Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 1 / Section B / 11

On discharge, lithium is oxidized at the negative electrode:At the positive electrode, carbon monofluoride is reduced:The net conversion reaction is thereforeFor general ${\mathrm{CF}}_x$, replace Li, lithium ions, electrons and LiF by $x$ equivalents per carbon atom. The carbon–fluorine bonds are consumed in forming different solid phases, rather than lithium simply intercalating reversibly into an unchanged host.

One mole of CF consumes one mole of electrons, so the equilibrium electrical work givesInterpreting the measured OCV as $E^{\circ }$ assumes an equilibrated cell and the appropriate standard-state activities; pure solid reactants and products make the ideal activity correction simple. A nonequilibrium or composition-dependent OCV would instead determine the corresponding reaction free energy under those conditions.

The temperature coefficient isThe net reaction involves condensed phases and no gas, so one expects a more modest entropy-driven voltage change than for a reaction creating or consuming substantial gas. However, it is not exactly zero, and its magnitude or sign cannot be calculated from the single OCV value without entropy or temperature-dependent data. This should be separated from potentially strong temperature effects on loaded-cell kinetics and resistance.

Make a composite positive electrode containing the active graphite fluoride, a connected conductive-carbon network and a binder, supported on a suitable current collector. Carbon black provides electronic pathways to distributed reaction sites; the binder maintains cohesion and contact.

Electrolyte-filled porosity provides ionic access, while particle dimensions and intimate mixing limit the distance electrons and lithium ions must traverse. Excess conductive additive or binder dilutes the capacity per gram of composite. The reaction can also alter the electronic network as carbon forms, but that does not remove the need for adequate initial connectivity or prevent insulating LiF from obstructing transport.

This is a primary battery with a strongly reconstructive conversion electrode. Discharge produces stable LiF and a carbon phase while breaking the original carbon–fluorine framework. Charging would have to separate and reorganize those products, restore the fluorinated carbon structure and recover the initial lithium electrode.

LiF is highly stable and poorly conducting, the phase distribution and electrical contacts have changed, and the reverse pathway can require a large overpotential. Electrolyte oxidation or other side reactions can occur before efficient reconstruction is achieved. Thermodynamic reversibility of an overall reaction equation therefore does not guarantee a practical rechargeable electrode.

Graphite starts with approximately planar sp2-bonded carbon sheets and delocalized pi electrons. Increasing fluorination introduces carbon–fluorine bonding, disrupts the extended pi system and increasingly produces puckered, more sp3-like local carbon environments. Layer structure and spacing change rather than remaining those of pristine graphite.

The loss of connected graphitic electronic states generally lowers electronic conductivity and can open a large gap as highly fluorinated material is approached. Low-fluorine arrangements can show more complicated doping and defect effects, so a strictly monotonic conductivity curve for every composition is not implied.

Ratios above one fluorine per carbon require attention to edge, defect and multiply fluorinated environments such as CF2 or CF3; they should not be pictured as adding more than one fluorine to every intact carbon in an otherwise unchanged three-neighbor basal network. The variable empirical composition averages over the actual carbon structure.

Each formula unit of ${\mathrm{CF}}_{0.8}$ accepts $0.8$ electrons. Using the supplied Faraday constant and the periodic-table masses,The factor $3.6$ converts coulombs to mAh. This value is per gram of the active fluorinated carbon, not per gram of the entire electrode.

The composite value is underdetermined: the mass of active CF₀.₈ is not supplied. If that mass is $m$ grams, and the carbon black and binder are inactive in the stated conversion reaction, thenThis uses cathode composite mass and excludes the lithium counterelectrode and hardware. No unique numerical composite capacity follows from the two additive masses alone; assuming an unprovided active mass would change the requested quantity.