Nanoparticles and surface-to-volume ratio
Nanoparticles are particles between 1 and 100 nm in size (roughly 100–1000 atoms across). Their tiny size gives them special properties not seen in bulk material.
Defining the size range
| Particle | Size | Number of atoms (approx.) |
|---|---|---|
| Coarse / dust | 2500 – 10 000 nm (PM10) | Many millions |
| Fine particles | 100 – 2500 nm (PM2.5) | Millions |
| Nanoparticles | 1 – 100 nm | Hundreds to thousands |
| Atom | ~0.1 nm | 1 |
Surface area to volume ratio (SA:V)
Smaller particles have larger surface area to volume ratios.
For a cube of side length l:
- Surface area = 6l²
- Volume = l³
- SA:V = 6/l
So as l decreases, SA:V increases. Halving the side length doubles the SA:V.
Worked example: compare a 10 nm cube to a 100 nm cube.
- 10 nm cube: SA:V = 6/10 = 0.6
- 100 nm cube: SA:V = 6/100 = 0.06
- The smaller cube has 10× higher SA:V — much more surface to react.
Why high SA:V matters
The surface is where particles interact with their environment (catalysis, drug release, antimicrobial action). High SA:V means:
- More efficient catalysts (lower mass needed).
- More active in chemical reactions.
- Stronger interactions per unit mass.
Uses of nanoparticles
- Sun creams — titanium dioxide and zinc oxide nanoparticles block UV without leaving white marks (transparent to visible light).
- Self-cleaning surfaces — TiO₂ catalyses breakdown of dirt with sunlight.
- Catalysts — high surface area increases activity per gram (e.g. in catalytic converters).
- Antimicrobial — silver nanoparticles in plasters, surgical equipment, deodorants.
- Drug delivery — nanoparticles target medication to cells.
- Cosmetics, electronics (transistors), advanced composites.
Possible risks
Because nanoparticles are so small, their effects on the body and the environment are not yet fully understood:
- They may enter cells, the bloodstream or organs more easily than bulk particles.
- Long-term effects on health are uncertain.
- Could persist in the environment.
This is why some products with nanoparticles are subject to ongoing safety research.
✦Worked example— Worked example — calculation
A scientist makes silver nanoparticles 5 nm across (treat as cubes).
a) State the SA:V ratio.
- SA:V = 6/l = 6/5 = 1.2
b) Compare to a 1 mm cube of silver.
- 1 mm = 10⁶ nm; SA:V = 6/10⁶ = 6 × 10⁻⁶
- The nanoparticles have SA:V 200,000 times larger — far more reactive surface available per unit mass.
⚠Common mistakes
- Saying nanoparticles are atoms. They contain hundreds to thousands of atoms.
- Ignoring units. Nanometres (nm) — 1 nm = 10⁻⁹ m. Be careful when comparing to mm or μm.
- Saying smaller = bigger volume. Smaller particles have higher SA:V, but each individual particle has a smaller volume.
- Listing only advantages. Exam questions almost always ask about risks too.
Links
Builds on C2.7 (carbon nanotubes are nanoparticles). Examiners often combine SA:V calculations with rates of reaction (C6.2).
AI-generated · claude-opus-4-7 · v3-deep-chemistry