Langmuir 1993,9,419-423
419
Dynamic Light Scattering of CTAB/NaSal Long Threadlike Micelles in the Semidilute Regime: Applicability of the Dynamic Scaling Law Norio Nemoto' and Mitsue Kuwahara Institute for Chemical Research, Kyoto University, Uji, Kyoto 611, Japan Received July 22,1992. In Final Form: November 9,1992
Dynamic light scatteringexperiments were done to study dynamic aspects of networks formed by long threadlike micelles of cetyltrimethylammoniumbromide (CTAB)in aqueous sodium Salicylate (Nasal) solutionsat three temperatures, T, of 25,40, and 60 O C . The surfactant concentration,CD,of six solutions teeted was fixed at 0.01 M,and a ratio of salt concentration, C,, to CD was varied from 1 to 41. The cooperative diffusion coefficient,D,, was obtained from extrapolation of the first cumulant, I'Jq2, to the zero scattering vector q. The D, showed complicated CS/CDdependence with a minimum at CS/CD= 10 that was followed by a maximum at C ~ C =D 20, while it monotonically increased with increasing T. All redata of the solutions with CS/CD= 1-41 at three temperatures were found to be superposed on one master curve in making a reduced plot of I',/q2D, vs &H, where the dynamic correlation length, [H, was estimated from D,. The master curve was found in agreement with the theoretical prediction developed for chain dynamics of linear flexible macromolecules in the semidilute regime.
Introduction The scaling theory developed by de Gennes is very successful in describingstatic properties of flexiblepolymer chains in the semidilute regime in terms of the correlation length, 4.' For example, the theory requests that the osmotic pressure, II, in the semidilute regime should be a function of [ only, which is dependent on polymer concentration, C, but independent of molecular weight M. This leads to the power law type of equation like II a MOc914 for semidilute solutions of polymers in good solvents. The prediction is well confirmed by experiments of Noda et ale2 In extending the static scalinglaw to dynamicalscaling, one of experimental quantities relevant for comparison with the theory is the first cumulant reor the line width Aw at the scattering vector q (=(4?r/h)sin (8/2))obtainable by either dynamic light scattering (DLS) or neutron spinecho experiments. Here h is the wavelength of the light (or the neutron) in the medium and B is the scattering angle. The cooperativediffusioncoefficient,Dc,is defined by (I'Jq2)q+ and the dynamic correlation length, &, can be estimated from D, employing the relationship of [H = k~T/6*&, where qais the solvent viscosity and kBT has its usual meaning. The D, characterizeslocal cooperative motion in a gel-like network formed by chain overlapping and [H is supposed to approximately represent the mesh sizeof the network. The dependenceof [H on C is predicted by the power law of [H a where the exponent a varies from 0.75 in the good solvent limit to unity at the theta state.3 The prediction was in semiquantitative agreement with experiments!-' At high q values of &H >> 1, reis predicted to become asymptotically proportional to 43,
* To whom correspondence should be addreseed.
(1) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornel1 University Press: Ithaca, NY, 1979. (2) Noda,L;Kato, N.; Kitano,T.;Nagaaawa,M. Macromolecules 1981, 14,668. (3) de Gennes, P A . Macromolecules 1976,9,594. (4) Adam, M.; D e h t i , M. Macromolecules 1977,10, 1229. (5) Chu, B.; Nose,T. Macromolecules 1980,13, 122. (6)Nytrom, B.; Roots, J. J. Macromol. Sci., Rev. Macromol. Chem. 1980, Cl9, 35. (7) Nemoto, N.; Makita, Y.; Tsunaehima, Y.; Kurata, M. Macromoleculea 1984,17, 2629. (8) Brown, W.;J o h n , R. Macromolecules 1986, 19, 2002.
0743-7463/93/2409-0419$04.00/0
which reflects a single chain dynamics of a network strand.lv3 DLS studies on semidilute flexible polymer solutions were so far unable to detect this asymptotic region, since the condition of q[H >> 1 for DLS is only achieved for a network prepared at low C with extremely high molecular weight polymer. On the other hand, Richter et al. reported using the neutron spin-echo technique that Aw of semidilute Solutions of poly(dimethyleiloxane) indeed showed the crossover from the gel mode of Aw a: q2 to the intramolecular mode of Aw 0: q3 with increasing qa9 Because of the rather limited q range accessible by this technique, however, quantitative comparison with the rigorous theory could not be made.lOJ1 It is well established by an electron microscopic observation that cetyltrimethylammonium bromide (CTAB), one of the popular surfactants, forms a very long threadlike micelle in aqueous sodium salicylate (Nasal) solution.12 The CTAB/NaSal micelles then form a viscoelastic network at CTAB concentration CDaslow as 6 X 1WM.19-20 This property may provide a unique opportunity to test the applicability of the dynamic scaling law over the wide range of q[H using the DLS technique. This is the first aim of the present study. Another purpose comes from experimental results obtained in an earlier investigation21that the CTAB/NaSal (9) Richter, D.; Hayter, J. B.; Mezei, F.; Ewen, B. Phys. Rev. Lett. 1978,41, 1484. (10) Doi, M.;Edwards,S. F. The Theory of Po1ymerDynomic.s; Oxford University Press: Oxford, 1986. (11) Kawaaaki,K.InCriticalPhenomeno;Green,M.S.,Eds.;Academic Press: New York, 1971; p 342. (12) Shikata, T.; Sakaguchi, Y.; Uragami, H.; Tamura, A.; Hirata, H. J. Colloid Interface Sci. 1987,119, 291. (13) Rehage, H.;Hoffmann, H. Faraday Discuss. Chem. SOC.1983,76, 363. (14) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74,933. (15) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987,3,1081. (16) Shikata, T.; Hirata, H.; Kotaka, T. Longmuir 1988,4, 354. (17) Imae, T. J. Phys. Chem. 1990,94, 5953. (18) Hashimoh, K.; Imae, T.; Nakazawa, K. Colloid Polym. Sci. 1992, 270, 249. (19) Clawn, T. M.; Vinson, P. K.; Minter, J. R.;Davis, H. T.;Talmon, Y.; Miller, W. G . J. Phys. Chem. 1992,96,474. (20) Yamamura, T.; Kusalra, T.; Takatori,E.; Inoue, T.;Nemoto, N.; Osaki, K.; Shikata,T.; Kotaka, T. Nthon Reoroji Gakkaashi 1991,19,45 (in Japanese). (21) Nemoh,N.;Yamamura,T.;Osaki,K.;Shikata,T.Langmw'r 1991, 7, 2607.
8 1993 American Chemical Society
420 Langmuir, Vol. 9, No. 2,1993
network exhibits diffusion and viscoelasticbehavior quite distinct from those observed for entanglement networks of flesiblepolymer chains.22-26The translational diffusion coefficient D of a micelle in the network showed complicated dependence on both CD and a ratio of salt concentration Cs to CD. The D took a maximum with increasing CDat CS/CD= 1, and at a fixed CDwith increasing CS/CD, D took a maximum which is followed by a minimum. Dependences of the relaxation time T~ on both CD and CS/CDestimated from a fit of the dynamic shear modulus data by a Maswell model were found consistent with the diffusion behavior. That complicated dependence motivated us to study the short-time behavior or the local molecular motion of the CTAB/NaSalmicelleswhich may be properly proved by the DLS experiments. The DLS experiments on aqueous solutions of threadlike micelles done so far were focused on dependences of D, on CD,CS, and Ta2(+W The rebehavior on this system in the q space is not yet explored. In this study, we performed DLS measurements on networks composed of long threadlike CTAB/NaSal micelles with CD= 0.01 M for an estimate of reas a function of q, CS/CD, and T. We shall show that D, and [H are dependent on CS/CDin a complicated manner, while they monotonically change with T. Nevertheless all redata for the samples with CS/CD= 1-41 at three temperatures are found to be superposed on one master curve in making areduced plot of l"$q2D,vs q[H, indicatingthe applicability of the dynamic scaling law.
Nemoto and Kuwahara
-,
2.0
..
1
I
I
I
1.0 10
,u
40
40
:.;lj
1:
tiHl II IEL
70
l,m[l I llJl IEEI:
i
Figure 1. A typical example of the normalized autcorrelation function Aq(7) of the light intensity scattered from aqueous solutions of CTAB/NaSal micelles plotted against channel number i. The CD and CS/CDof the solution are 0.01 M and 2, respectively. The sampling time AT = 45jm, the scattering angle 0 = 75' and T = 25 OC. The solid curve is one obtained by the fourth-order cumulant fitting and the deviation is shown at the bottom of the figure. 3 0 ~ 1I
I
I
I
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I
I
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Experimental Section Materials. Twice-recrystallized cetyltrimethylammonium bromide (CTAB) (Nakalai Tesque) and special-grade sodium salicylate (NaSal) (Nakalai Tesque) were chosen in this study as cationic surfactant and salt samples, respectively. Dust-free purified water (resistance > 16 Ma) was used as solvent. Six CTAB/NaSal Solutions were prepared by mixing prescribed amounts of aqueous CTAB solutions and of NaSal solutions at 40 OC. The CTAB concentration CDof the solutions waa fixed at CD = 0.01 M, and a ratio of salt concentration CSto CD was and 41. varied for respective solutions as CS/CD = 1,2,4,10,20, The solutions were made optically clean by filtering with a Millipore filter (nominal pore size, 0.22Im), and equilibrated at room temperature for at least 1 week for dynamic light scattering measurements. Methods. Dynamic light scattering measurementa were made with an instrument recently reconstructed in our laboratory. A vertically polarized single frequency 488-nm line of an argon ion laser (Spectra Physics, Model 2060) was used as a light source with an output power of 500 mW/mmz. The vertical component of the light intensity Z ( t ) scattered from the solutions was passed through two pinholes 20 cm apart and an optical fiber, and was detected by a photomultiplier (Hamamatsu Photonix) at 12 fixed scattering angles of B = lo', 15', 20°,25', 30°,45', 60°, 75', 90°, llOo,130°,and 150'. The pinhole sizeswere varied for respective scattering angles by taking into account the coherence area and the stray light. The minimum sizes were 0.1and 0.3 mm for the optical configuration at B = 10'. The normalized intensity (22) Nemoto, N.; Kishine, M.; Inoue, T.; Os&, K. Macromolecules 1990, 23, 659. (23) Nemoto, N.; Kiehine, M.; Inoue, T.; Oeaki, K. Macromolecules 1991,24,1648. (24) Nemoto, N. In Polymer Rheology and Processing; Collyer, A. A,, Utracki, L. A., E&.; Elsevier: London, 1999, p 3. (25) Lodge, T. P.; Rotatein, N. A.; Prager, S. Adu. Chem. Phys. 1990, 79, 1. (26) Makhloufi, R.; Himh, E.;Candau, S. J.; Binana-Limbele, W.; h a , R. J. Phy8. Chem. 1989,93,8095. (27) Ng, S. C.; Can, M. L.; Chew, C. H. Colloid Polym. Sci. 1992,270,
64. (28) Candau, S. J.; Hirsch, E.;Zana, R. J. Colloid Interface Sci. 1986, 105, 521. (29) Appell, J.; Porte, G.Europhys. Lett. 1990,12, 185.
0
5
10
q2/ 1010cm-2 Figure 2. Dependence of rdq*on the scattering vector q for the CTAB/NaSal solution with CS/CD= 1 at three temperatures of 25 'C (0),40 'C (01, and 60 'C (A). autocorrelation function Aq(7) (=(I(O)Z(r))/(1(0))2)was measured using the digital autocorrelator (Malvern, 48 channels). The experimentswere made at T = 25, 40, and 60 f 0.05 OC.
Results and Discussion Data Analysis. An example of time profiles of A,(r) obtained by the DLS experiments is shown in Figure 1for the CTAB/NaSal aqueous solution with CD= 0.01 M and CS/CD= 2 at 25 OC. Since Aq(T) could not be fitted to the singleexponentialtype of a decay function at any scattering angle, we applied the cumulant method to estimate the first cumulant refor Aq(T) data of all solutions
re= K,(r,)
(3)
Here 6 is the amplitude and gq(l)(7) is the autocorrelation function of the scattered electric field. The fitted curve shown as the solid curve in Figure 1 is a typical result obtained with the fourth-order cumulant fitting. Randomnessof smallresiduals given at the bottom of the figure indicates that reis obtained to an accuracy of about 1096. Figures 2,3,and4 showthe scatteringvector dependence of reof three CTAB/NaSal solutions with CS/CD= 1,10,
Dynamic Light Scattering of CTABINaSal 3 0 ~ 1I
I
2ol t
r
1
i
A
1
1
A
A
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Langmuir, Vol. 9,No. 2, 1993 421 1
1 4
30]T.
AAi
20
A
A
0
o
n 0
0
0
5
10
with CS/CD= 10. The symbols are the same as in Figure 2.
and 41 at three temperatures of T = 25,40,and 60 "C in the form of a re/q2 vs q2 plot. As was stated in the introduction, Fe/q2of a network should become constant in the low q region which satisfiesq[H C 1and may increase with an increase in q for q[H 1 1. The r e / q 2data of the solution with CS/CD = 1 in Figure 2 are, indeed, almost independent of the scattering vector for q2C 1. Therefore values of the cooperative diffusion coefficient D, defined by (I'e/q2)q+were easily estimated as indicated by arrows to the ordinate for the data at respective temperatures. The increase in re/q2with increasing q2above q2 = 1may be attributed to contributions from intramolecular relaxation modes of respective network strands. The re/q2 data of the solutions with CS/CD = 2 and 4 exhibited q2 dependencesvery similar to that observed for the solution with CSICD= 1,while D, itself varied with CS/CD. On the other hand, it appears that r e / q 2of the solution with CS/ CD = 10 in Figure 3 depends on q over the entire range of the scattering angle from 10" to 150" measured. In fact, the value of re/q2at q2 = 1 and 10 at 25 OC is about 3, which is slightly lesa than that of the corresponding two scattering vectors, 10'Wo*6 H 3.3. The strong q dependence may be ascribed to large [H values at this particular salt concentration of CS/CD = 10, which amounta to the largest value of 132 nm at 25 OC as will be discussed in detail later. The q2 value at q[H = 1 for [H = 132 nm is then estimated as 0.57. It can be seen from the figure that there are a couple of data points below q2 = 0.57 in the bottom data. Thus we tentatively estimated D, by linear extrapolation of the data at low q to q = 0, which is again designatedby arrows in the figure. An uncertainty caused by this extrapolation procedure seems not so serious as to affect later discuseion. With a further increase in CS/CD, rdq2became almost independent of q2 at low q as shown in Figure 4so that D, was easily estimated for the solutions with CS/CD= 20 and 41. Values of D, thus obtained are listed in Table I. Dependence of Dc on CS/CD. Figure 5 gives salt concentration dependence of D, of the CTAEVNaSal solutions at three temperatures. At 25 OC, D, starts to decrease with increasing C ~ C and D takes a minimum of about 1.8 X 10-8cm2 s-l at around CS/CD = 10. Above CS/CD= 10,D sharply increases with an increase in CS/CD and takes a maximum of about 5.5 X cm2s-l at around CS/CD = 20. In an earlier investigation,21we measured the tracer diffusion coefficient D of a dye-labeled CTAB/NaSal micelle in exactly the same system using the forced Rayleigh scattering technique. The plot of D vs CS/CD
0
0
0
5
0
q2/ 1010cm-2
Figure 3. Dependence of rJq2on q for the CTABINaSalsolution
0
0
10
10
1:
q2/ 1010cm-2
Figure 4. Dependence of rJq2on q forthe CTABINaSalsolution with CS/CD = 41. The symbols are the same as in Figure 2.
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Table I. Values of Dc and with
1 2 4
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25 40 60 25 40 60 25 40
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gave a very complicated curve with a maximum that is followed by a minimum with increasing CS/CD. C ~ C D values at the maximum and the minimum were about 4 and 30,respectively. Since D, and D are known to exhibit oppositeconcentration dependencein semidilutepolymer solution,3° the minimum and the maximum observed in D,are qualitatively consistent with the D behavior. The CS/CD values at the minimum and the maximum are, however, obviously different between two physical quantities. The CTAB/NaSal threadlike micelle is stabilized by forming a neutral 1:l complex of a cationic CTA+ ion and an anionic Sal- ion. The stiff structure of the micelle at CS/CD= 1may be deteriorated with increasing CS/CD, ~~
~~
(30)Leger, L.;Hervet,H.; Rondelez,F.Macromokcules 1981,24,1732.
422 Langmuir, Vol. 9,No. 2,1993
Nemoto and Kuwahara
since a number of Sal- ions can invade into the interior of the threadlike micelle. Electrophoretic experiments have revealed that the micelles change the sign of electric charge from plus to minus at around CS/CD= 6 and tend to level off at higher c&D.31 Excess Sal-ions incorporated in the micelle is expectedto make the micelles more flexible and also to make the equilibrium micelle length shorter than that at CS/CD= 1, which leads to the solution state that the micellesbecome less overlapped. This conjecture reasonablyexplainsthe increase in D and also the decrease in D,with increasing CS/CD.Above C ~ C=D6,the amount of excess Sal- ions in the micelles is going to be saturated, and a further increase in salt concentration gives rise to stiffeningand lengtheningof the micelles due to the normal salt-out effect. Then D, must increase with increasing CS/CDabove some CS/CDvalue. Dynamic viscoelastic measurements suggest that there occurred considerable breakdown of the micelles into shorter pieces at CSICD= 4L31This may explain why Detook a maximum at around CS/CD = 20. The CS/CDdependence of D,at elevated temperatures is fundamentallythe same as that at 25 "C. The minimum and the maximum look to occur at the same values of CS/CD= 10and 20,respectively. However, the difference in D,values at the maximum and the minimum decreases with increasing T. We have no explanation why the D, value at CS/CD= 4 is apparently larger than that at CSICD = 2. The D,values of all solutions appear to increase with an increase in T. Accordingto the conceptof the semidiluta polymer solutions,local friction experienced by a polymer segment is determined by the solvent viscosity qs. Therefore D, should increase in proportion to T/q8with an increase in T, whenever the solution structure does not change with T. The threadlike structure of the CTAB/ Nasal micelles is not formed by covalent bonds like polymer chains but by the intermolecular force between surfactant molecules and by their close packing. A rise in T enhances the thermal motion of each surfactant molecule in the micelles, resulting in an increase in flexibility. The threadlike structure is, as a matter of fact, unstable above 90 "C, so that micelles in a spherical form become thermodynamically stable. Contributionsfrom local friction and changes in micelle structure on the T dependence are effectively separated by calculating the dynamic correlation length [H defined by eq 4. For this purpose, viscosities, qm, of Nasal-water EH
= k, T/
q p c
(4)
mixtures were measured at three temperatures of 25,40, and 60 "C. The dependenceof qmonthe salt concentration CScould be expressed by straight lines up to CS = 0.4 M qm = s,(l+ aCs) (5) with values of the concentration coefficient a = 0.34,0.33, and 0.28 at T = 25,40,and 60 "C, respectively. The 7, in eq 5 denotes the viscosity of pure water. Then, qa in eq 4 was assumed identical to qm and was calculated for each pair of CS and T from eq 5. Decrease in CSof the solution due to incorporation of salicylate ions into the micelles negligibly affected qsvalues for the low detergent concentration of CD = 0.01 M. We calculated €H from values of D,listed in Table I with qrvalues,thua estimated, and give a plot of €H against CSICDin Figure 6. From the figure we see that correction of local friction gives same [H values only in the very limited range of C ~ C and D T, (31)In preparation.
0
0 0
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Figure 7. Reduced plot of rdq2D, against was made for all data of solutions with CS/CD= 1-41 measured at T = 26,40, and 60 O C to t a t the applicability of the dynamic scaling law in the q space. The master curve obtained is compared with the theoretical prediction (the solid curve) of eqs 6 and 7.
in which the stiff micelle structure seem distorted to a lesser extent by thermal agitation. The €H values at Cs/ CD = 4 and 10 increase by a factor of 2-3 as T changes from 25 to 60 "C. Such a strong T dependence of [H may be characteristic of the threadlike micelle system and is in contrast to that of neutral flexible chains where negligibly small chain expansion with T in good solvent does not alter the solution structure. It seem interesting that the flexibility of the micelle is most affected by Tin the region where the salt-out effect becomes dominant. The & obtained in this study ranges from 28 to 132nm. It may be noted that [H of polystyrene with molecular weight of 8 420 OOO in benzene is only 28 nm at low polymer concentration of 0.39w t % .7 Therefore large EH values of the CTAEVNaSal system made it possible to obsewe prominent q dependence of rein the semidilute regime by the DLS technique for the first time. The Dynamic Scaling Law. In order to test the applicability of the dynamic scaling law on the redata, some of which are shown in Figures 2-4,we f i t made a reduced plot of I'dqzD, against q[H for the data of each solution obtained at three temperatures. Good superposition was found for respective reduced data. Six reduced data of the solutionswith C ~ C=D1-41 are plotted together in Figure 7. Evidently,all data nicely composeone master
Langmuir, Vol. 9, No. 2, 1993 423
Dynamic Light Scattering of CTABINaSal
curve over a wide range of q 4 H except data scattering for q 4 H < 0.4, a little bit larger than an experimental error of about 10%. In the figure, the solid curve is the theoretical prediction for re behavior of flexible polymere in the semidilute regimelo re/q2D, F(qtH)
(6)
3 (1 + x 2 + ( x 3 - x-1) tan-l x ) F(x) = -
(7)
4x2
The scaling function F ( x ) is originally obtained in critical dynamics for binary solutions of low molecular weight substances by Kawasaki" and has properties of F(x) = 1 for x 0 and F(x) = 3 4 8 for x >> 1. It is remarkable that the reduced data are very closely located on the theoretical curve. It should be noted that a possible error in the estimate of D, for the solution with C ~ C = D 4 does not affect the agreement, because the correction merely shifts data points along the theoretical curve for q[H > 1 in this type of reduced plot. Thus we would like to conclude that, in spite of the complicated C&'D dependence of D, (or (H), the dynamic scaling law in the q space holds for the semidilute solutions of the CTAB/NaSal micelles and that thg transition behavior from the gelmodeto the single chain mode is quantitatively described by the formula which rigorously dealt with the time evolution of concentration fluctuation based on the Langevin equation.
-
It should be remarked that the theory is valid for description of the short time-scale dynamics, since the effect of topological constraints which dominates the long time-scale dynamics was not taken into account. Cates has argued that, in the threadlike micelle system,aciseion and recombination kinetics among micelles plays a deterministic role to the translational diffusion and viscoelasticity of the network in the terminal If the characteristic time Tb of the kinetics would be shorter than the characteristic time (-We)probed by the DLS experiments, the time evolution of concentration fluctuation must be described by q independent 7b. The applicability of the dynamic scaling law strongly suggests that Tb is larger than the largest value of We, about 50 ms. Acknowledgment. We are grateful to Professor K. Osaki for stimulating discussions. We also thank a reviewer who suggested the use of qm, instead of qw as q8 in eq 5. This work is partly supported by a Grant-in-Aid for Scientific Research (No.03453113) of the Ministry of Culture, Science and Education of Japan. (32) Catee, M.E.Macromolecules 1987,20, 2289. (33) Catas, M.E.J . Phys. (Paris) 1988,49,1593. (34) Turner, M. S.; Catee, M.E.J. Phys. (Park) 1990,61,307. (35) Catea, M.E.;Candau, S. J. J. Phys.: Condens. Matter 1990,2, 6869. (36) Granek, R.; Catas, M. E.J. Chem. Phys. 1992,96,4758.
