In the Classroom

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Chem. Educator 2007, 12, 80–84

The Effect of Hydrocarbon Chain Length on the Critical Micelle Concentration of Cationic Surfactants: An Undergraduate Physical Chemistry Experiment Benjamin Peterson and Charles J. Marzzacco* Department of Physical Science, Rhode Island College, Providence RI 02906, Department of Chemistry, Florida Institute of Technology, Melbourne, FL 32901, [email protected] Received June 23, 2006. Accepted January 11, 2007.

Abstract: A physical chemistry experiment is presented that examines the effect of hydrocarbon chain length on the critical micelle concentration of three alkyltrimethylammonium bromide compounds. The surfactants studied are dodecyltrimethylammonium bromide (DTAB), tetradecyltrimethylammonium bromide (TTAB) and cetyltrimethylammonium bromide (CTAB). The three substances are investigated by conductivity and fluorescence probe methods. The fluorescence probe method is based on changes in the fluorescence quenching of phenanthridine or 5,6-benzoquinoline as the concentration of the surfactant exceeds the CMC. It is shown that the phenanthridine and 5,6-benzoquinoline molecules associate with the cationic micelles where their fluorescence is strongly quenched by the Br– counter ions on the surface of the micelles. Fluorescence quenching results for the probe lucigenin (N,N′-dimethyl-9,9′-bisacridinium nitrate), which does not associate with the cationic micelles are also presented. The CMC values obtained by the conductivity and fluorescent probe methods exhibit excellent agreement with each other and also agree well with reported literature values. The results verify that the CMC decreases with increasing hydrocarbon chain length. The use of these methods to determine the fractional ionization of the micelle will also be discussed.

Introduction and Background N

Surfactants are amphiphilic substances containing a hydrophobic long-chain hydrocarbon attached to a hydrophilic group that is either polar or ionic. Soaps and detergents are good examples of such substances. This experiment involves a study of a series of compounds called alkyltrimethylammonium bromides. Tetradecyltrimethylammonium bromide (TTAB) is an example. It contains a hydrocarbon chain containing 14 carbon atoms attached to a trimethylammonium cation and has a Br– counter ion. H

H

H

C

H

H C

H

H

H

H

H

H

C H

CH3 +

C

C H

H

H

C

C H

H

H C

C H

H

C

C H

H

H

C

C

H

H

H

N

C H

H

CH3

-

Br

CH3 H

tetradecyltrimethylammonium bromide (TTAB)

Two other compounds being studied in this experiment are cetyltrimethylammonium bromide (CTAB) and dodecyltrimethylammonium bromide (DTAB). They contain hydrocarbon chains of 16 and 12 carbons, respectively. One of the goals of this experiment is to examine the effect of chain length on the critical micelle concentration. Two methods are used in this experiment. The first involves the traditional electrical conductivity method [1], and the second involves a fluorescence probe that associates with these cationic micelles. The fluorescence probe method utilizes either of the azine molecules phenanthridine or 5.6benzoquinoline shown below:

N

Phenanthridine

5,6-Benzoquinoline

The experiments described below will use phenanthridine as the fluorescent probe, but either compound can be used. Experiments involving the use of fluorescence probes to measure the CMC and other properties of surfactant solutions have been published [2–5]. They involve changes in the fluorescence intensity or vibrational structure as the CMC is exceeded and the probe moves from the aqueous phase to the micelle environment. This experiment is different in that it involves examining the change in the fluorescence quencing of phenanthridine by the Br– counter ion as the surfactant concentration passes through the CMC. Compared with this experiment, the previous methods do not yield as sharp a change in the fluorescence intensity as the surfactant concentration is exceeded. This method will be shown to yield a more precise value. This paper also has the added advantage of including supporting material that includes a laboratory version of the experiment. The experiment is also informative in that it examines the effect of the hydrophobic chain length on the critical micelle concentration. Description of the Experiment The students perform both conductivity and fluorescence intensity measurements on nine aqueous solutions that contain a very low concentration of the phenanthridine probe and

© 2007 The Chemical Educator, S1430-4171(07)22009-1, Published on Web 4/1/2007, 10.1333/ s00897072009a, 12070080cm.pdf

The Effect of Hydrocarbon Chain Length on the Critical Micelle Concentration…

350

-1

G /(μohm )

300

CMC = 0.0037 + 0.0001 M

250 200 150 100 50 0 0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

[TTAB]/M

Figure 1. Plot of the conductivity of aqueous TTAB solutions. Each solution also contained the phenanthridine probe at a concentration of 3.0 × 10–6 M. Table 1. CMC/M Values

DTAB TTAB CTAB a

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approximately 100 m–1. Fluorescence intensity measurements are made on the same solutions. A Perkin Elmer LS5 was used at Rhode Island College and a Jobin Yvon Horiba FluroMax-3 at Florida Tech.

400

Surfactant

Chem. Educator, Vol. 12, No. 2, 2007

Conductivity Method 0.017 + 0.001 0.0037 + 0.0001 0.00090 + 0.00004

Fluorescence Method 0.017+ 0.003 0.0038 + 0.0001 0.00089 + 0.00004

Literature Values a 0.016 0.0037 0.00087

referemce 6.

A

INTENSITY

H

340

360

380

λ/(nm)

400

420

440

Figure 2. The fluorescence spectrum of phenanthridine (3.0 × 10–6 M) in aqueous solution with various concentrations of TTAB. The TTAB concentrations are A. 0.0 M; B. 0.0010 M; C. 0.0020 M; D. 0.0030 M; E. 0.0040 M; F. 0.0050 M; G 0.0060 M; H. 0.0070 M. The excitation wavelength was 245 nm.

various concentrations of one of the three surfactants to be studied. Because of time limitations, a given group can study only one of the three surfactants. In subsequent laboratory sessions, other groups can be assigned different surfactants. Alternatively, students could be provided with results for the other two surfactants after they complete the experiment in order to make a comparison. These solutions are prepared from stock solutions that are made available to the students. The electrical conductance of each solution is measured by means of any conductivity meter capable of measurements in the range of 0 to 1600 μS (μohm–1). The conductivity cell should have a cell constant of

Results and Discussion Conductivity Method. The conductivity laboratory study involving the behavior of cationic surfactants similar to CTAB has been previously examined by Bachofer [1]. At concentrations below the CMC, the surfactant is completely ionized. The surfactant cations and the counter anions will mainly exist as monomer ions in solution. Because the conductivity is directly proportional to the concentration of ions, the conductivity will increase linearly with concentration. Once the critical micelle concentration is exceeded, the excess cation concentration will go into the formation of micelles rather than to increase the concentration of monomers. The CMC can be thought to be analogous to a solubility limit for the monomer. The average number of cations in the micelles is called the aggregation number and is given the symbol n. Some of the counterions will associate with the micelle. If we designate m as the average number of counterions associated with the micelle, the average charge on a micelle will be +(n – m) and the fractional ionization of the micelle will be α = (n – m)/n. Those counterions not associated with micelles will exist as monomer ions in solution. Because of the formation of micelles by the surfactant cations and the partial cancellation of charge due to counterion association, the conductivity will increase with concentration at a lower rate once the CMC is exceeded. Bachofer [1] also describes a method of obtaining the fractional ionization of the micelle from the slopes of the plots of specific conductivity versus surfactant concentration in the pre- and post-micellar regions. The method utilizes the use of an equation derived by Evans [6]. In the past, we have not had our students apply this method, because the calculations are a bit time consuming. We will show, however, that it does yield values that agree well with the literature. A plot of the conductivity versus the TTAB surfactant concentration is shown in Figure 1. It can be seen that the data points fall into two linear regions, one below the CMC and the other above it. Linear regression analyses were performed for each region. The CMC is determined from the calculated point of crossing of these two lines. The uncertainty in the CMC is calculated from the standard errors in the slope and the intercepts of the two lines. Details of the method are provided in the supporting material. The CTAB and DTAB surfactants show similar conductivity behavior. A comparison of the CMC values obtained in this study to those found in the literature [7– 9] is given in Table 1. Fluorescence Quenching Method. In aqueous solution the free-base forms of the phenanthridine and 5,6-benzoquinoline probes exhibits fluorescence from their lowest excited singlet states, which are of ππ* character and have quantum yields 0.19 and 0.30, respectively [10]. The fluorescence of azaphenanthrenes like these are known to be strongly quenched by halide ions [11]. The effect of increasing TTAB concentrations on the fluorescence spectrum of phenanthridine is shown in Figure 2. The fluorescence intensity shows a slight decrease in intensity as the concentration of the surfactant increases from 0 to 0.003


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1.0 0.9 0.8 0.7

I/Io

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

[TTAB]/M

Figure 3. Plot of I/I0 versus TTAB concentration. I0 and I are the peak fluorescence emission intensities of phenanthridine without and with TTAB present, respectively.

4.5 4.0 3.5

Io/I

3.0 2.5 2.0

CMC = 0 0.0037 + 0.0001 M

1.5 1.0 0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

[TTAB]/M

Figure 4. The fluorescence quenching of phenanthridine by TTAB. I0 is the fluorescence intensity of a phenanthridine solution without any TTAB, and I is the intensity with TTAB.

INTENSITY

C A

B

340

360

380

400

420

440

λ/(nm)

Figure 5. The effect of a large concentration of TTAB on the fluorescence spectrum of phenanthridine. Traces A and B are the fluorescence spectra of phenanthridine with TTAB concentrations of 0.0 M and 0.0225 M, respectively. Spectrum C is spectrum B normalized in intensity to that of spectrum A at 367 nm.

M; however, as the concentration increases beyond that point, the intensity decreases in a much more significant manner. This dramatic decrease in intensity corresponds to the point where the critical micelle concentration is exceeded. In order to determine the CMC by this method, the fluorescence intensities of phenanthridine solutions are measured as a function of surfactant concentration below and above the critical micelle concentration. Figure 3 shows a plot of I/I0 versus TTAB concentration where I0 is the intensity of the solution without any TTAB present. Before the critical micelle concentration is reached, the fluorescence shows little variation in the intensity with increasing concentration of the surfactant. Once the CMC is exceeded, the phenanthridine molecules become associated with micelles and a dramatic decrease in the fluorescence intensity is observed. The phenanthridine molecules are thought to reside near the surface of the micelle. The increase in the quenching is interpreted as being due to the proximity of the phenanthridine molecules and the Br– ions that are associated with the micelle. In order to determine the CMC from the graph, a linear equation fit was made for the pre-micellar points, and an exponential equation fit of the form I/I0 = A + Be–C[CTAB] was made for post-micellar points. The CMC was determined by locating the point of crossing on the graph or by determining the point of crossing mathematically. Although the CMC can be determined from the Figure 3 plot, we find that it is better to use a plot of I0/I versus surfactant concentration (Stern–Volmer type plot). Such a plot is shown in Figure 4 and results in a linear data array for premicellar concentration and a curved array for post-micellar concentrations. A linear fit is applied to the pre-micellar data points and a quadratic fit for the post-micellar points. DTAB also shows linear behavior for the pre-micellar data and curved behavior for the post-micellar data, while CTAB shows linear behavior for both regions. The CMC values were determined by solving the equation resulting from setting the best-fit equations for the pre- and post-CMC data regions equal to each other. The results for the three surfactants are also shown in Table 1. They agree well with the values obtained by the conductivity method, and they also agree well with the literature values. Why does the fluorescence of phenanthridine show such a dramatic decrease in intensity (increase in quenching) once micelles start to form? We can use spectral evidence to answer this question. It is well known that azines such as phenanthridine and 5,6-benzoquinoline exhibit sharper UV absorption and fluorescence spectra in nonpolar and nonprotic solvents than they do in aqueous solutions where hydrogen bonding is so significant [12]. We find that the UV absorption spectrum of phenanthridine in aqueous surfactant solutions does become somewhat sharper when the CMC is exceeded. The fluorescence emission spectrum is more dramatically affected. This is illustrated in Figure 5, which compares the fluorescence spectrum of phenanthridine in water without TTAB with that containing TTAB at a concentration well above the CMC. As can be seen, the spectrum in water without surfactant (A) is very broad. This broadening is due to hydrogen bonding between the solvent and the nitrogen atom. The formation and deformation of hydrogen bonds causes an inhomogeneous broadening of the spectrum. At the high concentration of surfactant, most of the observed fluorescence (spectrum B) is due to phenanthrene molecules that are associated with


The Effect of Hydrocarbon Chain Length on the Critical Micelle Concentration…

4.0

3.5

CMC = 0.0039 + 0.0002 M 3.0

Io/I

2.5

2.0

1.5

1.0 0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

[TTAB]/M

Figure 6. The fluorescence quenching of lucigenin by TTAB. The luciginin concentration was 2.2 × 10–6 M , and the excitation and emission wavelengths were 368 and 507 nm, respectively. This plot should be compared with the fluorescence quenching of phenanthridine in Figure 4.

micelles. Any residual fluorescence is due to micelleassociated phenanthridine molecules that haven’t been quenched. For comparison purposes, a spectrum that is normalized in intensity to that without surfactant (C) is also shown. This spectrum is considerably sharper than that of the phenanthridine without surfactant. In fact, this spectrum is about as sharp as that of phenanthridine in alcohol solution but not as sharp as that of phenanthridine in a hydrocarbon solvent [13]. This result provides good evidence that when phenanthridine molecules associate with the micelles, they are in a less protic environment than they are in pure water. The fact that the quenching shows such a dramatic increase once the CMC is exceeded suggests that the phenanthridine molecules reside near the surface of the micelles where they are readily quenched due to their close proximity to the Br– counterions. Such a location would be consistent with the observed spectrum being broader than that of phenanthridine in hydrocarbon solvent. It is instructive to compare the quenching of phenanthridine by TTAB solutions with that of a fluorescent probe that is not expected to associate with cationic micelles. Luciginin (N,N′dimethyl-9,9′-bisacridinium nitrate), shown below, is a good example of Me N+

N+ Me


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such a system. The lucigenin ion is strongly quenched by Br– ions. Because it has a +2 charge, it will not associate with cationic micelles such as TTAB. We have examined the effect of TTAB on the fluorescence of lucigenin. The Stern–Volmer type plot (I0/I versus [TTAB]) is shown in Figure 6. It can be seen that the plot shows a dramatic change in slope once the critical micelle concentration is exceeded. The slope of the post-CMC region is significantly lower than that of the pre-CMC region. Thus, the rate of quenching decreases once the CMC is exceeded and micelles start to form. This is in sharp contrast to the behavior of phenanthridine in which the rate of quenching increases. Because the lucigenin ion resides in the bulk solution rather than in the micelles, its fluorescence is quenched by Br– ions in the bulk solution. Once the CMC is exceeded, any excess concentration of the TTAB goes into the formation of micelles. A fraction of the Br– ions attach to these micelles and are not effective in quenching the fluorescence of the lucigenin ions in the bulk solution. Thus, the rate of fluorescence quenching decreases once the CMC is exceeded. How can we explain the effect of chain length on the CMC of these surfactants? One way to explore this question is to look at the water solubility of amphiphilic substances that do not form micelles. It has been shown by Tanford [14] that the relationship between the solubility of these compounds with chain length is analogous to the relationship between the CMC of surfactants with chain length. Long-chain aliphatic alcohols are a good example of such compounds. It is known that these substances have a low solubility in water and, that the solubility decreases as the hydrocarbon chain length increases. On a superficial level this is explained by saying that like dissolves like and that unlike substances are not soluble in one another. Water is a polar molecule and the polarity of the alcohols decreases as the length of the hydrocarbon chain increases. Thus, the aliphatic alcohols become more and more unlike water as the hydrocarbon chain length increases. But, what is the deeper reason why unlike substances do not dissolve in one another? In the cases of the alcohols, the low water solubility and the observed decrease in the solubility with chain length indicates that the free energy of solution is positive and that it becomes more positive as the chain length increases. At first glance one might think that this is primarily due to enthalpy changes associated with chain length. The argument would be that the introduction of the hydrocarbon chain into water causes a breaking of hydrogen bonds between the water molecules, and that this is the cause of a positive enthalpy change. Alcohols with longer hydrocarbon chains would cause more of a disruption of the hydrogen-bonding network in water and thus would exhibit more positive enthalpy of solution changes than shorter chain alcohols. It is now well known that this interpretation is incorrect. The decrease in solubility of alcohols and the decrease in the CMC of surfactants with increasing chain length is a result of the hydrophobic effect [14, 15]. This effect has been discussed in an education journal by Huque [16]. Experimental evidence shows that the dissolving of long-chain alcohols in water is generally an exothermic process and thus favored rather than hindered by this factor. The positive free energy of solution is thus due to negative entropy changes associated with the solution process. In order to explain this negative entropy change, it is necessary to consider structural changes in water accompanying the introduction of the hydrocarbon portion of the solvated molecule. According to the interpretation of Frank and Evans [15], when a hydrocarbon residue inserts itself into


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water, the water molecules on the surface of cavity form a more ordered arrangement than was the case before insertion. This increase in order may be similar to what happens when hydrocarbon clathrate compounds are formed. The negative enthalpy change associated with such insertion suggests that the hydrogen-bonding network is even stronger than it was before insertion. This interpretation is consistent with the observation of a net volume decrease when the solute dissolves in water [14]. As shown by Tanford [14] the decrease in the CMC of amphiphillic ionic compounds with increasing hydrocarbon chain length can be interpreted in the same way. For these compounds, however, once the solubility limit is exceeded, micelles start to form instead of phase separation. Like the aliphatic alcohols, a log relationship exists between the solubility (CMC for amphiphillic ionic compounds) and the number of carbons in the hydrocarbon chain [7, 14]. In the case of the alkyltrimethylammonium bromides the relationship is log(CMC)= –0.317N + 2.01 where N is the number of carbon atoms in the hydrocarbon chain [7].

Marzzacco et al. Acknowledgment. The authors would like to thank the Rhode Island College Faculty Research Fund and the Florida Tech Chemistry Department for support of this project. We also thank Laura Cooley and Tracy Gibson for their contributions to the preparation of the student experiment handout. Special thanks go to J. Clayton Baum of the Florida Tech Chemistry department for his support, advice and helpful suggestions. Supporting Material. A student laboratory handout and instructor notes are available in a Zip file (http://dx.doi.org/10.133/s00897072009a). References 1. 2.

Rujimethabhas, M.; Wilairat, P. J. Chem. Educ. 1978, 55, 342.

3.

Dominguez, A.; Fernandez, A.;Gonzalez, N.; Montenegro, L. J. Chem.Educ. 1997, 74, 1227–1231.

4.

Goodling, K.; Johnson, K.; Lefkowitz, L.; Williams, B. W. J. Chem. Educ. 1994, 71, A8–A11.

5.

van Stam, J.; Depaemelaere, S.; De Schryver, F. C. J. Chem. Educ. 1998, 75, 93–98.

6.

Evans, H. C. J. Chem. Soc.1956, 579–586.

7.

Zana, R., J. Colloid Interface Sci. 1980, 78, 330–337.

Determination of the Fractional Ionization of the Micelle As mentioned in the introduction, it is also possible to measure the fractional ionization constant degree of micelles from conductivity measurements [1, 6]. In order to do this the specific conductivity is plotted versus surfactant concentration and the slopes of the pre-micellar region (S1) and the postmicellar region (S2) are determined. The fractional ionization constant (α) is determined by solving the following equation: 2/3

where n is the aggregation number of the micelle obtained from the literature and Λanion, ∞ is the molar conductivity at infinite dilution of the Br– counterion. Based on our conductivity data, we obtain α values of 0.22, 0.16 and 0.16 for DTAB, TTAB and CTAB, respectively. These compare with literature values of 0.23, 0.20 and 0.16, respectively [7].

Iglesias,

E.;

8.

Roelants, E.; De Schryver, F. C. Langmuir 1987, 209–214.

9.

Reekmans, S.; Bernik, D.; Gehlen, M.; van Stam, J.; Van der Auweraer, M.; De Schryver, F. C. Langmuir 1993, 2289–2296.

10.

Marzzacco, C. J.; Deckey, G.; Colarulli, R.; Siuzdak, G.; Halpern, A. H. J. Phys. Chem. 1989, 93, 2935–2939.

11.

Carrigan, S.; Doucette, S.; Jones, C.; Marzzacco, C. J.; Halpern, A. H. J. Photochem Photobio A 1996, 99, 29–35.

2

0 = [n xS1 – Λanion, ∞)]xα + Λanion,∞xα – 1000xS1

Bachofer, S. J. J. Chem. Educ. 1996, 73, 861–864.

12. Badger, G. M.; Walker, I. J. Chem. Soc. 1956, 122–126. 13.

Marzzacco, C.; Peterson, B. unpublished results.

14. Tanford, C. The Hydrophobic Effect, Formation of Micelles and Biological Membranes; Wiley: New York; 1980. 15. Frank, H. S.; Evans, M. W. J. Chem. Phys. 1945, 13, 507–532. 16. Huque, E. M. J. Chem. Ed. 1989, 66, 581–585.
