The volume fraction of a component in a composite material is the ratio of the volume of that component to the total volume of the composite. In the case of a polymer matrix nanocomposite, you'll typically have a polymer matrix and some nanoscale reinforcement material (e.g., nanoparticles).
The formula for calculating the volume fraction (Vf) of the reinforcement material in a polymer matrix nanocomposite is
Vf =V reinforcement/ V total
where:
Vf is the volume fraction of the reinforcement material,
V reinforcement is the volume of the reinforcement material, and
V total is the total volume of the composite (matrix + reinforcement).
To determine these volumes, you may need experimental data or other information, such as the weight or mass fractions, densities, and geometrical considerations. Here's a general guide on how to obtain the necessary information:
Measure the mass or weight: Weigh the polymer matrix and the reinforcement material separately.
Determine the densities: Find the densities (ρ) of the polymer matrix (ρ matrix) and the reinforcement material (ρ reinforcement). The densities are typically given in units like g/cm³ or kg/m³.
Calculate the volumes: V reinforcement=mass of reinforcement / ρreinforcement Vmatrix= mass of matrix / ρmatrix
Calculate the total volume: Vtotal =Vmatrix+Vreinforcement
Calculate the volume fraction: Vf =Vreinforcement /Vtotal