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

The Electrochemical Cell 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. The chemical reaction 2 AgI (s) + Pb (s) → 2 Ag (s) + PbI 2 (s) consists of a reduction reaction and an oxidation reaction

The Electrochemical Cell The chemical reaction 2 AgI (s) + Pb (s) → 2 Ag (s) + PbI 2 (s) consists of a reduction reaction and an oxidation reaction standard potential # of electrons transferred in the reaction Faraday’s constant Absolute temperature Molar gas constant activity =1

The Electrochemical Cell The chemical reaction 2 AgI (s) + Pb (s) → 2 Ag (s) + PbI 2 (s) consists of a reduction reaction and an oxidation reaction standard potential # of electrons transferred in the reaction activity =1

The Electrochemical Cell

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

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

The Electrochemical Cell  S ~14.5 J/(mol-K)

We can use a standard half cell reaction such as Reference Electrodes &Electrode Potential NHE is commonly used to define the zero of the electrochemical potential scale.

More common reference electrodes are Reference Electrodes & Electrode Potential

The Absolute Electrode Potential 0 0 0

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 The Absolute Electrode Potential

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 Potentiometry: Equilibrium Measurements

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

Issues affecting Meaningful Measurements 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 … The 2 electrode cell:

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

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

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

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 V versus NHE K + reduction at -2.1 V versus NHE Note that H 2 O reduction is kinetically slow and does not interfere Gold Pt Gold SAMs hexanethiol on gold Kolb and coworkers, Langmuir (2001)

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 potentialPotential of Zero Charge Positive potential C = Q/E and Q = σ M x area

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) No direct charge transfer across capacitor, but current flows whenever the potential changes. Q = σ M * area

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, ….) Define IHP and OHP as centers of charge. Diffuse layer is > OHP and Stern layer is < OHP. σ S = σ i + σ d = -σ M IHP 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 V V V V V V V V V V V V V V V V OHP V V V V + V V V V σiσi σdσd

Double Layer Potential Profile and solve for the potential via

Model the electrochemical cell by a combination of circuit elements. 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/(RsC d )) and q = Ecd [1- exp(-t/RsC d ))] Potential and Current Flow: non-Faradaic which gives the result

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))] Potential and Current Flow: non-Faradaic

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

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

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

Factors affecting Faradaic Current (rxn rate) 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

Steady-State Voltammogram for Nernstian Reaction E = E 1/2 +(RT/nF) ln((i l -i)/i) and the limiting current is i l = n F A (D O /  0 ) C* O At the half-wave potential (i l = i l /2), then E = E 1/2 =E 0 ’ - (RT/nF) ln(m O / m R ) Potential and Current Flow: Faradaic 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

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

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

Electrochemical Characterization - Mott-Schottky analysis gives flatband of -0.7 V (vs. SCE) - Photocurrent onset is V (vs. SCE) j = k HT C D p s C8 C12 C16

Concentration Dependence of Photocurrent Bare Electrode Fe(CN) 6 3- /Fe(CN) 6 4- in 0.5 M K 2 SO 4

Intensity Dependence of Photocurrent Bias Voltage 0.0 V vs SCE 0.5 M Fe(CN) 6 3- /Fe(CN) 6 4- bare C10 (x50) C16 (x250) photocurrent / nA

Chain Length Dependence of Current Density  = InP/SAM/Fe(CN) 6 3-/4- Contact

Thickness and Tilt Angle of Chains on InP : escape depth of photoelectron through alkanethiol, 26.7 Å for In 3d 5/2 peak.  d (Å) Tilt  (  ) C8 6.4   4 C   3 C   4 Avg  = 55 ± 6  Measured film thicknesses for InP/SAMs d InP e-e- - Photoelectron Attenuation Curves of In core level

Tilt Angle and  Correlate System  (per CH 2 ) ln(I t /I 0 ) Tilt angle /  Hg1.14 ± 0.09 [1]   2 Au(111)1.02 ± 0.20 [2]   2 Au(111)0.90 ± 0.30 [3]   6 InP(100)0.54 ±   6 1. Slowinski, K.; Chamberlain, R. V.; Miller, C. J.; Majda, M, JACS 1997, 119, Xu, J.; Li, H-L.; Zhang, Y.; JPC 1993, 97, 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  tb = 0.91 per A;  ts = 1.31 per A

Yamamoto etal. JPC B 2002, 106, 7469 β tb β ts Hg /C n CH 3 Au/SC n OH Au/SC n CH 3 InP/SC n CH 3 1 interchain hop 2 interchain hops 0 interchain hop Tunneling Current versus Tilt Angle

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

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