1. What is Micellar Core Radius?

Definition: The micelle core radius is the distance from the center to the circumference of a micelle, which is an aggregate of surfactant molecules in a solution.

Purpose: This calculator helps determine the size of micelle cores based on aggregation number and hydrophobic tail volume, important in colloid chemistry and pharmaceutical applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( R_{mic} \) — Micelle core radius (Å)
• \( N_{mic} \) — Micellar aggregation number
• \( V_{hydrophobic} \) — Volume of hydrophobic tail (m³)
• \( \pi \) — Mathematical constant pi (~3.1416)

Explanation: The formula calculates the radius of a sphere that would contain the total volume of all hydrophobic tails in the micelle.

3. Importance of Micelle Core Radius

Details: Knowing the micelle core radius helps in understanding solubilization capacity, drug delivery systems, and surfactant behavior in solutions.

4. Using the Calculator

Tips: Enter the micellar aggregation number (typically 50-100 for common surfactants) and the volume of hydrophobic tail in cubic meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical micellar aggregation number?
A: For common surfactants like SDS, aggregation numbers range from 50-100 in aqueous solutions.

Q2: How do I determine the volume of hydrophobic tail?
A: It can be estimated using molecular modeling or from density measurements of the hydrocarbon.

Q3: Why is the result in Angstroms?
A: Micelle sizes are typically in the nanometer range (1 nm = 10 Å), making Angstroms a convenient unit.

Q4: Does this formula account for packing constraints?
A: This is a simplified model assuming spherical micelles and perfect packing. Real systems may vary.

Q5: What affects micelle core radius?
A: Surfactant chain length, temperature, and solvent conditions all influence micelle size.