Study of Mixed Micelles with Varying Temperature by Small-Angle

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Langmuir 1997, 13, 6388-6392

Study of Mixed Micelles with Varying Temperature by Small-Angle Neutron Scattering V. M. Garamus* Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia Received January 3, 1997. In Final Form: August 18, 1997X Micellar solution of ternary systems of nonionic/ionic (Triton X-100/1-bromo-4-tridecylpyridine) surfactants in water were studied by small-angle neutron scattering. Formation of mixed micelles was detected. It was found that system behavior versus temperature is strongly dependent on the ratio between surfactant concentrations. Aggregation number and surface charge of micelles were calculated using the rescaled mean spherical approximation.

1. Introduction Mixtures of surfactants can form mixed micellar aggregates.1 The behavior of such mixtures is quite different from that of the individual surfactants. That is why they are often used in industrial applications. The interaction between different surfactants may result in synergetic or antagonistic effects.2 On the other hand, total inmiscibility would cause the coexistence of two types of micelles, each type consisting only of one kind of surfactant.3 The simultaneous presence of two kinds of mixed micelles with different compositions is also possible and represents transitions between the two extreme alternatives mentioned above. The field of mixed micelles made of nonionic and ionic surfactants together is still an open field in terms of structural studies.4 A simple picture of interacting spherical droplets cannot account for light scattering experiments.5 Theoretical expressions of counterion binding to such mixed aggregates have been proposed by Rathman and Scamehorn.6 The concentration of monomers in equilibrium with mixed micelles and interaction parameters between molecules can be evaluated from critical micelle concentration (cmc) values of mixed systems.7 A number of studies were concerned with the effective charge of mixed nonionic/ionic micellar systems.8-12 The value of the maximum effective charge was 20% deduced from these experiments, and it was also observed that the effective charge rises linearly at first with increasing ionic content of the surfactant mixture and stays almost constant beyond a content of more than 20% (by moles) of ionic surfactant. * FAX: 7-09621-65882. E-mail: [email protected]. X Abstract published in Advance ACS Abstracts, October 15, 1997. (1) Scamehorn, J. F. Phenomenon in mixed surfactant systems; ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986. (2) Rosen, M.; Murphy, D. J. Colloid Interface Sci. 1986, 110, 224. (3) Haegel, F. H.; Hoffmann, H. Prog. Colloid Polym. Sci. 1980, 76, 132. (4) Chevalier, Y.; Zemb, Th. Rep. Prog. Phys. 1990, 53, 279. (5) Guering, P.; Lindman, B. Langmuir 1985, 1, 464. (6) Rathman, J. F.; Scamehorn, J. F. Langmuir 1987, 3, 372. (7) Asakawa, T.; Johten, K.; Miyagishi, S.; Nishida, M. Langmuir 1985, 1, 347. (8) Treiner, C.; Fromon, M.; Mannebach, M. H. Langmuir 1989, 5, 283. (9) Abuin, E. B.; Lissi, E. A.; Nunez, R.; Olea, A. Langmuir 1989, 5, 783. (10) Douglas, C. B.; Kaler, E. W. Langmuir 1994, 10, 1075. (11) Bucci, S.; Fagotti, C.; Degiorgio, V.; Piazza, R. Langmuir 1991, 7, 824. (12) Gorski, N.; Gradzielski, M.; Hoffmann, H. Langmuir 1994, 10, 2594.

S0743-7463(97)00011-5 CCC: $14.00

The shape investigation13 of mixed micelles was performed by using the contrast variation method of smallangle neutron scattering (SANS). The binary micellar mixtures of nonionic surfactant/ water and ionic surfactant/water show opposite tendencies with varying temperature. In the case of nonionic surfactants the ethylene oxide chain uncoils with increasing temperature, so that the net dipole moment of surfactant is decreased, eventually causing it to become insoluble, and the increasing temperature gives rise to the dehydration process of the ethylene oxide chain and increasing micelles.14 Ionic surfactant micelles become smaller and their net charge increases as the solution temperature increases.15 Which of the tendencies is stronger and under which conditions? This question is being solved in the present paper. The second aim was to obtain detailed information on the structure of mixed micelles of nonionic/ionic surfactants. The complex aggregation behavior of surfactants in solution especially mixtures of surfactants is a result of a delicate balance of opposing forces. The results of studies of structural and electrical parameters of micelles will be used for gaining an understanding of specific interactions between various surfactant species present in solution, which is of central importance to the surfactant technologist. The two well-known surfactants were taken as research objects whose properties in binary systems are widely studied. Micellar solutions of Triton X-100 in water are well studied by different experimental methods16-19 including SANS.20-22 Micellar size, shape, aggregation number, and degree of hydration of ethylene oxide chains versus surfactant concentration, temperature, and additives were obtained. (13) Pilsl, H.; Hoffmann, H.; Hofmann, S.; Kalus, J.; Kencono, A. W.; Lindner, P.; Ulbricht, W. J. Phys. Chem. 1993, 97, 2745. (14) Shonfeldt, N. Grenzflachenaktive Athylenoxid-Addukte; Wissenschaftliche Verlagesellschaft MBH: Stuttgart, 1976. (15) Vass, Sz. Struct. Chem. 1991, 2 (167), 375. (16) Krovvidi, K. R.; Muscat, A.; Stroeve, P.; Ruckenstein, E. J. Colloid Interface Sci. 1984, 100, 497. (17) Brown, W.; Rymden, R.; Stam, J.; Almgen, M.; Svensk, G. J. Phys. Chem. 1989, 93, 2512. (18) Corti, M.; Degiorgio, V. Opt. Commun. 1975, 14, 358. (19) Dennis, E. A. Adv. Colloid Polym. Sci. 1986, 26, 155. (20) Monohar, C.; Kelkar, V. K.; Mishra, B. K.; Rao, K. S.; Goyal, P. S.; Dasannacharya, B. A. Chem. Phys. Lett. 1990, 171, 451. (21) Bulavin, L. A.; Garamus, V. M.; Karmazina, T. V.; Shtanko, S. P. Colloid J. Russ. Acad. Sci.sEngl. 1995, 57, 856. (22) Goyal, P. S.; Menon, S. V. G.; Dasannacharya, B. A.; Thiyagarajan, P. Physica B 1995, 213&214, 610.

© 1997 American Chemical Society

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The structure of micellar aggregates in 1-bromo-4tridecylpyridine/water solutions was studied earlier and it was detected that the micelles are close to spheres.23 2. Experimental Section 2.1. Sample Preparation. The research cationic surfactant 1-bromo-4-tridecylpyridine (TPB), 1-Br-4-C13H27(C5H3N), was received from RIAP Kiev, the Ukraine, and recrystallized from alcohol to a constant value of cmc. The cmc, measured by the surface tension method, was equal to 5.0 mmol/L (1.7 g/L). The nonionic surfactant (1,1,3,3-tetramethylbutyl)phenolpoly(ethylene oxide) C8H17C6H4(OC2H4)nOH (Triton X-100), where n is equal to 9-10, was received from Rohm and Haas, USA. The cmc in aqueous solution, measured by the surface tension method,24 was equal to 0.24 mmol/L (corresponding to 0.15 g/L). The cloud point is 62 °C in heavy water.20 Doubly distilled light water, and heavy water with 98 mol % deuterium were used in preparing the samples. The samples were prepared by weight. 2.2. Small-Angle Neutron Scattering Measurements. The SANS experiments were performed on the “MURN” timeof-flight small-angle neutron scattering spectrometer of the IBR-2 pulsed reactor at FLNP JINR, Dubna, Russia. The samples were placed in quartz cells (Hellma) with 1 mm path. A 1 cm2 area was illuminated by the neutron beam. Incoherent scattering backgrounds were subtracted using the measured equivalent of H2O/D2O solutions. Systematic errors did not exceed 5%.25 The scattering vector range was from 0.008 to 0.4 Å-1. Throughout the data analysis, corrections were made for instrumental smearing.26 For each instrumental setting, the ideal scattering curves smeared by the appropriate resolution function were compared to the measured curves by means of the least-squares method. The parameters in the models were optimized by conventional least-squares analysis, and the errors of the parameters were calculated by conventional methods.27

Figure 1. Differential neutron scattering cross sections of binary mixtures: 0.022 mol/L Triton X-100 (empty square); 0.028 mol/L TPB (triangle); ternary mixture 0.022 mol/L Triton X-100, 0.028 mol/L TPB (solid square) in D2O at 20 °C.

3. Results Our first aim was to distinguish whether the two surfactants form mixed micelles or whether two types of micelles exist. To study the micellar composition three SANS experiments were performed on binary systems: TPB/water (D2O), Triton X-100/water (D2O), and ternary TPB/Triton X-100/water (D2O). The surfactant concentrations were the same in binary and ternary mixtures. The SANS spectra (Figure 1) in the case of binary mixtures show that there is a system of noninteractive particles and a system of strong repulsive particles which gives the interference maximum at low q values. The SANS curve in the ternary system is characterized by the interference maximum at higher q value as compared with TPB/water, which points to the increasing number of micelles. The neutron scattering from the ternary mixture of TPB/Triton X-100/water is not equal to the sum of scattering curves from the corresponding binary mixtures even taking into account “hard sphere” interaction among the Triton X-100 and TPB micelles. If the solution to be studied contains two different coexisting populations of micelles, the scattering curve has to exhibit the features of two populations, i.e., the plato in the low-q range is the feature of noninteractive micelles of Triton X-100 and the interference maximum is the feature of long-range repulsive micelles of TPB. The scattering curve of ternary solution exhibits the feature of only one population: the long-range repulsive (23) Bulavin, L. A., Garamus, V. M., Karmazina, T. V.; Pivnenko, E. N. Colloids Surf., in press. (24) Moraru, V. N.; Ovcharenko, F. D.; Kobylinskaya, L. I.; Karmazina, T. V. Colloid J. Russ. Acad. Sci.sEngl. 1984, 46, 1148. (25) Ostanevich, Yu. M. Makromol. Chem., Macromol Symp. 1988, 15, 91. (26) Kozlova, E. P.; Ostanevich, Yu. M.; Cser L. Nucl. Instrum. Methods 1980, 169, 597. (27) Bevington, B. R. Data Reduction and Error Analysis for Physical Sciences; McGraw-Hill: New York, 1969.

Figure 2. Differential neutron scattering cross sections for 1/1 (square) and 2/1 (triangle) solutions in D2O at 20 °C.

micelles. That is why one could conclude that mixed micelles are formed in the case of TPB/Triton X-100/water systems. We expect that cmc’s of Triton X-100 and TPB are not changed significantly because the most pronounce changes of cmc were observed in the mixture of the cationic/ anionic surfactants. Two ternary mixtures TPB/Triton X-100/water with compositions Triton X-100 13.9 g/L (0.022 mol/L) and TPB 9.7 g/L (0.028 mol/L) (1/1) and Triton X-100 27.9 g/L (0.0447 mol/L) and TPB 7.57 g/L (0.022 mol/L) (2/1) were prepared and measured with varying temperature. The main difference is that the ratio between the molar concentration of Triton X-100 and TPB increases from approximately 1 (taking into account the difference between cmc’s) to 2 at the same TPB concentration. The differential cross sections of neutron scattering at 20 °C (Figure 2) show the interference maximum which does not shift with increasing ratio between Triton X-100 and TPB. One could suggest that the number of micelles does not change because the position of maximum connected average distance between micelles and the change of maximum height (increasing) points to the increasing micellar size. The interval of the measured temperature was from 20 to 55 °C. The changes of the scattering curves were small, but tendencies for 1/1 and 2/1 compositions of the ternary systems were opposite. In the case of 1/1 composition the position of the interference maximum shifts at larger q value and the maximum height decreases. Only two extreme temperatures are shown in Figure 3. In the case

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Garamus

∫

P2(q) ) { (F(r) - Fs) exp(iqr) dv}2

(2)

where F(r) is the scattering length density of a particle with a radius r, and Fs is the scattering length density of the solvent. The structure factor S(q) is defined by

S(q) ) 1 + V-1

∫(g(r) - 1) exp(iqr) dv

(3)

where g(r) is the correlation function between particles and V is the volume of solution per particle. In the case of polydisperse or nonspherical particles, dΣ(q)/dΩ can be written as

dΣ(q)/dΩ ) n[〈|P(q)|〉2S(q) + (〈|P(q)|2〉 - 〈|P(q)|〉2)] (4) Figure 3. Differential neutron scattering cross sections for 1/1 solution versus temperature.

The decoupling approximation,29 that there is no correlation between interparticle separation and particle size and there is no correlation in the separation between particles and their orientation, could be used to calculate the second term of eq 4. In the present studies, the micelles are assumed to be monodisperse, prolate two-shell ellipsoids of volume V2 with semiaxes a, b, b. The inner shell is the nonwetted hydrocarbon volume V1 with a scattering length density F1; the outer shell is of volume V2 - V1 a with scattering length density F2. The definition of the single particle scattering function is given by the following equation:

∫01{(F1 - F2)V1F[qR1(µ)] +

P2(q) ) (

(F2 - Fs)(V2 - V1)F[qR2(µ)]} dµ)2 (5) where F(x) ) 3[sin(x) - x cos(x)]/(x)3 and Figure 4. Differential neutron scattering cross sections for 2/1 solution versus temperature.

of 2/1 composition the position of the maximum is approximately the same but the height increases (Figure 4), which points to the increasing micellar size. From this observation one could conclude that with increasing ratio between concentration of nonionic surfactant Triton X-100 to ionic surfactant TPB from 1 to 2 the system changes its properties from ionic-like to nonionic-like, i.e., for ionic surfactant the micelles become smaller with increasing temperature and for nonionic surfactant the micelles increase. 4. Modeling and Discussion All experimental curves exhibit interference maxima which points to long range interaction between particles in the studied systems. Ionic surfactants form charged micelles. That is why it seems reasonable to model the investigated system by population of the particles with the screened Coulomb potential. In the case of monodisperse spheres of number density n, the expression of the differential cross sections of neutron scattering by volume unit, dΣ(q)/dΩ,28 versus the scattering vector q ) 4π sin θ/λ (2θ is the scattering angle and λ is the wavelength) can be written as

dΣ(q)/dΩ ) nP2(q)S(q)

(1)

where the form factor P2(q), which expresses the scattering cross section of one particle, is (28) Glatter, O., Kratky, O. Eds. Small-Angle X-ray Scattering; Academic Press: London, 1982.

Ri(µ) ) bi[1 - µ2((ai/bi)2 - 1)]1/2 γ ) ai/bi for i ) 1, 2. The volumes and radii are calculated by assuming that each micelle consists of Na (mean aggregation number) surfactant molecules where ξ(1 + ξ)-1Na is the number of Triton X-100 molecules and (1 + ξ)-1Na is the number of TPB molecules, and the ξ is the molar ratio between Triton X-100 and TPB, ξ ) (CTriton - cmcTriton)/(CTPB - cmcTPB). Volumes V1 and V2 are defined as follows

V1 ) Na(1 + ξ)-1[6ν(CH3) + (ξ(n1 - 5) + n2 - 1)ν(CH2)] and

V2 - V1 ) Na(1 + ξ)-1{ν(C5H5N+) + $2HGν(D2O) + (1 - R)[ν(Br-) + $Brν(D2O) + ξν(C6H4(OC2H4)nOH) + ξ$1HGν(D2O)]} (6) where ν(CH2), ν(CH3), ν(C5H5N+), ν(C6H4(OC2H4)nOH), ν(Br-), and ν(D2O) are the volumes of the methylene, methyl, and head groups of TPB and Triton X-100 and the volumes of the bromide ion and solvent molecules, respectively, n1 and n2 are the numbers of carbon atoms in the hydrocarbon chains of Triton X-100 and TPB, $1HG, $2HG, and $Br stand for the hydration numbers of the head groups of Triton X-100 and TPB, respectively, and of the bromide ion, and R is the degree of dissociation of TPB molecules. The numerical values of the volumes and (29) Kotlarchyk, M.; Chen S.-H. J. Chem. Phys. 1983, 79, 2461.

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Table 1. Fitting Results on Solution Triton X-100 13.9 g/L (0.022 mol/L) and TPB 9.7 g/L (0.028 mol/L) in watera

Table 2. Fitting Results on Solution Triton X-100 27.9 g/L (0.0447 mol/L) and TPB 7.57 g/L (0.022 mol/L)a

T, °C

Na

Na(TPB)

Na(Triton)

D, Å

f.c.

z, e

T, °C

Na

Na(TPB)

Na(Triton)

D, Å

f.c.

z, e

20 25 30 35 40 45 50 55

71.6 ( 1.1 70.8 ( 1.1 69.8 ( 1.1 68.3 ( 1.1 67.3 ( 1.1 66.7 ( 1.1 65.8 ( 1.1 65.0 ( 1.1

36.9 36.5 36 35.2 34.7 34.4 33.9 33.5

34.7 34.3 33.8 33.1 32.6 32.3 31.9 31.5

48 47.9 47.7 47.8 47.5 47.4 46.6 46.4

0.360 ( 0.002 0.369 ( 0.002 0.374 ( 0.002 0.391 ( 0.002 0.400 ( 0.002 0.405 ( 0.003 0.401 ( 0.003 0.406 ( 0.003

13.3 13.5 13.5 13.8 13.9 13.9 13.6 13.6

20 25 30 35 40 45 50 55

75.6 ( 1.2 76.3 ( 1.2 76.3 ( 1.2 77.6 ( 1.2 78.2 ( 1.5 78.8 ( 1.5 79.5 ( 1.5 80.2 ( 1.5

21 21.2 21.2 21.6 21.7 21.9 22.1 22.3

54.6 55.1 55.1 56. 56.4 56.9 57.4 57.9

51.7 51.8 51.8 52.1 52.2 52.4 52.5 52.7

0.542 ( 0.003 0.548 ( 0.003 0.559 ( 0.003 0.565 ( 0.003 0.567 ( 0.003 0.571 ( 0.003 0.566 ( 0.003 0.568 ( 0.003

11.4 11.6 11.9 12.2 12.3 12.5 12.6 12.7

a N is the total aggregation number, N (TPB) is the number of a a TPB molecules in mixed micelle, Na(Triton) is the number of Triton X-100 molecules in mixed micelle, D is the diameter of micelle, f.c. is the fractional charge, and z is the charge of micelle in electron.

of the hydration numbers ($1HG ) 20, $2HG ) 5, $Br ) 5) are taken from refs 23 and 30. The screened Coulomb potential is

Vc(r) ) πod2ψo2 exp[-κ(r - d)]/r

r>d

(7)

where d is the particle diameter, r is the interionic centerto-center distance, ψo is the surface potential, o is the permeability of the free space, and  is the dielectric constant of the solvent medium. Here, κ is the usual Debye-Huckel inverse screening length, determined by the ionic strength of the solution. The surface potential is related to the charge z on the micelle, in a good approximation, by31

ψo ) z/[o〈d〉(2 + κ〈d〉)]

(8)

where 〈d〉 is the average diameter of the micelle. We used the rescaled mean spherical approximation (RMSA) structure factor for diluted charged colloidal dispersions calculated by Hayter and Hansen.32 This theory is valid if there is no correlation between particle orientation and/ or size and interparticle separation. This assumption is reasonable for charged micelles if γ is not much greater than unity. For the fitting procedure, we used a FORTRAN program written by Hayter. The fitting parameters were aggregation number, degree of disassociation (fractional charge) R, axial ratio γ, residual background, normalization parameter and then micellar radius, charge, and potential were calculated. The number of fitting parameters corresponds to the information content of the scattering patterns.33 The model describes the experimental data satisfactorily; normalization of χ2 did not exceed 3 (Figures 3 and 4). In our case, the fit resulted in a good approximation to the experimental points in the region of the scattering vector (q < 0.2 Å-1), which corresponds to the spacing and mean size of the micelles. We took the values of the mean aggregation number and electrical charge of the micelles. The value of the axial ratio did not exceed 2, the difference of the normalization parameter from 1 was less than 0.15, and the residual background was less than 0.01 cm-1. The resultant fitting parameters are presented in Tables 1 and 2. The quality derived conclusions from the shapes of scattering curves (Figure 3 and 4) obtained quantitative characteristics after the modeling. The value of aggregation number of pure TPB micelles23 is close to the total (30) Berr, S. S.; Jones, R. R. M.; Johnson, J. S. J. Phys. Chem. 1992, 96, 5611. (31) Verwey, E. J. W.; Overbeek, J. Th. G. Theory of the Stability of Lyophobic Colloids; Elsevier: New York, 1948. (32) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651. (33) Taupin, D.; Luzzati, V. J. Appl. Crystallogr. 1982, 15, 289.

a

The captions are the same as those in Table 1.

aggregation number which is observed in the present study. For solutions with the surfactant ratio 1/1 the total aggregation number decreases from 72 to 65 and the degree of dissociation increases. For the solution with the surfactant ratio 2/1 the aggregation number with varying temperature and fractional charge increases. The total aggregation number of micelles in the mixture with the surfactant ratio 2/1 is larger than for the ratio 1/1 and increases from 76 to 80 with varying temperature, but the number of TPB molecules in micelle is smaller. It could be concluded that 1/1 and 2/1 mixtures exhibit opposite tendencies with a change in temperature. The mixture with the surfactant ratio 1/1 demonstrates the property of ionic surfactant micelles, i.e., aggregation number decreases with increasing temperature, and the mixture with the surfactant ratio 2/1 demonstrates the property of nonionic surfactant micelles, i.e., aggregation number increases with increasing temperature. As described in ref 34 the free energy of micellization summarizes many physicochemical factors responsible for mixed micelle formation and depends on the molecular structure of the surfactants, as well as on the solution conditions such as temperature, pH, and the presence of additives. In the present study we obtained the change in the sign of the derivation of the free energy of micelization with respect to temperature when the ratio between the nonionic/ionic surfactants increases from 1/1 to 2/1. We can expect that there is a mixture between 1/1 and 2/1 where the micelles are not changed with increasing temperature. It means that the change of the contributions of the dehydration process of ethylene oxide chains and the net dipole moment of the nonionic surfactant molecule in the free energy of micellization is compensated by the change of electrical contribution of the head groups of the ionic molecule. The fractional charge for 2/1 ratio is greater than for 1/1 that could be explained by the less packing of TPB molecules at mixed micelles. For pure TPB micelles the fractional charge does not exceed 0.3. The dependence of the fractional charge versus temperature agrees with the kinetic model35

f.c. ∼ 4πo〈r〉kBT/e2|zk|

∑ni|zi|

(9)

where 〈r〉 is the average distance between ions and micelles, 〈r〉 ) (Ci + Cm)1/3, Ci is the concentration of free surfactant molecules, Cm is the micellar concentration, zk is the charge of counterions, ∑ni|zi| is the charge of the micelle, kB is the Boltzmann constant, and T is the absolute temperature. The electrical charge of the micelle stays practically constant with varying temperature and for the surfactant ratio 1/1 is slightly larger than for the surfactant ratio (34) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5567. (35) Rusanov, A. I. Micellisation in Solutions of Surface-Active Substances; Chimija: St. Petersburg, 1992 (in Russian).

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2/1. One may use Brjerrum’s criterion to test surfactant dissociation in micelles. According to Brjerrum it should stop if the particle radius R becomes smaller than half the Brjerrum length λB ) e2/4πkT times the charges of the micelles (∑ni|zi|) and counterion (zk).36 For a

R < |zk|

∑ni|zi|λB/2 ) |zk|∑ni|zi|e2/8πokBT

(10)

monovalent counterion, a radius 26 Å, and temperature 20 °C this point would be reached at a micellar charge of (36) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworths: London, 1959.

7e. More sophisticated models35 give the value 9e for the micellar charge. Conclusions The SANS measurements of aqueous solutions of nonionic/ionic surfactants have shown that mixed micelles are formed. The degree of dissociation of ionic surfactant molecules is higher than that for pure ionic surfactant micelles, which is expected from the electrostatic models. The dependence of aggregation number versus temperature changes from ionic-like micelles to nonionic-like as the ratio between Triton X-100/TPB increases from 1 to 2. LA970011E