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Interactions of Star Polymers with Surfactants Robin David Wesley and Terence Cosgrove* School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom
Laurie Thompson Unilever Research, Port Sunlight Laboratory, Quarry Road East, Bebington, The Wirral, L63 3JW, United Kingdom Received February 23, 1999. In Final Form: July 6, 1999 Binding isotherms between star poly(ethylene glycol) (s-PEG) and the anionic surfactant sodium dodecyl sulfate (SDS) have been measured. The onset of SDS/s-PEG binding happens at the same concentration for both star and linear PEG, but saturation of the star occurs at a lower surfactant concentration. The size of the star has been measured as a function of SDS concentration by NMR self-diffusion and smallangle neutron scattering (SANS) techniques. The star decreases in size at the normal critical micelle concentration (CMC) of the SDS but increases at higher SDS concentrations. These results echo the findings of photocorrelation spectroscopy and SANS studies on physically adsorbed PEG on polystyrene latex. At high surfactant concentrations the star adopts an elongated conformation. The surfactant binds to the star molecules in the form of spherical micelles, which are of similar size to free solution micelles.
Introduction There is a considerable literature on the interactions between polymer and surfactant molecules in solution. For systems where significant binding occurs, such as poly(ethylene oxide) (PEO) with sodium dodecyl sulfate (SDS) it is well documented1-4 that the presence of the polymer acts as a nucleation site for micelle formation at concentrations well below the surfactant’s normal critical micelle concentration (CMC). The concentration marking the onset of polymer/surfactant binding is known as the critical aggregation concentration (CAC) and is independent of polymer concentration and molecular weight. The polymer/ surfactant complex has been described5 as a “pearl necklace” structure where polymer wraps itself around surfactant micelles. As the concentration of surfactant is increased, the polymer becomes saturated with surfactant micelles and then solution micelles form. The critical micelle concentration in the presence of polymer therefore depends on the polymer concentration. In the presence of a solid/liquid interface, the situation becomes more complicated. Three scenarios exist, depending upon the nature of the polymer, the surfactant, and the interface. (a) If the polymer and surfactant are noncomplexing but both adsorb at the interface, there will be competition for surface sites.6 (b) If the polymer and the surfactant form a complex but only one adsorbs at the surface, the nonadsorbing species may complex with the adsorbed species thus becoming effectively attached to the interface. There may be competition between adsorbed polymer/surfactant complexes and solution complexes.7 (1) Jones, M. J. Colloid Interface Sci. 1974, 23, 36. (2) Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294. (3) Kang, Y. S.; Kevan, L. J. Phys. Chem. 1994, 98, 7624. (4) Brown, W.; Fundin, J.; Miguel, M. D. Macromolecules 1992, 25, 7192. (5) Shirama, K. J. Biochem. 1974, 75, 309. (6) Ghodbane, J.; Denoyel, R. Colloids Surf. A 1997, 127, 97.
(c) If both polymer and surfactant adsorb at the interface and they also form solution complexes, they may absorb as a complex direct from solution or they may absorb individually. In such a case competition may exist between surfactant, polymer, and the complex for adsorption.8 Previous studies have investigated the effect of surfactant on an adsorbed polymer layer at a solid/liquid interface where the surfactant will complex to the polymer (cases b or c). The systems studied were SDS with PEO adsorbed on either colloidal silica 9 (where SDS does not adsorb) or polystyrene latex10 (where significant SDS adsorption can occur) have shown similar findings. In both cases the surfactant causes the adsorbed layer to contract at concentrations around its normal CMC, but at higher surfactant concentrations the layer expands to around its original size. For both surfaces the addition of surfactant also leads to desorption of the polymer. The adsorbed amount falls rapidly up to the CMC but does not change substantially beyond this. This study is in part aimed at elucidating the nature of the surface complexes by using a model system where polymer desorption is not possible. Star polymers11 are molecules where several polymer arms are attached to a small central point. In the ideal case this point would be a single small multifunctional molecule. Obviously, as the number of arms increases, geometric (and chemical) constraints mean the central core must have a finite size. The simplest model for calculating the radius of gyration of a star polymer was proposed by Zimm and Stockmeyer.12 This model assumes that each of the arms on the star adopts a random walk. The mean squared radius of (7) Bury, R.; Desmazieres, B.; Treiner, C. Colloids Surf. A 1997, 127, 113. (8) Otsuka, H.; Esumi, K.; Ring, T. A.; Li, J. T.; Caldwell, K. D. Colloids Surf. A 1996, 116, 161. (9) Cosgrove, T.; Mears, S. J.; Thompson, L.; Howell, I. ACS Symp. Ser. 1995, No. 615, 196. (10) Cosgrove, T.; Mears, S. J.; Thompson, L.; Howell, I., in press. (11) Grest, G. S.; Fetters, L. J.; Huang, J. S.; Richter, D. Adv. Chem. Phys. 1996, 94, 67. (12) Zimm, B. H.; Stockmeyer, W. H. J. Chem. Phys. 1949, 17, 1301.
10.1021/la990200s CCC: $18.00 © 1999 American Chemical Society Published on Web 10/19/1999
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Table 1. Properties of the Star PEGs Used in This Work name
MW/g mol-1
no. of arms
use
s-PEG 130 s-PEG 170 s-PEG 429
130 000 ( 7000 170 000 ( 8000 260 000 ( 39 000
15 19-20 13
SANS, NMR, and surface tension SANS NMR and surface tension
gyration 〈Rg2〉Star for a star molecule is related to the average mean squared radius of gyration of each arm, 〈Rg2〉Arm and to the number of arms, f.
〈Rg2〉Star )
(3f -f 2) 〈R
〉Arm
2
g
(1)
This approach will tend to underestimate the radius of gyration of the star as it does not explicitly take into account excluded volume effects which becomes more important as f increases. A more sophisticated approach13-15 adapting the de Gennes scaling model16 has been developed. Close to the central point of the star, the polymer will behave as though it is in a polymer melt. In intermediate regions the polymer behaves as a concentrated solution. An outer semidilute region exists in good solvents for stars with high molecular weight arms. With these assumptions, the radius of gyration of a star polymer in a theta and good solvent has been calculated (eqs 2 and 3)
Theta solvent 〈Rg〉Star ∼ N0.5f 0.25
(2)
Good solvent 〈Rg〉Star ∼ N0.59f 0.205
(3)
Grest et al.11 have correlated a series of data sets for well characterized monodisperse star polymers. They have linked the data using an equation of the form:
〈Rg2〉Star1/2/〈Rg2〉Arm1/2 ) Kf β
(4)
where K and β are experimentally determined constants for various star polymers with 2-128 arms linked at a chlorosilane core. Under theta conditions it is found that K ) 1.29 and β ) 0.154, and in the limit of a good solvent K ) 1.33, and β ) 0.206. The value of the exponent in the theta solvent is significantly lower than the value of 0.25 predicted by scaling theory; however both approaches agree well in the case of a good solvent. Experimental Section Materials. Three star poly(ethylene glycol) (s-PEG) samples were obtained from Shearwater polymers and were used as supplied. The s-PEGs consist of several poly(ethylene glycol) arms joined at a small central divinyl benzene core. The properties of these polymers are summarized in Table 1. Hydrogenated sodium dodecyl sulfate (H-SDS) was obtained from Fluka chemicals (>98% purity). Deuterated sodium dodecyl sulfate (D-SDS) was obtained from Fluorochem (98.2% atom D). Both samples were used as supplied except for the surface tension measurements. The hydrogenated SDS used for surface tension measurements was recrystallized three times from ethanol. Samples were prepared either in MilliQ Millipore water or D2O (MSD Isotopes Limited). (13) Daoud, M.; Cotton, J. P. J. Phys. (Paris) 1982, 43, 531. (14) Birshtein, T. M.; Zhulina, E. B. Polymer 1984, 25, 1453. (15) Birshtein, T. M.; Zhulina, E. B.; Borisov, O. V. Polymer 1986, 27, 1078. (16) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: New York, 1970.
The surface tension results of Jones1 referred to in this paper were obtained from a linear poly(ethylene oxide) of molar mass 5400 g mol-1. Surface Tension Measurements. The surface tension of solutions of the s-PEG 429 was measured as a function of surfactant concentration at 25 °C using a Kruss K12 tensionmeter. (Measurements were carried out at the Unilever Research Laboratories Port Sunlight.) The concentration of star polymer was kept constant while the surfactant concentration was increased by adding a mixed solution of surfactant and polymer to a solution of polymer. Prior to use, the equipment was cleansed with chromic acid. The solution was stirred for 60 s after the addition of the mixed polymer/surfactant solution and allowed to equilibrate for a further 15 min before the surface tension was measured. Pulsed Field Gradient Spin-Echo NMR Diffusion Measurements. The self-diffusion coefficients, DS, of star polymers with added SDS dissolved in D2O were obtained using the pulsed field gradient spin-echo (PFGSE) sequence.17,18 The sequence was measured on a 300 MHz Bruker NMR spectrometer with a field gradient unit. (Measurements were carried out at the Unilever Research Laboratories, Port Sunlight.) A series of NMR spectra were recorded while increasing the time, δ, that the field gradient pulse is applied from 0 to 40 ms. The time between radiofrequency pulses, ∆, was held constant at 50 ms. The attenuation of the signal due to the PEG in the NMR spectra, A(δ) was measured as a function of the field gradient pulse length, δ. To obtain the self-diffusion coefficient, the data were fitted to eq 5.
ln[A(δ)] ) -γM2G2δ2(∆ - δ/3)DS
(5)
where γM is the magnetogyric ratio and G the field gradient strength. To obtain G, the spectrometer is calibrated with water, whose diffusion coefficient has been measured19 as 2.23 × 109 m2 s-1 at 25 °C. Neutron Scattering. Small-angle neutron scattering studies of the star PEG 130 were performed at the ISIS facility, Didcot, UK.20 The polymer concentration was fixed at 10 000 ppm and the concentration of either hydrogenated or deuterated SDS was varied. The CMC of hydrogenated SDS in D2O has been shown to be very similar to the CMC of hydrogenated SDS in H2O.21 The scattering from H-SDS in D2O and D-SDS in H2O yields data which gives micelles of the same shape and size.22,23 From this we may infer that substitution of D-SDS for H-SDS or D2O for H2O will not significantly alter the micellar properties of the surfactant. The scattering intensity (I(Q)) is measured as a function of the scattering vector, Q:
Q)
4π sin(θ/2) λ
(6)
(17) Blum, F. D. Spectroscopy 1986, 1, 32. (18) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (19) Gillen, K. T.; Douglass, D. C.; Hoch, J. R. J. Chem. Phys. 1972, 57, 5117. (20) Wesley, R. D.; Cosgrove, T.; Hone, J. H. E.; Mears, S. J. ISIS 1996: The ISIS Facility Annu. Rep. 1995-96 1995, A297. (21) Mukerjee, P.; Mysels, K. J. Critical micelle concentrations of aqueous surfactant systems; U.S. Government Printing Office: Washington, DC, 1971; Vol. 222. (22) Cabane, B.; Duplessix, R.; Zemb, T. J. Phys. (Paris) 1985, 46, 2161. (23) Cabane, B.; Duplessix, R. J. Phys. (Paris) 1982, 43, 1529.
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where λ is the neutron wavelength and θ the angle through which the neutrons are scattered. The total scattering, which contains information on shape, size, and interactions of the scattering entities is given by
I(Q) ) NbVb2∆F2P(Q) S(Q) + Binc
(7)
where Nb is the number concentration of scatterers and Vb is their volume. P(Q) and S(Q) are the form factor and structure factor, respectively. Binc is the incoherent background. ∆F is the difference in the scattering length density (SLD) between the scattering body and the surrounding medium. The SLD depends on the chemical composition of the material and its density. It is well-known24 that hydrogen and deuterium have very different scattering lengths so that substituting deuterium for hydrogen will greatly change the SLD. It can be seen (eq 7) that if the SLD of the medium is equal to that of a particular component present in the system, then that component will no longer contribute to the scattering. By deuterating certain parts of the system, it is possible to arrange for those components to have the same SLD as the solvent, thereby removing their contribution to the total scattering. The form factor contains information on the shape of the scattering centers. It has been shown25 that the radius of gyration of a star polymer can be determined by approximating the true form factor to the Gaussian star form factor evaluated by Benoit.26 The Gaussian star form factor is given by
P(Q) )
2 2 f-1 {1 - exp(-ν2)}2 ν - {1 - exp(-ν2)} + 2 fν4
[
]
Figure 1. Surface tension of a 500 ppm solution of s-PEG 429 as a function of SDS concentration. The first and second transitions (T1 and T2) in the surface tension as determined from the plot are marked. The normal CMC of the surfactant in the absence of polymer is also shown.
(8)
where f is the number of arms as in eq 1 and
ν)
x3f -f 2 Q〈R 〉
(9)
g Star
The Guinier approach27 was also used to determine radii of gyration. At low Q values (Q2Rg2 < 1) the scattering can be approximated by an expansion of the spherical form factor.
(
P(Q) ≈ exp -
)
(QRgStar)2 3
(10)
The structure factor S(Q) contains information about interparticle interactions and is normally only seen for concentrated or charged systems such as surfactant micelles where these interactions are strong. The Hayter-Penfold method28 can be used to calculate the structure factor for micelles with a given radius, surface charge, and intermicelle separation.
Results and Discussion Surface Tension Measurements. Following the work of Jones1 on linear poly(ethylene oxide), the surface tension, γ, of s-PEG 429 was measured as a function of SDS concentration (Figure 1). At the three star polymer concentrations investigated two transitions in the surface tension curves were observed. The first transition, T1, corresponds to the concentration of SDS at which the onset of polymer/surfactant binding occurs and is therefore the CAC of the system. It has been shown29 that the surfactant molecules in polymer/surfactant complex exist as bound micelles for linear nonionic polymers such as PEO and we shall assume that this is the case for the s-PEG. (24) Ottewill, R. H. Small Angle Neutron Scattering; Ottewill, R. H., Ed.; University of Bristol, 1981; p 143. (25) Willner, L.; Jucknischke, O.; Richter, D.; Roovers, J.; Zhou, L. L.; Toporowski, P. M.; Fetters, L. J.; Huang, J. S.; Lin, M. Y.; Hadjichristidis, N. Macromolecules 1994, 27, 3821. (26) Benoit, H. J. Polym. Sci. 1953, 11, 507. (27) Guinier, A.; Fournet, G. Scattering of X-rays; John Wiley: New York, 1955. (28) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983, 261, 1022. (29) Goddard, E. D. Colloids Surf. 1986, 19, 255.
Figure 2. Transition points of the surface tension data as a function of polymer concentration. The first (×) and the second transitions (b) for SDS as a function of s-PEG 429 concentration are shown. Also marked are the transition points with linear PEO (4 and 0) as measured by Jones. The solid line indicates a fit to the second transition for the s-PEG and the dashed line a fit to the second transition for linear PEG.
The second transition, T2, is attributed to the formation of solution micelles once the polymer is saturated with surfactant. The binding isotherms of the star polymer have been compared to those for linear PEO and the surfactant concentrations at T1 and T2 plotted as a function of polymer concentration (Figure 2). It is found that T1 is independent of polymer concentration and is the same for both the star and linear polymers. It is observed that the concentration of surfactant at which the polymer becomes saturated with surfactant, T2, increases with polymer concentration for both the star and linear polymers. However, T2 occurs at lower surfactant concentrations for the star polymer than for the linear polymer. The increase of T2 with increasing polymer concentration is simply due to the increasing amount of polymer available for surfactant binding. The decreased binding of the star polymer with SDS compared to its linear counterpart is due to steric restrictions at the center of the star where the high concentration of star polymer segments prevents binding with surfactant. In contrast all segments of the linear polymer are equally available for binding. Similar behavior is expected for the other star samples though these have not been measured.
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Table 2. Details of the Adsorption Isotherms of s-PEG 429 and Linear PEO with SDSa linear polymer1
star polymer
[T1 SDS 4.9 ( 0.4 4.4 ( 0.5 [T2]/mmol-1 SDS )(6.48 × 10-03) x + 8.20 )(2.53 × 10-03) x + 7.22 value of γ at high 39.8 37.25 ( 0.05 [SDS]/mN m-1 ]/mmol-1
a
The parameter x is the concentration of polymer in ppm.
Figure 4. SANS data for 10000 ppm s-PEG 130 in D2O as a function of D-SDS concentration. Data are shown in the absence of SDS (×), with 1500 ppm SDS (0), with 3000 ppm SDS (4), and with 10 000 ppm SDS (O). Fits to the Benoit form factor with no constraints are shown for each concentration of hydrogenated surfactant. Also shown is the scattering from s-PEG 130 with 10 000 ppm H-SDS (]). For the sake of clarity error bars are not shown.
Figure 3. Self-diffusion of 5000 ppm s-PEG as a function of SDS concentration. The star samples measured were s-PEG 429 (×) and s-PEG 130 (O). The first and second transitions in the surface tension data are marked on the chart, along with the normal CMC of the surfactant.
The intercept of the graph of T2 with polymer concentration corresponds to the CMC of SDS (Table 2). The literature21 value for the CMC of SDS of 8.27 mmol dm-3 is in good agreement with the intercept calculated from Jones’ data, but the intercept of the s-PEG is somewhat lower. Jones found that at surfactant concentrations greater than T2 the surface tension had a value very similar to that of pure SDS21 of 39.8 mN m-1, and for the s-PEG a value of 37.25 ( 0.05 mN m-1 was measured at 1000 ppm of polymer. We believe this lower surface tension may be due to the adsorption of polymer surfactant complexes at the air/water interface. NMR Self-Diffusion Measurements. The self-diffusion coefficient, Ds, of a polymer is inversely proportional to its hydrodynamic radius, RH, according to the StokesEinstein equation
Ds ) kBT/6πηRH
(11)
where kB is the Boltzmann constant, T the absolute temperature, and η the viscosity of the fluid medium. Figure 3 shows the self-diffusion coefficient of s-PEG 130 and s-PEG 429 as a function of surfactant concentration. Both samples show similar behavior with a maximum in the self-diffusion coefficient observed around the normal CMC of the surfactant. The hydrodynamic radius of the star is inversely proportional to the self-diffusion coefficient (eq 11). Even allowing for an increased solvent viscosity, it can be seen that the smaller star (s-PEG 130) contracts as surfactant is added with a minimum in its hydrodynamic radius of ∼74 Å around the normal CMC of the surfactant and expanding to ∼100 Å at high surfactant concentration. For the higher molecular weight star (s-PEG 429) the expansion at high surfactant concentration is greater and the star almost doubles in size compared to its value at the CMC. It is not possible to speculate whether there is a change in shape of the star, but this general behavior is qualitatively very similar
Table 3. Comparison of Experimentally Determined Values of the Radii of Gyration of Star PEG in D2O with Theoretical Models radius of gyration /Å method Guinier fit to the scattering data Benoit fit to the scattering data linear PEG of mol wt equal to the total star linear PEG of mol wt equal to a single arm fully extended linear PEG of mol wt equal to a single arm Gaussian model empirical (theta solvent) empirical (good solvent)
star 130
star 170
82.9 ( 0.8 68.6 ( 1.2 81.9 ( 0.7 78.1 ( 0.7 123.7 141.4 31.9
32.4
448
463
54.1 62.5 74.2
55.2 65.9 79.1
to the contraction and expansion of a physically absorbed PEO layer found on colloidal silica and polystyrene.9,30-32 These effects will be further discussed in the light of the SANS data given below. Small-Angle Neutron Scattering. Structure of the Star Polymer. Figure 4 shows the scattering from s-PEG 130 in D2O as a function of D-SDS concentration. In these data the surfactant is deuterated and therefore is “contrast matched” with the solvent. According to the s-PEG/SDS binding isotherm the surfactant concentrations used for the SANS experiments correspond to just above T1 (1500 ppm SDS), to the normal CMC of SDS (3000 ppm SDS), and to a point just above T2 (10000 ppm SDS). These scattering measurements were repeated for s-PEG 170, although for brevity the data are not shown. In the absence of surfactant the scattering from both s-PEGs fitted the Benoit form factor well (eqs 9 and 10). The radius of gyration determined from the Benoit fit was comparable with that obtained by the Guinier method for s-PEG 170 and in excellent agreement for s-PEG 130. Parameters are given in Table 3. This work can add little to existing studies11 comparing experimentally determined properties of monodisperse (30) Mears, S. J.; Cosgrove, T.; Obey, T.; Thompson, L.; Howell, I. Langmuir 1998, 14, 4997. (31) Cosgrove, T.; Mears, S. J. Abstracts of Papers of the American Chemical Society 1994, 208, 60. (32) Mears, S. J.; Cosgrove, T.; Thompson, L.; Howell, I. Langmuir 1998, 14, 997.
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Figure 5. Radius of gyration of s-PEG 130 in D2O with surfactant. Data shown are calculated from Guinier fits (4), and the Benoit star form factor (O). The number of arms calculated from the Benoit form factor is also shown (×). The first and second transitions in the surface tension data are marked on the chart, along with the normal CMC of the surfactant.
star polymers with theoretical predictions due to the relatively high polydispersity of the star polymer samples studied here. However, such a comparison (Table 3) shows us that the radii of gyration of the stars reassuringly lie between that of a linear polymer with a molecular weight equal to a single arm of the star and with a polymer of molecular weight of the total star. Equation 1 (Gaussian approximation) underestimates the size of the stars as expected as the arms cannot adopt a random walk configuration but stretch due to crowding at the star center. The empirical relations (eq 4) are perhaps the best models for the size of the stars although these relations were derived using highly monodisperse, well-characterized stars with a very small central core. Structure of the Star Polymer in the Presence of Surfactant. Figure 4 also shows the scattering from s-PEG 130 with D-SDS where the scattering only contains information about the star. In the presence of the deuterated surfactant the data would no longer fit to the Benoit star form factor (eqs 9 and 10) It was found that better computer-generated fits could be obtained by reducing the number of arms on the star. These fits are also shown in Figure 4. As the concentration of surfactant increased, the number of arms needed to obtain a good fit fell from the expected values in the absence of surfactant to approximately two arms for both s-PEGs at the highest surfactant concentration measured. The radii of gyration of the s-PEGs calculated according to the Guinier approximation show similar trends to those obtained using the Benoit method with a minimum seen at around the normal CMC of the surfactant. The radius of gyration of the star obtained from these fits along with the number of arms is shown in Figure 5. Figure 6 shows plots of Q2I(Q) against Q for the s-PEG 130 sample, and similar data were found for the other samples. The peak, which is characteristic of compact polymeric systems such as stars and rings,33 can be seen at the three lower surfactant concentrations for both stars. The peak however disappears at the highest surfactant concentration (10 000 ppm) suggesting the polymer no longer retains a star structure. The disappearance of the peak in the Q against Q2I(Q) plot agrees with the reduction in the number of arms given (33) Higgins, J. S.; Benoit, H. C. Polymers and Neutron Scattering; Clarendon Press: Oxford, 1994.
Wesley et al.
Figure 6. Plot of Q2I(Q) against Q for s-PEG 130 as a function of D-SDS concentration in D2O. Data are shown in the absence of SDS (×), with 1500 ppm SDS (0), with 3000 ppm SDS (4), and with 10 000 ppm SDS (O). Fits to the experimental data are the same as shown in Figure 4.
Figure 7. log-log plot of the neutron scattering data for s-PEG 130 (×) and s-PEG 170 (O) with 10 000 ppm D-SDS in D2O. The lines indicate fits to I(Q)-Q-1 suggesting the star polymers are scattering as rods.
by the Benoit form factor method. If at the highest SDS concentration the star polymer has less than three arms as the Benoit fit suggests, then the polymer can no longer be adopting a starlike conformation and hence the peak in the Q2I(Q) against Q plot is no longer seen. Although the scattering from the star at the highest surfactant concentration could not be fitted to the star model, the data show a strong Q-1 dependence. This relationship is characteristic of the scattering from a rodlike or cylindrical scatterer. Figure 7 shows the scattering data from two of the star samples along with a Q-1 fit. The scattering from the star at the lower SDS concentrations did not show this dependence. Structure of the Surfactant in the Presence of Star Polymer. To investigate the behavior of the surfactant in the presence of star polymer, the scattering of s-PEG and hydrogenated surfactant was measured. The peak in the data, characteristic of the presence of micelles, can clearly be seen for the highest surfactant concentration (10 000 ppm) and is shown in Figure 4. The scattering due to the surfactant alone in the presence of polymer may be extracted from the scattering of the star with D-SDS and H-SDS. The scattering, I(Q), from polymer with contrast matched surfactant (i.e., D-SDS in D2O) is given by eq 7
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Figure 8. Scattering data from h-SDS in the presence of s-PEG 130 in D2O. Data are shown for surfactant at 10 000 ppm in the absence of polymer (×) and for surfactant at 10 000 ppm in the presence of s-PEG 130 (O). The lines through the data are a result of Hayter-Penfold model fits. The fitting parameters are as given in Table 4. Table 4. Details of Fitting Parameters for 10 000 ppm SDS in the Presence of s-PEG Compared with Values for Solution Micelles complexed micelles solution micelles micellar diameter/Å fitted volume fraction/ppm
38.1 ( 0.2 6600 ( 200
s-PEG 130
s-PEG 170
35.1 ( 0.8 38.4 ( 0.7 9200 ( 1000 12 600 ( 1000
and is rewritten here as
Ip(Q) ) A[Fp(Q)]2 + Binc
(12)
where p denotes polymer scattering and A is a factor depending on the size, volume fraction, and scattering length density of the scattering bodies. The partial form factor Fp(Q) is given by Fp(Q)2 ) Pp(Q). The scattering from polymer and surfactant off contrast (i.e., H-SDS in D2O) is given by
Ip+s(Q) ) (Ap0.5Fp(Q) + As0.5Fs(Q))2 + Binc
(13)
where s denotes surfactant and Fs(Q) includes the structure factor, Ss(Q): Fs(Q)2 ) Ps(Q)Ss(Q). The first term in eq 13 was measured for polymer with contrast matched surfactant. This allows us to calculate the second term, which arises from the scattering due to surfactant, provided the form factors and structure factors remain real and positive. Figure 8 shows the data obtained from such an analysis. The data were fitted to the Hayter-Penfold model28 for micellar scattering, these fits are also shown and the parameters obtained from these fits are given in Table 4. The fits are quite reasonable given the complexity of the data analysis and clearly define the peaks in the scattering at both concentrations. The surfactant concentration at which the micellar diameters have been obtained is just above the saturation point of the star. It is therefore a reasonable assumption that the measured scattering is dominated by the complexed micelles with little or no contribution from solution micelles. The fitted neutron scattering data show that the bound micelles are similar in size to free micelles and that the bound micelles are spherical. This validates our earlier assumption that the star polymer/surfactant complex is very similar to those observed with linear polymers where the surfactant binds as micelles.
Figure 9. Schematic of the star polymer as a function of SDS concentration: (a) In the absence of surfactant; (b) at a surfactant concentration just above T1; (c) at the surfactant’s normal cmc; (d) on saturation with surfactant.
The volume fraction of the micelles obtained from the fit is inversely proportional to the distance between micelles. It appears that the complexed micelles are brought slightly closer together than their solution counterparts. If we can assume the aggregation number34 is the same for bound and free micelles (Table 4 shows that the micellar sizes are very similar), it can be calculated that each s-PEG 130 molecule will bind to around six micelles on saturation with surfactant. Each of the six micelles has a diameter of ca. 38 Å, which is approximately half the radius of gyration of the star. The neutron data show that the star adopts an elongated conformation at the highest surfactant concentration. At this concentration the star can be pictured as two “bundles” of arms stretching out in opposite directions. Each bundle will have several micelles associated along its length. The resultant shape is almost cylindrical and is consistent with the observed scattering which is close to a Q-1 dependence. Conclusions The binding isotherm of s-PEG to SDS is similar to the isotherm between linear PEO and SDS except that the star becomes saturated with SDS at lower surfactant concentrations. This behavior is due to the steric restrictions at the center of the star preventing all the polymer segments from being available for binding to surfactant micelles. As SDS is added to the star it first contracts, reaching a minimum size at the normal CMC of SDS and then reexpands to around its original size at higher surfactant concentrations. Both NMR and small angle neutron scattering data support this. The number of arms on the star as measured by neutron scattering appears to reduce as surfactant is added until the star appears to have only two arms; it is no longer a star. In fact, the star shows rodlike scattering behavior. We have shown that the surfactant is bound as micelles, which are very similar in shape and size to those found in free solution. A schematic model for the behavior of the star is put forward in Figure 9. Above the critical aggregation concentration (T1) the star forms complexes with surfactant micelles. To maximize the number of favorable star/ (34) Aniansson, E. A. G.; Wall, S. N.; Almgren, M.; Hoffmann, H.; Kielmann, I.; Ulbricht, W.; Zana, R.; Lang, J.; Tondre, C. J. Phys. Chem. 1976, 80, 905.
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micelle contacts the star adopts a conformation where several arms “embrace” each of the complexed micelles. This leads to a reduction in the size of the star (Figure 9b). The minimum in the star size, which occurs at approximately the normal CMC of the SDS, corresponds to a polymer/surfactant complex where micelles are not brought sufficiently close to one another to lead to significant electrostatic repulsion (Figure 9c). As the number of bound micelles increases the star is forced into a conformation that reduces electrostatic repulsion between neighboring micelles while retaining a large number of polymer/micelle contacts. At its saturation point the star is pictured as two ‘bundles’ of arms stretching in opposite directions. Each bundle will have several micelles associated along its length (Figure 9d).
Wesley et al.
The complexed micelles are virtually the same size as normal solution micelles, so we may assume that their aggregation number34 is the same in this case. From the experimentally determined binding isotherm (Table 2) it is found that each s-PEG 130 molecule will bind to approximately six micelles on saturation. Acknowledgment. The EPSRC and Unilever Research are acknowledged for the provision of grants in order to undertake this work. Dr. S. King is thanked for his help in the small-angle neutron scattering experiments. Finally, the authors are grateful to Jeff Rockcliffe for help with the NMR self-diffusion measurements. LA990200S
