Diffusion Coefficient of Solute in Composite given Volume Fraction Calculator

Diffusion Coefficient Formula:

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

Diffusion Coefficient in Composite (m²/s):

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1. What is Diffusion Coefficient in Composite?

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

Purpose: It helps predict how substances will diffuse through composite materials, which is crucial in materials science, chemical engineering, and pharmaceutical applications.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( D \) — Diffusion coefficient in composite (m²/s)
\( D_m \) — Diffusion coefficient in polymer matrix (m²/s)
\( \Phi \) — Volume fraction of filler (0 to 1)
\( \zeta \) — Tortuosity coefficient (dimensionless)

Explanation: The formula accounts for reduced diffusion due to the presence of filler particles (volume fraction) and the increased path length (tortuosity).

3. Importance of Diffusion Coefficient Calculation

Details: Accurate prediction of diffusion coefficients is essential for designing composite materials with controlled release properties, barrier performance, and transport characteristics.

4. Using the Calculator

Tips: Enter the diffusion coefficient in pure polymer matrix, volume fraction of filler (between 0 and 1), and tortuosity coefficient (typically >1). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for tortuosity coefficient?
A: For random composites, tortuosity typically ranges from 1.5 to 5, depending on filler shape and orientation.

Q2: How does volume fraction affect diffusion?
A: Higher filler fractions reduce diffusion by decreasing available pathways and increasing tortuosity.

Q3: Where can I find diffusion coefficients for polymers?
A: Polymer diffusion coefficients are typically found in materials science literature and range from 10⁻¹⁴ to 10⁻⁹ m²/s.

Q4: Does this formula work for all composite types?
A: This is a simplified model that works best for well-dispersed, non-interacting fillers in a continuous polymer matrix.

Q5: How accurate is this calculation?
A: It provides a reasonable estimate but actual values may vary due to factors like interfacial interactions and filler morphology.