- Email: [email protected]
The physicochemical properties of aqueous mixtures of cationic-anionic surfactants
The Physicochemical Properties of Aqueous Mixtures of Cationic-Anionic Surfactants II. Micelle Growth Pattern of Equimolar Mixtures ZHI-JIAN YU AND GUO-XI ZHAO 1 Laboratory of Colloid Chemistry, Institute of Physical Chemistry, Peking University, Beijing, China Received April 4, 1988; accepted August 19, 1988 An investigation of the micelle solution behaviors of the equimolar mixtures of octyltriethylammonium bromide-sodium octyl-, decyl-, and dodecyl-sulfate has been carried out by dynamic and static light scattering. It is shown that micelle size increases with surfactant concentration, the total hydrophobic chain length, and the lowering of temperature. The micelle is a rigid rod when the radius of gyration is, below 400 A; above this size, the mieelle has the shape of a semiflexible rod. At the limit of micelle growth, either by increase of micelle concentration or by decrease of temperature, a new liquid phase separates from the solution, and the surfactant concentration of this new phase could be rather dilute (could be less than 1.2%). This two-aqueous-phase-coexisting phenomenon may be interpreted as flocculation of micelles. The sphere-to-rod transition model is adapted to the mixed micelles of cationic and anionic surfactant systems, and some thermodynamical parameters in the sphere-to-rod transition are deduced from experimental results and this model. © 1989AcademicPress,Inc. INTRODUCTION
In the last decade many investigations have been carried out on micellar dimensions and structures by light scattering technique (1). Most of the micellar systems studied contained a single ionic surfactant. The interpretation of the experimental results is often complicated by the fact that there always exist intermicellar interactions. Two paths have been adopted to overcome this difficulty. One is to carry on the experiments under the conditions of high ionic strength to screen the electrostatic interaction between charged micelles. At high ionic strengths, micelles have the shape of a rod or a semiflexible rod (2, 3). The other is to use low ionic strengths and low micelle concentrations, assuming that in such cases the electrostatic interactions between ionized micelles are the predominant effect on micelle diffusion and the micelle shapes are minimal spheres i To whom correspondence should be addressed.
( 4 - 6 ) . T h e latter m e t h o d c a n o n l y be used to o b t a i n the micelle size at cmc. Recently, t h e r e a l m o f investigation o f m i celle systems has b e e n enlarged to i n v o l v e the systems c o n t a i n i n g i o n i c surfactants with organic c o u n t e r i o n s (7, 9). In such systems, large micelles u s u a l l y f o r m with the size increasing with c o n c e n t r a t i o n initially, going t h r o u g h a m a x i m u m a n d t h e n decreasing. Investigators in these studies believe t h a t the o v e r l a p p i n g o f the rodlike micelles m a y be responsible for this p h e n o m e n o n . A n o t h e r feature o f these syst e m s is t h a t s o m e o f t h e m have viscoelastic p r o p e r t i e s ( 8-1 1 ), while others have n o t ( 7 ) . H o w e v e r , no clear e x p l a n a t i o n has b e e n given for all a b o v e m e n t i o n e d e x p e r i m e n t a l results. The study of mixtures of cationic-anionic surfactants is o f great i m p o r t a n c e b o t h practically a n d theoretically. U n f o r t u n a t e l y , such systems usually f o r m opalescent mixtures with a n e m u l s i o n n a t u r e ( 12, 13 ). P r e v i o u s l y ( 1 2 ) , we h a v e o b t a i n e d the m i x e d s o l u t i o n o f oct y l t r i e t h y l a m m o n i u m b r o m i d e - s o d i u m oc-
421 0021-9797/89 $3.00 Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
Copyright © 1989 by Academic Press, Inc. All fights of reproduction in any form reserved.
422
YU AND ZHAO
tylsulfate which forms a transparent micelle solution. In this paper, we will systematically investigate the micellar properties of the aqueous solutions of the equimolar mixtures of octyltriethylammonium bromide-sodium alkylsulfate. For such mixed cationic-anionic surfactant systems, the low charge density on the micelle surface may be expected due to the neutralization of the two oppositely charged surfactant ions, which may simplify the analysis of the experimental results. EXPERIMENTAL
The octyltriethylammonium bromide (C8NEt3Br) and the sodium octyl-, decyl-, and dodecyl-sulfate (C8_12SO4Na) are the same as used previously (12). Stock solutions of the octyltriethylammonium alkylsulfate (C8 NEt3- CnSO4, n = 8, 10, and 12) were obtained by mixing equimolar proportions of the corresponding long chain compounds. In order to provide a constant ionic strength and, consequently, to simplify the interpretation of the experimental results, the total concentration of NaBr was kept at 0.1 M by adding NaBr. The solutions of various concentrations of C8NEt3 ° CnSO 4 were obtained from stock solutions by dilution with the 0.1 M NaBr. The experimental set-up for dynamic and static light scattering and the procedure for determining the apparent hydrodynamic radius of the micelles Rh are the same as in the previous works ( 12, 14). The detected relative intensity at a given scattering angle 0 was converted into reduced intensity R (0) by using a reference intensity scattered from a carefully prepared benzene sample under the same conditions, and the influence of the difference of refractive index between aqueous solution and benzene on calculating R(O) has been corrected. The refractive index increment dn/ dc was determined with the differential refractometer (RF Model 600) with its original light source replaced by a 632.8-nm wavelength He-Ne gas laser beam. The micellar weight averaged molecular weight (mol wt) (apparent) and the average radius of gyration Journal of Colloid and Interface Science, VUl. 130,No. 2, July 1989
of micelles Rg (apparent) were calculated from the Debye equation ( 15 ), assuming the intermicellar interaction is negligible in our case
K'(c - cmc) R(O) - R°(O) ×
1 mol wt
( 1 6 7 r 2 n 2 R 2 g sin20 1+
)
,
[11
where R ° (0) is the reduced intensity at the critical micelle formation concentration cmc, c is the total concentration of the surfactants, n is the refractive index of the solvent (or of the solution at cmc), )~o is the wavelength of the incident beam in vacuum, and K' is the optical constant
K' = 4r2n2(dn/dc)2Xo4NT, l,
[2]
where NA is the Avogadro number. RESULTS AND DISCUSSION
(A ) Influence of Micellar Concentration, Temperature, and Chain Length on Micelle Size Figures la and lb show the dependence of micelle molecular weight (apparent) upon the concentrations of C8NEt3"C8SO4 and CsNEt3.C10SO4, respectively, at various temperatures from 20 to 55°C. Figure lc shows the relationship between Rh and the concentration of CsNEt3. C 1 2 8 0 4 at various temperatures from 45 to 65°C. The NaBr concentration is kept at 0.1 Mfor all solutions in order to screen the possible charge on the micelle surface which may exist owing to the different surface activities between C8NEt3 Br and CnSO4Na. The cmc values used in calculating mol wt are 8.13, 2.09, and 0.427 m M for C8NEt3- C8SO4, C8NEt3. C l o 8 0 4 , and C8NEt3" C12SO4 systems, respectively ( 16 ). Mol wt (and Rg) is obtained by fitting the linear part of the K'(c-cmc)/(R(O) - R°(O)) versus sin2(0/2) curves to Eq. [1 ]. Every Rh value was obtained by measuring scattered intensifies at several scattering angles from 0 = 90 ° to 30 °. The measured Rh is independent of 0 when Rh < 300 A. In the range of 300
PROPERTIES OF AQUEOUS MIXTURES, II < Rh < 800 ~, the Rh versus sin2(0/2) curves are straight lines with small negative slopes (less than 10%). In this case, Rh is obtained by linear extrapolation to the zero scattering angle. In the range of 800-1200 A, Rh increases with the decrease of sin 2(0/ 2) rather dramatically. Beyond 1200 ,~, the curves Of Rh versus sinZ(0/2) are no longer linear. Generally, there are three factors responsible for the dependence Of Rh on 0. One is the dust contaminant which may exist in the samples. But the effect of the dust on Rh should be stronger for small particles, which is not our case. Thus this factor can be ruled out. The second factor is the polydispersity of the micelles. The variance in the systems deduced from the second cumulant is less than 0.2, which will probably not induce such strong dependence of Rh on 0 as in the case of large values ofRn. The third one is the existence of other forms of motions in addition to the translational motion for nonspherical micelles (17). The influence of the latter two factors on Rh may be excluded by extrapolating to zero scattering angle. The diffusive motion of the rodlike micelles will be influenced by the overlapping of the micelles. The larger the micellar dimension is, the more seriously the Rh value is affected. Considering this point, we will not plot Rh larger than 800 ~, in this paper. The equimolar mixtures of CsNEt3. CnSO4 have very low Krafft points (their aqueous solutions do not form precipitate or crystal in the temperature range above 4°C). But the correlation functions of the micelle solutions of C8NEt3-C12804 in the concentration range studied have a very slow decay in the long correlation time range in addition to the fast one in the initial correlation time range when the temperature of solutions is below 45 °C, which makes the cumulant method for data analysis invalid. Figure 1 indicates that the micelle size (mol wt or Rh) increases monotonically with surfactant concentration at a fixed temperature or with the lowering temperature at the fixed surfactant concentration. This increase is more
423
rapid as the total hydrophobic chain length becomes longer. At a fixed micellar concentration and temperature, the micelle size increases with the chain length. For example, Rh is 39 A (Ref. (12), Fig. 3), 132 A (Fig. 3), and 790 A for C8NEt3.C8SO4, C8NEt3. CloSO4, and C8NEt3-C12SO4, respectively, at the micelle concentration (c-cmc) of 10 m M at 55°C. Figures lb and lc also show some striking characteristics of the systems of C8NEt3. CloSO4 and C8NEt3. C12SO4. The rate of change of the micelle size increases with the concentration and the surfactants form giant micelles which are larger than any reported in the literature. Solutions become turbid when micelle size becomes sufficiently large as the result of concentration increase. The solutions of C8NEt3. C8SO4 contain relatively small micelles and are all homogeneous and clear in the concentration range studied.
(B) Micellar Shapes Figure 2a is the plot o f m o l wt/Rh as a function of Rh for C8 NEt3 ° C8 SO4 together with a series of the theoretical predictions for geometric models of spheres, rigid rods, and oblate ellipsoids. The formulae for calculating the theoretical curves are the same as in Ref. (18). The experimental data are taken from Fig. 3 in Ref. (12) and Fig. 1a at various temperature and micelle concentrations. Figures 2b and 2c are the experimental data of mol wt in Fig. 1 and Rg at various temperatures and various micelle concentrations compared with the theoretical curves of spheres, oblate ellipsoids, rigid rods, and semiflexible rods for CsNEt3- C10804 and CsNEt3" C12804. The formulae used for calculating the theoretical curves are also taken from Ref. (18). Those experimental data of Rg beyond 800 A are not plotted since the initial range of sin2(0/2) of the linear part of the K'(c-cmc)/(R(O) R ° (0)) vs sin 2( 0 / 2 ) curve becomes small when the value of Rg is large and thus the values of Rg calculated from Eq. ( 1 ) by neglecting the higher order terms become less accurate. The partial volume of the micelle used in con-
Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
424
YU AND ZHAO
I oi"
6O 7
40
o 2O
4 5
I
I
t
I
20
30
4o
50
~
600 j¼ %
4o0
4
/ 200
i
5 lO CsNCIoS ( mM )
15
8OO
o•
C
/0/3
600
400 / o / / / 200
//o
~ J
verting mol wt into micellar volume is taken approximately as 1 cm 3 g-l. The cross sectional radius of rods, the semiminor axis of oblate ellipsoids, and the radius of minimal sphere are estimated to be 17.3, 19.8, and 22.3 A for C8NEt3. C8804, C8NEt3- C10SO4, and CsNEt3, C12804, respectively, which are the fully extended lengths of the longer hydrophobic chain length molecules (i.e., alkylsulfate) plus the binding layer of water and inorganic counterions of approximately 2 A which is consistent with our earlier experimental result (14). From Fig. 2 it can be seen that the experimental data are in good agreement with the theoretical curves of rigid rods and well deviated from the theoretical curves of sphere and oblate ellipsoid when Rh < 200 A or Rg < 400-500 A; i.e., for the experimental range of the micelle concentration and temperature, the micelle shapes are all rigid rods for CsNEt3" C8 SO4. For larger micelles the agreement of experimental data with the theoretical predictions for a rigid rod is no longer maintained. Figures 2b and 2c show that in the case of large micelles the data fit the theoretical curves for semiflexible rods with persistence lengths (18, 19) equal to 370 and 750 A for CsNEt3-Cx0SO4 and CsNEt3"C12SO4, respectively. It seems that the flexibility increases with the decrease of the cross sectional radius of rods. From the above we can conclude that the small micelles (Rh < 200 A or Rg < 400500 A) are rigid rodlike and the large micelles (Rg > 400-500 A) are semiflexible rodlike for all three systems.
(C) The Coexistence of the Two Dilute Aqueous Phases
io 4
8
12
FIG. 1. (a) The micelle molecularweight, mol wt, as a function of the surfactant concentration for the solutions of CsNE%. CsSO4with 0.1 M NaBr. The temperatures of curves 1 to 5 are 20, 25, 35, 45, and 55°C, respectively. (b) The micelle tool wt as a function of the surfaetant concentration for the solutions of CsNEt3.C10SO4with Journal of Colloid and Interface Science. Vol. 130, No. 2, July 1989
The separation of two aqueous phases occurs in the solution of high surfactant concen0.1 M NaBr. The temperatures for curves 1 to 6 are 20, 25, 30, 35, 45, and 55°C, respectively. (c) The miceUe hydrodynamic radius Rh as a function of the surfactant concentration for solutions of CsNEh. C~2SO4with 0.1 M NaBr. The temperatures of curves 1 to 4 are 45, 50, 55, and 65°C, respectively.
PROPERTIES OF AQUEOUS MIXTURES, II
/
6
4
% 2
I 50
I IO0
l 150
b
200
/
I
400
300
C. 200
/4
-/
lO0
2O0
(~)
4OO
ag
GO0
8O0
3 400
"i
o
~I 300
~
200
100
20O
400
600
800
ag (2) FIG. 2. (a) mo1 wt/Rh versus Rh. (O) Experimental data of micelle solutions of CsNEt3. Cs SO4 taken from Fig. 3 in Ref. (12) and Fig. la; the curves l, 2, and 3 are theoretical predictions for spheres, oblate ellipsoids, and rigid rods, respectively.(b) The plot of tool wt versus radius of gyration Rg. (O) The experimental data of the micelle solutions of CsNEt3. C1oSO4 at various surfactant concentrations and temperatures with 0.1 MNaBr; the curves l to 4 are theoretical predictions for spheres, oblate ellipsoids, semiflexihle rods with the persistence length of 370 /~, and rigid rods, respectively. (c) The plot of mol wt
425
tration range. W h e n sufficient a m o u n t s o f equimolar C s N E t 3 B r and Cl0SO4Na or CIzSO4Na are brought together, an opalescent solution formed. Soon, numerous, oily droplets could be seen in the mixtures with the naked eye. The small spheres coalesced to f o r m large ones and eventually fused to f o r m a new liquid phase. Dilution o f this solution decreases the rate o f phase separation. At a concentration slightly larger than that o f the critical phase separation, the solution is very viscous a n d viscoelastic but still transparent in appearance like a genuinely h o m o g e n e o u s solution. The viscoelastical solutions separate into two transparent aqueous phases u p o n standing for 1 or 2 days. The critical phase separation concentrations are 18 and 10 m M for CsNEt3 • C10SO4 and CsNEt3 • C12 SO4, respectively, in 0.1 M N a B r solution, 25°C. Figures 1b a n d 1c show that the micelle size increases with the increase o f the surfactant concentration. At the limit o f micelle growth, a solution becomes turbid on initial preparation a n d separates into two transparent aqueous phases to reach its equilibrium state. The phase separation p h e n o m e n o n can also be observed by lowering the temperature o f a solution. Figure 3 shows the dependence Of Rh o n the temperature for C s N E t 3 . C10SO4 solutions o f various concentrations. At r o o m temperature, the solutions o f CsNEt3 • C10SO4 form two transparent liquid phases with a clear phase b o u n d a r y between t h e m when the total concentration is above 18 m M . These heterogeneous solutions b e c o m e h o m o g e n e o u s u p o n heating, and the critical h o m o g e n e o u s solution formation temperatures are dependent on concentration. For example, they are 35.5 a n d 2 0 ° C for concentrations o f 20 and 18 m M , respectively. Above the critical temperature, the solutions show the properties o f
versus Rg. (O) The experimental data of the micelle solutions of CsNEt3. C 1 2 8 0 4 at various surfactant concentrations and temperatures with 0.1 M NaBr; the curves 1 to 4 are theoretical predictions for spheres, oblate ellipsoids, semiflexible rods with the persistence length of 750 A, and rigid rods, respectively. Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
426
YU AND ZHAO
8O0 .~
60o
4 5 ~
6~i"¢~~o8
3~'~ \ / i ~ ~ ~~
;400
I
I
I
30
I
I
50
70
(*o) FIG.3. The dependenceOfRhon temperatureat various surfactant concentrationsof CsNEt3.C10SO4 and at 0.1 MNaBr. The concentrationsin curves 1to 8 are 4, 6, 8.2, 11.3, 13.5, 15.9, 18, and 20 raM, respectively.
yond 50 mM, the scattering intensity of the lower phase approaches that of pure solvent, indicating only a negligible quantity of micelles in the phase. The above phenomena could be still observed after the solution stands for one year. In conclusion, the upper layer is the surfactant rich phase, but both upper and lower phases are still dilute solutions. The concentration of the upper phase could be less than 2.4 and 1.2% for CsNEt3"C10SO4 and C8NEt3-C12SO4, respectively, if we suppose that the surfactants are all in this phase. The phase separation phenomenon may be interpreted in terms of flocculated micelles phase formation. According to the DLVO theory of colloid stability (20), the interparticle interaction potential consists of a hardsphere repulsive part, an electrostatic longrange repulsion, and a London-van der Waals attraction. If the attraction is larger than the electrical repulsion, a second minimum occurs in the potential curve. The depth of the minimum increases linearly with the increase of particle size for spheres or plates. In the case of semiflexible rods, the calculation of the interparticle potential might be very complex. We suppose that the above qualitative conclusion still holds; i.e., the depth of the second minimum increases with the size of micelles. If the micelles are sufficiently large, the potential minimum will be deep enough to prevent the micelles in the minimum position from leaving by the thermal motion. Thus the micelle flocculation occurs and the flocculated micelle solution phase separates. If the flocculation occurs at the second minimum rather than at the first one, the phase separation phenomenon must be reversible. The experimental results show that the phase separation always occurs at the limit of the micelle growth and the process is reversible by changing either the micelle concentration or the temperature, which is in line with the above analysis.
the normal homogeneous micelle solutions; i.e., the solution is in its equilibrium state and the particle size decreases with temperature in the same way as in normal micelle solutions. It can thus be concluded that the phase separation occurs at the limit of micelle growth with either increase of miceUe concentration or decrease of temperature. The surfactant concentrations in the two coexisting phases are both rather dilute. The volume ratios of the upper to lower phase are about 0.6 and 1 at 25°C for 20 mMC8NEt3. C i o S O 4 and 12 mMC8NEt3- C 1 2 S 0 4 , respectively. These two phases are all clear, and the upper one has a slightly bluish tint, which means that the particle size in it is larger than in the lower phase. The scattered light intensity ratio of the upper to the lower phase in the 20 m M C8NEt3 • CxoSO4 solution is 3.3, and the reduced intensity of the upper phase is about 4.4 × 10 -3 cm -1 at 0 = 90 °. Rh in the lower phase is about 1000 A and in the upper phase it cannot be obtained by the cumulant method since the correlation function decays very (D) Thermodynamical Description of the slowly in the long correlation time range which Micelle Growth might be induced by a serious overlapping of the particles or by the nontranslational motion Missel et al. (21 ) have proposed a "ladder of the particles. When the concentration is be- model" to describe the sphere-to-rod transition Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
427
PROPERTIES OF AQUEOUS MIXTURES, II
(24). The ladder model has successfully described the experimental results of micelle growth for single ionic surfactant systems (21, 22). Later, this model is improved by Porte and Apell (23). In the ladder model, it is assumed that the chemical potential associated with a monomer in a micelle is simply a function of the area per molecule at the surface of the micelle. Thus, the energy advantage associated with transferring a monomer from the solvent into the cylindrical region of the micelle can be represented with ladder spacings. In our cationic-anionic surfactant mixtures, the energy advantage in transferring cationic surface active ions is different from that of anionic surface active ions. Thus the ladder model cannot be applied to the mixed surfactant systems in its original form. For mixed micelle of ionic and nonionic surfactants (25), the composition may be asymmetric between the spherical and cylindrical regions. This is because the relief of electrostatic strain is more pronounced in regions of high charge density. In our mixed cationic-anionic surfactant systems, however, the micelle is essentially electrically neutral due to the strong coulombic interaction between the oppositely charged surface active ions. As a first approximation, therefore, the effect of the composition asymmetry arising from high charge density could be neglected in the case of mixed cationicanionic surfactant systems with a very low charge density. Under the assumption of a constant micellar composition between the spherical and cylindrical regions, we extend this sphere-to-rod model to the mixed micelles of cationic-anionic surfactant systems (see the Appendix). Figures 4a and 4b are the plots of log K versus 1/ T for the corresponding mol wt vs T data of Fig. 1 for CsNEt3-CsSO4 and C8NEt3. C10SO4, respectively, where K is a parameter which measures the tendency for no moles of surfactants to transform from the hemisphere part to the cylindrical part of the micelles (see Eq. [ A6 ] in the Appendix). The procedure for calculation of K value from the experimental results is similar to that described
in the literature (21 ): a theoretical curve of mol wt vs K ( X - XA+ -- XA_) was calculated from Eqs. [A7], [A9], and [A10], where X is the mole fraction of the total surfactants in solution, XA+ and XA_ are the mole fraction of cationic and anionic surfactants monomers, respectively, equilibrated with micelles; K ( X - XA+ -- XA_) was obtained from the experimental data of mol wt and the theoretical curve; then, K value was determined from K(X XA+ - XA_) assuming that the XA+ and XA_ were approximately equal to cmc value. We also calculated the values ofln K from the -
9.O a
8.5 1
8°0
7.5
I 3.1
I 3.2
I
I
3.3
3.4
IO00/T
b of
12
4
1
11 ~4 ~ o
,.4
10
9
I
I 3.1
I
I 3.3
I 3.5
1000/T
FIG. 4. (a) Plots of log K versus 1/ T obtained from the experimental data in Fig. la and the sphere-to-rod model. The concentrations ofCsNEt3. C8SO4 in curves 1 to 5 are 20, 25, 30, 40, and 50 mM, respectively. (b) Plots of log Kversus 1/ T obtained from the experimental data in Fig. lb and the sphere-to-rod model. The concentrations of CsNEt3. CIoSO4 in curves 1 to 6 are 4, 6, 8.2, 11.3, 13.5, and 15.9 mM, respectively. Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
428
YU AND ZHAO
experimental data of Rh of the C8NEt3 • CsSO 4 system at the same conditions as in Ref. (12) using Eq. [27] in Ref. (21) along with Eqs. [ A T ] and [A9]. The results are the same as those in Fig. 4a within the experimental error. To estimate the aggregation number of the minimal sphere of C8NEt3. C10SO4, the volume of a hydrophobic chain in micelles is taken as the arithmetic mean of the two chains of different length and the radius of the micelle sphere is determined by the longer chain (22). From Fig. 4 it can be seen that the plots of log K vs 1/ T of both systems are dependent on the surfactant concentration. This could be interpreted as follows. The micelles are charged due to the fact that the two surface active ions in micelles are not entirely equimolar at the beginning of micelle formation ( ~ c m c ) . The molar ratios of CsNEt3 to CnSO4 in the micelles at cmc are 0.8 and 0.71 for n = 8 and 10, respectively (16). Obviously, these ratios will approach one with the increasing total surfactant concentration. The enthalpy change AH ° in the process of the sphere-to-rod transition can be divided into an electrical part AHe~ and a nonelectrical part. The former is a factor against the sphereto-rod transition and increases with the charge density on the micelle surface. Thus, the parameter K increases with the total surfactant concentration as shown in Fig. 4. From equation [A6] we can obtain In K
AH °
AS °
no
RT
R + (al - aE)ln CB,
[3]
where AS ° is the entropy change in sphereto-rod transition. The third term on the right side of Eq. [3 ] can be neglected since the micelles are essentially neutral in our systems. Thus In K .
.
no
.
.
AH °
AS °
RT
R
[4]
Figure 4a shows that the plots of log K vs 1 / T of the Cs NEt3. C8 SO4 system are linear and the variation of log K with the surfactant conJournal of Colloid and Interface Science, Vol. t 30, No. 2, July 1989
centration is rather small (less than 4% in the concentration range from 20 to 50 m M ) . The average A H ° and AS ° values obtained by fitting the plot of log K vs 1 / T to Eq. [4 ] are - 2 . 2 5 + 0.07 k J - m o l e -1 and - 1 . 6 + 0.4 J . K - l - m o l e -~, respectively, which means that the driving force in the micelle growth is the enthalpy reduction. The plots of log K vs 1 / T o f C s N E t 3 • CloSO4 in Fig. 4b are nonlinear, which makes the analysis of the micelle growth using the sphere-to-rod model very difficult.
(E) Comparison with Other Ionic Surfactant Systems Many micelle solutions of ionic surfactants with organic counterions have a property of viscoelasticity (8-11 ). Some authors suggested that the viscoelasticity is induced by the existence of rodlike micelles ( 11 ). Hoffmann et al. found that some similar systems do not have such a property (7). In our present systems it is shown that the overlapping of rods in the homogeneous micelle solution does not induce such viscoelasticity, and the viscoelasticity is observed in the heterogeneous (apparently homogeneous) solution in the vicinity of the critical phase separation concentration before the phase separation occurs. It seems that the instability of solutions are responsible for the viscoelastical property of surfactant systems. Micelle size for ionic surfactants with organic counter ions are often going through a peak with increasing micellar concentration (7, 12). It is indicated (7) that the growth of micelles slows down and finally reverses itself when the rotational volumes of the rodlike micelles begin to overlap. In our present systems, the length of the rodlike micelles are longer and the overlapping of rods is more serious than those in the above mentioned systems. But the growth pattern of micelles is quite different: the rate of micelle growth is increased with micelle concentration in present systems. This proves that the overlapping of rods cannot prevent micelles from growing.
429
PROPERTIES OF A Q U E O U S MIXTURES, II
Table I compares the thermodynamical parameters in the sphere-to-rod transition of our present systems with those in the literature ( 14, 22). It seems that the entropy change of C8NEt3 • C8 SO4 is essentially the same as that of the single ionic surfactant systems, but the enthalpy change is twice as large. We suggest that the larger change of enthalpy in the cationic-anionic surfactant system than in ionic surfactant systems is due to the lower charge density on the micelle surface and consequently the lower value of AHg~ in the sphereto-rod transition. It seems, generally, from Table I, that the enthalpy reducing is a driving force for micelle growth of all ionic surfactant systems. CONCLUSIONS
1. Equimolar mixtures of C8NEt3Br and CnSOaNa form micelles in aqueous solutions in rather wide ranges of temperature and concentration. The micelles become larger as the surfactant concentration increases, the temperature decreases, and the total hydrophobic chain length increases. The overlapping of the rodlike micelles does not inhibit the micelle from growing.
centration or by decreasing the temperature, a new liquid phase separates from the solution. This new phase is still a rather dilute aqueous surfactant solution, the surfactant concentration of which could be less than 1.2%. This unusual phenomenon may be interpreted as the formation of the flocculated micelle solution. 4. The "ladder model" proposed by Missel et al. is adapted to the mixed micelles of cationic-anionic surfactant systems. The enthalpy and entropy change in the sphere-torod transition process are deduced for C8NEt3. C8SO4 system. The parameter K, which describes the tendency of micelle growth, increases with the surfactant concentration, which may be interpreted in terms of the change of the ratio of cationic to anionic surfactant in the micelles with concentration.
APPENDIX THERMODYNAMIC
ANALYSIS OF THE
GROWTH OF THE MIXED MICELLES OF CATIONIC-ANIONIC
SURFACTANTS
The mixed micelles consist of cationic surfactant ions A+, anionic surfactant ions A_ 2. C 8 N E t 3 " C 1 0 S O 4 and C 8 N E t 3 . C 1 2 S O 4 and counterinorganic ions B. The micelle Cn, could form giant micelles, and the shape of where n is the aggregation number, is in equithe micelles are semiflexible rods when the ralibrium with A+, A_, and B in aqueous sodius of gyration of the micelles is beyond 400lution: 500 A. All micelles are rigid rods when the radius of gyration is less than 400 ~ (or the nyA+ + n ( 1 - y ) A _ + a n B = C,, [A1] hydrodynamic radius is less than 200 A). where y is the mole fraction of A+ in the mi3. At the limit of micelle growth which is celles on the two component A+ and A_ basis, reached either by increasing the micelle cona is the molar ratio of B bound on the micelle surface to the total surfactants in micelles. AcTABLE I cording to the condition of chemical equilibA H ° and AS ° Values in the Sphere-to-Rod Transition rium for Different Systems
/~, = n (y/XA+ + ( 1 -- y) t~A_ + a#B),
Systems
A H ° (kJ-mole -~)
A S ° (J. mole -I K -t)
CsNEt3.CsSO4 TPB a CPB b
- 2 . 2 5 _+ 0.07 - 1 . 0 7 _+ 0.04 - 1 . 1 7 + 0.08
- 1 . 6 -+ 0.4 - 1 . 2 5 + 0.1 - 1 . 4 6 +_ 0.08
a Ref. (14). b Ref. (23).
[ A2 ]
where/~n is the chemical potential of the micelle with an aggregation number n, and gh+, #h_, and ~B are the chemical potentials of the relevant monomer in the aqueous solution, respectively. In the case of dilute solutions, Journal of Colloid andlntetface Science. Vol. t30, No. 2, July 1989
430
YU AND ZHAO with Eq. [A5], we obtain the contribution function of the micelles
#~ = #O + R T ln Xn o
#A+
#A+ + R T In XA+
[A7]
X, = Qn/K. #a_ = #~_ + R T l n X A _
F r o m the conservation of matter,
#B = # ~ + R T In XB,
[A3
]
where the Xn, XA+, XA_, and XB are the mole fractions of the corresponding species denoted by the subscripts and the superscript zero represents the standard state. On inserting Eq. [A3] into Eq. [A2] RTlnXn
[A8]
Inserting Eq. [A7] into Eq. [A8] K(X
-
XA+ -- XA_ )
[A4]
Assuming the ratio of cationic to anionic surfactant is the same at the hemisphere part as at the cylindrical part of the rodlike micelles, from Missel's ladder model (21 ) we have o #no ÷
(/'/ - -
[A5]
# o _ n ( y # ~ + + (1 - y ) # ~ _ + aUB)
= RTln
K = #,o
o0
no)
where #~ and #2 are the standard chemical potential of cationic and anionic surface active ions in the cylindrical part of the micelles, respectively; # ~o and no are the standard chemical potential and the aggregation n u m b e r of the minimal spherical micelle, respectively. L e t / t ° = y # ~ + (1 - y)#O. F r o m Eq. [A5], the first term on the right-hand side of Eq. [A4] can be expressed as
0
F r o m Eq. [A9] and Eq. [A7] we obtain the X. as a function of K ( X - XA+ -- XA_) and no. Thus the micelle weight averaged micelle weight mol wt can be calculated m
X(y#~+(1-y)#2),
RTln
nX,.
n=?/O
= _ ( # o _ n(y#~+ + (1 - y)#~_
+ cqzB)) + nRTln(X~+X~-__Y).
o JAn =
oo
X = XA+ + XA- + Z
--
K+
n R T l n K1
no(# ° + ( a l - a2)#B)
R T In/£1 = #o
-(y#~++(1-y)#~_)-a2#B,
[A6]
where al and a2 are the ratios of the n u m b e r of B to the n u m b e r of the surfactant in the hemisphere and cylindrical parts of the micelle, respectively; K is a parameter which measures the tendency for no moles of surface active ions to transform from the spherical part to the cylindrical part of the micelles. Let Q = ( x Y + x ~ - Y ) / K l . On combining Eq. [A6] J o u r n a l o f C o l l o i d a n d Interface Science,
Vol. 130, No. 2, July 1989
tool wt -
Y~ n2Xn
o~
,
[AIO]
nXn n=Ho
where m is the average molecular weight of the two kinds of surfactants in the micelles. REFERENCES 1. Mittal, K. L., and Lindman, B., "Surfactants in Solution." Plenum Press, New York, 1984. 2. Mazer, N. A., Benedek, G. B., and Carey, M. C., J. Phys. Chem. 80, 1076 (1976). 3. Appell,J., and Porte, G., J. Colloidlnterface Sci. 81, 85 (1981). 4. Corti, M., and Degiorgio, V., J. Phys. Chem. 85, 711 (1981). 5. Rohde, A., and Saekmann, E., J. Colloid Interface Sci. 70, 494 (1979). 6. Dorshow, R., Briggs, J., Bunton, C. A., and Nicoli, D. F., J. Phys. Chem. 86, 2388 (1982). 7. Hoffmann, H., Rehage, H., Platz, G., Schorr, W., Thurn, H., and Ulbrieht, W., Colloid Polym. Sci. 260, 1042 (1982). 8. Hoffmann, H., Platz, G., Rehage, H., and Sehorr, W., Adv. Colloid Interface Sci. 17, 275 (1982). 9. Angel, M., Hoffman, H., Lobl, M., Reizlein, K., Thurn, H., and Wunderlich, I., Prog. Colloid Polym. Sci. 69, 12 (1984). 10. Ulmius, J., Wennerstrom, H., Johansson, L. B. A., Lindblom, G., and Gravshoit, S., J. Phys. Chem. 83, 2232 (1979).
PROPERTIES OF AQUEOUS MIXTURES, II 11. Barker, C. A., Saul, D., Tiddy, G. J. T., Wheeler, B. A., and Willis, E., J. Chem. Soc. Faraday Trans. 170, 154 (1974). 12. Yu, Z.-J., and Zhao, G.-X., J. Colloid Interface Sci. 130, 414-420 (1989). 13. Hoyer, H. W., and Doerr, I. L., J. Phys. Chem. 68, 3494 (1964). 14. Zhou, Z.-K., and Yu, Z.-J., Acta Phys. Chim. Sinica 1, 141 (1985). 15. Ozeki, S., and Ikeda, S., ColloidPolym. Sci. 262, 409 (1984). 16. Yu, Z.-J., Doctoral thesis, Peking University, 1987. 17. Flamberg, A., and Pecora, R., J. Phys. Chem. 88, 3026 (1984). 18. Sande, W. V. D., and Persoons, A., Y. Phys. Chem. 89, 404 (1985).
431
19. Porte, G., Appell, J., and Poggl, Y., aT. Phys. Chem. 84, 3105 (1980). 20. Verwey, E. J. W., and Overbeek, J. T. G., "Theory of the Stability of Lyophobic Colloids." Elsevier, New York, 1948. 21. Missel, P. J., Mazer, N. A., Benedek, G. B., Young, C. Y., and Carey, M. C., J. Phys. Chem. 84, 1044 (1980). 22. Missel, P. J., Mazer, N. A., Benedek, G. B., and Carey, M. C., J. Phys. Chem. 87, 1264(1983). 23. Porte, G., and Appell, J., J. Phys. Chem. 85, 2511 (1981). 24. Mukerjee, P., J. Phys. Chem. 76, 565 (1972). 25. Gelbart, W. M., McMullen, W. E., Masters, A., and Ben-shaul, A., Langmuir 1, 101 (1985).
Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
In the last decade many investigations have been carried out on micellar dimensions and structures by light scattering technique (1). Most of the micellar systems studied contained a single ionic surfactant. The interpretation of the experimental results is often complicated by the fact that there always exist intermicellar interactions. Two paths have been adopted to overcome this difficulty. One is to carry on the experiments under the conditions of high ionic strength to screen the electrostatic interaction between charged micelles. At high ionic strengths, micelles have the shape of a rod or a semiflexible rod (2, 3). The other is to use low ionic strengths and low micelle concentrations, assuming that in such cases the electrostatic interactions between ionized micelles are the predominant effect on micelle diffusion and the micelle shapes are minimal spheres i To whom correspondence should be addressed.
( 4 - 6 ) . T h e latter m e t h o d c a n o n l y be used to o b t a i n the micelle size at cmc. Recently, t h e r e a l m o f investigation o f m i celle systems has b e e n enlarged to i n v o l v e the systems c o n t a i n i n g i o n i c surfactants with organic c o u n t e r i o n s (7, 9). In such systems, large micelles u s u a l l y f o r m with the size increasing with c o n c e n t r a t i o n initially, going t h r o u g h a m a x i m u m a n d t h e n decreasing. Investigators in these studies believe t h a t the o v e r l a p p i n g o f the rodlike micelles m a y be responsible for this p h e n o m e n o n . A n o t h e r feature o f these syst e m s is t h a t s o m e o f t h e m have viscoelastic p r o p e r t i e s ( 8-1 1 ), while others have n o t ( 7 ) . H o w e v e r , no clear e x p l a n a t i o n has b e e n given for all a b o v e m e n t i o n e d e x p e r i m e n t a l results. The study of mixtures of cationic-anionic surfactants is o f great i m p o r t a n c e b o t h practically a n d theoretically. U n f o r t u n a t e l y , such systems usually f o r m opalescent mixtures with a n e m u l s i o n n a t u r e ( 12, 13 ). P r e v i o u s l y ( 1 2 ) , we h a v e o b t a i n e d the m i x e d s o l u t i o n o f oct y l t r i e t h y l a m m o n i u m b r o m i d e - s o d i u m oc-
421 0021-9797/89 $3.00 Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
Copyright © 1989 by Academic Press, Inc. All fights of reproduction in any form reserved.
422
YU AND ZHAO
tylsulfate which forms a transparent micelle solution. In this paper, we will systematically investigate the micellar properties of the aqueous solutions of the equimolar mixtures of octyltriethylammonium bromide-sodium alkylsulfate. For such mixed cationic-anionic surfactant systems, the low charge density on the micelle surface may be expected due to the neutralization of the two oppositely charged surfactant ions, which may simplify the analysis of the experimental results. EXPERIMENTAL
The octyltriethylammonium bromide (C8NEt3Br) and the sodium octyl-, decyl-, and dodecyl-sulfate (C8_12SO4Na) are the same as used previously (12). Stock solutions of the octyltriethylammonium alkylsulfate (C8 NEt3- CnSO4, n = 8, 10, and 12) were obtained by mixing equimolar proportions of the corresponding long chain compounds. In order to provide a constant ionic strength and, consequently, to simplify the interpretation of the experimental results, the total concentration of NaBr was kept at 0.1 M by adding NaBr. The solutions of various concentrations of C8NEt3 ° CnSO 4 were obtained from stock solutions by dilution with the 0.1 M NaBr. The experimental set-up for dynamic and static light scattering and the procedure for determining the apparent hydrodynamic radius of the micelles Rh are the same as in the previous works ( 12, 14). The detected relative intensity at a given scattering angle 0 was converted into reduced intensity R (0) by using a reference intensity scattered from a carefully prepared benzene sample under the same conditions, and the influence of the difference of refractive index between aqueous solution and benzene on calculating R(O) has been corrected. The refractive index increment dn/ dc was determined with the differential refractometer (RF Model 600) with its original light source replaced by a 632.8-nm wavelength He-Ne gas laser beam. The micellar weight averaged molecular weight (mol wt) (apparent) and the average radius of gyration Journal of Colloid and Interface Science, VUl. 130,No. 2, July 1989
of micelles Rg (apparent) were calculated from the Debye equation ( 15 ), assuming the intermicellar interaction is negligible in our case
K'(c - cmc) R(O) - R°(O) ×
1 mol wt
( 1 6 7 r 2 n 2 R 2 g sin20 1+
)
,
[11
where R ° (0) is the reduced intensity at the critical micelle formation concentration cmc, c is the total concentration of the surfactants, n is the refractive index of the solvent (or of the solution at cmc), )~o is the wavelength of the incident beam in vacuum, and K' is the optical constant
K' = 4r2n2(dn/dc)2Xo4NT, l,
[2]
where NA is the Avogadro number. RESULTS AND DISCUSSION
(A ) Influence of Micellar Concentration, Temperature, and Chain Length on Micelle Size Figures la and lb show the dependence of micelle molecular weight (apparent) upon the concentrations of C8NEt3"C8SO4 and CsNEt3.C10SO4, respectively, at various temperatures from 20 to 55°C. Figure lc shows the relationship between Rh and the concentration of CsNEt3. C 1 2 8 0 4 at various temperatures from 45 to 65°C. The NaBr concentration is kept at 0.1 Mfor all solutions in order to screen the possible charge on the micelle surface which may exist owing to the different surface activities between C8NEt3 Br and CnSO4Na. The cmc values used in calculating mol wt are 8.13, 2.09, and 0.427 m M for C8NEt3- C8SO4, C8NEt3. C l o 8 0 4 , and C8NEt3" C12SO4 systems, respectively ( 16 ). Mol wt (and Rg) is obtained by fitting the linear part of the K'(c-cmc)/(R(O) - R°(O)) versus sin2(0/2) curves to Eq. [1 ]. Every Rh value was obtained by measuring scattered intensifies at several scattering angles from 0 = 90 ° to 30 °. The measured Rh is independent of 0 when Rh < 300 A. In the range of 300
PROPERTIES OF AQUEOUS MIXTURES, II < Rh < 800 ~, the Rh versus sin2(0/2) curves are straight lines with small negative slopes (less than 10%). In this case, Rh is obtained by linear extrapolation to the zero scattering angle. In the range of 800-1200 A, Rh increases with the decrease of sin 2(0/ 2) rather dramatically. Beyond 1200 ,~, the curves Of Rh versus sinZ(0/2) are no longer linear. Generally, there are three factors responsible for the dependence Of Rh on 0. One is the dust contaminant which may exist in the samples. But the effect of the dust on Rh should be stronger for small particles, which is not our case. Thus this factor can be ruled out. The second factor is the polydispersity of the micelles. The variance in the systems deduced from the second cumulant is less than 0.2, which will probably not induce such strong dependence of Rh on 0 as in the case of large values ofRn. The third one is the existence of other forms of motions in addition to the translational motion for nonspherical micelles (17). The influence of the latter two factors on Rh may be excluded by extrapolating to zero scattering angle. The diffusive motion of the rodlike micelles will be influenced by the overlapping of the micelles. The larger the micellar dimension is, the more seriously the Rh value is affected. Considering this point, we will not plot Rh larger than 800 ~, in this paper. The equimolar mixtures of CsNEt3. CnSO4 have very low Krafft points (their aqueous solutions do not form precipitate or crystal in the temperature range above 4°C). But the correlation functions of the micelle solutions of C8NEt3-C12804 in the concentration range studied have a very slow decay in the long correlation time range in addition to the fast one in the initial correlation time range when the temperature of solutions is below 45 °C, which makes the cumulant method for data analysis invalid. Figure 1 indicates that the micelle size (mol wt or Rh) increases monotonically with surfactant concentration at a fixed temperature or with the lowering temperature at the fixed surfactant concentration. This increase is more
423
rapid as the total hydrophobic chain length becomes longer. At a fixed micellar concentration and temperature, the micelle size increases with the chain length. For example, Rh is 39 A (Ref. (12), Fig. 3), 132 A (Fig. 3), and 790 A for C8NEt3.C8SO4, C8NEt3. CloSO4, and C8NEt3-C12SO4, respectively, at the micelle concentration (c-cmc) of 10 m M at 55°C. Figures lb and lc also show some striking characteristics of the systems of C8NEt3. CloSO4 and C8NEt3. C12SO4. The rate of change of the micelle size increases with the concentration and the surfactants form giant micelles which are larger than any reported in the literature. Solutions become turbid when micelle size becomes sufficiently large as the result of concentration increase. The solutions of C8NEt3. C8SO4 contain relatively small micelles and are all homogeneous and clear in the concentration range studied.
(B) Micellar Shapes Figure 2a is the plot o f m o l wt/Rh as a function of Rh for C8 NEt3 ° C8 SO4 together with a series of the theoretical predictions for geometric models of spheres, rigid rods, and oblate ellipsoids. The formulae for calculating the theoretical curves are the same as in Ref. (18). The experimental data are taken from Fig. 3 in Ref. (12) and Fig. 1a at various temperature and micelle concentrations. Figures 2b and 2c are the experimental data of mol wt in Fig. 1 and Rg at various temperatures and various micelle concentrations compared with the theoretical curves of spheres, oblate ellipsoids, rigid rods, and semiflexible rods for CsNEt3- C10804 and CsNEt3" C12804. The formulae used for calculating the theoretical curves are also taken from Ref. (18). Those experimental data of Rg beyond 800 A are not plotted since the initial range of sin2(0/2) of the linear part of the K'(c-cmc)/(R(O) R ° (0)) vs sin 2( 0 / 2 ) curve becomes small when the value of Rg is large and thus the values of Rg calculated from Eq. ( 1 ) by neglecting the higher order terms become less accurate. The partial volume of the micelle used in con-
Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
424
YU AND ZHAO
I oi"
6O 7
40
o 2O
4 5
I
I
t
I
20
30
4o
50
~
600 j¼ %
4o0
4
/ 200
i
5 lO CsNCIoS ( mM )
15
8OO
o•
C
/0/3
600
400 / o / / / 200
//o
~ J
verting mol wt into micellar volume is taken approximately as 1 cm 3 g-l. The cross sectional radius of rods, the semiminor axis of oblate ellipsoids, and the radius of minimal sphere are estimated to be 17.3, 19.8, and 22.3 A for C8NEt3. C8804, C8NEt3- C10SO4, and CsNEt3, C12804, respectively, which are the fully extended lengths of the longer hydrophobic chain length molecules (i.e., alkylsulfate) plus the binding layer of water and inorganic counterions of approximately 2 A which is consistent with our earlier experimental result (14). From Fig. 2 it can be seen that the experimental data are in good agreement with the theoretical curves of rigid rods and well deviated from the theoretical curves of sphere and oblate ellipsoid when Rh < 200 A or Rg < 400-500 A; i.e., for the experimental range of the micelle concentration and temperature, the micelle shapes are all rigid rods for CsNEt3" C8 SO4. For larger micelles the agreement of experimental data with the theoretical predictions for a rigid rod is no longer maintained. Figures 2b and 2c show that in the case of large micelles the data fit the theoretical curves for semiflexible rods with persistence lengths (18, 19) equal to 370 and 750 A for CsNEt3-Cx0SO4 and CsNEt3"C12SO4, respectively. It seems that the flexibility increases with the decrease of the cross sectional radius of rods. From the above we can conclude that the small micelles (Rh < 200 A or Rg < 400500 A) are rigid rodlike and the large micelles (Rg > 400-500 A) are semiflexible rodlike for all three systems.
(C) The Coexistence of the Two Dilute Aqueous Phases
io 4
8
12
FIG. 1. (a) The micelle molecularweight, mol wt, as a function of the surfactant concentration for the solutions of CsNE%. CsSO4with 0.1 M NaBr. The temperatures of curves 1 to 5 are 20, 25, 35, 45, and 55°C, respectively. (b) The micelle tool wt as a function of the surfaetant concentration for the solutions of CsNEt3.C10SO4with Journal of Colloid and Interface Science. Vol. 130, No. 2, July 1989
The separation of two aqueous phases occurs in the solution of high surfactant concen0.1 M NaBr. The temperatures for curves 1 to 6 are 20, 25, 30, 35, 45, and 55°C, respectively. (c) The miceUe hydrodynamic radius Rh as a function of the surfactant concentration for solutions of CsNEh. C~2SO4with 0.1 M NaBr. The temperatures of curves 1 to 4 are 45, 50, 55, and 65°C, respectively.
PROPERTIES OF AQUEOUS MIXTURES, II
/
6
4
% 2
I 50
I IO0
l 150
b
200
/
I
400
300
C. 200
/4
-/
lO0
2O0
(~)
4OO
ag
GO0
8O0
3 400
"i
o
~I 300
~
200
100
20O
400
600
800
ag (2) FIG. 2. (a) mo1 wt/Rh versus Rh. (O) Experimental data of micelle solutions of CsNEt3. Cs SO4 taken from Fig. 3 in Ref. (12) and Fig. la; the curves l, 2, and 3 are theoretical predictions for spheres, oblate ellipsoids, and rigid rods, respectively.(b) The plot of tool wt versus radius of gyration Rg. (O) The experimental data of the micelle solutions of CsNEt3. C1oSO4 at various surfactant concentrations and temperatures with 0.1 MNaBr; the curves l to 4 are theoretical predictions for spheres, oblate ellipsoids, semiflexihle rods with the persistence length of 370 /~, and rigid rods, respectively. (c) The plot of mol wt
425
tration range. W h e n sufficient a m o u n t s o f equimolar C s N E t 3 B r and Cl0SO4Na or CIzSO4Na are brought together, an opalescent solution formed. Soon, numerous, oily droplets could be seen in the mixtures with the naked eye. The small spheres coalesced to f o r m large ones and eventually fused to f o r m a new liquid phase. Dilution o f this solution decreases the rate o f phase separation. At a concentration slightly larger than that o f the critical phase separation, the solution is very viscous a n d viscoelastic but still transparent in appearance like a genuinely h o m o g e n e o u s solution. The viscoelastical solutions separate into two transparent aqueous phases u p o n standing for 1 or 2 days. The critical phase separation concentrations are 18 and 10 m M for CsNEt3 • C10SO4 and CsNEt3 • C12 SO4, respectively, in 0.1 M N a B r solution, 25°C. Figures 1b a n d 1c show that the micelle size increases with the increase o f the surfactant concentration. At the limit o f micelle growth, a solution becomes turbid on initial preparation a n d separates into two transparent aqueous phases to reach its equilibrium state. The phase separation p h e n o m e n o n can also be observed by lowering the temperature o f a solution. Figure 3 shows the dependence Of Rh o n the temperature for C s N E t 3 . C10SO4 solutions o f various concentrations. At r o o m temperature, the solutions o f CsNEt3 • C10SO4 form two transparent liquid phases with a clear phase b o u n d a r y between t h e m when the total concentration is above 18 m M . These heterogeneous solutions b e c o m e h o m o g e n e o u s u p o n heating, and the critical h o m o g e n e o u s solution formation temperatures are dependent on concentration. For example, they are 35.5 a n d 2 0 ° C for concentrations o f 20 and 18 m M , respectively. Above the critical temperature, the solutions show the properties o f
versus Rg. (O) The experimental data of the micelle solutions of CsNEt3. C 1 2 8 0 4 at various surfactant concentrations and temperatures with 0.1 M NaBr; the curves 1 to 4 are theoretical predictions for spheres, oblate ellipsoids, semiflexible rods with the persistence length of 750 A, and rigid rods, respectively. Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
426
YU AND ZHAO
8O0 .~
60o
4 5 ~
6~i"¢~~o8
3~'~ \ / i ~ ~ ~~
;400
I
I
I
30
I
I
50
70
(*o) FIG.3. The dependenceOfRhon temperatureat various surfactant concentrationsof CsNEt3.C10SO4 and at 0.1 MNaBr. The concentrationsin curves 1to 8 are 4, 6, 8.2, 11.3, 13.5, 15.9, 18, and 20 raM, respectively.
yond 50 mM, the scattering intensity of the lower phase approaches that of pure solvent, indicating only a negligible quantity of micelles in the phase. The above phenomena could be still observed after the solution stands for one year. In conclusion, the upper layer is the surfactant rich phase, but both upper and lower phases are still dilute solutions. The concentration of the upper phase could be less than 2.4 and 1.2% for CsNEt3"C10SO4 and C8NEt3-C12SO4, respectively, if we suppose that the surfactants are all in this phase. The phase separation phenomenon may be interpreted in terms of flocculated micelles phase formation. According to the DLVO theory of colloid stability (20), the interparticle interaction potential consists of a hardsphere repulsive part, an electrostatic longrange repulsion, and a London-van der Waals attraction. If the attraction is larger than the electrical repulsion, a second minimum occurs in the potential curve. The depth of the minimum increases linearly with the increase of particle size for spheres or plates. In the case of semiflexible rods, the calculation of the interparticle potential might be very complex. We suppose that the above qualitative conclusion still holds; i.e., the depth of the second minimum increases with the size of micelles. If the micelles are sufficiently large, the potential minimum will be deep enough to prevent the micelles in the minimum position from leaving by the thermal motion. Thus the micelle flocculation occurs and the flocculated micelle solution phase separates. If the flocculation occurs at the second minimum rather than at the first one, the phase separation phenomenon must be reversible. The experimental results show that the phase separation always occurs at the limit of the micelle growth and the process is reversible by changing either the micelle concentration or the temperature, which is in line with the above analysis.
the normal homogeneous micelle solutions; i.e., the solution is in its equilibrium state and the particle size decreases with temperature in the same way as in normal micelle solutions. It can thus be concluded that the phase separation occurs at the limit of micelle growth with either increase of miceUe concentration or decrease of temperature. The surfactant concentrations in the two coexisting phases are both rather dilute. The volume ratios of the upper to lower phase are about 0.6 and 1 at 25°C for 20 mMC8NEt3. C i o S O 4 and 12 mMC8NEt3- C 1 2 S 0 4 , respectively. These two phases are all clear, and the upper one has a slightly bluish tint, which means that the particle size in it is larger than in the lower phase. The scattered light intensity ratio of the upper to the lower phase in the 20 m M C8NEt3 • CxoSO4 solution is 3.3, and the reduced intensity of the upper phase is about 4.4 × 10 -3 cm -1 at 0 = 90 °. Rh in the lower phase is about 1000 A and in the upper phase it cannot be obtained by the cumulant method since the correlation function decays very (D) Thermodynamical Description of the slowly in the long correlation time range which Micelle Growth might be induced by a serious overlapping of the particles or by the nontranslational motion Missel et al. (21 ) have proposed a "ladder of the particles. When the concentration is be- model" to describe the sphere-to-rod transition Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
427
PROPERTIES OF AQUEOUS MIXTURES, II
(24). The ladder model has successfully described the experimental results of micelle growth for single ionic surfactant systems (21, 22). Later, this model is improved by Porte and Apell (23). In the ladder model, it is assumed that the chemical potential associated with a monomer in a micelle is simply a function of the area per molecule at the surface of the micelle. Thus, the energy advantage associated with transferring a monomer from the solvent into the cylindrical region of the micelle can be represented with ladder spacings. In our cationic-anionic surfactant mixtures, the energy advantage in transferring cationic surface active ions is different from that of anionic surface active ions. Thus the ladder model cannot be applied to the mixed surfactant systems in its original form. For mixed micelle of ionic and nonionic surfactants (25), the composition may be asymmetric between the spherical and cylindrical regions. This is because the relief of electrostatic strain is more pronounced in regions of high charge density. In our mixed cationic-anionic surfactant systems, however, the micelle is essentially electrically neutral due to the strong coulombic interaction between the oppositely charged surface active ions. As a first approximation, therefore, the effect of the composition asymmetry arising from high charge density could be neglected in the case of mixed cationicanionic surfactant systems with a very low charge density. Under the assumption of a constant micellar composition between the spherical and cylindrical regions, we extend this sphere-to-rod model to the mixed micelles of cationic-anionic surfactant systems (see the Appendix). Figures 4a and 4b are the plots of log K versus 1/ T for the corresponding mol wt vs T data of Fig. 1 for CsNEt3-CsSO4 and C8NEt3. C10SO4, respectively, where K is a parameter which measures the tendency for no moles of surfactants to transform from the hemisphere part to the cylindrical part of the micelles (see Eq. [ A6 ] in the Appendix). The procedure for calculation of K value from the experimental results is similar to that described
in the literature (21 ): a theoretical curve of mol wt vs K ( X - XA+ -- XA_) was calculated from Eqs. [A7], [A9], and [A10], where X is the mole fraction of the total surfactants in solution, XA+ and XA_ are the mole fraction of cationic and anionic surfactants monomers, respectively, equilibrated with micelles; K ( X - XA+ -- XA_) was obtained from the experimental data of mol wt and the theoretical curve; then, K value was determined from K(X XA+ - XA_) assuming that the XA+ and XA_ were approximately equal to cmc value. We also calculated the values ofln K from the -
9.O a
8.5 1
8°0
7.5
I 3.1
I 3.2
I
I
3.3
3.4
IO00/T
b of
12
4
1
11 ~4 ~ o
,.4
10
9
I
I 3.1
I
I 3.3
I 3.5
1000/T
FIG. 4. (a) Plots of log K versus 1/ T obtained from the experimental data in Fig. la and the sphere-to-rod model. The concentrations ofCsNEt3. C8SO4 in curves 1 to 5 are 20, 25, 30, 40, and 50 mM, respectively. (b) Plots of log Kversus 1/ T obtained from the experimental data in Fig. lb and the sphere-to-rod model. The concentrations of CsNEt3. CIoSO4 in curves 1 to 6 are 4, 6, 8.2, 11.3, 13.5, and 15.9 mM, respectively. Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989
428
YU AND ZHAO
experimental data of Rh of the C8NEt3 • CsSO 4 system at the same conditions as in Ref. (12) using Eq. [27] in Ref. (21) along with Eqs. [ A T ] and [A9]. The results are the same as those in Fig. 4a within the experimental error. To estimate the aggregation number of the minimal sphere of C8NEt3. C10SO4, the volume of a hydrophobic chain in micelles is taken as the arithmetic mean of the two chains of different length and the radius of the micelle sphere is determined by the longer chain (22). From Fig. 4 it can be seen that the plots of log K vs 1/ T of both systems are dependent on the surfactant concentration. This could be interpreted as follows. The micelles are charged due to the fact that the two surface active ions in micelles are not entirely equimolar at the beginning of micelle formation ( ~ c m c ) . The molar ratios of CsNEt3 to CnSO4 in the micelles at cmc are 0.8 and 0.71 for n = 8 and 10, respectively (16). Obviously, these ratios will approach one with the increasing total surfactant concentration. The enthalpy change AH ° in the process of the sphere-to-rod transition can be divided into an electrical part AHe~ and a nonelectrical part. The former is a factor against the sphereto-rod transition and increases with the charge density on the micelle surface. Thus, the parameter K increases with the total surfactant concentration as shown in Fig. 4. From equation [A6] we can obtain In K
AH °
AS °
no
RT
R + (al - aE)ln CB,
[3]
where AS ° is the entropy change in sphereto-rod transition. The third term on the right side of Eq. [3 ] can be neglected since the micelles are essentially neutral in our systems. Thus In K .
.
no
.
.
AH °
AS °
RT
R
[4]
Figure 4a shows that the plots of log K vs 1 / T of the Cs NEt3. C8 SO4 system are linear and the variation of log K with the surfactant conJournal of Colloid and Interface Science, Vol. t 30, No. 2, July 1989
centration is rather small (less than 4% in the concentration range from 20 to 50 m M ) . The average A H ° and AS ° values obtained by fitting the plot of log K vs 1 / T to Eq. [4 ] are - 2 . 2 5 + 0.07 k J - m o l e -1 and - 1 . 6 + 0.4 J . K - l - m o l e -~, respectively, which means that the driving force in the micelle growth is the enthalpy reduction. The plots of log K vs 1 / T o f C s N E t 3 • CloSO4 in Fig. 4b are nonlinear, which makes the analysis of the micelle growth using the sphere-to-rod model very difficult.
(E) Comparison with Other Ionic Surfactant Systems Many micelle solutions of ionic surfactants with organic counterions have a property of viscoelasticity (8-11 ). Some authors suggested that the viscoelasticity is induced by the existence of rodlike micelles ( 11 ). Hoffmann et al. found that some similar systems do not have such a property (7). In our present systems it is shown that the overlapping of rods in the homogeneous micelle solution does not induce such viscoelasticity, and the viscoelasticity is observed in the heterogeneous (apparently homogeneous) solution in the vicinity of the critical phase separation concentration before the phase separation occurs. It seems that the instability of solutions are responsible for the viscoelastical property of surfactant systems. Micelle size for ionic surfactants with organic counter ions are often going through a peak with increasing micellar concentration (7, 12). It is indicated (7) that the growth of micelles slows down and finally reverses itself when the rotational volumes of the rodlike micelles begin to overlap. In our present systems, the length of the rodlike micelles are longer and the overlapping of rods is more serious than those in the above mentioned systems. But the growth pattern of micelles is quite different: the rate of micelle growth is increased with micelle concentration in present systems. This proves that the overlapping of rods cannot prevent micelles from growing.
429
PROPERTIES OF A Q U E O U S MIXTURES, II
Table I compares the thermodynamical parameters in the sphere-to-rod transition of our present systems with those in the literature ( 14, 22). It seems that the entropy change of C8NEt3 • C8 SO4 is essentially the same as that of the single ionic surfactant systems, but the enthalpy change is twice as large. We suggest that the larger change of enthalpy in the cationic-anionic surfactant system than in ionic surfactant systems is due to the lower charge density on the micelle surface and consequently the lower value of AHg~ in the sphereto-rod transition. It seems, generally, from Table I, that the enthalpy reducing is a driving force for micelle growth of all ionic surfactant systems. CONCLUSIONS
1. Equimolar mixtures of C8NEt3Br and CnSOaNa form micelles in aqueous solutions in rather wide ranges of temperature and concentration. The micelles become larger as the surfactant concentration increases, the temperature decreases, and the total hydrophobic chain length increases. The overlapping of the rodlike micelles does not inhibit the micelle from growing.
centration or by decreasing the temperature, a new liquid phase separates from the solution. This new phase is still a rather dilute aqueous surfactant solution, the surfactant concentration of which could be less than 1.2%. This unusual phenomenon may be interpreted as the formation of the flocculated micelle solution. 4. The "ladder model" proposed by Missel et al. is adapted to the mixed micelles of cationic-anionic surfactant systems. The enthalpy and entropy change in the sphere-torod transition process are deduced for C8NEt3. C8SO4 system. The parameter K, which describes the tendency of micelle growth, increases with the surfactant concentration, which may be interpreted in terms of the change of the ratio of cationic to anionic surfactant in the micelles with concentration.
APPENDIX THERMODYNAMIC
ANALYSIS OF THE
GROWTH OF THE MIXED MICELLES OF CATIONIC-ANIONIC
SURFACTANTS
The mixed micelles consist of cationic surfactant ions A+, anionic surfactant ions A_ 2. C 8 N E t 3 " C 1 0 S O 4 and C 8 N E t 3 . C 1 2 S O 4 and counterinorganic ions B. The micelle Cn, could form giant micelles, and the shape of where n is the aggregation number, is in equithe micelles are semiflexible rods when the ralibrium with A+, A_, and B in aqueous sodius of gyration of the micelles is beyond 400lution: 500 A. All micelles are rigid rods when the radius of gyration is less than 400 ~ (or the nyA+ + n ( 1 - y ) A _ + a n B = C,, [A1] hydrodynamic radius is less than 200 A). where y is the mole fraction of A+ in the mi3. At the limit of micelle growth which is celles on the two component A+ and A_ basis, reached either by increasing the micelle cona is the molar ratio of B bound on the micelle surface to the total surfactants in micelles. AcTABLE I cording to the condition of chemical equilibA H ° and AS ° Values in the Sphere-to-Rod Transition rium for Different Systems
/~, = n (y/XA+ + ( 1 -- y) t~A_ + a#B),
Systems
A H ° (kJ-mole -~)
A S ° (J. mole -I K -t)
CsNEt3.CsSO4 TPB a CPB b
- 2 . 2 5 _+ 0.07 - 1 . 0 7 _+ 0.04 - 1 . 1 7 + 0.08
- 1 . 6 -+ 0.4 - 1 . 2 5 + 0.1 - 1 . 4 6 +_ 0.08
a Ref. (14). b Ref. (23).
[ A2 ]
where/~n is the chemical potential of the micelle with an aggregation number n, and gh+, #h_, and ~B are the chemical potentials of the relevant monomer in the aqueous solution, respectively. In the case of dilute solutions, Journal of Colloid andlntetface Science. Vol. t30, No. 2, July 1989
430
YU AND ZHAO with Eq. [A5], we obtain the contribution function of the micelles
#~ = #O + R T ln Xn o
#A+
#A+ + R T In XA+
[A7]
X, = Qn/K. #a_ = #~_ + R T l n X A _
F r o m the conservation of matter,
#B = # ~ + R T In XB,
[A3
]
where the Xn, XA+, XA_, and XB are the mole fractions of the corresponding species denoted by the subscripts and the superscript zero represents the standard state. On inserting Eq. [A3] into Eq. [A2] RTlnXn
[A8]
Inserting Eq. [A7] into Eq. [A8] K(X
-
XA+ -- XA_ )
[A4]
Assuming the ratio of cationic to anionic surfactant is the same at the hemisphere part as at the cylindrical part of the rodlike micelles, from Missel's ladder model (21 ) we have o #no ÷
(/'/ - -
[A5]
# o _ n ( y # ~ + + (1 - y ) # ~ _ + aUB)
= RTln
K = #,o
o0
no)
where #~ and #2 are the standard chemical potential of cationic and anionic surface active ions in the cylindrical part of the micelles, respectively; # ~o and no are the standard chemical potential and the aggregation n u m b e r of the minimal spherical micelle, respectively. L e t / t ° = y # ~ + (1 - y)#O. F r o m Eq. [A5], the first term on the right-hand side of Eq. [A4] can be expressed as
0
F r o m Eq. [A9] and Eq. [A7] we obtain the X. as a function of K ( X - XA+ -- XA_) and no. Thus the micelle weight averaged micelle weight mol wt can be calculated m
X(y#~+(1-y)#2),
RTln
nX,.
n=?/O
= _ ( # o _ n(y#~+ + (1 - y)#~_
+ cqzB)) + nRTln(X~+X~-__Y).
o JAn =
oo
X = XA+ + XA- + Z
--
K+
n R T l n K1
no(# ° + ( a l - a2)#B)
R T In/£1 = #o
-(y#~++(1-y)#~_)-a2#B,
[A6]
where al and a2 are the ratios of the n u m b e r of B to the n u m b e r of the surfactant in the hemisphere and cylindrical parts of the micelle, respectively; K is a parameter which measures the tendency for no moles of surface active ions to transform from the spherical part to the cylindrical part of the micelles. Let Q = ( x Y + x ~ - Y ) / K l . On combining Eq. [A6] J o u r n a l o f C o l l o i d a n d Interface Science,
Vol. 130, No. 2, July 1989
tool wt -
Y~ n2Xn
o~
,
[AIO]
nXn n=Ho
where m is the average molecular weight of the two kinds of surfactants in the micelles. REFERENCES 1. Mittal, K. L., and Lindman, B., "Surfactants in Solution." Plenum Press, New York, 1984. 2. Mazer, N. A., Benedek, G. B., and Carey, M. C., J. Phys. Chem. 80, 1076 (1976). 3. Appell,J., and Porte, G., J. Colloidlnterface Sci. 81, 85 (1981). 4. Corti, M., and Degiorgio, V., J. Phys. Chem. 85, 711 (1981). 5. Rohde, A., and Saekmann, E., J. Colloid Interface Sci. 70, 494 (1979). 6. Dorshow, R., Briggs, J., Bunton, C. A., and Nicoli, D. F., J. Phys. Chem. 86, 2388 (1982). 7. Hoffmann, H., Rehage, H., Platz, G., Schorr, W., Thurn, H., and Ulbrieht, W., Colloid Polym. Sci. 260, 1042 (1982). 8. Hoffmann, H., Platz, G., Rehage, H., and Sehorr, W., Adv. Colloid Interface Sci. 17, 275 (1982). 9. Angel, M., Hoffman, H., Lobl, M., Reizlein, K., Thurn, H., and Wunderlich, I., Prog. Colloid Polym. Sci. 69, 12 (1984). 10. Ulmius, J., Wennerstrom, H., Johansson, L. B. A., Lindblom, G., and Gravshoit, S., J. Phys. Chem. 83, 2232 (1979).
PROPERTIES OF AQUEOUS MIXTURES, II 11. Barker, C. A., Saul, D., Tiddy, G. J. T., Wheeler, B. A., and Willis, E., J. Chem. Soc. Faraday Trans. 170, 154 (1974). 12. Yu, Z.-J., and Zhao, G.-X., J. Colloid Interface Sci. 130, 414-420 (1989). 13. Hoyer, H. W., and Doerr, I. L., J. Phys. Chem. 68, 3494 (1964). 14. Zhou, Z.-K., and Yu, Z.-J., Acta Phys. Chim. Sinica 1, 141 (1985). 15. Ozeki, S., and Ikeda, S., ColloidPolym. Sci. 262, 409 (1984). 16. Yu, Z.-J., Doctoral thesis, Peking University, 1987. 17. Flamberg, A., and Pecora, R., J. Phys. Chem. 88, 3026 (1984). 18. Sande, W. V. D., and Persoons, A., Y. Phys. Chem. 89, 404 (1985).
431
19. Porte, G., Appell, J., and Poggl, Y., aT. Phys. Chem. 84, 3105 (1980). 20. Verwey, E. J. W., and Overbeek, J. T. G., "Theory of the Stability of Lyophobic Colloids." Elsevier, New York, 1948. 21. Missel, P. J., Mazer, N. A., Benedek, G. B., Young, C. Y., and Carey, M. C., J. Phys. Chem. 84, 1044 (1980). 22. Missel, P. J., Mazer, N. A., Benedek, G. B., and Carey, M. C., J. Phys. Chem. 87, 1264(1983). 23. Porte, G., and Appell, J., J. Phys. Chem. 85, 2511 (1981). 24. Mukerjee, P., J. Phys. Chem. 76, 565 (1972). 25. Gelbart, W. M., McMullen, W. E., Masters, A., and Ben-shaul, A., Langmuir 1, 101 (1985).
Journal of Colloid and Interface Science, Vol. 130, No. 2, July 1989