1. What is Standard Deviation of Diffusive Band Spreading?

Definition: This calculator determines the standard deviation (σ) of molecular spreading due to diffusion over time.

Purpose: It helps scientists and engineers quantify how much a band of molecules will spread due to random diffusion processes.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The standard deviation grows with the square root of time, showing how diffusion causes increasing spreading over time.

3. Importance of Diffusion Spreading Calculation

Details: Understanding diffusive spreading is crucial in fields like chromatography, chemical engineering, and biological transport processes.

4. Using the Calculator

Tips: Enter the diffusion coefficient (typically 10⁻⁹ to 10⁻¹¹ m²/s for liquids) and diffusion time. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What does the standard deviation represent in diffusion?
A: It quantifies the root-mean-square distance molecules spread from their origin due to random motion.

Q2: How does temperature affect the results?
A: Higher temperatures increase the diffusion coefficient (D), leading to faster spreading.

Q3: Why is there a factor of 2 in the formula?
A: The factor accounts for diffusion occurring in all spatial dimensions (1D, 2D, or 3D).

Q4: What are typical diffusion coefficient values?
A: In liquids: ~10⁻⁹ m²/s for small molecules, ~10⁻¹¹ m²/s for proteins. In gases: ~10⁻⁵ m²/s.

Q5: Can this be used for non-Fickian diffusion?
A: No, this formula applies only to normal Fickian diffusion where σ ∝ √t.