Question

The product of diffusivity and solubility is defined as............. coefficient

• A. Diffusivity
• B. Heat transfer
• C. Permeability
• D. Mass transfer

Hint:

For food packaging, a high-quality barrier film must minimize both solubility (\(S\)) and diffusivity (\(D\)) to maintain a low overall permeability (\(P\)) against gases and water vapor.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In food packaging, evaluating the barrier properties of polymer films against gases (like oxygen and carbon dioxide) and moisture is critical to extending food shelf life.
The migration of a penetrant through a polymer membrane involves a solution-diffusion mechanism, where the gas dissolves into the polymer on one side, diffuses through the matrix down a concentration gradient, and desorbs on the opposite side.
Key Formula or Approach:
The transmission rate of a gas through a polymer film is determined by its permeability coefficient (\(P\)).
The permeability coefficient is mathematically expressed as the product of the diffusion coefficient (\(D\)) and the solubility coefficient (\(S\)):
\[ P = D \times S \]
where:
- \(D\) is the diffusion coefficient, representing the rate of penetrant movement through the polymer matrix.
- \(S\) is the solubility coefficient, representing the amount of penetrant dissolved in the polymer under equilibrium conditions.

Step 2: Detailed Explation:
The solution-diffusion model shows how gas transmission depends on both thermodymic and kinetic factors:
- The solubility coefficient (\(S\)) is a thermodymic parameter that depends on the chemical affinity between the gas molecules and the polymer matrix.
- The diffusion coefficient (\(D\)) is a kinetic parameter that depends on the size of the gas molecules and the free volume within the polymer structure.
- Multiplying these two coefficients yields the permeability coefficient (\(P\)), which measures the overall rate at which a gas passes through a unit area of a polymer film of unit thickness under a unit partial pressure gradient.
- Diffusivity, heat transfer, and mass transfer coefficients are distinct thermodymic or kinetic parameters that do not represent this specific product.

Step 3: Fil Answer:
The product of diffusivity and solubility is defined as the permeability coefficient.
Hence, the correct option is (C).