11.c Critical micellar concentration
A micellar solution consists of a dispersion of micelles in a solvent (most usually
water). Micelles are formed by aggregated amphiphiles (i.e. molecules with both
lyophilic and lyophobic part) that are oriented in direction given by minimum energy of
the system. The spherical shape is the most frequent shape of the micelles. Micelles
in a micellar solution are in equilibrium with free, unaggregated amphiphiles. Micellar
solutions form when the concentration of amphiphile exceeds the critical micellar
concentration. Micellar solutions (colloids) can be formed if we dissolve some high
molecular weight substances (soaps, starches, surfactants, ...). The size of the
micelles dispersed in the colloidal solution is in the range of 2-100 nm. Micellar
solutions differ from true solutions in that they show a Tyndall effect.
Critical micellar concentration (CMC) can be determined from the breaks that show
the dependencies of various physicochemical quantities (see FIG. 1) on the
concentration of molecules forming the micelles. The CMC is temperature dependent
similarly as solubility limit of crystalline substances (see FIG. 2).
In case the micelle releases by solvation simple ion (ie amphiphiles is ionogenic), it is
suitable to use conductivity measurements (see instruction in chapter 6.c ) to
determine CMC. Below the CMC value, the solute behaves as a simple electrolyte.
The course of the molar conductivity λ as a function of the square root of the
concentration is in agreement with Onsager's theory, according to which the molar
conductivity of the uni-univalent electrolyte is:
λ = λ0 − 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐. √𝑐𝑐 (1.)
where λ0 is the limiting molar
conductivity, 𝑐𝑐 is molar
concentration of electrolyte.
After exceeding the CMC (see FIG.
1, the molar conductivity of the
solution decreases more rapidly
with increasing concentration and
at even higher concentrations it
either goes through a minimum or
no longer changes with the
concentration.
Another way to determine the CMC
is to measure the surface tension of
solutions. It is possible because the
substances capable of forming
associative colloids are surfactants.
Until micelles are formed in the
solution, the dependence of the
surface tension on the
concentration (see FIG. 1)
corresponds to the Szyszkowski
semi empirical equation (see
Chapter Chyba! Nenalezen zdroj
odkazů.):
λ0 − λ = 𝑎𝑎 ln(1 + 𝑏𝑏𝑏𝑏) if 𝑏𝑏𝑏𝑏 ≪ 1 then λ0 − λ = 𝑎𝑎 𝑏𝑏𝑏𝑏 (2.)

FIG. 1: Schematic representation of the
dependences of various physicochemical
quantities (ρ-density, π-osmotic pressure, ηviscosity,
γ-surface tension, λ-molar conductivity,
τ-turbidity) on the concentration of molecules
forming micelles of colloidal solution
where λ0 is the surface tension of the solvent, λ is the surface tension of solutions of
concentrations 𝑐𝑐 at the same temperature, 𝑎𝑎 and 𝑏𝑏 are empirical constants.
Associative colloidal molecules are incorporated into the micelles if the CMC is
exceeded. The concentration of free molecules in the solution remains the same as
well as surface concentration. Thus surface tension does not change either.
The association colloid molecules may not always form spherical micelles. Under
suitable conditions, for example at low temperatures, the molecules can form a solid
phase with all the features of an ordered crystalline structure. The transformation
temperature of micelles to the crystalline phase is called the Kraft point (see FIG. 2).
TASK: Determine the critical concentration of the micellar surfactant (sodium
lauryl sulphate is suitable) and its Kraft point in water by the conductivity method
and by measuring the surface tension.
LABORATORY AIDS AND CHEMICALS: Stock solution of 0.1 M sodium lauryl sulphate
(CAS No 151-21-3, 𝑀𝑀𝑟𝑟 = 288,38
𝑔𝑔
𝑚𝑚𝑚𝑚𝑚𝑚
), 2 beakers (250 cm3), 2 pipettes (20 cm3),
scale pipette (10 cm3). Conductivity measurement: conductometer, conductivity
electrode, thermostat, tempered vessel with tap outlet, thermometer. Capillary
Stalagmometer (suitable outer diameter approx. 8 mm, inner diameter approx. 2 mm),
thermometer, at least 2 weighing bottles with lid. Test tube, ice.
INSTRUCTIONS: The conductivity must be measured in a vessel at constant
temperature (it is advantageous to use a temperature control for accurate
measurements). Connect directly the outlet of the tempered vessel with the capillary
by hose for simultaneous surface tension measurement.
1. Measurement of specific conductivity of water. Rinse thoroughly the vessel with
capillary several times with distilled water. Monitor the conductivity. The assembly
is ready for measurement if there
is no significant decrease in
conductivity. Pour about 60ml of
water and let it equilibrated.
Record a stable value of specific
conductivity of water, it should be
close to pure distilled water.
2. Measurement of surface
tension of water. Wipe the two
marked weighing bottles dry with
a swab and weigh. Use
equilibrated water in previous
conductivity measurement.
Remove air bubbles between the
tap of the conductive vessel and
the end of the capillary. Adjust the
drain cock of the conductive
vessel so that the drops dripping
from the end of the capillary count
well. Place the first empty
weighing bottle under the
capillary and catch 20 drops of
water. Capture the same number
in the second weighing bottle.
FIG. 2: State diagram of associative colloidal
system. E… position of experimental solutions for
CMC determination at laboratory temperature.
KP… Kraft point. CE… cooling experiment gives
an estimation of KP (invariant point at 𝑐𝑐𝐾𝐾 𝐾𝐾. and
𝑇𝑇𝐾𝐾 𝐾𝐾 .
?


Weigh the scales with water drops. The difference in the weight of the water must
not be worse than half the weight of its drop, i.e. approx. 0,05g.
3. Measurement of specific conductivity and surface tension of solutions.
Proceed in the same way as in the case of measuring pure water. Pour about 60 ml
of stock solution into a conductivity vessel. Measure the conductivity and the surface
tension. Each subsequent solution is then prepared for further measurements as
follows. Pipette 40 ml of the solution from a conductive vessel and mix it with 20 ml
of water in a clean and dry beaker (i.e. 2/3 dilution). Drain the remaining contents of
the conductivity vessel to waste and replace it without rinsing with a newly prepared
diluted solution. Measure the conductivity and weight of 20 drops (a common
mistake is incorrect drop counting or insufficient drying of the weighing bottle). By
diluting to 2/3, we gradually obtain data for 12 different concentrations.
4. Simple measurement of Kraft point. Interpolate the CMC from the experiment
(see FIG. 2). Prepare a solution with interpolated concentration and measure twice
its conductivity and weight of 20 drops. Pour the solution into a test tube. Insert the
thermometer. Sink the tube in a beaker with water with crushed ice. Note the
temperature when the crystalline particles appear. Repeat the transformation effect
at heating and cooling twice.
REPORT: Table 1: values of concentration c, c1/2, measured specific conductivity
κ and molar conductivityΛ. Graph 1: dependence Λ on c1/2. Next: tabulated
value of water surface tension γº, averaged weight of empty weighing bottles and 20
drops of water. Table 2: values c, average weights of 20 drops of solutions, surface
tension γ of solutions. Graph 2: dependences of γ on c. Next: Interpolate critical
micellar concentration from the brakes on both curves. State the temperature and
composition corresponding to the Kraft point.
