Adsorption of Poly (acrylic acid) at an Oppositely Charged Langmuir

Langmuir 2003, 19, 7989-7994

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Adsorption of Poly(acrylic acid) at an Oppositely Charged Langmuir Film: Surface-Tension, Ellipsometry, and Elasticity Measurements Laurianne Vagharchakian and Sylvie He´non* Matie` re et Syste` mes Complexes, FR 2438, Laboratoire de Biorhe´ ologie et Hydrodynamique Physico-Chimique, UMR 7057, CNRS, Universite´ Paris 7, Case courrier 7056 - 2, place Jussieu - 75251, Paris, Cedex 05, France Received May 7, 2003. In Final Form: June 27, 2003 We have studied the adsorption of a weak polyelectrolyte at the free surface of water covered with an oppositely charged Langmuir film as a function of the surface density σ of the Langmuir film. The adsorption is slow (a few hours). The equilibrium surface pressure π of the mixed film and its compression elastic modulus  are dominated by the contribution of the polyelectrolytes in a large range of σ. In the entire range of σ studied (0.20-1.1 molecule/nm2) π scales as σ2. On the contrary, both  and the ellipticity of the film (which is a measure of the adsorbed quantity) show a regime change at σ ≈ 0.45 molecule/nm2, presumably from polymers lying flat at the surface to polymers forming a “carpet”, as was predicted by theory.

Introduction The adsorption of polyelectrolytes (charged polymers) at charged surfaces from aqueous solutions has been the subject of much theoretical and experimental work for the past 40 years.1-10 The problem is of great importance in formulation: for instance, tremendous amounts of manufactured products are suspensions of charged particles stabilized by the adsorption of polyelectrolytes. The interaction of polyelectrolytes with charged surfaces also plays a role in biology: proteins are charged polymers interacting with membranes containing charged lipids. The problem has regained attention in past years because of the rapid development of a new kind of self-assembled multilayers, the so-called layer-by-layer self-assemblies of polyelectrolytes.11,12 These multilayers are prepared by the successive adsorptions of alternating positively and negatively charged polyelectrolytes on charged substrates: flat surfaces (such as silicon, glass, gold wafers, or charged Langmuir films at the air/water interface) or colloidal particles (such as charged latex or silica particles). * Author to whom correspondence should be addressed. E-mail: [email protected]. (1) Netz, R. R.; Andelman, D. Phys. Rep. 2003, 380, 1, and references therein. (2) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at interfaces; Chapman and Hall: London, 1993. (3) Hoogeveen, N. G.; Cohen Stuart, M. A.; Fleer, G. J. J. Colloid Interface Sci. 1996, 182, 133, 146. (4) Filipova, N. Langmuir 1998, 14, 1162. (5) Netz, R. R.; Joanny, J.-F. Macromolecules 1999, 32, 9013. Joanny, J.-F. Eur. Phys. J. B 1999, 9, 117. Joanny, J.-F.; Castelnovo, M.; Netz, R. J. Phys.: Condens. Matter 2000, 12, A1. Andelman, D.; Joanny, J.-F. C. R. Acad. Sci., Ser. IV 2000, 1, 1153. (6) Dobrynin, A. V.; Deshkovski, A.; Rubinstein, M. Phys. Rev. Lett. 2000, 84, 3101; Dobrynin, A. V.; Deshkovski, A.; Rubinstein, M. Macromolecules 2001, 34, 3421. (7) Borisov, O. V.; Hakem, F.; Vilgis, T. A.; Joanny, J. F.; Johner, A. Eur. Phys. J. E 2001, 5, 37. (8) Ahrens, H.; Baltes, H.; Scmitt, J.; Mo¨hwald, H.; Helm, C. Macromolecules 2001, 34, 4504. (9) The´odoly, O.; Ober, R.; Williams, C. Eur. Phys. J. E 2001, 5, 51. (10) Manghi, M. Ph.D. Thesis, Universite´ de Grenoble, Grenoble, France, 2002. (11) Decher, G. Science 1997, 277, 1232. (12) Caruso, F.; Donath, E.; Mo¨hwald, H. J. Phys. Chem. B 1998, 102, 2011.

Figure 1. Chemicals used in this work: DODA and PAA.

The formation of these multilayers is made possible by an overcompensation of the substrate charge by the first polyelectrolyte layer. The second and following layers are then bound to the previous one by polyelectrolyte complexation.5 In this work, we have studied the properties of the first adsorbed polyelectrolyte layer. The charged surface consists of a Langmuir film made of molecules with a positively charged ammonium head, dimethyldioctadecylammonium bromide (DODA). The surface charge density is conveniently varied by varying the density σ of the Langmuir film. The polyelectrolyte is a weak polyacid, poly(acrylic acid) (PAA), which is negatively charged. It is adsorbed from a dilute solution in water, without added salt. We studied the properties of the mixed DODA-PAA film as a function of the DODA film density σ: we measured the equilibrium surface pressure, the elasticity of the film (by the capillarywaves technique and by fast-compression experiments), and the adsorbed quantity (by ellipsometry). Materials and Methods Figure 1 shows the structures of DODA and PAA. They were both purchased from Sigma-Aldrich and used without further purification. The purity of DODA is >99%. For the preparation of the Langmuir films, DODA was dissolved in chloroform at a concentration of about 0.5 mg/mL. PAA has an average molecular weight of 5000 g/mol and a polydispersity of 2.43. The average degree of polymerization N is about 70. The solutions of PAA were made in ultrapure water (18.2 MΩ‚cm, from a MilliporeSimplicity purifying system). The concentrations of the solutions were the same in almost all the experiments: 12.5 ppm (12.5 mg of PAA/kg of water), which corresponds to 1.7 × 10-4 mol of monomers/L. All experiments were performed at room temperature, 22-25 °C. Langmuir Film Preparation. Experiments were held either in a small round Teflon trough (Ø ≈ 6 cm) or in a homemade

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Langmuir trough, 13 × 30 cm2, 1-cm deep, coated with Teflon. For the preparation of a Langmuir film, first water or a PAA solution was poured in the trough, then its surface was cleaned with a suction device, and finally a controlled quantity of a solution of DODA in chloroform was deposited at the surface. The DODA film density was either constant during an entire experiment or varied by varying the surface of the Langmuir trough. The surface pressure π was measured with a Wilhelmy balance (R&K, Germany, resolution 0.1 mN/m). Ellipsometry. Ellipsometry allows us to investigate the optical properties of films at interfaces. In this study, we performed ellipsometry at the Brewster angle directly at the air/solution interface. The instrument we used was described elsewhere in detail.13 The measured quantity is the ellipticity, F ) rpp/rss, where rpp (rss) is the reflectivity of the interface for the electric field when the light is polarized in (perpendicularly to) the plane of incidence. The ellipticity of an ideal flat and infinitely thin interface between two media of refractive indices n1 and n2 vanishes at the Brewster incidence, θB ) tan-1(n2/n1). For a real interface, which has a thickness and a roughness, the ellipticity does not vanish at the Brewster angle but shows a minimum, which is a measure of the (optical) properties of the interfacial region. In particular, when a film of thickness D (,λ, wavelength of light) and refractive index n is present at the interface,14 2 2 π xn1 + n2 2 2 λ n 1 - n2

∫

F(θB) ) iFjB ≈ i

D

0

dz

[n(z)2 - n12][n(z)2 - n22] (1)

2 2 λ n1 - n2 n2 Fj 2 2 B 2 2 π xn12 + n22 [n - n1 ][n - n2 ]

(2)

Unfortunately, in general both n and D are unknown, and only qualitative information can be obtained on D. For adsorbed films, FjB is a measure of the adsorbed quantity rather than of D.15 Inside the adsorbed film, n is the refractive index of an aqueous solution of the adsorbed product at an unknown concentration c. For polymers, the dependence of n on c is tabulated,16 n ) nw + Rc, and eq 1 is rewritten:

π x1 + nw 2R λ nw 2

FjB ≈

∫ c(z) dz ) πλ x1 + n1 2RΓ D

0

[γk3 + Fgk - Fω2 - iηωk(k + m)][capk3 - iηωk(k + m)] [iηωk(m - k)]2 ) 0 (4) where F and η are the density and viscosity of the polyelectrolyte solution and m is the complex number defined by m2 ) k2 iFω/η. The first and second terms are the dispersion equations for pure capillary waves and for pure compression waves, and the last one gives the coupling between capillary and compression waves. In our experiments, the frequency ω/2π of the capillary waves was varied between 200 and 600 Hz.

Results

n(z)2

This formula is often used to measure D when n has a uniform and known value over the entire thickness D.

D)

Figure 2. Principle of the capillary-waves experiment. A capillary wave is excited at a frequency ω/2π by electrocapillarity at the free surface of the solution. The wavelength λ and the decay length of the wave are measured. The paths of some fluid particles are drawn, evidencing the coupling of the capillary waves to the compression waves in the surface film.

2

(3)

w

In this formula, n2 ) nw ≈ 1.33 and n1 ) 1 are the refractive indices of water and air and Γ is the density of adsorbed polymers (number of adsorbed monomers per unit area). Capillary Waves. To measure the compression modulus of the surface film, we used a device that takes advantage of the coupling between capillary waves and compression waves in the film. It has been described elsewhere in detail.17 Briefly, a plane capillary wave of pulsation ω is excited at the surface of water by electrocapillarity and is detected by the deflection of a laser beam (see Figure 2). This allows us to determine the real and imaginary parts of the wave vector k ) kr + iki (or the wavelength λ ) 2π/kr and the decay length 1/ki). The surface tension γ and the compression modulus of the film, cap ) -A(dγ/dA)dynamic (A is the surface of the trough), can be deduced from these measurements, using the dispersion equation18,19 (13) Meunier, J. In Colloides et Interfaces, Cazabat, A.-M., Veyssie´, M., Eds.; Les Editions de Physique: Les Ulis, France, 1984; p 181. (14) Drude, P. Ann. Phys. Chem. (Leipzig) 1891, 43, 126. (15) De Feijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17, 1759. (16) Brandrup, J.; Immergut, E. H.; Grulke, E. A.; Abe, A.; Bloch, D. R. Polymer Handbook, 4th ed.; J. Wiley & Sons: New York, 1999. (17) Saint-Jalmes, A.; Assenheimer, M.; Gallet, F. J. Phys. Chem. B 1998, 102, 5810. (18) Miyano, K. Langmuir 1990, 6, 1254. (19) Bock, E. J.; Mann, A. J. J. Colloid Interface Sci. 1989, 129, 501.

Polyelectrolyte Solution. We worked at a very low bulk concentration in PAA (12.5 ppm, or 1.7 × 10-4 mol of monomers/L) to study the adsorption of polyelectrolytes from a dilute solution. Furthermore, PAA has a slight surface activity, especially at pH < 4.6,20,21 but at such a low concentration, we can neglect self-adsorption at the free surfaces of its water solutions: we have checked that the surface tension of the solution decreases by less than 0.5 mN/m within a few hours. The pH of these solutions is about 4.7. The charge fraction f of the chains is, thus, ∼0.12, about one monomer out of eight is negatively charged, the other ones being neutral. The average distance between charged groups is >2 nm; there is no Manning condensation. PAA is a flexible polymer, its monomer length a is about 0.25 nm, and at room temperature it is close to thetasolvent conditions in water.16 The characteristic sizes of a polyelectrolyte in a theta solvent22 are its diameter De ) a(f2lB/a)-1/3 (size of the electrostatic blob) and its length L ) Na(f2lB/a)1/3. The Bjerrum length lB is about 0.7 nm at room temperature. For the PAA used in this work, we calculate De ≈ 0.7 nm and L ≈ 6 nm. Formation of the Mixed Film. The surface pressure π is followed from the moment the DODA film is deposited at the free surface of the PAA solution. It increases with time and reaches an equilibrium value πeq within a few hours. Figure 3 shows two typical π(t) curves for two different values of the DODA film density σ. The adsorption is as slow as σ is low, and πeq is reached within 2-6 h, for σ between 1.1 and 0.20 molecule/nm2. We did not study in detail the adsorption kinetics and focused on the equilibrium values. Compression/Expansion Cycles. In a series of experiments, after a first equilibrium was reached, σ was varied by successive compressions or expansions of the film at a moderate speed (∼10 cm2/min, or a few Å2 molecule-1 min-1). After each compression or expansion, the surface pressure relaxes and a new equilibrium state is reached within 10 min to 1 h. When a film is expanded (20) Ishiyama, Y.; Ueberreiter, K. Colloid Polym. Sci. 1980, 258, 928. (21) Okubo, T. J. Colloid Interface Sci. 1988, 125, 386. (22) De Gennes, P. G. Scaling Concepts in Polymers Physics; Cornell University Press: Ithaca, NY, 1979.

Poly(acrylic acid) Adsorption at a Langmuir Film

Figure 3. Surface pressure as a function of time for two films of DODA deposited at t ) 0 on a PAA solution, 12.5 ppm: upper curve, σ ) 0.72 molecule/nm2; lower curve, σ ) 0.48 molecule/ nm2.

Figure 4. Surface pressure as a function of time in out-ofequilibrium experiments. Solid line: starting from equilibrium at σ ) 0.42 molecule/nm2, the film is slowly expanded down to 0.35 molecule/nm2. During expansion, the surface pressure decreases. When the expansion is stopped, the pressure relaxes up to a new equilibrium value. Dashed line: starting from equilibrium at σ ) 0.32 molecule/nm2, the film is slowly compressed up to 0.36 molecule/nm2. During compression, the surface pressure increases. When the compression is stopped, the pressure relaxes down to a new equilibrium value.

from an equilibrium state, the surface pressure decreases during expansion and increases again during relaxation. The opposite behavior is observed when a film is compressed from an equilibrium state. Two examples of such experiments are shown in Figure 4. This type of experiment gives the same value of πeq as direct adsorptions, which supports the assumption that the equilibrium state is, indeed, reached. Furthermore, these experiments show that the number of adsorbed monomers per DODA molecule, Γ/σ, is a decreasing function of σ: when increasing σ from an equilibrium state, some polymers have to desorb to reach the new equilibrium state; when decreasing σ from an equilibrium state, the opposite behavior is observed. Equilibrium Surface Pressure as a Function of the Langmuir Film Density and Structure of the Mixed Film. Figure 5 shows an isotherm of DODA on water, pH ≈ 4.7 (without polyelectrolyte), and the equilibrium surface pressure πeq of mixed DODA-PAA films as a function of σ. On water, for σ < 0.85 molecule/nm2, π is very low and constant because the film is in a gas (G)-liquid expanded (LE) coexistence; for σ ≈ 0.85 molecule/nm2, the film enters the pure LE phase and π increases, and this isotherm is analogous to the ones found in the literature.10 On the contrary, the surface pressure of the mixed films continuously increases with σ, from ∼1 mN/m for σ ≈ 0.2 molecule/nm2 to ∼30 mN/m for σ ≈ 1.2 molecule/nm2, the surface pressure of the mixed films is

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Figure 5. Equilibrium surface pressure as a function of DODA film density σ. Solid line: isotherm of a DODA film on water, pH ) 4.7, T ) 22.5 °C. Circles: equilibrium surface pressure πeq for a film of DODA at the surface of a PAA solution, 12.5 ppm. A plot of the experimental results by a power law is also shown: πeq ∝ σR, with R ) 2.05 ( 0.05.

Figure 6. Some fast-compression isotherms of the mixed films, in log-log scale, along with the equilibrium values and their fit by a power law: πeq ∝ σ2.05.

much higher than that of pure DODA films, and there is no G-LE transition plateau. We have checked by Brewster angle microscopy23 the absence of a G-LE transition in the mixed DODA films: they always appear uniform, during their formation, and during compressions after adsorption. Both the surface pressure of the mixed DODA-PAA film and its structure are dominated by the polyelectrolyte. The values of πeq can be fitted by a power law: it scales as σR, with R ≈ 2.05 ( 0.05. Fast Compressions of the Film after Adsorption. In another series of experiments, after πeq had been reached, the film was compressed from σ ) σ0 at high speed (∼1 cm2/s). The entire compression was performed in a few minutes. Figure 6 shows some of these fast compressions, in log-log scale, together with the equilibrium pressures πeq(σ). The surface pressure in fastcompression experiments is always higher than the equilibrium value. For a given value of σ, the surface pressure is a decreasing function of σ0: with increasing σ0, the fast compressions come closer and closer to the equilibrium isotherm πeq(σ). Elasticity Measurements. We performed elasticity measurements with the capillary-waves technique, at different frequencies between 200 and 600 Hz. We deduced the values of the surface tension γ and of the dynamic compression modulus cap from the measured dispersion equation. The measured values of γ are in good agreement with the values of π () γwater - γ) measured with the (23) Lheveder, C.; He´non, S.; Mercier, R.; Tissot, G.; Fournet, P.; Meunier, J. Rev. Sci. Instrum. 1998, 69, 1446.

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Figure 8. Compression modulus of the mixed DODA-PAA films, measured by capillary waves (circles) and by fast compressions (diamonds), as a function of the film equilibrium surface pressure. Figure 7. Compression modulus of mixed films as a function of the DODA film density, as was measured by capillary waves (circles) and by the slope of fast compressions (diamonds). Dashed line: compression modulus of a DODA film on water, pH ) 4.7, T ) 22.5 °C.

Wilhelmy balance. We did not measure any significant dependence of γ and cap on the frequency in the explored range, which supports the assumption that we can neglect the surface viscosity. The compression modulus of DODAPAA films was also deduced from the initial slope of the fast-compression isotherms, iso(σ0) ) σ0(dπ/dσ)σ)σ0. The compression modulus of DODA films on pure water, DODA, was measured either by the capillary-waves technique or by the slope of the isotherms. Both techniques give the same value of DODA, within the experimental precision ( 0.85 molecule/nm2, DODA and  increase together:  ≈ DODA + (0), with (0) ≈ 24 mN/m. In the first regime, DODA has a negligible contribution to the value of , whereas in the second regime, both DODA and PAA play a role in the value of . More precisely, three different regimes are observed: for σ < 0.45 molecule/nm2, the compression modulus  increases rapidly with σ; for σ between ∼0.45 and ∼0.85 molecule/nm2, the increase of  with σ is much slower; and finally, for σ > 0.85 molecule/nm2,  increases again with σ. The three regimes also appear clearly on Figure 8, which shows cap and iso as a function of the measured values of πeq. In the first regime,  steeply increases with πeq:  ≈ 6πeq. In the second regime, the slope is only ∼1.2, and in the third regime,  increases again more rapidly with πeq, with a slope ∼2.2. Ellipsometry. We performed two series of ellipsometric of measurements. We measured the ellipticity FjDODA B films of DODA on water and the ellipticity FjB of films of

Figure 9. Ellipticity of DODA films at the surface of PAA solutions, as a function of time for three different values of σ. From bottom to top: 0.55, 0.69, and 0.88 molecule/nm2.

Figure 10. Ellipticity of pure DODA films (circles) and of mixed DODA-PAA films (diamonds, 4 h, and crosses, 10 h, after the beginning of the adsorption) as a function of surface density of DODA.

DODA on PAA solutions. Figure 9 shows FjB as a function of time for three different values of σ. Similarly to the surface-pressure measurements, FjB is observed to increase during the adsorption of PAA at the surface, with a characteristic time as short as σ is high. The technique is more sensitive than surface-tension measurements and shows that the equilibrium is reached in more than 10 h. Nevertheless, most of the increase of FjB is observed in the first few hours. Figure 10 shows FjB and FjDODA as a B function of the density σ of the DODA film. The values of FjB are shown at two different times: 4 and 10 h after depositing DODA. The values of FjB and FjDODA both B increase with increasing σ, and FjB increases faster . Figure 10 also shows fits of the ellipticities: than FjDODA B FjDODA ≈ β σ and FjB ≈ β2σ + Fj0B, with β1 ≈ 1.6 × 10-3 nm2/ 1 B molecule, β2 ≈ 2.9 × 10-3 nm2/molecule, and Fj0B ≈ 0.55 × 10-3.

Poly(acrylic acid) Adsorption at a Langmuir Film

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The thickness D of the adsorbed PAA film can be deduced from the measurement of FjB - FjDODA , using formula 2. B Unfortunately, the optical index n of the adsorbed film is unknown. The value n ≈ 1.45, which has been used for similar systems,24 gives D < 1 nm: the adsorbed layer is very thin. A closer analysis of the measurements suggests two regimes, as does the elasticity measurements. Between 0.2 and ∼0.45 molecule/nm2, the best fit is FjB ≈ β2′σ + Fj0B, with β2′ ≈ 3.3 × 10-3 nm2/molecule and Fj0B ≈ 0.4 × 10-3. Above 0.45 molecule/nm2, the slope of FjB(σ) decreases. An analysis of these results in terms of the adsorbed amount of polymers will be discussed in the following.

surface and the excluded volume repulsions between momoners. It increases with σ: D ≈ De(σ/σ*)1/3. In this carpet regime, Dobrynin et al.6 predict an overcharging decrease with increasing σ:

δσ ≈ κσ*De - κ2σD2 ) σ*κDe[1 - κDe(σ/σ*)4/3] (7) On the contrary, Joanny et al.5 predict an overcharging increase with σ. In our experiments, the value of Γ can be deduced from the ellipsometry measurements. As was discussed in Materials and Methods, ∆FjB ) FjB - FjDODA is proportional B to Γ, and with Γ ) (σ + δσ)/f, ∆FjB is expected to vary as

Discussion A major difficulty that arises when working with adsorbed layers of polyelectrolytes is that the structure of the film depends on its history.9,25 Such an effect does not seem to appear in this work: the state reached by the film is the same whether it has been obtained by direct adsorption, by compression, or by expansion of a previously adsorbed film. The reason is probably that the polyelectrolytes we use are very short so that the relaxation times are a few hours, rather than a few days. This allows us to compare our results with predictions for equilibrium states. The adsorption of polyelectrolytes at an oppositely charged surface has been the subject of much theoretical and numerical work. The questions that have been addressed concern the conformation of the molecules in the adsorbed layer and the origin and amplitude of the charge overcompensation. The main results of recent works1,5,6 for flexible polyelectrolytes in a theta solvent are as follows. In the low salt regime (Debye length κ-1 larger than the thickness D of the film) and at low surface charge density σ, the polyelectrolytes are strongly attracted to the surface and strongly repulse each other, they lie flat at the charged surface, and D, which is determined by the balance between the electrostatic attraction of the polymers to the surface and their confinement entropy, decreases with increasing σ: in a theta solvent, D ≈ (fσlB/a2)-1/3 (a is the monomer size, f the fraction of charged monomers, and lB is the Bjerrum length, ∼0.7 nm at room temperature). At the lowest order, the charge of the adsorbed polyelectrolytes exactly compensates the surface charge σ: Γ ) σ/f. At higher order in κ:5,6 Γ ) (σ + δσ)/f. The charge overcompensation δσ is the result of the formation of loops to gain some configuration entropy. It is always small (in the low salt regime). Joanny et al.5 predict

∆FjB )

2π λ

x

1+

1 R (σ + δσ) ) β(σ + δσ) nw2 f

(8)

For σ ) σ* ) f/a2, the adsorbed polymers come to close contact. The expected value of σ* in our experiments is about 2 molecule/nm2 (a ≈ 0.25 nm and f ≈ 0.12). For σ > σ*, the polymers cannot lie flat at the surface any longer; they form a self-similar carpet, and D is determined by the balance between the electrostatic attraction to the

This is in good agreement with the experimental results: for σ < 0.45 molecule/nm2, ∆FjB ) β(σ + δσ0) with β ) β2′ - β1 ≈ 1.7 × 10-3 nm2/molecule and δσ0 ≈ 0.2 molecule/ nm2 (cf. Results). The expected value of β is ∼1.7 × 10-3 nm2/molecule (λ ≈ 633 nm, nw ≈ 1.33, f ≈ 0.12, and R ≈ 0.137 mL/g ≈ 0.0164 nm3/monomer), in agreement with the measured value. The measured value of δσ0 is about 4 times larger than the predicted one (see eq 6: δσ ≈ κ(f/a2lB)1/3 ≈ 0.05 molecule/nm2, with κ-1 ≈ 20 nm). A regime change is observed for σ ≈ 0.45 molecule/nm2, a value smaller than the predicted σ* but on the right order of magnitude. In the second regime (σ > 0.45 molecule/nm2), a slower increase of ∆FjB with σ is observed, which could be the signature of the expected decrease of δσ with increasing σ in the “carpet” regime. The qualitative results about the charge overcompensation deduced from compressions after adsorption, as were discussed in Results, are also consistent with the theoretical predictions: δσ/σ and, thus, Γ/σ are expected to decrease with increasing σ, as was observed in our experiments. The elasticity measurements are also consistent with a transition from a flat layer to an “adsorbed carpet” at σ ) σ* ≈ 0.45 molecule/nm2. For σ < σ*, the adsorbed polymers form a dense two-dimensional film (monomers near to close contact), which is difficult to compress:  is high and rapidly increases with σ. For σ > σ*, the adsorbed polymers form a “carpet” that is easier to compress by changing its thickness, and  slowly increases with σ. Finally, predictions for the surface pressure can also be deduced from the previously described models. The amount of adsorbed polymer is high: there is more than 1/f ≈ 8 adsorbed monomers per amphiphile molecule. That is probably the reason the properties of the mixed DODA/PAA film are dominated by the polyelectrolyte (at least for σ < 0.85 molecule/nm2). The contribution of DODA to πeq can be neglected, contrary to what is in general observed when polyelectrolytes are adsorbed at an oppositely charged Langmuir film8,26 or when increasing f in mixed DODA/PAA films.27 Here, πeq is the surface pressure of an adsorbed film of polymers. For polymers lying flat at the surface (σ < σ*), π can be calculated as the osmotic pressure of a two-dimensional semidilute solution of polymers. When scaling arguments are used,22 π is written as kT(Γ/N)(Γ/Γ*)m and is independent of N. The overlap threshold Γ* is equal to

(24) Ruths, J.; Essler, F.; Decher, G.; Riegler, H. Langmuir 2000, 16, 8871. (25) Sukhishvili, S. A.; Dhinojwala, A.; Granick, S. Langmuir 1999, 15, 8474.

(26) Schnitter, M.; Engelking, J.; Heise, A.; Miller, R. D.; Menzel, H. Macromol. Chem. Phys. 2000, 201, 1504. (27) The influence of the charge fraction f of PAA on the properties of the adsorbed films will be discussed in a separate paper.

δσ/σ ≈ κD[1 + (D/De)2]

(5)

Dobrynin et al.6 predict

δσ/σ ≈ κ(f/a2lB)1/3/σ ) κD(D/De)2

(6)

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N/L2 ∝ 1/N. It follows that m ) 1, and π scales as Γ2. With Γ ≈ σ/f, π scales as σ2. This is consistent with our experimental results. The surface pressure of an adsorbed polymer layer in a theta solvent can be calculated as

π)

∫0D dz (1/6)wc(z)3

For a “self-similar carpet” (σ > σ*), with polymers in theta solvents, c(z) has been calculated:6 c(z) ∝ (D - z)2, and π ∝ D7 ∝ σ7/3. This scaling exponent is a little higher than the measured one. (Similarly, the surface pressure of a self-similar carpet in a good solvent28 would scale as σ17/9.) The signature of a transition from a flat layer to an “adsorbed carpet” on the π(σ) curve in log-log scale should be an increase in the slope by about 15%. It is not observed in our experiments. However, such a low increase is difficult to observe within the precision of the measurements. Furthermore, the scaling law for the “adsorbed carpet” (π ∝ σ7/3) is obtained with the approximation Γ ≈ σ/f. Γ) (σ + δσ)/f with δσ decreasing with increasing σ (28) Dobrynin, A. V. J. Chem. Phys. 2001, 114, 8145.

Vagharchakian and He´ non

could give a lower value of the effective slope (as was observed in the ellipsometry measurements). The surface-pressure measurements are consistent with polymers lying flat at the surface on the entire range of σ explored, but a transition to an adsorbed carpet would be difficult to evidence. Conclusion We have studied the properties of films of a weak polyelectrolyte adsorbed at a soft oppositely charged surface, the surface of water covered with a Langmuir film. Contrary to what is in general observed in similar systems, the properties of the film are dominated by the polyelectrolyte contribution. We have measured a scaling exponent for the surface pressure, and we have evidenced a transition in the behavior of the adsorbed layer (elasticity and adsorbed amount), probably from a flat layer to a “self-similar carpet”, as was predicted by theory. Acknowledgment. The authors are indebted to J. Meunier and D. Bonn for the use of ellipsometry and Brewster angle microscopy instrument and to F. Gallet, J.-F. Joanny, and P. Muller for enlightening discussions. LA030196R