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Chem. Educator2007,12, 327330 327

Variation of the Critical Micelle Concentration with Surfactant Structure:

A Simple Method To Analyze the Role of AttractiveRepulsive Forces on

Micellar Association

D. Lpez-Daz and M. M. Velzquez*

Departamento de Qumica Fsica, Facultad de Ciencias Qumicas. Universidad de Salamanca, 37008-Salamanca, Spain, [email protected]

Received September 3, 2006. Accepted July 1, 2007.

Abstract: In this laboratory experiment students analyze the role of attractive interactions between thehydrocarbon tails and repulsive interactions between the surfactant head groups on the micellar association

process by determining the CMC of two surfactant classes. Using electrical conductivity measurements and

pyrene fluorescence emission, the CMCs of two homologous series of sulfobetaines, zwitterionic surfactants, and

alkyl trimethyl ammonium bromide, cationic surfactants, were determined. In each surfactant family we use

surfactants with 12, 14, and 16 carbon atoms. From the correlation of the head group charge to the methylene

group contribution to CMC for the two surfactant classes, students can clearly analyze the influence of the

electrostatic repulsions on the self-assembly processes.

Traditionally undergraduate physical chemistry courses

briefly discuss surface and interfacial phenomena; however,

intensive research of recent years in the structure and

properties of microheterogeneous systems, in molecular

recognition at the membrane interface, and in the transport

across membrane shows the importance of the interfacial

phenomena. Consequently, colloid and surface chemistry must

be incorporated to the chemistry and biochemistry curriculum.

Experiments with colloids and surface chemistry can be

incorporated in physical chemistry laboratory. They can also

be designed as a complement to the concepts studied in the

traditional physical chemistry experiments. Experimentsfocusing on micellar association introduce students to the

concept of colloid stability and forces involved in molecular

aggregation. In addition, the formation of micellar aggregates

causes significant changes on a larger number of physical

properties, such as conductivity, molecular fluorescence, and

surface tension; therefore, with experiments focusing on the

determination of the concentration at which a surfactant forms

a micelle, called the critical micelle concentration or CMC,

students also learn about electrochemical or spectroscopic

techniques. Several experiments to determinate the CMC have

been published using several of these methods [15].

Micelles are formed and stabilized by a balance of forces;

the insolubility of the alkyl tail promotes aggregation

(hydrophobic forces), and the electrostatic repulsions of the

ionic head groups inhibit aggregation. The effect of a small

change in these forces can be seen in the experimental data as

changes in the CMC values; therefore, it is possible to analyze

the role of these forces on the micellar aggregation process

studying the effect of both, the electrical charge of the

surfactant head group and the hydrocarbon chain length on the

CMC. With this objective in mind we have designed one

laboratory experiment focusing to study the role of the

different forces responsible of micelle formation by analyzing

the CMC values of two families of surfactants of different head

groups: alkyl trimethyl ammonium bromide, cationic

surfactants and alkyl dimethyl ammonium propane sulfonate,

zwitterionic surfactants. The hydrocarbon chain length varies

between 12 and 16 carbon atoms.

Students can use electrical conductivity measurements to

obtain the CMC and the ionization degree of cationic micelles.

This methodology is widely used to characterize ionic

surfactants [3, 5]; however, it cannot be used for zwitterionic

surfactants because they do not conduce the electrical current.

In this case, the CMC is determined by measuring the change

in the fluorescence emission spectrum of pyrene monomers [4

6]. This method is based on the changes on the intensity of the

vibrational bands of pyrene emission caused by changes on thepolarity in the environment of the probe [7].

Experimental

The surfactants dodecyldimethylammonium propane sulfonate,

DDPS; tetradecyldimethylammonium propane sulfonate, TDPS;

hexadecyldimethyl ammonium propane sulfonate, HDPS;

dodecyltrimethylammonium bromide, DTAB; and

tetradecyltrimethylammonium bromide, TTAB, and the fluorescence

probe, pyrene, were from Sigma-Aldrich. Methanol and the surfactant

hexadecyltrimethylammonium bromide, CTAB, were from Merck.

Conductivity Measurements. Prepare 50 mL of the each cationic

surfactant in deionized water. A minimum of twenty surfactant

solutions, ten above and ten below the CMC of each surfactant are

necessary to the correct determination of CMC and ionization degree.These solutions are placed on a constant temperature bath at least 20

minutes before measurements.

The electrical conductivity was measured with a conductometer,

model 727 from Metrohm, operated at 2.4 kHz. A Metrohm Herisau

conductivity cell, model AG 9101, was used. The cell constant, 0.847

cm1

, was obtained by calibration with potassium chloride standards

(0.0100 and 0.0050 M).

Fluorescence Measurements. The solubilization of pyrene in

micelles was carried out as follows: 5 L of a solution of 0.002 M

pyrene dissolved in methanol, solution A, was placed into a 10-mL

volumetric flask and the solvent was evaporated till dryness by slow

passage of N2. The surfactant solution of each surfactant

concentration, solution B, was added to the evaporated residue and the

2007 The Chemical Educator, S1430-4171(07) 52075-X, Published on Web 9/25/2007, 10.1333/s00897072075a, 12070327mv.pdf


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328 Chem. Educator, Vol. 12, No. 5, 2007 Velzquez et al.

Figure 1. Variation of the electrical conductivity with concentration

for cationic surfactants.

resulting solution was stirred until pyrene was solubilized. Thus, in all

the surfactant solutions, pyrene concentration was kept at 1 M. The

pyrene concentration has to be less than 5mM to avoid excimer

formation. In general, the excimer molecules are formed between

electronically excited and other ground state molecules. Pyrene shows

a characteristic excimer emission at 480 nm [8].

Solution A: Prepare 25 mL of a 0.002 M of pyrene in methanol(~10 mg of pyrene). Solution B: Prepare 25 mL of each zwitterionic

surfactant in deionized water.

The surfactant concentration range was between 8 104

M and 6.4

103

M for DDPS; 1.4 105

M and 7 104

M for TDPS and 3

106

M and 1.5 104

M for HDPS. A minimum of twelve surfactant

solutions, below and above the CMC, are necessaries to calculate the

CMC values.

The experimental conditions to obtain the emission spectrum of

pyrene were the following: the excitation and emission slits used gave

a bandwidth of 2.5 nm and the excitation wavelength was 320 nm.

The wavelength emission range was between 350 and 440 nm. The

fluorescence spectra of pyrene were recorded in a Perkin Elmer

spectrofluorometer model LS-50B.

Results and Discussion

CMC and Ionization Degree Determination for Cationic

Micelles: Electrical Conductivity Measurements. Figure 1

shows the variation of the electrical conductivity with the

cationic surfactant, DTAB, TTAB, and CTAB, concentration.

The CMC is obtained from the interception of conductivity

lines above and below the CMC.

It is well accepted that below the CMC there are no micelles

in solutions; thus, the conductivity of an aqueous ionic

surfactant, SC, where S represents the surfactant ion and C the

corresponding counter-ion, is due to the independent

contribution of these ions. If the aqueous surfactant solutions

obey the Kohlrauschs law [9], the conductivity can be written

as:

= S(c + s) (1)

where c ands are themolar ionic conductivity of the counter-

ion and the surfactant, respectively; and S is the surfactant

concentration. Equation 1 explains the linear dependence

between conductivity and S below the CMC. The slope of this

line, s1, represents (c + s). Above the CMC, further additionof surfactant results in an increase in micelle concentration

while the monomer concentration remains constant in a value

close to the CMC. The ionic mobility of the micelle is very

different to that of the monomer molecule and, even though the

conductivity linearly increases with surfactant concentration,

the slope of this line is smaller than s1. The conductivity of

surfactant solutions at concentrations above the CMC is from

three different contributions: the independent ions S and C at

the CMC, the micelle conductivity and the counterions

unbonded in the micelle. Thus, the conductivity is given by:

[ ] ( )C S C( )CMC micelles CMCmic S = + + + (2)

Taking into account that [micelles] = (S CMC)/N, whereN

is the micelle aggregation number, and assuming that the

micelle conductivity is the same that the conductivity of all

monomers with electrical charge in the micellar aggregate, that

is, mic = SN, eq 2 can be rearranged:

( ) ( ) ( )C S C S o 2CMC 1 ( ) ( )S s = + + + = + S (3)

where s2 is the slope of the linear plot ofversus S above the

CMC. Consequently, the s2/s1 ratio represents the micelle

ionization degree, , [10], which is the fraction of surfactant

molecules in the micellar aggregate that do not have bound

counter-ions.Because the error of the slope and ordinate of these lines are

smaller than the conductivity uncertainty, one can consider the

error on the conductivity measurements (1.3%) as responsible

of the error in both, the CMC and values.

The values obtained in the work are collected in Table 1. As

can be seen the CMC values agree very well with values on

literature also presented in a table

The CMC values found in this work are in excellent

agreement with data in the literature [11]. The ionization

degree for cationic surfactants decreases from 0.26 to 0.24 in

going from hexadecyl trimethyl ammonium to dodecyl

ammonium bromide. This behavior was reported elsewhere for



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Variation of the Critical Micelle Concentration with Surfactant Structure Chem. Educator, Vol. 12, No. 5, 2007 329

Table 1. CMC and Values Found in This Laboratory Experiment

for Cationic Surfactants

Surfactant 103 CMC

M

103CMCbib

M

a

DTAB 15.6 0.2 0.261 0.003 16 -

TTAB 3.76 0.05 0.252 0.003 3.5 0.27

CTAB 0.924 0.001 0.245 0.003 0.92 0.24

aFrom reference 12

360 380 400 420 4400

100

200

300

400

500

5

4

32

1

I/a.u

/ nm

Figure 2. Fluorescence spectra of pyrene dissolved in aqueous TDPSsolutions of different concentrations: (--) 7.0 10

5M, () 1.4 10

4

M, (--) 2.1 104

M, (__

) 2.8 104

M.

0 1 2 3 4 5 6 71.3

1.4

1.5

1.6

1.7

CMC

I1/I

3

103

[DDPS] / M

0 1 2 3 4 5 6 7 81.3

1.4

1.5

1.6

1.7

1.8

I1/I3

104

[TDPS] / M

CMC

0.0 0.4 0.8 1.2 1.6

1.3

1.4

1.5

1.6

1.7

1.8

CMCI1/I

3

104

[HDPS] /M

Figure 3. Variation of the I1/I3 ratio with the zwitterionic surfactant

concentration.

alkyl sulfates or alkylcarboxilates and it was related with

changes of surface areas per head group [13]. Thus, in the case

of surfactants with great surface areas, shorter hydrocarbon

tails, geometric constraints prevent the approach of the

counterion to the head group increasing the ionization degree.

Determination of CMC Values for Sulfobetaines Micelles

by Using Pyrene Fluorescence Probing. Because zwitterionicsurfactants do not conduct electrical current, the CMCs of

these compounds have to be determinate by an alternativemethod. A widely used methodology is pyrene fluorescence

probing. This method is based on changes in the intensity of

the vibrational bands of pyrene solubilized in water and in

micellar medium.

Figure 2 presents the pyrene emission spectra of solubilized

aqueous surfactant solutions containing surfactant

concentrations below and above the CMC.

Figure 2 clearly shows that the vibrational structure of

fluorescence spectra depends on the surfactant concentration.

This is because the fluorescence of pyrene at low

concentrations in homogeneous solutions possesses fine

structure whose relative peak intensity undergoes significant

perturbation upon going from polar to nonpolar solvents. The

ratio of the first vibrational band (372 nm), the highest energyvibrational band, to the fluorescence intensity of the third

vibrational band (385 nm) has been shown to correlate with

solvent polarity [7]. For example in hydrocarbon solventI1/I3 =

0.6 and in water is around 1.6.

It is well established that in surfactant solutions the plot of

I1/I3 versus surfactant concentration shows a typical sigmoid

shape. Figure 3 shows the results found for sulfobetaine

zwitterionic surfactants.

Below the CMC the I1/I3 ratio corresponds to a polar

microenvironment; when the surfactant concentration increases

the ratio decreases rapidly as a consequence of the more

hydrophobic environment of pyrene. Above the CMC theI1/I3

ratio reaches a constant value due to the incorporation of

pyrene into the hydrophobic region of the micelle [6]. TheCMC is obtained from the interception of the horizontal and

the steep parts of the curve. The CMC values found in this

work are 3.3 103

M for DDPS, 3.1 104

M and 3.5 105

M for TDPS and HDPS, respectively. These values agree with

data in the literature [14].

It is well known that the CMC has a strong dependence on

the alkyl chain length of a surfactant, Nc. This dependence can

be described by eq 3, Klevens rule [15, 16].

Log CMC =A BNc (3)

In this equation, A depends on the surfactant head group,

temperature, and the addition of inert electrolytes and B

represents the contribution of each methylene group in the

lowering of the CMC by the tail. Figure 4 shows the CMC

values represented according to Klevens equation. Results are

in excellent agreement with eq 3.

The A and B values were calculated to be: sulfobetaines,A =

3.3 0.3 and B = 0.48 0.02, and for alkyl

trimethylammonium bromide surfactantsA = 1.77 0.02 andB

= 0.299 0.001. TheB values are in very good agreement with

data in the literature [17]. For the zwitterionic surfactants theB

value is higher than that for the cationic ones. This fact

indicates that in the balance of forces present during micelle

aggregation, the ability of the alkyl chain to lower CMC



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330 Chem. Educator, Vol. 12, No. 5, 2007 Velzquez et al.

11 12 13 14 15 16 17-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

logCMC

Nc

Figure 4. Dependence of the CMC on the alkyl tail for: (circles) alkyl

trimethyl ammonium bromide; (squares) sulfobetaines.

depends on the magnitude of the charge on the head group. A

larger value ofB indicates that each additional methylene has a

great effect on lowering the CMC. Thus, for the zwitterionic

surfactants, no head group charge, B is large, while, for the

cationic surfactants,B decreases due to the repulsions between

the positive charges of the head group. Consequently the CMC

values of zwitterionic surfactants are usually smaller than theCMCs of ionic ones.

From the B values students can obtain the charge on the

head group by using the following linear correlation betweenB

and the square of the charge of the head group, q2, [16]:

B = (0.499 0.007) (0.234 0.011)q2

(4)

From results obtained in this work we found a q2

of 0.12 and

0.85 for sulfobetaines and alkyltrimethyl ammonium

surfactants, respectively. These values are in good agreement

with the charge distribution estimated using semi-empirical

quantum chemical methods [16]. It is interesting to note that

the charge of the head group of the cationic surfactants, q =

0.92 is not exactly 1. This fact was predicted by semi-empiricalquantum chemical methods. Results obtained from these

methods show that the charge of the head group in ionic

surfactants is partially distributed to the rest of the molecule,

with significant charge on the -methylene group and a partial

charge on the remaining alkyl tail. Thus, for dodecyl trimethyl

ammonium surfactants, the charge of the combined head group

and the -methylene group obtained by semi-empirical

methods is around 0.89 and the partial charge on the surfactant

tail is 0.11 [16]. If one compares this value with that obtained

in this laboratory experiment, 0.92, it can be concluded that the

-methylene group is part of the head group of surfactants as

several studies have suggested [16].

Conclusion

In the design of this laboratory experiment we had several

goals in mind. First, we wanted to introduce colloidal

chemistry into the physical chemistry laboratory curriculum. In

addition, we wanted to introduce students to the concepts of

molecular photochemistry and electrochemical measurements.

This laboratory experiment is intended for the physical

chemistry laboratory curriculum. There are several ways to

organize the experiments depending on the time and the

equipment available. Assuming that the detailed experimental

procedure is provided in advance, students should be able to

carry out this experiment individually in two four-hour

laboratory periods. This requires groups of at least fivestudents. Each group can determine the CMC of two

surfactants using conductivity and fluorescence measurements,

for instance, dodecyl dimethyl ammonium propane sulfonate

(fluorescence) and dodecyl trimethyl ammonium bromide

(conductivity). Finally, the students analyze all results.

Acknowledgment. This work was financially supported bythe Ministerio de Ciencia y Tecnologa (BQU 2001-1507) and

the Ministerio de Educacin y Ciencia (MAT 2004-04180). D.

Lopez wishes to thank Ministerio de Educacin y Ciencia of

Spain for the grant AP2002-1734.

References and Notes

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4. Stam, J.; Depaemelaere, S.; De Schryver, F. C.J. Chem. Educ. 1998,

75, 9398.

5. Domnguez, A.; Fernndez, A.; Gonzlez, N.; Iglesias, E.;

Montenegro, L.;J. Chem. Educ. 1997, 74, 12271231.

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20392044.

8. Turro, N, J. Modern Molecular Photochemistry; Benjamin

Cummings: San Francisco CA, 1978, pp 137143.9. See for example Atkins P. W. Physical Chemistry, 4th ed.; Oxford

University Press: Oxford, 1990; p 750.

10. Weers, J. G.; Rathman, J. F.; Axe, F. U.; Crichlow, C. A.; Foland, L.

D.; Scheuing, D. R.; Wiersema, R. J.; Zielske, A. G.Langmuir, 1991,

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11. Rosen, M. J. Surfactants and Interfacial Phenomena, Wiley: New

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12. Sepulveda L., Corts, J. J. Phys. Chem.1985, 89, 53225324.

13. Zana, R. J. Colloid Interface Sci. 1980, 78, 330337

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15. Klevens, H. B.J. Am. Oil Chem. Soc. 1953, 30, 7479

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