Conversion of nanoparticle concentration units

[vc_row][vc_column width=”2/3″][vc_column_text]Depending on your end use application, you may prefer to know the concentration of  nanoparticles (silica, selenium, titanium) in terms of

• Parts per Million (PPM)
• WT%
• Particles/mL
• Molar
• Optical Density (OD).

[/vc_column_text][/vc_column][vc_column width=”1/3″][vc_single_image image=”14526″ img_size=”full” alignment=”center”][/vc_column][/vc_row][vc_row][vc_column width=”2/3″][vc_column_text]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%[/vc_column_text][/vc_column][vc_column width=”1/3″][vc_single_image image=”14514″ img_size=”600×511″ alignment=”center”][/vc_column][/vc_row][vc_row][vc_column width=”2/3″][vc_column_text]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.[/vc_column_text][/vc_column][vc_column width=”1/3″][vc_single_image image=”7151″ img_size=”600×600″ alignment=”center”][/vc_column][/vc_row][vc_row][vc_column width=”2/3″][vc_column_text]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[/vc_column_text][/vc_column][vc_column width=”1/3″][vc_single_image image=”4140″ img_size=”559×482″ alignment=”center”][/vc_column][/vc_row][vc_row][vc_column width=”2/3″][vc_column_text]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[/vc_column_text][/vc_column][vc_column width=”1/3″][/vc_column][/vc_row][vc_row][vc_column][vc_column_text]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[/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][vc_single_image image=”14493″ img_size=”1000×207″ alignment=”center”][/vc_column][/vc_row]