The Effect of Grafting Density on Binding Isotherms of Cationic

Jan 28, 2003 - Dick Gage and Martien Cohen Stuart*. Laboratory for Physical Chemistry and Colloid Science, Wageningen University,. PO Box 8038, 6700 E...
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Langmuir 2003, 19, 2000-2006

The Effect of Grafting Density on Binding Isotherms of Cationic Surfactants to a Polyacrylic Acid Brush Olga Pyshkina, Vladimir Sergeyev, Alexander Zezin, and Victor Kabanov Polymer Department, Faculty of Chemistry, M.V. Lomonosov Moscow State University, Moscow 119899, Russia

Dick Gage and Martien Cohen Stuart* Laboratory for Physical Chemistry and Colloid Science, Wageningen University, PO Box 8038, 6700 EK Wageningen, The Netherlands Received May 16, 2002. In Final Form: November 12, 2002 Adsorption (binding) isotherms of three cationic surfactants (hexadecyl trimethylammonium bromide, dodecyl trimethylammonium bromide, and decyl trimethylammonium bromide) bound to poly(acrylic acid) brushes were determined by means of optical reflectometry. The adsorption occurs reversibly. The shape of the isotherms and the maximum degree of binding depends strongly on the grafting density of the brush. Dense brushes exchanged at most about 40% of their counterions for surfactant ions and had isotherms that could be fitted to the Langmuir equation. For more dilute brushes the isotherms had a quite different shape: the quantity of surfactant could increase up to complete exchange in a second step occurring at higher concentrations. It is shown that these differences are due to the bulkiness of the surfactant ions; the volume required for full loading is so large that it forces the polymer chains to stretch too much. A lamellar structure of the complex occurring in the fully loaded brush is proposed.

Introduction The binding of ionic surfactants to polyelectrolytes carrying charges of the opposite sign has been amply studied.1-6 Part of these studies deal with solutions of free polymers,1,2 others with polyelectrolyte gels.3,4 For all these kinds of systems, the main conclusions are more or less similar. The general pattern observed is that binding is a kind of ion exchange process, which begins already at surfactant concentrations several decades below the cmc of the surfactant. At higher concentrations, an insoluble complex is formed with a binding fraction of unity (i.e. stoichiometric binding). Finally, around the cmc free chains may form soluble complexes by binding an amount surfactant in excess of the stoichiometric quantity. The binding is of a cooperative nature, in the sense that the second derivative of the isotherm with respect to the concentration has both positive and negative parts. When binding occurs to a weak (annealed) polyacid or polybase, the binding is of course pH dependent; in this case, it may well occur that binding takes place on neutral monomers and is then accompanied by uptake or release of protons. Above a given concentration of the free surfactant, when the critical surfactant/polyelectrolyte ratio is approached, the complex phase separates. With hydrogels, this phase separation manifests itself first as a local collapse of the polyelectrolyte network, which subsequently expands through the entire gel sample at higher surfactant loading. * Corresponding author. (1) Hayakawa, K.; Kwak, J. C. T. J. Phys. Chem. 1982, 86, 3866. (2) Picullel, L.; Lindman, B. Adv. Colloid Interface Sci. 1992, 41, 149. (3) Hansson, P.; Lindman, B. Curr. Opin. Colloid Interface Sci. 1996, 1, 604-613. (4) Picullel, L.; Lindman, B.; Karlstro¨m, G. In Polymer-Surfactant Systems; Kwak, J. C. T.; ed.; Marcel Dekker: Basel, 1998; p 65. (5) Mel’nikov, S. M.; Sergeyev, V. G.; Yoshikawa, K. J. Am. Chem. Soc. 1995, 117, 2401-2408. (6) Kabanov, V. A.; Zezin, A. B.; Rogacheva, V. B.; Khandurina, Yu. V.; Novoskol’tseva, O. A. Macromol. Symp. 1997, 126, 79-94.

From X-ray studies,8 it has been found that inside the precipitates and gels the sufactant is usually present as a mesophase, often with a lamellar structure. In most of the cases studied so far, the polymers, even when constrained in the form of a sparse network (hydrogel), were relatively free to adjust their conformations to the structure of lowest free energy, and volume constraints did not seem to play a significant role. This may be quite different for binding to a polymer brush, i.e., to an array of chains which are tethered to a surface up to high densities. Since the work of Alexander and de Gennes9 on such systems it is well-known that chains in brushes tend to be strongly stretched due to repulsive interactions between the segments. One might anticipate that at sufficiently high grafting densities the bulky surfactant ions cannot easily be accommodated in the brush, even though they have a strong affinity for the polymer. To the best of our knowledge it is presently unknown whether this will result in smaller binding fractions or whether binding will always reach the stoichiometric level at the expense of a perturbation of the brush conformations. Uptake of surfactant micelles in uncharged brushes was theoretically studied by Currie et al.10,11 These authors treated the micelles as nanoparticles that modify the excluded volume properties of the chains when they bind; as a result the degree of binding couples to the effective interaction between grafted chains and it is possible that (7) Ashbaugh, H. S.; Piculell, L.; Lindman, B. Langmuir 2000, 16, 2529-2538. (8) Bobrov, A. B.; Skorikova, E. E.; Sulyanov, S. N.; Rogacheva, V. B.; Zezin, A. B.; Kabanov, V. A.; Vysokomol. Soedin. A,B 1997, 39, 627. (9) (a) Alexander S. J. Phys. (Paris) 1977, 38, 983. (b) De Gennes P. G. Macromolecules 1988, 13, 1069. (c) De Gennes, P. G. J. Phys. (Paris) 1976, 37, 1443. (10) Currie, E. P. K.; van der Gucht, J.; Borisov, O. V.; Cohen Stuart, M. A. Langmuir 1998, 14, 5740. Currie, E. P. K.; Fleer, G. J.; Cohen Stuart, M. A.; Borisov, O. V. Eur. Phys. J. E 2000, 1, 27. (11) Currie, E. P. K.; van der Gucht, J.; Borisov, O. V.; Cohen Stuart, M. A. Pure Appl. Chem. 1999, 71, 8441-8446.

10.1021/la020457h CCC: $25.00 © 2003 American Chemical Society Published on Web 01/28/2003

Cationic Surfactants Bound to Polyacrylic Acid Brush

nanoparticles are “squeezed” out of the brush when the grafting density increases. Some experimental evidence in this direction was found for proteins11 and for silica nanoparticles.12 However, as yet no theory for binding of ionic surfactants to polyelectrolyte brushes has been forwarded. Polystyrene sulfonate brushes loaded with the surfactant hexadecyl trimethylammonium bromide (CTAB) at a single, fixed bulk concentration of 5 mM (beyond the cmc) were studied by Traˆn and Auroy.13 These authors used neutron reflectivity measurements to investigate the structure and homogeneity of the brush/surfactant complex, and found that stoichiometric binding occurred, but that the adsorption was irreversible, i.e., the surfactant could not be removed from the brush even at 1 M NaCl. In this paper we have studied the interaction between poly(acrylic acid) (PAA) brushes of different densities σ (here given as areas per chain, i.e., σ-1; the values chosen were 2.5, 6.4, 8.6, 11 and 14.5 nm2) and three different alkyltrimethylammonium surfactants, namely, hexadecyl trimethylammonium bromide (CTAB), dodecyl trimethylammonium bromide (DDTAB), and decyl trimethylammonium bromide (DTAB), having hexadecyl (C16), dodecyl (C12), and decyl (C10) as the long alkyl group, respectively. To obtain a binding isotherm of a surfactant by a brush we followed the adsorption by means of time-resolved optical reflectivity experiments in which the brush was brought into contact with flowing surfactant solutions of varying concentrations. The solutions had a fixed pH of 8.5 and contained 0.005 M NaCl. We have chosen pH 8.5 because it was known from titrations that for all densities studied the PAA-chains in brushes are largely charged at pH g 8.5.14 Materials and Methods Surfactants. The surfactants (CTAB, DDTAB, and DTAB, all Aldrich) were used as supplied. Analytical grade sodium chloride and demineralized water (Nanopure) were used to make up appropriate stock solutions. The cmc values of the surfactants depend somewhat on the type and concentration of the added salt (in our study 0.005 M NaCl) and are approximately equal to 0.8, 15, and 60 mM, for CTAB, DDTAB, and DTAB, respectively.15 Preparation of PAA Brushes. Brushes were prepared using the method of Currie et al.14 by means of a Langmuir-Blodgett deposition technique. First, substrates were prepared as follows. Silicon wafers were cleaned by ozonization for 30 min, followed by 2 min of plasma cleaning. Subsequently, they were etched in 5% HF for one minute after which a solution of vinyl-terminated polystyrene (Polymer Source, Inc.) in chloroform was immediately placed on the cleaned surface. The wafers were dried and then heated at 150 °C for 12 h in inert atmosphere. This allows the vinyl groups to react with the silicon, forming a covalent Si-C bond.14 After cooling, the wafers were rinsed in chloroform for 2 min and a layer of polystyrene was applied by spin coating, using PS (M 868800 g/mol) in chloroform (11 g/l) at 2000 rpm for 2 min. This gives a layer of about 70 nm thick. Then a monolayer of polystyrene-b-poly(acrylic acid) (PSPAA) block copolymer (Polymer Source Inc., Canada) of block lengths 43 (PS) and 316 (PAA), respectively, was prepared on a water surface. The polymer was added to 3 mL of 1,4-dioxane and allowed to dissolve in an oven at 60 °C for 48 h. After cooling, 2 mL of toluene was added. The solution was always prepared (12) Gage, R. A.; Currie, E. P. K.; Cohen Stuart, M. A. Macromolecules 2001, 34, 5078-5080 (13) Traˆn, Y.; Auroy, Ph.; Lee, L. T.; Stamm, M. Phys. Rev. E 1999, 60, 6984-6990. (14) Currie, E. P. K.; Sieval, A. B.; Avena, M.; Zuilhof, H.; Sudholter, E. J. R.; Cohen Stuart, M. A. Langmuir 1999, 15, 7116-7118. (15) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physical Chemical Properties of Selected Anionic, Cationic, and Nonionic Surfactants; Elsevier: Amsterdam, 1993.

Langmuir, Vol. 19, No. 6, 2003 2001 immediately before use. In a typical run, 400 µL of the block copolymer solution was spread with the help of a Hamilton microsyringe on a slightly acidic aqueous subphase (pH 4.7) in a Langmuir trough. With the use of the Schaeffer variant of the LB technique,16 the PS-PAA block copolymer was transferred to the substrates at a constant surface pressure, the value of which was chosen such as to achieve the desired density of coverage. As a rule, the transfer ratio was close to unity. Finally, the brushes were annealed as described by Currie14 by heating the dry wafers at about 100 °C for 10 min. This allows the PS block to diffuse into the PS film on the substrate. After cooling, the PAA brushes were stable and ready for use. The grafting density of the brushes so obtained can be reproduced to within about 15%. We ascribe variations from brush to brush mainly to variations in the pressure-area curve and in the transfer ratio, both of which are rather sensitive to minor changes in pH. Adsorption Measurements. Adsorbed amounts were measured by means of optical reflectometry using an impinging jet flow cell, as described by Dijt et al.17 The silicon wafer carrying the brush serves as the reflecting substrate. Calibration was achieved by means of reflectivity calculations, for which the thickness of the polystyrene film (70 nm as determined by ellipsometry) and the refractive indices for silicon (4.8), polystyrene (1.59) and water (1.33), respectively, and the refractive index increments of the surfactants in water are needed. For neutral compounds, the adsorbed amount is then simply obtained from the relation Γ ) Q(∆S/∆S0), where the sensitivity factor ∆S/∆S0 is the normalized change in signal and Q is the sensitivity factor (mg/m2 or mmol/m2). In our case, there is a complication, however, since we are dealing with adsorption of an ionogenic compound. To a certain extent, such adsorption is an ion exchange process. If we assume it is so, binding of a surfactant cation is accompanied by a release of a (sodium) cation, and therefore the refractive index increment of the neutral surfactant (on a molar basis) needs to be corrected for the refractive index increment of the corresponding sodium salt. For all three surfactants dn/dc (on a weight basis) equals about 0.146 mL/g;15 for NaBr the refractive index increment equals 13.8 mL/mol. With molar masses of 280 (DTAB), 308 (DDTAB), and 364 (CTAB) this leads to effective Q-values of 0.268, 0.228, and 0.184 mmol/m2 for DTAB, DDTAB, and CTAB, respectively. It should be realized, however, that it is likely that some (chloride) counterions can be coadsorbed, particularly around stoichiometric degrees of binding. This may lead to an overestimation of the adsorbed amounts by about 10%. Our optical technique does not provide the information to unambiguously correct for that.

Results and Discussion Figure 1 shows a typical result given as adsorbance Γ versus time t; the example is for a PAA-brush brought into contact with a 1 × 10-5 M CTAB solution (curve a). For comparison, we also show the adsorbance curve for a similar CTAB solution onto a (bare) silica surface (curve b). Immediately after the addition of the surfactant one observes a strong increase of G and within approximately 10 min the adsorbance value reaches a plateau. This plateau is maintained as long as the solution concentration remains constant (not shown), implying that the Γ value measured in the plateau region corresponds to equilibrium. The Γ value reached for the brush/CTAB system is about 60 µmol/m2, which is about 100 times higher than that observed for CTAB at the same concentration onto bare silica (Γ ≈ 0.6 µmol/m2). Therefore, we have multiplied the adsorption in this latter case by 100 in Figure 1. At saturation (near the cmc), the amount taken up by the brush still exceeds that of the bare silica by a factor of about 20. Thus, the brush completely dominates the adsorption behavior of the brushed surface, to the extent (16) Roberts, G., Ed. Langmuir-Blodgett Films; Plenum Press: New York, 1990. (17) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. Adv. Colloid Interface Sci. 1994, 50.

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Figure 1. Typical curve for binding (adsorption) of CTAB (1 × 10-5 M) (a) on a PAA-brush (b) onto a silica surface. The adsorbed amounts of curve (b) have been multiplied by a factor 100.

Figure 2. CTAB binding isotherms of the surfactant CTAB on polyanion chains (mol surfactant /mol of monomers): (a) grafted PAA (2.5 nm2 per chain), (b) grafted PAA 14.5 nm2 per chain), and (c) free PAA in solution. All data were obtained at pH 8.5 and at 0.005 M NaCl. CTAB concentrations in mol/dm3. The cmc of CTAB is indicated on the horizontal axis by a vertical line.

that in the presence of the grafted chains any extra adsorption on the substrate can be ignored. After replacing the surfactant solution by water the absorbance value decreases and reaches the baseline within approximately 50 min. This shows that the adsorption process is fully reversible (Figure 1, curve a), in contrast to what is reported for the case of CTAB adsorbing to surfaceattached sulfonated polystyrene.13 Adsorption-desorption curves for all brushes and the various surfactants (CTAB, DDTAB, and DTAB) have been obtained for concentrations ranging from 5 × 10-7 M up to just above the cmc. All of them have similar shapes, but the times needed to achieve the maximal adsorbance values are of course different for the various surfactant homologues and depend in a complicated way on the surfactant concentration. These kinetic effects will be the subject of a later paper; here we focus on the equilibrium binding isotherms Γ(c) which can be read from the plateau region in the Γ(t) curves. Figure 2 shows various binding isotherms for cationic CTAB on PAA. Two curves are for different PAA-brushes (2.5 nm2, a, and 14.5 nm2, b, respectively) and a third is

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Figure 3. Surfactant binding isotherms for a PAA brush with 2.5 nm2 per chain: (a) CTAB, (b) DDTAB, and (c) DTAB. The cmc of each of the surfactants is indicated by a vertical line on the horizontal axis.

for free PAA in solution (c). The binding isotherms are presented here as the ratio β of surfactant cations to PAA monomer units, as a function of concentration, on a logarithmic scale; for the brushes β is simply obtained (using appropriate units) from G by the relation β ) Γ/σP, where P is the degree of polymerization of the grafted PAA, in our measurements is equal to 316. For the free PAA the amount of binding was obtained from the decrease in free surfactant concentration caused by binding. One can see in Figure 2 that for both PAA-brushes binding becomes detectable at concentrations of order 1 × 10-6 M which is lower than for free PAA (∼5 × 10-6 M). A more important observation is that the binding isotherms for the two brushes have very different shapes. The isotherm for the dense brush with 1/σ ) 2.5 nm2 has the characteristic S-shape that one finds (in a logarithmic representation) for simple adsorption; it reaches a clear saturation plateau at a relatively low binding degree (β) of about 0.33. The binding isotherm for the dilute brush of 1/σ ) 14.5 nm2 is significantly higher. Moreover, it seems to have two distinct parts: first it seems to reach a plateau (at about 10-4 M), but then it has a tendency to increase further and eventually reaches a binding degree of about 1.2 at a concentration of about 5 mM. Apparently, it depends on the brush density what isotherm type is obtained, i.e., whether there are two binding modes. The cmc of CTAB is indicated in Figure 2 by a vertical bar on the horizontal axis. It can be seen that the surfactant binding isotherm does not level off at the cmc. This may be somewhat surprising given the generally accepted idea that at the cmc the chemical potential of surfactant molecules becomes independent of the total concentration. Yet, similar effects have been seen more often, e.g., when surfactants bind to polymer gels or to microgel particles. We may point out that the chemical potential of micelles does increase with increasing total concentration, so that it seems that the continued binding must be ascribed to increased micelle concentrations. This would imply that it is really the micelle that binds in this stage, rather than the individual surfactant molecules. For very dense brushes (approximately 130 monomers per nm2, σ ) 0.41 nm-2) the degree of binding is never higher than about 0.4 for any of the three surfactants. In Figure 3 we present the three binding isotherms for the very dense brush (2.5 nm2 per chain) plotted on a logarithmic concentration axis. The brush isotherms are similar in shape to those for free PAA in bulk solution,

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Figure 4. Binding isotherms of three surfactants on a PAA brush, as given in Figure 3 replotted in Langmuir coordinates; (a) CTAB, (b) DDTAB, and (c) DTAB.

but reach their plateau at a relatively low degree of binding. It can be seen that the isotherms are shifted toward higher concentrations for shorter hydrophobes, about in the same way as the cmc’s (indicated by vertical lines in Figure 3). Indeed, the value of c1/2/cmc, where c1/2 is the concentration where Γ is half the plateau value, are 0.05, 0.08, and 0.02 for DTAB, DDTAB, and CTAB, respectively. To analyze the isotherm shapes we replot, in Figure 4, the three isotherms of Figure 3 according to the simple Langmuir adsorption isotherm:18

Csurf Csurf 1 ) + Γ KΓmax Γmax

(1)

where Csurf is the concentration of the surfactant in the bulk solution, Γmax is the maximum (saturated) adsorption, and K is the equilibrium constant. All three isotherms are reasonably linear in this representation. This seems to imply that for this densest brush the surfactant molecules absorb onto the brush independently from each other, as if it were a simple noncooperative ion exchange process. In principle, one can obtain the value of K from the plot by taking the ratio of slope and intercept. We find K ) 7 × 102, 3 × 103, and 3 × 106 for DTAB, DDTAB, and CTAB, respectively. However, the error in the intercept of the fitted straight lines is substantial so that we do not intend to interpret these values further. (18) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: New York, 1995; Vol II.

Figure 5. Surfactant binding isotherms for a PAA brush with 8.6 nm2 per chain: (a) CTAB, (b) DDTAB, and (c) DTAB. As in Figure 3, the cmcs are indicated.

If we consider a brush with lower density (8.6 nm2 per chain) (Figure 5), we see that the binding isotherms again shift to higher concentrations for the surfactants with shorter hydrophobe. However, the low plateau of about β ∼ 35% is observed only for the longest surfactant (CTAB); the two shorter surfactantssDDTAB and DTABsboth appear to have a second adsorption mode where β increases sharply, bringing it close to unity. Note that we have an uncertainty of about 15% in σ, which may well account for the fact that some β-values may seem to exceed unity.

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Figure 6. Binding isotherms of Figure 5 replotted in Langmuir coordinates: (a) CTAB, (b) DDTAB, and (c) DTAB.

Figure 7. Surfactant binding isotherms for a PAA brush with 14.5 nm2 per chain: (a) CTAB and (b) DDTAB. As in Figure 3 and 5, the cmcs are indicated.

Plotting the same three isotherms on “Langmuir coordinates” (Figure 6) we find a straight line for CTAB but large deviations from linearity for DDTAB and DTAB, in line with the more complex shapes observed in Figure 5. Finally, we have decreased the grafting density to 14.5 nm2 per chain, which is close to the limit of the “brush” regime.9 Figure 7 shows binding isotherms for this brush and for the two longest surfactants (CTAB and DDTAB). For both surfactants, the isotherms have a “two step” character; for DDTAB, β reaches approximately 100% in

the second step. (For CTAB this does not seem to occur but the concentration corresponding to these data point may have been slightly in error). Figure 8 shows that the isotherms for these cases are definitely nonlinear in “Langmuir coordinates”. Considering the entire set of data, we draw as our first conclusion that the adsorption phenomena described above have new and unusual features that cannot be explained with traditional adsorption models. Clearly, the grafting density plays a significant role: the higher the density, the higher the surfactant concentration where the second step of the isotherm, leading to full loading of the polymer chains, occurs. Such a second step at higher concentration does not occur for free chains in solution and indicates that the chemical potential of the bound surfactant during this second step is enhanced, probably because of volume constraints. Indeed, when the grafting density is sufficiently high, the second step is even entirely suppressed (the case of 2.5 nm2 per chain). On the other hand, binding during the first step seems to occur more easily, i.e., at a lower chemical potential, than on free chains. To arrive at a qualitative explanation of these data we first recall that, initially, the brush is in a swollen state. A major part of the acid groups is dissociated and the sodium counterions exert a strong osmotic pressure, causing swelling. As a result, the chains in the brush are also stretched at the cost of some conformational entropy. (We should point out here, that the degree of dissociation is very likely below unity. From titration data, it is known that PAA in dilute solution is largely in the salt form at pH 8.5, the degree of neutralization a being 0.9 or more.

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Figure 9. Maximum degree of binding as a function of inverse grafting density () area per chain) for CTAB (a), DDTAB (b), and DTAB (c).

Figure 8. Binding isotherms of Figure 7 replotted in Langmuir coordinates; (a) CTAB and (b) DDTAB.

However, in dense brushes, neutralization is partly suppressed because of the entropic penalty connected to chain stretching. As a result, R is usually somewhat lower. From optically detected titrations as described by Currie14 we find that at pH 8.5 R ) 0.8-0.9 for the brushes with σ ) 2.5 and 6.4 nm2.) When sodium counterions in a dense brush are exchanged for trimethylammonium (surfactant) cations, this may occur in two ways. First, the surfactant could bind to the most accessible part of the brush, namely the periphery where the segment density is not as high as deeper inside the brush. In this case, a large fraction of the brush does not participate in the binding process, which might explain why the binding stops at a low degree. However, the strong stretching of the major part of the brush would be maintained, which is very unfavorable; therefore this situation is not very likely to occur. The second possibility is that the surfactant ions penetrate inside the brush but leave the majority of binding sites unoccupied. Because the surfactant ions are very hydrophobic, one should expect that they introduce an attractive interaction between the polymer segments so that in this case the osmotic pressure decreases very sharply. Indeed, it is well-known that swollen polyelectrolyte gels shrink (collapse) upon binding of an oppositely charged surfactant, which implies that the effective interaction between polymer segments has become attractive. The decrease in osmotic pressure allows the chains to reduce their degree of stretching, which thus favors the binding as compared to unstretched chains. If

the attraction is still stronger, it is even conceivable that the polymer chains collapse already at this low binding, and that this process is accompanied by exchange of sodium counterions for protons, so that the charge density drops to very low values. The surfactant ions are very bulky though, having volumes much larger than hydrated sodium ions. Typically, their apolar parts have molecular volumes vsurf on the order of 0.30-0.46 nm3,15 whereas one has about 0.002 nm3 for hydrated sodium ions. Stuffing a brush by exchanging each of the 316 small sodium counterions per chain by a surfactant ion would require an extra volume of about 100 to 120 nm3 per chain. Together with the volume of the chain itself (vmon equals about 0.26 nm3 per monomer if we do not allow for hydration) and the grafting density this gives a lower limit to the height of the brush needed to accommodate all the surfactant. For the densest brush at 2.5 nm2 per chain and CTAB one finds that this lower limit is even beyond the contour length (about 85 nm) of the chain. Clearly, full binding is entirely impossible in this case. For less dense brushes or smaller surfactants the height needed is still well beyond the radius of gyration of about 10 nm. Hence, it seems likely that the surfactant and polymer together prefer to form a highly ordered phase of low entropy, but for this phase to appear, the chemical potential of the surfactant must exceed a certain threshold value. One might even think that the transition between the fully loaded, swollen case and the partially loaded, collapsed state is discontinuous, but this is not supported by our data, probably because the configurational entropy of the chains does not allow this to happen. As can be seen in Figure 3, none of the three isotherms for the most dense brush has a second step. From the volume constraint argument we can see that indeed even the shortest alkyl tail requires stretching to about 80% of the contour length of 85 nm. This implies a highly constrained shape of the chain which may be incompatible with an optimal packing of surfactant and polymer in the fully loaded complex, to the extent that it does not occur. That it is indeed the surfactant volume that determines whether a transition to full loading is possible can be seen by considering the degree of binding at the highest surfactant concentration, as a function of (inverse) brush density. If the brush density would not play a role, this should be a constant. Figure 9 shows these results for CTAB, DDTAB, and DTAB. One can see that, for all three surfactants, the maximum degree of binding remains low

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Figure 10. Area per chain in the transition region (taken at β ) 1.0) as a function of the length (number of carbon atoms) of the surfactants’ alkyl tail.

at a level between 0.2 and 0.4 for dense brushes (small area per chain); increase to the stoichiometric binding level does not occur until the brush becomes sufficiently dilute. For DTAB this occurs at about 6.7 nm2, for DDTAB this is slightly higher (σ-1 ) 8.2 nm2) and for CTAB the increase occurs around σ-1 ) 10.2 nm2. Taking the area per chain for which β equals 1.0 as the (arbitrarily chosen) transition point beyond which the “second step” appears, we find that this shifts linearly with the number of carbon atoms in the alkyl chain, with a slope of 0.5 nm2 per carbon atom (Figure 10). As Figure 9 also makes clear, the transition from partial to complete loading of the brush occurs over an interval of about 3 nm2; in this range the isotherms probably gradually change their shape from the “Langmuir” type exemplified in Figure 3 to the “two mode” type as seen, e.g., in Figure 5. Unfortunately, we do not have a complete set of isotherms over this range that we can show here. Finally, the data of Figure 9 can also give us some idea of the approximate degree of stretching occurring in the fully loaded brush. For all three surfactants, we can calculate that when the degree of binding reaches a value of unity the volume of the “stuffed” chain (even without solvent) is such that the brush height is at least 20 nm, i.e., about twice the height of a dilute brush of PAA at high ionic strength.14 Hence the minimum area per chain that is needed to allow full stoichiometric binding equals [316(vmon + vsurf)]/20 nm2. This comes out at 8.8, 9.6, and 11.3 nm2 for DTAB, DDTAB, and CTAB, respectively. An interesting question is what structures are formed in the second step of the isotherm. It is known, e.g., from

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work by Zezin et al.8 and from Hansson19 that in gels a special phase is formed with a lamellar morphology in which the hydrocarbon tails partially overlap. The interlamellar spacing in these complexes were found to be 4.2 and 3.8 nm for CTAB and DTAB, respectively. It seems quite likely that a similar phase forms in the brushes. Since the brush has anisotropic character, one would expect that the lamellae also have a preferred orientation, e.g., parallel or perpendicular to the surface. Parallel orientation seems to be the best to adjust to the orientation of the interfaces (substrate/brush, brush/solution) and was recently found to occur for mixtures of free polyelectrolytes and ionic surfactants near a water/air interface,20 but perpendicular orientation allows for a more uniform distribution of conformations over the chains. Probably, the real structure is a compromise with perpendicular orientation within the brush, and parallel at its peripheries. Neutron reflectivity studies should be able to clarify this further. Conclusions Dense brushes of poly(acrylic acid) bind trimethyl alkylammonium surfactants reversibly. The binding isotherm, defined as the number of surfactant molecules per monomer unit as a function of concentration, has a shape that depends strongly on grafting density of the brush and on the surfactant’s alkyl chain length. Three alkyl chain lengths have been studied: decyl (C10), dodecyl (C12), and hexadecyl (C16). At small areas per chain (dense brushes) the maximum degree of binding, measured at concentrations around the cmc of the surfactants never exceeds about 40%. In this case the isotherms have shapes consistent with the simple Langmuir equation. For less dense brushes the isotherms have a second step which can lead up to full binding; for such brushes the isotherm shape deviates strongly from the Langmuir type. The maximum degree of binding shows a transition from about 40% to 150% over a range of grafting densities; the midpoint of this transition shifts linearly with the area per chain in the brush. The occurrence of the second step is probably due to the formation of a lamellar mesophase in the polyelectrolyte/surfactant complex, accompanied by increased stretching of the PAA chains. Acknowledgment. O.P. thanks dr. V. Rogacheva, Moscow State University, and dr. A.A. Zinchenko, Nagoya University, for helpful discussions. We also acknowledge the Dutch Science Foundation NWO for financial support of the collaboration between Wageningen and Moscow under Grant 047.007.001. LA020457H (19) Hansson, P. Langmuir 1995, 11, 4059-4064. (20) Thomas, R. K. Personal communication.