Diffusion Coefficient Calculation

Diffusion Coefficient Formula:

\[ D = \frac{\text{mean\_square\_displacement}}{2 \times d \times t} \]

Diffusion Coefficient (D):

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1. What is Diffusion Coefficient?

The diffusion coefficient (D) is a proportionality constant that relates the mean square displacement of particles to time in the context of diffusion. It quantifies how quickly particles spread out from an area of high concentration to an area of low concentration.

2. How Does the Calculator Work?

The calculator uses the diffusion coefficient equation:

\[ D = \frac{\langle r^2 \rangle}{2d t} \]

Where:

\( D \) — Diffusion coefficient (m²/s)
\( \langle r^2 \rangle \) — Mean square displacement (m²)
\( d \) — Dimension (1, 2, or 3)
\( t \) — Time (s)

Explanation: The equation relates the average squared distance particles move to the time taken and the dimensionality of the system.

3. Importance of Diffusion Coefficient

Details: The diffusion coefficient is crucial in fields like physics, chemistry, and biology for understanding molecular transport, predicting reaction rates, and modeling processes like drug delivery and membrane transport.

4. Using the Calculator

Tips: Enter mean square displacement in m², select dimensionality (1 for linear, 2 for planar, 3 for volumetric), and time in seconds. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for diffusion coefficients?
A: In liquids at room temperature, typical values range from 10⁻⁹ to 10⁻¹⁰ m²/s for small molecules, and 10⁻¹¹ m²/s or smaller for macromolecules.

Q2: How does temperature affect diffusion coefficient?
A: Diffusion coefficient increases with temperature, often following an Arrhenius-type relationship.

Q3: What's the difference between self-diffusion and mutual diffusion?
A: Self-diffusion refers to diffusion of identical particles, while mutual diffusion describes diffusion of different particle types relative to each other.

Q4: Can this equation be used for gases?
A: While the basic concept applies, gas diffusion is often described by different equations that account for pressure and molecular collisions.

Q5: How is mean square displacement measured experimentally?
A: Common methods include fluorescence correlation spectroscopy, dynamic light scattering, or single-particle tracking.