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Critical micelle concentration (CMC)

Pronunciation: /ˈkrɪtɪkəl maɪˈsɛl ˌkɒnsənˈtreɪʃən/

The critical micelle concentration (CMC) is the surfactant concentration at which molecules start to group into micelles in the bulk liquid. Below it, surface tension falls as surfactant is added; above it, surface tension stays almost constant.

Also called

CMC Critical micellization concentration

Related terms

Surfactant Static surface tension Dynamic surface tension

Topics

Surfactants Surface tension Formulation
Book a 15 minute demo Read the surface tension measurement guide

At a glance

What the CMC is, why formulators care, and what values to expect.

What it is

As surfactant is added to water, molecules first pack the surface. Once the surface is full, new molecules have nowhere better to go, so they cluster tails inward into micelles. The concentration where this switch happens is the CMC.

  • Units: mol/L, mM, or mass percent
  • Shows as a break in the surface tension curve
  • Depends on temperature, salt and impurities

Why it matters

The CMC tells you the least surfactant needed for the lowest surface tension, and the point where cleaning and solubilising start. Dosing well above it wastes material; dosing below it leaves wetting on the table. Our note on CMC assessment and surfactant efficiency covers uses from cleaners to contact lens solutions.

Typical values

  • Sodium dodecyl sulfate (SDS), water, 25 °C: about 8 mM
  • CTAB, water, 25 °C: about 0.9 to 1 mM
  • Nonionic surfactants: often well below 1 mM
  • Adding salt lowers the CMC of ionic surfactants

More values are in our CMC of common surfactants dataset.

Expert view

“Surface tension versus concentration is one of the few measurements that lets you watch a surfactant reorganise an interface in real time: read the curve, not just the endpoint.”

Dr. Alidad Amirfazli, Co-founder and Scientific Advisor, Droplet Lab

What the terms mean

The three regions of a surface tension versus concentration curve.

c well below the CMC

Few molecules at the surface. Surface tension is close to that of water and falls slowly at first.

c approaching the CMC

The surface fills quickly. Surface tension falls in a straight line against log concentration.

c above the CMC

The surface is saturated and micelles form in the bulk. Surface tension stays almost flat.

Always plot concentration on a log scale. On a linear scale the falling region is squashed and the break is hard to see.

CMC Critical micelle concentration, mM or mol/L
γ Surface tension, mN/m
γCMC Surface tension at the CMC, mN/m
c Surfactant concentration, mM
Π Surface pressure at the CMC, γ0 − γCMC, mN/m

Key equations

How the CMC is read from data and what it says about micelle formation.

Equation: γ = a1 + b1 log c (below) ; γ = a2 + b2 log c (above) ; log CMC = (a2 − a1) / (b1 − b2)

Variable legend:

  • a1, b1: intercept and slope of the falling region
  • a2, b2: intercept and slope of the plateau
  • c: concentration in the same units throughout

Worked example, c in mM: below the break γ = 58 − 22 log c, above it γ = 38.5 − 0.2 log c. log CMC = (38.5 − 58) / (−22 + 0.2) = −19.5 / −21.8 ≈ 0.894, so CMC ≈ 7.8 mM, close to the value for SDS.

Interpretation: The CMC is where the two straight lines cross. Fitting lines to several points on each side is more reliable than eyeballing the bend.

When to use: Use it with any surface tension versus concentration data set that has a clear break.

Assumptions:

  • Static (equilibrium) surface tension at every point
  • Same temperature for the whole series

Common mistakes:

  • Using readings taken before the surface has equilibrated
  • Too few points near the break

Equation: ΔG°mic ≈ R T ln (CMC)

Variable legend:

  • ΔG°mic: standard free energy of micelle formation (J/mol)
  • CMC: expressed as a mole fraction
  • R: 8.314 J/(mol K); T: temperature (K)

Example: a CMC of 1 mM in water is about 1.8 × 10−5 as a mole fraction (0.001 / 55.5). At 25 °C, ΔG°mic ≈ 2479 × ln(1.8 × 10−5) ≈ −27 kJ/mol.

Interpretation: A lower CMC means a more negative free energy, so micelles form more readily. Longer tails lower the CMC.

When to use: Use it to compare how strongly different surfactants drive micelle formation.

Assumptions:

  • Nonionic surfactant; ionic ones need a counterion term

Common mistakes:

  • Using mM instead of mole fraction inside the logarithm

How to read it

What the shape of the curve around the CMC tells you.

The CMC is only as good as the curve it comes from. Clean glassware, pure surfactant and equilibrated readings matter more than the fitting method. Students can produce the curve themselves in experiment 9 on CMC via surface tension versus concentration.

From curve to meaning

If you see It usually means Check next
A sharp break and a flat plateau A clean CMC from a pure surfactant Report the CMC with temperature and medium
A minimum just before the plateau A more surface active impurity is present Surfactant purity or recrystallisation
A gradual bend with no clear break A mixture or a polydisperse surfactant Use a second method such as conductivity
CMC lower than the literature value Added salt, or a different temperature Ionic strength and temperature of your sample

Common misconceptions

Where the CMC is most often misread.

Above the CMC, adding more surfactant does nothing

Surface tension stays nearly flat, but micelle numbers keep rising. That still changes solubilisation, viscosity and interactions with particles, as work on surfactants and the rheology of nanocrystal suspensions shows.

A quick reading at each concentration is enough

Near and below the CMC, surfactant can take a long time to reach the surface. Early readings sit too high and can shift the apparent CMC. Our guide to understanding surfactants explains why equilibrium matters.

Related terms

Where the CMC sits among other surface tension concepts.

Broader term

  • Surfactant
  • Surface tension

Related terms

  • Static surface tension
  • Dynamic surface tension (time-resolved pendant)
  • Interfacial tension (IFT)
  • Pendant drop method

Often confused with

  • Critical surface tension (Zisman)

FAQ

Short answers to the questions people ask most about the critical micelle concentration.

What is the critical micelle concentration in simple terms?

It is the amount of surfactant at which the liquid surface is full. Below it, every extra molecule helps lower surface tension. Above it, extra molecules cluster into micelles inside the liquid instead, so surface tension stops falling. It marks the most efficient dose for lowering surface tension.

How do you determine the CMC from surface tension data?

Measure the static surface tension at a series of concentrations and plot it against the logarithm of concentration. Fit a straight line to the falling region and another to the plateau. The concentration where the two lines cross is the CMC. Use enough points close to the break to place both lines well.

What affects the critical micelle concentration?

Longer hydrophobic tails lower the CMC. Adding salt lowers it for ionic surfactants by screening the charged heads. Temperature changes it, though the effect is modest for many ionic surfactants. Impurities and other additives such as polymers or alcohols can raise or lower it, so measure it in the formulation you use.

References

Primary sources and further reading.

1. Mukerjee, P., and Mysels, K. J. (1971). Critical Micelle Concentrations of Aqueous Surfactant Systems. NSRDS-NBS 36, National Bureau of Standards, Washington. https://nvlpubs.nist.gov/nistpubs/Legacy/NSRDS/nbsnsrds36.pdf
2. Rosen, M. J., and Kunjappu, J. T. (2012). Surfactants and Interfacial Phenomena, 4th edition. Wiley, Hoboken. https://doi.org/10.1002/9781118228920
3. Surface tension measurement guide
4. Surfactant
5. Static surface tension