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The Interaction between Sodium Alkyl Sulfate Surfactants and the Oppositely Charged Polyelectrolyte, polyDMDAAC, at the Air-Water Interface: The Role of Alkyl Chain Length and Electrolyte and Comparison with Theoretical Predictions J. Penfold,*,† I. Tucker,‡ R. K. Thomas,§ D. J. F. Taylor,§ X. L. Zhang,§ C. Bell,| C. Breward,| and P. Howell| ISIS, Rutherford Appleton Laboratory, Chilton, Didcot, OXON, U.K., UnileVer Research and DeVelopment Laboratory, Port Sunlight, Quarry Road East, Bebington, Wirral, U.K., Physical and Theoretical Chemistry Laboratory, UniVersity of Oxford, South Parks Road, Oxford, U.K., and Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, UniVersity of Oxford, 24-29 St Giles, Oxford, U.K. ReceiVed October 13, 2006. In Final Form: December 7, 2006 The effect of alkyl chain length and electrolyte on the adsorption of sodium alkyl sulfate surfactants and the oppositely charged polyelectrolyte, polyDMDAAC, at the air-water interface has been investigated by surface tension and neutron reflectivity. The variations in the patterns of adsorption and surface tension behavior with alkyl chain length and electrolyte are discussed in the context of the competition between the formation of surface active surfactant/ polyelectrolyte complexes and polyelectrolyte/surfactant micelle complexes in solution. A theoretical approach based on the law of mass action has been used to predict the surface effects arising from the competition between the formation of polyelectrolyte/surfactant surface and solution complexes and the formation of free surfactant micelles. This relatively straightforward model is shown to reproduce the principal features of the experimental results.
Introduction Polymer-surfactant mixtures are widely exploited in a range of commonplace formulations, where the polymer is used to manipulate the solution behavior and adsorption properties.1,2 Although much of the recent experimental work has focused on the solution properties, the surface adsorption and corresponding surface tension behavior of nonionic polymer/surfactant mixtures are also well established.3,4 However, as originally observed and highlighted by Goddard and others5,6 for polyelectrolyte/ionic surfactant mixtures, when a strong surface polyelectrolyte/ surfactant interaction exists, understanding the surface tension behavior in terms of the adsorption is less than straightforward. Nevertheless, understanding the details of the surface behavior of polyelectrolyte/surfactant mixtures remains an important objective because polyelectrolytes offer an attractive route for manipulating surfactant adsorption at a variety of interfaces, which is often relatively poorly exploited. This motivation has stimulated a number of recent studies on a range of different polyelectrolyte/surfactant mixtures.7-13 From our own work we †
ISIS, Rutherford Appleton Laboratory. Unilever Research and Development Laboratory, Port Sunlight. § Physical and Theoretical Chemistry Laboratory, Oxford University. | Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford. ‡
(1) Interaction of surfactants with polymers and proteins; Goddard, E. D., Ananthapandmanbhan, K. P., Eds.; CRC Press: Boca Raton, FL, 1993. (2) Polymer-surfactant systems; Kwak, J. C. T., Ed.; Surfactant Science Series; Marcel Dekker: New York, 1998; Vol. 77. (3) Jones, M. N. Colloids Interface Sci. 1967, 73, 36. (4) Chari, K.; Hossain, T. Z. J. Phys. Chem. 1991, 95, 3367. (5) Goddard, E. D. J. Colloid Interface Sci. 2001, 256, 228. (6) Goddard, E. D. Colloids Surf. 1986, 19, 301. (7) Staples, E.; Tucker, I.; Penfold, J.; Warren, N.; Thomas, R. K.; Taylor, D. J. F. Langmuir 2002, 18, 5147. (8) Staples, E.; Tucker, I.; Penfold, J.; Warren, N.; Thomas, R. K. Langmuir 2002, 18, 5139. (9) Taylor, D. J. F.; Thomas, R. K.; Hines, J. D.; Humphreys, K.; Penfold, J. Langmuir 2002, 18, 9787. (10) Taylor, D. J. F.; Thomas, R. K.; Penfold, J. Langmuir 2002, 18, 4748.
draw attention to two different polyelectrolyte/surfactant mixtures, sodium dodecyl sulfate (SDS)/polyDMDAAC and PSS/CnTAB, which exhibit contrasting surface tension behaviors and patterns of adsorption.7-11 For the polymer/surfactant mixture of SDS/polyDMDAAC the surface tension at low SDS concentrations shows a sharp decrease with increasing surfactant concentration, which is independent of polymer concentration. Following a relatively narrow region of SDS concentration where the surface tension is low, at higher SDS concentrations the surface tension markedly increases, before it decreases to a lower constant value at the critical micelle concentration (cmc).7 At low SDS concentrations there is significantly enhanced adsorption of SDS at the interface due to the adsorption of SDS/polyDMDAAC complexes. At higher SDS concentrations, associated with the increase in surface tension, there is partial depletion of SDS and polyDMDAAC from the surface. For the polymer/surfactant mixture of PSS/ CnTAB9-11 the surface tension and adsorption behavior shows some significant differences compared to the SDS/polyDMDAAC mixture. The initial decrease in the surface tension at low surfactant concentrations is dependent upon the polymer concentration, and this is now followed by a region of relatively constant and low surface tension up to the cmc of the system. This general pattern is observed for alkyl chain lengths of C10 and C12 for the cationic surfactant, but for C14TAB and C16TAB the surface tension variation has similarities with that observed for SDS/polyDMDAAC. For the CnTAB/PSS mixtures (for C10 to C14) the neutron reflectivity measurements show that the adsorption behavior is more complex. Although at low surfactant concentrations the enhanced adsorption is a monolayer due to the adsorption of polymer/surfactant complexes, at higher (11) Taylor, D. J. F.; Thomas, R. K.; Li, P. X.; Penfold, J. Langmuir 2003, 19, 3712. (12) Monteaux, C.; Williams, C. E.; Meunier, J.; Anthony, O.; Bergeron, V. Langmuir 2004, 20, 57. (13) Stubenrauch, C.; Albony, P. A.; von Klitzing, R.; Langevin, D. Langmuir 2000, 16, 3206.
10.1021/la063016x CCC: $37.00 © 2007 American Chemical Society Published on Web 01/24/2007
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concentrations multilayer adsorption of polymer/surfactant complexes is observed. These two different patterns of behavior represent the extremes of surface tension and adsorption behavior observed in a range of polyelectrolyte/ionic surfactant mixtures. We have now been able to rationalize these two patterns of behavior qualitatively as arising from competition between the formation of surface active polymer/surfactant monomer complexes and solution polymer/surfactant micelle complexes. The SDS/polyDMDAAC behavior arises because the free energies of formation of both types of complex are relatively similar; whereas the PSS/CnTAB behavior arises because the surface complex formation is energetically more favorable. Bell et al.14 have applied the law of mass action to provide a thermodynamic description based on these assumptions. The main features of the model are the formation of polymer/surfactant monomer complexes, polymer/ surfactant micelle complexes, and free surfactant micelles, where only surfactant monomer and polymer/surfactant monomer complexes are surface active. Apart from the critical micellar concentration, cmc, and the critical aggregation concentration, cac, the model is characterized by a critical surface complex concentration and surfactant and surfactant/polymer adsorption coefficients. This provides a theoretical framework in which a range of surface tension behaviors can be predicted and understood. Although much of our current understanding of the surface behavior of polymer/surfactant mixtures arises from the recent studies on SDS/polyDMDAAC,7,8 CnTAB/PSS,9-11 and related measurements,12,13 using a combination of surface tension, neutron reflectivity, and other techniques, there are limited systematic data that can be used to rigorously confront and challenge theory. We report here a combination of surface tension data and neutron reflectivity measurements for the adsorption of polyDMDAAC/ sodium alkyl sulfate mixtures (for alkyl chain lengths C10, C12, and C14 and in the absence and presence of 0.1 M NaCl) at the air-water interface. A key element of this study is a comparison of the results with the recent theoretical developments, which are shown to encapsulate the major features of the surface tension and adsorption behavior observed.
Experimental Details The specular neutron reflectivity measurements were made on the SURF reflectometer15 at the ISIS pulsed neutron source at the Rutherford Appleton Laboratory, U.K. The measurements were made using a single detector at a fixed angle, θ, of 1.5°, for neutron wavelengths, λ, in the range 0.5-6.8 Å to provide a Q range of 0.048 to 0.5 Å-1, and using what are now wellestablished experimental procedures. The basis of a neutron reflectivity experiment is that the variation in specular reflection with Q (the wave vector transfer normal to the surface, defined as Q ) (4π/λ) sin θ where λ is the neutron wavelength and θ is the grazing angle of incidence) is simply related to the composition or density profile in a direction normal to the interface, as described in detail elsewhere.16 In the kinematic or Born approximation, it is just related to the square of the Fourier transform of the scattering length density profile, F(z)
R(Q) )
2
∫
16π | F(z)e-iQz dz|2 Q2
(1)
(14) Bell, C.; et al. In preparation. (15) Penfold, J.; et al. J. Chem. Soc., Faraday Trans. 1997, 93, 3899. (16) Thomas, R. K.; Penfold, J. J. Phys.: Condens. Matter 1990, 2, 1369.
where F(z) ) Σi ni(z)bi, ni(z) is the number density of the ith nucleus, and bi is its scattering length. The key to the use of the technique for the study of surfactant adsorption is the ability to manipulate the scattering length density at the interface using hydrogen (H)/deuterium (D) isotopic substitution (where H and D have vastly different scattering powers for neutrons). This has now been powerfully demonstrated for the study of surfactant adsorption (for the determination of adsorbed amounts and surface structure) in a wide range of surfactants, surfactant mixtures, and polymer-surfactant mixtures.16 In particular, for a deuterated surfactant in null reflecting water, nrw (92 mol % H2O-8 mol % D2O has a scattering length of zero, the same as air), the reflectivity arises only from the adsorbed layer at the interface. This reflected signal can be analyzed in terms of the adsorbed amount at the interface and the thickness of the adsorbed layer, and the most direct procedure for determining the surface concentration of surfactant is to assume that it is in the form of a single layer of homogeneous composition. The measured reflectivity can then be fitted by comparing it with a profile calculated using the optical matrix method for this simple structural model,17 to provide the two key parameters, the scattering length density, F, and the thickness, τ, of the layer. The area per molecule is then given by
A)
∑i bi/Fτ
(2)
where ∑bi is the scattering length of the adsorbed surfactant molecule. This has been shown to be an appropriate method for surfactants, surfactant mixtures, and polymer/surfactant mixtures.18 In the evaluation of the adsorbed amounts of the SDS at the interface, it is assumed that for the polymer/surfactant mixtures discussed here, the polymer has a scattering length sufficiently close to zero that its contribution is negligible (∑b values for d-C10DS, d-C12DS, and d-C14DS are 2.36 × 10-3, 2.763 × 10-3, and 3.16 × 10-3 Å, for polyDMDAAC monomer is 0.39 × 10-4 Å, and the corresponding molecular volumes are ∼337, 388, 439, and 70 Å3). The surface tension measurements were made on a Kruss K10T maximum pull digital tensiometer using the du Nouy ring method with a Pt/Ir ring. Before each measurement the ring was rinsed in UHQ water and flamed with a Bunsen burner, and repeated measurements were made until equilibrium was established The protonated surfactants, sodium decyl (dodecyl, tetradecyl) sulfate (C10, C12, C14 alkyl chain length), h-surfactant, and chain deuterated sodium decyl (dodecyl, tetradecyl) sulfate, d-surfactant, were synthesized as described elsewhere19 and purified before use by recrystallization from an ethanol/acetone mixture. The cationic polymer, polyDMDAAC, was synthesized from the monomer dimethyldiallylammonium chloride by free radical polymerization, as described by Negi et al.20 The molecular weight was ∼100k, as determined by viscometry.21 Deuterium oxide was supplied by Sigma-Aldrich and high-purity water (Elga Ultrapure) was used throughout. The glassware and Teflon troughs used for the measurements and sample preparation were cleaned (17) Penfold, J. Neutrons, x-rays and light scattering; Lindner, P., Zemb, T., Eds.; Elsevier: New York, 1991. (18) Lu, J. R.; Thomas, R. K.; Penfold, J. AdV. Colloid Interface Sci. 2000, 84, 1433. (19) Lu, J. R.; Marrocco, A.; Su, T. J.; Thomas, R. K.; Penfold, J. J. Colloid Interface Sci. 1993, 158, 303. (20) Negi, Y.; Harada, S.; Ishizuk, O. J. Polym. Sci., Part A: Polym. Chem. 1967, 5, 1951. (21) Asnacios, A.; Langevin, D.; Argillier, J. F. Macromolecules 1996, 29, 7412.
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in alkali detergent (Decon 90), followed by copious washing in high-purity water. The surface tension and neutron reflectivity measurements were made at 25 °C. The polymer concentration was 20 ppm, and the surfactant concentration was varied in the range 10-6-0.02 M, depending upon the particular surfactant. Measurements were made predominantly for the isotopic combination d-surfactant/h-polyDMDAAC/nrw.
Theoretical Model Bell et al.14 have used the law of mass action to derive a relatively simple model to describe the surface behavior of the polymer-surfactant mixtures, and this is described in full elsewhere.22 On the basis of the competition between the formation of polymer-surfactant micellar aggregates and free surfactant micelles in solution, and the formation of polymer-surfactant complexes at the interface, this model has been shown14,22 to encapsulate the main features that have been observed experimentally7-13 in such systems. Without the strong electrostatic interaction between the polyelectrolyte and ionic surfactant of opposite charge and the formation of surface active polymer-surfactant complexes, the model reproduces the classical behavior observed in nonionic-surfactant mixtures3,4 and in accordance with more sophisticated theoretical treatments.23-26 The model assumes species defined as S, Sm, P, PSm, and PSs, representing the free surfactant monomer, surfactant micelle (of aggregation number N), free polymer, polymer/surfactant micellar complex (with micelle aggregation number M, and n micelles/ polymer chain), and polymer/surfactant complex (with L surfactants/polymer chain) concentrations, such that
Figure 1. Surface tension (mN/m) vs surfactant concentration (M) for alkyl sulfates/20 ppm polyDMDAAC: (red) C10, (green) C12, (blue) C14 alkyl chain length. Dashed lines are in the absence of polymer.
polymer, respectively. This gives us five equations and five unknowns, S, Sm, P, PSm, and PSs. Assuming a Langmuir isotherm for the only surface active components, S and PSs, and the Langmuir-Szyszkowski equation, the surface tension can be expressed as
γ - γ0 ) -RTΓ∞ log(1 + ks[S] + kPSs[PSs])
(6)
k+0 NS S Sm k-0
(3a)
ks and kPSs are the surfactant and polymer/surfactant adsorption coefficients. Sb can be written as
k+1 PSm P + nMS S k-1
(3b)
[Sb] ) [S] + [Scmc]
( ) [S] [Scmc]
N
(
+ nM
P + LS
k+2 S PSs k-2
[Pb]
(3c)
where k+0, etc., are reaction constants. Applying the law of mass action gives
( ) ( ) ( ) ( ) [S] [Scac]
1+
nM
+L
nM
[S] [Scac]
+
[S] [Sele]
L
[S] [Sele]
L
)
(7)
and
[Sm] ) K0[S]N
(4a)
[PSm] ) K1[PS]nM
(4b)
[PSs] ) K2[PS]L
(4c)
where K0 ) k+0/k-0, etc. We also know that the solution concentrations must satisfy
Sb ) S + NSm + nMPSm + LPSs
(5a)
Pb ) P + PSm + PSs
(5b)
where Sb, Pb are the solution concentrations of surfactant and (22) Bell, C.; et al. Langmuir, submitted. (23) Nagarajan, R. J. Chem. Phys. 1989, 90, 1980. (24) Nikas, Y. J.; Blankschtein, D. Langmuir 1994, 10, 3512. (25) Wallin, T.; Linse, P. J. Phys. Chem. 1996, 100, 17873. Wallin, T.; Linse, P. Langmuir 1996, 12, 3057. Wallin, T.; Linse, P. J. Phys. Chem. B 1997, 1010, 5506. Wallin, T.; Linse, P. Langmuir 1998, 14, 2940. (26) Diamant, H.; Andelman, D. Macromolecules 2000, 33, 8050.
[Scmc] )
( ) 1 NK0
1/(N-1)
, [Scac] )
() 1 K1
1/nM
, [Sele] )
() 1 K2
1/L
(8)
We refer to the [Scac] and [Sele] as the solution and surface critical aggregation concentrations and [Scmc] as the free surfactant cmc. The other principal parameters in the model are then Γ∞, the saturation adsorption, the surface tension at the cmc, and the surface tension corresponding to surface saturation of polymer/ surfactant complexes.
Results (i) Surface Tension. The surface tension data for C10, C12, and C14 alkyl chain length sulfate/polyDMDAAC mixtures in water and in 0.1 M NaCl are shown in Figures 1 and 2 as a function of alkyl sulfate concentration and at a polyelectrolyte concentration of 20 ppm (∼2 × 10-7 M). Shown also in Figure 1 are the surface tension data for the C10, C12, and C14 alkyl sulfate surfactants in the absence of electrolyte and polyelectrolyte.
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Figure 2. Surface tension (mN/m) vs surfactant concentration (M) for alkyl sulfates/20 ppm polyDMDAAC/0.1 M NaCl: (red) C10, (green) C12, (blue) C14 alkyl chain length. Table 1. cmc Valuesa surfactant C10 alkyl sulfate C12 C14
in D2O (mM) b
25-30, 28.6 8,b 7.5 2,b 1.5
in 0.1 M NaCl (mM) 5.0c 1.5b 0.3c
The values with no footnotes were measured in this study. b From ref 23. c Estimated values from extrapolation from the measured C12 dependence on electrolyte. a
The cmc’s of the pure surfactants, in the absence and presence of 0.1 M NaCl, are summarized in Table 1 and, where measured, are in good agreement with literature values.27 In the absence of electrolyte there are significant differences in the surface tension behavior with alkyl chain length of the anionic surfactant. For C12 and C10 the behavior is broadly similar to that previously reported for SDS (C12)/polyDMDAAC in 0.1 M NaCl.7 The initial decrease in surface tension with increasing surfactant concentration is followed by a marked increase and subsequent decrease at higher surfactant concentrations. However, the initial decrease is sharper for C12 than for C10, and the subsequent increase at higher surfactant concentrations is more pronounced. For the C14 alkyl chain length the surface tension remains close to that of pure water until it decreases at higher surfactant concentrations at a cmc which is similar to that of the pure C14 surfactant. In the presence of electrolyte (0.1 M NaCl) the surface tension results for SDS (C12)/polyDMDAAC are reproduced from ref 7 and show a form broadly similar to that observed in the absence of electrolyte. For the C10 and C14 alkyl chain length surfactants the surface tension behavior in the presence of electrolyte (for the surfactant/polyelectrolyte mixtures) is significantly different. With increasing surfactant concentration the initial decrease in the surface tension at the lower surfactant concentrations is followed by a broad plateau region up to the cmc. This is reminiscent of the surface tension behavior observed for the CnTAB/PSS mixtures.9,10 Here, however, for the C14 alkyl chain length surfactant, the surface tension is still relatively low even at the lowest surfactant concentration measured (∼10-6 M). For the C12, C14 alkyl chain length surfactants the surface tension for the polyelectrolyte/surfactant mixtures at high surfactant concentrations is systematically lower in the presence of electrolyte.
Figure 3. Variation in adsorbed layer thickess, d (in Å), with surfactant concentration (M) for the alkyl sulfates/20 ppm polyDMDAAC in the absence of electrolyte: (red) C10, (green) C12, (blue) C14 alkyl chain length.
This is not the case for the C10 chain length surfactant where the limiting values are similar with/without electrolyte but lower than the corresponding pure surfactant values. (ii) Neutron Reflectivity. The neutron reflectivity data, for the isotopic combination of d-surfactant/h-polyelectrolyte/nrw (not shown here) is typical of that reported for other surfactant and polyelectrolyte/surfactant adsorbed at the air-water interface. In the Q range measured the data are consistent with a thin monolayer adsorbed at the air-water interface and are analyzed using eq 1 to provide a thickness and a scattering length density (or refractive index), as described in the Experimental Section. Using eq 2, together with the known scattering length of the deuterium labeled surfactant, the product of the thickness and scattering length density provides an estimate of the amount adsorbed. This is on the basis that only the deuterium labeled surfactant contributes to the reflectivity for this isotopic combination and the adsorbed layer is well described as a layer of homogeneous composition. This has been well established for a wide range of similar systems18 and is a good assumption here. The variation in the thickness of the adsorbed layer with surfactant concentration, in the absence of electrolyte, is shown in Figure 3. A similar dependence (not shown here) is observed in the presence of 0.1 M NaCl. For all the reflectivity data reported here, the key model parameters are summarized in Table 2. In Figure 4 the variation of the amount adsorbed with surfactant concentration is shown in the absence and presence of 0.1 M NaCl. The variation in the thickness of the adsorbed layer shows no marked dependence on surfactant concentration or electrolyte. Furthermore the values of the thickness are consistent with a monolayer of surfactant at the interface, similar to that previously reported for SDS/polyDMDAAC.7,8 In Figure 4b the adsorption of SDS (in the absence of polyelectrolyte), reproduced from ref 7, is also plotted. For all the surfactant/polyelectrolyte mixtures the substantially enhanced adsorption of surfactant down to relatively low surfactant concentrations is consistent with the adsorption of polyelectrolyte/surfactant complexes at the interface, as previously reported for similar systems.7-13
Discussion (27) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-chemical properties of selected anionic, cationic, and nonionic surfactants; Elsevier: Amsterdam, 1993.
As previously discussed for SDS/polyDMDAAC7 the neutron reflectivity data are consistent with the adsorption of polymer/
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Table 2. Key Model Parameters from Analysis of Neutron Reflectivity Data C10 alkyl sulfate Γ
C12 alkyl sulfate
(10-
-
concn (M)
d ((1 Å)
10-1 10-2 5 × 10-3 10-3 5 × 10-4 10-4 5 × 10-5 10-5
18 17 17 17 17 19 17 20
4.7 4.4 3.0 3.6 3.6 3.3 2.2 1.6
4 × 10-2 10-2 5 × 10-3 2 × 10-3 10-3 5 × 10-4 10-4 5 × 10-5 10-5 5 × 10-6 10-6
19 19 18 18 18 20 18 17 17 19 19
4.3 4.6 4.6 3.2 3.1 4.2 3.1 3.0 2.2 1.9 0.6
10 mol cm 2)
concn (M)
d ((1 Å)
C14 alkyl sulfate -
-
Γ (10 10 mol cm 2)
(a) In Absence of Electrolyte (in D2O) 10-1 18 4.7 10-2 19 4.1 5 × 10-3 19 3.6 -3 10 19 2.5 5 × 10-4 18 2.1 10-4 19 2.5 5 × 10-5 17 3.1 10-5 18 2.5 -6 10 17 0.5 2 × 10-3 10-3 5 × 10-4 3.5 × 10-4 2.5 × 10-4 1.25 × 10-4 8.5 × 10-5 6.25 × 10-5 3.13 × 10-5 1.625 × 10-5
(b) In 0.1 M NaCl 20 20 20 20 18 18 18 20 19 20
surfactant complex over a wide range of surfactant concentrations and in both the absence and presence of electrolyte. The thickness of the adsorbed layer (see Figure 2, Table 2) is ∼17 to 20 Å and to first order is independent of surfactant type (alkyl chain length)
Figure 4. Adsorbed amount of surfactant, Γ (×10-10 mol cm-2), vs surfactant concentration for (red) C10, (green) C12, (blue) C14 alkyl chain length in 20 ppm polyDMDAAC: (a) in the absence of electrolyte; (b) in 0.1 M NaCl; (+) SDS alone.
4.1 3.9 3.6 3.5 3.1 3.0 3.4 3.5 3.2 3.3
concn (M)
d ((1 Å)
Γ (10-10 mol cm-2)
5e-2 10-2 5 × 10-3 10-3 5 × 10-4 10-4 5 × 10-5 10-5
19 19 18 20 19 17 17 20
4.6 4.3 4.3 3.9 3.6 3.5 2.7 1.9
10-1 4 × 10-2 10-2 5 × 10-3 2 × 10-3 10-3 5 × 10-4 10-4 5 × 10-5 10-5 5 × 10-6 10-6
21 21 20 20 20 20 20 20 20 18 19 19
5.0 4.4 4.5 4.4 4.3 4.3 4.4 3.6 3.4 2.9 2.5 1.4
and concentration. It is consistent with a monolayer of surfactant with polyDMDAAC incorporated in an extended conformation (parallel to the surface). The absence of any discernible change in thickness (within the measurement error ca. (1 Å) with alkyl chain length (from C10 to C14) is because the thickness has a significant contribution due to surface roughness.28 The pattern of adsorption with surfactant concentration is superficially similar for all three alkyl sulfates and in the presence and absence of electrolyte. The pattern of adsorption, in the absence of electrolyte and for 0.1 M NaCl, with surfactant concentration also shows the same broad trends. At high surfactant concentrations the adsorption saturates at ∼4 × 10-10 mol cm-2 and decreases with decreasing surfactant concentration such that at 10-5 M the adsorbed amount has decreased by a factor 2. However, there are some detailed variations in this general pattern which depend strongly upon the alkyl chain length and whether electrolyte is present (see Figure 4). In the absence of electrolyte (see Figure 4a) the adsorbed amount for C14 alkyl sulfate shows a smooth steady decrease in adsorption with no pronounced variation to that pattern. In contrast, the adsorption of the C10 and C12 alkyl sulfates exhibits a region of surfactant concentration where the adsorption decreases markedly, ∼10-4 to 10-2 M for C12 and ∼ 10-3 to 10-2 M for C10. As previously reported for SDS/polyDMDAAC in 0.1 M NaCl,7 this is associated with the partial depletion from the surface of alkyl sulfate/polyDMDAAC complex. Furthermore it corresponds closely to the surface tension region where a marked increase in the surface tension is observed (see Figure 1 for C10 and C12 alkyl sulfate/polyDMDAAC). This is also associated with the cac, Scac, the onset of solution polymer/surfactant complex formation, and hence associated with a shift toward the formation of solution polymer/surfactant micelle complexes being energetically more favorable. The subsequent increase in the adsorption at surfactant concentrations beyond that region is associated with surfactant monomer adsorption, as the free surfactant monomer concentration in solution increases. Indeed this is demonstrated in Figure 4a, where the adsorption of pure SDS is also plotted, and this coincides with the SDS adsorption for the SDS/ polyDMDAAC mixture at these higher surfactant concentrations. (28) Lu, J. R.; Li, Z. X.; Smallwood, J.; Thomas, R. K.; Penfold, J. J. Phys. Chem. 1995, 94, 8233.
Polymer-Surfactant Mixtures
This is also entirely consistent with the surface tension data, and the surface tension for C10, C12 alkyl sulfates with/without polyDMDAAC are very similar at this higher surfactant concentration region. There is no region of surface depletion observed for the C14 alkyl sulfate/polyDMDAAC mixtures in the absence of electrolyte. This is also manifested in a different surface tension behavior. Indeed, in the absence of electrolyte the surface tension for the C14 alkyl sulfate/polyDMDAAC is similar to that for just C14 alkyl sulfate alone. The variation in the surface tension data for both C12 and C14 alkyl sulfate/polyDMDAAC at surfactant concentrations
