Surface area to volume ratio

Nanomaterials have a relatively larger surface area, when compared to the same volume. Let us consider a sphere of radius ‘r’.

Surface area = 4pir²

volume = 4/3 pi r²

Hence, the surface to volume ratio for a sphere will be

The smaller the radius/size of any material, higher the surface area. Thus nanoparticles have a much greater surface area as compared with larger particles. It makes materials more chemically reactive. This affects their strength or electrical properties hence they are used mainly in sensors.

A characterization parameter for the effectiveness of a nanoparticle is the ratio of its surface area to its volume. Explain with example of a cube.

Let us consider an example. For a one cubic volume shown in figure, the surface area is 6m². When it is divided into eight pieces its surface area becomes 12m². When the same volume is divided into 27 pieces its surface area becomes 18m². Thus when given volume is divided into smaller pieces, the surface area increases. Hence as particle size decreases, a greater proportion of atoms are found at the surface compared to those inside. Thus nanoparticles have a much greater surface area compared with larger particles.