Interactions between Poly(Ethylene Oxide) and Sodium Dodecyl Sulfate as Studied by NMR, Conductivity, and Viscosity at 283.1–298.1 K

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

197, 191–197 (1998)

CS975231

Interactions between Poly(Ethylene Oxide) and Sodium Dodecyl Sulfate as Studied by NMR, Conductivity, and Viscosity at 283.1–298.1 K Magne Ivar Gjerde, 1 Willy Nerdal, and Harald Høiland Department of Chemistry, University of Bergen, Allegaten 41, N-5007 Bergen, Norway Received March 4, 1997; accepted October 17, 1997

The aggregation of sodium dodecyl sulfate (SDS) in aqueous solution containing a constant amount of poly(ethylene oxide) (PEO) at 2000 ppm has been investigated by several experimental techniques at three temperatures, 298.1, 288.1, and 283.1 K. The techniques include conductivity, viscosity, NMR self-diffusion, NMR chemical shift, and NMR relaxation. The critical aggregation concentration of SDS on the polymer strand (cac) as well as the concentration where ordinary micelles start forming (c2 ) has been determined. There are some inconsistencies in the data due to different measuring techniques. However, techniques that basically monitor the SDS molecules, for instance conductivity and SDSsensitive NMR techniques, provide cac values that are consistent. Above the cac the concentration of free SDS monomers will increase in parallel to the aggregation process. At c2 ordinary micelles will form, and in the concentration range of about 15–25 mmolal the SDS molecules will aggregate as normal micelles or in aggregates on the polymer, and these processes run in parallel. A crude calculation of the Gibbs’ energy of the two aggregation processes suggests that the energetics of the two processes are of similar magnitude, and thus consistent with observation. q 1998 Academic Press

Key Words: sodium dodecyl sulfate; poly(ethylene oxide); critical aggregation concentration; saturation of the polymer; micellization; viscosity; NMR; self-diffusion; chemical shift; relaxation; conductivity.

INTRODUCTION

Most of the published studies on surfactant-polymer interactions in aqueous solution have been based on using a neutral polymer and an anionic surfactant. Some review articles on this topic have also been published (1–3). The system poly(ethylene oxide), PEO, and sodium dodecyl sulfate, SDS, has been extensively investigated (4–28). A variety of experimental techniques have been used, including surface tension, conductivity, viscosity, dye solubilization, neutron and light scattering, fluorescence, calorimetry, and NMR spectroscopy. 1

To whom correspondence should be addressed.

The interactions between the polymer and SDS naturally depend on their mutual concentration. At constant polymer concentrations three regions appear when SDS is added. At low concentrations the SDS molecules remain as dissolved monomers. In a medium range the surfactant interact with the polymer and form aggregates on the polymer strand. The surfactant binds to the polymer at a critical concentration, normally termed cac. At the cac the surfactant forms micellelike aggregates or clusters on the polymer (1, 6, 8). The cac appears to be well defined and independent of the polymer molar mass (4, 5), as long as it exceeds 5000. At cac the SDS micellar aggregation number is lower than the corresponding micellar aggregation number of ordinary micelles in a solution without polymer (10, 17). At sufficiently high surfactant concentrations ordinary micelles start forming in the solution (4–6, 8). At this point the SDS molecules can either be free monomers in water, bound to the polymer as surfactant aggregates, or reside in normal micelles. The surfactant concentration where ordinary micelles are formed in the solutions is normally termed c2 and appears to be less distinct compared to the cac and the cmc. When the surfactant concentration has reached c2 it has been anticipated that the polymer has been saturated with surfactant molecules (8). The most frequently used methods to measure c2 are surface tension (4, 5, 8) and conductivity (4, 5, 8, 12, 15, 22, 27). Both methods register a c2 value, regarded as the concentration where ordinary micelles are formed in the solution. Hydrophobic and electrostatic interactions are the driving forces of the surfactant-polymer association (2). Dubin and co-workers (19, 20) suggest a model for the polymer-surfactant interactions in which the counterion in the double-layer coordinates with the nonionic polymer to form a ‘‘pseudopolycation.’’ This pseudopolycation then forms complexes with the anionic micelles. Cabane (6) found that the aggregates of SDS on PEO resemble ordinary micelles, and the polymer was thought to be wrapped around these micelles. However, recent NOESY NMR experiments show that PEO penetrates the aggregated micelles (28).

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Schwuger (5) has shown that the concentration interval between cac and c2 and the actual values of these surfactant concentrations depend on the pH of the solution, the type of counterions present, and the temperature. Furthermore, the Krafft temperature for a surfactant solution is found to decrease upon addition of a polymer (5, 28, 29). There is some controversy regarding the aggregation process. Cabane and Duplessix (8, 9, 14) have put forward a model of the polymer surfactant interaction which has generally been accepted. In their model the interaction starts at a well-defined surfactant concentration (the cac), then all added surfactant will bind on the polymer until the polymer is saturated. After saturation the concentration of free surfactant monomer will increase until it is sufficiently high for ordinary micelles to form in the solutions. The model has been subjected to some criticism since there are indications that the free surfactant concentration increases before the polymer is fully saturated (12, 15, 27). It has also been suggested that ordinary micelles may form before the polymer is saturated. In this study we have used several experimental techniques, conductivity measurements, NMR self-diffusion, NMR chemical shift, and NMR relaxation measurements to investigate the system SDS-PEO-water at temperatures of 283.1 and 288.1 K (below the SDS Krafft temperature (30)) and at 298.1 K (above the Krafft temperature).

cac (cmc for SDS in H2O without polymer) and c2 were found by the use of linear regression. The calculated correlation coefficients from linear regression were ú0.999. The specific conductivity was determined with a precision of {0.1%.

EXPERIMENTAL SECTION

where A/A0 is the ratio of echo amplitudes in presence (A) and in absence (A0 ) of the gradient, g is the gyromagnetic ratio, d is the duration of each gradient pulse, and D is the time delay between the two gradient pulses. A total of 30 spectra was acquired with different G values to calculate one D value. Experiments optimized to measure SDS had D set to 20 ms and G was varied between 12.2 (at low SDS concentration) to 24.2 G/cm (at high SDS concentration). Experiments optimized for PEO had D set to 60 ms and G was varied between 13.8 (at low SDS concentration) to 21.4 G/cm (at high SDS concentration). The reproducibility of D is {3%.

Materials Sodium dodecyl sulfate ‘‘gehalt’’ ú 99% and poly(ethylene oxide) (polyethylene glycol) with an average molecular mass of 20,000 and of a quality ‘‘for gas chromatography’’ were obtained from Merck. D2O of 99.96 at.% isotopic purity was obtained from Euriso-top. Conductivity Measurements An automatic LCR Meter 4219 from Wayne Kerr and a measuring cell with platinum electrodes, manufactured in our laboratory, were used to measure the electric resistance in the samples. The specific conductivity ( k ) was calculated from k Å K(1/RS 0 1/RW ),

[1]

where K is the measuring cell constant (2.89 cm01 ) and Rs and Rw are the electric resistance in the sample and in pure water, respectively. Water bath temperatures of 298.1, 288.1, and 283.1 K were maintained with a precision of {0.05 K by DBT Hetotherm heather and a Hetofrig cooling unit. The specific conductivity was plotted vs. the SDS concentration and the slopes obtained both above and below the

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NMR Self-Diffusion Measurements The self-diffusion measurements were carried out at 200.13 MHz on a Bruker AC-200 F spectrometer. The field gradients were generated by the Bruker BGU gradient unit. Eddy current effects were reduced by the use of a Z-shielded 5-mm probehead, and a Bruker B-VT 1000 temperature-control unit maintained stable sample temperatures ( {0.5 K ) . The self-diffusion coefficients (D) were determined by use of the pulsed field gradient spin echo method (31, 32) in the improved Fourier transformed mode (33, 34) (FTPGSE). The pulse sequence employed is similar to that originally described by Stilbs and Mosely (35, 36). The gradient pulse strength (G) was calibrated with a 6% H2O solution in D2O (37), and the self-diffusion coefficient (D), for a given species, was determined via the NMR signal intensity of that species according to A/A0 Å exp[ 0 ( gGd ) 2 D( D 0 d /3],

[2]

NMR Spin-Lattice Relaxation Measurements Proton spin-lattice relaxation times (T 1 ) were measured on Bruker Avance DMX 400 at 400.13 MHz by the use of the inverse recovery technique. The T 1 values were determined with a precision of {5%, and constant sample temperatures (precision of {0.5 K) were maintained by the use of a Bruker B-VT 2000 unit. 1

H-Chemical Shift Measurements

Proton chemical shifts were measured at a reconanse frequency of 400.13 MHz (on Bruker Avance DMX 400). The chemical shift of the HOD peak (calibrated with TMS) was set to 1848.6 Hz at 298.1 K, 1892.6 Hz at 288.1

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FIG. 1. The specific conductivity ( k ) for the SDS-PEO-H2O solution vs. SDS concentration at 298.1 K ( l ), 288.1 K ( h ), and 283.1 K ( m ) and for SDS in pure water at 298.1 K ( s ). The curves have been displaced upward to avoid mixing of the different plots. The curve which represents data at 283.1 K ( m ) is unchanged, but k found at 288.1 K ( h ) has been added 0.2 S/m and k at 298.1 K ( l, s ) has been added 0.4 S/m.

K, and 1912.6 Hz at 283.1 K and served as a chemical shift reference in the spectra. The chemical shift measurements have a precision of {0.3 Hz. Constant sample temperatures ( {0.5 K) were obtained by the use of a Bruker B-VT 2000 unit. Viscosity The viscosity measurements were carried out with an Ubbelohde viscometer, Schott Gerate capillary viscometer typnr. 525 01/ 0b. The viscosity was calculated from h Å K(t 0 q ),

[3]

where h is the kinematic viscosity, K is the viscometer constant (K Å 0.005591 mm2 /s 2 for the viscometer that was used), t is the average flow time, and q is a correction constant. The kinematics viscosity was determined with a precision of {1%. Water bath temperatures of 298.1, 288.1, and 283.1 K were maintained with a precision of {0.05 K by DBT Hetotherm heather and a Hetofrig cooling unit. RESULTS

The system studied is SDS in water, 99.9% D2O in all NMR experiments, and H2O in conductivity and viscosity experiments, with added PEO. The PEO concentration was kept constant at 2000 ppm. Figure 1 shows the specific conductivity of SDS as a

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function of concentration with and without added PEO at three temperatures. In the system with only SDS and H2O at 298.1 K, i.e., no added PEO, two linear regions appear. The intercept is the usual critical micelle concentration, 8.4 mmolal at 298.1 K, in agreement with the data in the literature (15, 27, 29). The conductivity of SDS with added PEO shows three linear regions. The first break is taken as the cac where surfactant aggregates start forming on the polymer. The second break is regarded as the concentration where normal micelles starts forming, termed c2 . The cac and c2 values thus determined are presented in Tables 1 and 2, respectively. The self-diffusion coefficients of PEO and SDS in the mixed aqueous (D2O) system are shown in Fig. 2, as functions of the SDS concentration. The PEO self-diffusion coefficient (Fig. 2, top) is an order of magnitude less than that of SDS (Fig. 2, bottom) in the monomeric form. The SDS self-diffusion coefficient at low SDS concentration (2 mmolal) is a little less with added PEO than without, 5.3 1 10 010 m2 /s compared to 5.7 1 10 010 m2 /s at 298.1 K, an effect that can be ascribed to differences in viscosity. The PEO self-diffusion curves show two distinct breaks. The first can be identified with the formation of surfactant aggregates on the polymer (cac) and the second with saturation of the polymer (c2 ). The SDS self-diffusion coefficient exhibits a sudden decrease around an SDS concentration of about 5 mmolal, leveling off about 20 mmolal. From these data it is not easy to determine the cac or the c2 . However, by plotting the SDS self-diffusion coefficient versus the inverse of concentration (29), the cac appears as a well-defined point. The cac and c2 values found from self-diffusion data are presented in Tables 1 and 2, respectively.

TABLE 1 The cac of SDS in the Presence of 2000 ppm PEO (Mw Å 20000), Determined by Conductivity, NMR, and Viscosity Measurements cac (mmolal) Experimental technique

298.1 K

288.1 K

283.1 K

Surfactant-sensitive methods NMR chemical shift NMR spin-lattice rate constant NMR self-diffusion of SDS Conductivity Average (mmolal) NMR self-diffusion of PEO Viscosity Average (mmolal)

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5.1

5.6

6.4

5.3

5.8

6.2

5.2 5.7 5.4 5.8 5.7 { 0.1 5.3 { 0.2 Polymer-sensitive methods 8.1 7.8 8.0 { 0.5

10.2 10.0 10.1 { 0.5

6.3 6.3 6.3 { 0.1

10.5 10.5 10.5 { 0.5

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TABLE 2 C2 , a1 , and a2 Found from Conductivity Measurements a1 ({0.02)

c2 (mmolal) Experimental techniques Conductivity NMR spin-lattice rate constant NMR self-diffusion of PEO Viscosity

298.1 K 15.4 14 23 25

{ { { {

0.3 1 1 4

a2 ({0.02)

288.1 K

283.1 K

298.1 K

288.1 K

283.1 K

298.1 K

288.1 K

283.1 K

{ { { {

18.9 { 0.4 19 { 1

0.56

0.52

0.49

0.39

0.37

0.36

16.6 17 25 25

0.4 1 1 4

25

{4

The relative viscosity of the SDS-PEO (2000 ppm)-H2O solutions at the three temperatures investigated has been measured. Two break points are observed. These can be taken as the cac and the c2 . The values are given in Tables 1 and 2. The spin-lattice relaxation rates (1/T 1 ) of SDS and PEO have been determined. The PEO and SDS spin-lattice relax-

ation rate are constant until an SDS concentration of 5–7 mmolal, dependent on temperature, where the 1/ T 1 starts to increase. This is the cac value, and the values are given in Table 1. The increases in 1/T 1 are most pronounced at 298.1 K. The increase of the PEO spin-lattice relaxation rates reachs a plateau at 14–19 mmolal (dependent on the sample temperature) where a further increase of the SDS concentration has no effect on the 1/T 1 . The SDS concentration where 1/T 1 reachs a plateau is identified as c2 . The values determined are given in Table 2. The SDS spin-lattice relaxation rate did not reach a plateau, so it is not possible to identify a c2 value. The cac values have also been found from chemical shifts of PEO and SDS by plotting the chemical shift as a function of the inverse SDS concentration (38). The results are presented in Table 1. DISCUSSION

FIG. 2. The self-diffusion coefficient (D) of the system SDS-PEO-D2O as a function of the SDS concentration at 298.1 K ( l ), 288.1 K ( h ), and 283.1 K ( m ). (Top) The PEO (2000 ppm) self-diffusion coefficient. (Bottom) The SDS self-diffusion coefficient ( D).

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In this work the system with pure D2O as solvent is compared to the system containing pure H2O. This could be a problem due to the different physical properties of the two solvents. However, it has been shown that solubilization (39) and cmc values (40, 41) differ only slightly when D2O is substituted for H2O. The only thorough investigation at low SDS concentrations has been carried out by Kamenka et al. (29) for the system SDS-ethyl(hydroxyethyl) cellulose (EHEC). The self-diffusion coefficient of SDS in this system is significantly lower with polymer present than without, the difference being more than 20% for SDS concentrations below the cac. They conclude that there must be some form of interaction between SDS monomers and polymer even below the aggregation point. For SDS-PEO the difference in the self-diffusion of SDS is practically within the experimental error, and it can be ascribed to the small difference in viscosity for a system with and without polymer added. Thus, contrary to the SDS-EHEC system, it appears that an SDS monomer does not interact with PEO or other SDS monomers below the cac. The cac can be identified by all the measuring techniques used in this investigation. The data are presented in Table

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1. Methods that are sensitive to the SDS molecules, conductivity, SDS self-diffusion, chemical shift, and spin-lattice relaxation rate, are in excellent agreement with respect to the cac obtained. Chemical shift and spin-lattice relaxation rate are sensitive to changes in the chemical environment, so these NMR methods respond immediately to surfactant aggregation. Thus, cac values found by chemical shift and spin-lattice relaxation rate of the polymer are consistent with surfactant-sensitive methods. The self-diffusion coefficient of PEO and viscosity data are also in agreement with each other, but exhibit cac values that are significantly higher than the cac values found by the other experimental method used in this study. The self-diffusion coefficient of PEO is an order of magnitude smaller than that of SDS, obviously due to the size of the polymer molecule. If SDS starts forming aggregates on the polymer strand it will certainly be registered by methods that monitor changes in the SDS molecular interactions. However, at first it may not appear as a significant change of the polymer size, and the PEO selfdiffusion and the solution viscosity may not be affected. A certain critical mass of SDS must apparently be bound to the polymer before it registers. Thus, if the cac is defined as the surfactant concentration where aggregation starts forming, polymer self-diffusion and viscosity are not the method to be used for measuring cac values. Conductivity can be used to calculate the degree of ionization ( a ) of the micelle, i.e., the ratio of free counterion in the solution. The simplest approach is where the degree of ionisation ( a ) is taken as the ratio of the slopes of the conductivity curve above and below the cmc (15). This works well since the contribution of the sodium ions to the conductivity outweighs the other contributions. Van Nieuwkoop and Snoei (42), however, have developed a more sophisticated approach, taking into account the contribution of the micelles and the monomers to the overall conductivity. Normally the degree of ionization calculated by the two methods does not differ significantly. The van Nieuwkoop and Snoeis method yields slightly higher values. We have used the first method to determine the degree of ionization. For SDS in water a was found to be 0.38, which is in consistent with data in the literature (15). The degree of ionization of the polymer bound ( a1 ) can also be calculated from the slopes, and it appears to be higher than the degree of ionization for ordinary micelles in a polymer containing solution ( a2 ), 0.56 compared to 0.39 at 298,1 K. These results are in good agreement with published data where the slope method has been used (15, 27). The results of the calculation of the degree of ionization are presented in Table 2. They show that the degree of ionization increases with increasing temperature. The fraction of counterions associated to the aggregates is less for those bound to the polymer. Since the polymer strands must somehow penetrate the palisade layer (28) of the aggregates, this will affect the aggregates just like any ordinary solubilized molecule. The surface

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FIG. 3. The concentration of free SDS monomers as a function of the total SDS concentration at 298.1 K ( l ), 288.1 K ( h ), and 283.1 K ( m ) as calculated from Eq. [4] with b2 Å 0.

charge density, as well as the fraction of associated counterions, will decrease. At low SDS concentrations the SDS molecules will dissolve in water as monomers, later they will aggregate on the polymer strand, and eventually they may aggregate as micellar entities as they do when no polymer is present. The self-diffusion coefficient, or for that matter any other thermodynamic quantity, can then be expressed as D Å b1 Dp / b2 Dm / (1 0 b1 0 b2 )Dw .

[4]

Here b1 and b2 are the fractions of SDS bound to the polymer and in the micellar state, respectively, and Dp , Dm , and Dw are the self-diffusion coefficients of SDS when bound to the polymer, in the micellar state, and as monomers in water, respectively. The equation implies that there is no coupling or interactions between the various entities which is not strictly correct at finite concentration, but at low concentrations it may be a reasonable assumption. Dp will be equal to the PEO self-diffusion coefficient which can be measured, Dm can be measured from systems without polymer added, and Dw is the measured self-diffusion coefficient of SDS as measured below the cmc. However, we still have one equation with two unknowns. If we assume that no micelles form between the cac and the c2 , b2 is zero and we can calculate the fraction of SDS molecules bound to the polymer. This is shown in Fig. 3; i.e., we have plotted the fraction of SDS molecules that remains in the monomeric state (1 0 b1 ) versus the total SDS concentration. At first, of course, all SDS remains in the monomeric state. At a critical concentration all added SDS molecules seem to aggregate on the

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polymer strand, but as the total SDS concentration increases, the fraction of free monomers will again increase. It appears to reach the normal cmc of SDS in pure water at a total SDS concentration between 12 and 16 mmolal depending on the temperature. Thus, it is likely that micelles will be forming and the assumption of b2 Å 0 will no longer hold. The concentration where normal micelles start forming, termed c2 , is normally more difficult to determine than cac, and agreement between various method of measurement is also poor, ranging from about 15.9 to about 20 mmolar for the SDS-PEO system (4, 8, 15, 22, 27). The data in Table 2 show that we also obtain poor agreement for the c2 values. However, as for the determination of cac values, it is important to consider what the various methods monitor. Conductivity basically measures the concentration of free sodium ions, and if the counterion association is different for micelles compared to SDS aggregates on the polymer, a break point in the conductivity versus SDS concentration curves should provide c2 as defined above. The spin-lattice relaxation rate, as for demonstration of the cac, is sensitive to the chemical environment, and it exhibits approximately the same c2 value as conductivity, though the break is less distinct. The PEO self-diffusion coefficient, on the other hand, will primarily monitor aggregation on the polymer strand itself. When this becomes saturated with SDS molecules, one would expect the self-diffusion coefficient to become constant. This happens at an SDS concentration well above 20 mmolal. The self-diffusion coefficient of SDS does not exhibit any c2 value at all. It is a complex function of all the SDS states, as indicated in Eq. [4]. If micelles and polymer-bound aggregates form in parallel, it seems likely that there will be no break point in the self-diffusion coefficient curves of SDS that can be easily identified with c2 . From Table 1 it is seen that the cac decreases with increasing temperatures. This decrease in cac as the temperature is increased was also observed for the SDS-EHEC system (29). The value of cac at 298.1 K found in this work is in agreement with data in the literature (4, 8, 15, 23, 24, 27). The data in Table 2 suggest that c2 , like the cac, decreases as the temperature increases in the temperature interval 283.1 to 298.1 K. This is different for the system SDS-EHEC, where Kamenka et al. (29) found that c2 was independent of temperature in this temperature interval. Schwuger (5) investigated cac and c2 for the system SDS and PEO at 298.1 and 323.1 K. He found that cac decreased and c2 increased as the temperature was increased. The critical aggregation concentration for the SDS/PEO system, defined as the point where SDS starts binding to the polymer, is well defined (using surfactant-sensitive methods). It can be used to calculate thermodynamic functions of this aggregation process. The enthalpy can be calculated from (43) DH 0m Å 0 (2 0 a1 )RT 2[ Ìln(cac)/ ÌT].

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TABLE 3 Thermodynamic Data of DG 0m , DH 0, and DS 0 Calculated According to Eqs. [5–8] Without PEO

With PEO

DG 0m (kJ/mol) DH 0 (kJ/mol) TDS 0 (kJ/mol)

298.1 K

288.1 K

283.1 K

298.1 K

019.4 11.6 31.0

018.9 11.1 30.0

018.6 11.0 29.6

019.2

The result is shown in Table 3, and there is reasonable agreement with data from calorimetric measurements (25). The standard Gibbs’ energy for transferring 1 mol of surfactant from a 1 molal surfactant solution into complex subunits containing m surfactant ions has been given as (7) DG 0m Å RT[(2 0 a1 ) ln (cac) / ln cp /Np ]

[6]

Np is the aggregation number and cp is the polymer concentration. For a system without added polymer the expression for micelle formation is DG 0m Å RT(2 0 a ) ln(cmc).

[7]

Taking N in Eq. [6] to be 35(11) the Gibbs’ energy can be estimated. The result is given in Table 3. The difference in DG 0m for the two processes is small, but favors the formation of aggregates on the polymer strand compared to normal micelles. Although these are crude calculations it appears that the difference is only about 0.2 kJ/mol at 298.15 K and it seems reasonable that micelles may start forming before the polymer strand is saturated. When the enthalpy and Gibbs’ energy is known, entropy ( DS 0m ) can be calculated. The result is given in Table 3 and shows that the driving mechanism is entropic. In conclusion it appears that the critical aggregation concentration, defined as the surfactant concentration where aggregates start forming on the polymer strand, can be determined precisely. However, one must take care to choose a method that monitors the surfactant molecules. The concentration where normal micelles start forming, c2 , is normally more difficult to determine. For the PEO-SDS system it appears that over a concentration range from about 15 to 25 mmolal SDS, normal micelles and SDS aggregates on PEO form in parallel, and this is most likely the cause for the difficulties encountered as far as determination of c2 is concerned. REFERENCES 1. Goddard, E. D., Colloids Surf. 19, 255 (1986). 2. Lindman, B., and Thalberg, K., in ‘‘Interaction of Surfactants with

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3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.

Polymer and Proteins’’ (E. D. Goddard and K. P. Ananthapadmanabhan, Eds.), p. 203. CRC Press, Boca Raton, FL, 1993. Brackman, J. C., and Engberts, J. B. F. N., Chemical Soc. Rev. 22, 85 (1993). Jones, M. N., J. Colloid Interface Sci. 23, 36 (1967). Schwuger, M. J., J. Colloid Interface Sci. 43, 491 (1973). Cabane, B., J. Phys. Chem. 81, 1639 (1977). Gilanyi, T., and Wolfram, E., Colloids Surf. 3, 181 (1981). Cabane, B., and Duplessix, R., J. Phys. 43, 1529 (1982). Cabane, B., and Duplessix, R., Colloids Surfaces 13, 19 (1985). Zana, R., Lianos, P., and Lang, J., J. Phys. Chem. 89, 41 (1985). Lissi, E. A., and Abuin, E., J. Colloid Interface Sci. 105, 1 (1985). Francois, J., Dayantis, J. F. J., and Sabbadin, Eur. Polym. J. 21, 165 (1985). Zana, R., Lang, J., and Lianos, P., in ‘‘Microdomains in Polymer Solution’’ (P. Dubin, Eds.), p. 357. Plenum, New York, 1985. Cabane, B., and Duplessix, R., J. Phys. 48, 651 (1987). Witte, F. M., and Engberts, J. B. F. N., J. Org. Chem. 52, 4767 (1987). Gao, Z., Wasylishen, R. E., and Kwak, J. C. T., J. Phys. Chem. 95, 462 (1991). van Stam, J., Almgren, M., and Lindblad, Progr. Colloid Polym. Sci. 84, 13 (1991). Brackman, J. C., Langumir 7, 469 (1991). Dubin, P. L., Gruber, J. H., Xia, J., and Zhang, H., J. Colloid Interface Sci. 148, 35 (1992). Xia, J., Dubin, P. L., and Kim, Y., J. Phys. Chem. 96, 6805 (1992). Brown, W., Fundin, J., and da Graca Miguel, M., Macromolecules 25, 7192 (1992). Benkhira, A., Franta, E., and Francois, J., J. Colloid Interface Sci. (1994).

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