Performance Modeling of the Metal Hydride Electrode

Transcription

1 Performance Modeling of the Metal Hydride Electrode by Bala S. S. Haran, Anand Durairajan, Branko N. Popov and Ralph E. E. White Center for Electrochemical Engineering Department of of Chemical Engineering Univerity of of South Carolina

2 Motivation to to provide a theoretical bai for the electrochemical characterization of of MH electrode to to undertand and predict the performance of of metal hydride (MH) alloy a electrode

3 Objective to to develop an an analytical model for the dicharge of of the hydride electrode under galvanotatic condition to to incorporate the effect of of hydrogen-metal ite interaction in in the dicharge model to to develop a mathematical treatment for determination of of the electrochemical kinetic and thermodynamic parameter for porou hydride electrode to to correlate experimental dicharge data with the theoretical electrode dicharge model to to experimentally characterize the LaNi Sn Sn electrode a a a function of of tate of of charge and compare with theoretical imulation

4 Theoretical Model Performance of of the hydride electrode i i controlled both by by the kinetic of of the electrode procee and by by the hydrogen diffuion within the bulk of of the alloy Electrode parameter uch a a exchange current denity and equilibrium potential depend on on both the procee mentioned above Previou model have neglected change in in the hydrogen concentration due to to reaction and diffuion while evaluating the electrode parameter Further, dicharge model for the hydride electrode do do not conider the change in in the exce free energy due to to hydrogen intercalation

5 Ni-MH Cell Reaction At Ni Electrode NiOOH + H dicharge + charge At MH Electrode dicharge - - MH + OH M + HO + e charge Cell Reaction dicharge NiOOH + MH Ni(OH) + M charge Overcharge Reaction 4OH O + e Ni(OH) OH O + H - 1 H O + e H + O + OH 4e - - (0.401 V) (-0.88 V)

6 Schematic of pellet electrode modeled Current collector Cylindrical pellet electrode Electrolyte Metal hydride particle r0 rr p

7 Dicharge Model Development Governing Equation: Initial Condition: Boundary Condition: r c D r t r r t 0,c Microkinetic current denity: j a r a MH R p MH c o c,d r c 0, 0 r jw V 3 MH ( 1 ε ) ( 1 ε ) R p c r j F

8 Analytical Solution: c c o j R FD p 3 td R p r R p 3 R r p Σ n 1 λ in R λ in n n p r ( λ ) n e λ n td R p Dimenionle Form: ĉ 1 δ 3τ ( ) in ( λ rˆ ) 5 rˆ 3 rˆ Σ n 1 λ n n in ( λ ) n e λ n τ δ j R Fc o p D τ td R p rˆ r R p

9 Surface concentration: δ 3 τ Average concentration: ĉ 1 + c Σ n 1 δτ λ 1 n e λ n τ Surface concentration for long period of of dicharge: Time for dicharge: Electrode Utilization: U [ 3 τ 0. ] c 1 δ + τ d j 1 δ τ d 3600 R Q 0. p o D 1 3 x100 %

10 Electrode Thermodynamic M Electrode potential: Total free energy: ch arg + xh O + xe MH + xoh Φ eq M Free energy of of reaction: T Φ Free dich R o e arg RT F Metal G G + G + R I e ln â â Site G E H M o o ( 1 ĉ ) µ M + ĉ H G µ x, ad Free energy of of mixing: I [( 1 ĉ ) ln ( 1 ĉ ) ĉ ln ĉ ] G RT +

11 Thermodynamic model for exce energy: G Total energy: G T E RT ln [( 1 ĉ ) ln γ + ĉ ln γ ] γ H ln γ M A RT M ( 1 ĉ ) RT A o o ( 1 ĉ ) µ M + ĉ µ H + RT [( 1 ĉ ) ln ( 1 ĉ ) + ĉ ln ĉ ] + A ĉ ( 1 ĉ ) Electrode potential conidering nonidealitie in in γ: γ: ĉ H Φ eq Φ o dg d ĉ RT F T ln F Φ ĉ ( 1 ĉ ) eq + A F [ ĉ 1]

12 j Electrode Kinetic Fk β F Φ p + â H e RT Fk â q M e ( 1 β ) RT F Φ η Φ Φ eq Modified Butler-Volmer expreion for hydride electrode: j j o ĉ β ( 1 ĉ ) β e β F RT Φ Φ o A F ( ĉ 1) ( 1 β ) ĉ 1 1 ĉ ( ) ( β ) e ( 1 β ) RT F Φ Φ o A F ( 1) ĉ

13 Concentration dependent exchange current denity: j o j o,ref ĉ p ( 1 β ) ( 1 ĉ ) q β e A RT p ( 1 ) ( 1 β ) ĉ + q β ĉ j o,ref State of ofdiharge: Parameter: 0.5 p + β SOD ν t j ( q p ) e 3600 D o,50 % SOC 0.5 A RT jt 3600 IR R Q p D p o Q o D [ p + β ( q p )]

14 Experimental pellet electrode wa prepared from nickel plated LaNi Sn alloy cycling and characterization tudie were done in in a 3 electrode etup with Pt Pt counter electrode and Hg/HgO reference electrode electrode wa activated with 10 charge-dicharge cycle electrode wa dicharged for a particular period of of time and left on open circuit tate of of charge tudie were done once the potential had tabilized

15 Experimental Cell

16 Margule parameter (A) Amount of material (w MH ) Cell temperature (T) Dicharge current (j ) Electrode capacity (Q o ) Model Parameter Exchange current denity at 50% SOC (j o,50% SOC ) 4800 J/mol 15 mg 98 K 4 ma/g 310 mah/g 14.4 ma/g Pellet electrode volume (V) 4.5x10 - cm 3 Poroity (ε) 0.4 Reaction order (p,q) 1 Electrode reference potential (Φ o ) V Reference hydrogen concentration (c o ) 91.3 mol/cm 3 Time for diffuion (t D ) Tranfer coefficient (β) x10 4

17 1.0 Change in Concentration A a Function of Time 0.5 hour Dimenionle concentration hour 5 hour 7 hour 10 hour Dimenionle radiu

18 Change in Concentration After 5 Hour of Dicharge Dimenionle concentration Dimenionle radiu

19 Change in Surface Concentration A a Function of Time Dimenionle concentration 1.0 δ δ0.5 δ1.0 δ1.5 δ.0 δ τ

20 Effect of Time for Diffuion on Hydride Electrode Utilization U (%) j (A) t D 10 k t D 17 k t D 4 k t D 33 k t D 50 k t D 67 k

21 Simulated Dicharge Curve for Different Value of ν ν0.047 ν0.081 ν0.116 ν0.33 ν0.470 ν Φ (mv v Hg/HgO) State of dicharge (%)

22 Φ (mv v Hg/HgO) Simulated Dicharge Curve for Different Dicharge Rate C/1 C/ C/3 C/5 C/ State of dicharge (%)

23 Comparion of Experimental and Theoretical Dicharge Curve Φ (mv v Hg/HgO) Experimental Without Margule Correction With Margule correction Time ()

24 Model Prediction of Change in Equilibrium Potential with SOC Experimental Model Φ eq (V) State of Charge (%)

25 Change in Exchange Current Denity with SOC j o (ma/g) Experimental Model fit State of Charge (%)

26 Φ (mv v Hg/HgO) Effect of Exchange Current Denity on Dicharge Curve 1.44 ma/g.75 ma/g 5.4 ma/g 14.4 ma/g 14.4 ma/g State of Dicharge (%)

27 Impedance Model for Determination of Diffuion Coefficient and Particle Size dicharge - - x, ad + xoh M + xho xe charge MH + Auming Fickian diffuion and olving for the concentration of hydrogen in the particle c o c p - a MH jwmhr V 1- FD ( ε) pr D Faradaic Impedance i given by inh pr coh D dη Z dj pr D - inh pr D

28 Impedance at the interface Z ( ω) η j + ω coth ( 1- i) σ [( 1 + i) ψ] - ( 1- i) ψ σ ( j/ c ) wmh ( j/ η ) a V( 1- ε) F D MH Im - σ ω ( T + T ) ( ω) Re i Im Z + Re ( ) 1 T + T 1 σ ω ( T - T ) ( ) 1 T + T 1 ψ ωr D

29 Imaginary Z (Ω) Model Simulation of of Hydride Impedance for Varying Diffuion Coefficient 5.0x10-10 cm / Increaing ω.5x10-10 cm / 1.5x10-10 cm / 8.0x10-11 cm / Semi-infinite diffuion 5.0x10-11 cm / Infinite diffuion Tranition Real Z (Ω)

30 Model Simulation of of Hydride Impedance for Varying Particle Size Imaginary Z (Ω) µm 10 µm 15 µm 0 µm 30 µm Real Z (Ω)

31 3 Nyquit Repone of Hydride Electrode at High SOC Imaginary Z (Ω) % SOC 80 % SOC Real Z (Ω)

32 Nyquit Plot of Hydride Electrode at Low SOC 5 Imaginary Z (Ω) % SOC 7 % SOC 18 % SOC 9 % SOC 0 % SOC Real Z (Ω)

33 Slope Determination at Tranition Region % 1 Imaginary Z (Ω) % 36% 7% 18% 9% Real Z (Ω)

34 D (cm /) 10-9 Change in Hydrogen Diffuion Coefficient with SOC SOC (%)

35 Particle Size Determination uing EIS - Imaginary Z Real Z Impedance repone of cobalt coated alloy characterized by emiinfinite, tranition and finite diffuion regime.6.4 Exponential fit of Nyquit tranition regime -Imaginary Z Im * e (0.4609*Re) 1. Particle Size 3 µm Real Z

36 Concluion A mathematical model for the dicharge of of a metal hydride electrode ha been developed. The analytical model coupled with the exce free energy correction ha been ued to to tudy the hydride electrode under different condition. Neglect of of the hydrogen-metal ite interaction reult in in dicharge curve which differ ignificantly with the actual phyical proce The particle ize and the hydrogen diffuion rate in in the alloy control the electrode utilization. Thermodynamic, kinetic and ma tranfer parameter critical for optimization of of electrode performance have alo been imulated.