Advanced Analytical Chemistry . . . . --- --- A B M X Y N A V 4πr2 {(4/3)πr3} = 3/r r r 1/ r2 1/r r --- --- --- Ox + ne vf Red vb vf = kfCOx(0,t) v: ( k: ( C(0,t): vb = kbCRed(0,t) ) ) mol s-1 cm-2 cm s-1 Q = -nFN F: N: Ox Red I = dQ/dt = -nFdN/dt = -nFAv dN/dt = vA A: I = -nFA(vf - vb)= -nFA(kfCOx(0,t) - kbCRed(0,t)) kf = Afexp(-ΔGf /RT) kb = Abexp(-ΔGb /RT) Af: ΔGf : ΔGf = ΔG0f + αnFE α: --0.5 ΔGb = ΔG0b - (1 - α)nFE kf = Afexp(-ΔG0f /RT)exp(-αnFE/RT) kb = Abexp(-ΔG0b /RT)exp((1 - α)nFE/RT) Afexp(-ΔG0f /RT) ---E = 0 kf = kf0exp(-αnFE/RT) Abexp(-ΔG0b /RT) (E )kf0 kb0 kb = kb0exp((1 - α)nFE/RT) kf = kb kf0exp(-αnFE0'/RT) = kb0exp((1 - α)nFE0'/RT) = k0 k0: E0': kf = k0exp(-αnF(E - E0')/RT) kb = k0exp((1 - α)nF(E - E0')/RT) I = -nFAk0(COx(0,t)exp(-αnF(E - E0')/RT) - CRed(0,t)exp((1 - α)nF(E - E0')/RT) --- t=0 C/ E1 E2 t = D 2C/ x2 t = 0, x ≥ 0 C = C0 x=0 C = 0; x I = nFAD1/2C0 / (πt)1/2 I t t C Cottrell C0 (1) << E = E0' + (RT/nF)lnCOx(0,t)/CRed(0,t) (2) >> (3) (1) (2) (WE) WE RE CE (RE) NHE H+ + e 1/2H2 0.0 V(pH = 0) AgCl + e KCl (CE) Ag + Cl0.199 V(vs. NHE) IR ----E E = Ea - IRs Ea I Rs - E I-E 2 Ox Red I / µA 1 Epa - Epc = 59/n (mV Epa 0 -1 -3 E1/2 = (Epc + Epa)/2 DOx ~ DRed E1/2 = E0' Epc -2 Ox 0 Ipc = 2.69x105An3/2COxDOx1/2u1/2 Red 100 25oC) 200 E / mV 300 400 I u 1/2 CV Ox + ne k Red Red P k: 5 Ox Red I / µA k=0 0 Ox -5 0 100 200 300 E / mV Red 400 k 500 CV Ox( ) + ne Red( ) Ip = n2F2AuΓ/(4RT) Γ: I/A I u ΔEp/2 = 3.53RT/(nF) [= 90.6/n (mV, 25oC)] E/V CV u (1) I = nFADC0{(πDt)1/2 + 1/r} r µm mm Cottrell /V S / nA (2) 1 nA 10 mV/1 nA = 10 MΩ 10 mV X X+ X X 2 µm X+ X+ mm Au 10 Pt 5 µm CCD RE C1+ A1- ( ) Xn+ C2+ A2- ( C1+ A1C2+ A2- / Xn+ ) RE Xn+ --/ RE C1+ A1- ( ) Xn+ C2+ A2- ( ) RE E = Δwoφ0Xn+ + (RT/nF)ln{aXn+(o)/aXn+(w)} Δwoφ0Xn+ :Xn+ aXn+(o) aXn+(w) n Xn+ Δwoφ0Xn+ = -ΔG0/nF ΔG0 Xn+ Xn+ (TMA+) 1,6- I / µA TMA+: 0.4 mM 50 mV/s : 0.07 cm2 E / mV Δwoφ0TMA+ = 0.17 V n2 n1 > n2 1 θi λ0 --- 00 nm dp = (λ0/4π)(n12sin2θi – n22)-1/2 RE CE RE CE 500 nm---0.5 µm F 25µm fL µm 10 µm µm 00 µm 10 µm µ µ µ µ µ 1. , , 2. , , , , 3. K. Nakatani, T. Sekine, and T. Negishi , Encyclopedia of Surface and Colloid Science, 1st Edition, Arthur Hubbard, Ed., Marcel Dekker, New York, Vol. 3, p.3391-3401 (2002).
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