Diffusion Coefficient of Solute in Polymer Matrix given Volume Fraction Calculator

Diffusion Coefficient Formula:

\[ D_m = \frac{D \times \zeta}{1 - \Phi} \]

Diffusion Coefficient in Polymer Matrix (D_m):

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1. What is Diffusion Coefficient of Solute in Polymer Matrix?

Definition: The Diffusion Coefficient of Solute in Polymer Matrix is the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient.

Purpose: This calculator helps determine the diffusion coefficient in the polymer matrix when considering the effects of filler materials in composites.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_m = \frac{D \times \zeta}{1 - \Phi} \]

Where:

\( D_m \) — Diffusion coefficient in polymer matrix (m²/s)
\( D \) — Diffusion coefficient in composite (m²/s)
\( \zeta \) — Tortuosity coefficient (dimensionless)
\( \Phi \) — Volume fraction of filler (dimensionless)

Explanation: The formula accounts for how filler particles affect solute diffusion by considering the tortuous path (ζ) and the volume occupied by filler (Φ).

3. Importance of Diffusion Coefficient Calculation

Details: Accurate diffusion coefficient values are crucial for predicting mass transport in polymer composites, which affects material performance in applications like membranes, drug delivery systems, and packaging materials.

4. Using the Calculator

Tips: Enter the diffusion coefficient in the composite (D), tortuosity coefficient (ζ), and volume fraction of filler (Φ). The volume fraction must be between 0 and 1 (exclusive).

5. Frequently Asked Questions (FAQ)

Q1: What is the tortuosity coefficient?
A: It's an intrinsic property of porous materials, defined as the ratio of actual flow path length to the straight distance between path ends.

Q2: How does filler volume fraction affect diffusion?
A: Higher filler fractions reduce the available space for diffusion and typically increase the tortuosity, decreasing the effective diffusion coefficient.

Q3: What are typical values for the tortuosity coefficient?
A: Values typically range from 1 (straight path) to 3-5 for highly tortuous paths in filled polymers.

Q4: Can the volume fraction be 1?
A: No, the formula becomes undefined at Φ=1 (complete filler with no polymer matrix).

Q5: How do I measure the diffusion coefficient in composite?
A: Common methods include sorption/desorption experiments, permeation tests, or inverse analysis of concentration profiles.