Chapter 4 Electrochemical kinetics at electrode / solution interface and electrochemical overpotential
Download ReportTranscript Chapter 4 Electrochemical kinetics at electrode / solution interface and electrochemical overpotential
Chapter 4 Electrochemical kinetics at electrode / solution interface and electrochemical overpotential Effect of potential on electrode reaction 1. Thermodynamic aspect If electrode reaction is fast and electrochemical equilibrium remains, i.e., Nernst equation is applicable. Different potential corresponds to different surface concentration. 2. Kinetic aspect If electrode reaction is slow and electrochemical equilibrium is broken. Different potential corresponds to different activation energy. 4.1 Effect of potential on activation energy 4.1.1 basic concepts For Elementary unimolecular process A kf kb B rf k f c A Rate expressions rb kb cB rnet rf rb k f c A kb cB rnet 0; kb (cB ) eq k f (c A ) eq At equilibrium K kf kb (cB ) eq (c A )eq Exchange rate of reaction Some important empirical formula: Arrhenius equation k Ae Ea RT According to Transition State Theory: kT k e h G RT Corresponding to steric factor in SCT For electrode reactions For reversible state Ox ne 0 C RT E E o ' ln o0 nF CR Nernst equation For irreversible state Tafel equation How to explain these empirical formula? kf kb Red Standard free energy Activated complex Gc In electrochemistry, electrochemical potential was used instead of chemical potential (Gibbs free energy) Ga Reactant re G product Reaction coordinate Potential curve described by Morse empirical equation Ox ne kf kb Red 4.1.2 net current and exchange current ia Cu Fe3+ Cu2+ ic ic ia Fe2+ Ox ne kc ka Red ic rc kc COx (0, t ) nFA ia ra ka CRed (0, t ) nFA Net current: ic nFAkc COx (0, t ) ia nFAka CRed (0, t ) Net current: i ic ia nFA[kc cOx (0, t ) ka cRed (0, t )] i ic ia nFA[kc cOx (0, t ) ka cRed (0, t )] If cOx = cRed = activity = 1 at re At equilibrium condition Then i net = 0 ic ia i0 standard exchange current Gc kT RT kc e h Ga kT RT ka e h 4.1.3 effect of overpotential on activation energy Ox ne Red ΔGc,0 ΔGa,0 ΔGa c ΔG transfer coefficient FΔ F Δ 1 F Δ polarization ir re ΔG nFE nFΔ ΔG ΔG0 nFΔ Ox ne Red ΔGc,0 c , re a ,0 ΔG ΔGa c ΔG FΔ F Δ nFΔ nFΔ nFΔ c ,ir a ,ir F Δ Fraction of applied potential alters activation energy for oxidation and for reduction Anode side cathode side Ga Ga,0 nFΔ Gc Gc,0 nFΔ 0 tan FE / x nFΔ x nFΔ deuce tan (1 ) FE / x tan tan tan is usually approximate to 1/2 4.1.4 Effect of polarization on reaction rate Marcus theory: transition state theory Gc ,0 nF k BT kc c exp( ) h RT G k BT nF c ,0 c exp( ) exp( ) h RT RT nF kc ,0 exp( ) RT Ga,0 nF k BT ka a exp( h nF ka ,0 exp( ) RT RT ) ic kc cOx (0, t ) nFcOx (0, t )kc ,0 exp( nF RT ) No concentration polarization ic ic ,0 exp( ia ia ,0 exp( nF RT nF RT If initial potential is 0, then ) ) 2.3RT 2.3RT lg ic ,0 lg ic nF nF 2.3RT 2.3RT lg ia ,0 lg ia nF nF 2.3RT 2.3RT c re lg ic ,0 lg ic nF nF 2.3RT 2.3RT a re lg ia ,0 lg ia nF nF At equilibrium ia ,0 ic ,0 i0 2.3RT ic c lg nF i0 2.3RT ia a lg nF i0 c lg ic 2.3RT 2.3RT lg i0 lg ic nF nF 0 re lg i lg i0 lg ia a 2.3RT 2.3RT lg i0 lg ia nF nF 4.2 Electrochemical polarization 4.2.1 Master equation ic nFcOx (0, t )kc ,0 exp( ia nFcRed (0, t )ka ,0 exp( nF RT nF RT ) ) inet ic ia nFcOx (0, t )kc ,0 exp( nF ) nFcRed (0, t ) ka ,0 exp( nF RT RT nF nF nFk0 cOx (0, t ) exp( ) cRed (0, t ) exp( ) RT RT Master equation ) Theoretical deduction of Nernst equation from Mater equation nF nF inet nFk0 cOx (0, t ) exp( ) cRed (0, t ) exp( ) RT RT At equilibrium inet 0 0 cOx (0, t ) cOx ; 0 cOx exp( nF RT 0 cRed (0, t ) cRed 0 ) cRed exp( 0 cOx nF exp( ) 0 RT cRed nF RT ) 0 RT cOx ln 0 nF cRed 0 RT cOx Nernst equation ln 0 nF cRed Butler-Volmer equation inet nF nF nFk0 cOx (0, t ) exp( ) cRed (0, t ) exp( ) RT RT nF nF i i0 exp( ) exp( ) RT RT Butler-Volmer equation nF nF i i0 exp( ) exp( ) RT RT 4.2.3 discussion of B-V equation 1) Limiting behavior at small overpotentials exp( nF RT ) 1 nF RT i nF nF i i0 1 1 RT RT nF nF nF i i0 1 1 i0 RT RT RT Current is a linear function of overpotential i nF RT i i0 nF Rct RTi0 Charge transfer resistance False resistance i/A Cathode Net current /V Anode 2) Limiting behavior at large overpotentials nF nF i i0 exp( ) exp( ) RT RT i/A Net current /V One term dominates exp( nF ) nF RT exp 1% nF RT exp( ) RT Anode Error is less than 1% 118 mV At cathodic polarization larger than 118 mV inet ic ia ic Cathode i i0 exp( nF RT ) Taking logarithm of the equation gives: lg i lg i0 nF 2.3RT 2.3RT 2.3RT lg i0 lg i nF nF Making comparison with Tafel equation One can obtain 2.3RT a lg i0 nF a b lg i 2.3RT b nF b At 25 oC, when n = 1, = 0.5 2.3RT nF b 118 mV The typical Tafel slope lg i 118 mV 118 mV lg i0 300 200 100 0 -100 -200 -300 / mV log i0 re Tafel plot: log i plot 4.2.4 determination of kinetic parameters 2.3RT a lg i0 nF 2.3RT b nF For evolution of hydrogen over Hg electrode 1.40 0.118lg i 0.5 i0 1.6 1012 A cm 2 i0 nFcOx (0, t )kc ,0 exp( nF RT ) k 5 1013 cm s1 4.2.5 Exchange current density 1) The exchange currents of different electrodes differ a lot Electrode materials solutions Electrode reaction i0 / Acm-2 H++2e– = H2 510-13 Cu2++2e– = Cu 210-5 H++2e– = H2 110-3 Hg 0.5 M sulfuric acid Cu 1.0 M CuSO4 Pt 0.1 M sulfuric acid Hg 110-3 M Hg2(NO3)2 Hg22++2e– = 2Hg + 2.0M HClO4 510-1 2) Dependence of exchange currents on electrolyte concentration Electrode reaction Zn2++2e– = Zn c (ZnSO4) i0 / Acm-2 1.0 0.1 0.05 0.025 80.0 27.6 14.0 7.0 High electrolyte concentration is need for electrode to achieve high exchange current. 2.3RT ic c lg nF i0 nF i RTi0 2.3RT ic c lg nF i0 When i0 is large and i << i0, c is small. When i0 = , c=0, ideal nonpolarizable electrode When i0 is small, c is large. When i0 = 0, c = , ideal polarizable electrode The common current density used for electrochemical study ranges between 10-6 ~ 1 Acm-2. If exchange current of the electrode i0 > 10~100 Acm-2, it is difficult for the electrode to be polarized. When i0 > 10-8 Acm-2, the electrode will always undergoes sever polarization. For electrode with high exchange current, passing current will affect the equilibrium a little, therefore, the electrode potential is stable, which is suitable for reference electrode. 4.2 potential on electrode kinetics Ox ne kc ka Red Gc k BT ic k COx (0, t ) exp( ) h RT Ga k BT ia k CRed (0, t ) exp( ) h RT Shift of potential Gc Go,c nF 1 keeps Ga Ga nF constant The nature of potential -dependence of rate ic nFAk f CO x (0, t ) G0.c k BT nF nFACOx (0, t )k exp( ) exp( ) h RT RT nF i0,c exp( ) RT At equilibrium: cox(0,t)= cox0 i0,c=i0,a=i0 i0 exp( nF RT ) Master equation: inet nF nF nFk0 cOx (0, t ) exp( ) cRed (0, t ) exp( ) RT RT Master equation: inet nF nF nFk0 cOx (0, t ) exp( ) cRed (0, t ) exp( ) RT RT At equilibrium inet 0 0 cOx (0, t ) cOx ; 0 RT cOx ln 0 nF cRed 0 cRed (0, t ) cRed Nernst equation Master equation: inet nF nF nFk0 cOx (0, t ) exp( ) cRed (0, t ) exp( ) RT RT Butler-Volmer equation nF nF i i0 exp( ) exp( ) RT RT Butler-Volmer equation nF nF i i0 exp( ) exp( ) RT RT at small overpotentials nF Rct RTi0 nF i i0 RT Charge transfer resistance at large overpotentials 118 mV inet ic ia ic 2.3RT 2.3RT lg i0 lg i nF nF 2.3RT a lg i0 nF Tafel equation 2.3RT b nF 4.3 Diffusion on electrode kinetic When we discuss situations in 4.2, we didn’t take diffusion polarization into consideration When diffusion take effect : G0.c k BT nF ic nFACOx (0, t )k exp( ) exp( ) h RT RT COx (0, t ) 0 k BT G0.c nF ic nFA COx k exp( ) exp( ) 0 h RT RT COx inet COx (0, t ) nF ic i0 exp( c ) 0 RT COx inet COx (0, t ) nF ic i0 exp( c ) 0 RT COx At high cathodic polarization i C C (1 ) id s i 0 i i nF i (1 )i0 exp( c ) id RT id i i nF ( ) exp( c ) i0 id RT id i i nF ( ) exp( c ) i0 id RT Taking logarithm yields Therefore: id i i nF ln ln( )( c ) i0 id RT id RT i RT c ln ln nF io nF id i Electrochemical term Diffusion term At this time the total polarization comprises of tow terms: electrochemical term and diffusion term. id RT i RT c ln ln nF i0 nF id i Discussion : 1. id >> i >> i0 No diffusion ec polarization At small polarization : i At large polarization: i c nF i i0 RT 0 c RT i c ln nF i0 id RT i RT c ln ln nF i0 nF id i 2. id i << i0 diffusion No ec RT i c ln 0 nF i is invalid Id RT d ln( ) nF id i i id i log i id RT i RT c ln ln nF i0 nF id i 3. id i >> i0 both terms take effect 4. i << i0, id no polarization id diff 1 id 2 ec 1/2 0 1/ 2 When id >>i0 id RT i RT c ln ln nF i0 nF id i 1 id RT RT 2 ln ln 2 nF i0 nF id RT RT RT ln ln id ln i0 nF i0 nF nF d1/ 2 RT d ln i0 id nF id diff id RT i RT c ln ln nF i0 nF id i ec 1/ 2 Id RT ln nF i0 lg id lg i 118 mV lg i0 400 300 200 100 0 -100 -200 -300 -400 Tafel plot under diffusion polarization / mV Tafel plot with diffusion control: i0 << i < 0.1 id Electrochemical polarization i between 0.1id 0.9id mixed control i >0.9 id diffusion control How to overcome mixed / diffusion control? The ways to elevate limiting diffusion current 4.4 EC methods under EC-diff mixed control 4.4.1 potential step Using B-V equation with consideration of diffusion polarization COx (0, t ) CRed (0, t ) nF nF it i0 exp( ) exp( ) 0 0 RT RT CRed COx at high polarization . c COx (0, t ) nF it i0 exp( c ) 0 RT COx c constant it CO(0,t) COx (0, t ) nF it i0 exp( c ) 0 RT COx nF at low polarization : RT exp( c nF RT is very small c ) (1 nF RT c ) CO (0, t ) CR (0, t ) nF CO (0, t ) CR (0, t ) it i0 ( ) 0 0 0 0 RT CR CO CR CO Constant Constant 1 1 2 it i exp( 2 t )erfc(t ) i 1 2 3 2 t is the current density at no concentration polarization at 0 cOx (0, t ) cOx ; t=0 0.5 0 cRed (0, t ) cRed 1 2 exp( 2t )erfc(t ) 1 i(0)= i no concentration polarization When t 1 2 it t 1 it ic 1/ 2 at time right after the potential step : it t1/2 is linear ic 1 2 t 1/ 2 ic it Double-layer charge i EC control Extrapolating the linear part to y axes can obtain 2 diff control C Making potential jump to different can obtain i at different . Then plot i against c can obtain i~c without concentration polarization. The way to eliminate concentration polarization effect c time constant s it > i due to charge of double layer capacitor 4.4.2 current step i cathodic current : 0 ic ic nF ic nFk ' COx (0.t ) exp ( 0 ) RT 0 t c at different i0 3.8.2 Current step / jump 1 2 t ci (0, t ) ci0 1 t 1 2 ic nFk ' C [1 ( ) ]exp( 0 Ox nF RT ) t 1 2 ic nFk ' C [1 ( ) ]exp( 0 Ox nF RT ) 1 0 nFk ' C RT RT t 2 Ox c (t ) ln ln[1 ( ) ] nF ic nF c (t ) t 1 2 [1 ( ) ] transition time c c c(0) when potential step to next rxn. 0 i= i charge t The slope of the linear relationship between c (t) can be used to determine n and . When t0 the second term = 0 (t 0) 0 nFK ' COx RT ln nF ic 4.4.3 cyclic voltammetry (CV) (t ) 0 vt COx (0, t ) CRed (0, t ) nF nF it i0 exp( c (t )) exp( c (t )) 0 0 RT RT CRed COx c (t ) (t ) 0 I Typical CV diagram for reversible single electrode I Pc Potential separation Δ Pc Pa I Pa 59 mV n For typical CV diagram of irreversible single electrode I I Pc 59 Δ mV n I Pa for fast EC reaction : i << i0 controlled by diffusion i v 0.2 0.1 0.0 0.1 0.2 for the reversible systems , use the forward kinetics only : i nFACO (0, t )k f (t ) can be only by numerical method: 1 2 Ox 1 2 0 i nFACOx D ( nF RT 1 2 1 2 ) x(bt ) Nicholson-Shain equation tramper coefficient n – number of electrons involved in charge transfer step 1 2 x(bt ) is tabulated x (bt) max =0.4958 For totally irreversible systems, peak potential shift with scan rate RT k nFv Ep E ( )[0.78 ln ln ] F RT D v i 0.2 0.1 0.0 0.1 0.2 for slow EC reaction : ii0 ( quasi reversible, irreversible) in comparison to the same rate, equilibrium can not establish rapidly. Because current takes more time to respond to the applied voltage, Ep shift with scan rate . 1.15 RT 30 Ep E mV n F n E p E1/ 2 p 1.857 RT 47.7 nF n per decade of change in scan rate 56.5 P P mV n 2 drawn - out ip (2.99 10 )n( n) 5 1/ 2 0 Ox 1/ 2 1/ 2 AC D v I P 2.69 10 n 5 ip COx0 lower due to if =0.5 n= 1 i p ,ir i p , re 0.78 3/ 2 D c 1/2 Ox 1/ 2 0 Ox i p 0.227 FAC k exp[ 0 Ox o RT nF ( E p E 0 )] lnip Ep E0 is linear with S= RT/nF, intercept is linearly proportional to k0 4.4.4 effect of 1 potential on EC rate : 1=0, validate at high concentration or larger polarization 1 nF x effect of 1: 1.on concentration 2. = 1 zi F C C exp( 1 ) RT i 0 i ( n z0 ) F nF ic nFAk C exp( ) exp( 1) RT RT 0 Ox ia nFAk 0 Re d 0 Ox 0 Re d C ( n z0 ) F nF exp( ) exp( 1) RT RT When z0 <0 ( minus ) n 1 large . For anion reduced on cathode , 1 effect is more significant. z0 n RT i ic ia const ln i 1 nF n z0 n RT c const ln i 1 nF n z0 n 1 0 1 made c shift positively n minus <0 When z0 n plus >0 -0 so: if 1 increases, i decreases 0.001M 0.01M 0.1M 1M 0.5 1M 0.1M 0.01M without specific adsorption reduction of +1 cation …… reduction of 1anion +0.5 1 accelerates 4 2 0 +2 reduction of cations slow reduction of anion +4 lgi z0 n RT c const ln i 1 nF n if: n =z0 =0.5 Cu2+ +2e- = Cu MnO4 +e = MnO42 H+ +e- = 1/2 H2 RT c const ln i 1 nF if :z0 =0 RT c const ln i 1 nF adsorption of anion slow reaction Electrochemistry of LB film exam: 1.Draw the potential change versus distance away from electrode surface according to Stern electric double-layer and indicate 1 potential 2. When the electrode was positively charged, the surface concentration of action is still more than that of bulk solution. Explain this phenomenon using specific adsorption model 3.The differential double layer capacitance of Cu/H2O surface is 10-5 Fcm-2 while that for Cu/HS(CH2)11CH3 is 10-9Fcm-2 (can be taken as zero). If the differential Cdl for a Cu/HS(CH2)11CH3 system is measured to be 10-7 Fcm-2. Please calculate the coverage of HS(CH2)11CH3 on copper. 4. Electro-capillary curves of Hg in KI and K2S solution are shown in the Figure. Please indicate the PZC of Hg on the curves and explain the difference in PZC. KI K2S The curves coincide with each other when potential is quite negative but differ a lot when potential is positive, please give explanation. 5.Tell how to determine whether or not a electrode process is governed by diffusion. Given id for RDE can be expressed as id= 0.62 nF Di2/31/2-1/6 ci0 Pt 6.This is a water drop with contact angle of on Pt surface. When potential shift negatively, plot the change of with potential, i.e., ~ . 7.Deposition of Cu nanowire in microspore of anodic alumina membrane (AAO) can be taken as ideal stable diffusion process. If 0 C the thickness of (AAO) is 1m Cu =0.1 mol cm-1, DCu =105cm2 s-1. Please calculate the limiting diffusion current. 2 2 8. Convection affects diffusion. If the slope of concentration gradient is Ci ,The effective thickness of diffusion layer E= x x 0 and the dimity diffusion current id = 9.a typical CV peak is shown in the figure. Please Indicate EP, EP/2, Ere, and iP on it. How can you determine whether or not this electrochemical process is electrochemical reversible?