I. 수퍼캐패시터특성분석을위한 transient 방법 EDLC analysis Pseudocapacitor analysis

Transcription

1 Theoretical consideration of electrochemical impedance spectroscopy based on 2-D transmission line model in the porous electrodes and its application into various mesoporous carbon materials 중앙대학교융합공학부나노소재전공윤성훈

2 I. 수퍼캐패시터특성분석을위한 transient 방법 EDLC analysis Pseudocapacitor analysis

3 Capacitor C S d C C S 2 2 sp (F/g) A(μF/cm ) (m /g)

4 Schematic Presentation of Composite Electrode Porous Carbon Particle Working Electrode Reference Electrode meso and micropore R bulk Current Collector macropore Inter-particle macropore Ionic movement similar to that of bulk phase(similar resistivity) Small contribution to total ESR Intra-particle meso and micropore Ionic movement different from that of bulk phase(high resistivity ~ 10 8 Wcm) Major contribution to ESR

5 Description of Electrochemical Capacitor Electrodes Flat and smooth electrodes 1-D transmission line model (TLM) 2-D transmission line model R1-C1 series R1-C1 trans. R1-C1 trans. /R2-C2 trans. electron ESR C c c c ESR = R electrode R pore R bulk r r r I(t) = (E/R) e -t/ Carbon ion R i R i R i Oversimplification bulk behavior of E-Cap. ResistanceMSC25-7%KB - R1 : ESR (Rb + Re+ Rct+ Rp) - Rp : total 5 pore resistance C1: total Time/s capacitance Easy to measure : simple equations NMC Representative pores : Intra-particle pores Total capacitance Complicate equations : analytical solution exists Representative pores : Intra-particle pores + Inter-particle pores Capacitance at inner pores : disregard cap. at outer pores Very complicate equations : very hard to acquire analytical solution

6 Electrodes thin composite electrode thicker electrode carbon current collector Flat electrode : simple RC circuit Thin electrode Pores: parallel connection 1-D TLM Common electrode Pores : not parallel connection 2-D TLM

7 1-D TLM

8 Impedance of electrode (a) carbon (b) Z Thin electrode Pores: parallel connection 1-D TLM pore Z Z Z R s Z( f) Z p N ( f) 1 Rp coth p 2fj m n 2fj p p (c) current collector Z p : impedance of one pore N p : total pore number m : particle number n : pore number of one particle c c c r r r

9 Differential equation for pore impedance c c c r r 2 V ( y, t) V ( y, t ) 2 y t r y = l/l p, = R p C p R p = r x l p, C p = c x l p l p : length of pore : time constant R p : pore resistance C p : pore capacitance Initial condition V(y,0) = 0 : zero initial over-potential Boundary condition dv(y,t)/dy y=1 = 0 : no potential gradient at y = 1 (end of pore) Different resulting equations according to individual BCs (potential/current step) In Laplace domain Z p V ( s) Rp ( s) coth[ s ] I( s) s Ref) R. de Levie, in Advances in Electrochemistry and Electrochemical Engineering, Vol. VI, P. Delahay, Editor, p. 329, John Wiley & Sons, New York, 1967.

10 Nyquist plot of ac-impedance experiment R Z( ) coth[ j ] j Z real R sinh 2 sin 2 2 cosh 2 cos 2 Z imag R sinh 2 sin 2 2 cosh 2 cos 2 2f RC

11 Nyquist Plot of Simple TLM Z( j ) R coth j j -Z imag * o slope : Warburg like behavior Z real * Z Z = R p /3

12 Imaginary Capacitance Analysis 2 cos 2 cosh 2 sin 2 sinh 2 ) ( C C im ) ( 1 ) ( Z j C 2 cos 2 cosh 2 sin 2 sinh 2 ) ( C C real

13 Imaginary capacitance plot (C im ): s-tlm peak frequency (f peak ) f peak Related with time constant Cim(f) f peak p C R p p C im ( ) C f/hz sinh 2 cosh 2 sin 2 2 cos 2 Peak area (A) Proportional to capacitance (C tot ) A C ( f ) d log f 0.682C im tot Ref) Jong H. Jang, Songhun Yoon, Bok H. Ka, and Seung M. Oh*, Journal of the Electrochemical Society 152 A1418 (2005).

14 II. 2-D TLM - Theoretical consideration of Nyquist plot

15 Double TLM for Composite Electrode t=1 t=2 t=3 thickness increase m=4 Z p Z p Z p Z p R e R e R e R e Z p R e Z p Z p R e R e Complicate connection : Z tot = f(z p,r e,t)/m Z p R e Z p R e Parallel connection : Z tot = (Z p + R e )/m

16 Theoretical Development for Double TLM Governing Equation Z tot ( p e Z,R, t) here, A = (k 2 +4k+2-(k+2)(k 2 +4k) 2 )/2 f p = Z p (k +(k 2 +4k) 1/2 )/2, q = Z p (k-(k 2 +4k) 1/2 ) /2, k = R e /Z p t : number of particles (thickness) p 1 qa t A t k : governing factor to determine Z tot k(r e /R p )

17 Double TLM Simple TLM Z p Z p R e R e Z p R e Z p R e Z tot = f(z p, R e, t) complicate connection : too complicate for fitting When R e << R p Z p Z p Z p Z p Z tot = Z p /t parallel connection : general consideration Breakage of parallel connection with thickness increase Critical thickness (t c )?

18 Simulation of Effects by Electrode Thickness Z e ~ Z pt : similar pore resistance to bulk less decrease of resistance 2.5 Effects of electrode thickness on the ionic resistance r = 1, R = 1 ~ D Graph Ze = Resistance Z pt = 1 -Z imag number of paticles t = 1 t = 2 t = Z e << Z pt : larger pore resistance than bulk distinct decrease of resistance Z real No change with thickness Z e : independent of thickness

19 Nyquist Plot of Simple TLM Z( jw) R p jw coth jw -Z imag * o slope : Warburg like behavior Z real * Z Z = R p /3

20 Thickness Effects : Nyquist Plots (R e /R p =10-3 ) Z imag * 0.2 -Z imag * t=1 t=5 t=10 2 t=50 t=100 t=200 ESR Z real * Decrease and increase More distributed resistance with thickness Intercept of Z real constant Z real *

21 Critical thickness (t c ) Z real (f=10-3 ) 6 4 t xz real (f=10-3 ) t c Thickness(t) Thickness(t) t < t c Parallel connection : Z tot = Z p /t t > t c Non-parallel connection : Z tot = f(z p, R e,t)

22 II. 2-D TLM - Imaginary capacitance analysis - CMK-3 carbon analysis

23 Imaginary capacitance plot (C im ): 2D-TLM 0.5 C im ( f )/C tot p = 1 sec f peak Related with r parameter Peak area (A) Proportional to capacitance (C tot ) 0.1 r = Log ( f /Hz ) C n 2f j 2 ( ) tanh f j C f f r p 2f j r coth p2f j coth p2f j Ctot R m R 1 1 p p ( ) 2 i r tot p p C mnc A C ( f ) d log f 0.682C im tot Ref) Jong H. Jang, Songhun Yoon, Bok H. Ka, and Seung M. Oh*, Journal of the Electrochemical Society 152 A1418 (2005).

24 Peak frequency (f p ) and peak area (A) 150 1/( 1 f p ) f 1 p 1 r Empirical relation between f p and r r A C ( f ) d log f 0.682C im 0 Relation between A and C 0 by numerical integration

25 Resulting equations using m parameter 0.4 RporeCpore RinterCporem f p R C tot tot 2 Rpore mr Rtot R0 Ri mn n inter C mnc 1 R0 C0 2 Ri C0 0 pore Calculation of m and n Possible for carbons having well-defined pore structure Separation between R 0 and R i R 0 : decrease, R i : increase according to increase of electrode thickness (m) Separation between 1 and 2 Find dominant factor affecting tot by experiments!

26 Description of electrode Describing equation Current collector a 0 HMC particle Intra-particle pore R R inter Z( f ) 1 R Z ( f ) coth m Rpore Z0( f ) coth j21f j2 f inter inter 0 n Z0( f ) 1 R Inter-particle pore C A Z 0 = m = 10, n = 4 case Ref) Songhun Yoon, Jong H. Jang, Bok H. Ka, and Seung M. Oh, Electrochimica Acta (2005).

27 CMK-3 pore structure Intensity/ A.U. dvdd -1 /cm 3 g Pore diameter/nm (b) 100 nm (a) 10 mm /degree (b) (a) HMC particle 5 mm l pore 100 nm a o (nm) 10.7 A BET ( m 2 g -1 ) 943 A electrode l pore Carbon wire a o b (nm) 6.7 l pore (mm) 2.5 Carbon rod b /2 Intra-particle pore Current collector 0 a 0 t (thickness) n (1 ) A al electrode 0 pore (electrode thickness) m a m ( number of intra-particle pores in electrode layer) n ( number of independent electric paths ) SBA-15 templated OMC Model electrode material for EDLC S. Yoon, J. H. Jang, B. H. Ka, S. M. Oh*, Electrochim. Acta (2005). (29 times cited) 27

28 Analysis of CMK-3 electrodes C im ( f )/F mm 90 mm 44 mm 71 mm According to increase of thickness Increase of A Decrease of f p Coincide to theoretical prediction log ( f /Hz) From least square fitting C pore : (2.0±0.1) x F R pore : (3.6±0.9) x W R inter : (2.9±0.1) x 10 5 W RporeCpore RinterCporem fp Cpore ( ) 10 F 0.4 R 12 2 Rpore ( ) 10 W pore C pore R inter C pore m f 5 p Rinter ( ) 10 W m 2 /10 8 S. Yoon*, C. W. Lee and S. M. Oh, J. Power Sources (2010). (6 times cited) 1/ f p From C pore C0 m n 28

29 Analysis of R tot with thickness R 0 R i R 0 Decrease with thickness Increase of pore number Resistance/W Thickness/mm R i Increase with thickness Extension of inter-particle pore length Dominant factor in R tot for thick electrode

30 Analysis of tot with thickness time constant/s Constant Reflect properties of intra-particle pores 2 Increase with thickness Dominant factor in tot for thick electrode Thickness/mm

31 II. Analysis of pore length effect

32 MCM-41 synthetic mechanism ~ a few min ~ a few hours Above several hours CTAB in solution CTAB TEOS rod-like SSM formation lengthening agglomeration MCM41 formation ph >14 SSM in solution : template (porogen) ref) J. Zhang, Z. Luz, H. Zimmermann and D. Goldfarb, J. Phys. Chem. B, 104, 279 (2000).

33 Control of pore length SSM 5 hr CTAB in solution CTAB TEOS ph >14 Low concentration 1) RF adding 2) carbonization 3) silica etchig High concentration 5 hr Concentration of CTAB : 1, 2, 5 and 10 wt% at 40 o C, 5 hr reaction time S. Yoon*, S. M. Oh, C. W. Lee, J.-W. Lee, Journal of the Electrochemical Society, 157, A1229-A1235 (2010)

34 SEM of carbons 1 wt% 2 wt% 5 wt% 10 wt%

35 TEM of carbons 1 wt% % 10 wt% 100 nm 50 nm Highly mesoporous and wormhole-like pore morphology Similar pore morphology irrespective of CTAB concentration

36 PSD of carbons 5 Similar pore size : ~ 3 nm Pore size : depend on reaction time of SSM SSM reaction time : fixed as 5 hr Dominant pores 10 % dv/dd 5 % % BET sruface area/m 2 g D/nm 1 % CTAB concentration / wt%

37 Imaginary capacitance analysis wt% wt% C im (f)/f mm 125 mm 83 mm C im (f)/f mm 119 mm 57 mm f/hz mm 5 wt% f/hz mm 10 wt% C im (f)/f mm 63 mm 113 mm C im (f)/f mm 94 mm 44 mm 35 mm f/hz 37 mm f/hz

38 Estimation of wt% wt% tot /s 0.3 tot /s = 28 s = 0.15 s 0.4 kt f p 2 1 tot t 2 /(10mm) wt% t 2 /(10mm) wt% tot /s = 0.18 s tot /s = 0.30 s t 2 /(10mm) t 2 /(10mm) 2

39 1 vs. CTAB concentration time constant of intra particle pores ( 1 )/s CTAB concentration/wt% Increase of CTAB concentration Pore length increase 1 increase 1 > 1

40 R tot vs. thickness plots R 0 R i 1 wt% wt% 1.0 R tot /W R tot /W thickness/mm wt% thickness/mm 5 10 wt% R tot /W 0.8 R tot /W thickness/mm thickness/mm

41 III. Analysis of pore size effect

42 Control of pore size ~ a few hours Above several hours CTAB in solution rod-like SSM formation and lengthening SSM condensation MCM41 formation CTAB TEOS ph >14 1) RF adding 2) carbonization 3) silica etchig Reaction time of silicate : 2, 5, 7 and 16 hr at 40 o C, 10 wt% CTAB Songhun Yoon*, Seung M. Oh and Chulwee Lee, Material Research Bulletin, 44, (2009).

43 SEM images of carbons 2 hr 5 hr Multi-faceted tubule morphology Inhomogeneous morphology after 7 hr 7 hr hr 16 hr Scale bar: 5 mm

44 TEM images of carbons 2 hr 5 hr Wormhole-like pores Increase of pore size 7 hr 16 hr Scale bar: 50 nm

45 Imaginary capacitance analysis hr hr C im (f)/f mm 66 mm 81 mm C im (f)/f mm 94 mm mm 5 47 mm f/hz hr 37 mm f/hz hr C im (f)/f mm 70 mm 99 mm C im (f)/f mm 120 mm 86 mm 61 mm 50 mm f/hz f/hz

46 Estimation of hr hr tot /s 0.4 tot /s = 0.23 s = 0.30 s kt f p 2 tot /s t 2 /(10mm) hr 1 = 0.14 s t 2 /(10mm) 2 tot /s t 2 /(10mm) hr 1 = 0.11 s t 2 /(10mm) 2

47 1 vs. reaction time time constant of intra particle pores ( 1 )/s Reaction time/hr 1 increase until 5 hr Pore length increase SSM lengthening 1 decrease after 5 hr Pore size increase SSM agglomeration 1 < 1

48 R tot vs. thickness plots hr R 0 R i hr R tot /W 0.6 R tot /W thickness/mm 7 hr 5 4 thickness/mm 16 hr R tot /W R tot /W thickness/mm thickness/mm

49 TLM in LIB by Toyota

50 18650 cell thickness effect

51 Symmetric cell thickness effect

52 Conclusions I. 1-D TLM I. Simple and easy to use II. Application into very thin electrode case II. 2-D TLM I. Consideration of inter-particle electrolyte resistance with thickness increase II. Higher contribution in total ESR for thick electrode III. More versatile equation in ICA than Nyquist form III. Application into LIB electrode simulation I. Advanced TLM model!!