Langmuir 2008, 24, 8507-8513
8507
Zeta Potentials and Debye Screening Lengths of Aqueous, Viscoelastic Surfactant Solutions (Cetyltrimethylammonium Bromide/Sodium Salicylate System) Anuj Shukla† and Heinz Rehage* Technische UniVersita¨t Dortmund, Physikalische Chemie, Otto-Hahn-Str. 6, D-44227 Dortmund, Germany ReceiVed March 16, 2008. ReVised Manuscript ReceiVed May 24, 2008 In a series of experiments, we studied the dynamic properties of aqueous surfactant solutions of cetyltrimethylammonium bromide (CTAB) at conditions after adding different amounts of sodium salicylate (NaSal). The aggregates, present in these solutions, are elongated, wormlike micelles, which tend to form entanglement networks. The viscoelastic, gel-like samples were analyzed by means of static, dynamic, and electrophoretic light scattering techniques. We separately investigated the effects of surfactant concentration and added salt on intermicellar interactions. The electrostatic interactions between the anisometric micelles were analyzed by considering the effective dimensions of the aggregates. We calculated the Debye-Hu¨ckel lengths from experimental data of the osmotic second virial coefficient and from the diffusion second virial coefficient. It turned out that the results were in good agreement with theoretically estimated values. We also measured the zeta potential and intensity of scattered light in a large range of different salt concentrations keeping the CTAB concentration constant. We observed an isoelectric point and charge reversal of the threadlike micelles at an excess salicylate concentration of about 100 mM. The observed decrease of the zeta potential points to striking processes of counterion condensation. In these solutions, the salicylate ion acts as a cosurfactant, due to its discrepancy between polar and hydrophobic groups. We also detected a simple linear correlation between the zeta potentials and the Debye screening lengths of the surfactant solutions.
Introduction Certain cationic surfactants, especially those with ammonium or pyridium head groups, can form rodlike or wormlike micelles (threadlike aggregates) in aqueous solutions when special salts such as sodium salicylate are added.1–8 It is now well established that the rheological and viscoelastic behaviors of these aqueous surfactant solutions depend strongly on the molar concentration of sodium salicylate. The formations of entanglements or branching processes between the wormlike micelles are thought to be responsible for the remarkable viscoelasticity and spinnability of the solutions.9 Recent observation with cryotransmission electron microscopy (TEM)10 has visually shown the presence of entangled threadlike or polymerlike micelles. The surfactant aggregates are often denoted as living or equilibrium polymers because the linear surfactant aggregates can break and recombine in a broad range of different time scales. The polymer-like micelles that have self-assembled in water have been rather widely studied to characterize their size and shape. These investigations have been performed by employing the theoretical concepts11 and experimental methods developed in polymer science. Typical experiments are based on static (SLS) * Corresponding author. Telephone: +49 (345) 7553910. Fax: +49 (231) 7555367. E-mail:
[email protected]. † Present address: European Synchrotron Radiation Facility, 6 rue Jules Horowitz, F-38043 Grenoble, France.
(1) Rehage, H.; Hoffmann, H. J. Phys. Chem. 1988, 92, 4712. (2) Fischer, P.; Rehage, H. Langmuir 1997, 13, 7012. (3) Kern, F.; Lemarechal, P.; Candau, S. J.; Cates, M. E. Langmuir 1992, 8, 437. (4) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456. (5) Buchanan, M.; Atakhorrami, M.; Palierne, J. F.; MacKintosh, F. C.; Schmidt, C. F. Phys. ReV. E 2005, 72, 011504. (6) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987, 3, 1081. (7) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988, 4, 354. (8) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1989, 5, 398. (9) Imae, T. J. Phys. Chem. 1990, 94, 5953. (10) Gonzalez, Y. I.; Kaler, E. W. Curr. Opin. Colloid Interface 2005, 10, 256 and references therein. (11) Cates, M. E.; Candau, S. J. J. Phys: Condens. Matter 1990, 2, 6869.
and dynamic light scattering (DLS),9,12–15 small-angle neutron scattering,16 forced-Rayleigh scattering,17,18 T-jump,19 dynamic viscoelastic measurements,1,2,6,7,17 and similar techniques. The contrast between our understanding of charged and neutral polymers results from difficulties encountered in experimental and theoretical investigations of charged systems. The main theoretical complication is the long-range nature of Coulomb interactions. The presence of charges introduces more than one new length scale, making scaling theories, so useful in neutral polymer theory, no longer as simple and clearly applicable to charged systems. In most cases, experimental methods use indirect means, which are susceptible to problems of interpretation and tend to rely on results of neutral polymer theory, which is often inapplicable. Scattering techniques collectively suffer from the disadvantage that, in order to obtain a reliable estimation of size and shape, measurements should be made in the highly dilute concentration regime. The data are usually extrapolated to infinite dilution in order to avoid the problems encountered as a result of intermicellar interactions. However, this extrapolation procedure is impossible if self-assembling systems with concentration-dependent aggregation numbers are studied. Cationic micelle solutions represent this kind of systems, since these micelles grow by varying the surfactant concentration or ionic strength. Consequently, to extract meaningful information at finite micelle concentrations, a scattering technique such as static light scattering (SLS) or dynamic light scattering (DLS) cannot be used without (12) Koike, A.; Yamamura, T.; Nemoto, N. Colloid Polym. Sci. 1994, 272, 955. (13) Nemoto, N.; Kuwahara, M.; Yao, M.; Osaki, K. Langmuir 1995, 11, 30. (14) Buhler, E.; Munch, J.; Candau, S. J. Phys. II 1995, 5, 765. (15) Amin, S.; Kermis, T. W.; van Zanten, R. M.; Dees, S. J.; van Zanten, J. H. Langmuir 2001, 17, 8055. (16) Aswal, V. K.; Goyal, P. S.; Thiyagarajan, P. J. Phys. Chem. B 1998, 102, 2469. (17) Nemoto, N.; Kuwahara, M. Colloid Polym. Sci. 1994, 272, 846. (18) Shikata, T.; Imai, S.-I.; Morishima, Y. Langmuir 1998, 14, 2026. (19) Kern, F.; Zana, R.; Candau, S. J. Langmuir 1991, 7, 1344.
10.1021/la800816e CCC: $40.75 2008 American Chemical Society Published on Web 07/17/2008
8508 Langmuir, Vol. 24, No. 16, 2008
Figure 1. Debye plot of samples with different salt-to-surfactant ratios at T ) 30 °C.
making assumptions about the nature of the intermicellar interactions. Concentration-dependent intermicellar interactions and growth of the aggregates simultaneously occur in the solutions. The contributions from both effects are not easily decoupled. A more convenient way to detect micellar growth is to maintain the interactions between charged micelles at a constant level. This can approximately be achieved by keeping the ratio of salt-to-surfactant concentration constant. Therefore, in the first sets of experiments, we performed such investigations. In the present work, we investigated polymer-like micellar aggregates that were formed in cetyltrimethylammonium bromide (CTAB) solutions either in dilute aqueous solutions or after addition of sodium salicylate (NaSal). To evaluate the contributions from micellar growth and intermicellar interactions, a homogeneous sphero-cylinder was considered to represent the micelle in the experimental data interpretation. The effects of electrostatic interactions between the micelles were approximated by considering the expansion of length and diameter of the spherocylinder, which were induced by the Coulomb forces. Another important problem in the study of charged micelles is the determination of the shear plane and its zeta potential. The shear layer is important, as it influences the stability of heterogeneous particles and affects particle hydrodynamic mobility.20 Reports concerning the determination of the zeta potential for viscoelastic surfactant systems are scarce. Here, we present new experimental measurements, which were performed in order to gain more insight into the complicated phenomena of concentrationdependent Coulomb interactions.
Shukla and Rehage results. This indicates that multiple scattering did not give significant contributions in our measurements. For all forthcoming experiments, the measurement position was determined automatically through an optimization procedure of the signal-to-noise ratio of the scattered light. The measurements were performed in the temperature range between 25 and 50 °C. In all experiments, about 1 mL of the sample was transferred to a special dust-free light scattering cell. In order to allow the temperature to equilibrate, we started the experiments 30 min after the cuvette was placed in the DLS apparatus. The temperature was controlled within ∆T ) (0.02 °C. The light-scattering process defines the wave vector q ) (4πn/λ) sin(θ/2), where λ is the wavelength of the incident light in a vacuum, θ denotes the scattering angle, and n describes the refractive index of the solvent. Data Analysis. Static Light Scattering. SLS measures the timeaveraged scattered intensity, known as the excess Rayleigh ratio Rθ. In 1948, Zimm derived the basic relationship between the concentration and the intensity of scattered light
K(Cd - C0) 1 ) + 2B2(Cd - C0) Rθ Mw P(θ)
Here, Cd denotes the concentration of surfactant, C0 describes the critical micelle concentration, B2 is the osmotic second virial coefficient, Mw is the molecular weight of the investigated particles, and P(θ) is the form factor. This parameter depends on particle shape when the particle is large enough to accommodate multiple photon scattering. In this work, we have not taken into account multiple scattering effects that may possibly appear in the regime of high concentration. Under the condition of Rayleigh scattering, P(θ) will reduce to 1. In the course of different experiments, we did not detect any process of multiple scattering, because no significant difference of experimental data was observed as a function of the measured position in the cuvette. (Measuring closer to the cuvette wall will reduce the effect of multiple scattering by minimizing the path length over which the scattered light has to pass.) This indicates that multiple scattering seems to not be significant in our measurements. The optical constant, K, is defined by
K)
(20) Xu, R. Langmuir 1998, 14, 2593.
( )
4π2n2 dn λ04NA dCd
(2)
Here, dn/dCd denotes the specific refractive index increment and NA is Avogadro’s number. In the dilute regime, the osmotic second viral coefficient derived for hard-body interacting rigid rods with a length L and a diameter d from the Mcmillan-Mayer theory can be written as follows:21,22
Experimental Section Preparation of the Solutions. Cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) were purchased from Merck and Fluka, respectively, and purified by recrystallization. The solutions were left standing for at least 1 week in order to reach equilibrium. Laser Light Scattering Measurements. The light scattering and zeta potential experiments were performed using the commercially available equipment Zetasizer Nano from Malvern. We used a 4 mW He-Ne laser (633 nm wavelength) with a fixed detector angle of 173° for dynamic light scattering and 17° for zeta potential experiments. In order to reduce the effect of multiple scattering, we used noninvasive back-scattering techniques. In a series of experiments, we measured the light scattering of the samples at different depths within the cuvette. The measurement positions were changed manually to record the effect of changing this parameter. We investigated all samples at least at five different positions. The minimum position was always selected near to the cuvette wall. The maximum position was chosen at the center of the cuvette. In all these experiments, we did not observe any differences between these
(1)
B2 )
( ) πNAd2L Mw2
f
(3)
where the factor f for a rodlike particle is
f)
1 L 1 πd + (3 + π) + 4 d 2 4L
[
]
(4)
In the present analysis, we have calculated L from Mw by the relation23
L)
4VMw 2
πNAd
+
d 3
(5)
where V is the partial specific volume of the surfactant. Dynamic Light Scattering. The parameter measured directly in the dynamic light scattering experiments was the time autocorrelation function of the scattered light intensity. The autocorrelation function of the scattered intensity was analyzed by means of the inverse (21) Onsager, L. Ann. N.Y. Acad. Sci. 1949, 51, 627. (22) Ishihara, A. J. Chem. Phys. 1950, 18, 1446; 1951, 19, 1142. (23) Yoshimura, S.; Shirai, S.; Einaga, Y. J. Phys. Chem. B 2004, 108, 15477.
Dynamic Properties of Aqueous CTAB/NaSal Solutions
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Table 1. Fitting Parameters for the SLS Data (Figure 1) and DLS Data (Figure 2)a SLS 3
DLS 3
2
Cs/Cd
Mw [10 g/mol]
B2 [cm mol/g ]
0 0.33 0.66 1 1.33
34.48 36.40 833.33 1.24 × 103 1.82 × 103
0.040 0.006 0.00030 0.00028 0.00030
a
-1
κ
[nm]
22 8
-6
D0 [10 1.025 1.206 0.370 0.284 0.286
2
cm /s]
ξΗ [nm]
kd [cm3/g]
κ-1 [nm]
2.7 2.3 7.5 9.9 9.8
756.27 269.78 23.28 12.52 -10.73
12.7 7
Parameters are given in the text.
Laplace transform program CONTIN.24 Alternatively, the data were analyzed using a biexponential fitting procedure. However, it must be remarked that the CONTIN method led, in our results, to distributions of relaxation times that were centered around the relaxation times which were obtained using just biexponential fitting. Therefore, for the sake of simplicity, we used the results obtained from biexponential fitting. The effect of entanglement interactions can be detected by DLS measurements as we have shown previously.25 When the diffusion process is coupled to viscoelastic relaxation due to entanglement effects, the autocorrelation function displays two different relaxation modes. Therefore, the second slow mode was not observed for the unentangled systems. Figure 2 shows the network cooperative diffusion coefficient, Dapp, estimated from the fast relaxation mode. Dapp can be expanded in power series of the surfactant concentration:26
Dapp ) D0[1 + kd(Cd - C0)]
(6)
In the dilute regime, the diffusion virial coefficient, kd, is described by27
kd ) 2B2M - kf - Vs
(7)
with the frictional virial coefficient
kf )
RTL2 3d 3ηD0M 8L
2⁄3
( )
(8)
This simple analysis holds for uncharged rodlike particles.28 The partial specific volume of CTAB29 is Vs ) 0.996. Zeta Potential. The Zetasizer Nano series apparatus calculates the zeta potential by determining the electrophoretic mobility. The zeta potential can afterward be calculated by applying the Henry equation.
UE )
2εζ f(κa) 3η
(9)
ζ is the zeta potential, UE denotes the electrophoretic mobility, ε is the dielectric constant, η describes the viscosity, and f(κa) is Henry’s function. The Smoluchowski approximation is used in order to determine f(κa). The advanced technique M3-PALS patented by Malvern was used to measure the electrophoretic mobility. This technique is based on a combination of Malvern’s improved laser Doppler velocimetry method (i.e., slow field reversal and fast field reversal measurement techniques to remove electro-osmosis effects) and phase analysis light scattering (detection of a phase change is more sensitive to changes in mobility than the traditional detection of a frequency shift). The mean zeta potential that was calculated by this technique is therefore very robust, as the measurement position in the cell is not critical. (24) Provencher, S. W. Comput. Phys. Commun., 1982, 27, 229–242. (25) Shukla, A.; Fuchs, R.; Rehage, H. Langmuir 2006, 22, 3000. (26) Imae, T. Langmuir 1989, 5, 205. (27) Yamakawa, H. Modern Theory of Polymer Solution; Harper and Row: New York, 1971; p 181. (28) Peterson, J. J. Chem. Phys. 1964, 40, 2680. (29) Husson, F. R.; Luzzati, V. J. Phys Chem. 1964, 68, 3504.
Results and Discussion Figure 1 presents typical Debye plots for different aqueous solutions of CTAB after addition of different amounts of sodium salicylate (NaSal). The Debye plot for aqueous solutions of CTAB without addition of NaSal (30 °C) linearly increases as a function of the micelle concentration but deviates downward at concentrations of about Ccross ≈ 0.005 g/cm3. Similar behavior has previously been observed for pure CTAB micelles in water.30,31 In this case, a sharp crossover between a regime of weak growth (due to electrostatic interactions) and a regime of accelerated micellar growth (when the size of the micelles becomes larger than the Debye length) was detected.32,33 This phenomenon was interpreted as a stronger adsorption process of Br- ions at the micellar surface above the concentration Ccross. This adsorption process thus weakens the intermicellar repulsion and reduces the value of the Debye length.30,31 The molecular weight and second virial coefficient were obtained from eq 1 (B2 ) 0.040 cm3 mol/g2 and Mw ) 34.48 kDa without addition of NaSal). These values are in good agreement with those reported in the literature.30,31 In order to investigate the salt effects on micellar growth and interaction, we also performed scattering measurements below Ccross. In a series of experiments, we investigated different salt-to-surfactant ratios. At a given surfactant concentration, larger salt concentrations induced a stronger screening of the repulsive forces, which reduced the intermicellar interactions and favored the growth of the micelles. Therefore, Ccross decreased as a function of the salt concentration. We observed, indeed, the decrease of the Ccross values with the addition of salt. As shown in Figure 1, for pure CTAB solutions, Ccross is of the order of 0.007 g/cm3. For a salt-to-surfactant ratio of 0.33, we obtained a lower value of Ccross of ∼0.002 g/cm3. The quotient Cs/Cd describes the saltto-surfactant ratio, where Cs is the concentration of salt. The molecular weights and second virial coefficients obtained from the Deby plots (Figure 1) below Ccross are summarized in Table 1. The molecular weights of pure CTAB solutions can be assigned to spherical micelles. However, smaller values of the second virial coefficients for salt added solutions suggest the screening of electrostatic interactions. The Debye plot above Ccross is a straight line, having a weakly negative slope, and this can be interpreted as the gradual formation of rodlike micelles with increasing concentration. After Cs/Cd exceeds a certain value, the Debye plots level off, implying that the entanglement density becomes practically constant. Rheological measurements on the same surfactant system have also indicated that the entanglement density of the network becomes constant after Cs/Cd exceeds a certain critical value.6 This suggests that, at Cs/Cd > 0.33, the intermicellar correlations diminish. In (30) Imae, T.; Kamiya, R.; Ikeda, S. J. Colloid Interface Sci. 1985, 108, 215. (31) Ekwall, P.; Mandell, L.; Solyom, P. J. Colloid Interface Sci. 1971, 35, 519. (32) Imae, T.; Kamiya, R.; Ikeda, S. J. Colloid Interface Sci. 1985, 108, 215. (33) Ekwall, P.; Mandell, L.; Solyom, P. J. Colloid Interface Sci. 1971, 35, 519.
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Figure 2. Apparent diffusion coefficient Dapp as a function of surfactant concentration.
this regime, rodlike micelles grow and tend to form a transient network structure analogous to neutral polymers in semidilute solutions. The constant value describes the reciprocal molecular weight of the entangled network structure.9 Table 1 describes values of molecular weight and second virial coefficient of the entangled network obtained from Debye plots. The second virial coefficient is negligible for very long micelles, and at elevated values of Cs/Cd we observed a strong shielding of electrostatic repulsion due to counterion condensation. The apparent diffusion coefficient showed a similar effect on Cs/Cd as obtained for the Debye plots. Relevant results are summarized in Table 1. The pure CTAB system showed a welldefined crossover concentration Ccross ∼ 0.007 g/cm3. For elevated salt concentrations of Cs/Cd ) 0.33, the crossover concentration decreased to Ccross ∼ 0.002 g/cm3. D0 and kd values obtained from eqs 6 and 7 are also shown in Table 1. These values are in good agreement with those reported in the literature.9 The concentration dependence of Dapp is affected by the kd parameter (eq 6), which is influenced by the nature of particle interactions. Generally, a simple hard-body interaction potential yields a positive value of kd. The repulsive electrostatic component of the potential increases the kd value, whereas the attractive part tends to reduce it and may even lead, if large enough, to negative values. Decreasing kd values with increasing Cs/Cd suggest the screening of electrostatic interactions. Dapp above Ccross (Cs/Cd ) 0.33) as a function of (Cd - C0) gave a straight line, having a weakly negative slope. This behavior can be interpreted as the gradual formation of rodlike micelles with increasing concentration. From D0, the so-called hydrodynamic correlation length ξΗ can be calculated using the Stokes-Einstein relation:
kBT ξH ) 6πηD0
(10)
Parameter kB is Boltzmann’s constant, T denotes the absolute temperature, and η describes the solvent viscosity. For our viscoelastic surfactant solutions, we replaced the solvent viscosity η by the zero-shear viscosities η0 of the NaSal/water system.34 The ξΗ values obtained using eq 10 are also summarized in Table 1. ξΗ is about 2.7 nm below Ccross. This suggests that the micelles are separated from each other; at these conditions, ξΗ is equivalent to the hydrodynamic radius of the micelles. On the other hand, upon increase of the salt-to-surfactant ratio to a value of 0.66, we observed the transition from the dilute regime to the semidilute concentration region. The characteristic behavior of the semidilute concentration regime is shown in the inset of Figure 2. The diffusion coefficient first decreases as a function of the surfactant concentration, goes through a minimum, and (34) Nemoto, N.; Kuwahara, M. Langmuir 1993, 9, 419.
Figure 3. Debye-Hu¨ckel length as a function of the surfactant concentration.
then increases again. This minimum reflects the crossover from the dilute concentration regime into the semidilute range where the elongated micelles form an entanglement network. In the semidilute regime, Dapp should obeys a power-law scaling law: Dc ∼ (Cd - C0)R. A value of R ) 0.77 is predicted for semidilute polymer solutions in a good solvent. To obtain reliable exponents of power laws, one needs to fit the experimental data measured in the range of several orders of magnitude. Such evaluation of true scaling exponents is out of the scope of this article. The diffusion coefficients, measured in the semidilute regime, correspond to the collective movement of the micelles. At these conditions, ξΗ represents the average mesh-size of the network9 and should be independent of the length of the micellar aggregates.11 As listed in Table 1, the mesh-size of the entangled networks is of the order of ξΗ ∼ 9.8 nm. The growth of cylindrical micelles is controlled by the competition between entropy of mixing and the scission energy Esciss required to create two new end-caps. For charged micelles, the energy of scission is composed of the repulsive energy of the surface charges that favors the end-caps over the cylindrical regions and end-cap energy that promotes the micellar growth.35 Decrease of the mean distance between charges or increase of the Debye-Hu¨ckel screening length enhances electrostatic repulsions. The Debye-Huckel length κ-1 due to the number of mobile ions in the solution depends on the ionic strength. The Debye-Hu¨ckel length κ-1 is then defined through36
(
κ2 ) 4πLBcd R + 2
CS Cd
)
(11)
LB describes the Bjerrum length and R ) 0.25 is the degree of surfactant ionization.37 Delsanti and co-workers36 used light scattering to probe differences in growth patterns in dilute and semidilute aqueous CTAB/KBr solutions at to different values of Cs/Cd. In a series of experiments, these authors observed that the crossover occurs when the Debye-Hu¨ckel length reaches κ-1 ∼ 5.5 nm. As shown in Figures 1–3, we observed that the crossover occurs when the κ-1 value becomes comparable to the micellar size. The present results together with literature data38 imply that the value of κ-1, at which micellar growth begins, depends on the chemical properties of the surfactant and salt. Therefore, one must consider dilute and (35) Magid, J. J. Phys. Chem. B 1998, 102, 4064. (36) Delsanti, M.; Moussaid, A.; Munch, J. P. J. Colloid Interface Sci. 1993, 157, 285. (37) Hayter, J. B. Langmuir 1992, 8, 2873. (38) Magid, L. J.; Han, Z.; Warr, G. G.; Cassidy, M. A.; Butler, P. D.; Hamilton, W. A. J. Phys. Chem. B 1997, 101, 7919.
Dynamic Properties of Aqueous CTAB/NaSal Solutions
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semidilute regimes, depending on whether the Debye-Hu¨ckel length is larger or smaller than the mean size of the micelles. In the dilute regime of weak growth, the data can be analyzed using eqs 3–8. The effect of electrostatic interactions between the charged rodlike particles can be approximated by considering the particles to be rods surrounded by cylindrical interaction shells. In a simple approach, we can incorporate the electrostatic interaction between the charged micelles into the hydrodynamicthermodynamic (virial) model for rods. This can be achieved by using the ionic strength-dependent extended length Leff and diameters deff instead of the length L and diameters d for the rods in eqs 3–8. The simplest case of a uniform thickness of interaction shell was assumed in the regime below the overlap concentration.39,40 This is not an unreasonable assumption, as eq 12 and Figure 3 make clear; this surfactant-to-salt ratio determines κ-1, since R ) 0.25. Hence, by considering this thickness to be equal to the Debye-Hu¨ckel screening length, κ-1, we can postulate: -1
Leff ) L + κ
and
-1
deff ) d + κ
Figure 4. Scattered light intensity, zeta potential, and Debye-Hu¨ckel length as a function of the salt concentration.
(12)
The static and dynamic light scattering values can be fitted using only one adjustable parameter κ-1 (see eqs 3–8 and 11). A reasonable fit of our experimental data below the crossover concentration can be obtained with κ-1 ) 22 nm and 10 nm for Cs/Cd ) 0 and 0.33, respectively. These results were obtained from static light scattering data. The results of DLS predict κ-1 ) 12.7 nm and 7 nm for Cs/Cd ) 0 and 0.33, respectively. We compared these values with the theoretically estimated values in this concentration regime (see Figure 3). The fact that one can obtain a qualitatively consistent interpretation of SLS and DLS data based on this simple model gives confidence to this interpretation. It is worthwhile to mention that both sets of data result from fundamentally different measurements. Below the crossover concentration for Cs/Cd ) 0 and 0.33, the lengths of the rod calculated from eq 5 are almost equal to the diameters. This points to the presence of spherical micelles. Above the crossover concentration, the decrease of Kc/R and the diffusion coefficient from the expected linear behavior can be traced back to the growth of micelles. In this regime, the interaction between the charged micelles did not vary by keeping the surfactant-to-salt ratio constant (eq 12 and Figure 3 show that the surfactant-to-salt ratio determines κ-1, since R ) 0.25). Following these arguments, the growth of micelles can be expected theoretically. In the second series of experiments, we fixed the concentration of CTAB at 15 mM and systematically varied the NaSal concentrations between 5 and 225 mM (T ) 40 °C). Relevant results of these measurements are summarized in Figure 4. Of peculiar interest of this study is that the apparent molecular weight (Mapp) of CTAB/NaSal solutions as a function of NaSal concentration (Cs) exhibits a striking double-peak behavior (see Figure 4). It is interesting to note that similar Cs/Cd ratios were observed for corresponding peaks in the zero-shear viscosity (η0).41 According to the best of our knowledge, the double-peak behavior of Mapp is, for the first time, reported in this article. The reasons for the double-peak behavior of Mapp and η0 as a function of the ionic strength are not yet completely understood. However, there are certain conjectures that micelles have attained their full length at the first viscosity maximum.42–45 At these conditions, (39) Liu, H.; Skibinska, L.; Gapinski, J.; Patkowski, A.; Fischer, E. W.; Pecora, R. J. Chem. Phys. 1998, 109, 7556. (40) Galantini, L.; Giglio, E.; Leonelli, A.; Pavel, N. V. J. Phys. Chem. B 2004, 108, 3078. (41) Menon, S. V. G.; Goyal, P. S.; Dasannacharya, B. A.; Paranjpe, S. K.; Mehta, R. V.; Upadhyay, R. V. Physica B 1995, 108, 604. (42) Raghavan, S. R. Langmuir 2001, 17, 300.
the system is entangled, forming a three-dimensional network. The decrease of the viscous resistance and Mapp with further addition of salt beyond the first maximum, however, is more difficult to explain. Several authors35,43,46 have proposed that this decrease at high salt concentrations may be due to the formation of a multiconnected network in which stress relaxation can occur by the sliding of cross-links along the wormlike micelles. The second peak in the zero-shear viscosity might then be connected with the charge reversal owing to excess counterion condensation at the surface of the threadlike micelles. Viscoelastic surfactant solutions have been rather widely studied to characterize the shape and size of anisometric micelles. Up to now, there are, however, very few studies dedicated to explore the zeta potential and the process of counterion condensation. These phenomena are certainly correlated with the double-peak behavior of CTAB solutions in the presence of excess NaSal. As discussed above, the origin of the first maximum is almost clear.42,43 The reasons for the appearance of the first minima and the second maximum are yet not completely understood. The double-peak behavior of Mapp and η0 suggests that both parameters depend not only on the dimensions of the micelles but also on the intermicellar interactions. In semidilute systems, the electrostatic repulsion between the micelles increases the effective excluded volume of the particles and thereby the effective volume fraction φ of the micellar aggregates. This phenomenon is known as the electro-viscous effect. The lengths and the viscous resistance of micelles can be scaled as η ∼ φa and L ∼ φb.35 Upon the addition of NaSal, which leads to electrostatic shielding, the dimensions of rod-shaped micelles L increase. The observed minima in Mapp and η0 around Cs/Cd ∼ 1.5 can be explained by competition of micellar growth and reducing interactions. It turns out that the growth of micelles is very effective at low Cs concentration close to Cs/Cd ∼ 1. The electro-viscous effect, however, is more pronounced at elevated salt concentrations. This suggests that, at low Cs concentrations close to Cs/Cd ∼ 1, the Sal- ions are strongly adsorbed at the surface of the anisometric micelles. This lowers the surface potential and causes an increase in the surfactant-packing parameter by decreasing the area occupied per surfactant monomer. In the regime of high Cs concentrations close to Cs/Cd ∼ 1.5, the zeta potential is very low, and in this region we observe (43) Cappelaere, E.; Cressely, R. Colloid Polym. Sci. 1998, 276, 1050. (44) Hartmann, V.; Cressely, R. Rheol. Acta 1998, 37, 115. (45) Joshi, J. V.; Aswal, V. K.; Goyal, P. S. Physica B 2007, 391, 65. (46) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456.
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Shukla and Rehage
Figure 5. (A) Measured values of the zeta potential as a function of theoretically calculated Debye-Hu¨ckel length. The solid line shows the result of linear fitting. (B) Theoretically calculated zeta potential measurements as a function of salt concentration. Solid lines represent the theoretical prediction according to eq 13.
the minimum of the zero-shear viscosity and the apparent molecular weight. These results are supported by cryo-TEM measurements, which also show that the micellar structures are nearly constant in regimes of excess salt.47 Above Cs/Cd > 1.5, the zeta potential slowly decays and finally reaches negative values due to excess counterion condensation. The second maximum appears in the regime of small zeta potentials, but it does not coincide exactly with the point of zero micellar surface charge. Coulomb interactions are small in this region, and this could lead to increased contacts between the rod-shaped micelles (fusion of threadlike micelles). In the concentration regime, where the zeta potential is small, we can also expect the formation of branched network structures. At elevated NaSal concentrations, Mapp and η0 decrease again. The excess adsorptions of Sal- or Br- ions induce negative net charges, but the zeta potential remains low, and in this regime branching processes may also occur. As discussed above, electrostatic interactions can play a very important role concerning the structure of entangled solutions of wormlike micelles. Counterion condensation is generally related to the appearance of attractive forces, which we also observed in DLS and SLS experiments. The process of salicylate ion condensation can lead to the reduction, the neutralization, or the inversion of charge. As seen in Figure 4, a net zero charge (isoelectric point) was observed for Cs/Cd ≈ 4.7. It is interesting to note that the experimental determined zeta potential is correlated with the theoretically calculated Debye-Hu¨ckel length. As shown Figure 5, the zeta potential varies linearly as the function of Debye-Hu¨ckel length calculated using eq 11. According to Gouy-Chapman or Eversole-Boardman theories, the zeta potential ζ can be calculated.48
Figure 6. Schematic drawing of the surface and zeta potential as a function of distance from the surface of the micelles.
Z denotes the valance of the ion; in this case, this parameter is equal to one and ζ is the zeta (shear plane) potential at distance ξΗ from the surface. Ψ0 represents the micellar surface potential, and κ-1 describes the Debye-Hu¨ckel length. In Figure 5, the theoretical predictions according to eq 13 are shown as solid lines for different surface potentials (the Debye-Hu¨ckel lengths were calculated using eq 11, and the ξΗ values were obtained from DLS). It is evident that, above the charge reversal, the zeta potential can be qualitatively and quantatively reproduced. The surface potentials obtained from fitting are consistent with the
measured values for similar systems.49 As discussed above, in our surfactant solutions, the existence of specific counterion adsorption processes is quite reasonable, which is responsible for the mobility reversal found experimentally. The fitted values of surface potentials differ substantially from the zeta potentials. The marked difference between the potential at the plane of the head groups and the plane of shear suggests that there is a second population of adsorbed Sal- and Br- ions beyond the head group region. These results are therefore consistent with the two-site model or a continuous variability in the adsorption sites proposed by Cassidy and Warr,49 in which intercalated salicylate ions are responsible for the shape transformation, whereas the surface adsorbed ions cause charge reversal. This mechanism is consistent with our interpretation of observed double-peak behavior. The results presented here suggest a model as depicted in Figure 6 where the micellar hard sphere is surrounded by a stationary diffuse layer as defined by the Debye screening length which encompasses a mobile diffusing unit defined by the zeta potential. Our results suggest the existence of two sites for salicylate binding to micelles. One of these layers is caused by conventional penetration of salicylate ions between the surfactant head groups, and the other one is related to the adsorption of salicylate ions onto the micelle surface. Now we can try to relate the change in persistence length to an electrostatic interaction effect that has been considered in the theory of polyelectrolytes. For charged macromolecules, it has become common practice to divide the total persistence length into an electrostatic lp,e and an intrinsic or “bare” part lp,0 such that lp,tot ) lp,0 + lp,e.50 Several theoretical models that account for the influence of electrostatic interactions on the persistence length and on the effect of screening from added salt have been
(47) Clausen, T. M.; Vinson, P. K.; Minter, J. R.; Davis, H. T.; Talmon, Y.; Miller, W. G. J. Phys. Chem. 1992, 96, 474. (48) Charlton, I. D.; Doherty, P. J. Phys. Chem. B 1999, 103, 5081.
(49) Cassidy, M. A.; Warr, G. G. J. Phys. Chem. 1996, 100, 3237. (50) Dautzenberg, H.; Jaeger, W.; Kötz, J.; Philipp, B.; Seidel, C. Polyelectrolytes: Formation, Characterization and Application; Hanser: Mu¨nchen, 1994.
(
ln tanh
) (
)
Zeψ0 Zeζ ) ln tanh - κ-1ξH 4kBT 4kBT
(13)
Dynamic Properties of Aqueous CTAB/NaSal Solutions
Langmuir, Vol. 24, No. 16, 2008 8513
phenomenon will produce the largest drops of the surface potential Ψ0. This rapid drop in charge should lead to a fast decrease of the persistence length. A considerable slow decrease in lp,e occurs for Cs/Cd > 1. This might be due to the formation of a second layer of adsorbed ions around the surfactant head group region. These results together with the zeta potential point to the presence of a two-site model or a continuous variability of adsorption sites.
Conclusions
Figure 7. Schematic drawing of the persistance length due to electrostatic contribution as a function of salt concentration.
presented in the past.51 A frequently used model to calculate lp,e is the so-called OSF theory, which has independently been derived by Odijk,51a Skolnick,51b and Fixman.51c In this theory, electrostatic contributions to the bending energy are calculated for a rather stiff, wormlike chain using a screened Coulomb potential (i.e., a Debye-Hu¨ckel approximation) for the electrostatic interactions. In this context, a wormlike chain is considered to be stiff at conditions where lp,0 . κ-1 holds. The OSF (Odijk, Skolinck, and Fixman) theory predicts the following expression for the electrostatic contribution to the persistence length.
lp,e )
1 4Z κ lB 2 2
(14)
Parameter lB denotes the Bjerrum length. The persistence lengths influenced by electrostatic contribution are plotted in Figure 7 as a function of the salt concentration using eq 14. As shown in Figure 7, lp,e decreases rapidly with increasing salicylate concentration until Cs/Cd ∼ 1 (close to the first maximum). This can be explained by the adsorption of Salions penetrating the layer of surfactant head groups. This (51) (a) Odijk, T. J. Polym. Sci., Polym. Phys. Ed. 1977, 15, 477. (b) Skolnick, J.; Fixman, M. Macromolecules 1977, 10, 944. (c) Fixman, M.; Skolnick, J. Macromolecules 1978, 11, 863. (d) Barrat, J. L.; Joanny, J. F. AdV. Chem. Phys. 1995, 94, 1. (e) Stevens, M.; Kremer, K. J. Chem. Phys. 1995, 103, 1669.
In a series of experiments, we performed light scattering studies in combination with electrokinetic measurements. The fast decay of the zeta potential in the presence of added salicylate ions points to strong processes of counterion condensation. At elevated concentrations of excess salt, we observed an isoelectric point and charge reversal of the anisometric, wormlike micelles. We also detected a simple, linear correlation between the zeta potential and the electrostatic screening length. Estimated values of the surface potential, which are associated with the plane of the polar surfactant head groups, were found to be considerably larger than the measured zeta potential, which is usually associated with the shear plane. This discrepancy can be described by a multilayer adsorption shell. The first layer could be formed by specific adsorption processes due to intercalated salicylate ions between the polar head groups of the surfactant molecules. These processes lead to a dense packing of the aggregates and favor, hence, the formation of rod-shaped micelles, which grow in size with increasing amount of salicylate counterions. The reduction of the zeta potential with increasing counterion concentration leads to electrostatic screening effects. As a consequence, the wormlike aggregates are more flexible and they form more contacts (entanglements) or branching processes can occur. The second maximum observed in the zero-shear viscosity and the apparent molecular weight was detected near the concentration of zero zeta potential. As the extreme values depend on several parameters such as growth of the aggregates, branching, micelle flexibility, interactions, and formations of entanglements, the exact position of the extreme values might be caused by a superposition of opposing effects. LA800816E
