Dynamics of Adsorption of an Oppositely Charged Polymer

Nov 3, 2006 - concentration for various polymer concentrations in the range 0-0.2 g dm-3. Laser Doppler velocimetry was used to determine the surface ...
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Langmuir 2007, 23, 3242-3253

Dynamics of Adsorption of an Oppositely Charged Polymer-Surfactant Mixture at the Air-Water Interface: Poly(dimethyldiallylammonium chloride) and Sodium Dodecyl Sulfate Richard A. Campbell, Philip A. Ash, and Colin D. Bain* Department of Chemistry, Durham UniVersity, South Road, Durham DH1 3LE, United Kingdom ReceiVed NoVember 3, 2006. In Final Form: December 17, 2006 The dynamic adsorption behavior of mixtures of the cationic polymer poly(dimethyldiallylammonium chloride) [poly(dmdaac)] and the anionic surfactant sodium dodecyl sulfate (SDS) has been studied at the expanding liquid surface of an overflowing cylinder. A combination of ellipsometry and external reflection Fourier transform infrared spectroscopy was used to measure the adsorbed amounts of poly(dmdaac) and SDS as a function of the bulk surfactant concentration for various polymer concentrations in the range 0-0.2 g dm-3. Laser Doppler velocimetry was used to determine the surface age, which was ∼1 s for solutions where the polymer adsorbed. The interfacial behavior is rationalized in terms of competition between surface activity and mass transport to the expanding surface. At low surfactant concentrations, adsorption of both poly(dmdaac) and SDS is enhanced as a result of the formation in solution of polymer-surfactant complexes that are more surface active than either component alone. The rate of adsorption of these complexes is diffusion-controlled, and their interfacial composition remains constant at three dmdaac units per SDS molecule over a 5-fold change in the surfactant concentration. For the higher polymer concentrations studied, the complexes saturate the air-water interface: the adsorbed amount is independent of the polymer concentration and remains constant also over a factor of 5 in the surfactant concentration. Once the number of bound surfactant molecules per dmdaac monomer exceeds 0.3, the complexes begin to form large aggregates, which are not surface active due to their slower mass transport. The adsorbed amount decreases rapidly on approach to the equivalence point (one SDS molecule per dmdaac monomer), and when it is reached, only a very small amount of material remains at the interface. At still higher surfactant concentrations, the free SDS adsorbs but there is no adsorbed poly(dmdaac). The dynamic adsorption data are compared with equilibrium measurements of the same system by Staples et al. (Langmuir 2002, 18, 5147), which show very different surface compositions and no significant change in surface coverage at the equivalence point.

Introduction Mixtures of polymers and surfactants are used extensively in industrial applications. The addition of polymer to aqueous surfactant systems can serve to modify the solution viscosity in shampoos and cosmetics or to stabilize systems with a high surface-to-volume ratio, such as paint emulsions and shaving foams.1,2 There is also considerable interest from the biomedical community in the use of polymer-surfactant mixtures as drug delivery aids.3-5 Substantial research effort has been directed toward the solution properties of polymer-surfactant mixtures,6-8 exploiting techniques such as small-angle neutron scattering,9 small-angle X-ray scattering,10 light scattering,11 optical microscopy,12 fluorescence * To whom correspondence [email protected].

should

be

addressed.

E-mail:

(1) Buckingham, J. H.; Lucassen, J.; Holloway, F. J. Colloid Interface Sci. 1978, 67, 423. (2) Goddard, E. D., Ananthapadmanabhan, K. P., Eds. Interaction of Surfactants with Polymers and Proteins; CRC Press: Boca Raton, FL, 1993. (3) Mel’nikov, S. M.; Dias, R.; Mel’nikova, Y. S.; Marques, E. F.; Miguel, M. G.; Lindman, B. FEBS Lett. 1999, 453, 113. (4) Malmsten, M. Surfactants and Polymers in Drug DeliVery; Marcel Dekker: New York, 2002; Vol. 122, No. 66. (5) Hwang, Y.-J.; Oh, C.; Oh, S.-G. J. Controlled Release 2005, 106, 339. (6) Kwak, J. C. T., Ed. Polymer-Surfactant Systems; Marcel Dekker: New York, 1998; Vol. 77, p 239. (7) La Mesa, C. J. Colloid Interface Sci. 2005, 286, 148. (8) Tam, K. C.; Wyn-Jones, E. Chem. Soc. ReV. 2006, 35, 693. (9) Penfold, J.; Staples, E.; Tucker, I.; Creeth, A.; Hines, J.; Thompson, L.; Cummins, P.; Thomas, R. K.; Warren, N. Colloids Surf., A 1997, 128, 107. (10) Svensson, A.; Sjo¨stro¨m, J.; Scheel, T.; Piculell, L. Colloids Surf., A 2003, 228, 91. (11) Yan, P.; Xiao, J.-X. J. Dispersion Sci. Technol. 2005, 26, 655. (12) Trabelsi, S.; Guillot, S.; Raspaud, E.; Delsanti, M.; Langevin, D.; Boue´, F. AdV. Mater. 2006, 18, 2403.

spectroscopy,13 and measurements of yield stress14 and viscosity.15 Comparatively little work has been carried out to characterize interfaces in polymer-surfactant mixtures. The principal technique that has been used is tensiometry,16-18 especially for weakly interacting systems, in which at least one component is neutral.19,20 These mixtures are easier to characterize than strongly interacting systems, such as a charged polymer and an oppositely charged surfactant.21,22 One problem is that such solutions often take a long time to equilibrate, and hence, there is doubt about whether the surface tension has reached true equilibrium. Even at equilibrium it is difficult to relate the surface tension to the extent of adsorption at the interface. The surface tension depends on the free energy of transfer of the polymer and surfactant from the bulk to the surface and hence on the chemical potentials of the adsorbing species in the bulk phase. Without prior knowledge of the bulk activities, which are highly dependent on interactions between components, one cannot interpret changes in surface tension with respect to changing solution conditions. This point (13) Yoshimura, T.; Nagata, Y.; Esumi, K. J. Colloid Interface Sci. 2004, 275, 618. (14) Marquez, M.; Robben, A.; Grady, B. P.; Robb, I. J. Colloid Interface Sci. 2006, 295, 374. (15) Chari, K.; Antalek, B.; Lin, M. Y.; Sinha, S. K. J. Chem. Phys. 1994, 100, 5294. (16) Goddard, E. D.; Hannan, R. B. J. Colloid Interface Sci. 1976, 55, 73. (17) Purcell, I. P.; Lu, J. R.; Thomas, R. K.; Howe, A. M.; Penfold, J. Langmuir 1998, 14, 1637. (18) Vieira, J. B.; Thomas, R. K.; Li, Z. X.; Penfold, J. Langmuir 2005, 21, 4441. (19) Jones, M. N. J. Colloid Interface Sci. 1967, 23, 36. (20) Goddard, E. D. Colloids Surf. 1986, 19, 255. (21) Goddard, E. D. J. Colloid Interface Sci. 2002, 256, 228. (22) Yan, P.; Chen, L.; Wang, C.; Xiao, J.-X.; Zhu, B.-Y.; Zhao, G.-X. Colloids Surf., A 2005, 259, 55.

10.1021/la0632171 CCC: $37.00 © 2007 American Chemical Society Published on Web 02/15/2007

Adsorption Dynamics of a Polymer-Surfactant Mixture

Langmuir, Vol. 23, No. 6, 2007 3243

Scheme 1. Chemical Structures of Poly(dmdaac) and SDS

is illustrated by the work of Staples et al.23-25 on mixtures of the cationic polymer poly(dimethyldiallylammonium chloride) [poly(dmdaac)] and the anionic surfactant sodium dodecyl sulfate (SDS), the chemical structures of which are shown in Scheme 1. Figure 1A shows the equilibrium surface tension, γe, of pure SDS solutions and two series of poly(dmdaac)-SDS mixtures as a function of the bulk SDS concentration, cSDS, in 0.1 M NaCl from the measurements of Staples et al.25 The remarkable feature of these plots is the “cliff edge” at which the surface tension suddenly rises with increasing cSDS. To investigate the reasons for this behavior, Staples et al.23-25 used neutron reflection to measure the adsorption of SDS and polymer. Figure 1B shows the concentration dependence of the equilibrium surface excess, Γe, of SDS and of the polymer in terms of the number of moles per unit area of the dmdaac monomer units for one polymer concentration close to that employed in our present study. The adsorbed amounts show no significant change at the concentration of the cliff edge in the surface tension: the unusual tensiometry must therefore arise from interactions in the bulk, which lower the bulk chemical potentials, and not from desorption of the surfactant or polymer from the surface. Thomas and co-workers have used this powerful combination of tensiometry and neutron reflection to study the equilibrium surface properties of a number of oppositely charged polymer-surfactant mixtures.23-30 The interaction between poly(ethyleneimine) and SDS was shown to be complex with high dependence on the solution pH, polymer molecular weight, and polymer architecture (linear or branched).29 While equilibrium studies of aqueous polymer-surfactant mixtures help us to understand the nature of the interactions occurring in the bulk and at the surface, they provide an incomplete understanding of the behavior of polymer-surfactant mixtures in practical applications, which frequently operate under conditions that are far from equilibrium.31 The dynamic interfacial properties depend on mass transport to the surface and on the kinetics of adsorption and of breakdown of bulk aggregates, in addition to thermodynamic properties. There have been only (23) Staples, E.; Tucker, I.; Penfold, J.; Warren, N.; Thomas, R. K. J. Phys.: Condens. Matter 2000, 12, 6023. (24) Staples, E.; Tucker, I.; Penfold, J.; Warren, N.; Thomas, R. K. Langmuir 2002, 18, 5139. (25) Staples, E.; Tucker, I.; Penfold, J.; Warren, N.; Thomas, R. K. Langmuir 2002, 18, 5147. (26) Taylor, D. J. F.; Thomas, R. K.; Penfold, J. Langmuir 2002, 18, 4748. (27) Penfold, J.; Taylor, D. J. F.; Thomas, R. K.; Tucker, I.; Thompson, L. J. Langmuir 2003, 19, 7740. (28) Taylor, D. J. F.; Thomas, R. K.; Li, P. X.; Penfold, J. Langmuir 2003, 19, 3712. (29) Penfold, J.; Tucker, I.; Thomas, R. K.; Zhang, J. Langmuir 2005, 21, 10061. (30) Zhang, J.; Thomas, R. K.; Penfold, J. Soft Matter 2005, 1, 310. (31) Edwards, D. A.; Brenner, H.; Wasan, D. T. Interface Transport Processes and Rheology; Butterworth-Heinemann: Boston, MA, 1991.

Figure 1. (A) Equilibrium surface tension, γe, as a function of SDS concentration, cSDS, for (9) no polymer and (4) 0.02 and (O) 0.08 g dm-3 poly(dmdaac). Measurements were carried out on a Kruss K10T maximum pull digital tensiometer with a du Nou¨y ring. (B) Equilibrium surface excess, Γe, of (b) SDS and (2) polymer (in terms of moles of dmdaac monomers per unit area) plotted as a function of cSDS for 0.08 g dm-3 poly(dmdaac). Measurements were carried out on the SURF reflectometer at the ISIS pulsed neutron source at the Rutherford Appleton Laboratory in the U.K. All solutions were in 0.1 M NaCl. All data were extracted from the work of Staples et al.25 The dotted and dashed lines mark the values of cSDS at which there is a sharp rise in γe for the 0.02 and 0.08 g dm-3 poly(dmdaac) solutions, respectively. The arrow marks the cmc for pure SDS solutions in 0.1 M NaCl.

intermittent studies of the dynamic surface tension of polymersurfactant mixtures, e.g., with the oscillating drop technique,32,33 with the maximum bubble pressure (MBP) method,34,35 with the combination of MBP and photographic observations of drop impact,36,37 or with an interfacial stress rheometer.38 In recent years, we have extensively employed a device known as an overflowing cylinder (OFC) to study the dynamic interfacial properties of both pure and mixed surfactant systems.39-48 In (32) Noskov, B. A.; Loglio, G.; Miller, R. J. Phys. Chem. B 2004, 108, 18615. (33) Ritacco, H.; Cagna, A.; Langevin, D. Colloids Surf., A 2006, 282-283, 203. (34) Ritacco, H.; Kurlat, D.; Langevin, D. J. Phys. Chem. B 2003, 107, 9146. (35) Marsella, J. A.; Mammarella, C. J.; Meier, I. K. Colloids Surf., A 2004, 234, 63. (36) Crooks, R.; Cooper-White, J.; Boger, D. V. Chem. Eng. Sci. 2001, 56, 5575. (37) Cooper-White, J. J.; Crooks, R. C.; Chockalingam, K.; Boger, D. V. Ind. Eng. Chem. Res. 2002, 41, 6443. (38) Monteux, C.; Fuller, G. G.; Bergeron, V. J. Phys. Chem. B 2004, 108, 16473. (39) Manning-Benson, S.; Bain, C. D.; Darton, R. C. J. Colloid Interface Sci. 1997, 189, 109. (40) Manning-Benson, S.; Bain, C. D.; Darton, R. C.; Sharpe, D.; Eastoe, J.; Reynolds, P. Langmuir 1997, 13, 5808. (41) Manning-Benson, S.; Parker, S. R. W.; Bain, C. D.; Penfold, J. Langmuir 1998, 14, 990.

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this study, we use the OFC to explore the dynamic interfacial composition of a strongly interacting polymer-surfactant system for the first time. The poly(dmdaac)-SDS system is interesting to study, both because polycation-SDS mixtures are used in conditioning shampoos,49 where dynamic properties are important, and because there is already an extensive body of work on the equilibrium surface properties from the work of Staples et al.23-25 This system has recently been modeled theoretically by Bell et al.50 As a prelude to a description of the dynamic interfacial properties of poly(dmdaac)-SDS solutions, we summarize the conclusions from the equilibrium data shown in Figure 1. The surface tension isotherm for pure SDS in 0.1 M NaCl (Figure 1A) adopts the characteristic shape for simple surfactant systems: γe decreases with increasing cSDS until the critical micelle concentration, cmc, is reached at cSDS ) 1.3 mM. In a separate neutron reflection study, Purcell et al. showed that the surface excess of SDS, ΓSDS, increases smoothly with increasing cSDS and reaches a plateau with ΓSDS ) 4.0 × 10-6 mol m-2 at the cmc.51,52 Figure 1A also shows surface tension isotherms of poly(dmdaac)-SDS mixtures for fixed polymer concentrations of 0.02 and 0.08 g dm-3. The isotherms have three distinct regions. (1) At cSDS ) 0, the surface tension is close to that of pure water, showing that pure polymer does not adsorb. As cSDS increases, γe decreases at much lower surfactant concentrations than for SDS on its own, as positively charged polymer-surfactant complexes adsorb to the interface. (2) There is a sharp increase in γe (marked with a dotted line for the 0.02 g dm-3 data and a dashed line for the 0.08 g dm-3 data) at a concentration of SDS close to the point where the cationic polymer is neutralized by the anionic surfactant. (3) As cSDS increases further, γe decreases toward the limiting value for a pure SDS monolayer. Figure 1B shows the surface excess of polymer and surfactant for a polymer concentration of 0.08 g dm-3. ΓSDS was measured directly from neutron reflection measurements on deuterated SDS, while Γdmdaac was inferred indirectly from the density profile of D2O. Γdmdaac decreases monotonically with increasing cSDS, while ΓSDS is almost independent of the bulk SDS concentration. The surface excess values show clearly that the pronounced change in γe at the equivalence point is not accompanied by a marked change in the extent of adsorption at the interface (ΓSDS does not deviate from the range (3.4-3.8) × 10-6 mol m-2). Staples et al. noted that the solutions around the neutralization points were opaque, indicating the formation of aggregates with a size at least comparable to the wavelength of light. Dynamic interfacial behavior can be studied either in the time domain, in which one studies the relaxation of a freshly created surface, or in a steady-state system in the presence of convection. (42) Bain, C. D.; Manning-Benson, S.; Darton, R. C. J. Colloid Interface Sci. 2000, 229, 247. (43) Battal, T.; Shearman, G. C.; Valkovska, D.; Bain, C. D.; Darton, R. C.; Eastoe, J. Langmuir 2003, 19, 1244. (44) Valkovska, D.; Wilkinson, K. M.; Campbell, R. A.; Bain, C. D.; Wat, R.; Eastoe, J. Langmuir 2003, 19, 5960. (45) Campbell, R. A.; Bain, C. D. Vib. Spectrosc. 2004, 35, 205. (46) Campbell, R. A.; Parker, S. R. W.; Day, J. P. R.; Bain, C. D. Langmuir 2004, 20, 8740. (47) Sekine, M.; Campbell, R. A.; Valkovska, D. S.; Day, J. P. R.; Curwen, T. D.; Martin, L. J.; Holt, S. A.; Eastoe, J.; Bain, C. D. Phys. Chem. Chem. Phys. 2004, 6, 5061. (48) Campbell, R. A.; Day, J. P. R.; Bain, C. D. Appl. Spectrosc. 2005, 59, 993. (49) Goddard, E. D. Cosmet. Sci. Technol. Ser. 1999, 22, 181. (50) Bell, C. G.; Breward, C. J. W.; Howell, P. D.; Penfold, J.; Thomas, R. K. Langmuir, submitted. (51) Dahanayake, M.; Cohen, A. W.; Rosen, M. J. J. Phys. Chem. 1986, 90, 2413. (52) Purcell, I. P.; Thomas, R. K.; Penfold, J.; Howe, A. M. Colloids Surf., A 1995, 94, 125.

Campbell et al.

The advantage of the latter approach is that the analytical techniques do not require fast time resolution. The OFC is a platform that creates a continuously expanding, steady-state liquid interface.39-41,53-58 Liquid is forced up the inner cylinder from a gravity-driven feed, spills over the rim, and collects in the outer cylinder for recirculation. The flow profile at the surface of the OFC is radial away from a stagnation point at the center of the cylinder. The presence of surfactants can result in surfacetension-driven flows (Marangoni effects59,60) that accelerate the surface motion, so it is necessary to measure experimentally the surface expansion rate, θ, which lies in the range of 0.5 s-1 for pure water to 7 s-1 for some surfactant solutions.42 The equivalent surface age, τ, in a time-domain experiment is given approximately by τ ) (2θ)-1. Thus, the OFC probes time scales on the order of 0.1-1 s. The OFC provides a large, flat liquid surface that can be studied by a wide range of surface analytical techniques, including ellipsometry,39 light scattering,40 neutron reflection,41 and infrared spectroscopy.46 To determine the dynamic surface composition for poly(dmdaac)-SDS mixtures, we have employed a combination of external reflection Fourier transform infrared spectroscopy (ER-FTIRS) and ellipsometry. ER-FTIRS was used to quantify the amount of adsorbed SDS, as the spectra are insensitive to the weak polymer peaks (vide infra). ER-FTIRS yields precision similar to that of neutron reflection and can be carried out in our own laboratory without consumption of precious beam time at national facilities.45-48 It has a secondary advantage that it does not require deuterated surfactants. Ellipsometry is sensitive to the total adsorbed amount of surfactant and polymer. The ellipsometric response to adsorbed poly(dmdaac) and SDS is additive to a first approximation; knowing ΓSDS from ERFTIRS allows us to determine the surface excess of adsorbed dmdaac monomer units, Γdmdaac. The precision of ellipsometry is 99% of the variation in the data set, were retained. Principal component analysis results in the production of orthogonal spectra and the weighting of each component in the spectral data set. These principal components are linear combinations of the actual species contributing to the spectra. “Target spectra” are required to rotate the abstract components into “refined spectra” of the actual species and to determine the corresponding real weighting profiles. Two target spectra were used to fit the variations in the spectra: a spectrum of pure water after a linear baseline subtraction (to account for baseline curvature from the aqueous subphase) and a spectrum of pure 1.01 mM SDS from which the water background had been manually subtracted as described above (to account for the surface peaks). The component weights, which are dimensionless, were scaled relative to a fixed value of 0.692 for 1.01 mM SDS, so that a saturated SDS monolayer had a value of unity. The scaling factor was calculated from the weight of the 1.01 mM SDS spectrum relative to the average weight of the data points at limiting surface coverage. Refractometry. Refractive index measurements of poly(dmdaac) solutions were made as a function of polymer concentration using a Bellingham and Stanley 60/LR Abbe´ refractometer. For dilute solutions, the variation in the refractive index, n, with concentration, c, for a polymer can be approximated by

3246 Langmuir, Vol. 23, No. 6, 2007 n ) n0 +

Campbell et al.

dn dc

(4)

where n0 ) 1.333 is the refractive index of water for light of λ ) 632.8 nm at 298 K. For nonabsorbing media, r ) n2, so eqs 3 and 4 may be combined to give η)

(

)

r,1 - r,3 dn 2n0 cd + ηr r,3 dc

(5)

where η is the ellipsometric thickness of the adsorbed layer and terms of higher order in dn/dc have been ignored since dn/dc is small. The surface excess is given by Γ ) cd, so eqs 1 and 5 may be combined to give λr,3Fjpoly

Γ)

2π(r,1 + r,3)1/2n0

dn dc

(6)

where Fjpoly is the contribution to the coefficient of ellipticity from the adsorbed polymer. For mixed poly(dmdaac)-SDS monolayers, we approximate Fjpoly(dmdaac) ) Fj - (FjSDS + Fj0), where we assume that the contributions of polymer and surfactant to the coefficient of ellipticity are additive, and we neglect the small variation in the roughness contribution with changing surfactant concentration (the dynamic surface tension is, in any case, unknown). Laser Doppler Velocimetry. Measurements of surface flow velocity, and hence of the surface expansion rate, were carried out by laser Doppler velocimetry. A 10 mW HeNe laser beam was split into two equal parts, which were refocused on the liquid surface of the OFC to generate interference fringes perpendicular to r at the intersection of the two beams. TiO2 particles (2 µm diameter), suspended in the liquid in the OFC, scatter light as they pass through the interference fringes. The concentration of particles is adjusted so that the passage of individual particles through the fringes may be observed. The scattered light is detected using a photomultiplier tube, filtered to remove high- and low-frequency noise, and collected on a digital storage scope (LeCroy 9350A). A Fourier transform of the signal yields the modulation frequency of the scattered laser light. The FT was averaged over 300 particles and the peak, f, in the frequency distribution recorded. The frequency, f, is related to the velocity of the particle perpendicular to the fringes, Vr, by f)

2νr sin χ λ

(7)

where χ is the half-angle between the two laser beams (31.5°). Values of Vr were measured as a function of r and fitted to the functional form νr ) a1r + a3r3

(8)

where a1 and a3 are fitting constants. The surface expansion rate at the center of the cylinder is given by θ)

1 d(rνr) ) 2a1 r dr

(9)

Measurements of Vr were taken on both sides of the center of the cylinder and averaged. Further details may be found in ref 42. Materials. UHP water (Millipore) was used throughout the experiments. Glassware and the OFC were cleaned in alkaline detergent (Decon 90) and rinsed thoroughly with UHP water. SDS (Sigma, 99+%) was purified by recrystallization three times from ethanol. Poly(dmdaac) (100K-200K molecular weight, Aldrich, 20% by weight in water) was purified by dialysis (regenerated cellulose, 12K-14K molecular weight cutoff, Medicell International Ltd.) in UHP water to remove low molecular weight species. The water bath in which the dialysis tubes were immersed was emptied, rinsed, and refilled twice daily for 3 days. All the solutions were made in the presence of 0.1 M NaCl (BDH, 99.9%).

Figure 2. Dynamic coefficient of ellipticity, Fjdyn, plotted as a function of cSDS for (9) no polymer and (O) 0.05, (b) 0.10, (4) 0.15, and (2) 0.20 g dm-3 poly(dmdaac) in 0.1 M NaCl. The solid line marks the value Fj ) 0.38 × 10-3 for pure water, and the dashed line marks the value Fj ) -0.73 × 10-3 for a full SDS monolayer in the absence of polymer. The vertical markers indicate the bulk SDS concentrations at which the charges on the cationic polymer are neutralized by those on the anionic surfactant molecules for (a) 0.05, (b) 0.10, (c) 0.15, and (d) 0.20 g dm-3 poly(dmdaac).

Results Ellipsometry. Figure 2 shows measurements of Fjdyn for pure SDS solutions and four series of mixed poly(dmdaac)-SDS solutions recorded at constant bulk poly(dmdaac) concentration in 0.1 M NaCl plotted with respect to the bulk SDS concentration, cSDS. A solid line shows the value Fj0 ) 0.38 × 10-3 for pure water. Independent ellipsometric measurements of pure poly(dmdaac) solutions showed that there was no measurable adsorption on the OFC in concentrations up to 0.5 g dm-3 (higher than in the mixed poly(dmdaac)-SDS solutions studied in this work). Surface tension and neutron reflectivity measurements of poly(dmdaac) solutions carried out by Staples et al. showed that the pure polymer is also not surface active under equilibrium conditions.25 At low concentrations of the pure surfactant (cSDS < 0.06 mM), the values of Fjdyn are close to that of pure water, which shows that there is negligible adsorption from these solutions on the time scale of the OFC. As cSDS increases, so does the adsorption of SDS molecules, and the values of Fjdyn decrease smoothly toward a minimum value, Fjdyn ) -0.73 × 10-3 (marked with a dashed line), which is reached at cSDS ) 1.8 mM when the air-water interface is saturated with SDS molecules. This concentration is higher than in the equilibrium case, where surface saturation occurs at the cmc, which is 1.3 mM for SDS in 0.1 M NaCl (Figure 1A).63 Under steady-state conditions in the OFC, the rate of loss of surfactant from the surface by dilation, θΓdyn (where Γdyn is the dynamic surface excess), is balanced by the diffusion of molecules to the surface from the bulk. Solution of the convective-diffusion equation yields the relationship42,64

θ)

2D(c - cS)2 πΓdyn2

(10)

where cS is the subsurface concentration and D is the diffusion coefficient of the adsorbate. Consequently, cS < c, and for the case of diffusion-controlled adsorption, the limiting surface coverage is not reached until cS ) ccmc. (63) Persson, C. M.; Jonsson, A. P.; Bergstro¨m, M.; Eriksson, J. C. J. Colloid Interface Sci. 2003, 267, 151. (64) Breward, C. J. W.; Howell, P. D. Eur. J. Appl. Math. 2004, 15, 511.

Adsorption Dynamics of a Polymer-Surfactant Mixture

For all four series of poly(dmdaac)-SDS mixtures, measurable adsorption takes place at low cSDS, at concentrations where neither polymer nor surfactant adsorbs to the interface in the absence of the other component. There were pronounced fluctuations in the ellipsometric readings for these solutions (cSDS < 0.15 mM): large negative excursions from base values were observed on a time scale of 1-2 s. This observation indicates that the surface is heterogeneous on the length scale of the laser spot (∼1 mm). A possible origin of the inhomogeneity is the arrival of large polymer-surfactant aggregates at a sparsely covered surface, which then adsorb and are torn apart by the resulting surface tension gradients. Such “popping” of aggregates is readily observed with very fine suspensions of insoluble surfactants (e.g., linear alcohols) in water. The repeatability of ellipsometry measurements at low cSDS was also poor, which prevents us from drawing quantitative conclusions on the surface composition at very low SDS concentrations. To allow a comparison of ellipsometric data with peak areas from ER-FTIRS, which is a technique that has neither the temporal nor spatial resolution to detect these fluctuations, we averaged the measurements of Fjdyn over several minutes. The values of Fjdyn decrease with increasing cSDS until either a minimum or a plateau is reached. With further addition of SDS, Fjdyn increases to a sharp maximum with a value close to, but slightly less than, that of pure water. Since both surfactant and polymer make a negative contribution to Fj, we infer that almost all the surfactant and polymer desorb from the surface. The minimum in the adsorbed amount occurs at a value of cSDS close to the equivalence point for each series of solutions, where the negative charges on the SDS molecules neutralize the positive charges on the polymers. Four short vertical lines in Figure 2 mark the values of cSDS of these equivalence points. Last, with continued increasing cSDS, the ellipsometric values decrease toward the minimum Fjdyn ) -0.73 × 10-3, which is consistent with the formation of a saturated SDS monolayer at the interface. A notable feature of oppositely charged polymer-surfactant solutions, which has been commented on previously for poly(dmdaac)-SDS by Staples et al.,25 is the formation of insoluble aggregates in regions of the phase diagram. We observed two different types of aggregates: (i) small aggregates, invisible to the naked eye, that give rise to completely polarized scattering of a laser beam and that do not settle out under gravity; (ii) large, visible aggregates that give depolarized scattering and settle out under gravity. For 0.1 g dm-3 polymer solutions with increasing cSDS, scattering by small aggregates in a laser beam was first observed at cSDS ) 0.12 mM (ln cSDS ) -9.0), just before the minimum in Fjdyn was reached. The solutions then became progressively more opaque until large aggregates began to precipitate. The balance between large and small aggregates was very sensitive to the solution composition. Near the equivalence point, however, the solutions were clear (nonscattering) if the large aggregates were allowed to settle out. At higher concentration (cSDS ≈ 2 mM), the opacity returned, which indicated the presence once more of small aggregates in the solutions. Fourier Transform Infrared Spectroscopy. With the aid of TFA, ER-FTIR spectroscopy can be used to determine the composition of adsorbed layers in aqueous binary surfactant systems.65 We set out with the intention of determining the surface excess of both surfactant and polymer in mixed poly(dmdaac) films by infrared spectroscopy. To assess the relative contributions that poly(dmdaac) and SDS would make to ER-FTIR spectra, we first recorded ATR-FTIR spectra of pure solutions of poly(65) Day, J. P. R.; Campbell, R. A.; Russell, O. P.; Bain, C. D. J. Phys. Chem. C, in press.

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Figure 3. ATR-FTIR spectra of absorbance, A, with respect to the wavenumber, ν˜ , of 20% by weight: (a) SDS and (b) poly(dmdaac).

(dmdaac) and SDS both at concentrations of 20% by weight in pure water (Figure 3). The polymer spectrum is much weaker: the integrated area under the C-H stretching bands is only 23% of that from the SDS peaks. On a molar basis, the difference in signal strength is even more marked, since the molecular weight of SDS is nearly twice that of the dmdaac monomer. As a result the signal from a dmdaac unit is only 13% of the magnitude of the signal from an SDS molecule. This large difference in sensitivity portends badly for the planned purpose. Attempts to analyze the ER-FTIR spectra with three significant componentss water, SDS, and poly(dmdaac)swere unsuccessful. Consequently, we retained only two principal components, yielding only the adsorbed amount of SDS. While ellipsometry provides an alternative route to the adsorbed amount of polymer, we have to estimate the consequences of neglecting the polymer signal in the ER-FTIR spectra on the component weight of SDS. To obtain such an estimate, we assume as an initial approximation that the polymer and SDS signals have similar shapes in the baseline-subtracted ATR-FTIR and ER-FTIR spectra, which is certainly valid for SDS. We then treat the baseline-subtracted ATR-FTIR spectra as vectors and evaluate the ratio of the scalar products (SDS‚polymer)/(SDS‚ SDS), where both spectra are scaled to the same monomer concentration. This step extracts the component of the polymer spectrum that would be along the SDS “axis” in principal component analysis (PCA) of ATR-FTIR spectra: the remainder of the poly(dmdaac) spectrum is orthogonal to the SDS component and would appear in other components after PCA. The value of this ratio is 0.09, which means that for ER-FTIRS 1 mol of adsorbed dmdaac (in terms of monomers) will be interpreted after TFA as 0.09 mol of adsorbed SDS. The presence of adsorbed polymer will therefore lead to an overestimation of the amount of adsorbed SDS. Subsequently, we present the data from the TFA without correcting for the neglect of polymer but discuss in the text the effect of this correction on the composition of the monolayers. Figure 4 shows a selection of subtracted monolayer spectra obtained by ER-FTIRS from the OFC for a range of bulk SDS concentrations: (A) pure SDS, (B) 0.1 g dm-3 poly(dmdaac), and (C) 0.2 g dm-3 poly(dmdaac). The pure SDS spectra are qualitatively similar with changing cSDS, and the antisymmetric CH2 peak is centered at 2925 cm-1, which indicates that the SDS monolayer is disordered. There is no evidence for changing structure with changing packing density. For both series of polymer-surfactant mixtures, the largest peaks are those recorded at the highest concentrations, where the coefficient of ellipticity has a constant value of -0.73 × 10-3. The antisymmetric CH2

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Figure 6. Values of Fjdyn plotted as a function of the component weights, determined by ER-FTIRS for SDS solutions in 0.1 M NaCl. The solid line is a cubic fit to the data.

Figure 4. Subtracted ER-FTIR spectra from SDS solutions with (A) 0, (B) 0.10, and (C) 0.20 g dm-3 poly(dmdaac) in 0.1 M NaCl. For each series of spectra, five examples are shown with cSDS increasing in the direction of the arrow for (A) 0.16, 0.47, 0.90, 1.4, and 3.0 mM SDS, (B) 0.13, 0.43, 0.91, 1.5, and 2.7 mM SDS, and (C) 0.13, 0.47, 1.7, 2.0, and 2.7 mM SDS.

Figure 5. Component weights as a function of cSDS for (9) 0, (O) 0.10, and (4) 0.20 g dm-3 poly(dmdaac) in 0.1 M NaCl. The dashed line indicates a saturated SDS monolayer. The two arrows indicate the bulk SDS concentrations at which the charges on the cationic polymer are neutralized by those on the anionic surfactant molecules: (left) 0.10 and (right) 0.20 g dm-3 poly(dmdaac). The component weights were scaled to a value of unity for a saturated monolayer of SDS at the air-water interface.

peak occurs at 2925 cm-1 at higher SDS concentrations, but at a slightly higher wavenumber (2929 cm-1) in spectra at low cSDS (Figure 4B,C). This apparent peak shift arises from the contribution of the poly(dmdaac) to the surface monolayer at low cSDS (see Figure 3). An increase in the conformational order in mixed monolayers can be ruled out since ordered alkyl chains have lower, not higher, vibrational frequencies. Three sets of spectra with fixed polymer concentration and varying SDS concentration, each containing more than 20 individual spectra, were analyzed by TFA: 0, 0.1, and 0.2 g dm-3 poly(dmdaac). Figure 5 shows the component weights for the SDS contribution to the adsorbed film. The weights are scaled to a value of unity for a saturated monolayer of SDS. For pure SDS solutions, the component weights increase smoothly from zero to limiting surface coverage. The mixed poly(dmdaac)-

SDS solutions show an increase in SDS coverage with increasing cSDS and then a decrease to a minimum value around the equivalence point (marked with arrows) before an increase to limiting surface coverage. In addition, the 0.2 g dm-3 poly(dmdaac) solutions have a plateau in the component weight between ln cSDS ) -9 and ln cSDS ) -7, mirroring a similar plateau in the ellipsometry data. We cannot assume a priori that the component weight obtained from analysis of ER-FTIR spectra is linearly related to the surface excess of the surfactant; either a change in orientation or a change in density with coverage can lead to deviations from linearity.46 However, previous experimental studies by ER-FTIRS on singlechain surfactants showed excellent linear relationships between Γdyn and component weight for the nonionic surfactant C10E8 (octaethylene glycol monodecyl ether) and the anionic surfactant APFN (ammonium perfluorononanoate).48 For the cationic surfactant CTAB (hexadecyltrimethylammonium bromide) there was a slight curvature, but the assumption of linearity would lead to a maximum error in the surface excess of 10% of a monolayer.46 There is no evidence for marked structural changes in the SDS monolayer with changing coverage (Figure 4), so we assumed a linear relationship to convert the values of the component weight into ΓSDS. The surface excess of SDS was scaled to the literature value of Γ ) 4.0 × 10-6 mol m-2 at monolayer coverage.51,52 To determine the amount of adsorbed polymer, we turn back to the measurements of Fjdyn by ellipsometry. We assume to a first approximation that the contributions of adsorbed poly(dmdaac) and SDS to Fjdyn are additive: Fjdyn ) FjSDS + Fjdmdaac. Figure 6 shows the relationship between FjSDS and the component weight of SDS for pure SDS solutions. While this relationship is nearly linear, a cubic fit was used to account for the slight curvature (a linear approximation would lead to errors of up to 6% of a monolayer of SDS). The cubic function is then used to determine the contribution of SDS to Fjdyn in the poly(dmdaac)SDS mixtures from the component weights of SDS in Figure 5. (This method also accounts for surface roughness, as long as it does not vary greatly with concentration.) Fjdmdaac is then found by subtraction of FjSDS from Fjdyn. There are many more ellipsometry measurements than ERFTIRS measurements, so we needed to interpolate between ERFTIRS data points. We fitted a series of polynomials piecewise to successive regions of the ER-FTIRS data sets (O and ] in Figure 5). The 0.2 g dm-3 data set varies very rapidly around cSDS ) 1 mM (ln cSDS ) -6.9), but lacks a data point exactly at the equivalence point. To interpolate this region, we introduced

Adsorption Dynamics of a Polymer-Surfactant Mixture

Figure 7. Measured values of Fjdyn ([) divided into contributions from SDS (solid line), including the surface roughness, and poly(dmdaac) (dashed line) for 0.10 g dm-3 poly(dmdaac) in 0.1 M NaCl. The SDS contribution was calculated from the component weight of adsorbed SDS (O in Figure 5 from ER-FTIRS) using the calibration plot in Figure 6. The polymer contribution was calculated from the difference between the SDS contribution and the measured values.

Figure 8. Measured values of Fjdyn ([) divided into contributions from SDS (solid line), including the surface roughness, and poly(dmdaac) (dashed line) for 0.20 g dm-3 poly(dmdaac) in 0.1 M NaCl. See the Figure 7 caption for further details.

a floating data point at cSDS ) 1.11 mM into the polynomial fit to prevent the surface excess of the polymer from adopting an unphysically negative value. Behavior in the neighborhood of the equivalence point will be discussed later. Figures 7 and 8 show the measured values of Fjdyn from ellipsometry (filled tilted squares), the calculated contribution of SDS from ER-FTIRS (solid line), and the calculated contribution of poly(dmdaac) from the difference (dashed line) for the 0.1 and 0.2 g dm-3 series of solutions, respectively. In both cases, only SDS adsorbs to the interface at values of cSDS above the equivalence point. We obtain Γdmdaac from Fjdmdaac with eq 6 using the value dn/dc ) 1.66 × 10-7 m3 g-1 measured by refractometry. Figures 9 and 10 show the variation of both Γdmdaac and ΓSDS with changing cSDS for the 0.1 and 0.2 g dm-3 poly(dmdaac) solutions, respectively. The equivalence point of each series is marked with an arrow. We note that, for cSDS above the equivalence point, no polymer is adsorbed to the dynamic airwater interface. A simple model to explain this observation is that all the polymer is sequestered as approximately neutral aggregates that are not adsorbed at the air-water interface under dynamic conditions (e.g., due to precipitation or low diffusion coefficients). Any overcompensation of the charge would lead

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Figure 9. Relative contributions to Γdyn plotted as a function of cSDS for 0.10 g dm-3 poly(dmdaac) in 0.1 M NaCl: (9) SDS calculated from the component weight; (]) poly(dmdaac) calculated from Fjdyn. Γdyn for the polymer is expressed in terms of dmdaac monomer units. The horizontal dashed line indicates the limiting value of Γdyn ) 4.0 × 10-6 mol m-2 for a saturated monolayer of pure SDS. The curved dashed line above the equivalence point indicates the dynamic surface excess of SDS that would result if every monomeric unit of dmdaac in the system were to sequester one SDS molecule.

Figure 10. Relative contributions to Γdyn plotted as a function of cSDS for 0.20 g dm-3 poly(dmdaac) in 0.1 M NaCl resulting from (9) SDS calculated from values of the component weight and (]) poly(dmdaac) calculated from values of Fjdyn. Γdyn for the polymer is expressed in terms of dmdaac monomer units. The dashed lines are explained in the caption for Figure 9.

to negatively charged aggregates that would be repelled electrostatically from the surface. The properties of the mixed solution would then be those of a pure surfactant solution containing only the SDS in excess of that required to neutralize the polymer. The dashed lines show the predicted surface excess if excess SDS molecules only were present in solution. The prediction lies very close to, but slightly below, the measured surface excess, which suggests that the extent of surfactant overcharging in the aggregates is not large. An interesting question is how the ratio of adsorbed dmdaac to SDS varies with the bulk SDS composition. Figures 11 and 12 show the variation of Γdmdaac/ΓSDS with changing cSDS for the 0.1 and 0.2 g dm-3 poly(dmdaac) solutions, respectively. One might naively expect the surface to become progressively richer in SDS as the bulk concentration of SDS increases, but the behavior is more complex than this. We find that, for a 5-fold change in concentration of SDS below the equivalence point, the surface composition is essentially independent both of the concentration of the surfactant and of the polymer: the ratio of dmdaac units to SDS molecules lies in the range of 2.5-3. We

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Figure 11. Ratio of the dynamic surface excesses of poly(dmdaac) to SDS as a function of cSDS for 0.10 g dm-3 poly(dmdaac) in 0.1 M NaCl. Γdmdaac is expressed in terms of monomer units.

Figure 12. Ratio of the dynamic surface excesses of poly(dmdaac) to SDS as a function of cSDS for 0.20 g dm-3 poly(dmdaac) in 0.1 M NaCl. Γdmdaac is expressed in terms of monomer units. The trend in composition is shown as a dashed line at low concentrations due to uncertainties introduced by fluctuations in the readings (see the text).

have shown that the neglect of contribution of the polymer to the ER-FTIR spectra results in an overestimation of the amount of adsorbed SDS: correcting for this overestimation gives a ratio of 3-4 dmdaac units per SDS molecule in the monolayer. As the bulk composition approaches the equivalence point, both surfactant and polymer desorb from the surface; above the equivalence point only SDS adsorbs. Laser Doppler Velocimetry. For quantitative modeling of dynamic adsorption data, the surface expansion rate, θ, needs to be known. The variation of θ with concentration also gives insights into the dynamic adsorption behavior. Figure 13 shows values of θ, measured by laser Doppler velocimetry, for SDS solutions with and without 0.1 g dm-3 poly(dmdaac). For the pure SDS solutions, the shape is a typical volcano plot for monomeric surfactants under diffusion control.66 Maximum Marangoni effects occur at intermediate concentrations where the surface can support surface tension gradients: at low concentrations adsorption is too slow to give an appreciable surface pressure; at high concentrations adsorption is too fast and the surface is everywhere saturated with surfactant. For the poly(dmdaac)-SDS solutions, the measured values of θ are the same as for pure water (surface age, τ ) (2θ)-1 ) 1 s) over most of the solution compositions (66) Valkovska, D. S.; Shearman, G. C.; Bain, C. D.; Darton, R. C.; Eastoe, J. Langmuir 2004, 20, 4436.

Campbell et al.

Figure 13. Surface expansion rate, θ, plotted as a function of cSDS for (9) 0 and (]) 0.10 g dm-3 poly(dmdaac) in 0.1 M NaCl. Values of θ were determined using laser Doppler velocimetry. The equivalence point of the mixed poly(dmdaac)-SDS solutions is marked with an arrow.

where poly(dmdaac)-SDS complexes adsorb, i.e., cSDS < 0.6 mM. We infer that these polymer-surfactant complexes do not generate surface tension gradients that might sustain Marangoni flows. Above the equivalence point adsorption is dominated by free SDS in solution, which is at a concentration lower than the total bulk concentration. It follows that the maximum in θ occurs at higher cSDS for the mixtures than for pure SDS solutions. The increase in θ in the mixed polymer-surfactant solutions begins at concentrations below the equivalence point, suggesting that not all the SDS is associated with polymer chains at that point. If we hypothesize that free SDS alone is responsible for the surface tension gradients that lead to Marangoni flow, then we infer a free SDS concentration at the equivalence point of 0.09 mM by comparison with the expansion rate curve for SDS in the absence of polymer. From Figure 5, this free SDS concentration would lead to a dynamic adsorption of 5-10% of a monolayer of SDS. The coefficient of ellipticity at the equivalence point, for all four concentrations of polymer, does not quite return to the value for pure water, implying that there is still adsorbed material at this pointsan amount corresponding to ∼10% of a monolayer of SDS. The ER-FTIRS data also show ∼10% of a monolayer of SDS at the equivalence point (O in Figure 5), though there is some scatter in the data. One interpretation is that not all the SDS is bound to the polymer, even below the charge neutralization point. This behavior contrasts with that of binary mixtures of cationic and anionic surfactants, where the free surfactant concentration in equimolar solutions is extremely low.67,68 We have to be cautious in this interpretation, however, since polymer-surfactant mixtures are notoriously slow to reach equilibrium: our measurements of the coefficient of ellipticity do drift more positive very slowly with time, which provides some evidence that the system is not fully equilibrated on the time scale of the data acquisition (