In a water-in-oil microemulsion (reverse micelles), surfactant molecules (e.g. AOT) trap nanolitre-scale water droplets inside a nonpolar oil phase. Each droplet is a nanoreactor whose radius is set almost entirely by the water-to-surfactant molar ratio:
r_droplet ≈ 0.17 × w0 (nm, empirical AOT/isooctane/water relation)
w0 = [H2O] / [surfactant]
Droplets undergo Brownian motion (diffusion coefficient D ∝ T / r_droplet, Stokes–Einstein) and collide constantly. On collision, the surfactant film can transiently open, letting the two droplets coalesce and exchange their aqueous contents before re-separating — the inter-micelle exchange rate:
k_ex ∝ film flexibility, collision frequency, temperature
P(exchange | collision) = 1 − exp(−k_ex·Δt)
When a droplet carrying dissolved metal salt (A) exchanges with one carrying reducing/precipitating agent (B), the mixed contents react and nucleate a solid nanocrystal. Every later collision between that nucleus-bearing droplet and a fresh A or B droplet feeds it more monomer, growing the crystal — but only up to the confinement limit imposed by the droplet's own water-pool volume.
- w0 — sets droplet (and therefore maximum crystal) size; larger pools also diffuse more slowly, so kinetics slow down as w0 grows.
- Exchange rate — a high rate causes many droplets to nucleate almost simultaneously (LaMer-style burst nucleation), giving many small, uniform crystals; a low rate spreads nucleation over time, giving fewer, more size-disperse crystals as early nuclei keep growing while late ones just start.
- Reactant concentration — more dissolved monomer per droplet means more material available for nucleation and growth before donors run dry.
- Temperature — speeds both diffusion (more collisions per second) and the exchange rate itself.
Real-world relevance: this intermicellar-exchange picture (Bagwe & Khilar and related models) is the standard explanation for why AOT reverse-micelle synthesis gives such tight control over quantum-dot and metal-nanoparticle size distributions — tune w0 and exchange kinetics, and you tune the product. This 2D version renders the same population of droplets on a flat, pannable/zoomable reactor cross-section, driven by the identical exchange-probability and growth rules as the 3D version.