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 pharmacy (I).Such important roles are related to their ability to form aggregates (micelles)when the surfactant concentration in aqueous solution exceeds a critical concentration, 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 measure 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, parameters such as aggregation number, the fraction of bound counterions, and thermodynamic and geometric aspects, have been ignored completely. Although these parameters are mentioned in textbooks (13), theories and experimental 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 spectrofluorimeters 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 become famiharwith bothyhebasic the& and experimental details required. This aspect is particularly important, bccause the tcchniquc is bccom~ngvery common in physicochemical and analytical laboratories. Once the micellar aggregation 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 undergraduate students in the third year (of a total of five) in chemistly. Previously, students have to know general aspects of surfadants and at least one cmc determination should be performed. The cmc determination for SDS described in reference (15)takes less than one hour. The basic light-scattering theory is explained in a two-hour session. 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 solutions in aqueous NaClO.l M was prepared by the dilutionextraction method (15).For the sphere-rod transition study, a set of solutions was prepared by dissolving a constant 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 measurement 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 technique 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 experiments is given by eq 1(19)
where Kis the scattering wave vector, Corefers 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 molecular weight given by eq 1is only an apparent value (16). Figure 1shows 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-
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log ([NaCl]/mole dm-') (C-0.42)/g
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.
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, a t 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 geometric parameters such as micellar radius, r , chain monomer volume, u, maximum length that the chain can assume (critical chain length), and interfacial area per monomer, a (see Fig. 2). For spherical micelles, simple geometry 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=54A'for ndo 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
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Journal of Chemical Education
close to the cmc making the denominator in eq 1close to zero, and, finally, the use of solutions that are Go concentrated. To obtain the best results, the concentrations emnloved here are recommended. Students do not have diffi'euliy in understanding the geometric calculations. Fieure 3 shows a double loearithmic lot of the denendence"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 a t the poGt [NaCll = 0.47M. which aerees well with the Havashi and Ikeda result (16). ~ e c a & ethe 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~molecularweight for this large micelle mav be estimated from Firmre 3 and the assum~tionsthat 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 factor at 90' is 1. From eq 1is easily deduced eq 5,
where the subscript 1is used for the value corresponding to [NaClI = 0.1 M and 2 is used for other NaCl concentrations. With Nl = 89, a value of 1028 is deduced for the aggregation number a t [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 aggregation 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). Accepting 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 therefore the value for the cylinder length obtained here is a minimum one. From angular dependence of light scatter-
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 difficulties concern the preparation of SDS solutions at the highest 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, Israelachvili (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 Israelachvili (21) is recommended for the analysis of the relationship 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, it must be ern~hasizcdthat this sphercrod transition is not but S is common to many other surfactants exclusive ~ ~ ' S D (28).
We thank the DGICYT for financial support (project PB90-0758). Literature Cited 1. Many examples can befoundinSurfmtanf Scknm Ser!ia(47uolumesl pvblishedby Marcel DekLer, New York; and, i~ Svrfacfonfs in Solution (11 volwnesl publkhed by Plenum Press,New York. 2. Tanford, C. T k Hydrophobic EMt: Formation of Mimllea a n d Biological Membranes: Wilev: New York. 1960.
6. Furton, K G.; Norelus, A J ~ h e ; E d u e 1993,7O, 254. 7. Conam, G.' C k m . Edue 1980.57.225. 8. Reinsborough, V C.: Rebinaon, B. H. J. Chem. Edue. 1981,56,586. 9. Rodenas, E.; Vera, S. J. Chem. Ed=. 1985 62,1120. 10. Abuin. E. B.: Lissi, E. A J. C k m . E d v c 1992,69.340. 11. Shah,8. S.; Henacheid, L. C. J. Chom. E d u c 1983.60.685. 12. Ebeid,E-2. M. J. Chem Edue 1985.62.165. 13. Leuine, I. N. Physiml Chemistry: MrG-w-Hill: New York. 1988. 14. Mougsn. M. A,: Coello, A,: Jover. A,; Meijide, F:VgLquez Tate, J. J. C k m Educ in "mes -...
F.Mosguera. V : Varquez Tab. J J Chrm F d w 1890.57.SR0 1G l l n y . ~ ~ l ~ c , S . I k ~ ~ .I dPh,s a . S L'km 1980.84.lM. l l o h o r n l r n Ezpenmenta: h n u r c H a l . Ncu JcrI: Whttr. .l \I P h $ ~ , , oCkna,iln I
J ,s , . A . Mretllc
sq: 19-5. 18 . \ I ~ I I I P * ,W P h w d C h e m w q ; W o r d l ' n s c r s q l k r s Orfud. 19% 19 Candru. S .I 111 Sur%wront S d u t t o n ~Sa Methmoflntrsnporron. h n o . R 6:d. %,,rununrsrunrr srnrsNO 22. .$foni.l r)rkkrr :su york, i d : 20 Con.. M .Dcmom..Y - . J Ph,i ('hem 18Rl.ci . . :Il 21. Israelachvlli, J.N. inPhy~iiaifAmphiphil~s:Mhlle~, Maieksowi Minopmukioro; Deporgio, Y and Cortl, M. Eds, North Holland: Amsterdam, 1985. 22. Missel. P J.:Mazer,N.A.;Benedek,C.B.;Young,C.Y; Csrey.M. C.J Phys C k m 1980,84,1044. 23. Missel, P. J.; Mazer, N. A,: Benedek. G. B.: Carey, M. C. J Fhya C k m . l W , 87, 12M. 24, leraelaehvili, J.N.; Mitchell, D.J.;N i b , B. W. J C h .Sm. Fomdoy %ns 2,
. .
Conclusion The utilization of spectmfluorimetersas light-scattering apparatus for the study of micellar systems may be used as a pedagogical tool for reinforcing the concepts of the lightscattering technique and micellization processes.
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