398
Langmuir 1989, 5 , 398-405
Micelle Formation of Detergent Molecules in Aqueous Media. 3. Viscoelastic Properties of Aqueous Cetyltrimethylammonium Bromide-Salicylic Acid Solutions Toshiyuki Shikata* and Hirotaka Hirata Department of Physical Chemistry, Niigata College of Pharmacy, Kamishin-ei-cho, Niigata 950-21, Japan
Tadao Kotaka Department of Macromolecular Science, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan Received January 19, 1988. I n Final Form: October 2, 1988
Viscoelastic properties were examined in aqueous solutions of cetyltrimethylammonium bromide (CTAB) complexed salicylic acid (HSal),coded as CTAB:HSal/W (W represents water), as a function of the detergent, CD, and acid, CA, concentrations. Effects of adding NaBr were also examined. The results were compared with those of CTAB:NaSal/W containing sodium salicylate (NaSal) instead of HSal. In the solutions of CD I1.0 X mol L-' and CACD-' > 0.5, the CTA+:HSalcomplex formed fully entangling threadlike micelles. 'H NMR spectroscopy conducted on the D20 solutions with a similar range of C D and CA suggested that besides free HSal of concentration CA*existing in the aqueous medium, HSal molecules immobilized in the micelles appear to exist in at least two different states through complexation with CTA+. One is the state equivalent to that occupied by Sal- in CTAB:NaSal micelles, and the other is a more nonpolar environment. While CTAB:NaSal/ W systems exhibited only one relaxation mode with strength G N o c: CD2.'and relaxation time T , a function only of the concentration Cs* of free Sal- ions in the medium, the corresponding CTAB:HSal system exhibited two relaxation modes. The slow mode, specific to the CTAB:HSal/W systems, has the relaxation time T~ c: CA*-5CD-2,which becomes shorter with increasing CD. The fast mode has the relaxation time r2 c: CA*-2CDo,similar to the T , of the CTAB:NaSal/W systems. The corresponding relaxation strengths G1 and G2 are approximately (G, + G2) N GNo CD2.'CAo. Addition of NaBr produced little effect on the CTAB:NaSal/W systems but led to significant reduction in the relaxation time T , of the CTAB:HSal/ W systems. especially of their slow mode, which merged to the fast mode with increasing NaBr concentration.
Introduction Cationic detergents complexed with certain organic salts or acids often form threadlike micelles and exhibit intriguing viscoelastic behavior even in dilute solution.'+ We reported t h a t a cationic detergent, cetyltrimethylammonium bromide (CTAB), complexed with sodium salicylate (Nasal) in aqueous solution formed very long and stable threadlike micelles that were essentially an intermolecular 1:l complex of CTA+ cations and Sal- ani o n ~ We . ~ also ~ reported that the CTAB:NaS,al/W micellar solutions exhibited pronounced viscoelastic behavior, which changed dramatically with increasing salt concentration, Cs, while the detergent concentration C D was kept The viscoelastic behavior of the CTAB:NaSal/ W micellar solutions of low-to-intermediate Cs ( CD was a rapidly decreasing function of the concentration Cs* (= Cs - CD) of free salicylate ions in the bulk aqueous phase and was implicitly dependent on CD through Cs*.6 The presence of excess Sal- ions appeared to be essential in promoting the relaxation processes involving actual breakdown of the network of the threadlike micelles at the entanglement points.6 In addition to the above findings, we also found that replacing NaSal in the CTAB:NaSal/ W system by salicylic (9) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Oxford University Press: Oxford, 1986. (10) Nilsson, P. G.; Wennerstrom,'H.; Lindman, B. J . Phys. Chem. 1983, 87, 1377. (11) Kato, T.; Anzai, S.;Seimiya, T. J. Phys. Chem. 1987, 91, 4655.
0743-7463/89/2~05-0398$01.50/0 0 1989 American Chemical Society
Langmuir, Vol. 5, No. 2, 1989 399
Micelle Formation of Detergent Molecules
acid (HSal) still produces threadlike micelles of appearance similar to CTA+:Sal- micelles of the CTAB:NaSal/W system^.^ Salicylic acid, however, has a limited solubility and relatively large pK, value in aqueous media, as opposed to Nasal. At 25 "C, saturation of water with HSal occurs at the concentration CAsW of about 1.8 X mol L-l. Saturation of deuterium oxide (DzO) occurs at CASd of about 1.0 X mol L-l, and the pK, in water is 3.0 at 25 "C. We anticipated that these differences would lead to differences in the micellar structure and lifetime of the entanglement network between the CTAB:NaSal/W and CTAB:HSal/ W systems. We thus compared the viscoelastic properties and 'H NMR spectra of these two systems. The relatively large value of pK, of HSal molecules should result in formation of positively charged micelles composed of a CTA+:HSal complex, being subject to strong electrostatic repulsion. We also compared the effects on the viscoelastic properties of adding a simple electrolyte such as NaBr to the CTAB:HSal/W and CTAB:NaSal/W solutions.
Experimental Section Materials. Cetyltrimethylammonium bromide (CTAB), salicylic acid (HSal), deuterium oxide (D20),and water (W) were obtained through the same methods described in previous pap e r ~ Sodium . ~ ~ bromide (NaBr) was a special grade reagent purchased from Wako Pure Chemical Ind., Ltd., Osaka, and was used without further purification. The sample solutions for rheological measurement were aqueous solutions of CTAB and HSal coded as CTAB:HSal/W. The concentration CD of CTAB was varied from 1.0 X to 1.0 X lo-' mol L-l, while the concentration CA of HSal was varied in the range of the acid-to-detergent ratio CACD-Ifrom 0.3 to CA = CAS CD+ CAm, at which needlelike crystallites of HSal appeared in the systems. To examine the effects of adding a simple electrolyte, we added NaBr to the micellar solutions with concentration CASvarying from 0 to CAs = CD. The resulting solutions were coded as CTAB:HSal:NaBr/W or CTAB:NaSal:NaBr/W. For NMR measurements we used D 2 0 as the solvent instead of water. The solutions were coded as CTAB:HSal/D20. The range of C D was chosen essentially the same as the ordinary water systems, but the range of C A was somewhat limited because of the small difference in the solubility CAsd of HSal in D 2 0 from CABW in ordinary water. All the solutions were kept standing at 25 "C for equilibration more than 2 days before the measurement. Rheological Measurement. Dynamic measurement was carried out a t 25 OC on a conventional rheometer of a cone and plate type (MR-3, Rheology Engineering, Kyoto). The radii of the cone and plate were both 16 mm, and the angle between the cone and plate was 3.0'. The amplitude of the strain was 0.33. The angular frequency w covered the range between 6.28 X lo9 and 6.28 rad s-l. The storage, G', and loss, G", moduli were determined by using the Markovitz equation.12 The same rheometer was used to carry out shear-stress relaxation experiments on CTAB:HSal/ W systems under a small step strain y. Stress relaxation was followed for a few tens of minutes after applying the step strain y. The magnitude of y imposed on the systems was 0.1-0.2, under which conditions the stress-relaxation moduli G(t) were independent of y. NMR Measurement. Proton 'H NMR measurement on CTAB:HSal/D20 systems was carried out a t 25 'C with a 200MHz NMR spectrometer (Fx-200, Jeol, Tokyo) in the Fourier transform (FT) mode. We examined mainly the chemical shift of the signals of phenyl protons of HSal molecules.
Results and Discussion Phase Behavior. Since HSal has a limited solubility in pure water, we first examined the phase behavior of the (12) Markovitz, H. J. Appl. Phys. 1952, 23, 1070.
"0
2
4 6 8 1 0 1O2Co/moli'
Figure 1. Phase diagram for CTAB:HSal/W systems a t 25 "C. Solid circles represent two-phase solutions containing needlelike crystallites of HSal; open circles represent clear one-phase solutions.
CTAB:HSal/W systems a t 25 "C. Figure 1 shows the results, in which the acid concentration CA is plotted against the detergent concentration CD. When CA of HSal is below C D plus CASW,the system gave a clear one-phase solution (open circles), while for CA > CD + CAsw, needlelike crystallites of HSal precipitated, resulting in a two-phase solution (closed circles). In Figure 1, the area above the heavy solid line is the two-phase region and the area below the line the one-phase region. The slope of the phase boundary line is approximately 1. The result implies that the molar ratio of CTA+:HSal is presumably 1:l in the threadlike micelles in the solutions on the phase boundary. In DzO, the solubility CAsd of HSal at 25 "C is slightly lower than that in ordinary water. However, in saturated DzO solutions with CAS C D CAd, the threadlike micelles are presumably a 1:l complex as in ordinary aqueous solutions. Dynamic Behavior. In our previous papers on CTAB:NaSal/ W systems,5P6we classified their viscoelastic behavior into three types, which changed with increasing Cs when C D was kept c o n ~ t a n t . ~We first examined CTAB:HSal/ W systems to see whether their viscoelastic behavior follows the similar pattern as that of the CTAB:NaSal/ W systems5y6upon changing CA relative to
+
CD.
Figure 2 shows dynamic G'and loss G"modu1i vs angular frequency, w, curves (in a double-logarithmic scale) for three CTAB:HSal/W systems with CD = 6.0 X mol L-' and C A from CACD-l of 0.4-0.8. When C A = 2.4 X lo-' mol L-' (or CACD-l = 0.4), the slopes of the G' and G" curves are 2 and 1, respectively, at their low-frequency ends. They merge in the high-frequency region to a curve with slope 1/2. This behavior resembles that of dilute polymer solutions of high molecular weight or of concentrated solutions of low molecular weight polymer, in either of which polymer chains are not entangling with one another.8AW4 mol L-' (or CACD-l When CAis increased to 3.0 X = 0.5), the longest relaxation time is increased about 100-fold, and the G"curve shows a maximum and a long (13) Rouse, P. E., Jr. J. Chem. Phys. 1953,21, 1272. (14) Zimm, B. H.J. Chem. Phys. 1956,24, 269.
400 Langmuir, Vol. 5, No. 2, 1989 CTAB:HSOl/W
Shikata et al.
25'C C D = 6 . 0 ~ 1 0 moll ~
\
C4
4 . 8 I~O Z mol I-
:
o
G' G"
Ca = 3 . 0IO' ~ mol i' log(w /s.l)
Figure 3.
Frequency (a) dependence of G' and G" for CTAB:HSal/W systems at 25 "C with the detergent concentration CD = (A) 6.0 X mol L-' and different acid and (B) 3.0 X concentrations CA. Solid lines represent the calculated G'and G"curves obtained by using a simple mechanical model consisting of two Maxwell elements with the modulus Gi and the relaxation time T; (i = 1 and 2) connected in parallel.
Figure 2.
Frequency ( w ) dependence of G' and G" for CTAEkHSal/W systems at 25 "C with the detergent concentration CD = 6.0 X mol L-' and three different acid concentrations, CA. tail extending toward the high-frequency side. Obviously, the system now has a broad distribution of relaxation times similar to concentrated polymer solutions of high molecular weight, in which entanglement effects become dominant.5~6*8 The threadlike micelles of the CTAB:HSal/W systems appear to become longer with increasing CACD-' from 0.4 to 0.5 so that the threadlike micelles begin to entangle among one another. Thus we may say that the CTAB:HSal/ W systems with a low-to-intermediate CACD-' ratio exhibit typical polymer solution behavior similar to the corresponding CTAB:NaSal/ W system^.^,^ When CA is further increased to 4.8 x lo-' mol L-' (or CACD-' = 0.8), the G' curve exhibits a plateau with the height nearly independent of w and the G " curve rapidly decreases in the high-frequency side. The low-frequency ends of the curves become no longer observable in the frequency range accessible to our rheometer because of the limited capacity. In the G'curve, we see a small bump in the nearly flat plateau and in the G"curve a shoulder a t around w = 0.1 s-l in the rapidly decreasing tail of the frequency side of the G'' peak (although the peak itself cannot be seen in the frequency range examined here). These features imply that the CTAB:HSal/ W system possesses at least two relaxation modes: a slow mode and an additional fast mode existing at around w = 0.1 s-l. For other CTAB:HSal/W systems with CD = 1.0 X lo-', 3.0 X lo-', and 1.0 X lo-' mol L-l, we observed similar systematic change in the viscoelastic behavior with increasing CA or CACD-l.
Parts A and B of Figure 3 are typical examples of the G'and G"vs w curves for the CTAB:HSal/W systems with CD = 6.0 X and 3.0 X mol L-l, respectively, with CA varying from O X D up to saturation, CAS. These systems with CACD-l = 0.8-1.0 exhibit at least two relaxation
modes with the characteristic times 7, and 7' from the low-frequency side. The relaxation time 7 1 at the lower frequency side seems to shift faster with increasing CA than the other one, r2, at the high-frequency side. Thus the two modes merge to a single mode, as CA is increased to CAS. The single-mode behavior of the CTAB:HSal/ W systems at high CACD-l resembles the Maxwell model behavior of the CTAB:NaSal/W systems with a CSCD-' ratio of the same leveL6 We attempted to separate the relaxation mode of these systems into two modes by employing a four-element model8 composed of two Maxwell elements with the relaxation strengths Gi and times 7 i (i = 1 and 2), connected in parallel. The G'and G"modu1i can thus be expressed as
Since the G and G" data have been obtained only in the limited range of w , we determined the model parameters in eq 1 and 2 by applying a nonlinear least-squares fitting technique on a microcomputer, repeating the calculation until the calculated curves fitted the observed curves. The results are summarized in Table I. Also in parts A and B of Figure 3 we reproduced the best fit G'and G" curves. We see that the agreement between the experimental and calculated curves is fairly good. Shear-Stress Relaxation. The above analysis of the G'and G" data based on the four-element model may be too ambiguous, and the tabulated values of log G1 and log 7, could be a mere artifact of the least-squares fitting technique employed here, because the present rheometer we used cannot effectively cover the frequency range lower than log o = -2.2, where the G'' peak of the slow relaxation mode, if it exists, should appear. We thus carried out direct stress relaxation measurement on these systems. Figure 4A shows a typical example of a semilogarithmic plot of the relaxation modulus G(t) vs time t for CTAB:HSal/W with CD = 6.0 X lo-' and CA = 4.8 X lo-' mol L-'. As seen in Figure 4A, we determined the longest relaxation time 71 and its strength G,, respectively, from the slope and the intercept of the straight portion of the
Langmuir, Vol. 5, No. 2, 1989 401
Micelle Formation of Detergent Molecules Table I. Relaxation Strength Gi (Pa) and Time i i ( 8 ) (i = 1 and 2) for the Slow and Fast Relaxation Modes of CTAB:HSal/W Systems at 25 OC 102CD, 102c.4, mol L-I mol L“ log r1 log GI log 7 2 log G2 0.8 1.25 1.9 1.5 10.0 7.0 1.25 1.45 0.5 8.0 1.6 1.07 1.5 0.6 6.0 3.6 3.1 1.15 1.4 0.6 2.8 4.8 0.57 1.15 1.44 4.P 2.78 1.15 1.1 0.7 5.4 2.2 1.12 0.8 0.7 6.0 1.7 1.12 0.3 0.7 7.2 0.8 1.25 0.25 3.2 0.63 2.4 3.0 0.6 1.2 0.0 3.0 3.1 0.57 1.1 0.13 3.6 2.24 0.5 0.65 0.2 3.9 1.75 0.5 0.25 0.2 4.8 0.98 1.0 1.5 3.2 -0.45 1.2 -1.3 0.85 -1.25 2.0 2.5 -0.52 2.5 1.5 -0.68 0.4 -1.25 Detected from the shear-stress relaxation measurement. 1.51
I
,
1
1
“a,
1
1
j ( A ) CTAB:HSal/W
“’5t
25‘C
C, =6.Ox1O2mol j’ CA =4.8x1O2mol
r’
Figure 4. (A) Semilogarithmicplot between a stress relaxation and function G(t) vs time t for the system with CD = 6.0 X mol L-I. (B) Comparison between G’and G” CA = 4.8 x curves (solid lines) estimated with eq 1and 2 from stress relaxation data shown in the above figure and G’ and G” data (circles) obtained from the dynamic measurements.
curve at the long-time end. Then, subtracting the contribution of the longest relaxation-time mode from the G(t) curve, we again obtained a straight line in the semilogarithmic scale, from which we determined the contribution of the second longest relaxation-time mode with r2 and G2 and so on. This procedure, developed by Tobolsky and Murakami,16 is called “procedure X”. The relaxation modulus of the present system was split practically into two modes as G(t) = G1 exp(-t/rl) + G2 exp(-t/r2) (3) The Gi and r1 values thus determined are listed in Table (15) Tobolsky, A. V.; Murakami, K.
J. Polym. Sci. 1959, 40, 433.
I with an asterisk. The agreement between the values determined through the curve fitting and the procedure X is excellent. According to the theory of linear viscoelasticity,8 the G’ and G”modu1i are obtained from G(t) by Fourier transform
G’ = uJmG(t) 0 sin (ut) dt
(4)
G ” = wJmG(t) cos (ut) d t
(5)
0
Substituting observed G(t) data (eq 3) into eq 4 and 5, we obtain G’(u)(eq 1) and G”(u)(eq 2), respectively, in the frequency range where the dynamic experiments could not cover. The G’and G”curves thus calculated are shown in Figure 4B together with the directly observed G’ and G” data points. Again the agreement is excellent. The above results indicate that the two-mode model reasonably explains the behavior of the CTAB:HSal/ W systems with CA in the range 0.8CD < C A < CAS. NMR Analysis of CTAB:HSal Complex. In our previous studies on CTAB:NaSal/ W systems with high CSCD-’, we found that while the plateau modulus GNo varied as CDz,2but was independent of CSCD-’, the relaxation time r , was affected only by excess Sal-’ ions of concentration Cs* in the bulk aqueous p h a ~ e . Likewise, ~,~ in the present systems the relaxation processes might be affected by free HSal molecules in the bulk aqueous phase. The phase behavior of CTAB:HSal/ W systems shown in Figure 1suggests that the threadlike micelles are likely to be an equimolar complex between CTA+ ions and HSal molecules. However, this information alone is not enough to understand the structural features of the CTA+:HSal micelles. Then, we carried out NMR m e a s ~ r e m e n t ~ + ’ ~ - ’ ~ on CTAB:HSal/D20 systems to examine the state of complexed HSal molecules and to determine the concentration CA* of the free HSal in the bulk aqueous phase. Figure 5 shows typical NMR signals of phenyl protons of CTAB:HSal/D,O systems with CD= 1.0 X lo-’ mol L-’ and CA varying from 0.4CDto l.locD, at which the bulk DzO phase just begins to be saturated with HSal. In Figure 5, we see that at CA = (4.0-5.0) X lo-, mol L-’ or CACD-I = 0.4-0.5, the signals of both para (4H) and ortho (6H) protons appear at the positions shifted by 0.34 and 0.07 ppm, respectively, from their positions for free HSal molecules in D20. The signals then gradually shift toward the higher magnetic field, as CAis further increased. Similar behavior was observed for other CTAB:HSal/D20 and 6.0 X lo-’ mol L-’. systems with C D = 3.0 x Figure 6 shows plots of the differences in the chemical shift, As, of 4H and 6H signals between those of the free and immobilized HSal molecules in CTAB:HSal/DzO against the CACD-’ ratio. This CACD-’ dependence of the chemical shift difference in CTAB:HSal/D,O systems is quite different from the CSCD-’ dependence of those in CTAB:NaSal/D20 systems, shown by the broken lines in Figure 6.6 In CTAB:NaSal/DzO systems, when CsCD-’ was below 1 and most of the Sal- ions were immobilized in the micelles, the 4 H signal shifted by 0.34ppm and the 6 H signal by 0.07ppm to the high magnetic field from the positions for free Sal- ions in D20. However, with a further increase of CSCD-lbeyond 1, the signals shifted backward to the lower magnetic field side, as shown in Figure 6 by the broken lines.6 Moreover, the magnitudes of the shift were essentially independent of CD. We thus postulated that the Sal- ions may assume two states: a free ion state in the bulk aqueous phase and an immobilized state in the
Shikata et al.
402 Langmuir, Vol. 5, No. 2, 1989 CTAB : HSal / DO ,
25OC
6G3!H 5 4
cn=~ . o x i O ~ m ~ i i ' CD= O
4H
6H
+
moll"
CD = 1.03 10-1
Figure 5. 'H NMR signals at 25 x mol L-' and varying CA.
-A8
1
I
7
O C
6 /ppm
of phenyl protons for HSal in DzO solution and in the CTAB:HSal/D,O systems with CD = 1.0
25°C
Employing the difference A6 (= 6 - 6,) in the chemical shift between HSal in the micelles and D20, we can rewrite eq 6 as
COOH 6 H 5 4
'
A6 = 6 - 6, = (Cbh6b
-
- ---. . --_.
''*I-9,-1 6H
01 0
I__
8
".V
CTAB:HSol>D:O CD /mol I 0 3.0~10.~ 0 6.0~ 10.' 0.4- 4 I . 0 X IO - I
6.0x IO2
..........................
1
I
1.0
0.5
I
1.5
C A CDI
Figure 6. Dependence on the acid-to-detergentCACD-~ ratio of the differences A6 in NMR chemical shifts of para (4H) and ortho (6H) protons for CTAB:HSal/D,O systems. The broken lines represent the similar data for CTAB:NaSal/DzOsystems.
micelles. The molar ratio of the immobilized to free Salions, (C, - Cs*):Cs*, may be determined from their chemical shift data.fi However, we see in Figures 5 and 6 that the present CTAB:HSal/D,O systems behave quite differently from these CTAB:NaSal/D,O systems. With CACD-' increasing up to 0.5, the chemical shift differences are just the same as those in the CTAB:NaSal/D,O systems. Beyond a CACD-' of 0.5, however, the signals shift to the higher field side further away from those of the free HSal molecules, and the shifts, A6, are dependent on CD as well. To interpret these results, we postulate that HSal molecules may assume three different states: a free molecular (or ion) state in the bulk aqueous phase and two immobilized states in the micelles, which we call the free (a) state and the immobilized (b) and (c) states, respectively. We further assume that the free (a) state is the same as that defined already for Sal- ions in CTAB:NaSal/D20 systems. Then, the observed chemical shift 6 of the protons distributed over these three states with the chemical shift 6, in the molar ratio CiCA-' (i = a, b, or c) may expressed as16 b = (C,6, + Cb6b + Cc6,)/CA (6) (16) Pople, J. A.; Schneider, W. G.; Bernstein, H. J. High Resolution Nuclear Magnetic Resonance; McGraw-Hill: New York, 1959.
+ CCA6,)/CA
(7)
where = 6b - 6, and Ab, = 6, - 6, by definition. In Figure 6, we see that the chemical shift differences A6 for both 4H and 6H protons are the same for all the CTAB:HSal/D20 systems with different CD but with the same CACD-l I0.5 and also the same for those of the immobilized Sal- ions in CTAB:NaSal/D,O systems at CSCD-l5 1.0. This result implies that the b state at the low field is in much the same environment as that of the immobilized state in CTAB:NaSal/D,O systems. In other words, in the CTAB:HSal/D,O systems with CACD-'I0.5, all the HSal molecules are presumably complexed with CTAB and immobilized at the sites in the b state. We thus assume that CA = Cb when CA 5 0.5CD, and Cb = 0.5CD when CA 1 0 . 5 C ~ .Then, from the data for the systems with CACD-l = 0.5, we may assign A6b4H = -0.34 ppm for 4H protons and A6bfiH = -0.07 ppm for 6H protons. As CA is further increased beyond 0 . 5 C ~ some , HSal molecules presumably remain in the bulk aqueous phase, but some others might be pushed deeper into the micelles and may occupy the c state sites in a more nonpolar environment. Thereby, on the average, the proton signals shift to the higher field side. Finally, when CAreaches saturation, CAS( z CD + CAd), the c state sites should now be fully occupied, and C, = 0.5CD, because the molar ratio of CTA+ to HSal in the micelles is 1:1 at CA = CAS,€or which we can write C, = CAsd(= 1.1 X lo-' mol L-l) and Cb = c, = 0.5CD. Then, from eq 7, the chemical shift difference AaS a t the saturation CA = CASmay be given as
+
ASs = 0.5C~(A6b A6,)/CAs
(8)
Using the observed values of Ah8 for the saturated solution and the value of Abb assigned as above, we determined from eq 8 the chemical shift difference As, for the c state. The results are summarized in Table 11. The (17) Muller, N.; Birkhahn, R. H. J. Phys. C h e n . 1967, 71, 956.
Langmuir, Vol. 5, No. 2, 1989 403
Micelle Formation of Detergent Molecules Table 11. Chemical Shift Difference and of Para and Ortho Protons, Respectively, in the Phenyl Ring of HSal for the Immobilized State (c) in the Threadlike Micelles for CTAB:HSal/D,O Systems with Several CTAB Concentrations (Cn*) CD,mol L-' 3.0 X 6.0 X lo-* 1.0 X lo-' -0.54 -0.54 A6,4H, ppm -0.59 -0.34 -0.34 -0.37 A6,BH, ppm CTAB:HSOl/D2O
3-
-
2 5 *C
I
A)
CTAB:HSol/W
00 0 00
&,
E 2-
CD /mol 1.'
G, G;
1.0x10-' 0 0 6.0~ IO-' 0 3.0~ lo-' A A LOX 10-2
v v
A
,
o 4H
"
I-
\ fU
,I
25'C
6H ~
~
410'. mol 0 i l ~ 6.0~10~
v V
1.0 x Io-'
0 GN' I
I
I
2
c, c;'
3jf
I
1
-2
-I
log(& /mol I )
Figure 8. Dependence of the relaxation strengths G1 and G2 (A) on the acid-to-detergent (CACD-') ratio and (B) on the detergent concentration C D for CTAB:HSal/W systems a t 25 "C. The C dependence of GNofor the CTAB:NaSal/ W system is also plotted.9 A broken line represents G1 + Gz.
values of and thus determined are independent of CD, as we have anticipated from the three-state model employed here. The above analysis suggests that HSal molecules may assume two different type of immobilized sites in the threadlike micelles of the CTA+:HSal complex. Both of the and values of the c state are much smaller than those of the b state, as seen in Table 11. In particular, the large difference between A6,6H and ASb6H compared with that between and suggests that the location of the c state sites should be in a much deeper position in the threadlike micelles relative to the location of the b state sites. On the other hand, the location of b state sites should be equivalent to the location of Sal- ions in the CTAB:NaSal complex, in which Sal- ions should be arranged side by side the cationic ammonium head groups on the micelle surface.6J8-20 Now, using eq 7 with the assigned Adi (i = b and c) values (and assuming Cb = 0.5CD for the systems with CA > 0.5CD),we estimate the concentration C, of HSal occupying the c state sites; then, we estimate CA* (=C,) of the free HSal in the bulk aqueous phase for the systems with CAS 2 CA I 0.5CD as follows: CA* = CA - 0.5CD - (CAA6 - O . ~ C D A ~ ~ ) / A(9) ~, Because the solubility of HSal in D20 at 25 "C is lower than that in ordinary water, we could not determine CA* in the region CA > ( C D CA") = CAScovered by the viscoelastic measurement. However, since the molar ratio in the micelles should reach 1:lat the saturation, we assumed that CA* should be given by6
+
CA* = C A - CD
(10)
(18) Bunton, C.A.Reaction Kinetics in Micelles; Plenum: New York, 1973. (19) Bunton, C. A.;Minch, M. J.Phys. Chem. 1974, 78, 1490. (20) Eriksson, J. C.;Gillberg, G. Acta Chem. Scand. 1966, 20, 2019. (21) Bunton, C. A.; Minch, M.; Hidalgo, J.; Sepulveda, L. J. Am. Chem. SOC. 1973,95, 3262.
in the range (CD + CA") ICA 5 (CD + CA'~). Figure 7 shows plots of CA* vs CA obtained from the data shown in Figure 6 and from use of eq 9. The CA* values estimated from 4H and 6H proton signals show a fairly good agreement, again as anticipated from the three-state model for the location of HSal in the micelles. Relaxation Strengths. Now we turn our attention to the rheological data of the CTAB:HSal/ W systems on the two-mode model with G1and r1 and G2and r2for slow and fast modes, respectively. Parts A and B of Figure 8 show the dependence of the relaxation strengths Gl and G2 and the sum GI + G2 on CACD-l and CD, respectively. The magnitude of G2is about one-third that of G1.We see that both G1and G2 are independent of CACD-l but are proportional to CD2.2 when CACD-' > 0.8. This power law index of 2.2 is identical with that for the plateau modulus GNo vs CD for CTAB:NaSal/W systems5 shown in the same figure and also to that usually found for concentrated, high molecular weight polymer solution^.^^^ The sum G1+ G2 is equal to GNo of the CTAB:NaSal/ W systems not only in CDdependence but also in absolute magnitude, as seen in Figure 8B. The origin of the elasticity of the present CTAB:HSal/ W systems is undoubtedly due to the entanglement network among the threadlike micelles existing in the systems. The observation of the CTAB:HSal/W systems made on a transmission electron microscope (TEM) confirmed that the threadlike micelles were densely entangling among one a n ~ t h e r . ~ Relaxation Times. In the previus studies on CTAB:NaSal/ W s y ~ t e m s ,we ~ , found ~ that the relaxation time r , was independent of CD but a function of the concentration Cs* of free Sal- ions in the bulk aqueous phase. We anticipated that this could also be the case for the present CTAB:HSal/ W systems. We thus examined the dependence of r1 and r2 on cA* of free HSal in the bulk aqueous phase. Figure 9 shows the results. We see that the relaxation time r1 for the slow mode strongly depends on both CA*and CD,while the r2 of the fast mode is independent of CDbut depends on CA*. Interestingly, the
Shikata et al.
404 Langmuir, Vol. 5, No. 2, 1989
>
C, /mol 1.'
C T A B : H S a1 W
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Figure 9. Dependences of the relaxation times T~ and 7 2 of the slow and fast relaxation modes on the concentration CA* for CTAB:HSal/W systems at 25 "C. behavior of the fast mode is identical with that of T , of CTAB:NaSal/ W systems, indicated by the dashed line in the figure. Figure 10 shows double-logarithmic plots of 7 2 vs CA*for the CTAB:HSal/W systems with different CD. Another interesting feature is that T~ of the slow mode decreases with increasing CD and decreases much faster than 7 2 with increasing CA*. Therefore, the slow mode merges into the fast mode as CAis increased relative to CD. Although T~ is strongly dependent on CD,the dependence of T~ on CA*is quite similar among all the systems examined here. We therefore shifted the log T~ vs CA* curves vertically by an amount log a, relative to that of the system with CD = 1.0 x mol L-' chosen arbitrarily as the reference. Figure 10 shows the obtained composite curve of log ( T ~ U , ) vs log CA*. The insert in Figure 10 indicates the plot of log a, vs log CD, which has a slope of 2. Figure 10 also shows the double-logarithmic plot of T~ vs CA* for the CTAB:HSal/ W systems with different CD. The T~ are' independent of CD but dependent on CA* as T~ a CA*-2. Thus, we can summarize the T~ and T~ data (for the systems with (CD + CAsw)> CA > 0.8CD) shown in Figure 10 as follows: 7 1 a cA*-5cD-2 (11) CA*-'C D (12) Figure 10 also shows, for the sake of comparison, a similar double-logarithmic plot of T, vs Cs* for the CTAB: NaSal/W systems.6 We see that the values of T~ with varying CA* agree well with that of T , on Cs* in the region of relatively low CA* or Cs*, where T , a Cs*-2CDo. On the other hand, since HSal has limited solubility in water, we could not observe the behavior corresponding to those of the CTAB:NaSal/W systems with relatively high CA*, where 7, a cS*-'CDo. We see, however, that the slope of the log ( T ~ U , ) vs log CA* curve is -5.0. 72
0:
0
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I
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Figure 10. Double-logarithmicplots of the reduced relaxation times ~~a~of the slow mode and 72 of the fast mode on the concentration CA* for CTAB:HSal/W systems at 25 "C. Hexagonal symbols represent T , vs Cs* for CTAB:NaSal/W systems.6 An insert shows double-logarithmicplots of the shift factor a, vs the detergent concentration CD. These results suggest that the relaxation mechanism of the fast mode in the CTAB:HSal/W systems is basically the same as that of the Maxwell-type-relaxation mode in the CTAB:NaSal/W systems with relatively low Cs or Cs*. The results also suggest that the relaxation mechanism of the slow mode is similar to that of the CTAB:NaSal/ W systems with relatively high Cs*. Relaxation Mechanisms. For concentrated polymer solutions of high molecular weight M and concentration C, the plateau modulus GNois proportional to MOC2.2,and the longest relaxation time is proportional to Mj.4C1.5.889 Obviously, in the polymer solutions, the relaxation is far slower in a more condensed and fully entangled higher molecular weight system rather than in a dilute and less fully entangled lower molecular weight system. In terms of the tube theory of polymer dynamics? the relaxation in such a system is governed by diffusion of the polymer molecules along their own contour through the entanglement network with the mesh size dependent on the polymer c o n c e n t r a t i ~ n . ~ ~ ~ However, in the micellar solutions, diffusion of the micelles along their contour appears to have nothing to do with the relaxation of the entanglement network. The relaxation appears to be taking place via actual breakdown of the entanglement network of the threadlike micelles, presumably by passing through each other at the entanglement p o i n t ~ . ~ . ~As J ~we J ~discussed in the previous article! in the concentrated CTAB:NaSal/W systems with a high CsCD-l ratio, exchange between the immobilized Salions at the entanglement points of the micelles and free Sal- ions in the bulk aqueous phase appears to be promoting dissociation of the complex at the entangled sites, leading to the relaxation in the CTAB:NaSal/W systems. The relaxation time T , was accordingly a function of Cs* alone.
Micelle Formation of Detergent Molecules
In the present CTAB:HSal/W systems, on the other hand, free HSal molecules in the medium may play the same role the free Sal- ions are playing in the CTAB:NaSal/ W systems. If this is the case, the HSal molecules in the different immobilized sites of the micelles presumably contribute to the relaxation of the CTAB:HSal/W systems in a different manner. The fact that the CTAB:HSal/W systems exhibited two relaxation modes might be reflecting this situation. The HSal molecules in the c state might contribute to the slow relaxation mode with 71,while those in the b state may contribute to the fast mode with 72. A striking fact is that the relaxation time 71 of the slow mode becomes shorter as 71 0: CD-2, while the relaxation strength G1 varies as G1 CD2.2,when CA* is not very high or CACD-' is in the range 0.8-1.0. The slow relaxation mode proceeds much faster, as the system becomes more and more condensed: this behavior is just opposite that usually seen in concentrated polymer solutions and is not seen even in the CTAB:NaSal/W systems. A possible explanation of these features is as follows: Disentanglement of network junctions in the system in which free HSal molecules or Sal- ions are not abundant must be taking place through the reaction involving collisions, fusion, and separation between the segments of the threadlike micelles a t the entanglement junctions, as depicted in Figure 6 of part 2 of this series.6 Electrostatic repulsion between the threadlike micelles, especially between those composed of CTA+:HSal complex, may retard primarily the collisions involved in such a reaction. Under such a mechanism, the relaxation time should be inversely proportional to the frequency of such collisions, while the relaxation strength or the modulus must be proportional to the density of the entanglement junctions, both of which are in turn proportional to CD2. This speculation may explain the difference and similarity in the relaxation modes between the CTAB:NaSal/ W and CTAB:HSal/ W systems. Namely, the surface of the threadlike micelles in the former should be electrically neutral, because the micelles are essentially a 1:1 complex of CTA+ cations and Sal- anions, while that in the latter is presumably positively charged, because the micelles are essentially a 1:l complex between CTA+ cations and neutral HSal molecules. The electrostatic repulsion between the neutral micelles in the CTAB:NaSal/ W systems should be weak, and consequently, the collisions may not be the rate-determining process. On the other hand, the electrostatic repulsion between the charged micelles in the CTAB:HSal/ W systems should be much stronger, especially in those with low CD and CA concentrations, thereby retarding the relaxation more severely in the systems with low CD and low CA*rather than that in those with high CD and high CA*. Effect of Added NaBr. The speculation mentioned above on the electrostatic effects in the micellar solutions may be tested by examining the effects of adding a simple
Langmuir, Vol. 5, No. 2, 1989 405
C s = 6 . 0 x 1 0 ' 2 mol 1.'
25%
V
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( E ) CTAB: HSal:NaBr/W 25'C
-0
I
0
-I
-3
-2
-I 0 l o g ( w /s" )
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Figure II. (A) Frequency ( w ) dependence of storage (G9 and loss (~(9 moduli for CTAB:NaSakNaBr/W with cD= 6.0 x 10-2 mol L-*, NaSd concentration Cs = 6.0 x mol L-l, and several concentrations CM of NaBr. (B) Frequency dependence of storage and loss moduli for CTAB:HSal:NaBr/W solutions with CD = 6*o 'O-', 'A = 6.0 lo-' and 'AS. $'-'
electrolyte such as NaBr to the systems. The effects of adding NaBr on the viscoelastic behavior of the micellar solutions are demonstrated in parts A and B of Figures 11. The figure shows the G' and G" curves of CTAB:NaSal: NaBr/ W and CTAB:HSal:NaBr/ W systems, respectively, in both of which CD and Cs (or CA) were 6.0 X lo-' mol L-' and the concentration CASof NaBr varied from 0 to 6.0 x mol L-l. As seen in Figure 11A, the G' and G" curves of the CTAB:NaSal:NaBr/ W systems are hardly altered, while as seen in Figure 11B those of the two modes merge into one with strength G1 G2 and time 7 2 , as CASof added NaBr is increased. The same feature was observed for all other systems with different CD, Cs (or CA), and CAS: the CTAB:NaSal/ W systems are practically unaffected, but the CTAB:HSal/ W systems exhibit behavior similar to the former systems. Evidently, the excess Br- ions from the added NaBr shield the electrostatic repulsion among the CTA+:HSal micelles so that the collision frequency is increased to accelerate the slow mode of the CTAB:HSal/ W systems. On the other hand, electrically neutral micelles of the CTAB:NaSal/W systems are unlikely to be affected by adding a simple electrolyte.
+
