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2 Fig V 2.3.3

3 C CmAh = ImA th (2.1) 1000mAh 1A 1 2 1C C (Capacity) 1 3Ah 3A Rrate CAh = IA (2.2) * *1 10 2

4 ( ) E(ω) I(ω) Z(ω) Z(ω) = E(ω) I(ω) (3.1) Z ( θ)

5 3 6 I E *1 1Hz 1 10mHz ( Cole-Cole Plot) 2 f Z θ ( ) Z = Z Re jz Im Z Re x Z Im y j x y R C y -y log f log Z θ Fig. 3.3 Table.3.1. *1 (4.29)

6 R C (Fig. 3.1) Fig.3.1 R C. Fig. 3.1 Z = R 1 + jωcr (3.2) Z = Z Re jz Im (3.3) = R 1 + (ωcr) 2 j ωcr (ωcr) 2 (3.4) Z Re = Z Im = R 1 + (ωcr) 2 (3.5) ωcr (ωcr) 2 (3.6) (3.5) (3.6) ω (3.5) ω ω = 1 R 1 (3.7) CR Z Re (3.7) (3.6) Z Re 2 RZ Re + Z Im = 0 (3.8) ( Z Re R 2 ) 2 + Z Im = ( ) 2 R (3.9) 2

4) Z Re = Z Im = R 1 + (ωcr) 2 (3.5) ωcr 2 1 + (ωcr) 2 (3.6) (3.5) (3.6) ω (3.

7 3 8 R C (R/2, 0) R/2 ( ) Z Im = R 2 (3.10) (3.6) (ωcr) 2 2ωCR + 1 = 0 (3.11) ω = 1 CR (3.12) CR = τ C Fig.3.2 R/C.

8 3 9 Fig.3.3.

9 vb kb vf γkf Fig.4.1. (Fig. 4.1) O + ne R (4.1) v f/b mol/cm 2 s k f/b cm/s f b n (O) (R) C O (x, t) C R (x, t) mol/cm 3

10 4 11 ( x = 0 ) v f = k f C O (0, t) (4.2) v b = k b C R (0, t) (4.3) 4 QC (O) (R) N mol Q = nf N (4.4) F *1 I I = dq dt = nf dn dt (4.5) dn/dt mol/s v mol/cm 2 s A cm 2 I I = nf Av (4.6) I v (4.6) (4.2) (4.3) I f = nf Av f (4.7) I b = nf Av b (4.8) I f I b (4.6) I I f I b I = ( I f I b ) = nf A(v f v b ) { } = nf A k f C O (0, t) k b C R (0, t) (4.9) k f k b (Arrhenius equatio) *2 k f = A f e G f / (4.10) k b = A b e G b / (4.11) *1 1 e N A F = 96485C *2 plot.htm

7) I b = nf Av b (4.8) I f I b (4.6) I I f I b I = ( I f I b ) = nf A(v f v b ) { } = nf A k f C O (0, t) k b C R (0, t) (4.9) 4.2.

11 4 12 G G f b ( ) A f A b Fig. 4.2 E = 0 0 E = E E nfe E E E Gof nfe Gob nfe Gf Gb Fig.4.2. Fig. 4.2 E (nf E) α (0 < α < 1) E = 0 E E = 0 (1 α)nf E α G f G b = G 0f + αnf E (4.12) = G 0b (1 α)nf E (4.13) (4.12) (4.13) (4.10) (4.11) k f = A f exp G 0f exp k b = A b exp G 0b exp αnf E (1 α)nf E (4.14) (4.15) kf 0 = A f exp G 0f kb 0 = A b exp G 0b (4.16) (4.17)

12 4 13 (4.14) (4.15) k f = kf 0 exp αnf E k b = kb 0 (1 α)nf E exp (4.18) (4.19) kf 0 k0 b E E = 0 I = 0 CO = C R *3 v f = v b (4.2) (4.3) k f = k b k f = k b (4.18) (4.19) E ( ) E = ln k0 f nf kb 0 + ln C O CR = E 0 + nf ln C O C R (4.20) *4 E = E eq CO C R E0 a O/R γ O/R a O/R = γ O/R C O/R (4.21) (4.21) (4.20) E 0 = E nf ln a O a R + nf ln γ O γ R = E 0 + nf ln γ O γ R (4.22) E 0 E eq = E 0 + nf ln C O C R E 0 (4.23) = E 0 + nf ln γ O γ R (4.24) E eq E 0 E 0 *3 C0 C R C O = C O(0, t) C R = C R(0, t) *4

20) *4 E = E eq CO C R E0 a O/R γ O/R a O/R = γ O/R C O/R (4.21) (4.21) (4.20) E 0 = E nf ln a O a R + nf ln γ O γ R = E 0 + nf ln γ O γ R (4.

13 k f = k b k O = kf 0 exp αnf E0 = k 0 b exp (1 α)nf E 0 (4.25) k O 1 k O (4.18) (4.19) k f = kf 0 αnf E exp αnf = k O E 0 exp αnf E = k O exp αnf (E E0 ) (4.26) k b = k O exp (1 α)nf (E E 0 ) (4.27) k f k b (4.9) I = nf Ak O {C O (0, t)exp αnf (E E0 ) C R (0, t)exp (1 α)nf (E E 0 ) } (4.28) k O α k O α Fig. 4.2 (E = E eq ) (I=0) I 0 = nf A k O C O exp = nf A k O C R exp αnf (E eq E 0 ) (1 α)nf (E eq E 0 ) (4.29) I 0

14 4 15 (4.23) (4.29) i 0 = I 0 /A i 0 = nf k O C R exp (1 α) ln C O C R = nf k O (C O) 1 α (C R) α (4.30) (4.29) (4.30) { } (CR i f = I/A = i ) α 0 (CO C Oexp αnf η (C O )α 1 )1 α (CR C (1 α)nf η Rexp ) α { } C O = i 0 CO exp αnf η C R (1 α)nf η CR exp (4.31) η = E E eq 4.3 Fig. 4.1 (O) (R) *5 C O/R (x, 0) = C O/R (4.32) C O/R (x, t) = C O/R (x ) (4.33) i f nf = D C O O x = D C R R x (4.34) (4.34) C O = CO C R = CR E = E eq i f = i f 0 + i f 1 (4.35) i f 0 = 0 η = 0 (4.31) i f 1 = i f CO1 s + i f CR1 s + i f η s η1 s (4.36) x=0 x=0 x=0 C s O C s R *5

(4.31) η = E E eq 4.3 Fig. 4.1 (O) (R) *5 C O/R (x, 0) = C O/R (4.32) C O/R (x, t) = C O/R (x ) (4.33) i f nf = D C O O x = D C R R x (4.

15 4 16 s surface i f = i 0 C O C (4.37) x=0 O i f = i 0 C R C (4.38) x=0 R i f αnf = i η 0 (4.39) x=0 (4.36) αnf i f 1 = i 0 η 1 i 0 CO C O1 + i 0 CR C R1 (4.40) i f 1 = i f exp jωt (4.41) η 1 = η exp jωt (4.42) (C O/R ) 1 = C O/R exp jωt (4.43) i αnf f = i 0 η i 0 C O C O + i 0 C R C R (4.44) η η/ i f Z η i f = Z = nf i f CR i 0 nf CR C O CO (4.45) g = C R /CR i f (4.46) C h = O /CO i f (4.47) (4.45) η = nf i f + g + h i 0 nf (4.48) (diffusion equation) ( ) C O/R 2 C O/R = D O/R t x 2 (4.49)

42) (C O/R ) 1 = C O/R exp jωt (4.43) i αnf f = i 0 η i 0 C O C O + i 0 C R C R (4.

16 4 17 C O/R = C O/R0 + C O/R1 (4.50) C O/R1 = C(x) O/R exp jωt (4.51) (4.49) (4.50) (4.51) C R jωc 2 CR R (x) = D R x 2 (4.52) C R (x) = N R exp( λx) (4.53) (4.52) ( ) C jω R (x) = N R exp x D R i f nf = D C R R x ( ) jω jω = D R N R exp x D R D R (4.54) (4.55) (4.54) (4.55) C R (x) C i R (x) = f 1 (4.56) nf jωdr C O (x) = i f nf 1 jωdo (4.57) (4.56) (4.57) (4.46) (4.47) g h g = 1 nf jωd R CR h = 1 nf jωd O CO (4.58) (4.59) g h (4.45) ( ) Z = nf i 0 n 2 F 2 C + (4.60) jωdo jωdr 1 2 i 0 C D

17 4 18 Fig.4.3.

46 Y 5.1.1 Y Y Y 3.1 R Y Figures 5-1 5-3 3.2mm Nylon Glass Y (X > X ) X Y X Figure 5-1 X min Y Y d Figure 5-3 X =X min Y X =10 Y Y Y 5.1.2 Y Figure 5-

46 Y 5.1.1 Y Y Y 3.1 R Y Figures 5-1 5-3 3.2mm Nylon Glass Y (X > X ) X Y X Figure 5-1 X min Y Y d Figure 5-3 X =X min Y X =10 Y Y Y 5.1.2 Y Figure 5- 45 5 5.1 Y 3.2 Eq. (3) 1 R [s -1 ] ideal [s -1 ] Y [-] Y [-] ideal * [-] S [-] 3 R * ( ω S ) = ω Y = ω 3-1a ideal ideal X X R X R (X > X ) ideal * X S Eq. (3-1a) ( X X ) = Y ( X ) R > > θ ω ideal X θ =