Variation of the Critical Micelle Concentration with Surfactant Structure: A Simple Method To Analyze the Role of Attractive-Repulsive Forces on Micellar Association

Variation of the Critical Micelle Concentration with Surfactant Structure: A Simple Method To Analyze the Role of Attractive–Repulsive Forces on Micellar Association

D. López-Díaz and M. M. Velázquez*

Departamento de Química Física, Facultad de Ciencias Químicas. Universidad de Salamanca, 37008-Salamanca, Spain, mvsal@usal.es

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

Abstract: In this laboratory experiment students analyze the role of attractive interactions between the hydrocarbon 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. Experiments focusing 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 [1–5].

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 the polarity 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 cm^–1, 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 mL 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

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 mM. 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 ´ 10^–4 M and 6.4 ´ 10^–3 M for DDPS; 1.4 ´10^–5 M and 7 ´ 10^–4 M for TDPS and 3 ´ 10^–6 M and 1.5 ´ 10^–4 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 Kohlrausch´s law [9], the conductivity can be written as:

k = S(l_c + l_s) (1)

where l_candl_sare 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 (l_c + l_s). Above the CMC, further addition of 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:

(2)

Taking into account that [micelles] = (S – CMC)/N_,where N 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, l_mic = l_SNa, eq 2 can be rearranged:

(3)

where s₂ is the slope of the linear plot of k versus S above the CMC. Consequently, the s₂/s₁ ratio represents the micelle ionization degree, a, [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 avalues.

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

Table 1. CMC and a Values Found in This Laboratory Experiment for Cationic Surfactants

Surfactant	10³CMC M	a	10³CMC_bib M	a^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

Figure 2. Fluorescence spectra of pyrene dissolved in aqueous TDPS solutions of different concentrations: (-×-) 7.0 ´ 10^–5 M, (××××) 1.4 ´ 10^–4 M, (--) 2.1 ´ 10^–4 M, (^__) 2.8 ´ 10^–4 M.

Figure 3. Variation of the I₁/I₃ratio 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 zwitterionic surfactants do not conduct electrical current, the CMCs of these compounds have to be determinate by an alternative method. 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 energy vibrational 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 solvent I₁/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 the I₁/I₃ ratio reaches a constant value due to the incorporation of pyrene into the hydrophobic region of the micelle [6]. The CMC is obtained from the interception of the horizontal and the steep partsof the curve. The CMC values found in this work are 3.3 ´ 10^–3 M for DDPS, 3.1 ´ 10^–4 M and 3.5 ´ 10^–5 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, N_c. This dependence can be described by eq 3, Klevens rule [15, 16].

Log CMC = A – BN_c (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 surfactants A = 1.77 ± 0.02 and B = 0.299 ± 0.001. The B values are in very good agreement with data in the literature [17]. For the zwitterionic surfactants the B 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

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 of B 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 the CMCs of ionic ones.

From the B values students can obtain the charge on the head group by using the following linear correlation between B 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-empirical quantum 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 a-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 a-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 a-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 five students. 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 by the Ministerio de Ciencia y Tecnología (BQU 2001-1507) and the Ministerio de Educación y Ciencia (MAT 2004-04180). D. Lopez wishes to thank Ministerio de Educación y Ciencia of Spain for the grant AP2002-1734.

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