Electrochemistry & Energy Storage

Where a cell's voltage goes, and what that means for batteries and fuel cells

About this course

Electrochemistry from cell potential and the Nernst equation through interfacial kinetics, overpotential and mass transport, applied to lithium-ion batteries, fuel cells, electrolysers, corrosion and supercapacitors.

What you will be able to do

  • Apply the Nernst equation and reference electrodes to measured cell potentials
  • Use Butler-Volmer kinetics and Tafel slopes to analyse electrode reactions
  • Break an overpotential into kinetic, ohmic and mass-transport contributions using impedance
  • Calculate the energy density of a cell and explain the mechanisms of battery degradation
  • Compare fuel cells, electrolysers and supercapacitors by efficiency, energy and power

What this course covers

  • Reductio argument from measured capacitance
  • Dielectric saturation in the compact layer
  • Two-layer (Stern) structure and the Debye length
  • Supporting electrolyte and the Frumkin correction
  • Evidential status of the two-layer model
  • Charge-storage ceiling: one-eighth of a monolayer
  • Why fuel cells escape Carnot's theorem
  • Reversible voltage from third-law entropies
  • Fuel-cell ceiling vs. Carnot: crossing temperature
  • Oxygen reduction as the binding kinetic limit
  • Part-load efficiency advantage over heat engines
  • Platinum supply as the deployment constraint
  • Application selection by arithmetic: buses vs. cars
  • Theoretical specific capacity as an arithmetic ceiling
  • Intercalation vs. lithium plating and the dendrite premium
  • Voltage curve as a phase diagram (Gibbs phase rule)
  • Mandatory electrolyte decomposition and the solid electrolyte interphase (SEI)
  • Cell voltage of 3.7 V and the asymmetric electrolyte window
  • Silicon anode case study: capacity gain vs. mechanical and SEI costs
  • Why a single electrode potential is unmeasurable
  • Electrode potential as a gauge quantity
  • The volt as energy: the Faraday constant and key conversions
  • The standard hydrogen electrode convention and its payoff
  • The absolute electrode potential scale
  • Worked cell assessment and the water window
  • Nernst Equation Derivation from Thermodynamics
  • Logarithmic Range and Precision of Voltage Measurements
  • First Silence: The Nernst Equation Says Nothing About Rate
  • Second Silence: Voltage Reveals N but Not Reaction Mechanism
  • Third Silence: Activity vs. Concentration and the Ionic-Strength Fix
  • pH Electrode as Convergence of All Three Silences
  • Worked Sensor Design and Five-Point Summary
  • Potential changes activation energy: the core idea
  • The exponential and its natural voltage scale
  • Exchange current density and ten orders of magnitude
  • Equilibrium as dynamic balance and charge-transfer resistance
  • What a catalyst does (and cannot do)
  • Lead-acid kinetic protection and water loss
  • Thermodynamic energy floor for water splitting
  • Real cell overpotential and the oxygen electrode overhead
  • World-scale electricity demand and cost parity
  • Iridium supply constraint for PEM electrolyzers
  • Alkaline electrolysis as the escape and its turndown trade-off
  • Worked plant decision: alkaline vs PEM for ammonia supply
  • Jet fuel energy density from bond enthalpies
  • Cell mass ledger: active fraction and inactive components
  • Copper current collector as a thermodynamic constraint
  • Honest fuel-vs-battery energy comparison
  • Upper bound on future cell energy density improvement
  • Battery aviation: what the arithmetic forbids and permits
  • Liquid junction potential and ion mobility
  • Why KCl (and KNO₃) is the salt-bridge choice
  • Practical secondary reference electrodes vs. the SHE
  • Ambiguity of an unreferenced potential (the 44 mV problem)
  • Detecting and correcting a drifting reference
  • Full error budget and ranking errors by recoverability
  • Calendar aging vs. cycle aging
  • Square-root-of-time law for calendar aging
  • Two controllable knobs: temperature and state of charge
  • Cycle aging: linear, mechanical, depth-driven
  • Diagnosing degradation mechanism non-destructively
  • Fleet charging policy: applying all factors together
  • Two voltage zero points and efficiency denominators
  • Voltage audit as Kirchhoff's law
  • Residual as measurement: bubble void fraction
  • Conservation-law residuals as discovery method
  • Time-domain separation of loss terms
  • Four levers, four terms, and the gap-optimum limit
  • Thermodynamic driving force for corrosion
  • Pilling-Bedworth ratio and passive film protection
  • Mixed-potential corrosion rate and oxygen as bottleneck
  • Localised (pit) corrosion and area-ratio amplification
  • Corrosion protection strategies and their cost
  • Worked inspection decision: carbonation vs. chloride
  • Hydration shell and effective ionic size
  • Limiting current density: the transport ceiling
  • Concentration overpotential: logarithmic cost of approaching the ceiling
  • What catalysis cannot buy: chemistry vs. geometry
  • Solid-state diffusion, particle sizing, and the power–energy trade-off
  • Transport timescales and the course audit
  • Supercapacitor operating principle and activated carbon area
  • Device-level specific energy and the factor-of-four error
  • Energy–power trade stated as a characteristic time
  • Surface-to-volume scaling and inversion of the nanostructuring rule
  • Cycle lifetime and total lifetime energy
  • Sizing for the binding constraint: the bus case and hybrid design rule
  • External pinning as the course's epistemological spine
  • Grid storage scale and the primacy of duration
  • Capital-cost crossing and the ~9-hour boundary
  • Round-trip efficiency of hydrogen storage
  • The course as one argument: seven statements
  • Method transfer: bounding an unfamiliar technology
  • Impedance Spectroscopy: Core Principle
  • Kramers–Kronig Relations and Causality
  • The Randles Circuit and the Nyquist Semicircle
  • Equivalent-Circuit Ambiguity: An Exact, Irresolvable Degeneracy
  • Warburg Diffusion Element and Sweep-Range Rationale
  • Drift Detection Protocol and Technique Limits

Syllabus

  1. Thermodynamics of the Cell

    1. L1 · What a Cell Voltage Is: the Quantity You Cannot Measure
    2. L2 · The Nernst Equation, and the Three Things It Does Not Say
    3. L3 · Reference Electrodes: Measuring Half of Something

  2. Interfaces and Kinetics

    1. L4 · The Double Layer: a Capacitor One Nanometre Thick
    2. L5 · Butler-Volmer and the Tafel Slope: Kinetics at an Interface
    3. L6 · Overpotential: an Audit of Where the Voltage Went
    4. L7 · Mass Transport and the Limiting Current
    5. L8 · Impedance: Separating Processes That Share a Wire

  3. Batteries

    1. L9 · The Lithium-Ion Cell: Intercalation and the Voltage Curve
    2. L10 · Energy Density: the Arithmetic That Constrains Everything
    3. L11 · Degradation: Why a Battery Dies, and of What

  4. Conversion, Corrosion and Storage

    1. L12 · Fuel Cells, and the Efficiency Limit That Is Not Carnot
    2. L13 · Electrolysers: the Real Cost of Breaking a Bond
    3. L14 · Corrosion: Thermodynamics Says Yes, Kinetics Says When
    4. L15 · Supercapacitors, and What Energy and Power Actually Trade
    5. L16 · Grid Storage, and the Course as One Argument