Chapter 2. Electrode/electrolyte interface: ----Structure and properties
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1 Chapter 2 Electrode/electrolyte nterface: ----Structure and propertes
2 Electrochemcal reactons are nterfacal reactons, the structure and propertes of electrode / electrolytc soluton nterface greatly nfluences the reacton. Influental factors: (1) Chemstry factor: Chemcal composton and surface structure of the electrode: reacton mechansm electrocatalytc effect. (2) Electrcal factor: Potental dstrbuton: actvaton energy of electrochemcal reacton
3 Chapter 2 Electrode/electrolyte nterface: 2.1 Interfacal potental and Electrode Potental Electrochemcal potental For process nvolvng useful work, W should be ncorporated n the followng thermodynamc expresson. dg = -SdT + VdP + W + dn For electrochemcal system, the useful work s: W = z e Under constant temperature and pressure, for process A B: G z e ( ) A B B A B A 0 ( z e ) ( z e ) B B A A 0 0
4 Chapter 2 Electrode/electrolyte nterface: Electrochemcal potental 1) Defnton: G ( z e ) ( z e ) A B B B A A 0 0 z e 0 Electrochemcal potental z s the charge on speces,, the nner potental, s the potental of phase. G A B In electrochemcal system, problems should be consdered usng electrochemcal potental nstead of chemcal potental.
5 Chapter 2 Electrode/electrolyte nterface: Electrochemcal potental 2) Propertes: 1) If z = 0 (speces uncharged) z e 0 2) for a pure phase at unt actvty, 3) for speces n equlbrum between and. 3) Effect on reactons 1) Reactons n a sngle phase: s constant, no effect 2) Reactons nvolvng two phases: a) wthout charge transfer: no effect b) wth charge transfer: strong effect
6 Chapter 2 Electrode/electrolyte nterface: 2.2 Inner, outer and surface potental (1) Potental n vacuum: The potental of certan pont s defned as the work done by transfer unte postve charge from nfnte to ths pont. (Only Coulombc force s concerned). x Fdx dx x F e - strength of electrc feld
7 Chapter 2 Electrode/electrolyte nterface: 2.2 Inner, outer and surface potental e e (2) Potental of sold phase Electrochemcal reacton can be smplfed as the transfer of electron from speces n e soluton to nner part of an electrode charged sphere Vacuum, nfnte Ths process can be dvded nto two separated steps ~ 10-7 m W 2 + W 1
8 Chapter 2 Electrode/electrolyte nterface: 2.2 Inner, outer and surface potental 10-6 ~ 10-7 m W 1 The work (W 1 ) done by movng a test charge from nfnte to 10-6 ~ 10-7 m vcnty to the sold surface (only related to long-dstance force) s outer potental. Outer potental also termed as Volta Potental () s the potental measured just outsde a phase. W 2 + Movng unt charge from vcnty (10 6 ~10-7 m) nto nner of the sphere overcomes surface potental (). Short-dstance force takes effect. W 2 For hollow ball, can be excluded. arses due to the change n envronment experenced by the charge (redstrbuton of charges and dpoles at the nterface)
9 Chapter 2 Electrode/electrolyte nterface: 2.2 Inner, outer and surface potental 10-6 ~ 10-7 m W 2 W 1 The total work done for movng unt charge to nner of the charged sphere s W 1 + W 2 = (W 1 + W 2 ) / z e 0 = + The electrostatc potental wthn a phase termed the Galvan potental or nner potental (). If short-dstance nteracton,.e., chemcal nteracton, s taken nto consderaton, the total energy change durng movng unte test charge from nfnte to nsde the sphere: W1 W2 ze ze ( ) 0 0
10 Chapter 2 Electrode/electrolyte nterface: 2.2 Inner, outer and surface potental
11 work functon Chapter 2 Electrode/electrolyte nterface: 2.2 Inner, outer and surface potental (4) Work functon and surface potental The mnmum energy (usually measured n electron volts) needed to remove an electron from a sold to a pont mmedately outsde the sold surface or energy needed to move an electron from the Ferm energy level nto vacuum. We z e 0
12 Chapter 2 Electrode/electrolyte nterface: 2.3 measurablty of nner potental (1) potental dfference For two conductors contactng wth each other at equlbrum, ther electrochemcal potental s equal. e e = 0 e e e 0 e e e Δ 0 e e e Δ e 0
13 Chapter 2 Electrode/electrolyte nterface: 2.3 measurablty of nner potental e e e 0( ) e e e e e 0 0 e 0 0 e e ( ) ( e ) ( e ) 0 0 e 0 e 0 W e e0 e W e e 0 dfferent metal wth dfferent We Δ 0 Therefore 0 Δ 0 W e
14 Chapter 2 Electrode/electrolyte nterface: 2.3 measurablty of nner potental No potental dfference between well contactng metals can be detected V 0 Δ 0 e Δ 0 Δ 0 Concluson e 0 V e e V ~ Δ,not Δ nor Δ e Galvanc and voltac potental can not be measured usng voltmeter.
15 Chapter 2 Electrode/electrolyte nterface: (2) Measurement of nner potental dfference n If electrons can not exchange freely among the ple,.e., poor electrcal conductng between phases. 1 n Ferm level 1 n1 1 n 1 Δ V 1 0 n1 1 Δ Δ n 1 n 1 Δ V n e Δ 1 n 1 Δ n e e 1' e e e 1 Ferm level n 1 Δ 1 (3) Correct connecton
16 Chapter 2 Electrode/electrolyte nterface: 2.3 measurablty of nner potental (4) Analyss of real system Consder the cell: Cu Cu 2+ Zn 2+ Zn/Cu I S 1 S 2 II I I V I II I ( S I V S S S S II II I ' ) ( ) ( ) ( ) 1 I ' S 1 I S 2 I S 2 ' II II I ' For homogeneous soluton wthout lqud juncton potental II V Δ Δ const. I II I S S II the potental between I and II depends on outer potental dfference between metal and soluton. I
17 V Δ Δ const. I II I S S II Usng reference wth the same I V II I Δ S const. I II Chapter 2 Electrode/electrolyte nterface: 2.3 measurablty of nner potental the exact value of unknown electrode can not be detected. I S I I S V 1 const. V 2 const. 1 ( I V II ) ( I S ) II The value of I S s unmeasurable but the change of s [ ( I S )] can be measured. 2 I S absolute potental
18 Chapter 2 Electrode/electrolyte nterface 2.4 orgnaton of nterfacal charge (1) Transfer of electrons 2) Transfer of charged speces
19 Chapter 2 Electrode/electrolyte nterface 2.4 orgnaton of nterfacal charge 3) Unequal dssoluton / onzaton (4) specfc adsorpton of ons
20 Chapter 2 Electrode/electrolyte nterface 2.4 orgnaton of nterfacal charge (5) orentaton of dpole molecules (6) Lqud-lqud nterfacal charge Dfferent transference number
21 Chapter 2 Electrode/electrolyte nterface 2.4 orgnaton of nterfacal charge 1) Transfer of electron 2) Transfer of charged speces 3) Unequal dssoluton 4) specfc adsorpton of ons 5) orentaton of dpole molecules 6) lqud-lqud nterfacal charge 1), 2), 3) and 6): nterphase potental 4), 5) surface potental.
22 Chapter 2 Electrode/electrolyte nterface 2.4 orgnaton of nterfacal charge Electrc double layer capactor Electroneutralty: q m = -q s Holmholtz double layer (1853)
23 Chapter 2 Electrode/electrolyte nterface 2.5 deal polarzable and deal non-polarzable electrodes equvalent crcut = ch + ec Charge of electrc double layer Electrochemcal rxn Faradac process and non-faradac process
24 Chapter 2 Electrode/electrolyte nterface 2.5 deal polarzable and deal non-polarzable electrodes deal polarzable electrode an electrode at whch no charge transfer across the metal-soluton nterface occur regardless of the potental mposed by an outsde source of voltage. no electrochemcal current: = ch
25 Chapter 2 Electrode/electrolyte nterface 2.5 deal polarzable and deal non-polarzable electrodes Vrtual deal polarzable electrode K + + 1e = K -1.6 V 2Hg + 2Cl - - 2e - = Hg 2 Cl V Hg electrode n KCl aqueous soluton: no reacton takes place between +0.1 ~ -1.6 V
26 Chapter 2 Electrode/electrolyte nterface 2.5 deal polarzable and deal non-polarzable electrodes deal non-polarzable electrode an electrode whose potental does not change upon passage of current (electrode wth fxed potental) no charge current: = ec Vrtual non-polarzable electrode Ag(s) AgCl(s) Cl (aq.) Ag(s) + Cl AgCl(s) + 1e
27 Chapter 2 Electrode/electrolyte nterface 2.5 deal polarzable and deal non-polarzable electrodes For measurng the electrochemcal behavor of electrode/electrolyte nterface, whch knd of electrode s preferred, deal polarzable electrode or deal non-polarzable electrode?
28 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure Expermental methods: 1) Electro-capllary curve measurement 2) Dfferental capactance measurement surface charge-dependence of surface tenson: 1) Why does surface tenson change wth ncreasng of surface charge densty? 2) Through whch way can we notce the change of surface tenson?
29 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (1) Electro-capllary curve measurement Expermental setup for Electrocapllary curve measurement Electrocapllary curves for mercury and dfferent electrolytes at 18 o C.
30 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (1) Electro-capllary curve measurement The Gbbs adsorpton sotherm n n n n n n n n dg n A SdT da dn When T s fxed dg da dn
31 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (1) Electro-capllary curve measurement dg da dn Integraton gves G A n dg da Ad dn n d Ad n d 0 d d Σ d d d Σ e e Gbbs adsorpton sotherm d e Fd e q F d d qd Σ
32 2.5 Interfacal structure Lppman equaton d Chapter 2 Electrode/electrolyte nterface (1) Electro-capllary curve measurement d When the composton of soluton keeps constant qd d qd q,,, Zero charge potental: 0 ( pzc: potental at whch the electrode bears zero charge) m C 2 2
33 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (1) Electro-capllary curve measurement Theoretcal deducton of d qd; q C; d Cd m C 2 2 m d C 0 d C m 0
34 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement 2 q c( ) d 1 Dfferental capactance
35 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement capactor The double layer capactance can be measured wth ease usng electrochemcal mpedance spectroscopy (EIS) through data fttng process.
36 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement C d = C() Dfferental capactance curves Integraton of capactance for charge densty
37 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement Dependence of dfferental capactance on potental of dfferent electrolytes. Charge densty on potental
38 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement dfferental capactance curves for an Hg electrode n NaF aqueous soluton Dependence of dfferental capactance on concentraton Potental-dependent Concentraton-dependent Mnmum capactance at potental of zero charge (E pzc ) 36 F cm -2 ; 18 F cm -2 ;
39 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement Surface excess charge q z F z F q q M A v M v A v v v z z+ z- v z d v d v d MA s
40 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement d d 0 d qd d qd d d d d d For R.E. n equlbrum wth caton WE.. R.E. d z Fd R.E. d v d v d MA For any electrolyte v v MA MA R.E. R.E.
41 Chapter 2 Electrode/electrolyte nterface 2.5 Interfacal structure (2) Dfferental capactance measurement Surface excess curves
42 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer 1) Helmholtz model (1853) Electrode possesses a charge densty resulted from excess charge at the electrode surface (q m ), ths must be balanced by an excess charge n the electrolyte (-q s )
43 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer 1) Helmholtz model (1853) C A 0 r q V 0 r d A d q charge on electrode (n Coulomb)
44 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (2) Gouy-Chappman layer (1910, 1913) Charge on the electrode s confned to surface but same s not true for the soluton. Due to nterplay between electrostatc forces and thermal randomzng force partcularly at low concentratons, t may take a fnte thckness to accumulate necessary counter charge n soluton.
45 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (2) Gouy-Chappman layer (1910, 1913) Gouy and Chapman quanttatvely descrbed the charge stored n the dffuse layer, q d (per unt area of electrode:) Boltzmann dstrbuton C C ( x) ( x) C 0 C xf exp RT 0 xf exp RT Posson equaton 2 2 x x F C E 4 x x ( x) C ( x)
46 RT F RT F F C x x x exp exp 0 RT F RT F F C x x x x exp exp x x x x x RT F RT F F C x x x x x exp exp Integrate from x = d to x = (2) Gouy-Chappman layer (1910, 1913) 2.6 Models for electrc double layer Chapter 2 Electrode/electrolyte nterface
47 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (2) Gouy-Chappman layer (1910, 1913) For 1:1 electrolyte q RTc 2 0 exp 1F 2RT exp 1F 2RT For Z:Z electrolyte q 0 RTc z1f z F 1 exp exp 2 2RT 2RT
48 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (2) Gouy-Chappman layer (1910, 1913) 1 zf q d RTC 2 snh 2RT * 0 8 Expermentally, t s easer to measure the dfferental capactance: * zf( 2C ) zf0 C d cosh RT 2RT 1 2 snh x e x e 2 x Hyperbolc functons
49 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (2) Gouy-Chappman layer (1910, 1913) For a 1:1 electrolyte at 25 o C n water, the predcted capactance from Gouy- Chapman Theory. 1) Mnmum n capactance at the potental of zero charge 2) dependence of C d on concentraton
50 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (3) Stern double layer (1924) Combnaton of Helmholtz and Guoy-Chapman Models The potental drop may be broken nto 2: ( ) ( ) m s m 2 2 s
51 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (3) Stern double layer (1924) ( ) ( ) m s m 2 2 s Inner layer + dffuse layer Ths may be seen as 2 capactors n seres: 1 C t 1 C 1 C d C : nner layer capactance C d : dffuse layer capactance-gven by Gouy-Chapman
52 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (3) Stern double layer (1924) 1 C t 1 C 1 C d Total capactance (C t ) domnated by the smaller of the two. At low c 0 At hgh c 0 C d domnant C domnant C d C t C C t
53 C Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (3) Stern double layer (1924) Stern equaton for double layer q RTc 1F F exp exp 1 C 2 2RT 2RT Dscusson: When c 0 and are very small 1 1 C RT 2 1F 2RT c 0
54 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (3) Stern double layer (1924) Dscusson: When c 0 and are very large 1 1 C RT 2 exp 1F 2RT c 0 1 C RT 2 exp 1F 2RT c 0 0 C dq F RTc 1F F 1 exp exp d d 2RT 2 2RT 2 1 RT C d plays a role at low potental near to the p. z. c.
55 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (3) Stern double layer (1924) Fttng of Gouy-Chapman model to the expermental results Fttng result of Stern Model.
56 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (4) BDM model Bockrs-Devanathan-Muller, 1963 Only electrostatc adsorpton Not only electrostatc adsorpton
57 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer Inner Helmholtz plane IHP 1 Outer Helmholtz plane, OHP, 2 (4) BDM model Specally adsorbed anon Solvated caton Prmary water layer Secondary water layer Weak Solvaton and strong nteracton let anons approach electrode and become specfcally adsorbed.
58 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (4) BDM model Delectrc saturaton d =5-6 d o =40 C d C 4 d If the dameter of adsorbed water molecules was assumed as m, = 6, then Cc 20μF cm d The theoretcal estmaton s close to the expermental results, F cm -2, whch suggests the reasonablty of the BDM model.
59 Summary: What have been solved, what have not?
60 Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer (5) Gramham Model-specfc adsorpton Trple layer Specfcally adsorbed anons Helmholtz (nner / outer) plane
61 Overload adsorpton Chapter 2 Electrode/electrolyte nterface 2.6 Models for electrc double layer Normal adsorpton due to electrostatc attracton of catons Specfc adsorpton due to chemcal adsorpton of anons
62 Summary: For electrc double layer 1. A unambguous physcal mage of electrc double layer 2. The change of compact layer and dffuson layer wth concentraton 3. The fne structure of compact layer
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