Nanoparticles: surface area to volume sim
Drag a slider to cut a cube into smaller and smaller cubes, record the surface area and volume, and plot SA:V against 1/a to see why nanoparticles behave differently.
Structure and bonding: nanoparticles · covers the GCSE topic
What the sim shows
A model particle is a cube of side L. Cutting each edge into n equal parts makes n³ smaller cubes of side a = L ÷ n. One small cube has surface area 6a² and volume a³, so all of them together have surface area 6a² × n³ = 6L² × n, while the volume stays L³. The surface area to volume ratio is SA:V = 6a² ÷ a³ = 6 ÷ a: make the side 10 times smaller and SA:V gets 10 times bigger. Nanoparticles are 1 to 100 nm across (1 nm = 1 × 10⁻⁹ m), only a few hundred atoms; fine particles (PM2.5) are 100 to 2500 nm; coarse particles (PM10, dust) are 2500 nm to 10 µm. 100 nm is the border between nanoparticle and fine. The pieces are drawn pulled a little apart so the new faces show, and the drawing is the same size whatever L is. Real nanoparticles are not perfect cubes, but SA:V still rises as they get smaller. They are far too small to see with a lens or a light microscope: an electron microscope is needed.
- The model particle: every small cube keeps all six faces
- Slider: how many parts each edge is cut into (1 to 10)
- Wires on the frame: one for every cut
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