PbO, i s very unfavourablc, AG = + 394 k J m o l - ' and, hence, the recharging o f the battcry only occurs when we introduce this encrgy into the system by means o f an external power supply.

The equilibrium cell voltage for the water electrolysis cell, with the overall ccll reaction (1.14). is - 1.23V and the free cnergy change + 472 kJ mol-' (d oxygen). Hence, the conversion of water to hydrogen and oxygen i s thcrmo-

Fundurne~ztcrl concepts 5

dynamically unfavourablc and can only occur when electrical cnergy i s suppl~ed. Conversely, a cell which combiner the reduction ofoxygcn and thc oxidation of hydrogeniscapable of supplyingmergy and,indra-'. 0,-H, fuel e l l s have b a n construacd (Chapter I I).

Hcne, a l t i rmodynamic discusion would lcad to the conclusion that thc overall ccll reaction wil l o a u r and current will flow whenever the two clcclrodcr of thc cell arc inlcrconnectcd by an external elstr ical circuit and either: ( I) the cell reaction has a negative fret energy; or (2) (he cell reaction has a positivc free energy but a vollagc larger than the qu i l ib r ium cell potential I S applied across the two electrodes to drivs the chcmical change. Thcrc conolusions are sound but do not consider lhe rate at which the chemical changccan takc plam, 1.c. the ccrr2:.t !L.at hill god. T h i r z l cfcte,niczi rlsan:e wi:I 3c~:nd on th: kincticr GI the two elcctrode reactions. Some clcctrode reactions are inhcrcnlly fast and give a reasonable current density (currcnt/unil arcs of electrode surfaa) closc l o the equilibrium potcntial. I n contrast, others arc inhcrcntly slow and then an overpolcnlial q ( = E - E,), is nnasary in ordcr to obtain any required current density. The k ine t ia oleltctrodc reactions arc discussed below and we shall see that q inneases with currcnt density I.

We noted above that, for thc all reaetion to occur, ions must pass through the solution and separator belween the electrodes. An input o f energy is also essential l o drivc this migration proccss and kads to a potential drop iR,,,, (where R,,,, is the internal resistance of the all, a function of clcctrolytc properties, the form of the clcclrodcr and ccll design) within the ccll. llcnce. lhc cell voltage required t o observe a current i in a real ccll is given by:

Both the q and iR,,,, t c rks increase wirh current density and may bc regarded a 5 inefficicncics whereby clcclrical encrgy is degraded into hcat which mual be taken into account i n any consideration o f hcat halanoe. Indeed, the pcrccntsgc cnergy efficiency of a ali may be defined as:

% energy efficiency = IE - E:)100 A: --

and onc reason for elwtrochcmical technologists t o be concerned with c ls t rodc kinetics, electrolyte properties and crll design can be sen.

These conclusions are understood best by considering h~ r thc r our two particular ccllr, the lead-acid battcry and a water clcctrolyscr. The propert in sought i n secondary batteries arc discussed i n detail i n Chaplcr II. Ilcre, i t i a suficient to note that the ballery should be b a d on a all reaction where the free encrgy is large and ncgalive so that the equilibrium all voltage i: large In addition, as current is drawn from the battcry, the all voltrpe thould remain a: close as possible to the equilibrium value and this require: that the over. potentials at anode and cathodc are low (i.e. that the kinelira are fa:t)and that

(he IR,,,, d rop through the cell is small. i.c. a narrow interelectrode gap and a high electrolylc conduclivily. For a secondary battery, i t is also necessary lo r recharge l o be pos~ihle; by supplying energy to the bauery, i1 musl be possible l o reverse the ccll chemistry occurring during discharge and the active materials ( i c lhe PbO, and P h in the lead-acid battcry) must he reformed in a suitable stalc for further discharge, Thc lcadacid battery meets these idcals to somc extent. Similarly. the yr formancc o fa u'atcr electrwlvier will bc enhanccd i f the ccll potenliiul rcm:lins close to ihc c q ~ ~ i l i h r i ~ l l n porcnli:~l durine opcralion. T h i i again rcquires that the 11 and iH,,,, icrmr arc minimilcd.

I t wi l l already be clear that i n ordcr to understand the way i n which thc variou3 c~perimcnl.- l paramclcrs can allrcr the performance o f electrochemical cells and, i n particular. the khav iou r of thc two elccrrode reactions. ;I will be necessary i o hme a knowledge or the lhcrmodynamics and kinetics olelcctrode reactions. Thus. one purpose of this chaptcr i s l o develop the concepts and equalions which wi l l he uscful for chic purposc.

Firs!, howcvkr. we necd l o recognize thc nature o f eleclrode rcactions. Perhays the simplcst elcctrode reaction is onc which intcrcon\,erts, at an inert surlace. l w o spccics 0 and R which arc completely srable and soluble i n the elcctrolyris medir~m containing an excess of eleclrolyie which is etectroinactive:

Even i n this casc. ~ h c clccrrvde roc t lun i s a sequence of more basic steps: l o maintain a current i t is csscutial to supply reactant to /he elcctrode surface and In remove ihe product, as \\.ell as lor the eleclron Iranqfcr rcaction a1 the surlace to occur. Hence, for cxamplc. in expcr~mcnial conditions where 0 i s rcduced to R. the elcclrodc rc:~ct io l~ tnusl h:l\c i l l lce steps:

a1.J since the rate o f rcduction and hence lhc cathodic current density is de~ermincd by the rate of the overall sequcnce, i t musl be depcndenl o n the rate of the slowest step. Thus, l o understand The characteristics of such an elcctrode rcaclion, we need !o know about both mars transport and electron transfer.

A n examinalion or reactions (I.IHI.1 I ) quickly shows that eleclrode re- actions ofintcrcst i n electrochemical technology are seldom that simple. They involve multiple-electron transfers and at least three additional types o f tame steps also occur: chcmical reactions, adsorption and phase formation.

Fundumental concepts 7

I. Chemical reactions. The s p i e s formed by e lw l ron transfer may not he slablc in the elslrolyais medium: il may only be an intermediate which undergoes chemical change t o form the observed product. I n favourable conditions, there may he a single rcaction pathway leading t o one product but wi th reactive intermediates i t is common for thcrc t o be competitive rcactions leading to a mixlure ofproducts. I n general. the chemical reaction may be a homopcneous p rou rs c-xurring as the species R is rans sported away from the surracc o r a heterogeneous proccss occurring while Ihc spfcies R is adrorbed on thc sur lau (see below). Rcacti.,ns (1.4) and (1.1 I) are cxamplcs where such lol lowing chemical reactions are important.

Less frequcgtly, i t is found that the electroactive spccies 0 is not the major species i,i bulk solr!ion t s l i s m l y icrmcd t y a ;I,cmica! p o ~ s ~ s , i.t. the eleclrode reaction is disturbing an equilibrium i n homogeneous solution. A n example is the rcduction of acetic acid to hydrogen which promeds via dissociation o f the wtak acid and reduction of the proton.

2. Adsorplion. The sequenae ol reactions (1.20)

8 Fundamental concepts

generally be sufficient for us to understand most cells i n industrial practice provided wc can rccognizc which o f the lundamcntal steps i n the overall electrode processes predominantly determine the cell characteristics.

I.! ELECTRON TRANSFER

I n this section, the thermodynamics and kinetics o f the clectrode reaction:

O + n e = R (1.19) will kc C:vclo,xd. 0 ar.d R ace co!nplrlLly stable, solution-soluhle sp~cies. The working clectrodc is totally inert and the solution has been thoroughly dc- oxygenated so that thcrc arc no competing electron-transler reactions at the surface. The solution around the working electrode contains 0 and R, at concentrations c," and c." respectively (which are sufficiently low that the resulting currcnts do not give rise to significant iR drop) and a high concentra- t ion o fan inert eleclrolytc. Thc cell lor this discussion also contains a large area relerencc electrode which ncvcr becomcs polarized (its putential remains con- stant cven when current is passed).

As with any chcmical proms, i t is logical first to consider the thermodynamics. Suppose the potential o f the working electrode vs. the reference electrode is monitored while no current is allowed l o flow. Under these circumstances no chemical change can occur at the surrzce and the solution composition will remain unchanged and unilorm. The working electrode will rake up i t s equilib- r ium (or reversible) potential E,, which may also be calculated from the Nernst cquation:

R T E, = c+ ~- ln(c,"/c.") (1.23)

n t

whcrc E: is the formal potential lor thc couple O/R i n the electrolyte medium. Strictly this cquation should be written i n terms o l the activities o f 0 and R but lo r simplicity i t will be assumed that thc rat io o f activity coefficients i s I. I t should bc rccognizcd, howcvcr, that in many industrial cells wi th high conan- trations o f electroactive species and maybe no additional elcctrolyle, such an assumption would introduce an error and i t would be better to include the appropriate activity coefficients o r fugacities (section 1.8). Also in general, the Nernst equation should be writtcn in terms o f activities o r concentrations at the electrode surlace (c;, and c;) but throughout this section i t is also assumed that the currcnts are low enough for the surface and bulk concentrations t o be esscntially the same. Certainly, when no current flows, no approximation is involved.

A t thcequilibrium potcntial, atthough no net current is observed, there will be a dynamic equilibrium at the electrode surlace. Both reduction o f 0 and oxidation o f R wil l be taking place, but these proccsscs will have an equal rate so

that thev lead to no ahange in the composition o l the solution I n terms of current density this may be written:

- -

- / = I = 1, (1.24) where 7 and arc the reduction and oxidation partial current densities. They have direrent signs because oxidation and reduction causes electrons to Row i n oppocile airat ions thl'ough the extcrnal circuit; by conventiun, oxidation i s taken to lead to a positive current. I, is known as the exchange currenn density. I t i 9 a very useful parkmeter in the description o f the kinetics of electrode rcactions but is primarily a measure o f the amount ofelectron-translcr activity i n the equilihrium s i t~~at ion. A high v:~lue indicates that much simultaneous oxidation and reduction i s talierg place and is inuicative u l an inhcrcntly l a ~ t reaction. A small value suggests that only a small amount of electron transler occurs at the equilibrium potential and is a symptom o l a slow clectrodc reaction.

The cquilihrium potential E. and the exchange current density I, togcther totally characterize the equilibrium situation at an electrode.

I f a potential more negative than E , is applied to the working electrode. equation (1.23) requires that a slight change or r r~ rs to the ratio c:/c; at the electrode surface. In lact.a decrease i n this ia t io i s necessary and thiscan only be achieved by the conversion 010 and R by !hc passage o l a reduction current. I n general, the magnitude o f thc net cathodic current and thc time i t takes to establish the concentration ratio dcmandcd by equation (1.23) will depend on the kincticr of the elatron-transfer reaction. The net cathodic cumnt is achieved by an increase in the partial cathodic current and a decrease in the partial anodic current compared t o theequilibrium potcntial, ie , at this new potential E I-ore negative than E.). - 7 z I, and i c I,. Convcrsely, i f the potential G: the working electrode ismade positive t o E.. a similar argument will show tha! a net anodic current will %ow (Fig. 1.3).

i - - At the equilibrium -- I = l t l = 0 potent~ot, E, - NO ner current f l ~

1

i - - Negative to E, - I = I ~ I ~ O

- I ~~f ~ ~ t h o d ~ c currenr flows

P o s , ~ , " ~ to fe i 1. j + j > o F ~~t onodnc current l lows I

Fig. 13 Illustration of thc way the cxpcrimcntal current density I varies with potential. Rcmemkr that cathodic and anodic partial currcnt dcnsilies havc opp0SilC ~ i g n ~ : by convention. anodic currcntr are taken as positive.

10 Fundntnotrn i concepts

Now i t is ncccrsary to formulate the equations which describe the kinetics 01 an electron transler reaction such as reaction (1.19). I t is normal to assume that electron-transfer pro~csses arc first-order reactions and then the raie o l reduc- t i o t ~ of 0 depends only on a rate constant and thc concentration of 0 at the site o f electron transfer (at the elcctrode surlace) As noted above. only situations where the h u l l and surf8ce concentrations arc similar will be considered lor the present. This is cqutvalcnt l o m u l l t i n e that mass tranTport plays no rolc in dctcr11,ining thc overall rate (see p 30). Then we may write:

Rate of reduction o f 0 = i c ; (1.251 and therelore the partial catho.fic current density is given by:

- -

- I = nFkc," (1.26) But the rate constant for a licteropeneous elcctron transler process has a particular properly. i t is dependent on tlte potcntial field close to the surface driving the movement of electrons and hence on the applicd electrode potential. We shall assume, as is pncra l l y round erperlnrentally. that the potential dependence is o f the form:

where a, is the cathodic transler cncflicient and h , I< the rate constant lor electron tranqfer at E -0 v5 the relcret~cc elcctrode Therclore

Thc corresponding equations lor the ~ x i d a l i o n or R, which i s occurring simulta- neously with the reduction 01 0. are:

Rate o f oxidation = &c;

i = "F i r , "

Thc observed current densiLy at any potential is given by:

I - i t i

Electron transfer 1 1 This equation may be simplified by de f in in~ a new parrmztcr, thc overpotential v :

which is simply a measure o l the deviation of the erperimental potential from the equilibrium potential lor the solution being considcrrd In addition, one may use cquation (1.24) which applies only at E = E. and leads 117:

Then substitution ofequation (1.34) into equation (1.33) end use of the equalities i n equation (1.35) gives the Butler-Volmer equatlun:

This i s a very usclul equation i n experimental and applied electrochemistry and shows that the measured current dcnsity is a function 01: (I) overpotential; (2) exchange current density. I,; and (3) the transfer coelf,cients, a, and m,. The t.ancfcr c~~ell ic ienls arc, a: least [or simple electron translcr processes. not independent variahles. I n general:

and, i n fact, i t is common for a, = a,== 0.5. The above discussion is complicated by the number o f ditlerent potentials and current densities used, and to aid understanding t hc~ r definitions are summarized i n Table 1.1.

Tablc 1.1

Symbol Definition

f;P Formal clcctrode potential measured vr. a rclercncc cltctrode E. Equilibrium potential measured vs a relercnn elcctrodc E Experimental potential measured vs. a rclcrcnoe electrode 'I Ovcrpotentisi-the dcviation o l the cxpcrimcntal potential

lrom ihc cquilibrium potcntisi, i.e. q = E - E, I Eapcrimcntal current dcndly a1 the ovcrpotcntial. q (or actual

potential, E) 1. Exchange current dcnsity i.e. the partial anodic and cathodic

currcnt densities (01 equal magnitude but opposite s i p ) at the cquilibrium jmtcntial

I Partial cnthodic currcnt density at the patcntial E i Partial anodic culrcnt density at lhc putent~al E

12 Fundamental concepts

I t should be noted that equation 11.36) retains a form wh~ch emphasircs that the measured current density at each overpotential is the sum of the partial cathodic and anodic current densities. Morcovcr, this indicetcs useful limiting forms. Thus. as the ovcrpoten$al is made morc negative. I increases while 7 decreases and quite rapidly - I B 7. Then the first term in the Butler-Volmer equation has become negligjble compared with the second and one can write;

l 3 i s equation applies when the overpotential is larger than abou( 52 mV and shows that in this potsntial r a n g the

1 14 F u n d o n ~ r ~ ~ t a l concepts So far, our trcatmant o f the kinetics o l electron transfcr has been rather

pragmatic and gives no insight in to how the act occurs on a molecular lcvel. Our undcrstnnding of the factors which control the kinetics o~ electrode reactions can bc increased by applying transition-state theory to the heterogeneous proccss occurring i n a potential gradient. In general. the theory is based o n the concept that !he rate of reaction is delcrrnincd by an activation barricr i n free cncrgy. I.C. the rate constant is given hy tlic equation:

wncrc L is i l t c : i ~ q c t ~ ~ ; . 1j:tor -on AG, thc enc:grr o l activ*tion. 11, electrode reactions, the true driving lorce for elcclron lronsler is ihc polcntial dilicrence 4, - 4, created between the electrode and the soluti~,n. and i t should be emphasized that this potential drop occurs over molecular dimensions (ie. maybe 2 V i;) 0.1-1 nm) at the electrode-clec~rolytc intcrlacc. Figure 1.5 shows the lree energy curves for the ini t ial and final states o l the electrochemical reduction o l O 4 R at two overpotenlialc: clearly, overpotent;31 and 4, - $, must be related and because O and R, i n gcncral, and also the electron, are charged specie:. their free energies umill depend on the electric potential o n the phase in which th ry reside. In the ini t ial state, the total lree energy G. is the sum o l that lor 0 and for the electron. ie.:

G, = Gb + z.(;+, - rrF4. (1.45) where G; is the free energy o l the oxidized species i n the absence of any potentinl field and takes into account all the chemical lactors and 2, is the chargc on 0. Thc equivalent equation for the final state is:

GR = Gk .+ Z , , F $ ~ ( 1 461 since only the species R is involved. Mak ing the ovcrpclential morc ncgalive will have the sameclfect on 6. - 4,. I f one assumes that the change in polcntial only occurs on the solurion-side of the interlace. the solution potenlial #I, will hecornc morc positive. If, l o r simplicity, one also consiclers only the case where both O and R are positively charged, the changr i n 05. wil l lead to destabilization o lho th 0 and R. Hut 0 rnusl carry a larger positive charge than R and hence, will be clcstabilized l o a greater extent and this is recngn~zed in Fig. 1.5 b y a larger shift i n the potential energy surlace on changing the overpotential. I t can also be seen i n ihc figurc that the free energies o f activation, zx and are less sensitive than cilher Go o r G, to the change in 4,4, (or q). Hence. the lree energy of activation lo r thc lorward process is given by:

Jet =const +nflF($.-~$,) (1.47) a staterncnl ,which is equivalent to noting !hat only a lraction a, o f the applied

18 Fundamental concepts

within the bulk solution. The double layer causes the potential dilferencc ), - 4, t o be smeared out over several molecular dimensions (Fig. 1.qb)). The kinetic parameters should therefore be corrrcted for: I. The eRcct or the smeared-out potential field on :he driving force Tor electron

t ransl r . F rom the model i n the figure, i t can he seen that the species O is, at hcst, at the plane ofclosest approach to the electrode and at the centre of the species the ponrrtial available to drive the reaction 6 only 4, - 4, (which is less than 6. - 0,).

2. 11 0 is charged, its concentration at lhc plane o f closest approach diflers from, that in hulk solution because o f the potential field.

A detailed treatment o f these 'doublc-laver corrections' is available in the teats recommended at the cnd or this chapter.

The last 25 years have seen sevcral attcnipls id de\'clop a stalistical- mechanical theory of electron transfer. These treatments, however, do not predict the simple linear l og1 vs. E rclalionship o f thr Taicl equations which seems adequate for the description of charge transfer controlled electrode reactions i n electrochemical technology. Therelore, thcy will not hc d~scusscd here.

1.2 MASS TRANSPORT I n general, i t 1s necessary to consider thrcc modes o r mass transport in elcctro. chemical systems: ( I ) dillusion; (2) migration: and (3) conrectlon. I. Diflusion. Diffusion is the movement o f a species d0u.n a concentration

gradient and i t occurs whenever there is a chemical change at a surfacc. A n electrode rca-tion cons,er:r stzr!i?!g m a w i a ! t o product 1e.g. 0 -1 R) and hence closc t o tlie electrode sutface there is a boundary layer (up to 1 0 ' cm thick) i n which the concentration of 0 is lower at thc surface than i n the bulk while the opposite is the case ior R and, hence, 0 wi l l dilluse towards and R away from the electrode.

2. Migrotion. Migrat ion is the movemcnl o f charged species due to a potential gradient and i t is the mechanism b y which charge passes through :he electrolyte; the current o f electrons through the external circuit must be balanced by thc passage o l ions through the solution betu,een the electrodes (hoth cations t o :he cathode and anions t o the anode). I t is, however, not ncccssarily .,n important form of mass transport for the electroactive species, even i f i t i; char~cd. The forces leading to migration are purely electrostatic and, hence, d o not diccriminarc betwcen types of ions. As a result, i f the eleclrnlysis is carried out with a large excess o f an inert electrolyte i n thc solution, this carrim most of the chargc. and l i t t le or the elcctroactivc species 0 is transported by migration, i c . tlic transport nombcr of 0 i s low.

M a s s transport 19

3 Cr,nuccrimrt. Convection is the rnovemcnt of a species due t o a ntcchanical force. I n practice, convection is usually induced by stirring or agitating the clectrolyle solution or by flowing i t through the ccll. Sometimcs the electrode i s moved. When such fcrms or forced convection arc present, thcy are normally the predominant modc ofmass transport. I t is possible to carry out clcctrochemistry in the absence of convection by using a still solution i n a thermostat, but only o n a short timcscale. say less than 10s. O n a longer timcscalc. natural convcction arises from small dilTercnces in density caused I)? llac chcmical c h a ~ i ~ c at the clcctrodc surface.

The trcatmcnt of mas: transport. more than any other aspect o f the subject. h~gh:ights the drfirences betwucn laboraiory crpetimenlr arrd inoustrial-scalc clcctrolyses. In the former, there is great conctrn to ensure that the mass transport conditions may be described precisely by mathematical equations (which, moreover. are soluble) since this i s essential t o obtain reliable mechan- istic and quantitative kinetic information. The need i n an industrial ccll is only to promote the desired ercct within technical and economic restraints and this permits the use

20 Fundamental concepts Mass transport 21 d species i through a plane parallel to the electrode surlace(Fig. l . l(a)) is given by: such as chronopotentiometry. chronoampcrometry and cyclic voltammetry.

The solutions to cquation (1.50) show that thc concentrations 010 and R vary dc

Flux = - D, 2 (1.49) with timc as well as distance from the clcctrode. Plots of c, vs. x are known as d r concentration profilcs and considcrarion or their variation with time is an i where D, is its dimusion cocfficicnt. Fick's second law discusses the change in concentration 01 i with timc duc to diffusion. At a point at the centre of an element olsolution bouvded by two planes parallel to the electrode (Fig. l.l(b11 the concentration will change becausc diffusion is occurring both into and 0111 of the element. This leads to the cquation:

Integration olequation (1.50) with i n ~ t ~ a l and boundary conditions appropriate to the particular experiment is the basis of the theory 01 instrumental methods

Flat eleclmde of Plane wraltel infinite dimensions to electrode Surface

flux, = -

O Perpmdvzular @ @..I to the plane . *

a (4

Centte of volume element ( X from eleclrode)

I Nel accumulalion in volume element/u~it lame

ac, aZc -, h . 2

Plane al x-dx Plane 01 r + dx (b)

Fb. 1.7 Model used lor the description olthe diffusion ofthe eleclroactive spccicr 0 and product R during an electrosnalytiol experiment. (a) Ficl;'r first law, (b) Fick's second law.

excellent way 1.0 understand non-steady-state experiments. I t in impoflanl to recognize that diffusion occurs so as to minimize dimerences i n conantration at all points in rpaa. Hence, in thesteady stale the concentration profilmarclinear (if the profilcs arc non-linear, there are some points i n space where diRerences i n concentration have not been minimized).

Fick's first law applied at the electrode surface can always tc ustd to relate the currcnt density to the chemical change at theelectrode by equating the Rux o f 0 or R with the flux ofeicclrons:

or: I

A rotating disc acts as a pump, pulling solution up to the disc and throwing i t oul across the shroud (Fig. 1.8); hence, i n experiments with a rctating-disc electrode,concentration shangcs will arisedue to both diffusion and mnvection. l f the radius ofthediscis rmall compared with that ofthe shroud, wecan sssumc that access of the solution to the whole electrode surlace is uniform. Thcn

Fig. 1.8 Convection resulting from s rotatingdisc electrode. Streamlinn Irom: (8) lido view. (b) bclow the disc.

22 Fundamental concepts

concetttration wil l again be a function only o f thc direction perpendicular to the disc surface. The equation:

dillusion convection

includes both forms of mass transport. I 1 rcfcrs to 'convective dillusion'. UilTusion is again expressed by Fick's second law whilc the changcs i n concentrarlnn due t o convection depend on the vclocity of solution movement in the .Y direction 18, and the concentration gradient ar,/i)+ i n the same direction Lommonly ottly steduy-stale tneasuretncnts alc ni;tdc in ;s,dt~np disc :;PC-.- ments; then. r'c,/icr is zero and equation 11.53) reduces to:

A solution o f this problem depends on knowing the relationship between 11, and x as well as other parameters, particularly the rotation rate o f the disc since i t i s clearly ihc rotation which is responsible for the cortrection i n the system A study of thc fluid mechanics (sec below) or tlic systcni. lcads to expression:

where sis the kinematic viscosity (dynamic vitcnrityidensity) ofthe solution and v l i s the rotat ion rate or the disc. I n fact. this expression is valid only for small: since, well away from the surface, r, is clearly indepcndent o f x. I t is, however. the basis of a very useful approximate modcl lo r rotauncdtsc experiments which has analogies i n al l systenis involving cnnv:ction. At thc surface. the flaw ofsolut ion must bezero(thc solution cannot pass t h r h g h the solid rdrface) but closc to the surface, the velocity of solution flow increases rapidl!. ( i . s r2 ) . I n thc Ncrnst diflusion-layer model, one defines a hypothetical boundary layer o I thickness 6, inside which mass transport is considered t o be onl!. by diflusion. O n the other hand, convection is strong lo r 116, and maintains the conccn- trnlions at the bulk values. h:ore precise mathematical treatments of !he rotatinedisc electrode are equivalent t o this model u-itli 6, given by:

Sincc only thc slcndy state i s being considered, the concentration profiles are liltcar (1.1~ 1.9) Ilcncc. the modcl predicts that the fluxes t o the surface and. hence, tlic ctlrrcnt clcttr~ly depend on: ( I ) electrode potential which determitles tlic ntrfacc cnnccttlrati~r~ts; ( 2 ) hulk co~icentrations: and (3) rotation rate which

Mass transport 23

t 'i

Fig. 1.9 Stcady-scare concentration profiles for thc els~trode pr-s O + n e - R. solutton contains c," - 3 ~ ; .

controls 6,' i.c.:

Moreover, at very high overpotentials. theelectron translcr is very fast, so c&=O. Then the m x s transport limited-currcnt density is given by*:

The steady state limiting cuncnt can also be written in terms or a mass transpod coefficient kL i.e.:

-IL-#FkLc: I t can bc sen that the mars transport caefficient :; related lo the thicknas of the Ncrnrr dimusion layer by k,=D/d, and hence. k,=0.62D"'v~"6w"' E ngnnsn ' onen prcfcr the u s of mass transport cafficient becaux i t avoids the discussion of thc Nernst diKusion laycr,a w n a p t usdvl to an undcrstanding o lex~r imcnts and widely met in the electrochemical liaraturc bur. i n b c k kticious sincc mnmtrat ion profiles are never linear. ' A wmmmt about the rclativc siza of the boundary layers discus4 in elenrochemistry is ncccssary. The dimensions of lhc double l a p may be 5 x 10-8m. I n contrast. the Nernst diflusion l a y r may have a lhickness of fO-'cm while thc real layer cffcctcd by the clatrodc reaction may he an ordcr of magnitude thicker.

As noted above, a similar model is appropriate t o all systems involving stirred or flowing solutions and the problem is to relate the thickness o f the 'equivalent' boundary layer to the mass trmsport in the system.

1.2.2 Mass transport in industrial electrolysis

I n industrial practice, i t is possible l o find examples o f cells which m e unslirrcd solutions (e.g. electrorefinin& batteries), stirred or agitated solutions (e.g electro- plating) and flowing electrolytes, e.g. synthesis. water treatment. Moretrver, i t is unusual for the flow of solution and the current path-which depend on cell geometry - t o be pa;allcl, arrd ,he ciectrude may no1 be 2 flat ph te (e.g. bed electrodes, cathodes for plating); as a result, we must write our mass transport expressions in three dimensions. N o r i s i t always possible to assuni? that migration o f the electroactivc species is unimportant.

Thus the most general forms o f the rnass.transport equations are:

(Flux), = - D, grad c, - u,c, grad (I + c,u (1.291 diffusion migration convection

where u, i s the mobility of species i and + the potential field strength, and: aci -=D,V2c, u , grad II, grad c , i . grad ci (1.601 '71

These equations may be written in the most convenient coordinatsr for the cell and electrode geometry but as an example. equation (1 601 in cartesian co-ordinates becomes:

ii+ JC, all;.( i # ? c +-2+-f

J r 2.; ax J y 21 ?.- r: 1 Clearly, such general expressions are intractable and we need t o consider l imit ing cases o r use other approaches.

F lu id mechanics is the study of the motion of f lowing or stirred fluids, usually liquids o r gases. I n clcctrochcmical technology i t has !wo direrent applications: ( I ) t o describe the movement of electrolyte solutions in a cell, since this wi l l be a principal driving force for mass transport to theelectrodes; and (2) t o ensure the proper design o f the pipes, valves and junctions which jo in the cell t o the rest of the plant. Quantitative fluid mechanics is based upon the continuity equations which stale that at al l points in space, charge, mass, momcntum and, for inviscid flow (i.c. fluids where no vircous forces operate) energy must be conserved. This section wil l deal mainly with the qualitative concepts becausc of the very complex nature off low in most electrolyscrs.

Mass rransporr 25

We shall cons~der firsi the flow o f solulion over a flat plate. T w o forces will be acting upon the fluid in $uch systems:(l) the cause o i l he flow (that eeneratcd bv

- - . -

a pump or a solution heid) known as the inertial force; and (2) that for- which opposes the Ro:v and results from viscous forms at the interlac+ between the plate and the solution. - I

Suppose we assume that the solution may be dividcd into clemcnts, then the viscous loroe will initially cause that element next to the stationary plate to be retarded and later each element will be slowed down by that closer to the plate. tience, as the solution flows over the plate, a boundary layer of more slowly moving solution will develop (F ig 1.10). I n an elcctrolytic cell. the flat plate

rC would normally be thc electrode and therefore the formation o f such boundary laver> h u parl~cular importance The e l r c t r dc rezztior. ta!.cs place i n the boundary layer in the presence of velocity gradients.

" - "\J\\,,g,\\@\,,g uo

U l a )

lnv ixa f l a lnvixid

f b w Non-linarr -

Re1ard.d flow intease in Uo

Fig. 1.10 Three diRercnr rcpresenrations of the devclapment of a boundary layer over 1 Rat plate, e.8, an elcelrode.

26 Fundomrntol concepts

With such a Rat plate, the boundary layer will increase i n thickness in- definitely, i f slowly (Fig. I.lO(c)). O n the other hand, i f thc flow is in a restricted channel ( e . ~ a circular-tube or a parallel-plate cell) the boundary layers at the (WO walls must merge at somc point and beyond, a steady-state situation or 'lully developed laminar flow' will result (Fig. 1.1 I). Fundamental mass trans- port studies in electrolytic cells are usually carried out in cells with an entry lcngth wilhout electrodes so that the boundary-layer thickness i s uniform over thc current-carrviag surlace.

I t can already be seen that the development and scale of the boundary laycr will be dcpendent on the relative importance of the iqcrtial and viscous forces. For this mason the ratio ofinertial.viscc~xs fnrces is piven a nave, the Reynolds number Re, and it may be calculated from the formula:

where p is the density of the solution, p its dynamic vircosity, 1, its kinematic viscocily, li a mean flow velocity and I a characteristic lengtli (in the cxample abovc. the lcngth o f lhc plate) I n fact. the boundary laycr develops in the way discussed only below a critical value of Reynolds number where the viscous damping is sulXcient to suppress any perturbations which arise. At higher Rcynoldr number, the ~.iscot~c damping i s no longer predominant and turbulence commences: in effect. the high rates or shear induce rotation of thc solution arid small eddies are formed. This may he shown clearly by ~xperimenls where dye is injccted into a solulion Rowing down a plas~ tube (Fig. 1.12). Any obstacles to fluid Row, or roughness i n the channel wall will cause thc com- menccment of turbulence at lower Reynolds numher.

bundory layers merge

Growing boundary

k::i:o sk@;g Enlry length Fully developed laminar llow

- -

Vil . 1.11 Ikvclnprncnl o l a hydrodynamic boundary layer for rolulion Rowing through n luhc

Fig. 1.12 Solution flow through a lube as shown by !he dye tcchniquc. (a) Reynolds numbcr Re < 2WO. (b) Reynolds number Rc > 3WO.

Turbulence in elcctrolylic cells is usually advantageous sinct the eddies both incrcase mass transport 01 the elcctroactive species to the electrode surlaoe and promote the exchange of species between the bulk solution and the boundary laycr. minimizing local p H and othc: concentration changcs due to the electrode reaction. Indced, i t is not uncommon to introduce insulating nets, bars or other structur4 features into the cell to act as turbulence promoters. I n ccrtain cases. the elcctrudc itself may be in a form (c.g. mesh, reticulated metal, particulate bed, fihrous material) whereby i t acts as a turbulence promoier.

I t will be seen in the next and subsequent chapters that a wide variety orcell geometries (e.g. parallel-plate. concentric-cylinder, Swiss-roll), types 01 electrode (e.g. plates. beds, porous expanded metals and gauzes) and flow patterns are used in i,~dustrial electrochemistry. I n most, the flow is too complex to warrant a detailed fluid mechanical calculation. Rather. the normal approach to mass transport in electrolytic cells is to treat the cell as a unified whole and to seek expressions in lerms of space-averaged quantities which permit some insight into the mass transport conditions within the cell.

Once again, considering the simplified problem of laminar flow over a flat plalc, i t is possible to derive an expression for the Sherwood number Sh:

Sh= 0.646 ReoJSco.33 (1.63; I IIcre. Sh is a mcasurc of the rale of mass transport, which i s usually cnlcolatcd

lrom the limiting current density I, for the plate electrode (i e. the potential o f I the plate is held at a value where all theelectroactivespecies reaching the surlace I undergo the electrode reaction) using the relationship:

28 Fundamenrol concepts

where L is the length o l thc plate. The Reynolds number, as was discussed above, compares the relative magnitudes of the inertial l o r a s to thc viscous lorccs i n the cell. The Schmidt number Sc, defined by:

compares the rate o f transport by convection t o that by diffusion. In general, mass transport in electrolytic cells with Row may be d~scussed i n

terms o f the expresrion:

wherc t k Lunstant; 7 . a :ad 5 -any k 3b:airrd fro- rxoerimental mearure- ments of f , under various Row conditions. For each reactor, i t wi l l be necessary t o dcfinc a r t a i n average parameters. For example, il one considers a paralle!. platc ccll where the rectangular anode and cathode are inset in the walls o f a flow channcl i n a position where onc has fully developed laminar flow (Fig, l.l;), the appropriale equation is:

Sh = 1.85 ~e"'Sc'''(d./L)"' (1.67)

Anode

v

Entry zone Cothcde I I

(b) 4 L -

Fig. 1.13 Parallel-plate cell without separator but with fully developed laminar flow. Critical dl dimensions are B/S > 6 and 10 < L/d, < 40. (a) Vicw along all at the beginning of the clcctrodcs. (b) Vicw across ccll.

Mass rransporr 29

where Rc=pud./p, Sc=p/pDand Sh=- and d, is the equivalent diameter nFc,"D

(sometirns. sallcd the hydraulic diamctcr) which is defined by:

O f course, crprcssio,> (1.67) is only afiplicahlc in the absence o f turbulence and, hence, abovc a critical value of Reynolds number where turbulence is observed. For thc parallel-plate cell Re>2000, a different expressiun must be ured:

I t cannot be cmphasizd too strongly that this approach, based on dimen- sionlcsr cuirelalionr, only givcs an insight into macroscopic space-avcragcd mass transport condilions within the cell. II wil l not, lor cxamplc, show the extent t o which the flow between two parallel-plate electrodes is divided into a rapidly moving bulk phase and a slowly moving wall phase(Fig. 1.14) Nor will i t demonstratc .;/hcthcr ihc clcctrolylc feeds and outlets to thc cell arc dcsigncd so as to give a uniform electrolyte flow over the whole eleclrode surface, an

Retarded wall phases

Cathode Anode

I Bulk I phase

1 Fir. 1.14 Electrolyte how through a parallel-platc reactor crnphasizins the re#rel(slion 01 the Row into the rapidly movlng bulk phax and slowly moving wall p h a m I

30 Fundoinento1 concepls

irnporlant lactor in determining cell pcrlormance. Such questions rcquirc q~qitc direrent approaches and experimental techniqocs may be based on: I . Segmented electrodcr. 2. Microprohcs dcsrgned to measure parameters sijcl~ as local currcnt density,

potential or pressure drop. 3. hlnrkcr t r chn~ques -a well defined pulse o f a dgc o r an ion is introduced at

thc cell ~nlcl and thc d i spc rs io~~ o f thc spccics mnrker is nieasurcd at thc cell nutlet.

Such t cchn~qr~cs are discussed furthcr in scction 2.6.1. From the ahovc diccussion, it can he scen that the mass transport lor a given

clcctrodc-elcctro!ytc gcornetry and elcctrolytc hjdror lynan~ics ma) he lclatcd to thc proccss parameters by a suitablc dirne~lsionlcss grnup correlation, eg.. mas5 transport t o the rotating disc in laminar flow conditions may he dcscribcd by thc equation (see footnote, page 22).

kL=0,62DIil,.-8!6 u > " ~ ( 1 701 Multiplying by the ratio r fD , where r is the radius of the disc, pives:

k,r -. = 0.61 ,,,, l ' 1 , , 1 ' " - l 3 D

(1.711

or:

Electron trunsfer and mass l ransporl con t ro l 31 complete I-E curvelor thecouple O/R (Fig. I.IS(a)). It should be noted that the rate 01 the electron transfer process is a lunction of potential ( q u a t i o n (1.36)) and that whatever the mass transport conditions in the a l l , there will be a maximum rate a t which electroacliue s p c ~ i e s can reach the su r faa .

A1 the equilibriuin potential, n o net curienl flows. As !be potential is made negative t o E,, a reduction current is observed. Initially, it will be vcry small and the surface conccnlration 01 0 remains close t o its bulk concentration: this potential region will lead t o a linear Talel plot (Fig. I.IS(b)). As the potential is made more ncgalive. the rate o l reduction increases rapidly, in lac1 exponcnt ia l l~

Reductton 0 - R

L L 1 or (in dimensionless group format):

-800 -600 -400 -200 1 - (8) 200 400 600 800 V I m V Sh=0.62Re1~'Sc"' ( 1 . 7 3 ) I Mixed Mass

t ' I tronsfer

I ~nntrnl control It can be seen that equations I 1 3 P I and (1.73) are csscntiall!. cq~.::alcnt (note -- . T h e former is used by elcctrochcmists. while the latter is preferred

nFc"D by chemical engineers since i t facilitates a compnrisan between other cell geometries/flow conditions and allows analogies with heat and momentum Irnnsfcr.

Mixed ~ o f e c - .- (charge I (chorge

tronsler I t ransfer

I 3 T I I T . INTERPLAY OF ELECTRON TRANSFER AND MASS TRANSPORT C O N T R O L

CC

! Mass 200 mv

It was notcd in the introduction t o this chapter that the reduction of 0 - R is a t t ronsfer 1 control least a three-step process, equations (1.20)iI ,221 inrolving both mass transport and electron transler, and Illat the rate o f the overall sequence, and therefore 1 1b) current density, rlcpcnds on the slowest s t c p Having considered electron trans- j Fit. l.IS(a1 Complete I-b curve. (b) LO^ 111. vs. ,, curve for !he o + ~ ~ - = R fcr and rnnsr trnnsporl indcpcndcntly. we can n o u consider the s h a p of a when the solution contains c; = 3 d . Case 01 slow electron tranrfcr, ie. low I,.

32 Fundnmenrol concepts

(equation (1.38);. and is eventually rapid enough for c;, to become significantly less than c,". Then mass transport will need to occur and the current comes under mixed control; the Tafel plot is non-linear and the current density bccornes sensitive to the mass transport conditions. On making the potential even more negative, the surlace concentration o r 0 decreases from c; effectively to zero. At this point, the current density becomes independent of potential and thc process is said to be mass transport controlled. The value of current density will depend strongly on the mass transport conditions in the cell and will have a characteristic variation with rotation rate. flow rate, etc, e.g equation (1.58) for the RDE. A parallel discussion applies to the section oftlie I -E curve positive to E. but relates to ths oxidation of R-0.

In Fig. 1.15, the data are shown as both I-E and iog I -q plut, and !he correlation between Tafel. mixed and mass transport controlled regions on lhe two figures should hc noted. It is also important to note that a linear Talel region can sometimes be observed over several orders of magnituds of current density but the range is limited by: 1 . Iz51, . Below this current the back-reaction is significant lequafion 11.34)). 2. 1 1 0 ' 1 , o r k'z 1 0 ' c m s ' ) . Then theelectron tranrfer reaction a t the surface is rapid enottgh that under most mass transport condit~ons obtainable rxperimentally, the electron transfer couple at the surface appears to be in cquilibrium. Then the surlacc concentrations may, at each potential, he calcul;.cd lrom the Nernst equation, a purely thermodynarn~c cq71ation. and t l l i current may be calculated. lor example, from equation (1.57). The I - t curve has the form shown in Fig. 1.16; the I-E curvecrosses the zero current axis sleeply and there is no ovetpotenlial for oxidation or reduction. Systems with tl~ese characteristics arc onen termed 'reversible'. On the othcr hand. the limiting current densities d o not depend on the kinetics o l electron ttansler closer to E.. H c n a the limiting current densities lor 'reversible' and irrcvcrsible reactions are the same.

1.4 ADSORPTION The electrochemistry of many industrial processes is dependent totally on the ability of the electroactivc species, reaction intermediates, product or, indeed, species apparently not involved in thc electron lransler process, to adsorb on the electrode surface, i.c. to form some type o l bond with thc electrode material. Thc role of the adsorbed species is to accelerate or to decrease reaction rates, and in

Adsorption 33

Fig. 1.16 Complcle I-Echaractcristic for a rcverriblc couplc O/R (a couple where I, is Inrgc). The solution contains c;=3c,0. The unequal conantrations arc chorcn to emphasize the relation between currcnls and conantralions.

rxlrerne situations this may lead to a total change in the dominant pathway and. hence. in the products of electrolysis. Important examples of the application of ddsorption in electrochemical technology would include eleclrocatalysis. the inhibition of corrosion and the control of electroplating by organic additives. and the variation ol product selectivity in organic electrusynthtsis.

Adsorption resulls lrom a wide variety of interactions between the adsorbing species and the electrode surface. In some cases, the driving force lor adsorption IS merely dislike of the adsorbate for the electrolytc solution phase (c.l. ad- sorption ol neutral organic moltcules at the gas-liquid interlace). In other cases. adsorption results lrom elcctrostatic (e.g. the adsorption of ions on a surface of opposite charge) or charge-dipole interactions. (e.8. the adsorption of thiourea, arnina, aromatic mokculcs). The strongest intcnctions result front formation of a covalent bond bclwan the adsorbate and the surface, c.g. the reduction of Proton on PI:

I or the dissociative adsorption ol formic acid on Pt from aqueous acid solutions: This is the first step in the complete oxidation of lonnic acid to carbon dioxide. Moreover, one sees great Jariations in the strcngtha of the bonds between the

clntrode and the adsorbate and the degree of rcversibilily of the adsorption process.

1.11 Adsorptio? equilibria in the ahcnce of r lrrfrnn lranrlrr

The extent of adcorption i s lormally described by d. the surface coverage or lraction or surlnce covered. I n the abcenm of electrpn transfer processes, the value for any species udl be dctcrmincd by two factors: Ill the allinill; or otherwise of the species lor bolh the electrode and the solution; and (2) Ihc ability of all othcr species in the solt!tion lo adsorb. I i e~~cc . the surfacc coverapc is dctcrin;ned by comyetltioz het,**cn tl,e c!cctrr.de, i n d t h e s~ lu t i on for ihr species undcr Qiscussion and betuecn scvcr;tl sl>cciec io,r silec on the clcctrn~lc surface. Adsorption is therefore, cven in the siniplest of s i l u o t ~ n ~ ~ i . a diqrlacc- ment reaction, the adsorbate dirplacing molecules of solvent or ions of the hasc electrolyte.

At each potential. the elcctrode rurlacc will carry a ch;lractcristic surfacc charge which depends on the electrode malcrial. solvent and clcctrolylc. As the potential is madc morc pos~tive. the srnrlace charge will also hccome niore positive while thc revcrrc ail1 happen uhcn thc pntcntial I< madc nLgative, There must also be one particular potent!sl. known as the polnt of zero charge or E , , . , , , whcre lhe surface is uncharged. When the aJsorbinp species i s an ion or a dipole which w i i l shous a prclcrrcd oricnt;ttion in the potrntial field. the adsorption will he stronEcst uhcn tllc surface i s lliglilv charged and, hcnce, occur on one sidc o l E D . . . In cnlltra

36 Fundnrnentol concepts

screw dislocations) where otherwisc the rate of deposition would be most rapid. creating an uneven thickness of the electroplated layer.

1.4.2 The effect of a neutral adsorbate on an electron transfer process

The presence o f an organic molecule capable of adsorbing on the electrode surface will, i n general, cause a decrease in the rate o f electron transfer for a couple O / R The explanation will depend on the most appropriate model for the electron transfer process.

Thus, i f electron transfer occurs while an adsorbate layer remains on the electrode >urf:cr, tk: oxidetion or redx t ion murt occur by the tralsfer o f an electron over a far greater distance. Figure 1.6 showed the potential distribution on a molecular scale close to the electrode and i t was noted that only the potential difference 4,-4, (not 4,- 4,) was available t o drive electron transfer; the adsorbate layer will cause a substantial decrease i n the potential dillerence available t o drive the electron transfer. I n the limit, the prcsenw of an adsorbate may totally prevent electron transfer and then only x fraction ( I -8) of the electrode is available for the O/R couple. An alternative model would require displacement of adsorbate by O o r R before electron transfer can occur and the extent o f such a process wil l depend on AG:,. Finally, the adsorbate may also be able to act as a ligand for 0 and R and complex formation at the electrode surface may increase or decrease the k~netic parameters for electron transfer.

These are the roles of additives lor corrosion inhibition and the modification of electrodeposits. Fo r electrode reactions where the overall sequence includes chemical steps, however, the role of the adsorbate layer may be quitc difTerent. Rather, i t may he to create an environment which is more favourable than the bulk solution for a particular reactinn, eg. the proton availability may bc dimerent; i t is not unusual for an adsorbate layer t o be relatively aprotic compared with an aqueous electrulyte and such mod~ficstions of electrode processes have been used i n the electrosynthesis of adiponitrile (Chapter 6). The presence o f tetraalkylammonium ions i n the electrolyte lcads to the desired hydrodimerization v f acrylonitrile to adiponitrile. In their absence, only propionitri le is formtd. I t is thought that the tetraalkylammonium ions adsorb on the cathode surface and create an environment where an intcrmcdiatc is protected from protonation.

1.43 Adsorption in #he presence o f electron transfer

When the electroactive species o r an intermediate adsorbs onto the electrode surface, the adsorption prmess usually becomes an integral part o f the charge- transfer poccss and therefore cannot bc s t u d i d without the interierence of a faradaic currcnt. In thissituation. surfacccovcregcs cannot be measured directly and the role o f an adsorbate must be inferred from a kinetic investigation. Tafcl slopes and reaction orders wil l deviate substantially from those for a simple

Adsorption 37

eleclron transfer pro- when an adsorbed intermediate is involved. Moreovcr, the kinetic parameter* exchange current o r standard rate constant, are likely to become functions o f the dcctrodc material and even the finat products may change. These factors will be discussed further in section 1.5.

I t i s possible in a few cases to take data for the coverage by the elcctroactive species at potentials prior t o the onset o f elcctron transler and to extrapolate such data into the potential region where oxidation or reduction occurs. In any case. the conczpt o f competition between species for rites on the electrode surlan. the form o f the isotherms and the qualitative variation i n the coverage with potential, are likely to remain valid. Hence, the earlier discussion remains a useful guide even when there is a faradaic current.

1.4.4 Dissociative adsorption

The adsorption of some molecules occurs by a more complex proczss where bonds are broken and the fragments adsorb at different sites on the electrode surface. In the caw of small molecules, such as oxygen, this may remain a relatively simple proass:

0, - 2 0 , ~ (1.83) H i - 2Hms (1.84)

although thc bond cnc rg i , ~ of such diatomic gases arc high and few materials will have all the characteristics essential t o make these steps effective in the catalysis o f oxygen reduction or hydrogen oxidation. W i th organic molecules. however. the adsorption process, e.g.

h CHIOH- II,M+CH,OH,,s- - ZH,,,+CFIOH,~~

-r ~ H ~ ~ + & o ~ ~ - ~ H ~ ~ ~ +co,,~ (1.85) must be much more complex and involve a number o f bond-hreaking processes. The overall reaction is unlikely to be reversible and coverages by each species will be determined by kinetic rather than thermodynamic faclors. Even so, such i dissociative adsorption processes arc very important and arc at the hear! of the

I eleclrmalalysis necessary for fuel cells because the direct loss o fan electron from potential fuels always requires a substantial overpotential. 'The coverage by such organic fragments cannot be dcscrihrd i n terms or isotherms (since the adsorption is not an equilibrium proccss) and. indeed. i t is urually difficult to identify with certainty the structure o f the adsorbed species. In the past, the information available has k e n deduced from measurement or the charges lor:

I. The adsorption proass. 2. The complete oxidation o f all fragments o n the surface; this is nicasurcd by

sweeping or stepping the potential to a very positive value.

40 Fundamental concepts (B) H * + e + M - M - H (I!

M-H+H'+e--M+H, (3) whcre the adsorbed hydrogen is written in a way emphasizes the importance of the electrode material in determining the properties of the surface bond. I t may be notcd immcdiately that both mechanisms require the formation and then the cleavage of an M-ll bond. Hence, while a variation of the cathode so as lo increase the free energy of adsorption will favour the formation of the adsorbed spccics, it will have the opposite eRect on the second step in the cverall process. As a result, it is t o be expected that the maximum rate of hydrogen evolution will occur at iqtermediste value, of nr;,,, which lead to a significant, but no( monolayer, covcrage by adsorbed hydrogen aloms. Thin is, indeed, obszrved and Fig. 1.17 shows a 'volcano plot' of exchangc current density vs. the free encrgy of hydrogen atom adsorption for a series of metal cathodes. Similar dependences o f rate parameters on the free energy of adsorption of an inter- mediate arc common in gas-phase catalysis. Experimental studies o f hydrogen evolution a t many cathodes have shown a widc range of exchange current densities as well as different Tafel slopes and dcpcndenes on proton concen- tration. This is typical of reactions which involve adsorbed species. In the following paragraphs thc way to derive the Tafcl slopes and reaction orders expected for mechanisms (A) and (8) will be outlined.

F3g. 1.17 Dcpcndcna olcrchangc current density lor the hydrogen cvolution reaction on the strcn@h of thc metal-hydrogen bond formed in the elatrode reaction. (Dorniroti Trasatti, S. (1972) 1. Elecrrwnel Chem 39. 163.

Elrctrorafalysis 41

lo) Rcaction (1) a s the rare-deren~~irtina sren - ,

The formation ol adsorbed hydrogen as the first step is common to both mechanisms (A) and (B).'Hence. when i t is the ratedetermining step, we cannot distinguish bctwnn the two mcrhanisms.The rate of reaction ( I ) (and, hence. of 1i2 evolutinn il i t is the slowest step in the overall reaction) may be written:

where c,,, is rate constant for reaction (11 in the forward direction, potential- dependent because the reaction involvcs the transfer of an electron. The rate depends on the concentration of protons in solution c,. and the free surlace available for adsorption of further hydrogen atoms (I - 0). Moreover, if reac- tlon (I) is slow compared to reactions ( 2 ) o r (3), the adsorbed hydrogel, crnno, be present at high coverage and one can use the approximation (I - 0)- I . Then.

:~nd the current for H, evolution is =ivcn by:

urhcreZ,, is the valur of&,, at E=O. Nolc that ihroughou~ this drsc~~ssion orthe H, evolution reaction, wc shall assume that for each elementary reaction. a, + a,= I and we shall write the ca thod~r transfer coetiicienl a. whcre n is the reaction concerned. Reaction (1.94) tnay tx converted lo the f ~ r t n :

a , F log - I = l o g ~ E , , + l o ~ c , . - - - - E 2.3RT (1.95)

and i t may be seen that the reaction is first order in proton and 11%, =0.5, then the Tafel slope J(log -I)!dE is (120 mV)- ' .

(6) Mechanism (A), rare-defermining s tep reaction (2) In this situation, the current density lor H, evolution is given by:

I = ~ F ~ , O ' ( 1.96) A where i , is a chemical rate constant, i.c. independent of potential. The coverage by H atoms 0 can in the steady state be found by noting that dO/dt=O, or:

8, = V , + 8* (1.97) If, in fact, vlg B, under all conditions and close to the cquilibrium potential p1 < p,, and then we can treat reaction ( I ) as a pre-equilibrium. Using P, = P, giver:

~ , c , , . ( I -o)=!ile (1.98)

42 Fundnmrntal concepts

and. since both E , and it are potential-dependent:

which rearranges lo:

where K , = 6, ,I&, and, hence:

which substituted into equation ( 1 96) gives.

and: ?F

lop - I= loe2Fk ,K~~? lngc , . - 2?.9T (1 1031

For this mechanisn~. therelore. the Talc1 slope i s (30mV)- ' and the current verier as the square or the proton concenlratlon.

( r ) Mecho,~is~n ( B ) , rate-deter~~~i l l r~ig step reactlor1 (31 Thc relc or reaction (3) i s given b?:

if, = l;,,:,. 0 (1.104) since if depends on the concentration or proton and the availability of adsorbed hydrogen atoms; E, i s potential-dependen:. Two limiting forms or the fate enprcnrion nrc pssible at low _and high ovcrpoten:ials.

At low overpotentials. both If , and T', are much raster than if, and 0 can be Llttnrl hy nn identical argument to (b) above. Then:

-I-2f&,,cxp- - - - L c,,.K,c,.cxp ("a: ) (I.lO5)

Electrocatolysis 43

and:

(1 + 4 F E log -I=IO~ZF~;,,K, +zIo~c,,. R T (1.107)

when. for a,==0.5, the Takl slope i s (40 mV)- ' , At high overpotentials, if,% r', and T', =Iz,,.

Therefore:

2nd if a , =a,. 0 i s indepndcnt or i>oten:ial. Tt,c ratc zxp;cssion lor ::ii$ mechanism is:

and:

a,F l og - I= logZF~, ,~+ lo~c , . 2 JRT (1.110)

The reaction at high overpotentials has become first order in proton with a Talel slope of (120mV)-'.

Table 1.3 summarizes the conclus~ons from these calculations lor the mccha- nisms considered. The dillerent mechanisms lead to different reaction orders and Talel slopes, bet the experimental data are not completely diagnostic because diKerent mechanisms lead to the same values. Moreover, we havenot considered a l l the likely possibilities. e.g. the discussion above assumes the coverage by adsorbcd hydroeen lollows the Langmuir isotherm the use of othcr isotherms would lead to dillcrent conclusions.

Fram the viewpoint o l electrochemical technology, however, the major point to be emphasized i s that the choice or the electrode material influences exchange current density, Tabl slope and reaction order with respect to proton. Hence.

Table 1.3 Tarcl rlopcr and reaction ardcrr calculated lor some mnhanisms of the H, evolution reaction

Rate- Over- Reactinn dctcrrnining potential Tarel order

Mcchnnism step range slopc/mV-' in H '

(A) or (Dl I A ~ I 120 I (A) 2 Low 30 2 (8) 3 Low 40 2 (8) 3 High I20 I

44 Fundamental concepts Elecrroramlysis 45

the selection o f cathode material can have a large eRect on the observed overpotential for Hz evolution. This conclusion is general lo r reactions in- volving adsorbed intermediates and is at the heart of electrocatalysis. The relation hetwcen electrocntalysi~ and cell energclics is disc~~s.ied i n Chapter 2 .

1.5.2 Oxygen reduction

I n almost all applications 01 the oxygen reduction reaction (but not H,O, pro- duction!), i t is desirable t o select conditions where the complete 4e- reduction occurs, 1.e. i n acid solution:

0 , + 4 h q +4c- -21i,C (:.I 1 ' ) o r in basic solution:

O l + 2 H , 0 + 4 e ~ - 4 0 H - (1.1 I? ) and at p H 0 and 14. the lormal potrntials o f reactions (1.1 l I) and (1.1 12) are + 1.23 V and 0.39 V (vs. NHE) respctively. The lormal potentials for the O,/H,O, couple are +0.68 V and -0.16 V at p H 0 and 14 respectively.

Particularly i n acid solution relatively few cathodc materials, capable of operating at these potentials, are arailable bccausc most metals dissolve anodically at potentials well negative to the equilibrium potential lor oxygen reduction. Moreover, even wi!h the more nohle metals which do not dissolve. the study of oxygen reduction i s hampered by oxidation and/or reduction of their surlace within the potential range 01 interest; this makes the experimental data for oxygen reduction less precise and perhaps also leads l o a change in mechanism when the electrode surface changes from metal oxide to metal or vice versa. I n this respect the oxygen evolution reaction i s easier t o study since i t generally occurs o n a fully oxidized anode surlace, and Ccr ??ch r~lrfaces its study gives information relevant to its reverse reaction, providing the principle o l microscopic reversibility may be applied.

In any case, the oxygen electrode is a complex system and the overall reaction i n either direction requires the transfer of four electrons and four protons. As a result, i t is possible to write a very large number o f reaction mechanisms but they a ic essentially o f two types:

I H + + ~ / 2 H z 0 (A) /

ZH.+ZC' O1\ H202-2H,O Z H + + > ~ - (B)

Route (A) leads to water as the first identifiable product whil: in rou:e 10) the reduction l o water clearly occurs in two steps with hydrogen peroxide as an intermediate. Indeed, i n some conditions the reaction stops at the hydrogen

peroxide stage, (e.g. at mercury or carbon. oxygen is reduced i n two well defined steps, separated by up to IV), and i n this mechanism caulysls may well havc the role ofensuring the rapid and total disproportionation ofthc hydrogen peroxide to oxygen and walcr. Koutc (A) implies thc cleilvagc o f the 00 bond by ~ l~rscxiat ive adsorption at an early stage i n the reduction whereas in roule (U), the first step i s the reduction o f oxygen to superoxide (or H 0 ; t o H O j ) The two types o l mechanism are most readily distinguished by an experimcnl with a rotating ring-disc electrode, Oxygen is reduced at a rotat