CHE465/865, 2006-3, Lecture 6, 18 th Sep., 2006 Electrochemcl Thermodynmcs Interfces nd Energy Converson Where does the energy contrbuton F zϕ dn come from? Frst lw of thermodynmcs (conservton of energy): U = T S + W ove smll mount of chrge ( electrcl potentl dfference ϕ. Q ) of speces through ϕ 0 W = ϕ Q = z Fϕ N el ϕ = 0 Q = z F N Work on chrge gnst nner potentl dfference. Correspondng dfferentl of the nternl energy: duɶ = TdS pdv + µ d N + F z ϕ dn Correspondng dfferentl chnge of Gbbs free energy dgɶ = SdT + Vdp + µ d N + F z ϕ dn
Importnt observton: Only dfferences ( ) z F ( ) ɶ µ ɶ µ = µ µ + ϕ ϕ between phses nd re expermentlly vlble. Gbbs, concluson of fundmentl mportnce: Electrcl potentl drop cn be mesured only between ponts whch fnd themselves n the phses of one nd the sme chemcl composton,.e. µ = µ, nd thus, Glvn potentl ϕ = ϕ ϕ = ɶ µ ɶ µ zf Otherwse, when the ponts belong to two dfferent phses, µ µ, expermentl determnton of Recll: ϕ s mpossble! generl stuton consdered n electrochemstry: phses n contct V σ V potentl dfferences ϕ control equlbrum between phses nd rtes of recton t nterfce The problem s: ϕ s not mesurble!
Wht s the electrosttc potentl of phse? Relted to work needed for brngng test chrge nto the phse. ϕ = ψ + χ V ϕ ψ 10-5 10-3 cm ϕ : nner or Glvn potentl; work requred to brng unt pont chrge from to pont nsde the phse ; electrosttc potentl tht s ctully experenced by chrged prtcle n tht phse. Unfortuntely: ϕ cnnot be mesured! Why not????? Involves trnsfer cross nterfce wth ts nhomogeneous chrge dstrbuton Rel chrged prtcles nterct wth other prtcles n tht phse, e.g.: brng n electron nto metl not only electrosttc work (potentl of other chrges), but: work gnst exchnge nd correlton energes (Pul excluson prncple).
ψ : outer or Volt potentl; work requred to brng unt pont chrge from to pont just outsde the surfce of phse ; just outsde : very close to surfce, but fr enough to vod mge nterctons (nducton effects n metl), 10-5 10-3 cm from surfce. ψ cn be mesured! Why cn ths be mesured???? e.g.: no free chrges, metl, unchrged ψ = 0 Why s metl unchrged? Why s ψ = 0? Inner nd outer potentls dffer by surfce potentl: χ = ϕ ψ Unchrged phse (metl): χ = ϕ χ 0 due to nhomogeneous chrge dstrbuton t surfce
etl: χ = ϕ, electroneutrlty nsde of metl postve chrge resdes on metl ons, fxed t lttce stes, electronc densty decys over ~ 1 from bulk vlue to 0 onc excess chrge densty metl electronc excess chrge densty surfce dpole resultng surfce dpole potentl: ~ few Volts (smller surfce potentls t surfces of polr lquds)
Dfferent surfce plnes of metl sngle crystl: dfferent χ Brng chrged prtcles (speces ) nto unchrged phse : Electrochemcl potentl: ɶ µ = µ + zfχ, ψ = 0 metl: ɶ µ = µ F χ, z = 1 Electrons n metl: e e e Hghest occuped energy level s the Ferm level E F, At T = 0: E ɶ F = µ e 1 π kbt Fnte T: ɶ µ e = EF 1 3 2 EF Correcton ~0.01% t room T neglgble n most cses! 2
Work functon, Φ : mnmum work requred to tke n electron from nsde the metl to plce just outsde extrct n electron from Ferm-level ~ hlf the onzton energy of free metl tom, (Cesum: onzton energy 3.9 ev, work functon 2.0 ev) mesured by photoemsson experment contns surfce term dfferent for dfferent surfces, more specfclly: metl surfce Φ ( 111) ( 100) ( 110) ncreses wth densty of toms on Φ > Φ > Φ for fcc metls, e.g. Pt = 3.9 Å ( 2 2) ( 2 2) Pt(111) ( 2 2) ( 2 2) Pt(100) ( 2 2) Pt(110) reference pont for E F just outsde metl: E = Φ Wht would be relton between F E F nd pont for Ferm energy s tken t nfnty? E = Φ e ψ F 0 Φ, f reference
Element Cesum (Cs) Sodum (N) Znc (Zn) Beryllum (Be) Cdmum (Cd) Antmony (Sb) Tungsten (W) Work functon (ev) 1.96 2.06 3.08 3.17 3.68 4.01 4.25 Summry: Energy of prtcle n phse: mesurble: ɶ µ, not mesurble: ϕ, µ ψ nd for neutrl speces: ϕ χ nd for chrged speces: µ
Electrochemcl equlbrum between two phses nd Equlty of electrochemcl potentls for ll components n the contctng phses speces cn freely cross the nterfce V V dn µ, ϕ µ, ϕ Equlbrton: trnsfer of chemcl speces between phses Electrochemcl equlbrum (n system t constnt p nd T): ɶ = rg 0 for ny smll N ɶ µ ɶ = µ, where ɶ µ = µ + z F ϕ [Note: system not n chemcl equlbrum! Wht does t men?] fter rerrngng: In words: µ µ ϕ ϕ = z F µ ϕ = z F Electrcl forces blnce chemcl forces 0 [re-cton] 0 [ntl cton] ϕ µ Dependence of Glvn-potentl on the ctvtes of the nvolved ons cn be determned. Ths represents the Nernstequton for certn Glvn potentl.
Electrochemcl Equlbrum Electromotve Force Relton between chemcl nd electrc drvng forces Electrochemcl system t constnt T nd p: consder G ɶ Consder electrochemcl recton (nvolvng trnsfer of e ): ν A + ν B + ν e ν C + ν D + ν e (1) A B e R C D e L rectnts products Note: Stochometrc coeffcents ( ν ) of rectnts (A, B) hve negtve sgn, those of products (C,D) re postve Electrons re wrtten explctly n ths equton snce they wll pper n the condton of electrochemcl equlbrum! Objectve: use thermodynmc rguments to derve electrcl potentl (the so-clled electromotve force, EF) of cell nd relte ths EF to the composton of electrochemcl cells Thermodynmcs Composton Electrcl potentl, EF