2899
Langmuir 1991, 7, 2899-2903
Size of Spherical Micelles of Dodecylpyridinium Bromide in Aqueous NaBr Solutions Katsuhiko Fujio and Shoichi Ikeda* Department of Chemistry, Faculty of Science, Nagoya University, Nagoya 464, J a p a n Received January 28, 1991. I n Final Form: April 18, 1991 Static light scattering from aqueous NaBr solutions of dodecylpyridinium bromide (DPB) has been measured over the range of NaBr concentrations from 0 to 6.00 M. The reduced scattering intensity does not show any angular dependence. At a given NaBr concentration, the reduced intensity increases with increasing micelle concentration. At a given DPB concentration, it is higher at higher NaBr concentrations if the NaBr concentration is lower than 0.50 M, but it decreases when the NaBr concentration increases further. The Debye plots give micelle molecular weights from 15 100 in water to 23 200 in 0.30-6.00 M NaBr, corresponding to micelle aggregation numbers from 46.0 to 70.7, respectively. Spherical micelles are stable over the whole range of NaBr concentrations. The micelle size increases with increasing NaBr concentration from 0 to 0.30 M, but it remains unaltered from 0.30 to 6.00 M NaBr. The linear double logarithmic plot between molecular weight and ionic strength consists of two parts, crossing at 0.30 M NaBr. The micelle charge is estimated as 26.7 from the slope of the line between 0 and0.30 M. The degree of ionization is high and is 0.580 in water and 0.378 above 0.30 M NaBr. From 0 to 3.00 M NaBr the second virial coefficient is positive, but beyond 3.00 M it is slightly negative. Introduction
An ionic surfactant can generally form rodlike micelles in aqueous salt solutions, if it has an alkyl chain longer than decyl and if a simple salt having a common counterion is added to a concentration exceeding a certain threshold.lS2 The threshold salt concentration of a cationic surfactant is lower for ita bromide than for its chloride, when corresponding sodium halide is added to its aqueous solution. For example, tetradecyltrimethylammonium bromide can form rodlike micelles a t NaBr concentrations above 0.12 M, while its chloride can form rodlike micelles at NaCl concentrations above 2.70 M.3 Dodecyltrimethylammonium bromide forms rodlike micelles when the NaBr concentration is higher than 1.80 M,2 while dodecyltrimethylammonium chloride continues to form spherical micelles, as long as NaCl is the added salt, which is soluble up to 4.50 M.5 When the counterion is more polarizable or more hydrophobic, the threshold salt concentration for the sphere-rod transition is lowered. It is known that, among various cationic species having a dodecyl group, only dodecyltrimethylammonium chloride cannot form rodlike micelles in aqueous solutions, even in the presence of NaCl to its saturation. All the other N-methyl-substituted dodecylammonium chlorides and bromides can form rodlike micelles, when corresponding sodium halides are present beyond their threshold concentrations. In order to investigate the effect of the ionic head group on the sphere-rod transition of cationic micelles further, light-scattering studies on aqueous micellar solutions of dodecylpyridinium bromide (DPB) are undertaken. Lightscattering measurements on aqueous solutions of DPB were conducted by Venable and Nauman6 in water and 0.05 M NaBr, by Ford et al.7 from 0 to 0.10 M KBr, and (1) Ikeda, S. In Surfactants in Solution; Mittal, K. L., Ed.; Plenum Press: New York, 1984; Vol. 2, p 825. (2) Imae, T.; Ikeda, S. Colloid Polym. Sci. 1987,265, 1090. (3) Imae, T.; Ikeda, S. J. Phys. Chem. 1986,90, 5216. (4) Ozeki, S.; Ikeda, S. J . Colloid Interface Sci. 1982, 87, 424. (5) Ozeki, S.; Ikeda, S. Bull. Chem. SOC.Jpn. 1981, 54, 552. (6) Venable, R. L.; Nauman, R. V. J . Phys. Chem. 1964,68, 3498.
(7) Ford, W. P. J.; Ottewill, R. H.; Parreira, H. C. J. Colloid Interface Sci. 1966, 21, 522.
0743-7463/91/2407-2899$02.50/0
by Jacobs et a1.8 in 0.5 m NaBr. However, their results have not made clear whether DPB can form rodlike micelles or not in the presence of NaBr or KBr. In the present work, static light scattering is measured on aqueous NaBr solutions of DPB at 25 "C,in which the NaBr concentration extends from 0 to 6.00 M. Experimental Section Materials. DPB was synthesized from dodecyl bromide and
pyridine. Dodecyl bromide was obtained from Tokyo Kasei Co. and redistilled in vacuo. Pyridine obtained from Tokyo Kasei Co. was dried over molecular sieve 4A. A 105.9 g (0.425 mol) sample of freshly distilled dodecyl bromide and 137.1 g (1.732 mol) of dry pyridine were refluxed for 30 min. The mixture became turbid, but, on further heating for 10 min, it became clear. After the mixture was cooled, precipitates separated. The precipitates were recrystallized several times from acetone and acetoneisopropyl ether with a yield of 32.8 g (23.5%). The surface tension of an aqueous solution of the DPB sample did not show any minimum around the critical micelle concentration, which was found to be 12.0 X M, as shown in Figure 1. The molecular area at the critical micelle concentration is calculated to be 59.3 Az molecule-' by means of the Gibbs adsorption isotherm. These values are in good agreement with those reported by Venable and Nauman? 12.1 X M and 59 Az molecule-'. Apparatus. Light scattering was measured on a Laser Light Scattering Photometer DLS-700 manufactured by Otsuka Denshi Co., Inc., Osaka, Japan. The light source was a 5-7-mW argon ion laser, and the selected wavelength was 488 nm. Temperature was regulated to 25 f 0.2 "C, by circulating water of constant temperature from a Julabo F10-VC Thermostat. The reduced intensity of scattered light at a scattering angle, 6, is calculated by r2i, RB,U" =
IO
where l o is the intensity of incident light, which is vertically polarized. The intensity of light, ie, scattered from a solution of unit volume at a distance, r , is derived from the intensity of light, l e , scattered from the solution of scattering volume, VO,which is proportional to l/sin 6, and measured at a distance, r. With reference to a standard liquid for calibration, it is given by (8) Jacobs, P. T.; Geer, R. D.; Anacker, E. W. J . ColloidInterface Sci. 1972, 39, 611.
0 1991 American Chemical Society
Fujio and Ikeda
2900 Langmuir, Vol. 7, No. 12, 1992
I
*t
-3
-4
P
'a)
9
-1
c Figure 1. Relationship between surface tension and logarithm of concentration for aqueous solutions of DPB. log
where #t, is the calibration constant, and f i 0 and f i b are refractive indices of the solvent and the standard liquid, respectively.The instrument was calibrated by using purified benzene as the standard liquid. The equation
is used, where Rw,uVand Rw,uu are reduced scattering intensities in the 90" direction when irradiated by the vertically polarized (v) and unpolarized (u) light, respectively, and pu is the depolarization ratio for unpolarized light. The values, Rw,uu = 24.54 X 10%cm-l and pu = 0.439,were assumed for ben~ene.~ Solutionsand solventsfor light-scatteringmeasurements were filtered four to five times through a Millipore filter VC having a 0.10-pm pore size. The specific refractive index incrementa of solutions were measured on a DifferentialRefractometer RM-102 manufactured by Otsuka Denshi. The light source was a 50-W iodine lamp, from which the light of wavelength 488 nm was isolated by an interference filter. The instrument was calibrated by using aqueous solutionsof NaCl and NaZS04 at 25 "C, whose refractive indices at 488nm were obtained by interpolatingtabulated values of refractive index at other wavelengths.1° The refractive index of solvents, i.e. of aqueous solutions of NaBr, at 488 nm and 25 "C was calculated by first extrapolating tabulated values at other (higher) temperatures and at other wavelengthsllto 25 O C , interpolating these values to 488nm, and then interpolatingor extrapolatingthose values at differentNaBr concentrations to a desired concentration.
Results Light Scattering. It was found that light scattering
from aqueous NaBr solutions of DPB showed no angular dependence. Accordingly, all the measurements were carried out at the scattering angle, 0 = 90°. The excess reduced scattering intensity of aqueous NaBr solutions of DPB Jer aqueous solutions of NaBr, Rw RwO, is shown in Figure 2 as a function of DPB concentration, c (g ~ m - ~at) ,different NaBr concentrations, CS 42
(9) Pike, E.R.;Pomeroy, W. R.; Vaughan, J. M.J.Chem. Phys. 1975, 62, 3188.
(10) H u g h , M.B.,Ed. Light Scattering from Polymer Solutions; Academic Press: New York, 1972; p 181. (11)Timmermans, J.Physical Chemical Constants 0fBimrySystem.s; Interscience Publishers, Inc.: New York, 1960; Vol. 3, p 348.
0
1
1
c ( to-'g cm-3
)
Figure 2. Excess reduced intensity of scattered light from 0; ( 0 )0.01; ( 0 ) aqueous NaBr solutions of DPB. (a) CS(M): (0) 0.05; ( 0 )0.10; (A)0.50. (b) c s (M): (A)1.00; (A)2.00; (A)3.00; (0) 4.00; (m) 5.00;( 0 )6.00.
(M). Its values are nearly constant below the critical micelle concentration, co (g ~ m - ~and ) , they suddenly increase with increasing DPB concentration above the critical micelle concentration. With increasing NaBr concentration up to 0.50 M, the critical micelle concentration decreases and the excess scattering intensity at a given micelle concentration increases steadily with curvature concave downward. The behavior of light scattering is normal, as has been observed for many surfactant solutions. At NaBr concentrations beyond 0.50 M, the critical micelle concentration also decreases further but the excess scattering intensity decreases, with increasing NaBr concentration. Such a phenomenon, that light scattering decreases with increasing salt concentration, has never been observed; it cannot be attributed to a large decrease in the optical efficiency of DPB, i.e. in the specific refractive index increment, but it has to be ascribed to the effects of micelle size and intermicellar interaction, as shown below. Above 3.00 M NaBr the curvature of the scattering intensity is slightly concave upward.
Size of Spherical Micelles of Dodecylpyridinium Bromide
Langmuir, Vol. 7, No. 12, 1991 2901
Table I. Critical Micelle Concentration and Specific Refractive Index Increment of Aqueous NaBr Solution of DPB cot io-* co, ( a i i l a ~ ) ~ , , K, 10-7 Cs, M Ao g cm-3 M cm3 g-* cm2 g-2 0 0.01 0.05 0.10 0.50 1.00 2.00 3.00 4.00 5.00 6.00
1.3367 1.3368 1.3372 1.3379 1.3431 1.3494 1.3597 1.3677 1.3745 1.3813 1.3880
0.384 0.297 0.162 0.100 0.040 0.023 0.020 0.013 0.015 0.012 0.011
11.70 9.05 4.93 3.05 1.22 0.70 0.61 0.40 0.46 0.37 0.34
0.175 0.175 0.174 0.173 0.168 0.162 0.150 0.138 0.125 0.113 0.101
6.299 6.292 6.259 6.222 5.918 5.542 4.806 4.092 3.426 2.809 2.252
I
-2
0
-1
l o g CCO+CS)
- -
Figure 3. Corrin-Harkins plot for DPB micelles in aqueous
NaBr solutions: (0) present work; (0)Venable and Nauman;6 (0)Jacobs et a1.;8 (A)Ford et a1.: in KBr solutions.
-
7
r
-
Table I gives values of the critical micelle concentration,
CO(M) = lOOOc0/328.3, and the specific refractive index increment, (aii/ac)c,,of the solution, as well as the solvent refractive index iio. The critical micelle concentration follows the Corrin-Harkins equation
+
log Co = -0.573 log (Co C,) - 3.046 0 IC , 5 6.00 M
(4)
as shown in Figure 3. This straight-line relationship holds over the whole range of NaBr concentrations. The values in other ~ o r k ~measured , ~ , ~ by light scattering are also given, and they fall on the same line. Even in KBr solutions, the critical micelle concentration follows the same equation, eq 4. This fact was also observed for aqueous NaBr and KBr solutions of dodecyltrimethylammonium b r ~ m i d e . ~ The specific refractive index increment follows the equation
(aii/ac),* = 0.175
-0 . 0 1 2 ~ ~
o 5 c, I6.00 M (5)
The dependence is moderate and normal. Figure 4 shows the Debye plots for aqueous NaBr solutions of DPB a t different NaBr concentrations. The linear relation
holds for Debye plots, where M is the micelle molecular weight (without correction for micelle charge) and B is the second virial coefficient. The optical constant, K, is given by
'T 30
1
2
Figure 4. Debye plots for light scattering from aqueous NaBr 0; ( 0 )0.01;( 0 )0.05; ( 0 )0.10. solutions of DPB. (a) CS(M):(0) (b) cs (M):(A)0.50; (A)1.00;(A)2.00;(A)3.00; (0) 4.00;(0)5.00; ( 0 )6.00.
(7) for polarized incident light of wavelength, A, where N Ais Avogadro's number. Table I1 gives values of micelle molecular weight, M, micelle aggregation number, m = M/328.3, and second virial coefficient, B. The molecular weight of the micelles is 15 100 in water and 23 300 in 6.00 M NaBr. The aggregation numbers are 46.0 and 71.0, respectively. The value in water is in good agreement with that reported by Venable and Nauman? The value in 0.50 M NaBr is also comparable with that in 0.5 m NaBr given by Jacobs et a1.* The micelle size indicates that the micelle of DPB remains spherical or globular over the whole range of NaBr concentrations. From 0 to 3.00 M NaBr, the second virial coefficient is positive, but from 4.00 to 6.00 M NaBr, it is negative. In water, the Debye plot slightly deviates from the straight line, eq 6. This has also been observed previously for the other micellar solutions.2J
Fuji0 and Zkeda
2902 Langmuir, Vol. 7,No. 12, 1991 Table 11. Molecular Weight, Aggregation Number, and Second Virial Coefficient of DPB Micelles in Aqueous NaBr Solutions Cs, M M m B, cm3 g-* 0 0.01 0.05 0.10 0.50 1.00 2.00 3.00 4.00 5.00 6.00
15 100 15 100 20 000 20 400 24 000 23 500 24 800 23 000 22 900 21 600 23 300
L
9.85 5.50 1.46 0.643 0.175 0.110 0.165 0.040 -0.063 -0.103 -0.235
46.0 46.0 60.9 62.1 73.1 71.6 75.5 70.1 69.7 65.8 71.0
4.0‘
log M = A , log (C, + Cs) + B , (8) Figure 5 shows the double logarithmic plot for DPB micelles. The linear relationship for micelles a t low NaBr concentrations and the horizontal relationship a t higher NaBr concentrations give the equations
+ 4.434
log M = 4.365 0.30 IC, I6.00 M
(9a) (9b)
Thus the spherical micelle of DPB grows from molecular (12) Ikeda, S. Colloid PoEym. Sci. 1991,269, 49.
’
-1
The second virial coefficient indicates that electric repulsion operates between spherical micelles in aqueous solutions up to 3.00 M NaBr. It decreases with increasing NaBr concentration, because of the increase in electric shielding of the micelle charge. Above 3.00 M NaBr intermicellar attraction is operative between spherical micelles, but it is not sufficiently strong to promote their aggregation into larger micelles such as rodlike micelles. Micelle Size. Table I1 shows that the micelle molecular weight increases with increasing NaBr concentration up to atout 0.50 M, and it remains constant above about 0.50 M NaBr. Even with bromide, dodecylpyridinium ion cannot form rodlike micelles. This high stability of spherical micelles of DPB appears to be characterized by their low aggregation number,12 as in the case of dodecyltrimethylammonium ~ h l o r i d e . ~ In our previous work on various cationic s~rfactants,l-~ it was assumed that the size of a spherical micelle continues to increase with increasing salt concentration even beyond the threshold salt concentration. However, it would sometimes happen above a certain salt concentration that spherical micelles cease to grow with increasing salt concentration and retain their size unchanged. That is, with increasing salt concentration the intermicellar interaction could change from repulsive to attractive above the threshold, but, even before it, i.e. even with intermicellar repulsion, the intramicellar interaction could be already constant above a certain limit of salt concentration. As was seen in Figure 2, the reduced scattering intensity of micellar solution of DPB is a maximum a t an NaBr concentration around 0.50 M, irrespective of micelle concentration. This suggests that the micelle attains the largest size around 0.50 M NaBr and a further increase in NaBr concentration does not affect the intramicellar interaction. It has been observed for ionic surfactants that the logarithm of molecular weight of spherical micelles is linearly related to the logarithm of ionic strength or counterion concentration,12 that is
log M = 0.132 log (C, + C,) 0 IC, 5 0 . 3 0 M
I
1
-1
0
I
1
l o g ( C , + cs 1 Figure 5. Double logarithmic relationship between molecular weight and ionic strength for DPB micelles in aqueous NaBr solutions: (0) present work; (0)Venable and Nauman;6 (0) Jacobs et al.;8 (A) Ford et al.,7in KBr solutions. weight, 15 100, in water to 23 200 in 0.30 M NaBr and continues to have the molecular weight, 23 200, from 0.30 to 6.00 M NaBr. (The difference in NaBr concentrations, 0.50 and 0.30 M, that appeared above, would partly come
from the fact that the reduced scattering intensity reflects the effects of micelle size and intermicellar interaction, while eq 9 takes account of the micelle size alone.) The values by other workers6p8for water and NaBr solutions fall on the same lines, eqs 9a and 9b. However, the values by Ford et al.7 in water and aqueous KBr solutions are higher than those predicted by eq 9a. Although their values are too high even in water, it is certain that the molecular weight of spherical micelles is higher in aqueous KBr solutions than in aqueous NaBr s o l ~ t i o n s . ~ J ~ J ~ Discussion
According to Tartar15 and Tanford,16 the maximum aggregation number of a “spherical” micelle (a micelle having the shape of a sphere) can be calculated from the volume of micelle core filled by alkyl chain of a given length. Dodecyl group has an extended length 15.42 8, and a volume 323.3 A3 in a micelle core, and it can make a “spherical” micelle having core volume, 15 360 A3. Then the maximum aggregation number of “spherical” micelles is 47.5 for dodecyl derivatives, which is nearly equal to that of DPB micelles in water, 46.0. This means that dodecylpyridinium ions accommodate well with a sphere to form a stable “spherical” micelle. With increasing NaBr concentration, more dodecylpyridinium ions are incorporated in a micelle, and the micelle aggregation number increases. Then their packing in the sphere becomes closer, the sphere may swell, or the micelle shape deviates from the sphere toward an oblate ellipsoid. Above 0.30 M NaBr, 70.7 dodecylpyridinium ions form a closely packed “spherical” micelle with the core radius larger than 15.42 A, or an oblate ellipsoidal micelle with the semiminor axis 15.42 A and the axial ratio 1.22. The areas per DPB ion on the spherical micelles are calculated to be 63.6 A2 and 55.5 A2 for the “spherical” and oblate ellipsoidal micelles. These values are comparable with the molecular area of DPB on an aqueous surface, 59.3 Az. The micelle would have a compact structure. The presence of the threshold salt concentration for limiting the size of spherical micelles has been suggested by Anacker17J8for cetylpyridinium chloride and trifluorododecyltrimethylammonium bromide. The present (13) Trap, H. J . ; Hermans, J. J. Proc. K . Ned. Akad. Wet. 1955,B58, 97. (14) Imae, T.; Ikeda, S. J. Colloid Interface Sci. 1985,108, 215. (15)Tartar, H. V. J. Phys. Chem. 1955,59,1195. (16)Tanford, C.J. Phys. Chem. 1972,76, 3020. (17)Anacker, E.W. J. Phys. Chem. 1958,62,41. (18)Gerry, H.E.; Jacobs, P. T.; Anacker, E. W. J. Colloid Interface Sci. 1977,62, 556.
Size of Spherical Micelles of Dodecylpyridinium Bromide results definitely show the existence of such a threshold. Consequently, it seems likely that, when the salt concentration is increased, spherical micelles of ionic surfactants either undergo a transition to rodlike micelles or reach a maximum size, depending on the species of ionic surfactant. The implication of the relationship between micelle size and ionic strength was recently elucidated on the basis of the electrostatic effect in micelle formation.12 The coefficient, A,, of eq 8 is related to the micelle charge, ma,, and is given by the equation ma,e
Langmuir, Vol. 7, No. 12,1991 2903 Table 111. Molecular Weight, Aggregation Number, and Electric Charge of Spherical Micelles Corrected by Prins-Hermans-Princen-Mysels Theory Cs, M 0 0.01 0.05 0.10 0.50 1.00 2.00 3.00
Mt
mt
P
Plmt
18600 16 600 20900 21 000 24 800 24300 26400 23 900
56.7 50.7 63.6 64.0 75.4 74.0 80.3 72.8
11.4 10.2 11.6 10.9 14.5 15.9 29.4 16.3
0.202 0.202 0.183 0.167 0.192 0.215 0.366 0.223
MtIM ~
~~
1.24 1.10 1.04 1.03 1.03 1.03 1.07 1.04
2
A,=-8ckTb
1
where a, is the degree of ionization of micelle, b the radius of micelle, e the dielectric constant of water, and T the temperature. Here e is the elementary charge, and k is Boltzmann's constant. It is noted that the applicability of eq 10 is confined to the range where the electrostatic effect is effective, i.e. below 0.30 M NaBr, or for eq 9a only. Assuming b to be 21.0 A, the micelle charge is calculated to be ma, = 26.7. As the aggregation number, m, changes with NaBr concentration, the degree of ionization of the micelle is 0.580 in water and 0.378 in 3.00 M NaBr. If the micelle charge is also kept constant beyond 0.30 M NaBr, the degree of ionization remains 0.378 in aqueous NaBr solutions from 0.30 up to 6.00 M. The degree of ionization of the micelle, especially in water, in very large, which is also exhibited in the large value of the second virial coefficient in water, and this fact must be related to high stability of spherical micelles of DPB. However, the constant radius of micelle is not likely, but with increasicg NaBr concentration, the micelle may swell and its radius would increase from 21.0 A in water to 23.8 A in 0.30 M NaBr. The high ionization of DPB micelle can be ascribed to reduced attraction between Br-and pyridinium ion, which arises from a-electron clouds on the pyridinium ring. Actually, it was shown that the effective charge on the nitrogen atom of methylpyridinium ion was 0.53 instead of unity.19 From the measurement of membrane potentials,20the degree of ionization of DPB micelles was estimated to be 0.235 in water and 0.19 in 0.01 M KI. These values are too low, although there is a good possibility for different values of degree of ionization, depending on the method of determination. The coefficient, B,, of eq 8 is related to the free energy of hydrophilic hydration, q, through the equation (19) Jacobs, P. T.; Anacker, E. W. J. Colloid Interface Sci. 1973,44, 505. (20) Ingram, T.; Jones, M. N. Trans. Faraday SOC.1969, 65, 297.
2.3O3Bm = mame2(In- 8aNAe2b 2 - 4 ) +$$+lnM,
8ekTb
10%k~
(11)
where t i s the free energy of hydrophobic interaction, M1 is the molecular weight of surfactant, i.e. 328.3, and N Ais Avogadro's number. Assuming NA{to be 0.42nc kcal mol-', where nc is the number of carbon atoms in the alkyl chain, it is found that NAQ= 2.33 kcal mol-'. The hydrophilic hydration of DPB is strongly repulsive among dodecyl derivatives,12and it prevents the micelles from growing further and converting to rodlike micelles. An aqueous salt solution of ionic surfactant is a ternary system, and its micellar solution can be regarded as a solution of macroion in an aqueous solvent containing added salt,together with the surfactant monomer of critical micelle concentration. The Prins-Hermans-Princen-Mysels theory21s22treats light scattering from such a system, by taking account of the difference in optical efficiency between surfactant ion and salt co-ion, and the application of its results gives the molecular weight or aggregation number of spherical micelles, Mt or mt, corrected for micelle charge, as given in Table 111. The apparent micelle charge,p, can be derived from the second virial coefficient, and the apparent degree of ionization, pfmt, can be obtained. As shown in Table 111, the values of pfmt are as high as 0.20. The high ionization of spherical micelles has also been attributed to characteristics of its stability5 and is in agreement with the results from eq 10. The present results, that spherical micelles of DPB are very stable against increase in ionic strength, arise from the fact that pyridinium groups have reduced positive charges owing to the a-electron clouds and are more hydrophilic on the spherical micelle, when compared with dodecyltrimethylammonium b r ~ m i d e . ~ Registry No. DPB, 104-73-4; NaBr, 7647-15-6. (21) Prins, W.; Hermans, J. J. Proc. K . Ned. Akad. Wet. 1956, B59, 162. (22) Princen, L. H.; Mysels, K. J. J. Colloid Interface Sci. 1957, 12, 594.
