Nanoparticle Etch Kinetics: Shrinking-Core Dissolution

Particle Lattice

Atoms per edge N 14

Atomic spacing a (nm) 0.30

Fragmentation & Etch

Split factor k (pieces per edge) 1

Interface etch velocity v (nm/s) 0.25

Playback speed 1.0×

Live Readouts

Elapsed time t

— s

Time to full dissolution

— s

Atoms remaining (exact)

—

Atoms remaining (continuum)

—

Fraction dissolved

—%

Current core P/A

— nm⁻¹

How it works

Start with one square nanoparticle, N atoms per edge, atomic spacing a, so its edge length is L = N·a. Split it into k² smaller squares of equal size while keeping the total mass constant — the same atoms, just fragmented. Each fragment has m = round(N/k) atoms per edge and edge length L_frag = m·a.

Then every fragment etches from a chemically reactive interface that recedes inward at a constant velocity v (nm/s) — the standard "shrinking-core" model used for interface-limited nanoparticle dissolution and uniform corrosion. Unlike the static 3D fragmentation view, this is a real time-dependent process: atoms peel off layer by layer as the reaction front advances.

Remaining half-extent   R(t) = max(0, L_frag/2 − v·t)
Time to fully dissolve  T_diss = L_frag / (2v) = (N·a) / (2·k·v)

Atom (ix,iy) survives while its Chebyshev distance from the
fragment center, in nm, is ≤ R(t) — an exact discrete layer-peel.

Current core perimeter-to-area  P/A(t) = 2 / R(t)   (→ ∞ as R → 0)

N / a sliders — set the original particle's size and real-world lattice spacing, exactly as in the 3D fragmentation view.
k slider — fragments the particle into k² smaller pieces of the same total mass. Because T_diss scales as L_frag = (N/k)·a, doubling k halves the time every fragment takes to fully dissolve at the same etch velocity.
Etch velocity v — how fast the reactive interface eats into each fragment; higher v dissolves everything proportionally faster without changing the k-dependence.
Highlight boundary atoms — colors the atoms currently sitting on each fragment's shrinking outer edge; the rest (already-consumed layers) are simply gone.

Real-world relevance: this is the quantitative reason smaller nanoparticles dissolve, corrode or react to completion far faster than the same mass of bulk material or larger grains — interface-limited (zero-order) dissolution kinetics used for drug-carrier nanoparticles, catalyst supports and nanoscale corrosion studies. Watch the "current core P/A" readout climb as a fragment shrinks: the smaller the remaining core, the more reactive its surface becomes relative to what's left, right up until the last atomic layer disappears.

Fragment lattice (etching)Fraction remaining vs. time

Boundary atom Core atom Exact (discrete) Continuum estimate