This 2D build solves the exact same surface chemistry as the 3D version, but instead of instancing ligand rods around a sphere, it simulates the QD surface as an unrolled hex lattice of ~169 individual binding sites (left panel) and plots the resulting kinetics directly as strip charts (right panel) — a representation no camera angle on the 3D sphere could show at once.
Every site independently runs a Monte Carlo Langmuir process each frame — occupied sites desorb with probability koff·dt, vacant sites adsorb with probability kon[L]·dt — so coverage θ(t) emerges bottom-up from ~169 coupled coin-flips, not a single mean-field number:
P(desorb this frame) = k_off · dt
P(adsorb this frame) = k_on[L] · dt
k_off = ν0 · exp(−ΔE / (kB·T))
θss = k_on[L] / (k_on[L] + k_off)
Excitons spawn at a random lattice site and sample the local passivation fraction of that site plus its (up to 6) hex neighbours. That local fraction gates a stochastic radiative/quench decision:
P(radiative | local θ) = θ_local^m / (θ_local^m + (1−θ_local)·(k_nr/k_r))
- [L] concentration — more free ligand in solution drives adsorption (k_on[L]) up, raising equilibrium coverage.
- Bond energy ΔE — a stronger head-group/surface bond lowers the Arrhenius desorption rate k_off exponentially.
- Temperature — higher T accelerates desorption, stripping ligands faster.
- Trigger Ligand Exchange — swaps the native long-chain ligand for a shorter one, strips ~90% of sites bare at once, and lets you watch the lattice and the θ(t)/PLQY(t) strip charts re-equilibrate toward the new θss in real time.
Real-world relevance: this same trade-off — shorter, more conductive ligands binding more weakly — is the central design tension in QLED displays and quantum-dot solar cells.