Depending on your end use application, you may prefer to know the concentration of nanoparticles (silica, selenium, titanium) in terms of
For illustration purposes we will use our selenium nanoparticles but the same principles apply for other nanoparticle types.
Glantreo quantifies the mass of selenium in end products using ICP-OES analysis. Knowing the total selenium in mg/Litre allows us to start calculating the concentration in other forms.
The conversion of mg/Litre to PPM is 1:1. Therefore 1 mg/Litre is the same as 1 PPM. The conversion of PPM to WT 10,000 PPM to 1 WT%.
Therefore:
10,000 mg/Litre = 10,000 PPM = 1 WT%
We need to calculate the particles/ml but before we do this we need some additional information, namely the mass of 1 nanoparticle.
Calculating the mass of 1 nanoparticle
Firstly, we must calculate the volume of a nanoparticle. Our nanoparticles are spherical, so we can use the equation for the volume of a sphere.
V= 4/3 π r3
Radius (r): Nanoparticle size can be elucidated using SEM or zeta sizing. To calculate the mass of 1 nanoparticle, multiply the calculated volume of 1 nanoparticle by the material density of the element.
Worked Example:
The material density of selenium is 4.32 g/cm3
For a Selenium Nanoparticle of 350 nm diameter, its volume is calculated as (4/3 * π * 175 nm3)
Volume = 2.24 x 107 nm3
This needs to be converted to cm3 by dividing by 1e+21, then multiplied by the material density.
Nm3 to cm3: 2.24E x 107 nm3 ÷ 1 x 1021 nm3/cm3 = 2.24 x 1014 cm3
Multiply by material density: 2.24 x 1014 cm3 x 4.32 g/cm3 = 9.70 x 1014 g
Mass of one 350 nm Selenium nanoparticle is 9.70 x 1014 g
Calculating particles/mL
To calculated nanoparticles/mL we use:
N = MC / m
MC is the mass concentration of element used in the experiment in g/mL
m is the mass of an individual nanoparticle
If our final concentration of selenium is 4 g in 1 L, this can be converted to g/mL by dividing by 1,000.
MC = 0.004 g/mL
m = 9.70 x 1014 g/particle
Therefore, in our 4 g in 1 Litre solution of 350 nm Selenium nanoparticles, we have: 4.12 x 1010 particles/mL
Express in molar concentration
If we want this same solution concentration expressed in molar (Mols/Litre) we use:
M = N / 6.02214 × 1023
Where N is the number of particles in solution expressed in particles/L.
Firstly, convert the particles/mL to particles/L by multiplying by 1,000.
4.12 x 1010 particles/ mL x 1000 = 4.12 x 1013 particles/Litre
Then divide by Avogadro’s number
4.12 x 1013 particles/Litre ÷ 6.02214 x 1023 particles/mol = 6.85 x 1011 M
Nanoparticle concentrations are usually expressed in picomole for ease of use
To convert M to pM, multiply by 1 x 1012
6.85 x 1011 M x 1 x 1012 = 68.49 pM
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