5435
J. Phys. Chem. 1986,90, 5435-5441 and 2.5 for H 2 0and HC1 as donors, respectively. These ratios, as they are an indication of the relative acceptor strength, seem very large. However, in Ar matrices a compression effect occurs, which results in shorter equilibrium distances than in the gas-phase dimer. From our calculation at R = 5.0 au it was found that the methyl substituent effect is enhanced by a factor 1.5 relative to the equilibrium distance ( A M d p values are now -0.87 and -0.94 kcal/mol for the first and second substitution, respectively). The finding that methyl substitution at the acceptor increases the binding energy considerably and that this effect is enhanced at shorter distances could be of importance for simulation studies of hydrogen bonding in solution and in crystals. The potential functions used should allow for this effect in order to predict good binding energies and 0-0 distances. However, it should be mentioned that potential functions that do not allow for this effect might still yield good results because other effects that have the opposite trend, such as the cooperative effect, are also ignored. The differences in AEdp energies in the basis set DZP' are the best estimates of the methyl substituent effect given so far. Our results may slightly overestimate the effect since the equilibrium distances are somewhat too short in the present calculations. However, it is unlikely that basis set extension or improvement of the method would change the trend in or the size of the methyl substituent effect. For (H20), S C F + dispersion corrected multipole energies were also calculated in the larger EZPP basis
+
set.29 It was found that the major difference between DZP' and EZPP is in the exchange contribution (0.4kcal/mol). However, since Mex hardly contributes to the methyl substituent effect in DZP' we do not expect that the extension of the basis set would lead to other conclusions. Similar reasoning holds for improvement of the method by performing C I calculations. For (H20), DZP' showed a lack of exchange repulsion at C I level (scheme 3(L)) as compared to EZPPZ9but differences in exchange energy between the three complexes will still be small. Thus we feel that both our basis set DZP' and the (SCF + dispersion + corrected point-charge) method are sufficiently accurate to reproduce the trend in the methyl substituent effect.
Conclusion The binding equilibrium energy calculated in the DZP' basis with the (SCF + dispersion corrected point-charge) method for the (H20), complex increases by 0.54kcal/mol when one of the H atoms at the acceptor is replaced by a methyl group and by another 0.60 kcal/mol when the second H atom is replaced. The 4-31Gbasis does not give a good account of the subtle effect of methyl substitution due to unbalanced separate contributions to the interaction energy. The main contributions to the methyl substituent effect are due to changes in the Coulomb and dispersion energies. Registry No. MeOH, 67-56-1; MeOMe, 115-10-6;H20, 7732-18-5.
+
Growth and Counterion Binding of Cetyltrimethylammonium Bromide Aggregates at 25 'C: A Neutron and Light Scattering Study Francois Quirion DZpartement de Chimie. UniversitP de Sherbrooke, Sherbrooke, Quebec, Canada Jl K 2Rl
and Linda J. Magid* Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996- 1600 (Received: November 13, 1985: In Final Form: January 27, 1986)
Neutron and light scattering were used to study the aqueous'solutions (D20 and H20, respectively) of cetyltrimethylammonium bromide (CTAB) up to 0.3 m. The effect of added KBr and KC1 on 0.03 rn CTAB in H 2 0 was also investigated. Neutron scattering data were analyzed with a homogeneous-monodisperse-dry ellipsoid form factor combined with the rescaled mean spherical approximation (RMSA) for the interparticle structure factor. Around 0.15 rn CTAB the fraction of counterion binding increases by about 0.08 while rapid micellar growth commences around 0.2 rn. When KBr is added to 0.03 rn CTAB, a change in the interparticle interactions is observed around 0.026 m KBr; the micellar growth starts around 0.04 rn KBr. The scattering curves for the large micelles were fitted well with a cylindrical form factor. The axial ratio reaches a value of 10 in the range 0.08-0.10 rn KBr. Dynamic and static light scattering measurements for 0.01, 0.03, and 0.05 rn CTAB in H 2 0 with added KBr up to 0.1 rn allowed us to separate the effects of micellar growth from the change in the interparticle interactions. We suggest that this change is associated with an increase of the counterion binding. When KC1 is added to 0.03 rn CTAB in H20, the aggregates show no significant growth. If a mixture of KBr and KC1 is added, the growth seems to be dependent only on the bromide content of the solution. Moreover, for CTAB > 0.03 rn, the increase in counterion binding seems to begin at a constant free bromide concentration of 0.03 rn.
Introduction It is now generally agreed that cety~trimethy~ammonium bromide (CTAB) aggregates go through a Sphereterod tramition as the concentration is increasd.i-4 Lindman and ~ ~
and Anacker6 mentioned that this transition is associated with an increase in the fraction of counterion binding, @. Porte and APPell' computed B values about 0.07 higher for the monomers of cetylpyridinium bromide in the ~cylindrical part~ of the aggregates ~ ~ ~
(1) Ekwall, P.; Mandell, L.; Solyom, P. J . Colloid Interface Sci. 1971, 35, 519. (2) Backlund, S.;Hoiland, H.; Kjammen, 0. J.; Ljosland, E. Acta Chem. Scand., Ser. A 1982, 36, 698. (3) Lindblom, G.;Lindman, B.; Mandell, L. J. Colloid Interface Sci. 1973, 42, 400.
Reiss-Husson, F.; Luzatti, V. J. Phys. Chem. 1964, 68, 3504. (5) Lindman, B.; Wennerstrbm, H. In "Solution Behavior of Surfactants; Fendler, E. J., Mittal, K. L., Eds.; Plenum: New York, 1982; Vol. 1, p 3. (6) Anacker, E. W. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 247. (7) Porte, G.; Appell, J. In Surfactants in Solution; Mittal, K. L. Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 805.
0022-3654/86/2090-5435$01.50/0
(4)
0 1986 American Chemical Society
~
5436
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986
compared to those in the spherical part. From heat capacity measurements, Quirion and Desnoyers' suggested an increase of 0.08 in p around 0.15 m CTAB at 25 OC. They also suggested that the increase in p is not necessarily correlated to the micellar growth. We used small-angle neutron scattering (SANS) and light scattering to get quantitative information on the behavior of p and on the micellar growth. SANS measurements have been used widely to get information on the size and shape of particles in s o l u t i ~ n .More ~ ~ ~ recently, ~ Hayter and Penfold" and Hansen and HayterI2 showed that the apparent micellar charge could be obtained through an analytical expression for the interparticle structure factor ( S ( Q ) ) . From a macroscopic point of view Dorshow et al.I3 and Corti and Degi~rgio'~ used quasi-elastic light scattering (QELS) to study the overall interactions of CTAB aggregates in the presence of added NaBr. Dorshow et al.I5 concluded that a shift from repulsive to attractive interactions is a requirement for micellar growth. We studied the systems CTAB and 0.03 m CTAB KBr in DzO at 28 O C using SANS. QELS and static light scattering were performed on the systems 0.01, 0.03, and 0.05 m CTAB KBr in HzO at 25 "C. We extended our study to the effect of chloride counterions on CTAB aggregates for the systems 0.03 m CTAB KCl or K[Br:Cl] = 0.04 and 0.08 m in H20. For the mixed salt, the mole fraction of bromide (XBr)was varied from 0 to 1.
+
+
+
Materials CTAB was purchased from Sigma Chemicals, Inc., and recrystallized twice from a mixture of acetone and methanol (80/20 v/v). Surface tension showed no minimum in the vicinity of the m from Br- emf measurements at 25 "C). DzO cmc (8.0 X (99.8%) was obtained from Norell and Aldrich Chemicals, Inc. Deionized water was obtained from a Millipore-Q apparatus. KBr and KCl were Fisher certified ACS, and they were used as received. For SANS measurements, all samples were equilibrated around 35 OC for several hours and preequilibrated at 28 OC at least 5 min before the experiment. For light scattering, all solutions were equilibrated at least 12 h at 25 OC, passed through 0.2-pm Millipore filters, and centrifuged at 1500g.
Methods Small-Angle Neutron Scattering. SANS measurements were performed with the 30-m SANS instrument of the National Center for Small Angle Scattering Research located at the High Flux Isotope Reactor a t the Oak Ridge National Laboratory. Samples were prepared in D 2 0 (99.8%) and analyzed in cylindrical spectrophotometric cells of 2-mm path length at 28.0 f 0.1 OC. According to Schelten and Schmatz,16 multiple scattering was negligible for all runs. Data were collected at sample-todetector distances of 1.3 and 5.0 m for neutrons of wavelength X = 4.75 A. The source and sample slit were 3.5 cm (square) and 1.2 em (diameter), respectively. Scattering from samples and solvent was corrected for detector background, detector sensitivity, empty cell scattering, calculated incoherent scattering, and sample transmission. Solvent intensty was subtracted from that of the sample for each detector element. The differences were converted to radially averaged intensities vs. the wavevector Q = 4 7 ~sin (0/2)/X (0 is the scattering angle) (8) Quirion, F.; Desnoyers, J. E., submitted for publication in J . Colloid Interface Sci. (9) Magid, L. J. In Nonionic Surfactants, 2nd ed.;Schick, M., Ed.; Marcel Dekker: New York, in press. (10) Chen, S.-H.; Lin, T.-L. In Methods of Experimental Physics; Skold, S., Price, D. L., Eds.; Academic: New York, Vol. 11. (11) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (12) Hansen, J. P.; Hayter, J. B. Mol. Phys. 1982, 46, 651. (13) Dorshow, R. B.; Briggs, J.; Bunton, C. A,; Nicoli, D. F. J . Phys. Chem. 1982, 86, 2388. (14) Corti, M.; Degiorgio, V. Chem Phys. Lett. 1978, 53, 237. (15) Dorshow, R. B.; Bunton, C. A,; Nicoli, D. F. J. Phys. Chem. 1983, 87, 1409. (16) Schelten, J.; Schmatz. W. J . Appl. Crystallogr. 1980, 13, 385.
Quirion and Magid by using programs provided by the Center. Absolute intensities were computed from calibration constants based on the known scattering of water. The 1.3 apd 5.0 m runs were combined to give a Q range from 0.015 to 0.3 A-1. The overlap range was from 0.07 to 0.1 A-l. In order to eliminate most of the effect of polydispersity at high Q, data were analyzed up to 0.16 A-' except when a cylindrical form factor was used (then Q,,, is 0.3 A-1). SANS data were analyzed with a weighted nonlinear least-squares routine. The weight was defined as the reciprocal of the statistical error of the individual points. Light Scattering. QELS and static light scattering measurements were performed on an apparatus built in our laboratory. We used the 5145-A vertically polarized (V) radiation from a Spectra-Physics argon ion laser. The output power of the incident beam was adjusted (0.1-0.5 W) to give good counting statistics. Samples were analyzed in a cylindrical cell of 1-cm diameter (Wilmad N M R tube, optical quality, 7 cm long). The cell was immersed in a toluene bath of 4-cm diameter and thermostated a t 25.00 f 0.01 O C with a Hart scientific circulating constanttemperature bath. The optical path of the scattered light was defined by two pinholes of 0.03 cm, leading to a coherence area number of 0.6. Ail polarizations (V H ) were detected at the photomultiplier. Rayleigh ratios at 90° were calculated for all samples using benzene as a reference [R(90)$fj?2E°C= (30.0 f 0.6) X cm-'1. Refractive indices of aqueous CTAB were measured with a Brice-Phoenix differential refractometer at room temperature ([dnldc] = 0.155 cm3/g CTAB). Refractive indices of aqueous CTAB were assumed independent of KBr or KC1 concentration. The reliability of the scaling procedure described above was checked for carbon disulfide [R(90)$!$223'c= (136 f 2) X cm-'1 and carbon tetrachloride [R(90)$&Dc = (13.5 f 0.5) X 10" cm-I]. Our calculated R(90) from the scattered intensities and R(90) of benzene agreed with those values within 2%. QELS was performed with a Brookhaven correlator (BI2020, 72 channels). The autocorrelation function was obtained from channels 2 to 62. The calculated base line was subtracted, and the resulting function (lg(t)l)was analyzed with a single-exponentiai least-squares fit as proposed by Pusey et a1.I'
+
order 1: order 2:
+ constant log Ig(t)l = r2t + pzt2 + constant
(1/2) log Ig(t)l = r , t (1/2)
(1)
For all samples rl and r2were obtained for at least five sample times (dt). ri were then plotted against ri dt. The extrapolation at ri dt = 0 gives the reciprocal of the averaged correlation time The apparent diffusion coefficient (Dapp)was calculated with Dapp= r / Q 2 . The quality p2/rZ2is a measure of the size distribution of the particles:" its square root is the z-average normalized distribution of D's. R(90), rl,r2,and p 2 were obtained about 10 times for each sample. Monitoring the total scattered intensity allowed us to eliminate runs poisoned by the presence of dust.
r.
SANS Model It has been shownI8 that SANS data can be analyzed with the general equation I ( Q ) = Np[S(Q) p ( Q ) + A(Q)1 + B
(2)
where N p is the number particle density, S(Q) is the interparticle structure factor, P(Q) is the single-particle form factor, and B is the base line. A(Q) can be related to polydispersity or asphericity depending on the model used. In our experiments, the contrast is between the total particle volume (V,) and the solvent (DzO).Because the chemical composition of the head group of CTAB is similar to that of the tail (17) Pusey, P. N.; Schaeffer, D. W.; Koppel, D. E.; Camerini-Oteri, R. D.; Franklin, R. M. J . Phys. (Paris)1972, 33, C1-163. (18) (a) Hayter, J. B.; Penfold, J. ColloidPolym. Sci. 1983, 261, 1022. (b) Kotlarchyk, M.; Chen, S.-H. J . Chem. Phys. 1983, 79, 2461.
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 5437
Cetyltrimethylammonium Bromide Aggregates 44,
I
I
I
I
30 25
t
1
c
’
6 20
\
15 10
5 0
0
0.00
0.16
a/%-’ Figure 2. SANS data and best fits using a prolate ellipsoid model for CTAB + D20a t 28 OC. 0.00
Q
0.16
la-’
Figure 1. Spherical (A) and prolate ellipsoid (-) fit for (a) 0.03 m and (b) 0.30 m CTAB in D 2 0 .
and assuming no hydration, we chose a homogeneous distribution of the scattering length density (p,) over the particle. This allows us to rewrite P ( Q )
p ( Q ) = (pp - P,)’VP~(F(Q))~
(3)
where ps is the scattering length density of the solvent, F ( Q ) is the normalized single-particle form factor, and ( ) denotes the average over all orientations of the particle with respect to Q. The equation for Z(Q) becomes
where A’(@ = (IF(Q)l2) - (F(Q))2. For monodisperse spheres A’(Q) is zero because (IF(Q)I2)= (FG?))2. Modelfor F(Q) and S(Q). Assuming monodisperse particles, we used a spherical and a prolate ellipsoid form factor to fit the data for 0.03 and 0.3 m CTAB, respectively, the lowest and highest surfactant concentrations investigated by SANS. This is shown in Figure 1. At 0.03 m CTAB both models gave a good fit; at 0.3 m CTAB only the prolate ellipsoid model succeeded. This is consistent with the evolution in micellar shape inferred by other investigators.I4 At 0.3 m, the micelles (neglecting lydispersity) contain 275 monomers, which corresponds to a 34- sphere. This is 7.5 A more than the extended length of the surfactant, so it is not surprising that the micelles deviate from a spherical shape. Since the mean micellar size (aggregation number, mass) is concentration dependent, there is a distribution of micellar sizes in the solutions. However, that distribution is quite narrow for CTAB in water (note the dependence of aggregation number on concentration, Figure 3; see also ref 18), so we have fit the SANS data taken at the higher concentrations using a monodisperse prolate ellipsoid model for F(Q). In such a model A’(Q) becomes the mean-square deviation of the elliptic integral.lg We note also that we have attempted to use the decoupling approximation18 for the higher CTAB concentrations, assuming that plydispersed spherical (or ellipsoidal) micelles are present; the fits are very poor at low Q, and the apparent micellar charges are too large. This has been observed by others as well (T. Zemb, private communication). For all samples the volume fraction of particles lies between 1% and lo%, and the axial ratio does not exceed two, except at
w“
(19) Hayter, J. B. In Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V., Corti, M.; Eds.; North-Holland Amsterdam, 1985.
high KBr concentrations. This allows us to use the rescaled mean spherical approximation as developed by Hayter et al.”J2 for the interparticle structure factor S(Q). For solutions of 0.03 m CTAB in D 2 0 containing more than 0.033 m KBr, the electrostatic repulsions between the micelles are screened. (See for example the behavior of the apparent diffusivities measured by QELS.) Because of the low volume fraction of micelles present, hard-sphere repulsions will have little effect on S(Q),and we make the approximation S(Q) = 1 at all Q. The data a t higher KBr concentrations are fit well by using the form factors for either prolate ellipsoids or cylinders.20 Model Variables. The variables used in our model are B, Np, Z (number of charges per micelle), and Rtot(equivalent sphere radius). The base line, B, was varied as a constant correction of the absolute intensity. From Npexpressed in M (mol/L) we calculated the aggregation number (a) with ff = ([CTAB]
- cmc)/Np
(5)
All molalities (m)were converted to molarities (M) for the calculations by using density measurement^.^^ From the aggregation number and the value obtained for Z, we calculated the fraction of counterion binding (0) with
p = (ii - Z)/rt
(6)
We used our model with a calculated Vp from fi and the molecular volume of CTAB and with R,, (and hence Vp) as a variable. The models agreed within 2%. Because of the good agreement, we kept R,,, as a variable to compensate for small volume changes of the monomers that could occur when the surfactant concentration increases. The prolate ellpsoid is defined by three semiaxes: a, a, and b. a is the semiminor axis and b the semimajor. Tabony2I and Zana et a1.22 obtained 24 A for Rtot of spherical micelles of tetradecyltrimethylammonium bromide. From the results of TanfordZ3 (1.265 A per CH2) we calculated a = 26.5 A for CTAB. From the calculated Vp from R , and assuming a = 26.5 A, we obtained the axial ratio ( b / a ) from Vp = (4/3)rRtOt3= ( 4 / 3 ) r a 2 b
3Vp/(4ra3) = b/a
(7) (8)
(20) Guinier, A.; Fournet, G. Small Angle Scattering of X-rays; Wiley: New York, 1955; p 19. (21) Tabony, J. Mol. Phys. 1984, 51, 975. (22) Zana, R.;Picot, C.; Duplessix, R. J . Colloid Interface Sci. 1983, 93, 43. (23) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes; Wiley: New York, 1980; p 52.
5438 The Journal of Physical Chemistry, Vol. 90, No. 21, 1986
Quirion and Magid
A
0.80
0
/-
/--J0
0.10
0.20
4
0
0.30
0.03
0
C T A B (mol kg-’)
Figure 3.
it,
(3, and b / a extracted from the best fits for CTAB
at 28 O C .
+ D20
Figure 4. SANS data and best fits using a prolate ellipsoid model (0, A) and a cylindrical model (0, 0)for 0.03 m CTAB + KBr.
S(Q) was computed with 2R,,, and F ( Q ) with a and b. The scattering length density of the solvent was kept constant a t ps = 6.319 X 10” A-2 for all samples, and the scattering length density of the particle was calculated with
’O
t
/
n
pp = ~ ~ ~ C T A B / ~ P
bCTAB = [-2.1408
+ p(0.677)] x io-4 A-I
0.06
Q /&-‘
(9)
4
(10)
where bCTABis the molecular scattering length of CTAB.
Results and Discussion We will present first the results for SANS measurements of CTAB in D 2 0 and 0.03 m CTAB in aqueous (D20) KBr. This part will be completed with our results from light scattering. Only grpahical presentations will be given since the data appear elsewhere.24 Small-Angle Neutron Scattering. Figure 2 shows the scattered intensities for CTAB up to 0.3 m. The full lines are the best fits obtained with the prolate ellipsoid form factor as described above. The agreement is better than 2% at the maximum intensities. li, b, and b/a extracted from the fits are presented in Figure 3. Extrapolation to the cmc (8.0 X lo4 m ) gives fi = 115, p = 0.81, and b / a = 1.0; error bars (from weighted nonlinear least-squares fits) are 10% on fi and 7% on p. Our value for fi is larger than those reported in the literature (75,2j 89,% 9 9 ) for CTAB in water. The disagreement could be related to the effect of D 2 0 on the micellar size. Recently, Magid et aL2’ observed a 15% increase in the aggregation number at 0.12 M CTAB when changing the solvent from H 2 0 to D 2 0 . This would give us a value of 100 in water, still higher than the average but in reasonable agreement. Anacker6 reported a range of p = 0.78-0.82 for CTAB close to the cmc. Our value is within this range. The extrapolated axial ratio of 1 suggests that the aggregates are spherical at the cmc, which is realistic for this system. Up to 0.15 m fi is about constant at 0.81 A 0.01. At higher concentrations it increases up to 0.90. This increase of 0.09 in /3 is in very good agreement with the 0.08 reported by Quirion and Desnoyerss from their heat capacity measurements. fi and b / a increase rapidly with concentration up to 0.08 m , where they reach constant slopes up to 0.2 m. (Afi/A(concn) and A(b/a)/A(concn) are 300 and 2.2, respectively.) At higher concentrations the slopes increase by a factor of ca. 2.5 (725 and 5.8). This break in ii and b / a is related to the rapid micellar (24) Quirion, F. Ph.D. Thesis, Bibliotheque des Sciences, Universite de Sherbrooke, 1986. (25) Atik, S . S.; Thomas, J. K. J . Am. Chem. SOC.1981, 103, 4367. (26) Lianos, P.; Zana, R. J. Colloid Inrerfuce Sci. 1981, 84, 100. (27) , k r r , S.; Caponetti, E.; Johnson, J. S.; Jones, R.; Magid, L. J. J . Phys. Chem., i n press.
IC
800
t
/
I
0
0.02
0.04 0.06 mol kg-’ (KBr)
I 0.08
0.10
Figure 5. ri, 6, and b / a extracted from the best fits for 0.03 m CTAB KBr in D20.
+
x
growth of CTAB aggre ates. Ulmius and Wennerstrom28reported an upper limit of 160 for the total length of CTAB aggregates at 0.3 m. At this concentration we get 110 A, in reasonable agreement. Our value may in fact not to be lower than theirs: they do not report the value they used for the semiminor axis. From these results we see that an increase in p occurs prior to the micellar growth. We checked that order of occurrence also for CTAB aggregates with added salt. The scattered intensities for 0.03 m CTAB with added KBr up to 0.1 m are presented in Figure 4. For clarity, the scattering curves are plotted only up to Q = 0.06 A-1. At higher Q,the curves merge. The ability of the interacting prolate ellipsoid model to fit the scattering data at Q < 0.05 A-‘ gets worse as KBr increases; at 0.033 m KBr, the apparent micellar charge is zero, so that reliable values of @ are no longer obtained. Above 0.033 m KBr, we set S(Q) = 1.0, as described previously. The dependences of fi, b / a , and /3 upon the KBr concentration are presented in Figure 5. Extrapolation of li and b / a to zero added KBr gave the same results as were obtained for 0.03 m CTAB. This is not true for 0: the extrapolation gave a value of 0.87 compared with 0.81 for 0.03 rn CTAB. The disagreement may be to the S(Q) expression, since only the charge seems to be affected. Recently, Nagele et al.29 discussed the effect of neglecting the finite size of the counterions in the computation of S(Q). The effect of polydis(28) Ulmius, J.; Wennerstrom, H. J. Magn. Reson. 1977, 28, 309. (29) Nagele, G.; Klein, R.; Medina-Noyola, M. J. Chem. Phys. 1985, 83,
2560.
The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 5439
Cetyltrimethylammonium Bromide Aggregates
1 1
I
T = 25OC CTAB + KBr
'/6
W0 E
&
5
8
Y
= 0.01 A = 0.03 0 = 0.05
800
I
l o
-
A
T=25T CTAB + K B r
0.08
i
I
0.04
I
0
4
o
0
LI
1
400
0.02
A
O
A
I
I
0
0.06 CTAB (mol kg-')
0.12
Figure 7. Growth and interaction diagram for CTAB + KBx Results from light scattering (0) and SANS (0). 0.05
0
0.10
KBr (mol kg")
I
I
I
I
b
T =25OC CTAB
+ KBr
= 0.01 A 0.03 o = 0.05 0
I"
2
u)
to 1
1
Aooo A 0
0
0
0.04 0.08 KBr (mol kg-')
0.12
Figure 6. R(90)(a) and Dapp(b) for 0.01 (O), 0.03 (A),and 0.05 m (0) CTAB + KBr in HzO.
persity on apparent charge may also affect our results; this effect has been discussed by Klein et aL30 and by Senatore and B l ~ m . ~ ' The dependences of fi and b/a on [KBr] show a rapid micellar growth (to ii = 1700 and b/a = 10) from 0.04 to 0.08 m KBr. These values remain about constant up to 0.1 m KBr. Candau et al.32obtained b/a = 6.3 for CTAB in 0.1 m KBr close to the cmc. They suggest that b/a increases with CTAB concentration, which is in agreement with our observation. For the large cylinders at high KBr concentrations, the semiminor axis obtained is smaller than the one for spheres (a(cy1inder) = 23.2 A and a(sphere) = 26.5 A). Attempts to fit the data with "a" fixed a t 26.5 A gave much poorer fits. This decrease of "a" is consistent with the X-ray measurements of Ekwall et who obtained a cylinder radius of 22.5 8,in the hexagonal liquid crystal phase of CTAB. Light Scattering. We used dynamic and static light scattering to get additional (qualitative) information about the interactions and growth of CTAB aggregates. Figure 6 shows R(90) and Dam for 0.01,0.03, and 0.05 rn CTAB as KBr is added at 25 OC. The (30) Klein, R.;Hess, W.; NBgele, G. In Proceedings of the International Symposium on Physics of complex and Supermolecular Fluids: Colloids, Micelles and Microemulsions, Annandale, NJ, June 17-21, 1985. (31) Senatore, G.; Blum, L. J . Phys. Chem. 1985,89, 2676. (32) Candau, S.J.; Hirsch, E.; Zana, R. J . Phys. (Paris) 198445, 1263. (33) Ekwall, P.;Mandell, L.; Fontell, K.J. Colloid Interface Sci. 1969, 29, 639. (34) Mukerjee, P. J . Phys. Chem. 1972, 76, 565.
rapid increase in R(90) at 0.07, 0.05, and 0.04 m KBr for 0.01, 0.03, and 0.05 m CTAB, respectively, reflects the growth of the aggregates. At low KBr concentration, the increase in R(90) indicates a very limited growth or an increase in S(Q) (through R(90) 0: R(0) S(O)),or both. The limited growth and the increase in S(0) were both observed in our SANS results. The rapid growth of the aggregates is also observed through a decrease of Dappat 0.065, 0.05, ad 0.04 m KBr for 0.01, 0.03, and 0.05 m CTAB, respectively. For 0.03 m CTAB plus 0.094 m KBr, RH (from Dappand the Stokes-Einstein relation) is 104 A. For a cylinder with a radius of 23.2 A, this corresponds to a length of 480 A, in good agreement with the SANS results. An interesting feature is the behavior of Dappat low added KBr. For 0.01 m CTAB, Daw decreases rapidly, reaching a plateau at around 0.015 rn KBr. This could be related to a change from strong to weak interparticle repulsions. The same trends are observed for 0.03 and 0.05 m CTAB. In these cases, Dappreaches a constant slope (rather than a plateau) at 0.025 and 0.02 m KBr, respectively. The slope increases with CTAB concentration. From the results obtained for the growth limit of CTAB aggregates, we draw a diagram which separates small spheroidal aggregates from large cylinders. This is shown in Figure 7. The diagram also includes a limit that separates strong and weak interparticle repulsions. From thermodynamic properties8 and our SANS results, we can say that an increase in counterion binding occurs around 0.15 m CTAB in water. From @ = 0.81 at this concentration, we calculated the free bromide concentration, (1 - 0.81)([CTAB] - cmc) = 0.03 m. This concentration represents the free bromide limit for an increase in @ which will be reflected by a change in the interparticle repulsion. Assuming that this holds as well for the system CTAB KBr, we can calculate a limit that represents a change in the interactions. The calculated limit is plotted as a dashed line in the diagram of Figure 7. For 0.03 and 0.05 m CTAB, our results from D,, and R(90) agree very well. For 0.01 m CTAB, our value is smaller. At low CTAB concentrations the screening of the interparticle repulsions is complete at low KBr concentrations as observed from the zero slope of Dapp.In such conditions, an increase of the counterion binding would not be necessary to decrease the interparticle repulsions. Effect of CI Counterions on CTAB Aggregates. We extended our study to the effect of a different added counterion. Figure 8 shows R(90) and D., for 0.03 m CTAB with added KCI in H,O at 25 OC' The with those Obtained for KBr. At low added KCl, the trend for both properties is about the same as for added KBr. Notice that with added KC1 no micellar growth is observed. Interpolated Dapp)sfrom Dorshow et a l , ~ sfor CTAC + NaCl at 25 oc are also presented. ~h~ behavior of CTAB in the presence of KC1 is almost the same as for CTAC aggregates. This suggests that CTAB aggregates
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The Journal of Physical Chemistry, Vol. 90, No. 21, 1986 /
I
l
Quirion and Magid 1000
l
I
I
0.2
0.4
I
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T = 25°C CTAB = 0.03 t KX
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i
I
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E a
t
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"
0
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0.04 0.08 KX (mol k g - ' )
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XBr
3 T=25'C CTAB = 0.03 + KX 0
X=Br
e X=CI A CTAC = 0.03 t NoCl
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7
e**
I
0.8
6
'D
0
0
i
e
0
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5 0.6 T=25"C CTAB 0.03 + K(CI:Br)
d
= 0.04 0
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0.04 0.00 KX (mol kg-')
0
0.12
= 0.08
0.2 0
0.4
0.2
Figure 8. R(90) (a) and DaPs(b) for 0.03 m CTAB wth added KBr (0) or KC1 ( 0 )and the change In the intermicellar repulsion limit. I
t6
t
T; 2 8 ° C CTAB = 0.03 t KX
0
I
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:
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= 0.04 = 0.08
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o X=Br 0 X = C I
0
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0 0
l
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0.1
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0
i
0 .
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8 0 ul
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"
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T = 2 5 T CTAB 0 . 0 3 t K(CI: B r )
P a
0.8
0.6 Xer
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a/%-' Figure 9. Neutron scattering curves in D20for 0.03 m CTAB + 0.08 m KBr (0)or 0.08 m KCI ( 0 ) .
0
0.2
0.4
0.6
0.0
4.0
X Br
Figure 10. R(90)(a), Dapp(b), and k2/I'? (c) in H20for 0.03 m CTAB + 0.04 m ( 0 )and 0.08 m (0)K(Br:Cl) as a function of the bromide molar fraction of the added salt (XBr).
This value is in good agreement with the range quoted by exchange some of their Br for C1 counterions; this has already R o m ~ t e d(1.9-5 ~ ~ with an average of 3.0 h 1.2). This implies been noted by Quirion and Desnoyerss from their emf measure0.1 m KCI, about 63% of the Br ments. Using a pseudophase model as proposed by R o m ~ t e d , ~ ~ that, at 0.03 m CTAB counterions have been exchanged. Figure 9 presents SANS data they obtain the following binding constant ratio: for 0.03 m CTAB + 0.08 m KCl or KBr in D,O. From these results, it becomes evident that in the presence of added KCI the aggregates of CTAB remain small, while they grow substantially when KBr is added. (See Figure 5 . ) It is interesting to look at the evolution of the growth as the (35) Romsted, L. S. In Surfactants in Solurion; Mittal, K.L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 2, p 1015. bromide content increases at constant ionic strength. This was
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J. Phys. Chem. 1986, 90, 5441-5448
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done with the system 0.03 m CTAB 0.04 and 0.08 m K(Br:Cl). The results for R(90) and Dappare plotted against the bromide molar fraction XB,in Figure 10, a and b. At 0.04 m both systems have small aggregates and the difference in all properties is small and monotonic from X,, = 0 to 1. At 0.08 m K(Br:Cl), R(90) and Dappare almost constant up to XB,= 0.6. At higher bromide content the growth is reflected in both properties. The parameter p 2 / r 2 *is related to the polydispersity of the system.” It has been mentioned that the polydispersity of spherical aggregates is smaller than for large cylinders.” From our results, we notice an increase in p 2 / r ? (Figure 1Oc) in the same range of concentration where the micellar growth is observed from R(90) and Dapp.For this system, X,, = 0.6 corresponds to an effective bromide concentration of 0.05 m. This value is the same as the growth limit observed when only KBr is added. (See Figure 7). This suggests that the micellar growth of CTAB aggregates is not dependent on the ionic strength but mostly on the bromide content of the mixed added salt K(Br:Cl). From this we suggest that if the bromide content of CTAB solutions is high enough to be over the growth limit, extra addition of chloride ions will have almost no effect on the size of the aggregates. If the system is initially under the growth limit, extra addition of chloride ions will result in an exchange of bromide for chloride counterions. We mentioned that the counterion binding of Br is higher for large aggregates. Taking 0.81 at 0.03 m and 0.9 at 0.3 m CTAB, we estimated that the binding constant increases by a factor of 2 when the aggregates become large. This is in agreement with the results of Porte and A ~ p e l lwho , ~ suggested that the binding constant of bromide ions is larger for rod-shaped than for spherical aggregates. Over the growth limit, the binding constant of Br increases and the effect of C1 is much smaller.
5441
This explains why Porte and Appel17observed almost no change of aggregate size for 0.006 M CTAB 0.2 M NaBr upon addition of 0.02 M NaC1. The bromide content of their system was well over the growth limit. Our hypothesis also explains why the CTAB aggregates do not grow for 0.03 m CTAB upon addition of KC1, since the bromide content is well below the growth limit.
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Conclusions From neutron and light scattering measurements, we showed that a change in the interparticle interactions occurs prior to the micellar growth. We suggest that this change is related to an increase of the counterion binding. For CTAB without added salt, this increase in p would be about 0.08, in good agreement with heat capacity results8 This increase in counterion binding for CTAB > 0.03 m seems to occur at a constant free bromide concentration around 0.03 m. When KCI (up to 0.1 m ) is added to 0.03 m CTAB, the aggregates show no significant growth. When a mixture of KBr and KCl is added to CTAB solutions, the growth limit seems to be dependent only on the bromide concentration. The hypothesis we made in this paper holds for the systems and the range of concentrations we studied. We do not generalize our conclusions for every surfactant and added salt, but we feel it may give a new insight on the phenomena associated with micellar growth. Acknowledgment. F.Q. thanks the Conseil National de la Recherche en Science et en Genie and the Fonds Canadien de 1’Aide a la Recherche for financial support; L.J.M. thanks the National Science Foundation (Grant CHE-8308362). Registry No. CTAB, 57-09-0; KBr, 1910-42-5;KCI, 7447-40-7.
Correlation between Molecular Reorientation Dynamics of Ionic Probes in Pdlar Fluids and Dielectric Friction by Picosecond Modulation Spectroscopy Eva F. Gudgin Templeton and Geraldine A. Kenney-Wallace* Lash Miller Laboratories, University of Toronto, Toronto M5S 1A1, Canada (Received: December 2, 1985; In Final Form: March 20, 1986)
The dye molecules resorufin, thionine, and cresyl violet are studied in amides, alcohols, and water-alcohol binary systems in order to investigate the correlations between orientational relaxation times ( T , , ~ ) and properties of the single-solvent or binary systems. A sequence of normal and substituted alcohols, dimethyl sulfoxide, formamide, N-methylformamide, and dimethylformamide has been investigated. While good agreement with hydrodynamic-based theories is seen for the pure alcohol systems, the binary propanol-H20 systems show a surprising curvilinear dependence of T , , ~vs. 7 beyond the realms of any expectations in simple hydrodynamic responses, as has been shown previously. If a dielectric friction model is applied, then these curvilinear profiles are predicted at least qualitatively. The successful ingredients of such a model are discussed and its limitations assessed for its application to polar fluids, given the poor agreement with the relaxation times or trends in the dimethyl sulfoxide and amide solvents.
Introduction An understanding of the mechanisms responsible for rotational relaxation of molecules in liquid solution is required for a complete description of solution-phase reaction dynamics. Molecular interactions and solvent motion influence the shape of the potential energy surface, and reaction rates can be enhanced or impeded by molecular motions at the barrier crossing which might involve conformational or configurational changes as part of the reactive sequence. For small nonpolar molecules in noninteracting solutions, often reorientational motion can be adequately described with various modifications of the simple Debye-Stokes-Einstein (DSE) equation,’ which relates rotational reorientation time to 0022-3654/86/2090-544l$01.5d/0
the macroscopic solvent viscosity. These modifications include considerations such as changing boundary conditions from stick to slip,2 relative solvent-solute size,3 free space in the solvent structure causing deviations from continuum behavior,’” and ~~~
(1) (a) A good review of a number of hydrodynamic models is presented in: Dote, J. L. Kivelson, D.; Schwartz, R. N. J . Phys. Chem., 1981,85, 2169.
(b) Current theory, experiment and simulation approaches are discussed by a number of authors in: Barnes, A. J., Orville-Thomas, W., Yarwocd, J., Eds. Molecular Liquids: Dynamics and Interactions; (D. Reidel: Dordrecht, 1984). (2) Hu, C.-M.; Zwanzig, R. J . Chem. Phys. 1974, 60, 4354. (3) Gierer, A.; Wirtz, K. Z . Naturforsch. A , 1953, 8, 532.
0 1986 American Chemical Society
