Hi Safi Ullah Butt

I will walk you through how to calculate and send all the calculations in the attachment. Given the density of the filler (ρFiller = 5 g/cm3) and the density of the polymer (ρPolymer = 1 g/cm3), and assuming that the composite is a mixture of filler and polymer with no voids, you can calculate the volume percentage of filler as you see in the first formula. After transforming this formula, you can calculate volume of filler required for the desired composite volume percentage. Then, calculate the volume of polymer needed. Finally, calculate the mass of filler and polymer using their respective densities. Let's assume you want to prepare a composite with a total volume of 100 cm3. Given:

• Density of Filler (ρfiller​) = 5 g/cm³
• Density of Polymer (ρpolymer​) = 1 g/cm³
• Desired Volume % of Filler = 45 vol%
• Total Volume of Composite (Vtotal​) = 100 cm³

Substitute your data into the volume of filler formula. You need to take the difference in density into account (filler is 5 times denser than polymer) and include it in your calculations. Now, to find the volume of the polymer, subtract the volume of filler from the total volume.

Good luck

Dear Safi,

For quick answers and to obtain more information for various compositions/composites (e.g., the weight of the filler and of polymer matrix, “estimated”/theoretical composite density, etc.) I will recommend also using some online calculators/programs for fiber/filler composites, see you the calculus of volume or weight fraction (I will give only one example): https://www.gislite.com/app/s2202

However, for us, it’s important to understand the relations of calculus and to simulate ourselves some typical experimental situations (please take a look here, https://crescent.education/wp-content/uploads/2021/03/Volume-fraction-of-composites.pdf, see similar questions on RG).

In your case, to obtain 100 g composite (NB: containing 45% vol. filler, density= 5 g/cm3), you will need to use 80.36 g filler and 19.74 g polymer (density = 1 g/cm3). You have the possibility to verify it! This is a theoretical calculus, some practical factors (e.g., the presence of porous structures in composites, changes in the density of the polymer matrix, etc.) can lead to some differences, but I will refrain from more comments.

Good luck with your R&D project and best regards,

Marius

Use this formula:

Filler Vol% = (Filler Density / (Densities of Filler + Polymer)) x Volume Fraction x 100

Therefore, Filler Vol% = (5/(5+1)) x 0.45 x 100 → Filler Vol% = 83.33% and polymer Vol% = 100 - 83.33% → polymer Vol% = 16.67%

Mohammad Razmara Can you please throw some light on the calculation of wt% of the fillers when there are two or more fillers involved within a polymer composite system?

Anju Anju Sure, In the given example, suppose two fillers A and B were used. Filler A has a density of 3 g/Cm3 and B has a density of 2 g/Cm3. Calculate the volume fraction for Filler-A first:

Filler-A Vol. Fraction = (ρfiller-A) / (ρfiller-A+ρfiller-B + ρComposite)

= 3 g/cm³ / (3 + 2 + 1) g/cm³ = 0.5

Filler-A Vol% = Filler-A Vol. Fraction x Composite Vol.

= 0.5 x 100 cm³ = 50 cm³

Filler-B Vol. Fraction= 2/6 = 0.3333

Filler-B Vol% = Filler-B Vol. Fraction x Composite Vol.

= 0.3333 x 100 cm³ = 33.33 cm³

Therefore, Polymer Vol% = 100 - (50 + 33.33) = 16.67%

Mohammad Razmara Thank you for your answer.