Spherical and Rod SDS Micelles Adela Coello, Francisco Mellide, Manuel A. Mougan, E. Rodriguez NuAez, and Jose Vizquez ~ a t o ' Universidade de Santiago, Campus de Lugo, Facultade de Ciencias, Departamentos de Quimica Fisica e Fisica Aplicada, 27002 Lugo, Spain

The growing interest in surfactants is due mainly to their many applications in chemistry, biology, and phar- macy (I). Such important roles are related to their ability to form aggregates (micelles) when the surfactant concen- tration in aqueous solution exceeds a critical concentra- tion, the cmc value (2). This Journal has published several papers on the physical chemistry of micelles (3-I2), some of which illustrate the use of different techniques to meas- ure the cmc ( 3 4 , while others analyze the micellar effects on chemical kinetics (7-91, chemical equilibrium (101, and fluorescence and absorption spectra (11,12). However, pa- rameters such as aggregation number, the fraction of bound counterions, and thermodynamic and geometric as- pects, have been ignored completely. Although these pa- rameters are mentioned in textbooks (13), theories and ex- perimental techniques involved in their determination are usually not commented on.

In a previous paper (14) we pointed out some reasons for the scarce utilization of the light-scattering technique in educational chemistry laboratories and showed that spec- trofluorimeters can be used for a basic training in it (14). Here, we extend the application of the method to micellar systems; that is, light-scattering intensity, measured with a spectrofluorimeter, is applied to the determination of micellar molecular weieht. allowine the students to be- come famiharwith bothyhebasic the& and experimental details required. This aspect is particularly important, bc- cause the tcchniquc is bccom~ng very common in physico- chemical and analytical laboratories. Once the micellar ag- gregation number is known, geometric parameters as micellar radius or head group area are easily deduced.

Sodium dodecylsulfate (SDS) is chosen because it is a very well-known surfactant of both academic interest and industrial use. The experiment is camed out by under- graduate students in the third year (of a total of five) in chemistly. Previously, students have to know general as- pects of surfadants and at least one cmc determination should be performed. The cmc determination for SDS de- scribed in reference (15) takes less than one hour. The ba- sic light-scattering theory is explained in a two-hour ses- sion. The experiment is carried out in two sessions. In the first one, which takes about four hours, the aggregation number is determined. In the second session, which takes two hours, the sphere-rod transition that appears when increasing amounts of inert salts are added is studied.

'Author to whom correspondence should be addressed.

Experimental Details SDS (Sigma, purity higher than 99%) and NaCl (Merck)

were used without further purification. Water was Milli-Q grade. Temperature was kept constant at 25.0 "C. The Rayleigh band was used to measure the intensity of the scattered light. Other experimental conditions were the same as those described in (14).

To determine the aggregation number, a set of SDS solu- tions in aqueous NaClO.l M was prepared by the dilution- extraction method (15). For the sphere-rod transition study, a set of solutions was prepared by dissolving a con- stant amount of SDS in NaCl aqueous solutions. Because the experimental temperature was lower than the critical micelle temperature for SDS in NaCl solutions of 0.6,0.7, and 0.8 M, the surfactant was dissolved and clarified at 35 "C and cooled to the final temperature (16). Precipitation of SDS did not occur during the time over which the meas- urement was camed out. The change in refractive index with SDS concentration (= 0.1188 cm3/g) and cmc (= 0.420 g/dm3) at [NaCl] = 0.1 M were taken from the literature (16).

Results and Comments The theoretical background of the light-scattering tech-

nique has been commented on in our previous paper (14) where two textbooks were recommended (17, 18). For micellar systems, in which the micelles exist only above the cmc, the Debye equation for light-scattering experi- ments is given by eq 1 (19)

where Kis the scattering wave vector, Co refers to the cmc, R is the Rayleigh ratio at the scattering angle, 90°, M is the weight average molecular weight and A2 is the second virial coefficieen Here it is assumed that the micellar size is much smaller than the wavelength of the incident light. This equation does not take into account the effect of micelle charge on light scattering and the micelle molecu- lar weight given by eq 1 is only an apparent value (16).

Figure 1 shows the results obtained by us when we were preparing the experiment. From the intercept, a value of 25,500 was obtained for M from which the weight average aggregation number was deduced, the result being N = 89. Such a value is close to those published by Hayashi and Ikeda (16) and Corti and Degiorgio (20),97 and 94, respec-

Volume 72 Number 1 Januaty 1995 73

(C-0.42)/g dm"

Figure 1. Debye plot for SDS solutions in 0.1 M NaCl at 25 'C.

Figure 2. Geometric parameters of an idealized spherical micelle.

tively, at the same NaCl concentration. In the absence of inert electrolytes, aggregation numbers near 60 have been published (21).

In micelle formation, monomer packing depends on geo- metric parameters such as micellar radius, r , chain mono- mer volume, u, maximum length that the chain can as- sume (critical chain length), and interfacial area per monomer, a (see Fig. 2). For spherical micelles, simple ge- ometry gives eqs 2 and 3 (21),

4nr3 N = - 3" (2)

Tanford (2) has related the monomer chain volume to the number of carbon atoms, n,, of the alkyl chain as in eq 4.

Substitution of u = 350 Aqn previous equations gives r = 1 7 ~ a n d a = 6 1 ~ ' f o r ~ = 6 0 a n d r = 2 0 ~ a n d o =54A'for N = 89. Therefore, the addition of an Inert salt reduces the head-group area; i.e., the ionic head groups are closer to each other.

The aggregation numbers obtained by students are within 20% of the values shown. We have observed that this disparity is normally due to improper clarification of solutions, the use of solutions with concentrations very

log ([NaCl]/mole dm-')

Figure 3. Logarithmic relation of the dependence of light-scattering intensity of SDS solution with NaCl concentration at 25 C; [SDS] = 8 g/dm3.

close to the cmc making the denominator in eq 1 close to zero, and, finally, the use of solutions that are Go concen- trated. To obtain the best results, the concentrations em- nloved here are recommended. Students do not have diffi- 'euliy in understanding the geometric calculations.

Fieure 3 shows a double loearithmic lot of the denend- ence"of lighescattering i n t e r k t (from'a fixed amo;nt of SDS) with NaCl concentration. Data fit two straieht lines withvery different slopes, intersecting at the poGt [NaCll = 0.47 M. which aerees well with the Havashi and Ikeda result (16). ~ e c a & e the SDS concentration is constant throughout the series, the increase in intensity can only be attributed to formation of bigger aggregates; i.e., very large micelles are generated. &I approximate~molecular weight for this large micelle

mav be estimated from Firmre 3 and the assum~tions that int&molecular interactions are negligible (see 20 for a careful study of the dependence of the virial coefficient on electrolyte concentration) and the particle-scattering fac- tor at 90' is 1. From eq 1 is easily deduced eq 5,

where the subscript 1 is used for the value corresponding to [NaClI = 0.1 M and 2 is used for other NaCl concentra- tions. With Nl = 89, a value of 1028 is deduced for the ag- gregation number at [NaClI = 0.8 M. Such a value is comparable with the one given by Hayashi and Ikeda (16) equal to 1630. Students easily realize that this high an ag- gregation number is incompatible with a spherical shape. The proposed structure is that of a rod and the change in structure is known as the sphere-rod transition (16). Ac- cepting that the cylinder radius of the rod micelle is equal to the spherical micelle radius, and that monomer volume is given by eq 4, then eq 6 results,

cylinder volume = nr2h =Nu (6)

where h is the cylinder length. The resulting value of h is 400 A. In fact, the cylinder radius of a rod micelle is smaller than that of the spherical micelle (211, and there- fore the value for the cylinder length obtained here is a minimum one. From angular dependence of light scatter-

74 Journal of Chemical Education

ing in 0.8 M NaCl at 35 C, Hayashi and Ikeda obtained a value of 597 A.

In this second part of the experiment, the only difficul- ties concern the preparation of SDS solutions at the high- est NaCl concentrations. This particular point has been commented on in the Experimental Details section and for further details reference (16) should also be consulted.

Many other aspects concerning the formation of sphere and rod micelles are far from the purposes of the present experiment. Here, we briefly refer to some papers related to the subject, although only those concerning alkyl sulfate surfactants are considered. Missel et al. (22, 231, Is- raelachvili (21, 241, Nagarajan et al. (25-271, and Ikeda (28) have presented detailed thermodynamic models for micelles and the sphere-rod transition. The review by Is- raelachvili (21) is recommended for the analysis of the re- lationship between geometric and thermodynamic aspects. Ikeda (28) has treated the sphere-rod transition with a statistical thermodynamic theory, and derived equations for the double logarithmic relationship between micelle molecular weight and ionic strength (similar to Fig. 3). Missel et al. (23) have studied the influence of akyl chain length. Nguyen and Bertrand (291, Missel et al. (30) and De Vijdel (31) have studied the influence of electrolytes and non-electrolytes (29). The effect of temperature has been studied bv Missel et al. (22. 23). Mishich and Fisch have studied tke flexibility of rod micelles (321. Finally, i t must be ern~hasizcd that this sphercrod transition is not exclusive ~ ~ ' S D S but is common to many other surfactants (28).

Conclusion

The utilization of spectmfluorimeters as light-scattering apparatus for the study of micellar systems may be used as a pedagogical tool for reinforcing the concepts of the light- scattering technique and micellization processes.

- We thank the DGICYT for financial support (project

PB90-0758).

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