Nanoparticle Dimensions

Comparing Particle Sizes

• Particles can be compared and categorised primarily by their diameter.
• While nanoparticles, fine particles, and coarse particles are all categories of microscopic particles, they differ significantly in their scale.
• Nanoparticles are the smallest, with diameters between 1 nm and 100 nm.
• Larger suspended materials in the air (solid particles and liquid droplets) are referred to as particulate matter (PM). The number in labels like $\text{PM}_{2.5}$ refers to the maximum diameter in micrometres ($\mu\text{m}$).
• Fine particles (also known as $\text{PM}_{2.5}$) are larger than nanoparticles, with a diameter range between 100 nm and 2,500 nm.
• Coarse particles (also known as $\text{PM}_{10}$ or commonly referred to as dust) are the largest of the three categories, with a diameter range between 2,500 nm and 10,000 nm.

Particle Type	Also Known As	Diameter Range (nm)	Diameter Range (m)
Nanoparticles	-	1 to 100 nm	$1 \times 10^{-9}\text{ m}$ to $1 \times 10^{-7}\text{ m}$
Fine particles	$\text{PM}_{2.5}$	100 to 2,500 nm	$1 \times 10^{-7}\text{ m}$ to $2.5 \times 10^{-6}\text{ m}$
Coarse particles	$\text{PM}_{10}$ or dust	2,500 to 10,000 nm	$2.5 \times 10^{-6}\text{ m}$ to $1 \times 10^{-5}\text{ m}$

The Surface Area to Volume Ratio

• The unique behaviour of nanoparticles is driven mathematically by their surface area to volume ratio (SA:V).
• The surface area to volume ratio is inversely proportional to the size of the particle: as the particle gets smaller, the ratio gets larger.
• The Factor of 10 Rule: As the side length of a cube decreases by a factor of 10, its surface area to volume ratio increases by a factor of 10.
• For example, a 10 nm cube has a SA:V ratio of $0.6:1$. If you decrease the side length by a factor of 10 (down to 1 nm), the ratio increases by a factor of 10 (up to $6:1$).

Worked Example: Calculating SA:V Ratio

Calculate the surface area to volume ratio of a cubic nanoparticle with a side length of 60 nm.

Step 1: Calculate the surface area (SA) using the formula $\text{SA} = 6 \times (\text{side length})^2$.

• Area of one face = $60 \times 60 = 3600\text{ nm}^2$
• Total SA = $3600 \times 6 = 21600\text{ nm}^2$

Step 2: Calculate the volume (V) using the formula $\text{V} = (\text{side length})^3$.

• $\text{Volume} = 60 \times 60 \times 60 = 216000\text{ nm}^3$

Step 3: Calculate the ratio using the formula $\text{SA:V Ratio} = \frac{\text{Surface Area}}{\text{Volume}}$.

• $\text{Ratio} = 21600 \div 216000 = 0.1$
• Final ratio = 0.1:1

Why Nanoparticles Behave Differently

• Bulk materials are materials in standard, large-scale sizes where properties are constant regardless of size (like a standard gold bar).
• Nanoparticles have vastly different physical and chemical properties compared to the exact same material in bulk form.
• The Causal Mechanism: Because nanoparticles have such a high surface area to volume ratio, a very high proportion of their atoms are located on the surface.
• Since chemical reactions happen at the surface of a material, this high proportion of surface atoms makes nanoparticles extremely reactive.
• This means that much smaller quantities of nanoparticles are needed to be effective compared to materials with normal particle sizes.

Examples of Altered Properties

• Titanium dioxide: In bulk form, it is white and opaque (used in paint). In nanoparticle form, it is transparent but still highly effective at blocking UV light (used in suncreams to avoid white marks).
• Gold: Bulk gold is chemically unreactive. Gold nanoparticles are so reactive they are used as highly efficient catalysts.
• Carbon: Bulk graphite is incredibly soft. Carbon nanotubes (nanoparticles) are exceptionally strong and can conduct electricity.