Electrochemistry Notes

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Electrochemistry Notes

  1. 1. BASIC ELECTROCHEMISTRY
  2. 2. THE CHARGE AND CURRENT •Electrochemistry studies the processes which involve charge •The charge is a source of electric field Element of charge: 1.602·10-19 C The energy change is ±1.602·10-19 J if we move the charge across the potential drop of 1V If we do the same with 1 mol of charges, we obtain… A + B 1V - - The current is the change of charge per time I= dQ dt
  3. 3. FARADAY’S LAWs (1834) “The chemical power of a current of electricity is in direct proportion to the absolute quantity of electricity which passes” “Electrochemical Equivalents coincide, and are the same, with ordinary chemical equivalents” m Q = M zF MIt m= zF t M m= ∫ Idt t =0 zF Area under current-time curve (and freqently the currentpotential curve also) is the charge!! This way can be deduced how much material was transformed.
  4. 4. CONDUCTIVITY R≈ l A l (Ω) A E R = (Ohmś law) I + + - Electrolytes: same principle, but conductivity is preferred A G=χ l The unit for conductivity is Siemens, what is the unit of specific conductivity? For species KXAY: Migration velocities can be different Stokes force is balanced by force induced by electric field Only the cations distant from the plane by vA or nearer will cross the plane. In unit field (1V) and unit area will cross the boundary xcαFz cat ucat cations χ = xcαFzcat ucat + ycαFz anuan
  5. 5. CONDUCTIVITY V A Solutions can have different concentrations: χ  S m3 2 −1  Λ=  m mol = Sm mol  c   Λ ΟΟ This is used for measurements of dissociation constants: AB c (1 -α) Λ α= Λ∞ C A + cα + B - cα  Λ  c Λ   2 2 cα KD = =  ∞ c (1 − α ) 1 − Λ Λ∞ 2
  6. 6. HOW AND WHERE THE POTENTIAL DIFFERENCE DEVELOPS s o lu tio n 1 s o lu tio n 2 Junction potential (Henderson) Donnan potential m e m b ra n e Potential difference develops where a charge separation in space occurs
  7. 7. THE NERNST EQUATION The combination of two basic physical chemistry equations: − ∆G = zFE and − ∆G = RT ln K All processes in which charge separation occurs go to equilibrium …but what is K?
  8. 8. DANIEL CELL Zn | ZnSO4 | | CuSO4 | Cu Zn+CuSO4→ Cu+ZnSO4 [ Cu ][ ZnSO4 ] zFEMN = RT ln [ Zn][ CuSO4 ] …is it OK?
  9. 9. BACK TO NERNST EQUATION RT aox E=E + ln zF ared 0 RT ared E=E − ln zF aox 0 aox 2.303RT E=E + log zF ared 0 2.303RT = 0.059 V F (at 25°C )
  10. 10. ELECTRODES OF THE FIRST KIND The term electrode is here used in a sense of a half-cell. Metal immersed into the solution of its own soluble salt. The potential is controlled by the concentration of the salt. E=E 0 Me / Me + RT + ln aMe+ zF Zn in ZnCl2, Ag in AgNO3, Cu in CuSO4 etc. Non-metallic electrodes – gas electrodes (hydrogen and chlorine electrode)
  11. 11. THE HYDROGEN ELECTRODE
  12. 12. THE HYDROGEN ELECTRODE Pt Pt E = E 0 at / H + − H H H [ ] RT RT ln KK H p H 2 + ln H + F F
  13. 13. ELECTRODES OF THE SECOND KIND Argentochloride Ag | AgCl | KCl | | Calomel Hg | Hg2Cl2 | KCl | | Mercurysulphate Hg | Hg2SO4 | K2SO4 | | 0 SHE 197 m V 244 m V 640 m V SCE . A g /A gC l s a t. H g /H g 2S O sat 4 REDOX ELECTRODES F e 2+ e- F e 3+ e- Fe 3+ The electrode serves as an electron sink Redox combo F e 2+ P t e le c tr o d e
  14. 14. ELECTRODES OF THE THIRD KIND ..just a curiosity Zn | Zn2C2O4 | CaC2O4 | CaCl2 | | We can measure the concentration of Ca2+, but there’s a better device to do this…
  15. 15. THE ABSOLUTE SCALE OF POTENTIALS R E D (v a c u u m ) -∆ G s o lv ∆G IO N O X (v a c u u m ) -∆ G (R E D ) zF∆E s o lv (O X ) Reference to vacuum (instead of hydrogen electrode) ABS R E D (s o lu tio n ) O X (s o lu tio n ) H Thermodynamic cycle for hydrogen -∆ G H 0 -∆ G (v a c u u m ) H . (v a c u u m ) -∆ G s o lv + -F ∆ E (s o lu tio n ) d is s /2 0 ABS 1 /2 H 2 4420 m V 0 Vacuum IO N SHE 197 m V 244 m V SC sa t. The most commonly accepted value is 4.42V, but values around 4.8V are also reported + E 640 m V s a t. H g /H g 2S O 4 Ag /A gC l
  16. 16. ION SELECTIVE ELECTRODES Membrane potential reflects the gradient of activity of the analyte ion in the inner and outer (sample) solutions. •The trick is to find a membrane material, to which an analyte is selectively bound. The membrane must be conductive (a little bit, at least), but it should not leak Liquid junction for reference electrode (sometimes is high) Li Li + H Si Li O h y d r a te d H a u g a a r d la y e r s + L i io n s p a r tia lly fr e e + 400 M Ω + Si Nikolski eq. E = Eassym + RT RT ln aH O + + X ⋅ ln a Na + 3 F F
  17. 17. MEMBRANES FOR ISEs •Glass membranes (H+, for other cations change in the composition of glass membrane (Al2O3 or B2O3 in glass to enhance binding for ions other than H + (Na+, Li+, NH4+, K+, Rb+, Cs+ and Ag+) •Crystalline Membranes (single crystal of or homogeneous mixture of ionic compounds cast under high P, d~10 mm, thickness: 1-2 mm. Conductivity: doping or nonstechiometry, Ag+ in AgCl or Ag2S, Cu+ in Cu2S. Fluoride electrode: determines F-, LaF3 crystal doped with EuF2). •Liquid membranes (organic, immiscible liquid held by porous (PVC) membrane with ion exchange properties or neutral macrocyclic compouds selectively binding the analyte in their cavities)
  18. 18. POTENTIOMETRY Cell and voltmeter behaves as a voltage divider circuit E(cell) Ri RM V E(measured) R2 E2 = E1 R1 + R2 R1 E1 Emeasured = Ecell R2 E2 RM RM + Ri
  19. 19. POTENTIOMETRY AND PHYSICAL CHEMISTRY 1. Activity coefficients determination 2. Solubility products determination 3. Ion product of water determination Pt | H2 | HCl | AgCl |Ag Ag | AgNO3 | |KNO3 | | KX, AgX | Ag Pt | H2 | KOH | |KCl | AgCl |Ag Ionic product of water: 1.008·10-14 (25°C) – good agreement with conductivity measurement
  20. 20. 3-ELECTRODE CELLS AND POTENTIOSTATS Polarizable and nonpolarizable
  21. 21. ELECTRODE MATERIALS Inert metals (Hg, Pt, Au) •Polycrystalline •Monocrystals Carbon electrodes •Glassy carbon •reticulated •Pyrrolytic graphite •Highly oriented (edge plane, ) •Wax impregnated •Carbon paste •Carbon fiber •Diamond (boron doped) Potential window available for experiments is determined by destruction of electrode Semiconductor electrodes (ITO) material or by decomposition of solvent (or Modified electrodes dissolved electrolyte)
  22. 22. ELECTRON TRANSFER PHENOMENON 1-10 nm 1-10 nm in thickness ↓ ↓ ↓ ↓ ↓ ↓ ↓ ~1 volt is dropped across this region… Which means fields of order 107-8 V/m ↓ ↓ ↓ ↓ ↓ ↓ l ↓ + + ↓ ↓ ↓ + + ↓ ↓ l ↓ Where the truncation of the metal’s Electronic structure is compensated for in the electrolyte. + + ↓ ↓ ↓ l ↓ ↓ Solvated ions ↓ ↓ ↓ l ↓ ↓ ↓ Electrode surface ↓ The double-layer region is: ↓ ↓ ↓ ↓ ↓ ↓ + + ↓ ↓ l ↓ “The effect of this enormous field at the electrodeelectrolyte interface is, in a sense, the essence of electrochemistry.” [1] l IHL OHL [1] Bockris, Fundamentals of Electrodics, 2000
  23. 23. BUTLER-VOLMER AND TAFEL EQUATIONS - ne + ox = re d E ∆G E # - 2 zF ∆E E αzF ∆E (E 2) ∆G # - (E 1) ∆G # + (E 1) ∆G # + (E 2) 1 E 2< E 1 r e a c tio n c o o r d in a te
  24. 24. BUTLER-VOLMER AND TAFEL EQUATIONS i i0 , α = 0 .7 i0 , α = 0 .5 Exchange current density Depends on the species undergoing redox transformation and on the electrode material i0 . α = 0 .3 0 i0 ' < i0 , α = 0 .5 η    exp  (1−α ) nF ( E − E ° )  − exp  αnF ( E − E ° )       0  RT   RT   i=i In fact, large overpotential for hydrogen evolution on Hg surfaces enables us to observe reductions in aqueous solutions Also, the development of modern modified electrodes is based on finding the modifying layer which increase the exchange current density on the electrode surface
  25. 25. BUTLER-VOLMER AND TAFEL EQUATIONS i lo g (a b s ( i0 ) ) η i0 η   α i = i0  exp  (1−RT) zF ( E − E ° )  −exp  αzF ( E − E ° )        RT       2.303αzF  log( i ) = log( i0 ) −  (E − E ° )  RT  
  26. 26. MASS TRANSFER •Migration •Convection •Diffusion We try to avoid migration by the addition excess supporting electrolyte
  27. 27. TRANSPORT BY DIFFUSION t1 C t2 t3 t= 0 1st Fick Law j = − D ∂C ∂x C s 0 x ... d is ta n c e fr o m th e e le c tr o d e C t= 0 Nernst diffusion layer c0 − cs i = zFD δN Cs ilim 0 δN x  ∂c  i = zFD   ∂x  x =0 c0 = zFD δN η D = E − E′ = η D = E − E′ = RT cS ln zF c0 RT  i  ln1 −  i   zF  lim 
  28. 28. THE COTTRELL EQUATION t1 C t2 t3 t= 0 E C s t= 0 0 x ... d is ta n c e fr o m th e e le c tr o d e t ∂c ∂ 2c =D 2 ∂t ∂x Mathematical solution for boundary conditions of CA experiment is very complicated, but the result is simple: Second Fickś law i c0 − cs i = zFD πDt This is how Nernst layer thickness changes over time t
  29. 29. TRANSPORT BY CONVECTION Rotating disk electrode (RDE) Rotating ring disk electrode (RRDE) c u rre n t ta k e -o ff r o ta tin g c y lin d e r s o lu tio n " ro ta tin g d is k " A c tiv e a re a o f th e e le c tro d e IL = (0,620)∙z∙F∙A∙D2/3∙ω1/2∙ν–1/6∙c Levich Equation ω speed of rotation (rad∙s-1), ν kinematic viscosity of the solution (cm2∙s-1), kinematic viscosity is the ratio between solution viscosity and its specific weight. For pure water: ν = 0,0100 cm2∙s-1, For 1.0 mol∙dm-3 KNO3 is ν = 0,00916 cm2∙s-1 (at 20°C). c concentration of electroactive species (in mol.cm-3, note unusual unit) D diffúsion coefficient (cm2∙s-1), A electrode area in cm2
  30. 30. POLAROGRAPHY Halfwave potential Limiting diffusion current (Ilkovic equation)
  31. 31. CYCLIC VOLTAMMETRY CV – the most important electrochemical method One or more cycles …CV Half cycle … LSV 0 ≤ t ≤ t r : E = Ei + vt t r ≤ t ≤ 2t r : E = Ei + v( t − t r ) v… the scan rate
  32. 32. REVERSIBLE CYCLIC VOLTAMMOGRAM Electroactive species attached to the electrode, both redox forms stable I ( )  F  exp  E − E0  F  RT  I = FAΓ0 v 2 RT    F  E − E 0  1 + exp RT    ( E 0 E )
  33. 33. REVERSIBLE CYCLIC VOLTAMMOGRAM 4.0×10 -6 B O fo rw a rd scan 0 -2.0×10 -6 -0.50 Electroactive species in solution, both stable C 2.0×10 -6 I/A R A re ve rs e scan R IUPAC convention O D -0.25 0.00 0.25 E/V vs. reference electrode Randles-Sevcik equation: 0.50 Peak separation is 59 /z mV Ipc = Ipa = 2,69.105 ∙ A ∙ z3/2 ∙ D1/2 ∙ c ∙ v1/2 A in cm2, D in cm2s-1/2, c in molcm-3, v in V/s
  34. 34. QUASI AND IRREVERSIBLE VOLTAMMOGRAMS 4.0×10 -6 Black: k=1cmsec-1 Blue: k=0.001 Red: k=0.00001 0 Black: alpha=0.5 Blue: alpha=0.3 Red: alpha=0.7 -2.0×10 -6 -0.50 -0.25 0.00 0.25 0.50 E/V vs. reference electrode 3.0×10 -6 I/A I/A 2.0×10 -6 1.0×10 -6 -1.0×10 -6 -3.0×10 -6 -0.5 0.0 E/V vs. reference electrode 0.5
  35. 35. BASIC MECHANISMS IN CV E, C notation (E… electron transfer, C… coupled chemical reaction) E, EE, CE, EC, ECcat etc. Mechanisms can be very complex even for simple systems Two electron-two proton system = „square scheme“
  36. 36. THE EE MECHANISM 7.0×10 -6 7.0×10 -6 ∆E= 400 mV 5.0×10 -6 3.0×10 -6 I/A I/A 3.0×10 -6 1.0×10 -6 1.0×10 -6 -1.0×10 -6 -1.0×10 -6 -3.0×10 -6 -3.0×10 -6 -5.0×10 -6 -1.0 -0.5 0.0 0.5 -5.0×10 -6 -1.0 1.0 E/V vs. reference electrode 0.0 0.5 1.0 1.0×10 -5 5.0×10 -6 ∆E= 50mV ∆E= -100mV 5.0×10 -6 I/A 3.0×10 -6 1.0×10 -6 -1.0×10 -6 0 -5.0×10 -6 -3.0×10 -6 -5.0×10 -6 -1.0 -0.5 E/V vs. reference electrode 7.0×10 -6 I/A ∆E= 200 mV 5.0×10 -6 -0.5 0.0 0.5 E/V vs. reference electrode 1.0 -1.0×10 -5 -1.0 -0.5 0.0 0.5 E/V vs. reference electrode 1.0
  37. 37. THE EC MECHANISM I/A 3.0×10 -6 O X RED Black: kf=0 cm.s-1 Blue: 0.2 Red: 0.5 Orange: 1 Green: 10 RED Z 1.0×10 -6 -1.0×10 -6 -3.0×10 -6 -0.5 0.0 0.5 E/V vs. reference electrode There are many variations of this mechanism: Reaction with solvent Dimerization Radical substrate reaction EC catalytic … etc.
  38. 38. EC catalytic 3.5×10 -5 I/A 2.5×10 -5 O X R ED RED + A O X + Z 1.5×10 -5 Black : no A Blue: A (c=1) Red: A (c=10) Green: A (c=100) 5.0×10 -6 -5.0×10 -6 -0.5 0.0 E/V vs. reference electrode 0.5
  39. 39. THE CE MECHANISM 4.0×10 -06 1.0×10 -07 3.0×10 -06 1.0×10 -1.4×10 -14 -06 I/A I/A 2.0×10 -06 -2.3×10 -13 -1.0×10 -06 -2.0×10 -2.0×10 -07 -06 -3.0×10 -06 -0.5 -1.0×10 -07 0.0 E/V vs. reference electrode 0.5 -3.0×10 -07 -0.5 0.0 E/V vs. reference electrode 0.5
  40. 40. MICROELECTRODES Microelectrode: at least one dimension must be comparable to diffusion layer thickness (sub μm upto ca. 25 μm). Produce steady state voltammograms. Converging diffusional flux E le c tro d e M e ta l c o n ta c t C o n d u c tiv e jo in t  1 1 I = nFADc0  +  δ r  E le c tro d e b o d y F ib e r A ) In s u la to r B) C) δ = 2πDt Advantages of microelectrodes: • fast mass flux - short response time (e.g. faster CV) • significantly enhanced S/N (IF / IC) ratio • high temporal and spatial resolution • measurements in extremely small environments • measurements in highly resistive media
  41. 41. PULSED TECHNIQUES TAST POLAROGRAPHY SAMPLED DC POLAROGRAPHY
  42. 42. NORMAL PULSE VOLTAMMETRY
  43. 43. DIFFERENTIAL PULSE VOLTAMMETRY
  44. 44. SQUARE WAVE VOLTAMMETRY
  45. 45. AC voltammetry E I tim e E

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