Sources and References

• Fuller, T. F., and Harb, J. N. Electrochemical Engineering. Wiley, 2018. (primary text)
• Newman, J., and Thomas-Alyea, K. E. Electrochemical Systems. 3rd ed., Wiley-Interscience, 2004.
• Bard, A. J., and Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications. 2nd ed., Wiley, 2001.
• Prentice, G. Electrochemical Engineering Principles. Prentice Hall, 1991.
• Hamann, C. H., Hamnett, A., and Vielstich, W. Electrochemistry. 2nd ed., Wiley-VCH, 2007.
• Revie, R. W., and Uhlig, H. H. Corrosion and Corrosion Control. 4th ed., Wiley, 2008.
• MIT OpenCourseWare, 10.626 Electrochemical Energy Systems (Bazant).
• Stanford University, MSE 302 Thermodynamics and Phase Equilibria lecture materials on electrochemical equilibria.
• Cambridge University, Part II Chemical Engineering notes on electrochemical reactors and fuel cells.

Chapter 1: Foundations of Electrochemistry and Faraday’s Law

Electrochemical engineering studies systems in which chemical change is coupled to the passage of electric charge across an interface between an electronic conductor and an ionic conductor. Unlike homogeneous reactions, where reactants collide in a well-mixed fluid, electrochemical reactions occur heterogeneously at electrode surfaces, and the driving force for reaction can be adjusted continuously by varying the electrode potential. That single feature, the ability to tune reaction driving force by applying a voltage, is what makes the discipline simultaneously useful for energy conversion, for synthesis of chemicals and metals, and for controlling material degradation.

Redox Reactions and the Electrochemical Cell

Every electrochemical process can be decomposed into two half-reactions. The anode is the electrode where oxidation occurs, meaning electrons are released to the external circuit; the cathode is where reduction occurs, meaning electrons are consumed. A typical half-reaction is written in the reduction direction,

\[ \mathrm{Ox} + n e^- \rightleftharpoons \mathrm{Red}, \]

with \( n \) the stoichiometric number of electrons per molecular event. A complete cell pairs two such half-reactions, and the two electrodes must be joined by an ionic path (an electrolyte, often with a separator or salt bridge) and an electronic path (the external circuit). Because the total charge transferred must be conserved, the coupling of the two half-reactions forces stoichiometric relationships between current and reaction rate.

Faraday’s Law

The proportionality between charge passed and extent of reaction is Faraday’s law. For a single reaction of stoichiometry \( n \), the moles of reactant consumed are

\[ N = \frac{Q}{nF} = \frac{1}{nF}\int_0^t I\,\mathrm{d}t', \]

where \( F = 96{,}485\ \mathrm{C\,mol^{-1}} \) is the Faraday constant. In differential form, the reaction rate per unit electrode area is related to the current density \( i \) by \( r = i/(nF) \). When several electrode reactions occur simultaneously, only a fraction of the current contributes to the desired product; this fraction is called current efficiency or faradaic yield, and the remainder is lost to parasitic reactions such as hydrogen or oxygen evolution.

Mass balance for an electrolyzer or battery then links operating current, faradaic efficiency, and production rate. For instance, the chlorine produced in a chlor-alkali cell operated at current \( I \) and current efficiency \( \eta_F \) is \( \dot{N}_{\mathrm{Cl_2}} = \eta_F I/(2F) \). These simple accounting equations are the skeleton on which every electrochemical reactor design is built.

Chapter 2: Thermodynamics, Cell Potentials, and Pourbaix Diagrams

Free Energy and the Nernst Equation

An electrochemical cell converts the Gibbs free-energy difference of a chemical reaction into electrical work. For a reversible cell operating at constant temperature and pressure, the maximum work available is

\[ \Delta G = -n F E_{\mathrm{cell}}, \]

where \( E_{\mathrm{cell}} \) is the equilibrium cell potential (the open-circuit voltage). The standard-state potential \( E^{\circ} \) is tabulated for each half-reaction relative to the standard hydrogen electrode (SHE). For non-standard activities, the Nernst equation gives the equilibrium potential of a single half-reaction,

\[ E = E^{\circ} - \frac{RT}{nF}\ln\!\left(\frac{\prod a_{\mathrm{red}}^{\nu_{\mathrm{red}}}}{\prod a_{\mathrm{ox}}^{\nu_{\mathrm{ox}}}}\right). \]

At 25 \(^\circ\)C, \( RT/F \approx 25.7\ \mathrm{mV} \) and the pre-log factor becomes \( 0.0592/n \) V per decade of activity ratio.

Entropy, Enthalpy and the Thermoneutral Voltage

Because \( \Delta G = \Delta H - T\Delta S \), the temperature dependence of the cell voltage carries entropic information,

\[ \left(\frac{\partial E}{\partial T}\right)_p = \frac{\Delta S}{nF}. \]

For an electrolyzer, the thermoneutral voltage \( E_{\mathrm{tn}} = -\Delta H/(nF) \) is the voltage at which electrical input equals the total enthalpy change. Operating below \( E_{\mathrm{tn}} \) means the cell must draw heat from the surroundings, while operating above it generates waste heat. Water electrolysis, for example, has \( E^{\circ}\approx 1.23\ \mathrm{V} \) but \( E_{\mathrm{tn}} \approx 1.48\ \mathrm{V} \), and industrial electrolyzers usually run at 1.7 to 2.1 V because of kinetic and ohmic losses.

Pourbaix Diagrams

The stability of metals, oxides, and dissolved species in aqueous systems depends on both potential and pH. A Pourbaix diagram plots the regions of thermodynamic stability on a \( E \) versus pH plane, with boundaries traced by equilibria of three types. Electron-only reactions appear as horizontal lines, proton-only reactions as vertical lines, and mixed proton–electron reactions as sloped lines, with Nernst slope \( -0.0592\,(m/n) \) V per unit pH for \( m \) protons and \( n \) electrons. Two dashed reference lines, the hydrogen evolution line and the oxygen evolution line, delimit the water stability window.

Pourbaix diagrams are a first-pass screen in corrosion engineering (immunity, passivation, and corrosion zones for a given metal), in electrodeposition (choosing a plating bath that avoids hydrogen co-evolution), and in electrosynthesis (locating conditions where the target oxidation state is thermodynamically accessible).

Chapter 3: Electrode Kinetics and Overpotentials

Equilibrium thermodynamics tells us what is possible; it does not tell us how fast a reaction runs under finite driving force. Once a net current flows, the electrode potential departs from its Nernst value by an amount called the overpotential, \( \eta = E - E_{\mathrm{eq}} \). The overpotential is the price paid to drive the heterogeneous reaction at a finite rate.

The Butler-Volmer Equation

A single-step, single-electron-transfer reaction obeys the Butler-Volmer equation,

\[ i = i_0\!\left[\exp\!\left(\frac{\alpha_a F \eta}{RT}\right) - \exp\!\left(-\frac{\alpha_c F \eta}{RT}\right)\right], \]

where \( i_0 \) is the exchange current density, a kinetic figure of merit that captures the rate at equilibrium, and \( \alpha_a \), \( \alpha_c \) are the anodic and cathodic charge-transfer coefficients summing (for a single-electron step) to unity. Physically, \( i_0 \) depends exponentially on the activation energy of the rate-determining step and linearly on the concentrations of electroactive species near the surface; it can span more than ten orders of magnitude across electrocatalysts. Platinum for hydrogen evolution gives \( i_0 \sim 10^{-3}\ \mathrm{A\,cm^{-2}} \); mercury gives \( i_0 \sim 10^{-12}\ \mathrm{A\,cm^{-2}} \). This spread is why catalyst choice dominates cell efficiency.

Tafel Behavior and Linear Regime

Two useful limits emerge from Butler-Volmer. For \( |\eta|\gg RT/F\approx 25\ \mathrm{mV} \), one exponential dominates and the expression linearizes on a semilog plot; this is Tafel behavior,

\[ \eta = a + b\,\log_{10}|i|,\qquad b=\frac{2.303\,RT}{\alpha F}. \]

The slope \( b \), called the Tafel slope, diagnoses the rate-determining step, and the intercept back-extrapolated to \( \eta=0 \) recovers \( i_0 \). For \( |\eta|\ll RT/F \) the equation becomes linear,

\[ i\approx \frac{i_0 F}{RT}\,\eta, \]

which defines a charge-transfer resistance \( R_{ct} = RT/(nFi_0) \) useful in small-signal impedance analyses.

Multistep Reactions and Reaction Orders

Most electrode reactions involve several elementary steps: adsorption, electron transfer, surface migration, and desorption. When one step is rate-determining, Tafel slopes cluster around integer multiples of \( 2.303 RT/F \) such as 30, 40, 60, and 120 mV/decade, and the apparent transfer coefficient reports on the stoichiometric number of that step. Classical mechanism assignments in the HER (Volmer-Heyrovsky-Tafel pathways) and the ORR (associative and dissociative pathways) are built on this logic.

Chapter 4: Transport in Electrolyte Solutions

Far from the electrode, the bulk solution is electroneutral; near the electrode, reactant must be supplied and product carried away. Current in the electrolyte is carried by migration of ions, and reactants reach the surface by a combination of diffusion, migration, and convection.

The Nernst-Planck Equation

The molar flux of species \( i \) is

\[ \mathbf{N}_i = -D_i\nabla c_i - z_i u_i F c_i\nabla\phi + c_i\mathbf{v}, \]

where the three terms are diffusion, migration, and convection. The mobility \( u_i \) is related to the diffusivity by the Nernst-Einstein relation \( u_i = D_i/(RT) \). Current density in the electrolyte is obtained by summing flux contributions weighted by charge,

\[ \mathbf{i} = F\sum_i z_i \mathbf{N}_i. \]

Combined with electroneutrality \( \sum_i z_i c_i = 0 \) in the bulk, this set of equations governs concentration and potential fields in the electrolyte.

Transference Number and Migration

The fraction of the current carried by species \( i \) in the absence of concentration gradients is the transference number \( t_i \). Transference numbers control how supporting electrolytes simplify analysis. In an excess of inert supporting electrolyte, migration of the reactant becomes negligible and the Nernst-Planck equation reduces to pure diffusion-convection, which is why electroanalytical experiments are almost always run this way.

Diffusion Layers and Limiting Current

If a flat electrode is immersed in a stirred solution, a stagnant diffusion layer of thickness \( \delta \) develops, and steady-state Fick diffusion yields a linear concentration profile. The limiting current density is reached when the surface concentration of reactant falls to zero,

\[ i_{\mathrm{lim}} = \frac{n F D c^{\mathrm{bulk}}}{\delta}. \]

Operating at or near the limiting current causes concentration overpotential,

\[ \eta_{\mathrm{conc}} = \frac{RT}{nF}\ln\!\left(1 - \frac{i}{i_{\mathrm{lim}}}\right), \]

which diverges as \( i\to i_{\mathrm{lim}} \). Hydrodynamic conditions, such as channel flow, rotating-disk rotation, or forced convection in porous electrodes, are tuned to push \( i_{\mathrm{lim}} \) well above the desired operating current.

Ohmic Losses

The potential drop across a column of electrolyte with conductivity \( \kappa \) and length \( L \) is \( \Delta\phi = iL/\kappa \). Minimizing ohmic losses drives the geometry of practical cells: thin electrolyte gaps, high ion concentrations, and carefully chosen separators. Because ohmic drop is linear in current while activation overpotential is logarithmic and concentration overpotential diverges, the relative ranking of loss mechanisms shifts across the operating curve.

Chapter 5: Electrodes and the Electrochemical Interface

Electrical Double Layer

At the electrode-electrolyte interface a compact electrical double layer forms, with ions electrostatically organized within a few nanometers of the surface. The classical Helmholtz model treats this as a parallel-plate capacitor; Gouy-Chapman theory extends it to a diffuse layer obeying a Poisson-Boltzmann equation; the Stern model combines them with an inner Helmholtz plane of specifically adsorbed ions and an outer plane marking the onset of the diffuse region. The differential capacitance of a typical metal-aqueous interface is 10 to 40 \( \mathrm{\mu F\,cm^{-2}} \) and depends on potential, electrolyte concentration, and specific adsorption.

The double layer matters for three reasons. First, faradaic charge transfer occurs across the inner Helmholtz plane, so the potential drop that drives kinetics is not the full electrode potential but the Frumkin-corrected fraction. Second, the double layer stores charge capacitively and shows up as a parallel pathway in any transient experiment. Third, it is the thermodynamic basis for supercapacitors (Chapter 9 below).

Porous Electrodes

Real electrochemical devices use porous electrodes to multiply surface area: a 1 mm thick carbon cloth can provide hundreds to thousands of square meters of active area per cubic meter. Porous-electrode theory, developed by Newman and coworkers, treats the electrode as two interpenetrating continua (solid phase \( \phi_s \) and pore phase \( \phi_e \)) with a local reaction current \( j \) coupled through Butler-Volmer kinetics:

\[ \nabla\cdot(\sigma_{\mathrm{eff}}\nabla\phi_s) = a j,\quad \nabla\cdot(\kappa_{\mathrm{eff}}\nabla\phi_e) = -a j, \]

where \( a \) is specific area and effective conductivities reflect the Bruggeman-corrected tortuosity. The solution of these coupled equations shows a characteristic penetration depth for reaction: if matrix conductivity is high, reaction peaks at the membrane side; if ionic conductivity dominates, reaction peaks at the backing side. Optimal electrode thickness is a trade-off between ohmic penalty and available surface.

Chapter 6: Electroanalytical Techniques

Electroanalytical methods extract kinetic and mechanistic information by applying a controlled waveform and measuring the response.

Cyclic Voltammetry

In cyclic voltammetry, the potential is swept linearly at rate \( \nu \) between two limits and the current recorded. For a reversible, diffusion-limited couple on a planar electrode, the Randles-Sevcik equation,

\[ i_p = 0.4463\,n F A c^{*}\sqrt{\frac{nF D \nu}{RT}}, \]

predicts a peak current proportional to \( \sqrt{\nu} \) and a peak separation of \( 59/n \) mV. Departures from these ideal values diagnose sluggish electron transfer, adsorption, or coupled chemical reactions (EC, CE, ECE mechanisms).

Chronoamperometry and Chronocoulometry

Applying a potential step from a non-reactive value to one beyond \( E^{\circ} \) drives a diffusion-controlled current decay, the Cottrell equation,

\[ i(t) = \frac{nFAc^{*}\sqrt{D}}{\sqrt{\pi t}}. \]

Integrating gives the charge, which grows as \( \sqrt{t} \); plots of charge versus \( \sqrt{t} \) reveal double-layer and adsorbed contributions as an intercept.

Electrochemical Impedance Spectroscopy

Small-signal sinusoidal excitation yields the frequency-resolved impedance of an interface. The simplest model, the Randles circuit, places a double-layer capacitance in parallel with a series combination of charge-transfer resistance and Warburg diffusion impedance. On a Nyquist plot, high-frequency semicircles report charge transfer, and low-frequency \( 45^\circ \) tails report semi-infinite diffusion. Impedance spectroscopy is indispensable in battery and fuel cell diagnostics because it deconvolutes processes that all show up in a single DC current.

Chapter 7: Batteries

A battery is a galvanic cell that stores energy in electroactive materials and releases it on demand. Its figures of merit are specific energy (Wh kg\(^{-1}\)), specific power (W kg\(^{-1}\)), energy efficiency, cycle life, calendar life, and safety.

Primary and Secondary Cells

Primary cells (for example alkaline \( \mathrm{Zn/MnO_2} \), lithium primary) are used once. Secondary cells are rechargeable. The lead-acid cell, invented in 1859, remains ubiquitous for starter batteries and stationary backup, and relies on the \( \mathrm{Pb}/\mathrm{PbSO_4}/\mathrm{PbO_2} \) couples in sulfuric acid; its practical specific energy is 30 to 50 Wh kg\(^{-1}\). Nickel-metal-hydride replaces the toxic cadmium of NiCd with a hydrogen-storing intermetallic and reaches roughly 80 Wh kg\(^{-1}\).

Lithium-Ion Chemistry

The lithium-ion cell is the modern workhorse for portable and automotive applications. Both electrodes are intercalation hosts: during discharge, lithium deintercalates from a layered cathode such as \( \mathrm{LiCoO_2} \), \( \mathrm{LiFePO_4} \), or \( \mathrm{LiNi_{x}Mn_{y}Co_{z}O_2} \), migrates through a non-aqueous electrolyte (commonly LiPF\(_6\) in carbonate solvents), and intercalates into a graphite anode. The cell voltage is the difference of the two Li chemical potentials expressed electrochemically, typically 3.3 to 4.2 V. State-of-charge, cell resistance, and capacity fade are modeled with the Newman pseudo-two-dimensional (P2D) framework, which couples porous-electrode equations to spherical solid-phase diffusion in each particle. Degradation pathways include SEI growth, lithium plating at the graphite surface, electrolyte oxidation at high voltages, and transition-metal dissolution.

Chapter 8: Redox Flow Batteries and Fuel Cells

Redox Flow Batteries

A redox flow battery decouples power and energy. Electroactive species are dissolved in two tank-stored electrolytes and pumped through an electrochemical stack; power scales with stack area and energy scales with tank volume. The all-vanadium system uses \( \mathrm{VO_2^+/VO^{2+}} \) on the positive side and \( \mathrm{V^{3+}/V^{2+}} \) on the negative, separated by a proton-exchange membrane. Cell voltages are 1.2 to 1.6 V and round-trip efficiencies 70 to 85 percent. Engineering challenges center on membrane crossover, shunt currents in manifolded stacks, pumping parasitics, and electrode activation. Emerging chemistries using organic quinones, iron-chromium, and zinc-bromine push toward lower cost.

Fuel Cells

A fuel cell is an open-system galvanic device: reactants are fed continuously and products removed, so run time is limited only by fuel supply. The proton-exchange-membrane (PEM) fuel cell runs hydrogen on a platinum anode and oxygen on a platinum or platinum-alloy cathode, joined by a Nafion membrane and operating near 80 \(^\circ\)C. The cathode ORR is the dominant kinetic loss, with Tafel slopes of 60 to 120 mV/decade; membrane hydration dictates cell ohmic resistance. Solid-oxide fuel cells operate at 600 to 1000 \(^\circ\)C on oxide-ion-conducting electrolytes such as yttria-stabilized zirconia; they tolerate fuels beyond hydrogen, including reformed natural gas, and achieve system efficiencies above 60 percent. The ideal cell voltage is set by the Nernst equation applied to the full reaction \( \mathrm{H_2 + \tfrac12 O_2\to H_2O} \), giving \( E^{\circ}\approx 1.23 \) V at 25 \(^\circ\)C and dropping slowly with temperature.

Chapter 9: Electrolysis, Electrodeposition, and Supercapacitors

Water Electrolysis and Electrosynthesis

Electrolysis is the inverse of a galvanic cell: electrical energy drives a non-spontaneous reaction. Low-temperature alkaline electrolyzers and PEM electrolyzers currently dominate hydrogen production; high-temperature solid-oxide electrolysis cells trade catalyst cost for thermodynamic benefit by operating at 700 to 900 \(^\circ\)C, lowering the electrical voltage required. Efficiency is expressed as voltage efficiency \( E_{\mathrm{tn}}/E_{\mathrm{cell}} \) or as energy per kilogram of hydrogen. The chlor-alkali process, using a cation-exchange membrane to separate anodic chlorine evolution from cathodic hydrogen evolution, produces chlorine, hydrogen, and caustic soda simultaneously and accounts for a sizeable fraction of global industrial electricity use.

Electrodeposition and Electroplating

Electrodeposition grows a metal film by cathodic reduction of dissolved metal ions, \( \mathrm{M^{n+}} + n e^-\to \mathrm{M} \). Deposit morphology, adhesion, and throwing power depend on plating-bath composition, pH, temperature, additives (levelers, brighteners, and grain refiners), and current waveform. Current distribution analysis distinguishes three regimes: primary distribution set by geometry and electrolyte resistance, secondary distribution by kinetics, and tertiary distribution by mass transfer. Pulse plating and reverse-pulse plating tailor grain structure and reduce hydrogen co-deposition. Industrial uses range from automotive chrome and decorative nickel to precision copper interconnects in microelectronics fabrication.

Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors, or supercapacitors, store energy purely in the electrical double layer of a high-surface-area electrode, typically activated carbon with \( \sim 2000\ \mathrm{m^2 g^{-1}} \). Because no faradaic reaction occurs, charge and discharge are highly reversible, power density is very high, and cycle life exceeds one million cycles. The cell voltage is limited by the stability window of the electrolyte (about 1 V for aqueous, 2.7 V for organic, and up to 3.5 V for ionic liquids). Hybrid or pseudocapacitive devices blend capacitive carbon with faradaic materials such as \( \mathrm{RuO_2} \), \( \mathrm{MnO_2} \), or conducting polymers to increase energy density at the cost of some cycle life. Energy stored is \( W = \tfrac12 C V^2 \), and the area-normalized capacitance is proportional to both the double-layer capacitance per unit surface and the accessible internal area.

Chapter 10: Corrosion Science and Engineering

Mixed Potential Theory

A corroding metal in an aqueous environment supports at least two coupled half-reactions: an anodic metal dissolution, \( \mathrm{M}\to \mathrm{M^{n+}} + n e^- \), and a cathodic reduction such as oxygen reduction or hydrogen evolution, running on the same piece of metal. The surface floats at the corrosion potential \( E_{\mathrm{corr}} \), where the total anodic current equals the total cathodic current. At that mixed potential the net external current is zero, but the corrosion current density \( i_{\mathrm{corr}} \) is not; it corresponds to the internal exchange of electrons between the two reactions and is directly proportional to mass-loss rate. Graphically, an Evans diagram plots the two Tafel lines on a \( E \) versus \( \log|i| \) axis, and their intersection gives \( (E_{\mathrm{corr}},\,i_{\mathrm{corr}}) \). The Stern-Geary equation,

\[ i_{\mathrm{corr}} = \frac{1}{2.303\,R_p}\cdot\frac{\beta_a\beta_c}{\beta_a+\beta_c}, \]

links \( i_{\mathrm{corr}} \) to the polarization resistance \( R_p \) measured by small-signal polarization near \( E_{\mathrm{corr}} \), and it underlies nondestructive corrosion rate monitoring.

Forms of Corrosion

Corrosion takes many forms, each with its own mechanism. Uniform corrosion is relatively benign because it is predictable; pitting and crevice corrosion are localized breakdowns of passive films, often in chloride-rich environments, and can perforate a structure without visible warning. Galvanic corrosion arises when dissimilar metals are electrically connected in an electrolyte, with the more active metal accelerating its dissolution to protect the nobler metal. Stress-corrosion cracking and corrosion fatigue couple mechanical stress with electrochemical attack. Intergranular corrosion attacks grain boundaries sensitized by precipitation of secondary phases.

Protection Strategies

Three engineering strategies dominate corrosion protection. Barrier coatings isolate the metal from the electrolyte; paints, polymers, and conversion coatings such as chromate or phosphate fall here. Cathodic protection drives the structure cathodic enough to suppress metal dissolution, either by coupling to a sacrificial anode (zinc or magnesium on steel hulls and pipelines) or by impressed current from a rectifier. Anodic protection exploits passivation by holding the potential inside the passive window, useful for stainless steels in concentrated acids. Alloy design, inhibitors, and careful control of environment pH, oxygen, and chloride content round out the toolkit.

Closing Perspective

Electrochemical engineering unifies thermodynamics, kinetics, and transport phenomena within a single framework, the electrode-electrolyte interface. Its reach extends from nineteenth-century chlor-alkali cells to twenty-first-century grid-scale flow batteries, from the copper interconnects inside a microprocessor to the cathodic protection of an offshore wind turbine. The common thread is that reaction rate and free energy can be controlled by a voltage, which makes electrochemistry uniquely compatible with renewable electricity, and makes the discipline a keystone of the energy transition.