PC Praktikum
Surface Tension
Critical Micellization Concentration Determination using Surface Tension Phenomenon
1. Introduction
Surface-active agents (surfactants) were already known in ancient times, when their properties were
used in everyday life (soaps, oils, detergents, etc.). Later, when the mechanism of their behavior became
known, theoretical studies were initiated and the range of industrial applications was introduced.
Presently, surface-active compounds are studied in most physicochemical, physical and biological
laboratories of the universities worldwide, and are widely applied in industry by food,
pharmaceutical, cosmetic, computer and textile companies.
Such versatile applications of such surface active compounds originate from their amphiphilic
structure. Typically, they are built of two parts: A hydrophobic tail, which may be built by one or
more aliphatic chains, either saturated or unsaturated, aromatic system of condensed or uncondensed
rings, or an aliphatic-aromatic system. The other part is a hydrophilic head-group, e.g., amine,
hydroxyl, carboxyl, ester, sulfate, etc. Due to such a structure, the surfactants gather at the free water
surface in a particular way, namely, their hydrophilic part is anchored in the aqueous phase, whereas the
hydrophobic part is directed towards the air.
1.1 Surface Tension
In the bulk of a solution, adhesion forces are present, which balance as each molecule, surrounded
by the statistically equal number of neighboring molecules, experiences symmetrical
intermolecular interactions. On the other hand, molecules present at the surface, experience imbalanced
forces from the air and aqueous phases, as illustrated in figure 1. The surface tension (γ) is defined as the
force (F) between the molecules in the liquid per unit length (L) [5]:
𝜸=
𝑭
(1)
𝑳
Figure 1: Schematic representation of
intermolecular interactions for a molecule in
the water bulk phase and at the phase
boundary. A molecule in the bulk liquid phase
experiences a potential field of spherical
symmetry, whereas a molecule in the phase
boundary region experiences asymmetric
interactions
Due to such dissymmetric interactions, molecules present in the phase boundary region move towards
the interior of aqueous phase and are immediately replaced by other molecules, heading to the interfacial
region from inside the bulk phase. Transferring a molecule from the bulk phase to the phase boundary
demands certain work against adhesion forces, which is equal to the change of the system free energy in
isothermal-isobaric conditions at constant liquid volume. In the formula 2 below dW is the work needed
to increase the free surface of the liquid by the area dA:
𝜸=
1
𝒅𝑾
𝒅𝑨
(2)
Rev2-30.12.2015
PC Praktikum
Surface Tension
Surface tension is one of the most important physicochemical properties characterizing surfactant
solutions. The existence of non-balanced surface forces is responsible for a change in the number of
molecules present in the surface layer as compared to the interior of any surrounding phase. In aqueous
surfactant solution, this can be macroscopically observed as decrease of surface tension of water
(72.80 mN/m at 200C).
The phenomenon of transferring the molecules from the bulk solution to the boundary surface is called
adsorption. If the surfactant concentration is higher in the phase boundary region than in the bulk phase,
adsorption is called positive. Negative adsorption occurs when the surfactant concentration in the phase
boundary is lower than in the bulk.
Quantitatively, adsorption is described by the isotherm: surface tension is plotted against the activity of
surfactant solution (for diluted solutions it is assumed that activity is approximately equal to
concentration). Three types of adsorption isotherms are described in literature [1], and are schematically
presented in figure 2.
Figure 2: Surface tension is plotted against
surfactant concentration and shows three
typical kinds of adsorption isotherms. Curves
1 and 3 represent positive adsorption,
characteristic of most non-ionic surfactants
(curve 1) and ionic amphiphilic compounds
(curve 3), whereas curve 2 represents
negative adsorption, which is often the case
in solutions of simple inorganic electrolytes.
The detailed, thermodynamic description of the adsorption process at the air-water interface was
presented by Gibbs. He introduced the concept of surface excess (Γ), characterizing the excess of
surfactant molecules at the interface as compared to the equivalent volume of a neighboring phase with
following formula 3 [6], where R represents the gas constant, T the absolute temperature and c the
molar concentration of surfactants in the solution:
𝚪=−
𝒄
𝒅𝜸
𝟏
𝒅𝜸
( ) = − 𝑹𝑻 (𝒅𝒍𝒏𝒄)
𝑹𝑻 𝒅𝒄
𝑻
𝑻
(3)
According to the Gibbs’ law, surface excess is interpreted as the tangent of the slope of the surface
tension, γ, plotted against the natural logarithm of surfactant solution concentration, c. Thus, it is
possible to quantitatively determine a molecular property (surface excess) from the macroscopic
measurements of surface tension. It is assumed, that the solvent surface excess is zero. Consequently,
from equation (3) the relative surface excess of the dissolved substance is obtained.
The graphic representation of the surface excess plotted against the surfactant concentration is called a
Gibbs isotherm. Since surface excess increases as the surfactant solution concentration in the aqueous
phase increases, for a certain concentration one can expect that the surface will be saturated by most
densely packed surfactant molecules. Surface tension will no longer change and the surface excess will
achieve the maximum value, Γmax, as illustrated in figure 3. The surface excess, Γ, is given in mol/m2,
whereas its inverse, given in m2/mol, is the area occupied by one mole of molecules on the free surface of
a solution. Dividing this area by the Avogadro number leads to the area available to one molecule in the
adsorption film (area per molecule).
2
Rev2-30.12.2015
PC Praktikum
Surface Tension
Figure 3: A Gibbs adsorption isotherm.
Surface excess Γ is plotted against the
surfactant concentration c.
1.2 Self-assembly into micelles
Another possibility of stagnation in surface tension with increasing surfactant concentration is the
consumption of the surfactant by another process. Such a process would need to remove or absorb the
freely available surfactant molecules from the bulk solution, leading to a constant concentration on the
water-air interface. Such a free molecule absorbing processes can occur with tensides. In solution
amphiphilic molecules are able to form supramolecular aggregates in order to shield their hydrophobic
parts from the aqueous environment and overcoming thereby solubility problems. Most often, spherical
micelles are formed, as presented in Figure 4, with aggregation numbers of about. 50-100 (average
number of amphiphilic molecules per micelle) [7]. Bulk surfactant concentration, at which micelle
formation occurs, is called Critical Micelle Concentration (CMC). It strongly depends on the solubility
of the surfactant and is therefore also linked to temperature. The CMC can be measured by many
physicochemical methods, since the properties of a solution, such as turbidity, conductivity, o r
surface tension, change abruptly once micelles appear in solution.
Figure 4: Schematic representation of surfactants as monomers and
self-assembled into spherical micelles as soon as the CMC is reached.
3
Rev2-30.12.2015
PC Praktikum
Surface Tension
1.3 Surface tension measurement
In this experiment we will measure surface tension of a detergent solution to determine the CMC. The
measurement will be done by the Wilhelmy Plate method [2], Figure 5 [8].
Figure 5: A scheme of the surface tension
measurement by Wilhelmy plate method
with σ as surface tension and ϴ as contact
angle.
Shortly, a thin plate made of a very wettable material (rough platinum, aluminum, filter paper) is placed
at the air-water interface. If a surfactant monolayer is present, the height of the meniscus between the
plate and the liquid will change (with regard to pure water). The force related to that process by pulling
the plate out of the solution will be measured by a very sensitive balance. This force corresponds to the
surface tension multiplied by the Wilhelmy plate perimeter, if the contact angle remains zero (this
needs to be assured by very careful cleaning of the plate!). Other experimental methods to measure
surface tension include the ring (Du Noüy) method, pendant drop or bubble pressure method [3].
2. Experimental
a) Materials and Methods
Hexadecyltrimethylammonium bromide (CTAB):
Sodium dodecyl sulfate (SDS):
b) Preparation
1)
2)
3)
4)
Calculate the molecular mass for each material
Estimate which material will have the higher CMC
Prepare the stock solutions of SDS at 0.1 M (20 mL)
Dilute the stock solutions (do not take the other solutions, since this will increase the error due to
multiple dilution!) to obtain the following concentrations [M] (10 mL each) of SDS: 3x10-2,
2x10-2, 1x10-2, 5x10-3, 2x10-3, 1x10-3, 5x10-4, 2x10-4, 1x10-4
4
Rev2-30.12.2015
PC Praktikum
Surface Tension
c) Procedure
1) Familiarize yourself with the KSV Sigma tensiometer, make sure to always lock the screw when
you aren’t measuring (introduction by assistant).
2) Carefully clean and flame the Wilhelmy Plate (the platinum plate you are going to use costs ca.
600 Euro, so please try not to break the connecting wire). Cleaning has to be repeated before
changing to a new concentration of SDS.
3) Measure surface tension of water and the surfactant solutions at room temperature. Repeat each
measurement three times. Start with water as a reference and then continue with the most diluted
solution.
3. Exercises
Write a report containing introduction, materials & methods, results, and conclusion/discussion. Also
include the following exercises:
1) Describe in detail one method that can be used for surface tension measurement.
2) Calculate the mean value for surface tension for each concentration.
3) Plot « surface tension γ » versus « ln (c) », including the errors for each point in x and y.
4) Determine the CMC: Fit two linear functions trough the two linear parts of the plot.
5) Where would you expect the CMC of CTAB compared to SDS? Why?
6) Calculate the Gibbs surface excess for each surfactant concentration and plot it versus the
concentration, including the errors for each point in x and y.
7) Try to estimate Γmax. What is the mean molecular area (area per molecule) for a dense monolayer
(at Γmax)? Is the measurement precise enough? Why is it so sensitive?
8) How does the CMC of SDS change when we use water/ethanol mixture, instead of pure water?
9) How does the CMC change with temperature and why?
10) Which detergent concentration (below or above CMC) should be best used to reach the highest
efficiency for dishwashing/laundry? Why?
11) Small objects like paper clips can swim on water surface, even though they are heavier than
water. Some insects can ‘walk’ on water. These phenomena are related to surface tension of
water. What happens to a paper clip / insect, if we add some soap to water? Why?
12) The maximum size of water droplets is always bigger than for an aqueous solution of a
detergent. Why?
4. Literature
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
P.C. Hiemenz, Principles of colloid and surface chemistry, Marcel Dekker Inc., New York and
Basel, 1986
N.R. Pallas, Colloids and Surfaces, 6 (1983), 221-227
http://www.kibron.com/company/science-technology/surface-tension-measurement-techniques
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
http://physics.tutorvista.com/fluid-dynamics/surface-tension.html
http://www.kruss.de/de/service/schulung-theorie/glossar/ueberschusskonzentration/
C. Thévenot, B. Grassi, G. Bastiat, W. Binana, Colloids and Surfaces A: Physicochem. Eng. Aspects
252 (2005) 105-111
http://www.kruss.de/en/theory/measurements/surface-tension/plate-method.html
5
Rev2-30.12.2015