Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 2 / Section B / 20 / iii / Solution

Write the reaction using the species actually supplied by solution. For either halide, a bulk contribution per converted formula unit isThe stated room-temperature feasibility means that the overall reaction free energy is negative under those conditions; it does not say that each microscopic step is downhill. Equal nominal $50\mathrm{mM}$ concentrations also do not make iodide and bromide activities or solvation free energies identical.

At the nanoscale the balance additionally contains changing interfaces:Here $N_c$ is the number of converted formula units, and $j$ includes solvent-facing surfaces and contact with the titanium-dioxide support. Surface terms scale approximately as size squared whereas bulk terms scale as size cubed. Particle size, wetting, expansion during conversion and new grain interfaces can therefore shift both the conversion driving force and the nucleation barrier.

Microscopically, conversion requires desolvation, uptake of the organic cation and halide, redistribution through the precursor, and reorganization of the lead-halide framework. A study using these conversion conditions found energetically costly dispersed-ion intercalation for both compounds, with a much larger calculated penalty for MABr in PbBr${}_2$ than for MAI in PbI${}_2$. The iodide's layered framework accommodates the cation more favorably; the bromide's undulated framework gives poorer coordination and greater local distortion. Stabilization on forming intermediate compounds and the final perovskite can nevertheless make the complete reaction favorable. The calculations are approximate energetic comparisons, not measured finite-temperature activation free energies.^[ref]

Thus both reactions can be spontaneous yet proceed at very different rates: the same study observed faster MAPbI${}_3$ formation. One must distinguish net reaction free energy from intermediate penalties and diffusion barriers. Spontaneity alone supplies no quantitative ranking of the complete iodide and bromide reaction free energies.