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Langmuir 2004, 20, 1138-1143
Surfactant/Nonionic Polymer Interaction. A NMR Diffusometry and NMR Electrophoretic Investigation Erik Pettersson,† Daniel Topgaard,‡ Peter Stilbs,*,† and Olle So¨derman‡ Physical Chemistry, Royal Institute of Technology, SE-10044 Stockholm, Sweden, and Physical Chemistry 1, Lund University, P.O. Box 124, SE-22100 Lund, Sweden Received September 12, 2003. In Final Form: December 15, 2003 The interaction between the nonionic polymer poly(ethylene oxide) (PEO) of molecular weight 20 000 and surfactants of various types [sodium dodecyl sulfate (SDS), dodecyl trimethylammonium bromide, octyl β-D-glucoside, and potassium laurate] has been investigated in an aqueous solution at 25 °C by 1H NMR pulsed-gradient spin-echo self-diffusion techniques. The SDS/PEO study was further complemented by component-resolved 1H NMR-based studies of the electrophoretic mobility of PEO and the alkyl part of SDS under the same measurement conditions. Through such combined studies, a much more complete picture of the binding and aggregation processes becomes accessible.
Introduction The interaction (or lack of interaction) between watersoluble nonionic polymers and surfactants has been the subject of large interest over the years.1,2 The subject matter is of considerable technological interest; in many formulations containing surfactants, polymers are used to enhance the performance (such as in adjusting rheological properties), and it is also interesting from a basic scientific point of view. What is the nature of the interaction and what are the properties of the surfactant/ polymer complexes are typical questions that are posed. Of course, fundamental studies provide us with means to improve the applications in desired directions. A common polymer used in these studies is poly(ethylene oxide) (PEO). Its interaction with anionic, nonionic, and cationic surfactants has been rather thoroughly investigated.3-11 A general conclusion is that while anionic surfactants such as sodium dodecyl sulfate (SDS) interact with PEO (at least for a degree of polymerization, dp, larger than 50) at room temperature,7,10 cationic and nonionic surfactants require elevated temperatures to bind to PEO.12 The mutual interaction leads to surfactant selfassembly at a lower concentration than the critical micellization concentration (cmc). The term critical aggregation concentration (cac) is often used to indicate the onset of this consequence of surfactant/polymer interactions. The term “aggregate concentration” thus implies * To whom correspondence should be addressed. E-mail: peter@ physchem.kth.se. † Royal Institute of Technology. ‡ Lund University. (1) Hansson, P.; Lindman, B. Curr. Opin. Colloid Interface Sci. 1996, 1, 604-613. (2) Lindman, B. In Surfactant-polymer systems; Holmberg, K., Ed.; John Wiley & Sons, Ltd.: Chichester, U.K., 2002; pp 445-463. (3) Brackman, J. C.; Engberts, J. B. F. N. Langmuir 1991, 7, 20972102. (4) Brackman, J. C. Langmuir 1991, 7, 469-472. (5) Brackman, J. C.; Engberts, J. B. F. N. Chem. Soc. Rev. 1993, 22, 85-92. (6) Brackman, J. C.; Engberts, J. B. F. N. ACS Symp. Ser. 1994, 578, 337-349. (7) Cabane, B. J. Phys. Chem. 1977, 81, 1639-1645. (8) Cabane, B.; Duplessix, R. J. Phys. (Paris) 1982, 43, 1529-1542. (9) Cabane, B. Colloids Surf. 1985, 13, 19-33. (10) Cabane, B.; Duplessix, R. J. Phys. (Paris) 1987, 48, 651-662. (11) Zana, R.; Lianos, P.; Lang, J. J. Phys. Chem. 1985, 89, 41. (12) Anthony, O.; Zana, R. Langmuir 1994, 10, 4048-4052.
that the surfactant in the surfactant/polymer complex is in the form of a surfactant aggregate and not in the form of individual monomers. This description is valid when water-soluble homopolymers are considered; for polymers containing hydrophobic portions or groups, the situation is different, and one can also have interaction between individual surfactant and the polymer. Here, we will only consider the former class of polymers. For the case of PEO/ SDS, the cac at room temperature is roughly half the cmc, that is, the concentration where surfactant micelles are formed in the absence of PEO. In the micellar phase separation model, the difference in chemical potential in the presence and absence of micelles is (counted per surfactant) ∆µ ) kT[ln(cac) - ln(cmc)], and because the ratio between the cmc and the cac is roughly a factor of 2, the interaction between the surfactant micelle and the polymer thus corresponds to approximately 0.7kBT per surfactant. The nature of this stabilizing interaction is not obvious; several suggestions as to its nature have been put forward. Hydrophobic interactions between the methylene units of the polymer and the micelle alkyl groups are one suggestion.8,10 Others pertain to electrostatic interactions mediated by the counterions13 and to changes in water structure.14 The structure of the surfactant/polymer complexes has been extensively studied. Twenty years ago, Cabane and Duplessix8 established, on the basis of small-angle neutron scattering data, a model for the complex in the PEO/SDS case that has since not been challenged.10 In this model, the complex is described as micelles (one or several, depending on the concentrations of surfactant and polymer) decorated by the polymer, which is adsorbed to the surface of the micelle. Later studies have indicated that the first micelles formed in the polymer solution are smaller than those formed in the absence of polymer but that the aggregation number increases upon further addition of surfactant.11 Few NMR studies have been reported on the interaction between polymers and surfactants. Cabane argues from 1H, 13C, and 23Na NMR that the complex can be described as a mixed micelle with some of the monomers directly adsorbed at the hydrocarbon/ water interface but most of them forming loops in the (13) Dubin, P. L.; Gruber, J. H.; Xia, J.; Zhang, H. J. Colloid Interface Sci. 1992, 148, 35-41. (14) Alexandridis, P.; Nivaggioli, T.; Hatton, T. A. Langmuir 1995, 11, 1468-1476.
10.1021/la035703j CCC: $27.50 © 2004 American Chemical Society Published on Web 01/21/2004
Surfactant/Nonionic Polymer Interaction
surrounding water solution.7 Gao et al. used paramagnetic relaxation techniques to investigate the distribution of PEO in SDS micelles; their conclusions are similar to those of Cabane, except that they found a significantly higher degree of solubilization in the micelles of PEO.15,16 NMR diffusometry is an important technique in the investigation of surfactant systems.17-22 The technique measures the mean square displacement over length scales in the micrometer regime. These are typical colloidal length scales, and, thus, NMR diffusometry data yield easily interpretable information about aggregation processes and microstructure in surfactant systems. In this article, we will show how this approach can be used to study surfactant/polymer interactions. We present NMR diffusometry data pertaining to the interaction between one nonionic, two different anionic, and one cationic surfactant and PEO. In addition, we also present electrophoretic NMR (ENMR) data23-29 for the SDS/PEO system and show how these data when combined provide a rather rich description of the system. For NMR experimental reasons, the study has been carried out entirely in a D2O solution at a single temperature. Hereby, data from the different diffusion and electrophoretic magnetic resonance data sets become comparable. Questions may be raised as to isotope effects on the aggregation properties. We believe these are small and will not affect the conclusions in an investigation of the present kind.30 Only in some extreme exceptions have significant isotope effects been observed in polymer or surfactant systems,31 and then on phase boundaries, which depend on delicate balances between various interactions in systems of the present kind. Experimental Section Materials. “Monodisperse” PEO 20 000 (dp ≈ 450) was obtained from Fluka Chemie AG. The polydispersity index was 1.06 according to the manufacturer. SDS, dodecyltrimethylammonium bromide (DoTAB), and Octyl β-D-glucoside (C8G1) were purchased from Sigma and used without purification. Potassium laurate (KC12) was obtained by ion exchange on sodium laurate from BDH. Samples were prepared by mixing and diluting freshly prepared 1 wt % surfactant stock solutions and a 2 wt % PEO solution into NMR tubes. All concentrations are given in wt % in D2O. To convert from wt % to C in moles L-1 solvent, the (15) Gao, Z.; Kwak, J. C. T. NMR studies of interactions between neutral polymers and anionic surfactants in aqueous solution. In Surfactants in Solution; Mittal, K. L., Shah, D. O., Eds.; Plenum Press: New York, 1991; Vol. 11, pp 261-275. (16) Gao, Z.; Wasylishen, R. E.; Kwak, J. C. T. J. Phys. Chem. 1991, 95, 462-467. (17) Furo, I.; Dvinskikh, S. V. Magn. Reson. Chem. 2002, 40, S3S14. (18) So¨derman, O.; Olsson, U. Curr. Opin. Colloid Interface Sci. 1997, 2, 131-136. (19) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445-482. (20) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45. (21) Stilbs, P. Surf. Sci. Ser. 1998, 77, 239-266. (22) Chachaty, C. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 183222. (23) Holz, M. Chem. Soc. Rev. 1994, 23, 165-174. (24) Johnson, C. S., Jr.; He, Q. Electrophoretic NMR. In Advances in Magnetic Resonance; Warren, W. S., Ed.; Academic Press: San Diego, 1989; p 133. (25) Johnson, C. S., Jr. Transport Ordered 2D-NMR Spectroscopy. In NMR Probes of Molecular Dynamics; Tycko, R., Ed.; Kluwer Academic Publishers: Dordrecht, 1994; pp 455-488. (26) He, Q. H.; Lin, W.; Liu, Y. M.; Li, E. C. J. Magn. Reson. 2000, 147, 361-365. (27) He, Q. H.; Wei, Z. H. J. Magn. Reson. 2001, 150, 126-131. (28) He, Q.; Johnson, C. S., Jr. J. Magn. Reson. 1989, 81, 435-439. (29) He, Q.; Johnson, C. S., Jr. J. Magn. Reson. 1989, 85, 181-185. (30) Carlfors, J.; Stilbs, P. J. Colloid Interface Sci. 1985, 104, 489499. (31) Whiddon, C.; So¨derman, O. Langmuir 2001, 17, 1803-1806.
Langmuir, Vol. 20, No. 4, 2004 1139 following formula can be used:
C)
FD2O
wt % MS 100 - wt %
(1)
Here, FD2O is the density of D2O (in g L-1) and MS is the molecular weight of the surfactant. The polymer concentration was 0.2 wt % throughout. Methods. All NMR experiments were made at 25.0 °C. The diffusion measurements were performed on a Bruker DMX 200 operating at a proton resonance frequency of 200.13 MHz. Pulsed field gradients were generated in a Bruker DIFF-25 gradient probe driven by a Bruker BAFPA-40 unit. Diffusion was measured with the pulsed field gradient spin-echo pulse sequence32 utilizing two gradient pulses of strength g and duration δ. The distance between the leading edges of the pulses is denoted ∆. The parameters for surfactant diffusion were: δ ) 1 ms, ∆ ) 20 ms, and g increasing in a linear sequence up to 3 T/m in 16 steps. The corresponding settings for PEO diffusion were δ ) 2 ms and ∆ ) 20 ms, with g increasing in a linear sequence up to 4.5 T/m in 16 steps. The intensity I of the echo is then given by
I ) I0 exp[-γ2g2δ2D(∆ - δ/3)]
(2)
where I0 represents the echo intensity in the absence of gradients, γ is the magnetogyric ratio of the observed nucleus, and D is the self-diffusion coefficient. D is obtained by regressing eq 2 onto the experimental data using a nonlinear fitting routine with D and I0 as adjustable parameters. A problem when applying eq 2 to polymer diffusion is that often their spin-echo decays are not monoexponential on account of the polymers being polydisperse in molecular weight. However, in the present case, dealing with a rather monodisperse polymer, the PEO diffusion could be reasonably well-evaluated in terms of a single diffusion coefficient. The ENMR experiments were performed on a Bruker AMX 300 NMR spectrometer. The pulsed-gradient field was generated by a Bruker BAFPA-30 unit. The samples were put in a 1-mm inner-diameter glass U-tube that, in turn, was carefully placed from the top of the spectrometer into the center of the active volume of a 10-mm diffusion probe (Cryomagnet Systems, Indianapolis, IN). Two Pt-blackened electrodes were dipped just below the surface of the sample at each entrance of the U-tube. A constant-current pulsed electric field generator designed by S. Woodward (University of North Carolina, Chapel Hill, NC, similar to one described previously)33 was used to feed the electrodes with up to (1 kV electrophoretic direct current pulses. The settings for the applied current from the generator were changed via a programmable PC-parallel port interface. The inner U-tube wall was coated with poly(acryl amide)34 to prevent electroosmotic flow. The electrophoretic mobility is measured by using a modified version of eq 2:
I ) I0 cos(µIE∆E/σκ) exp[-γ2δ2g2D(∆ - δ/3)]
(3)
where σ is the cross-sectional area of the U-tube and κ is the conductivity of the sample. By applying an electrophoretic current, IE, during the “diffusion time” ∆E, an extra coherent phase is added to the signal when the ion is moving in the field. The cosine modulation of this dephasing is proportional to the electrophoretic mobility, µ, of the ion. All ENMR experimental data above cmc/cac were acquired using a new pulse sequence based on the pulsed-gradient double stimulated echo sequence (PGDSTE).35 The electric field is active during both “diffusion times” but with reversal of electrophoretic polarities between the two halves of the experiment. The sequence filters several artifacts while preserving the phase shift from mobility of charges. The data below cmc/cac were obtained using the traditional ENMR pulsed-gradient stimulated echo sequence (ENMR(32) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288-292. (33) Saarinen, T. R.; Woodward, W. S. Rev. Sci. Instrum. 1988, 59, 761-763. (34) Hjerte´n, S. J. Chromatogr. 1985, 347, 191-198. (35) Jerschow, A.; Mu¨ller, N. J. Magn. Reson. 1997, 125, 372-375.
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increased, also the cationic surfactants will start to interact with the polymers.12,39 In regard to the polymer diffusion, it is also constant up to a rather well-defined concentration for the surfactants that show interaction but then changes at a rather well-defined surfactant concentration, which we shall designate cBP (“breakpoint concentration”). However, cBP is higher than that for the surfactant. This is an important observation, which we will return to in the following. The established procedure to analyze NMR diffusometry data pertaining to surfactant micellization makes use of a two-site exchange model, in which the observed diffusion coefficient is written as a population-weighted average between “free” and “bound” surfactant:
( )
Cf Cf D ) Df + 1 D Ct Ct b Figure 1. Observed self-diffusion data for four different surfactants in the absence (O) and presence (0) of PEO. Also given is the PEO diffusion (]). PGSTE).36,37 Both pulse sequences use eq 3 in the evaluation of the raw data; the only difference is that the electrophoretic mobility time, ∆E, is the same as the diffusion time ∆ for the ENMR-PGSTE experiment but becomes slightly smaller for the ENMR-PGDSTE experiment as a result of hardware-related limitations. The experiments were performed by increasing the electrophoretic current, IE, while keeping the other parameters constant. This will turn the diffusion term in eq 3 into a constant during the experiment. More detailed information on the ENMRPGDSTE sequence will be published elsewhere.38 The experimental data were collected using δ ) 1 ms and with ∆E ) 300 ms and g ) 0.936 T/m above cmc/cac and ∆E ) 600 ms and g ) 0.198 T/m below cmc/cac. The electrophoretic current was varied in 16 equal steps between 0 and slightly below the resulting current at the maximum voltage of 1 kV. A pre-estimate of the maximal ENMR current (corresponding to the maximum voltage 1 kV) for each sample was calculated from the conductivity κ and the tube cross section σ. The conductivity was measured using a microsample conductivity cell CDC749 and a CDM210 conductivity meter, both from Radiometric Analytical.
Results and Discussion NMR Diffusometry. We present in Figure 1 the NMR diffusion data for four different surfactants (see Materials). The logarithms of the diffusion coefficients for both the surfactants and PEO are plotted versus the logarithm of the surfactant concentration. The PEO concentration was kept constant in all experiments at 0.2 wt %. A general feature of the data is that the surfactant diffusion coefficients remain almost constant up to a rather welldefined concentration, after which their values start to decrease. The breakpoint is a manifestation of the onset of surfactant self-assembly into micelles. Thus, we can already at this stage draw the conclusion that SDS and KC12, the latter to a lesser extent, interact with the polymer because their breakpoints are lower when polymer is present, indicating that micelles form at a lower concentration as compared to the polymer free situation, and, consequently, the micelles are stabilized by the presence of the polymer. For the cationic and nonionic surfactant, no interaction is indicated. This is in agreement with prior work.12,39 We note that, if the temperature is (36) Holz, M.; Lucas, O.; Mu¨ller, C. J. Magn. Reson. 1984, 58, 294305. (37) He, Q.; Johnson, C. S., Jr. J. Magn. Reson. 1989, 85, 181-185. (38) Pettersson, E.; Furo´, I.; Stilbs, P. 2003, submitted for publication. (39) Mya, K. Y.; Jamieson, A. M.; Sirivat, A. Langmuir 2000, 16, 6131-6135.
(4)
where Df,b are the diffusion coefficients of free (i.e., nonmicellized) and bound (i.e., micellized) surfactant, respectively. Cf,t are the concentrations of free and total surfactant, respectively. Three parameters can be extracted from eq 4: Cf and Df,b. To facilitate the fitting procedure of the D versus Ct data, eq 4 is recast into
( )
D ) Df + 1 -
Cf (Db - Df)H(Ct - Cf) Ct
(5)
where H(x) is the Heaviside step function
H(x) ) 1 if x g 0 H(x) ) 0 if x < 0 We note that eq 5 can also be applied to the polymer diffusion. In this case, the term bound implies those polymers that are part of the surfactant/polymer complex. Before showing the results of regressing eq 5 onto the data in Figure 1, we will make some comments on the use of eq 5. First, we are assuming that the concentration of free surfactant is constant above the aggregation concentration (cac or cmc). This amounts to using the phaseseparation model, in which the aggregation process is described as a macroscopic phase separation. For ionic surfactants, the concentration of free surfactant does decrease above the cmc on account of the increased counterion concentrations.40,41 However, close to the cmc the free surfactant concentration remains reasonably constant. Second, we are assuming that Db is constant. Again, for ionic surfactants this is a questionable assumption because the aggregation number for these surfactants will increase as the concentration increases. However, close to cmc it is a reasonable assumption. We note that, for the case of the surfactant/polymer complexes, the aggregation number does increase also close to the cac (see also discussion to follow). However, for a moderate increase in the aggregation number, Db remains reasonably constant (recall that D scales roughly with the aggregation number as N-1/3). The results of analyzing the data in Figure 1 with eq 5 are summarized in Table 1. To estimate the uncertainties in the obtained parameters, Monte Carlo error analysis was performed on the data for SDS, following procedures outlined in a paper by Alper and Gelb.42 The statistical (40) Stilbs, P.; Lindman, B. J. Phys. Chem. 1981, 85, 2587-2589. (41) Lindman, B.; Puyal, M. C.; Kamenka, N.; Rymde´n, R.; Stilbs, P. J. Phys. Chem. 1984, 88, 5048-5057. (42) Alper, J. S.; Gelb, R. I. J. Phys. Chem. 1990, 94, 4747-4751.
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Table 1. Results of Fitting Eq 5 to the Data of Figure 1a system
Df,surf, 10-10 m2 s-1
Db,surf, 10-10 m2 s-1
cmc and cac
DoTAB DoTAB/PEO KC12 KC12/PEO SDS SDS/PEO C8G1 C8G1/PEO
4.46 4.45 4.16 4.09 4.30 ( 0.025 4.24 ( 0.065 3.59 3.62
0.43 0.31 0.31 0.6 0.28 ( 0.13 0.44 ( 0.21 0.86 0.80
0.388 0.396 0.587 0.459 0.203 ( 0.004 0.121 ( 0.011 0.596 0.590
a
Df,poly, 10-10 m2 s-1
Db,poly, 10-10 m2s-1
CBP, breakpoint/PEO
0.43 0.42 0.42
none 0.2
0.594
0.42 ( 0.004
0.18 ( 0.041
0.269 ( 0.035
0.43
none
The confidence intervals correspond to one standard deviation.
Figure 3. Electrophoretic mobility µb of SDS micelles (O) and SDS/PEO aggregates (]). The dotted and dashed-dotted vertical lines indicate the cmc/cac. Figure 2. Electrophoretic mobility (lower panel) and diffusion data (top panel) for the SDS and PEO/SDS solution versus the amount of added SDS. Symbols are the same as in Figure 1.
error estimates are included in Table 1. The diffusion coefficients for free surfactant and polymer are in all cases well-determined. For all surfactants, the diffusion coefficient for free surfactant is the same within the experimental accuracy with and without polymer. Moreover, the polymer diffusion Df,poly is constant and equal for all surfactants. The cac/cmc and the breakpoint in the polymer diffusion are also rather well-determined. The quantity Db is more uncertain, however. In principle, one could calculate the hydrodynamic radius, RH, of the complexes from Db ) kT/6πηRH. However, on account of the rather poor accuracy in Db we have refrained from doing this. The general features of and conclusions drawn from the data were summarized previously. ENMR. The electrophoretic mobility and diffusion data of SDS and SDS/PEO samples are presented in Figure 2 plotted versus the logarithm of the surfactant concentration. A comparison of the mobility data for the SDS and SDS/PEO with the diffusion data shows common features. The mobility is approximately constant until a certain breakpoint, where the mobility starts to increase as more surfactant is added. For the pure SDS solution, this breakpoint coincides with the cmc breakpoint in the diffusion data. In the SDS/PEO mixture, the cac is clearly indicated as the point where the PEO mobility starts to increase from zero. The same two-state model as that used for the diffusion data was also used for the pure SDS solution mobility data. The relation between the mobilities given in eq 6 is analogous to that of eq 5, where the observed mobility, µ, is related to the mobility of free SDS, µf, and
Table 2. Results of Fitting Eq 6 to the Data in Figure 2 system SDS SDS/PEO
µb,SDS, µf,SDS, 10-8 m2 V-1 s-1 10-8 m2 V-1 s-1 1.82 1.73
3.86 3.37
cmc
µb,PEO, 10-8 m2 V-1 s-1
0.208 0.134
4.12
the mobility of the micelles, µb, as follows:
( )
µ ) µf + 1 -
Cf (µ - µf)H(Ct - Cf) Ct b
(6)
Equation 6 was used when fitting the pure SDS solution data and PEO data (see also the discussion to follow) of Figure 2. The resulting parameters, µb, µf, and cmc are shown in Table 2. The so-obtained value of the cmc is in good agreement with the breakpoint from the diffusion experiments. The micelle and aggregate mobility, µb, versus SDS concentration, shown in Figure 3, is calculated by inserting the fitted values for µf from Table 2 and the cmc from Table 1 back into eq 6 for each observed mobility measurement. The charge z for small ions, like DS- (the dodecyl sulfate ion), is related to µ and D through the Einstein expression:
µ)
zeD kBT
(7)
where D is the diffusion coefficient, e is the elementary charge, T is the temperature, and kB is the Boltzmann constant. Applying the Einstein relation to the pure SDS solution, with Df and µf taken from Tables 1 and 2, results in the charge zf,SDS ) 1.08 ( 0.04 for free DS- surfactant ions, which is in excellent agreement with the expected value for a single DS- ion. The charge of a SDS micelle
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using the same method is calculated to be zb,SDS ) 35.4 ( 1.75. This value is only a rough estimate of the charge because the equation strictly only applies to small spherical ions. The more general analysis of charged colloids relates the mobility of the macromolecule/aggregate to the surface ζ potential according to eq 8:43
0rζ η
µ)C
(8)
where η is the solution viscosity, 0 and r are the vacuum and the relative electrical permittivities, and C is a constant that usually, in a quite complex form, depends on the product of the characteristic radius R of the charged particle and the inverse Debye length κ of the solution. The relation is only trivial in the two limits κR < 0.1, where Hu¨ckel calculated C ) 2/3, and κR > 100, where the Helmholtz-Smoluchowski limit gives C ) 1. The κR for our SDS micellar solution lies in the range 0.5-1, which makes the interpretation somewhat more complicated because retardation effects will become important. Using the results by Loeb et al. for spherical charged particles gives a C ≈ 0.48 for the SDS micelle at the lowest concentration if the radius of the slipping plane is assumed to be at 25 Å.43 The obtained ζ potential of -100 mV from eq 8 can be compared to the result from the numerical solution of the Poisson-Boltzmann equation for a spherical SDS micelle (the software is freely available at http:// www.membfound.lth.se/chemeng1/Prog.html). Calculations corresponding to the lowest SDS concentration (with a micelle radius of 20 Å) yield the same ζ potential of 100 mV 5 Å out from the micellar surface, which would indicate that the slip plane is positioned one to two water diameters from the charged surface. As is evident in Figure 3, the micellar mobility increases slightly when more SDS is added to the solution. This is probably due to aggregate growth; recall that µ ) q/f, where the charge q is proportional to NAgg while the friction coefficient f is proportional to NAgg1/3. This gives µb ∝ NAgg2/3. A peculiar feature of the data in Figure 2 is the fact that the breakpoint in the SDS mobility versus concentration curve is the same in the absence and presence of PEO. On the other hand, the breakpoint of the PEO mobility is lower and coincides with the breakpoint in the corresponding diffusion curve. Thus, the mobility of the SDS/ PEO complex is the same as that for the SDS monomers over a certain concentration interval. This is most likely due to a compensation effect; the first PEO complex formed has a rather low aggregation number (see the following) and a low value of the diffusion coefficient (see Table 1). Thus, in the framework of eq 7, the term zD is approximately the same for the SDS monomer and the first formed SDS/PEO complexes. As the SDS concentration increases, the number of SDS per PEO increase and the mobility too will increase. We note that the breakpoint in the PEO diffusion for the SDS/PEO system roughly coincides with that of the SDS mobility in Figure 2 (see the following). This fact implies that the PEO/SDS data do not follow a pure two-site model with exchange between free SDS and aggregates with just one size. Instead, the data was here analyzed according to the following procedure. The cac concentration was taken from the breakpoint of the SDS diffusion data in Figure 1. An assumption was made that all SDS, above the cac, aggregates with PEO and forms micellar structures (43) Wiersema, P. H.; Loeb, A. L.; Overbeek, J. T. G. J. Colloid Interface Sci. 1966, 22, 78-99.
Figure 4. Average number of SDS molecules, NAgg, per PEO molecule versus SDS concentration.
attached to PEO. The analysis does not require information concerning the actual structure of the aggregates. The fraction of PEO molecules aggregated with SDS molecules can be expressed as
pb,PEO ) Cmicelle/CPEO )
CSDS - cac /CPEO NAgg
(9)
where Cmicelle represents the concentration of micelles bound to the PEO molecules and NAgg is the mean number of SDS molecules in the PEO/SDS aggregates per PEO molecule. The amount of occupied PEO molecules above the cac can also be expressed as the ratio
pb,PEO ) µPEO/µb,SDS
(10)
where µPEO is the measured mobility of the PEO, which is a combination of charged PEO aggregates moving in the field and nonmoving neutral PEO molecules. µb,SDS is the average mobility of the PEO/SDS aggregate formed. This parameter is extracted from the SDS data in the SDS/PEO mixture using the two-site model implied in eq 5, with the cac from the diffusion data and µf,SDS taken from the average of the mobility data below the cac, all listed in Table 2. Using eqs 9 and 10 and substituting µb,SDS with eq 6 for the SDS data will, after algebraic rearrangement, result in eq 11 for the number of SDS molecules bound per PEO molecule.
NAgg )
µSDS - (cac/CSDS)µf,SDS CSDS µPEO CPEO
(11)
The number of SDS molecules for each PEO in the PEO/ SDS complexes is plotted in Figure 4 as a function of the wt % SDS. The fraction of bound PEO molecules shown in Figure 5 was calculated by inserting the calculated aggregation number into eq 9. Finally, we present the mobility µb for the SDS/PEO complexes in Figure 3, evaluated as outlined previously for the case of pure SDS solutions. An analysis of the ζ potential for the SDS/PEO aggregate is more difficult here because both the size and the shape are unknown quantities. In general, the mobility is lower for the complex than for the pure micelles. It also shows a stronger concentration dependence for the complexes, presumably as a result of the change in the number of associated SDS per polymer.
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Langmuir, Vol. 20, No. 4, 2004 1143
to any greater degree in the complex. Within the RouseZimm model, the radius of gyration, RG, for a polymer can be computed from the translational diffusion coefficient from a modified version of the Stokes-Einstein relation:
RG )
Figure 5. Fraction of PEO molecules bound to SDS versus the SDS concentration.
One feature remains to be interpreted, namely, why the cac and cBP differ for KC12 and SDS. Before doing this, we need the following background information. The cac is only weakly dependent on the polymer concentration for a dp in excess of roughly 200.8 At the cac, the formation of surfactant/polymer complexes starts. The formation of complexes then continues until the polymer is saturated. In fact, the saturation point corresponds to a stoichiometric ratio of polymer to surfactants and can be expressed for the case of SDS/PEO as8
nS ) MP0.007 nP
(12)
kBT 6πη0.7D
(13)
where η represents the solvent viscosity and the other symbols have their usual meanings. From the data in Table 1, we obtain for the “free” polymer as well as for the polymer interacting with one micelle RG ) 73 Å, which can be compared with the size of a (spherical) surfactant micelle containing 12 carbons in the surfactant hydrocarbon chains, which is roughly 25 Å. Thus, the polymer dimensions are considerably larger than those of the micellar and it can apparently interact with the micelles without changes in its RG. At cBP, a second micelle starts to interact with each polymer, and, consequently, the surfactant/polymer changes its conformation on account of the rather strong repulsive interaction between the two micelles. From the cac and CBP, the aggregation number of the first micelle can be estimated and the number obtained is 55 for SDS and 60 for KC12, which are reasonable numbers for spherical micelles. From eq 7, it appears likely that the saturation point for the polymers corresponds to two micelles per polymer for the polymer molecular weight used here. It should be added that similar conclusions from rheology measurements have previously been discussed.39 The NAgg for PEO/SDS calculated from the mobility data show that the initial micelles formed on PEO will be made up of 35 SDS molecules, which is somewhat less than the suggested value for pure SDS micelles. The evaluated aggregation number increases when more SDS is added. Conclusions
where nS,P are the moles of surfactant and polymer in the complex, respectively, and MP is the polymer molecular weight. In the present case, MP is 21 500 g mol-1, and, thus, the molar ratio of SDS to polymer is ≈150 at the saturation, which occurs at a SDS concentration of 0.6 wt %. This is in agreement with the results obtained in this study as presented in Figures 4 and 5. We note that the last measured point at 0.66 wt % is above the saturation point at 0.6 wt %. The corresponding aggregation number of 178 is higher than the aggregation number at saturation predicted by eq 12. The reason for this is presumably that eq 11 is based on the assumption that all SDS above the cac binds to PEO. This is not true when PEO becomes saturated, as it does for the last data point. Much in line with the original suggestions by Cabane, the following picture then emerges from the present study. Between the cac and cBP, each surfactant/polymer complex contains one micelle. This complex has roughly the same diffusion coefficient as the “bare” polymer (cf. Table 1), indicating that the PEO does not alter its conformation
For the first time, detailed ENMR studies of surfactant/ polymer systems have been carried out. When combined with self-diffusion data, one arrives at a detailed picture of the aggregation processes, including both polymer, surfactant, and partially also on the electrostatics of counterion binding through the variation of the ζ potential induced by concentration changes and aggregation processes. For a surfactant with a NMR-suitable counterion, an extended study could also quantify the counterion electrophoretic mobility and diffusional transport. The present results support the accepted picture of the aggregation process in the SDS/PEO system and gives strong indications that a maximum of two SDS micelles are formed on the PEO of the molecular weight used here (20 000 g mol-1, dp ≈ 450). Acknowledgment. This work has been supported by the Swedish Research Council, VR. LA035703J
