Question

Polylactic-co-glycolic acid (PLGA) is combined with an equal amount (by weight) of hydroxyapatite (HA) to make a bone scaffold. If the porosity of the scaffold is 80%, what is the scaffold density in g/cm\(^3\)? (rounded off to two decimal places)
Assume densities of PLGA and HA to be 1 g/cm\(^3\) and 3 g/cm\(^3\), respectively.

Hint:

To calculate the density of a material with porosity, adjust the volume by the porosity factor and then use the standard density formula.

Answer 1

Given:
Densities of PLGA and HA are \( 1 \, {g/cm}^3 \) and \( 3 \, {g/cm}^3 \), respectively. The porosity of the scaffold is 80%. Let’s assume we have 100 grams of the scaffold. Since the scaffold consists of PLGA and HA in equal amounts by weight:
The mass of PLGA = 50 g, The mass of HA = 50 g. 
Step 1: Volume of PLGA and HA in the scaffold.
The volume of each component can be calculated using the formula: \[ {Volume} = \frac{{Mass}}{{Density}} \] For PLGA: \[ V_{{PLGA}} = \frac{50 \, {g}}{1 \, {g/cm}^3} = 50 \, {cm}^3 \] For HA: \[ V_{{HA}} = \frac{50 \, {g}}{3 \, {g/cm}^3} = 16.67 \, {cm}^3 \] Step 2: Total volume of the scaffold before accounting for porosity.
The total volume of the scaffold (without considering porosity) is the sum of the volumes of PLGA and HA: \[ V_{{total}} = V_{{PLGA}} + V_{{HA}} = 50 \, {cm}^3 + 16.67 \, {cm}^3 = 66.67 \, {cm}^3 \] Step 3: Adjusting for porosity.
The porosity of the scaffold is 80%, which means 80% of the volume is empty space, and 20% of the volume is the actual material (PLGA and HA). Therefore, the effective volume occupied by the materials is: \[ V_{{effective}} = 0.2 \times V_{{total}} = 0.2 \times 66.67 \, {cm}^3 = 13.33 \, {cm}^3 \] Step 4: Calculating the density of the scaffold.
The total mass of the scaffold is 100 g (50 g of PLGA and 50 g of HA), and the effective volume is 13.33 cm\(^3\). The density of the scaffold is given by: \[ {Density} = \frac{{Mass}}{{Effective Volume}} = \frac{100 \, {g}}{13.33 \, {cm}^3} \approx 0.28 \, {g/cm}^3 \] Thus, the scaffold density is: \[ \boxed{0.28 \, {g/cm}^3} \]