Question

The aluminum oxide layer on aluminum nanoparticles is about 1.5 nm thick and is relatively independent of diameter. Assuming a shperical nanoparticle, calculate the volume fraction of the particle that is aluminum oxide from a radius of 4-20 nm at 2-nm intervals. Plot the volume fraction of the material that is aluminum oxide. (That's 4-20nm, not 4.2 nm.)

Answer 1

Let us define

is the diameter of the nanoparticle.

where is the volume of the nanoparticle.

where is the total volume of the nanoparticle with the aluminum oxide layer.

where is the volume of the oxide layer.

Using these equations the following table is made

Where is the desired values.

Plotting these values with radius of nanoparticles we get

X-axis is the diameter in nm and Y-axis is the fraction(desired ratio).