Topics

Here is a table of contents for the Electrochemical Species Band Diagram (ESBD) project.

As a main prerequisite, please read the intro page for the definition and motivation for species voltage $V_i$ .

The $V_i$ landscape:

Materials I - Dilute Charge Carriers:

Solutions - Concentrations, standard states $V^\circ_i$ . Ion activities.
Semiconductors - Conduction/valence bands as $V^\circ_i$ levels, electrons/holes as ion analogs.
Charge neutrality and mass action - Doping, Donnan potential, and the common-ion effect.
Bipolar membranes and pn junctions (application spotlight) - The visual twin of water-splitting and electron-hole pair generation.

Materials II - Electrostatics, Transport, and Complex Materials:

Basic electrostatics - Debye screening and the local charge neutrality approximation.
Capacitance - Dielectric and chemical capacitance; the capacitive divider.
Basic transport - Ohm's law, concentration polarization, and liquid junction potentials.
Saturation (application spotlight) - The common reason why current saturates in transistors and electrochemical processes.
Other conductors - Metals, fast ionic conductors, and mixed conductors.

Redox and electrode potentials:

Half-reactions - Electrons "in solution": redox and the Nernst equation in $V_i$ land. Standard electrode potentials as floating levels $V^\circ_{\mathrm{e}^-}(\mathrm{Ox}/\mathrm{Red})$ .
Electrode potential - One electrode: visualizing $E$ , overpotential, and mixed potentials.
Reference electrodes & cells - Reference electrodes, full cells, liquid junction potentials, and the "absolute" vacuum reference.
Interface kinetics - The current–overpotential law: Butler–Volmer as the exponential interface element, Tafel, the diode connection, and Marcus–Gerischer.

Application highlights: (Planned, coming soon! Follow my twitter for updates.)

Redox-flow batteries: one redox couple per tank, exchanging $\mathrm{H}^+$ across a membrane.
Acid–base flow batteries: a bipolar-membrane stack whose interior runs entirely on ions; tanks in series as mutual chemical capacitors.
Solid oxide fuel cells: $V_{\mathrm{O}^{2-}}$ landscape.
Cell biology: The proton motive force as a $V_{\mathrm{H}^+}$ drop; the electron transport chain as a $V_{\mathrm{e}^-}$ cascade.
Lead-Acid Batteries: A system where the electrolyte is a reactant.
Electroplating: A kinetic-driven process.
Corrosion: A mixed-potential, non-equilibrium system.

The rabbit holes -- appendices, advanced topics, notes:

Thermodynamics:

Understanding electrochemical potential - Why $\bar\mu_i$ is the real, indivisible chemical potential — and why that makes $V_i$ (and band diagrams) work.
Reaching any $V_i$ - Are $V_i$ "real voltages"? How to access each one in practice.
Offsets galore - An interactive tour of every arbitrary convention in the framework — and which ones actually move anything.
Non-ideal solutions - Focussing on technical difficulties of single-ion activities.
Chemical capacitance matrices - Mutual chemical capacitance (thermodynamic) vs internal chemical capacitance (extrathermodynamic), as capacitance matrices.

Messy electrostatics:

$\phi$ under the microscope - Which $\phi$ ? The microscopic potential, its smoothed average, and the working convention: why ions answer to none of them.
Vacuum levels - The one honest potential: real, measurable, and ending at the surface.
Inhomogeneities and electrostatics - Per-species quasi-electric fields: what replaces "the electric field" inside materials. Plus the beyond-the-simple-case catalog.

Appendices:

Standard state data - Numerical data for ionic solutes' $V^\circ_i$ values in water.
Traditional electrochemistry, translated - A Rosetta Stone: standard symbols and equations in $V_i$ terms.
About - How this project came about.