1. What is Diffusion Coefficient given Standard Deviation?

Definition: This calculator computes the diffusion coefficient (D) based on the standard deviation (σ) of particle displacement and the diffusion time (t).

Purpose: It helps in studying diffusion processes in physics, chemistry, and biology by relating the spread of particles to the diffusion coefficient.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( D \) — Diffusion coefficient (m²/s)
• \( \sigma \) — Standard deviation of particle displacement
• \( t \) — Time for diffusion (seconds)

Explanation: The standard deviation squared (variance) is proportional to the diffusion coefficient and time, following Einstein's relation for Brownian motion.

3. Importance of Diffusion Coefficient Calculation

Details: The diffusion coefficient quantifies how quickly particles spread out and is fundamental in understanding transport phenomena in various systems.

4. Using the Calculator

Tips: Enter the standard deviation of particle displacement and the diffusion time in seconds. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of standard deviation in diffusion?
A: It represents the root-mean-square displacement of particles from their starting point during the diffusion time.

Q2: What units should I use for standard deviation?
A: The standard deviation should be in meters (m) for the result to be in standard SI units (m²/s).

Q3: Does this formula work for all dimensions?
A: This is the 1D version. For 2D, divide by 4t; for 3D, divide by 6t.

Q4: What affects the diffusion coefficient?
A: Temperature, particle size, and medium viscosity primarily influence the diffusion coefficient.

Q5: How is this related to Fick's laws?
A: This is derived from Fick's second law of diffusion, relating concentration gradients to the diffusion coefficient.