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Electrochemical Techniques Electrochemical Techniques CHEM 269 Course Content This course is designed to introduce the basics (thermodynamics and kinetics) and applications (experimental techniques) of electrochemistry to students in varied fields, including analytical, physical and materials chemistry. The major course content will include Part I Fundamentals Overview of electrode processes (Ch. 1) Potentials and thermodynamics (Ch. 2) Electron transfer kinetics (Ch. 3) Mass transfer: convection, migration and diffusion (Ch. 4) Double-layer structures and surface adsorption (Ch. 13) Part II Techniques and Applications Potential step techniques (Ch. 5): chronoamperometry Potential sweep methods (Ch. 6): linear sweep, cyclic voltammetry Controlled current microelectrode (Ch. 8): chronopotentiometry Hydrodynamic techniques (Ch. 9): RDE, RRE, RRDE Impedance based techniques (Ch. 10): electrochemical impedance spectroscopy, AC voltammetry Grade: 1 mid-term (30%); 1 final (50%); homework (20%) Chronoamperometry (CA) Chronoamperometry E i i i LIM,c E4 E 3 E E1 E2 4 E3 t E2 t 0 0 t E Sampled-current voltammetry Co Co Co* Co* – E t x x Current-Potential Characteristics Large-amplitude potential step Totally mass-transfer controlled Electrode surface concentration ~ zero Current is independent of potential Small-amplitude potential changes i =iof RT C Reversible electrode processes E Eo ln O nF CR Totally irreversible ET (Tafel region) nF nF EE o' 1 EE o' i nFAko C 0,te RT C 0,te RT O R Electrode Reactions Osurf O’surf O’bulk electrode Oads electron mass chemical transfer transfer Rads Rsurf R’surf R’bulk Double layer Mass-transfer control Kinetic control Mass Transfer Issues In a one-dimension system, C z F (x) J (x) D j(x) j D C C v(x) j j x RT j j x j In a three-dimension system, z j F J (r) D C (r) D C (r) C v(r) j j j RT j j j diffusion migration convection diffusion migration convection current current current Potential Step under Diffusion Control Planar electrode: O + ne R CO(x,0) = CO* 2 Fick’s Law CO (x,t) CO (x,t) DO CO(0,t) = 0 t x2 LimC (x,t) = C * Laplacian transformation x∞ O O s * x st C L{F(t)} e F(t)dt C (x, s) O A(s)e DO 0 O s CO (0, s) 0 s C * x C (x, s) O 1 e DO O s Cottrell Equation i(t) CO (x,t) JO (0,t) DO nFA x x0 i (s) CO (x, s) DO nFA x x0 CO(0,t) = 0 1 2 * i (s) DO * nFADO CO CO Reverse LT i(t) 1 1 nFA s 2t 2 Frederick Gardner Cottrell (1877 - 1948) was born in Oakland, California. He received a B.S. in chemistry from the University of California at Berkeley in 1896 and a Ph.D. from the University of Leipzig in 1902. Although best known to electrochemists for the "Cottrell equation" his primary source of fame was as the inventor of electrostatic precipitators for removal of suspended particles from gases. These devices are still widely used for abatement of pollution by smoke from power plants and dust from cement kilns and other industrial sources. Cottrell played a part in the development of a process for the separation of helium from natural gas. He was also instrumental in establishing the synthetic ammonia industry in the United States during attempts to perfect a process for formation of nitric oxide at high temperatures. Depletion Layer Thickness Do * i nFA Co o (t) 30 mm 1 s = DOt 1 mm at t = 1 ms O (t) DOt 30 nm 1 ms Co Co* t x Concentration Profile s C * x C (x, s) O 1 e DO O s x x C (x,t) C* 1 erfc C* erf O O O 2 Dot 2 Dot In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) which occurs in probability, statistics, materials science, and partial differential equations. It is defined as: Sampled Current Voltammetry Linear diffusion at a planar electrode Reversible electrode reaction2 CO (x,t) CO (x,t) Stepped to an arbitrary potentialDO t x2 RT C (0,t) C (0,t) E Eo ln O O expnf E Eo nF CR (0,t) CR (0,t) 2 CR (x,t) CR (x,t) DR t x2 CO(x,0) = CO* CR(x,0) = CR* = 0 LimC (x,t) = C * LimC (x,t) = C * = 0 x∞ O O x∞ R R Flux Balance s C * x C (x, s) O A(s)e DO O s CO (x,t) CR (x,t) DO[ ]x 0 DR[ ]x 0 0 x x s x DR Incoming flux Outgoing flux CR (x, s) B(s)e s s A(s) B(s) 0 s DO DR x DR CR (x, s) A(s)e D B(s) R A(s) A(s) DO I-E at any Potential C (0, s) O CR (0, s) 1 2 * nFADO CO CO (0,t) i(t) o 1 1 * expnf E E 2 2 CO CR (0,t) t 1 A(s) A(s) s s x DR * CO e CO (x, s) s 1 1 * CO A(s) s 1 C (x,t) i nFAD O s O * x x C D x0 C (x, s) O e R R s 1 Shape of I-E Curve At very negative potentials, 0, and i(t) id y 1 2 * nFADO CO id Slope n i(t) 1 1 2t 2 1 1 E1/2 E RT D RT i i(t) E Eo' ln R ln d nF DO nF i(t) E1/2 Wave-shape analysis CA Reverse Technique 1 E nFAD 2C* i (t) O O E f 1 1 f 2t 2 1 Ei E 1 * r nFAD 2C 1 1 1 1 t i (t) O O t r 1 1 0 2 1 ' 1 " 2 t t (1 )t o o ' expnf E f E " expnf Er E 1 2 * nFADO CO 1 1 ir (t) 1 when ’ =0 and ” =∞ 2 t t t i t t i t r f f r 1 1 tr – tf = t i f tr t tr i f tr Semi-Infinite Spherical Diffusion C (r,t) 2C (r,t) 2 C (r,t) O D O O O 2 t r r r 1 2 * 1 1 i(t) nFADO CO 1 1 2t 2 ro CO(r,0) = CO* boundary C (r ,t) = 0 conditions O 0 1 * LimC (r,t) = C * nFAD 2C r∞ O O O O i(t) 1 1 2t 2 1 2 * 1 1 i(t) nFADO CO 1 1 2t 2 ro Cottrell equation Ultramicroelectrode Radius < 25 mm, smaller than the diffusion layer Response to a large amplitude potential step First term: short time (effect of double-layer charging Second term: steady state 1 2 * 1 * 1 i(t) nFADO COnFAD 1OC1O * iss 2t 2 4ronFD OroCO ro i spherical electrode 1 nFAD 2C* planar O O i i(t) 1 1 ss electrode 2t 2 t 1 2 * 1 1 i(t) nFADO CO 1 1 2t 2 ro Amperometric glucose sensor based on platinum–iridium nanomaterials Peter Holt-Hindle, Samantha Nigro, Matt Asmussen and Aicheng Chen Electrochemistry Communications, 10 (2008) 1438-1441 This communication reports on a novel amperometric glucose sensor based on nanoporous Pt–Ir catalysts. Pt–Ir nanostructures with different contents of iridium were directly grown on Ti substrates using a one-step facile hydrothermal method and were characterized using scanning electron microscopy and energy dispersive X-ray spectroscopy. Our electrochemical study has shown that the nanoporous Pt– Ir(38%) electrode exhibits very strong and sensitive amperometric responses to glucose even in the presence of a high concentration of Cl− and other common interfering species such as ascorbic acid, acetamidophenol and uric acid, promising for nonenzymatic glucose detection. (a) S0: Pt–Ir(0%), (b) S1: Pt–Ir(22%), (c) S2: Pt–Ir(38%). (d) EDX spectra of samples S0 and S2. Insert: the enlarged portion of the EDX spectrum of samples S0 and S2 between 9.0 and 12.0 keV. (a) Chronoamperometric responses of S0, S1, S2 and S3 measured at 0.1 V in 0.1 M PBS (pH 7.4) +0.15 M NaCl with successive additions of 1 mM glucose (0– 20 mM). (b) The corresponding calibration plots. Interference Study Pt–Ir(38%) Pt–Ir(0%) Chronoamperometric curves of S0 and S2 recorded in 0.1 M PBS +0.15 M NaCl with successive additions of 0.2 mM UA, 0.1 mM AP, 0.1 mM AA and 1 mM Glucose at 60 second intervals under the applied electrode potential 0.1 V. Electroanalysis 1997, 9, 619. Microelectrode Voltammetry Fig. 1 Plot showing cyclic voltammograms recorded for a series of 25 mm Pt microelectrodes recorded at 2 mV/s in a solution containing 10 mM K3[Fe(CN)6] in Sr(NO3)2 at 25 mm under anaerobic conditions. The insert in the figure shows a SEM image of the 93 mC HI-ePt modified microelectrode recorded after the experiments were performed. The scale bar on the SEM represents 10 mm. Electrochemical reduction of oxygen on mesoporous platinum microelectrodes Chronocoulometry (CC) Cottrell Equation (at large potential steps) 1 2 * Surface adsorbed species nFAG* nFAD C 1 O O 2 1 Q(t) t Q Q 2 * 1 DL nFADADS CO 2 i(t) O 1 1 Q 2 2 Double-layer charging t intercept t1/2 Reverse CC 1 2 * nFAD C 1 1 O O 2 2 Qd (t t ) 1 t t t 2 So the net charge removed in the reverse step is 1 2 * nFAD C 1 1 1 O O 2 2 2 Qr (t t ) Q(t ) Qd (t t ) 1 t t t t 2 Q t < t t1/2 t > t Potential Sweep Techniques C O R x Nernstian Processes CO (0,t) nF o' O + ne R f (t) exp Ei vt E St CR (0,t) RT E(t) = Ei - vt 2 nFv CO (x,t) S(t) eCOt (x,t) DO RT t x2 Laplacian transformation s C * x C (x, s) O A(s)e DO O s i(t) C (x,t) J (0,t) D O O O 1 t 1 nFA * x 2 CO (0,t) CO xi0(t )(t t ) dt nFA DO 0 i(t ) f (t ) nFA t 1 * 1 2 CO (0,t) CO f (t )(t t ) dt DO 0 t 1 1 2 CR (0,t) f (t )(t t ) dt DR 0 CO (0,t) nF o' f (t) exp Ei vt E St CR (0,t) RT t 1 * CO f (t )(t t ) 2 dt 1 1 0 2 2 S(t)(DR ) (DO ) D O DR 1 t 1 2 * nFA(DO ) CO i(t )(t t ) 2 dt 0 S(t) 1 Let z = t so that t = z/ At t = 0, z = 0, and at t = t, z = t t 1 t z 1 dz f (t )(t t ) 2 dt g(z)(t ) 2 0 0 nFv t * RT 1 1 CO DO g(z)(t z) 2 2 dz 0 1 s(t) t 1 1 (z)(t z) 2 dz 0 1 s(t) g(z) i(t) (z) * * CO DO nFACO DO * i nFACO DO (t) Numerical Simulations Linear Sweep / Cyclic Voltammetry Key Features For Reversible Reactions i v1/2 for linear diffusion Peak current at 1/2(st) = 0.4463, 5 3/2 1/2 1/2 thus iP = (2.69 10 )n ADO CO*v Peak potentials E1/2 EP = E1/2 – 1.109(RT/nF) EP/2 EP/2 = E1/2 + 1.09(RT/nF) |EP – EP/2|= 2.20(RT/nF) E1/2 = |EP,a + EP,c|/2 Totally Irreversible Reactions O + ne R i CO x,t DO k f CO 0,t nFA x x0 E Ei vt nF nF nF EEo' E Eo' vt o RT o RT i RT bt k f k e k e e k f ,ie * i nFACO DOb(bt) 1 * 1 F 2 i nFACO DOv2 (bt) RT Key Features At 1/2(bt) = 0.4958, 1 1 1 5 2 * 2 2 iP (2.9910 ) nACODOv * o F o' iP 0.277nFACOk exp EP E RT Peak potential |EP – EP/2|= 1.857(RT/nF) 1 2 1 D 2 o' RT O Fv E E 0.780 ln ln P nF o RT k Reversible vs Irreversible Reactions Cyclic Voltammetry Current reflects the combined contributions from Faradaic processes and double-layer charging For chemically reversible reactions, iP,a = iP,c (independent of v) Peak splitting DEP = |EP,a – EP,c|=2.3RT/nF DEP = 59/n mV at 298 K, or at steady state, 58/n mV.
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