Micelle Formation Model Calculator

Calculator Inputs

Total Surfactant Concentration (mM)

Reference CMC (mM)

Aggregation Number

Temperature (°C)

Reference Temperature (°C)

Salinity (mol/L)

Reference Salinity (mol/L)

Degree of Ionization (0 to 1)

Solution Volume (L)

Temperature Coefficient

Salinity Coefficient

Micellization Enthalpy (kJ/mol)

Example Data Table

Sample	Total Surfactant (mM)	Reference CMC (mM)	Temperature (°C)	Salinity (mol/L)	Aggregation Number	Ionization
Nonionic Lab Mix	18.0	9.4	25	0.00	55	0.05
Anionic Buffered System	35.0	8.0	30	0.10	60	0.25
High Salt Formulation	50.0	7.2	40	0.30	75	0.35

Formula Used

Temperature and salinity adjusted CMC

ln(CMC_adj) = ln(CMC_ref) + a(T − T_ref) − b(S − S_ref)

Monomer and micellized surfactant split

Monomer concentration = min(C_total, CMC_adj)

Micellized surfactant = max(0, C_total − CMC_adj)

Micelle concentration = Micellized surfactant / Aggregation number

Standard Gibbs free energy estimate

ΔG°_mic = (2 − α)RT ln(X_cmc)

X_cmc = (CMC_adj / 1000) / 55500

Entropy estimate

ΔS°_mic = (ΔH°_mic − ΔG°_mic) / T

This calculator uses a practical modeling approach for dilute aqueous systems. It is best for screening, comparison, and formulation planning rather than replacing detailed experimental characterization.

How to Use This Calculator

Enter the total surfactant concentration for your prepared system.
Add the reference CMC measured or sourced for your surfactant.
Set the operating temperature, reference temperature, salinity, and reference salinity.
Provide the aggregation number and ionization level for your surfactant family.
Adjust temperature and salinity coefficients if you have fitted experimental data.
Enter solution volume and enthalpy if you want amount and entropy outputs.
Click Calculate Model to show the result block above the form.

Frequently Asked Questions

1. What does this model estimate?

It estimates adjusted CMC, monomer concentration, micellized surfactant, micelle concentration, micellized fraction, and basic thermodynamic indicators for a surfactant solution.

2. Why does salinity reduce CMC in many systems?

Added salt can shield electrostatic repulsion between charged head groups. That often makes aggregation easier and lowers the concentration needed for micelle formation.

3. What is the aggregation number?

It is the average number of surfactant molecules inside one micelle. Larger values generally mean fewer micelles for the same micellized surfactant amount.

4. Is the free energy output exact?

No. It is an informed estimate based on a simplified relation using CMC mole fraction, temperature, and ionization. Experimental methods remain more accurate.

5. Can I use this for nonionic surfactants?

Yes. Set ionization close to zero and use temperature and salinity coefficients that fit your nonionic system or literature values.

6. Why is my micellized fraction zero?

Your total surfactant concentration is likely below the adjusted CMC. In that region, the model assumes nearly all surfactant remains as monomers.

7. When should I adjust the coefficients?

Adjust them when you have experimental or literature data for how your surfactant responds to temperature and ionic strength changes.