America’s Smartest City by Movoto Blog

1. University of Pittsburgh Cathedral of Learning • America’s Smartest Cityby Movoto Blog • Rated Most Livable City by Places Rated Almanac and The Economist • Named among Best in the World Places to Visit • by National Geographic Traveler

2. Basic Introduction to Electrochemical Cells and Methods David H. Waldeck Department of Chemistry University of Pittsburgh

3. Chevron Science Center Ashe Website: http://www.chem.pitt.edu/ Eberly Hall Chevron Annex

4. The Electrochemical Cell The chemical reaction 2 AgI(s) + Pb(s) → 2 Ag (s) + PbI2(s) consists of a reduction reaction and an oxidation reaction An electrochemical cell is a device that transduces energy between chemical and electrical forms. An electrochemical cell has at least two electrodes and an electrolyte, as such both ion and electron transport are important to consider.

5. The Electrochemical Cell The chemical reaction 2 AgI(s) + Pb(s) → 2 Ag (s) + PbI2(s) consists of a reduction reaction and an oxidation reaction A reduction, which occurs at the cathode AgI (s) + e- → Ag (s) + I- (aq) = -0.1522 V Absolute temperature Molar gas constant activity =1 activity activity =1 Faraday’s constant standard potential # of electrons transferred in the reaction

6. The Electrochemical Cell The chemical reaction 2 AgI(s) + Pb(s) → 2 Ag (s) + PbI2(s) consists of a reduction reaction and an oxidation reaction … and an oxidation which occurs at the anode Pb(s) + 2 I- (aq) → PbI2(s) + 2e-= 0.365 V activity =1 activity activity =1 standard potential # of electrons transferred in the reaction

7. The Electrochemical Cell Hence, we find that Ag I (aq) + e- → Ag (s) + I- (aq) = -0.152 V Pb (s) + 2 I- (aq) → PbI2(s) + 2 e- = 0.365 V 2AgI (s) + Pb(s) → 2Ag (s) + PbI2(s) = 0.213V = =0.213V

8. The Electrochemical Cell 0.213 V Small changes in the applied potential allows us to reverse the direction of the chemical reaction. A galvanic cell; i.e., chemical reaction does electrical work. Electrolytic cell; i.e., electrical work drives chemical reaction.

9. The Electrochemical Cell The connection between the electrochemical potential and G. The reversible work done by the system is -wrev = E∙I∙t + PΔV and it is related to the Gibbs energy at constant T and P, namely ΔG = wrev+ PΔV = - E∙I∙t= - E∙Qtotal = - E∙n∙F or ΔrG =ΔG/n = - E∙F The cell’s EMF is a direct measure of the Gibbs energy for the reaction. E = 0.213 V

10. The Electrochemical Cell Because ΔrG =- E∙F we can measure the temperature dependence of the EMF and find the molar entropy = , and thus we also have the molar enthalpy, via ΔrH= ΔrG + T ΔrS= - E∙F + 0.213 V DS ~14.5 J/(mol-K)

11. Reference Electrodes &Electrode Potential We can use a standard half cell reaction such as 2 H+ (aq) + 2e- → H2 (g) and measure the potentials of other half cell reactions, such as Cu2+ (aq) + 2 e- → Cu(s) with respect to it. For the electrochemical cell reaction H2(g) + Cu2+ (aq) → Cu (s) + 2H+ (aq) Under standard state conditions (all activities equal to one), we find that - = 0.345 V. If we define = 0.0 V, then = 0.345 V NHE is commonly used to define the zero of the electrochemical potential scale.

12. Reference Electrodes & Electrode Potential More common reference electrodes are AgCl (s) + e- → Ag (s) + Cl- (aq) EAgCl = - For a saturated KCl solution EAgCl = 197 mV at 298 K Hg22+ + 2e- → 2 Hg Ecalomel = + For a saturated KCl solution ESCE= 241.2 mV at 298 K

13. The Absolute Electrode Potential Relate the half cell reaction: 2 H+ (aq) + 2e- → H2 (g) w to the vacuum potential, by using a thermodynamic cycle. 0 0 0 = - so that depends on intrinsic properties of the redox couple and the electrode material.

14. The Absolute Electrode Potential Define (H2/H+)= =(H2/H+) - Using experiment, workers have related the half-cell potential to the vacuum potential (e.g., measure work function Pt in contact with solution (values range from 4.4 to 4.8 V --- IUPAC recommends 4.44 ± 0.02 V. Thus (H2/H+) =(H2/H+) - • Comments • about 1.21 V below W(Pt) measured in vacuum • use to find =-1102.4 kJ/mol (excellent agreement with -1104.5 kJ/mol as found from cluster ion data) • For a half-cell reaction, M+ + e-  M, we find that • (M+/M) =(M+/M) -

15. Potentiometry: Equilibrium Measurements • No current flows and system at equilibrium. Potential provides information on • Gibbs energy, entropy, etc. • Nernst Equation • Activities of ions, such as pH, etc. • Concentration cells • Activity coefficients and solution thermodynamics • Equilibrium constants • Titrations • Solubility products • Fuel cell and battery energetics

16. Kinetics through Electrochemical Measurements Apply perturbation and measure response: Voltammetry example: Apply a potential jump and measure a current response.

17. Issues affecting Meaningful Measurements The 2 electrode cell: Current can affect Reference Electrode Potential iR drop: The current flow through the solution causes a voltage drop so that the applied potential between the working and reference electrode is not the true potential drop … For example, at high currents the Cl- concentration of Ag/AgCl reference electrodecould change and affect E EAgCl = -

18. Issues Affecting Meaningful Measurements Ohmic losses (iR drop) The resistive loss in the solution causes a change in the potential and can affect the measurement. current source Electron current, Ie, is flowing in the metal wires, while ion current, Iion, is flowing in the cell. In total Iion=Ie

19. A Potentiostatic Cell Can Resolve these Issues Use a 3-electrode cell The reference electrode measures potential and has little current flow. Most of the current goes between working and auxiliary electrode

20. A Potentiostatic Cell Can Resolve these Issues iRs Drop becomes an iRu drop In this way the potential drop is minimizes if the reference is placed close to working.

21. Potential and Current Flow: non-Faradaic • Ideal Polarized Electrode -- An electrode in which no charge transfer occurs as the potential is changed. • Some electrodes approximate over limited ranges: • Hg electrode over 2V range in KCl solution • Hg oxidation at +0.25 V versus NHE • K+ reduction at -2.1 V versus NHE • Note that H2O reduction is kinetically slow and does not interfere • Gold • Pt • Gold SAMs hexanethiol on gold Kolb and coworkers, Langmuir (2001)

22. Potential and Current Flow: non-Faradaic Ideal Polarized Electrode Applying a potential causes charge rearrangement: excess charge on electrode surface and ion charge near electrode (electrode double layer) Negative potential Potential of Zero Charge Positive potential - - + + - - + + - - + + - + - - + - + - + - + - + + + - + - - - - - + + - + + + + - + - - + + - + - - + C = Q/E and Q = σM x area

23. Potential and Current Flow: non-Faradaic Ideal Polarized Electrode Applying a potential causes charge rearrangement: excess charge on electrode surface and ion charge near electrode (electrode double layer) Q = C E i = dQ/dt i = C (dE/dt) Q = σM * area No direct charge transfer across capacitor, but current flows whenever the potential changes.

24. Potential and Current Flow: non-Faradaic Electrode Double Layer Typically it is divided into an inner layer (also called compact, Helmholtz, Stern) and an outer layer (also called diffuse layer, ….) IHP OHP σS =σi + σd = -σM V V V V - V V + V V V V V – + V V V - V V V V V V V + V - V V V V – Define IHP and OHP as centers of charge. Diffuse layer is > OHP and Stern layer is < OHP. V V V V V + V V V V V + V V V V V V V V - V V V V V V σi σd

25. Double Layer Potential Profile Solve the Poisson-Boltzmann Eqn: and solve for the potential via so that the capacitance is

26. Potential and Current Flow: non-Faradaic Model the electrochemical cell by a combination of circuit elements.

27. Potential and Current Flow: non-Faradaic Imagine a potential step experiment We begin with the system at equilibrium and E=0, then we ‘rapidly’ jump the potential to E. Q = Cd x EC and E = ER + EC so that E = iRs+ Q/Cd or which gives the result i = E/Rs ∙ exp(-t/(RsCd)) and q = Ecd [1- exp(-t/RsCd))]

28. Potential and Current Flow: non-Faradaic Imagine a potential step experiment We begin with the system at equilibrium and E=0, then we ‘rapidly’ jump the potential to E. i = E/Rs * exp(-t/(RsCd)) and q = Ecd [1- exp(-t/RsCd))]

29. Potential and Current Flow: non-Faradaic Imagine a potential sweep experiment Let us vary the potential in a triangle waveform and measure the current.

30. Potential and Current Flow: Faradaic Origin of Faradaic Current Changes in the charge state of atoms and molecules

31. Potential and Current Flow: Faradaic Ideal Polarizable Electrode versus Ideal Nonpolarizable electrode

32. Potential and Current Flow: Faradaic Factors affecting Faradaic Current (rxn rate)

33. Potential and Current Flow: Faradaic Nernst Diffusion Layer When the electrode reaction is fast compared to the diffusion of species to the surface, a depletion layer is formed. The two cases (1 and 2) correspond to two potentials

34. Potential and Current Flow: Faradaic Steady-State Voltammogram for Nernstian Reaction The case of only the oxidant being present initially. For the case of both reductant and oxidant present initially in the solution, one finds that E = E1/2 +(RT/nF) ln((il-i)/i) and the limiting current is il = n F A (DO/d0) C*O At the half-wave potential (il= il/2), then E = E1/2=E0’ - (RT/nF) ln(mO/mR )

35. Potential and Current Flow: Faradaic Cyclic Voltammograms and Kinetics We will discuss this topic next time.

36. A Case Study with Steady-State Photocurrent & a Slow Rxn Goal:Determine the distance dependence of the electron tunneling. Method: A) Prepare monolayer films of alkanethiols. B) Measure the photocurrent for different alkane chain lengths. InP

37. Electrochemical Characterization C8 j = kHT CD ps C12 C16 - Mott-Schottky analysis gives flatband of -0.7 V (vs. SCE) - Photocurrent onset is -0.65 V (vs. SCE)

38. Concentration Dependence of Photocurrent Bare Electrode Fe(CN)63-/Fe(CN)64- in 0.5 M K2SO4

39. Intensity Dependence of Photocurrent Bias Voltage 0.0 V vs SCE 0.5 MFe(CN)63-/Fe(CN)64- bare C10 (x50) photocurrent / nA C16 (x250)

40. Chain Length Dependence of Current Density InP/SAM/Fe(CN)63-/4- Contact  = - 0.54

41. Thickness and Tilt Angle of Chains on InP Photoelectron - e- f Attenuation Curves of In core level d : escape depth of photoelectron through alkanethiol, 26.7Å for In 3d5/2 peak. InP Measured film thicknesses for InP/SAMs Avg = 55 ± 6 

42. Tilt Angle and b Correlate System  (per CH2) ln(It/I0) Tilt angle / Hg 1.14 ± 0.09 [1] -13.68  1.08 16  2 Au(111) 1.02 ± 0.20 [2] -12.24  2.40 32  2 Au(111)0.90 ± 0.30 [3] -11.70  3.60 27  6 InP(100) 0.54 ± 0.07 -5.88  0.84 55  6 1. Slowinski, K.; Chamberlain, R. V.; Miller, C. J.; Majda, M, JACS1997, 119, 11910. 2. Xu, J.; Li, H-L.; Zhang, Y.; JPC1993, 97, 11497. 3. Miller, C.; Cuendet, P.; Grätzel, M.; J.PC 1991, 95, 877.   Hg studies are particularly important because tilt angle can be systematically changed. Slowinski used model with single interchain tunneling ‘hop’ allowed and found btb = 0.91 per A ; bts = 1.31 per A

43. Tunneling Current versus Tilt Angle 2 interchain hops βts InP/SCnCH3 βtb 1 interchain hop Au/SCnCH3 Au/SCnOH 0 interchain hop Hg /CnCH3 Yamamoto etal. JPC B 2002, 106, 7469

44. Summary Electrochemical Cells – Definitions etc. Equilibrium properties of Echem cells – potentiometry etc. Some features of kinetic and transient measurements (more to come ….) Citations Many of the figures used in the talk are taken from two textbooks. Electrochemical Methods by Bard and Faulkner Principles of Physical Chemistry by Kuhn, Waldeck, and Foersterling

45. Homework Assignment 1. Find an example of a potentiometric measurement and explain how the electrochemical cell operates. 2. Show that the charging current that results froma sweep in the potential of an ideally polarizable electrode at a rate of v, is given by 3. Consider the data given in the table for the alkali ions. Write out a thermodynamic cycle and extract the Gibbs solvation energy for each of the ions. Examine the relationship between the solvation energy and the ionic radius, and compare it to the predictions of the Born model of solvation. Note that the sublimation energies are given in kJ/mol.