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Langmuir 1999, 15, 2112-2119
Adsorption of Hydrophobically Modified Poly(acrylic acid) Sodium Salt at the Air/Water Interface by Combined Surface Tension and X-ray Reflectivity Measurements Fre´de´ric Millet,*,† Michael Nedyalkov,†,‡ Benjamin Renard,† Patrick Perrin,§ Franc¸ oise Lafuma,§ and Jean-Jacques Benattar† CEA/Saclay, Service de Physique de l’Etat Condense´ , F-91191 Gif sur Yvette Cedex, France, and ESPCI-CNRS-UPMC, UMR 7615, Physico-chimie des Polyme` res, 10 rue Vauquelin, 75005 Paris, France Received October 22, 1998. In Final Form: December 10, 1998 The adsorption at the air/water interface of hydrophobically modified poly(acrylic acid) sodium salt (HMPAANa) with various degrees of grafting and lengths of graft has been investigated using both tensiometry and X-ray reflectivity techniques. Tensiometry has provided the Gibbs adsorption isotherms and has revealed that HMPAANa associating copolymers behave like low molecular weight surfactants with surface tensions leveling off at the critical aggregate concentrations (cac) determined from viscosity measurements. However, very long times (up to 2 days) were required to achieve equilibrium. X-ray reflectivity measurements have permitted us to detect a monomer units-rich zone at the air/water interface, corresponding to the proximal zone of the adsorbed polymer layer. This zone thickens with increasing either the bulk polymer concentration or the salt concentration but remains unchanged with varying the polymer backbone molecular weight. The polymer concentration within the zone is 40% in volume fraction with a bulk concentration equal to cac. By coupling both techniques, we show that the Gibbs adsorption theory is valid for HMPAANa copolymers and that the longest polymer loops and tails extending into the sublayer do not contribute to the surface activity. As a matter of fact, a good agreement between the values of the excess surface concentration Γ is obtained using both techniques.
Introduction Amphiphilic associating polyelectrolytes such as hydrophobically modified poly(acrylic acid) sodium salt (HMPAANa) are known to be very efficient stabilizers of oil in water macroemulsions.1,2 HMPAANa copolymers consist of a hydrophilic polyelectrolyte backbone onto which hydrophobic grafts are covalently attached. Hydrophobic moieties are responsible for the interface activity of the polymer: they anchor in the nonpolar medium (oil) thus diminishing the interfacial energy while the polyelectrolyte backbone remains in water surrounding the oil droplets. Under the action of gravitational forces, the droplets collect at the top of the emulsion. Once packed in a creamed layer, the droplets are separated by an aqueous polymer film preventing coalescence. Surprisingly, large oil droplets (with a diameter of about 10 µm) are then stable for months. The description of the interfacial phenomena is thus of crucial importance for the understanding of the stabilization process. It is now well-known that polymer molecules adsorbed at an interface form a fluffy layer consisting of trains (monomers in direct contact with the surface), loops (polymer sections coming back to the surface), and tails (polymer chain ends) with a broad distribution of sizes.3-11 * Corresponding author. † CEA/Saclay. ‡ Permanent address: Department of Physical Chemistry of the University of Sofia, 1, bul. “James Bourchier”, Sofia, Bulgaria. § ESPCI-CNRS-UPMC. (1) Perrin, P.; Lafuma, F. J. Colloid Interface Sci. 1998, 197, 317. (2) Perrin, P.; F.Lafuma, F.; Audebert, R. Prog. Colloid Poly. Sci. 1997, 105, 228. (3) de Gennes, P.-G. Scaling concepts in polymers physics; Cornell University Press: Ithaca, NY, 1979. (4) de Gennes, P.-G. Macromolecules 1981, 14, 1637. (5) de Gennes, P.-G. Adv. Colloid Interface Sci. 1987, 27, 189.
The particular case of adsorbed grafted polymers has been investigated theoretically12-14 and experimentally using small-angle neutron scattering15,16 and neutron reflectivity.17-20 An ellipsometry study21 has permitted one to describe the adsorption of HMPAANa copolymers at a liquid/solid interface and has determined the variations of the adsorbed amount and the thickness of the interfacial layer with the copolymer composition. A recent X-ray investigation of vertical free-standing films drawn from HMPAANa aqueous solutions showed that the largest loops and tails determine the equilibrium film thickness and explained the remarkable stabilization of macroemulsions by HMPAANa.22 Nevertheless, little is still known about the proximal zone of the adsorbed layer (the trains and the shortest loops of HMPAANa molecules close (6) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at interfaces; Chapman and Hall: London, 1993. (7) Israelachvili, J. Intermolecular and surface forces; Academic: San Diego, CA, 1985. (8) Semenov, A. N.; Bonet-Avalos, J.; Johner A.; Joanny, J.-F. Macromolecules 1996, 29, 2179. (9) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980, 84, 178. (10) Hoeve, C.; Di Marzio; Peyser, P., J. Chem. Phys. 1965, 42, 2558. (11) Silberberg, A. J. Chem. Phys. 1967, 46, 1105. (12) Alexander, S. J. Phys. (Paris) 1977, 38, 983. (13) de Gennes, P.-G. Macromolecules 1980, 13, 1069. (14) Milner, S. T.; Witten, T. A.; Cates, M. E. Europhys. Lett. 1988, 5, 413. (15) Auroy, P.; Auvray, L.; Le´ger, L. Phys. Rev. Lett. 1991, 66, 719. (16) Auroy, P.; Auvray, L.; Le´ger, L. Macromolecules 1991, 24, 5158. (17) Kent, M. S.; Lee, L. T.; Farnoux, B.; Rondelez, F. Macromolecules, 1992, 25, 6240. (18) Kent, M. S.; Factor, B. J.; Satija, S.; Gallagher, P.; Smith, G. S. Macromolecules 1996, 29, 2843. (19) Peace, S. K.; Richards, R. W.; Taylor, M. R.; Webster, J. R. P.; Williams, N. Macromolecules 1998, 31, 1261. (20) Deme´, B.; Lee, L., T. J. Phys. Chem. B 1997, 101, 8250. (21) Poncet, C.; Tiberg, F.; Audebert, R. Langmuir 1998, 14, 1697. (22) Millet, F.; Perrin, P.; Benattar, J.-J. Submitted for publication.
10.1021/la981481r CCC: $18.00 © 1999 American Chemical Society Published on Web 02/26/1999
Adsorption of Poly(acrylic acid) Sodium Salt
to the air/water interface) forming a monomer units-rich zone, responsible for the surface activity of the polyelectrolyte.23 Lochhead24 has studied the interfacial properties at the oil/water interface of a commercial hydrophobically modified poly(acrylic acid) with trade name Pemulen TR-2. Although the effect of pH was discussed, the influence of hydrophobic modification of polymers was not investigated. Moreover, the length of the alkyl grafts is not wellcharacterized since the hydrophobic modification was accomplished by the incorporation of alkyl acrylate chains with a length ranging from C10 to C30. We believe that it is worth using well-characterized polymers of various architectures in order to shed light on the fundamental mechanisms of polymeric adsorption. In this paper, we have coupled tensiometry and X-ray reflectivity techniques. Surface tension measurements have already given useful information regarding the adsorption at the air/water of some proteins25-29 and polymers.30-36 For HMPAANa, we have recorded the kinetics and the steady-state values of the surface tension in order to obtain information about the adsorption mechanisms and the state of the final adsorption layers. In particular, the steady-state values have permitted us to obtain the Gibbs adsorption isotherms from which excess surface concentrations and areas per monomer are deduced. With X-ray reflectivity, the thickness of the adsorbed layers and their polymer concentration were determined. We then have investigated the influence of various parameters (polymer bulk concentration, polymer molecular weight, chemical composition, and salt addition) on the adsorbed layer. Experimental Section Materials. A series of modified polymers were synthesized from a poly(acrylic acid) precursor polymer. They were obtained under their neutralized salt form:
with τ the degree of grafting (τ ranging from 1 to 20 mol %) and n the length of the alkyl chain (n ) 12 or 18 carbon atoms). Details of the synthesis were previously reported.37 The chemically grafted hydrophobic moieties along the polymer backbone are randomly distributed. The degree of grafting was determined by 1H NMR spectroscopy and elemental analysis. Two different backbone molecular weights appear in this work: 120 000 and (23) des Cloizeaux, J. J. Phys. (Paris) 1988, 49, 699. (24) Lochhead, R. Y.; Rulinson, C. J. Colloids Surf. A 1994, 88, 27. (25) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403. (26) McRitchie, F.; Alexander, A. E. J. Colloid Interface Sci. 1963, 18, 453. (27) Damodaran, S.; Song, K. B. Biochim. Biophys. Acta 1988, 954, 253. (28) McRitchie, F. Colloids Surf. 1989, 41, 25. (29) Beverung, C. J.; Radke C. J.; Blanch H. W. Biophys. Chem. 1998, 70, 121. (30) Nahringbauer, I. J. Colloid Interface Sci. 1995, 176, 318. (31) Lankveld, J. M. G.; Lyklema, J. J. Colloid Interface Sci. 1972, 41, 454. (32) Chang, S. A.; Gray, D. G. J. Colloid Interface Sci. 1978, 67, 255. (33) de Feijter, J. A.; Benjamin, J. J. Colloid Interface Sci. 1981, 81, 91. (34) Okubo, T. J. Colloid Interface Sci. 1988, 125, 386. (35) Rios, H. E.; Rojas, J. S.; Gamboa, I. C.; Barraza, R. G. J. Colloid Interface Sci. 1993, 156, 388. (36) Rios, H. E.; Aravena, M. H.; Barraza, R. G. J. Colloid Interface Sci. 1994, 165, 259. (37) Wang, K. T.; Iliopoulos, I. Polym. Bull. 1989, 20, 577.
Langmuir, Vol. 15, No. 6, 1999 2113 Table 1. Excess Surface Concentration, Average Area/ Monomer Unit, and Cac
polymer
excess surface concn Γ (mg/m2)
av area/ monomer 2 (Å /monomer unit)
tensiometry
viscometry
120 1C12 120 3C12 120 10C12 120 1C18 120 3C18
1.3 ( 0.1 1.3 ( 0.1 1 ( 0.1 1.6 ( 0.1 2.5 ( 0.2
11 ( 1 11 ( 1 14 ( 1 9(1 6(1
8(2 1.5 ( 0.5 0.4 ( 0.1 3 ( 0.5 1 ( 0.1
2 ( 0.5 0.5 ( 0.1 2 ( 0.5 0.5 ( 0.1
cac (w/w%)
900 000 g/mol with a polydispersity index equal to 2.6 and 4, respectively. A recent capillary electrophoresis experiment38 has achieved the differentiation of the electrophoretic mobilities of HMPAANa copolymers with regard to their degree of grafting (unmodified PAANa precursor homopolymer and HMPAANa copolymers with τ ) 3, 7, and 10 mol %). The degree of grafting is then well-characterized, and the polydispersity of grafting is negligible. For the sake of clarity, the modified polymers are referred to as (weight average molecular weight × 10-3) τCn. HMPAANa are associative copolymers in water: at polymer concentrations higher than the critical aggregate concentration (cac), alkyl grafts form hydrophobic intramolecular and intermolecular aggregates in bulk to protect themselves from water. For the whole series of copolymers reported in this paper, both kinds of aggregations seem to form simultaneously.1,2 Intermolecular aggregations lead to the formation of a physical network and, hence, to a strong increase in the viscosity of the solution. The values of the cac have been determined by viscosity measurements for the whole series of HMPAANa copolymers.1,2,37 (Table 1). Aqueous solutions were prepared by dissolving polymers in double-distilled deionized water (Milli-Q system from Millipore). After dissolution of the appropriate amount of polymer, the solutions were gently stirred for 24 h before use. The concentrations are expressed in weight percentage (w/w%). Since the polymer samples were used in their fully neutralized salt form, these solutions were basic (pH ∼ 9). Methods and Equipment. Surface tensions were measured by the Wilhelmy method using a Cahn 1000 electrobalance and a paper filter plate which length is 2 cm. The paper filter ensures a zero contact angle. The electrobalance is sensitive to a variation of weight as small as 0.5 mg corresponding to a variation of surface tension of 0.1 mN/m. Measurements were carried out in a Teflon trough (4 cm diameter) housed in a Plexiglas box. Prior to each run, the surface tension of pure water was measured. After each run with polymer solution, the surface tension of pure water was measured with the same plate. The surface tension was always within 2% of that of pure water, indicating that negligible adsorption of the polymer on the plate had occurred. The approach of equilibrium being very long, it was assumed arbitrarily that equilibrium had been reached when the surface tension variation was less than 0.1 mN/m over a period of 100 min (corresponding to a rate of loss equal to 0.001 mN/(m‚min)). The X-ray reflectivity method is briefly presented here since it has been described in previous papers.39,40 An X-ray reflectivity experiment consists of the measurement of the ratio R(θ) ) I(θ)/ I0, where I(θ) is the intensity of the specular beam reflected by a surface at an angle θ. The wave vector transfer is perpendicular to the surface, and the experiments provide information about the mean electron density along the normal z to the surface. The refractive index is given by n ) 1 - δ - iβ, where δ is proportional to the electron density:
δ(z) )
λ2 r F(z) 2π e
(1)
where λ is the X-ray wavelength, re is the classical radius of the (38) Collet, J.; Tribet, C.; Gareil, P. Electrophoresis 1996, 17, 1202. (39) Schalchli, A.; Sentenac, D.; Benattar, J.-J. J. Chem. Soc., Faraday Trans. 1996, 92, 553. (40) Benattar J.-J.; Schalchli, A.; Sentanac, D.; Rieutord, F. Prog. Colloid Polym. Sci. 1997, 105, 1113.
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and the activation energy of adsorption at the interface is zero because the surface is bare. The surface concentration Γ versus time is given by the following equation:42
(Dtπ )
Γ(t) ) 2C0
1/2
(2)
Here D is the diffusion coefficient. Assuming that the adsorbed layer is an ideal twodimensional gas of monomer units, the surface pressure Π ) γ0 - γ can be expressed as follows:
Π(t) ) γ0 - γ(t) ) 2C0(RT) Figure 1. Decrease of the surface tension with time for the 120 1C12 copolymer at various concentrations (w/w%) indicated above. electron, F(z) is the electron density along the z axis, and β is proportional to the linear absorption coefficient. In fact, we use the original matrix formalism,41 which is valid at all angles, to compute a reflectivity curve. Such a method consists of a treatment of the system as a succession of homogeneous slabs, where each slab is considered by three parameters: thickness, electronic density, and interfacial roughness. The analysis of the experimental reflectivity curve is made via a fit of the theoretical curve with respect to those three parameters. We may achieve for each homogeneous slab a determination of the electronic density, the thickness, and the interfacial roughness. Finally, we obtain the real electronic density profile δ(z). Contrary to the step profile, which presents electronic density discontinuities between two adjacent slabs, the real δ(z) profile is continuous, the discontinuities being smoothened off by the interfacial roughness between slabs. Reflectivity experiments are performed using a high-resolution diffractometer (Micro-Controle). The X-ray wavelength is λ ) 1.5405 Å (Cu KR1 line), and a small vertical slit (100 µm) ensures a low divergence of the beam (0.1 mrad). Surface tension and X-ray reflectivity measurements were performed at room temperature (20 ( 1 °C).
Results and Discussion Surface Tension. Long times have often been reported for the surface tension relaxation of protein or amphiphilic polymer solutions.25-32 The kinetics generally indicate that the adsorption process is initially diffusion-controlled.25,26,30-32 In the longer times, interactions between the existing adsorbed layer and molecules migrating from the bulk to the interface create an energy barrier for the adsorption.25-28 Reconfiguration of the adsorbed layer has also been reported27,29 and could lead to a collapse of the adsorbed layer under compression.29 The analysis of the variation of the surface tension with time has thus permitted us to elucidate some adsorption mechanisms. The surface tension γ of various copolymer solutions (120 1C12, 3C12, 10C12, 1C18, 3C18) was then investigated as a function of time t and copolymer bulk concentration C0. The decrease of the surface tension with time has been followed in order to be sure to obtain equilibrium values. Very long times (typically 10-15 h) were necessary for γ to level off (Figure 1 for 120 1C12). We now show that the decrease of the surface tension versus time is not diffusion-controlled and that there exists an energy barrier for the adsorption of the polymer molecules at the air/water interface. At the early stage of an adsorption process, the rate of arrival of molecules at the interface is diffusion-controlled (41) Born, F.; Wolf, E. Principles of Optics, 6th ed.; Pergamon: London, 1984; p 51.
(Dtπ )
1/2
(3)
Here γ0 is the surface tension of the bare air/water interface and R and T have their usual meaning. In the case of a diffusion-controlled adsorption kinetic, plotting γ as a function of t1/2 leads to the value of D from the slope 2C0RT(D/π)1/2 of the linear portion of the curve in the small times. The values obtained for D for 120 1C12 (∼10-20 m2 s-1) are much smaller than the value reported for the corresponding unmodified poly(acrylic acid) sodium salt of equivalent molecular weight43 (10-11 m2 s-1). The huge discrepancy between both values indicates that the process is actually not diffusion-controlled. In other words, eq 3 does not hold anymore in the present situation. In fact, our experiments were performed at higher concentrations (C0 > 0.1%) than in refs 25, 26, and 30-32 (C0 < 10-3%) for which a diffusion-controlled adsorption was observed. In our case, the diffusion process is then too rapid to be observed and the slowness of the decrease of the surface tension is likely to be due to surface phenomena. The same considerations still hold for the adsorption of the other copolymers (different τ and n). Since the decrease of the surface tension is much slower than predicted by the diffusion-controlled theory, there exists an energy barrier to adsorption. Ward and Tordai44 have proposed a model in which a surface area ∆A must first be cleared by compressing the molecules already adsorbed for another molecule to take place. Consequently, the adsorption of a molecule at a pressure Π requires a work Π∆A. The rate of adsorption is then given by the Boltzmann factor:
(
)
(
)
Π(t)∆A Π(t)∆A dΓ ) k1C0 exp - k2Γ exp dt kT kT
(4)
Here k1 and k2 are the first rate constants for the adsorption and desorption process. This equation has already revealed to be very useful in interpreting the kinetics of adsorption of proteins at the air/water interface.25-28 The adsorption of a randomly grafted polymer is very strong because of the numerous anchorage points of the molecules at the interface4 and the desorption term is then negligible. Following the assumption of the two-dimensional ideal gas (eq 3) and taking logarithms of both sides of eq 4, we obtain
∆A + log(k C RT) ( dγdt ) ) (γ(t) - γ )2.3kT
log -
0
1
0
(5)
Figure 2 exhibits a linear dependence of log(-dγ/dt) with γ for 120 1C12 at various concentrations. The slope is independent of the concentration and gives an area ∆A (42) Ward, A. F. H.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (43) Polymer Handbook, 3rd ed.; Brandrup J., Immergut, E. H., Eds; John Wiley & Sons: New York 1989; p VII, 70. (44) Ward, A. F. H.; Tordai, L. Rec. Trav. Chim. 1952, 71, 572.
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Langmuir, Vol. 15, No. 6, 1999 2115
Figure 2. Adsorption of 120 1C12. Variation of -dγ/dt with the surface tension γ for the 120 1C12 copolymer at concentrations of 3, 6 and 12%. log(-dγ/dt) varies linearly with the surface tension γ in agreement with eq 5.
Figure 3. Decrease of the surface tension with time for the 120 3C18 copolymer at a concentration of 1%. In this particular case, there is a surface rearrangement, indicated by the changes of the concavity of γ(t). Two mechanisms occur (a and b). Inset: log(-dγ/dt) is not a linear function of γ.
equal to 120 ( 20 Å2. This value could correspond to the area that must be cleared for the penetration of a C12 alkyl chain through the already adsorbed polymer layer. The same result holds for the 120 3C12 and 10C12 copolymers leading to similar values of ∆A. More surprisingly, an increase in the length of the alkyl graft (C18 instead of C12) does not lead to a higher value of ∆A: once again, an area of about 120 ( 20 Å2 is obtained for the 120 1C18 copolymer. It must be pointed out that the ∆A value does not depend on the bulk concentration nor on the surface pressure Π and thus seems to be an intrinsic characteristic of the individual molecules. However, the 3C18 copolymer behavior is different (Figure 3 and inset). At the beginning of the surface organization process (t < 10 h, γ > 60 mN/m), the kinetics resemble that of the other copolymers, with log(-dγ/dt) varying roughly linearly with γ with a slope corresponding to an area ∆A of about 100 Å2. Nevertheless, after 10 h, the γ(t) curve exhibits a change of concavity indicating the emergence of a second mechanism. This phenomenon is all the more obvious on the inset: log(-dγ/dt) is not a monotonic function of γ, contrasting with the behavior of the other copolymers (Figure 2). A rearrangement of the adsorbed layer could occur in order to minimize the interfacial tension, resulting in a very long surface relaxation time (2 days). In the following, we will discuss the surface relaxation of the 3C18 copolymer in the light of the X-ray reflectivity measurements. Plots of steady values of γ versus the concentration (Figure 4a,b) show that all copolymers are surface active when the concentration is high enough and that surface
Figure 4. Gibbs isotherms for (a) the 120 1C12, 3C12, and 10C12 copolymers, (b) 120 1C18 and 3C18 copolymers, and (c) newtonian viscosity of solutions of 120 unmodified precursor homopolymer and 120 3C12 and 120 10C12 copolymers. γ levels off at the cac: the copolymers behave like small molecular weight surfactants.
tensions as low as 38 mN/m are reached, except for the 120 10C12 copolymer (55 mN/m). The alkyl grafts are solely responsible for the adsorption of the copolymers since the poly(sodium acrylate) homopolymer does not adsorb at the air-water interface even at high concentration.34 At low polymer concentration, the alkyl grafts concentration in solution is not high enough for the copolymer to adsorb at the interface and the value of γ is that of the pure water. With increasing concentration, a larger amount of polymer molecules adsorbs at the surface thereby decreasing the surface tension. Above a determined concentration, depending on both the degree of grafting and the length of the grafts, the surface tension levels off. Furthermore, earlier works1,2,37 have determined the values of the critical aggregate concentrations (cac) by viscosimetry measurements. Figure 4c presents the newtonian viscosity of the unmodified precursor homopolymer solution and the HMPAANa copolymer solutions as a function of the concentration. The 120 3C12 and 10C12 copolymer solutions become more viscous than the precursor homopolymer solution at the cac (arrows in
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Figure 4c), when a physical network of hydrophobic aggregates is formed. The same behavior is observed for the 120 1C18 and 3C18 copolymers (result not shown). Figure 4a,c reveals that γ levels off at the cac for each copolymer. Consequently, the adsorption process stops with the formation of hydrophobic aggregates in bulk. HMPAANa copolymers thus behave like small molecular weight surfactants.45 The Gibbs isotherms then provide a determination of the respective cac, and the values are in excellent agreement with those obtained by viscosimetry (Table 1). It is also worth noting that it has been reported for some amphiphilic diblock polyelectrolytes46 that aggregation in bulk occurs prior to any adsorption process. Once the aggregates have formed in bulk, they migrate and adsorb at the interface then inducing a decrease in the surface tension. In our case, the surface activity originates from the adsorption of individual molecules. Finally, the original behavior of the 120 10C12 copolymer deserves further comments. An attempt must be made to explain the leveling off of γ at rather high value (55 mN/ m). We suggest that the adsorption of the relatively large number of grafts (τ ) 10 mol %) at the air/water interface would require an entropically disfavored stretched conformation of the macromolecules. As a result of the high density of grafts along the chain, an important fraction of the grafts of the adsorbed polymer molecules preferentially form intramolecular or intermolecular hydrophobic associations that are not in direct contact with the interface and do not contribute to the lowering of the surface tension. This could explain why the 10C12 copolymer is less surface-active than the 1C12 and 3C12 copolymers for which the topologic constraints are less important. The values of the excess surface concentrations Γ can be determined from the Gibbs adsorption theory. When the valencies of monomer units and their counterions are Zp and Zg, respectively, Γ is given by34
ZpZg 1 dγ d ln(m) Γ)Zp + Zg RT d ln(m) d ln(a)
It is more convenient to write eq 9 as follows:
(6)
where a and m are the mean activity of the polyelectrolyte and the polymer concentration (in moles of monomer units per liter), respectively. The last term of the right-handside of eq 6 can be evaluated according to Manning’s theory47 by
d ln(a) 1 -1 -1 ) Z ξ d ln(m) 2 g
(7)
where ξ is the linear charge density parameter:
ξ ) e2/kTb
(8)
Here e is the charge of an electron, the bulk solvent dielectric constant, and b the average distance between charges on the polyions framework. With b ) 2.5 Å, a value of 2.836 is obtained for ξ. Then, eq 6 becomes
ξ dγ Γ)RT d ln(m)
Figure 5. (a) Reflectivity curves of the 120 3C12 copolymer solutions at a concentration of 0.4% (squares) and 2% (circles). The thickness of the polymer chains layer increases with the bulk polymer concentration. (b) Reduced electronic density profiles at the air/water interface. Step profile for 0.4% concentrated 120 3C12 copolymer solution (dashed line) and step and real profile for 2% concentrated 120 3C12 copolymer solution (solid line) are represented. Contrary to the step profile, the real profile does not present any discontinuity of δ(z). As a matter of fact, the discontinuities are smoothened by the roughness of the interfaces between slabs.
(9)
(45) Interactions of surfactants with polymers and proteins; Goddard, E. D., Ananthapadmanabhan, K. P., Eds.; CRC Press Inc.: Boca Raton, FL, 1993; Chapter 2. (46) Guenoun, P.; Davis, H. T.; Tirrell, M.; Mays, J. W. Macromolecules 1996, 29, 3965. (47) Manning, G. S. J. Chem. Phys. 1969, 51, 924.
2.3ΓRT d log(m) ξ
dγ ) -
(10)
The surface excess concentrations Γ at saturation can be obtained from the slopes -2.3ΓRT/ξ of the isotherms just below the cac. Table 1 summarizes the values obtained for Γ, the average area per monomer unit, and the cac obtained by viscosimetry and surface tension measurements. The adsorbed amounts (typically 1 mg/m2) are of the same order of magnitude as those obtained by ellipsometry measurements at solid/liquid interface.21 For the polymers carrying C12 grafts, the slopes of the Gibbs isotherms, and consequently Γ, depend only weakly on the degree of grafting. For the 3C18 copolymer, the calculated adsorbed amount is clearly higher than that of the other copolymers. A reorganization process of the solution surface, which has been suggested above for the 3C18 copolymers (Figure 3), could allow the adsorption of this larger amount. X-ray Reflectivity. We have carried out X-ray reflectivity measurements on the surface of 120 τC12 (τ ) 1, 3, 10, and 20 mol %), 120 3C18, and 900 1C12 copolymer solutions. The influence of the polymer concentration, the degree of grafting, and the backbone molecular weight as well as the salt concentration on the adsorbed layer have been investigated in this paper. For the 120 3C18 copolymer, a set of reflectivity profiles has permitted to determine the thickening of the adsorbed layer as a function of time. Figure 5a presents the reflectivity curves of 120 3C12
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Langmuir, Vol. 15, No. 6, 1999 2117
Figure 6. Description of the polymer adsorbed layer. Only the proximal zone is detected.
copolymer solutions at concentrations of 0.4% and 2% (cac). These curves cannot be fitted with a one-slab model, corresponding to a homogeneous adsorbed layer. It is then necessary to introduce an additional slab with a low electronic density (see Figure 5b) corresponding to the alkyl grafts emerging from the solution (see Figure 6). The calculations using the matrix formalism (solid lines in Figure 5a) then fit well the shape of the experimental curves. The variation of the reduced electronic density δ as a function of the distance z from the interface is shown in Figure 5b. For the 2% concentrated solution, the exact reduced density profile, for which the steps are smoothened by the roughness of the interfaces between slabs, is also represented (solid line). For each solution, we found the same value for the roughness of the three interfaces (air/ alkyl grafts, alkyl grafts/polymer chain layer, and polymer chain layer/bulk). This roughness is equal to 4.4 ( 0.2 and 5 ( 0.2 Å for the 0.4% and the 2% concentrated solution, respectively, and is essentially due to the thermal excitation.48 The thickness of the polymer chains layer varies from 21 ( 1 Å at a concentration of 0.4% to 27 ( 1 Å at 2%. The polymer volume fraction Φ within the polymer chains layer is determined through the relation
δ ) (1 - Φ)δwater + Φδpolymer
Table 2. Proximal Zone Investigated by X-ray Reflectivity polymer thickness vol fraction e (Å) Φ (%) 120 1C12 (8%, cac) 120 3C12 (0.4%, 0.2 cac) 120 3C12 (2%, cac) 120 3C12 (0.4% + 1 M NaCl) 120 10C12 (0.5%, cac) 120 20C12 (0.25%, cac) 120 3C18 (1%, cac) 2h 48 h 900 1C12 (8%)
excess surface concn Γ (mg/m2)
27 ( 1 21 ( 1 27 ( 1 32 ( 1 34 ( 1 17 ( 1 24 ( 1 34 ( 1
40 ( 5 40 ( 5 40 ( 5 40 ( 5 40 ( 5 55 ( 5 30 ( 5 40 ( 5
1.2 ( 0.1 1 ( 0.1 1.2 ( 0.1 1.5 ( 0.1 1.6 ( 0.1 1 ( 0.1 1 ( 0.1 1.6 ( 0.1
27 ( 1
40 ( 5
1.2 ( 0.1
(11)
where δ is the reduced electronic density of the polymer adsorbed layer (4.05 ( 0.05 × 10-6) determined from the best fit for both concentrations, δ water is the water density (3.56 × 10-6), and δpolymer the density of the pure polymer (4.7 × 10-6) calculated from ref 49. Then
Φ ) (δ - δwater)/(δpolymer - δwater) ) 40 ( 5%
Figure 7. Reduced electronic density δ(z) profile at the air/ water interface for the 120 1C12 copolymer solution (dashed line) and the 120 20C12 copolymer solution (solid line) at cac (respectively 8% and 0.25%). For the 120 20C12 copolymer, the slab corresponding to the grafts is denser and the proximal zone of the adsorbed layer is thinner.
(12)
The polymer volume fraction in the polymer chains layer is independent of the bulk concentration and is equal to 40 ( 5%. A recent vertical aqueous polymer film22 has shown that long loops and tails of HMPAANa copolymers extend in the sublayer (Figure 6) and that the thickness of the entire adsorbed layer is 240 ( 20 Å for the 120 τC12 copolymers (τ ranging from 1 to 10 mol %). The X-ray reflectivity measurements in Figure 5a are solely sensitive to the dense layer very close to the surface (proximal zone) consisting of trains and short loops. The sublayer, which concentration is lower, has not been detected. We have also investigated the surface profiles of 120 1C12, 3C12, 10C12, and 20C12 copolymer solutions at their cac (8, 2, 0.5, and 0.25%, respectively) to determine the influence of the degree of grafting on the saturated adsorbed layer. Figure 7 shows the reduced electronic (48) Daillant, J.; Bosio, L.; Benattar, J.-J.; Meunier, J. Europhys. Lett. 1989, 8, 453. (49) L’Alloret, F. Ph.D. Thesis, Universite´ Pierre et Marie Curie, Paris, 1996.
density profiles obtained for the proximal zone of the adsorbed layer of the 1C12 and 20C12 copolymer solutions. As expected, the electronic density of the slab corresponding to the grafts increases with the degree of grafting of the polymer. The proximal zone thickness decreases with the degree of grafting. This phenomenon has already been observed for the adsorbed layer of other hydrophobically grafted water-soluble polymers.20 Increasing the degree of grafting results in a smaller distance between the grafts along the backbone and, hence, reduces the size of the loops that constitute the adsorbed layer. Nevertheless, the proximal zone for the 10C12 copolymer solution is thicker than that of the 1C12 copolymer (Table 2). This result confirms the hypothesis of hydrophobic associations within the proximal zone for the more hydrophobic copolymers. Consequently, one can suggest that there exists a competition between two mechanisms. On one hand, a highly grafted copolymer forms small loops, and on the other hand, an important fraction of the grafts may not emerge at the interface because of the entropic constraints of the polymer chain. Intermolecular or intramolecular associations then form thereby increasing the thickness of the proximal zone. This thickness thus seems to result from the competition of both phenomena. As shown from the surface tension measurements presented above, a slow reconfiguration process occurs at the interface of the 120 3C18 polymer solutions. The reflectivity profiles on the surface of a solution at a concentration of 1% left at rest respectively for 2 h and 2 days are presented in Figure 8a. It appears from the best fit using the two slab model that the thickness of the proximal zone increases from 24 Å after 2 h to 34 Å after
2118 Langmuir, Vol. 15, No. 6, 1999
Millet et al.
Figure 8. (a) Reflectivity curves of a 120 3C18 polymer solution at 1% (cac) after the solution has rested for 2 h (squares) and 2 days (circles). (b) Reduced electronic profile δ(z) at the interface after 2 h (dashed line) and 2 days (solid line). The thickness of the adsorbed layer increases with time.
2 days and the density of the slab corresponding to the alkyl grafts doubles (Figure 8b). Consequently, the shape of the dynamic surface tension curve (Figure 3) could be due to a folding back process of the polymer loops in order to optimize the coverage rate of the surface, resulting in a thickening of the proximal zone. For the whole series of copolymers, the excess surface concentration within the proximal zone Γ at cac can be calculated using its definition:
Γ ) eΦF
(13)
Here e is the thickness of the proximal zone, Φ the polymer volume fraction within this zone (Table 2), and F the pure polymer density (1.3 g/cm3).49 Γ values (1-1.6 mg/m2) are close to those calculated from the Gibbs adsorption isotherms (Tables 1 and 2). It is also possible to have an estimation of the total amount of polymer Γtot within the whole adsorbed layer (Figure 6) of a 120 1C12 copolymer solution concentrated at 8% through the relation
Γtot ) etotΦavF
(14)
Here, etot is the thickness of the whole adsorbed layer (etot ) 240 Å from ref 22) and Φav is the average polymer volume fraction within this layer (Φav > 8% since the adsorbed layer is more concentrated than the bulk). Equation 14 yields Γtot > 2.5 mg/m2. Consequently, the Gibbs adsorption theory, from which an excess surface concentration of 1.3 ( 0.1 mg/m2 is calculated, gives the amount of polymer Γ within the proximal zone (1.2 ( 0.1 mg/m2 with X-ray reflectivity) and not the total amount Γtot (>2.5 mg/m2) within the whole adsorbed layer. Then, the largest loops
and tails do not have any influence on the interfacial activity. This result confirms theoretical investigations23 that showed that only the monomer units very close to the interface contribute to diminish the surface tension. Moreover, the discrepancy between the Γ values for 120 10C12 (1 mg/m2 with tensiometry and 1.6 mg/m2 with X-ray reflectivity) could be due to the fact that the interaction between the surface and the monomers falls within the 35 Å-thick proximal zone so that some monomers of this zone do not contribute to the surface activity. Finally, preliminary results dealing with the effect of adding a salt to the polymer solution and changing the polyelectrolyte molecular weight are now discussed. The thickness of the proximal zone for a 120 3C12 copolymer solution concentrated at 0.4% was found to increase from 21 Å for the salt-free solution to 32 Å in the presence of NaCl (1 M). The salt screens the electrostatic repulsions between charged chains in the proximal zone, and the short loops come closer to each other, inducing an evolution from a stretched to a folded back conformation of the loops. The quality of the solvent is decreasing when salt is added and an increasing amount of polymer adsorbs, resulting in a thicker layer. Last, the reflectivity profiles of 120 1C12 and 900 1C12 copolymer solutions were compared to investigate the influence of the polyelectrolyte backbone molecular weight on the proximal zone. The best fits of the data give the same structure and thickness in both cases (Table 2). As a matter of fact, it has been proposed for polymer adsorbed layers that the short-range monomer-surface interactions vanish within the monomer-rich zone (or proximal zone) in direct contact with the air.23 The structure of this zone is then independent of the molecular weight of the polymer. Our observation is hence in agreement with these results. The proximal zone of the adsorbed layer is not affected by the coils of polymer molecules extending from the surface to the sublayer. Conclusion We have obtained the Gibbs isotherms for HMPAANa copolymer solutions with various degrees of grafting and lengths of graft. HMPAANa copolymers behave like small molecule surfactants with the surface tension leveling off once hydrophobic aggregates appear in bulk. From the isotherms, the respective critical aggregate concentrations and the excess surface concentrations (typically 1-1.6 mg/m2) were determined for each copolymer. The values of the cac measured by tensiometry and viscosimetry are in good agreement. The relaxation of the surfaces is slow (typically 10 h) and the kinetics of the surface tension cannot be explained by a diffusion process but rather by a slow penetration of the grafts through the adsorbed layer. For the whole series of copolymers, the X-ray reflectivity curves evidenced the thin (17-35 Å) proximal zone of the adsorbed layer at the cac with a polymer concentration equal to 40% (v/v). The thickness of the proximal zone increases with increasing the bulk polymer concentration or the ionic strength and is independent of the polymer backbone molecular weight. The combined investigation using X-ray reflectivity and tensiometry showed that the polymer loops and tails in the sublayer do not participate to the lowering of the surface tension of the solution and that the Γ values obtained from the Gibbs theory correspond to the amount of polymer within the proximal zone in the vicinity of the interface. The very long surface organization times
Adsorption of Poly(acrylic acid) Sodium Salt
recorded for the 120 3C18 copolymer could be due to a surface rearrangement consisting of a folding process of the polymer loops near the surface. Finally, tensiometry and X-ray reflectivity have been revealed to be complementary techniques.
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Acknowledgment. We thank Nicolas Cuvillier for his help in the X-ray data treatment, and we are very grateful to Olivier Mondain-Monval for very fruitful discussions. LA981481R
