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Polyacrylic Acid Brushes: Surface Pressure and Salt-Induced Swelling E. P. K. Currie,*,†,‡ A. B. Sieval,§ G. J. Fleer,† and M. A. Cohen Stuart† Laboratory of Physical and Colloid Chemistry, and Laboratory of Organic Chemistry, Wageningen University, 6703 HB Wageningen, The Netherlands Received November 24, 1999. In Final Form: July 3, 2000 Polyelectrolyte brushes consisting of polystyrene-poly(acrylic acid) (PS-PAA) diblock copolymers were investigated experimentally using surface pressure isotherms and ellipsometry. The surface pressure π of the block copolymers at the air/water interface was measured as a function of the grafting density σ at various salt concentrations and pH. It is concluded that the scaling behavior of π(σ) of long PAA chains at high ionic strengths and low pH agrees with predictions of analytical mean-field models. The theoretical predicted scaling behavior of π(σ) for annealed brushes at low ionic strength and low pH is not observed because of adsorption of the polyacid chains to the air/water interface. The thickness of PAA brushes on hydrophobically modified Si wafers was measured with ellipsometry as a function of pH, total ionic strength I, and σ. It is observed that at a given pH the brush thickness behaves nonmonotonically as a function of I (i.e., it initially increases and subsequently decreases with increasing I). This nonmonotonic behavior agrees with theoretical predictions for annealed brushes. The experimentally observed scaling exponent R in the power law H ∼ IR is ∼0.1, which is less than that predicted theoretically (1/3).
Introduction Charged brushes (i.e., polyelectrolytes end-grafted at high grafting densities) have in the past decade been recognized as an exciting state of matter. The combination of short-range steric forces, long-range electrostatic interactions, and conformational effects (also referred to as elastic forces) has yielded a large variety of predicted brush regimes in theoretical studies.1-8 A distinction is generally made in these studies between brushes consisting of grafted polyelectrolytes with a fixed fraction of charged monomers (quenched) and polyelectrolytes with a variable fraction of charged monomers (annealed). An example of the former are brushes consisting of sodiumpolystyrene-sulfonate (NaPSS).9-11 An example of the latter are brushes consisting of poly(acrylic acid) (PAA) or poly(methacrylic acid) (PMAA), the charge density of which depends on the pH and the salt concentration, but also on the grafting density and on the distance from the grafting plane.4-6,12,13 In this paper we concentrate on the experimental properties of the latter brush species. * To whom correspondence should be addressed (e-mail:
[email protected]). † Laboratory of Physical and Colloid Chemistry. ‡ Current address: DSM Research, P.O. Box 18, 6160 MD Geleen, The Netherlands. § Laboratory of Organic Chemistry. (1) Pincus, P. Macromolecules 1991, 24, 2912. (2) Borisov, O. V.; Birshtein, T. M.; Zhulina, E. B. J. Phys. II Fr. 1991, 1, 521. (3) Borisov, O. V.; Zhulina, E. B.; Birshtein, T. M. Macromolecules 1994, 27, 4795. (4) Zhulina, E. B.; Birshtein, T. M.; Borisov, O. V. Macromolecules 1995, 28, 1491. (5) Lyatskaya, Y. V.; Leermakers, F. A. M.; Fleer, G. J.; Zhulina, E. B.; Birshtein, T. M. Macromolecules 1995, 28, 3562. (6) Israe¨ls, R.; Leermakers, F. A. M.; Fleer, G. J. Macromolecules 1994, 27, 3087. (7) Misra, S.; Tirrell, M.; Mattice, W. Macromolecules 1996, 29, 6056. (8) Zhulina, E. B.; Borisov, O. V.; Birshtein, T. M. Macromolecules 2000, 33, 3488. (9) Mir, Y.; Auroy, P.; Auvray, L. Phys. Rev. Lett. 1995, 75, 2863. (10) Guenoun, P.; Schlachli, A.; Sentenac, D.; Mays, J. W.; Benattar, J. J. Phys. Rev. Lett. 1995, 74, 3628. (11) Amiel, C.; Sikka, M.; Schneider, J. W.; Tsao, Y.; Tirrell, M.; Mays, J. W. Macromolecules 1995, 28, 3125. (12) Currie, E. P. K.; Sieval, A. B.; Avena, M.; Zuilhof, H.; Sudho¨lter, E. J. R.; Cohen Stuart, M. A. Langmuir 1999, 15, 7116.
Theoretical studies predict that the annealing of charge on the grafted chains results in a rather complicated behavior of annealed brushes. As the fraction of dissociated monomers R can be expected to vary as a function of the pH, salt concentration, grafting density, and distance to the grafting plane, the effective osmotic pressure in the grafted layer is expected to vary as well.4-6 In this paper we consider weak polyacid polymers for which a degree of dissociation Rb in the bulk is defined. This amount is the average degree of dissociation a monomer has in the bulk solution at a certain pH:
Ka 1 - Rb ) Rb FH+
(1)
where Ka is the monomer dissociation constant and FH+ is the proton concentration in the bulk solution. Note that Rb is fully determined by the pH of the solution and varies between 0 and 1. At high salt concentrations (i.e., FS . FH+), the proton concentration in the brush is approximately equal to that in the bulk because the dissociated protons in the brush are exchanged with indifferent salt ions from the bulk while maintaining electroneutrality in the brush.1,4,5,14 This regime is known as the salted brush (SB) regime. Mean-field models predict the scaling relationships for the height and surface pressure of annealed brushes to be4
()
H ∼ Nσ1/3 and
R2b Fs
1/3
()
π ∼ Nσ5/3
R2b Fs
(2)
2/3
(3)
(13) Kurihara, K.; Kunitake, T. Langmuir 1992, 8, 2087. (14) We remark that the phrase indifferent counterions denotes electrolytes that solely screen electrostatic interactions and do not alter the electrostatic potential of the screened species (see, e.g., Hunter, R. J. Foundations of Colloid Science, Oxford University Press: New York 1986, Vol 1). An alternative definition is counterions with a sufficiently large dissociation constant.
10.1021/la991528o CCC: $19.00 © 2000 American Chemical Society Published on Web 09/29/2000
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where N is the chain length and the grafting density σ is defined as the number of grafted chains per unit area. In the limit of zero salt concentration, the proton concentration in the brush is significantly higher than in the bulk phase because the exchange of dissociated protons with indifferent counterions is suppresed. As a result, the degree of dissociation in the brush is lower than that of the bulk (i.e., R < Rb). The overall counterion density, in the brush however, is low and each ion is assumed to contribute on the order of kBT to the osmotic pressure in the grafted layer. This regime is referred to as the annealed osmotic brush regime (O ˜ sB). In a mean-field scaling model, the average degree of dissociation in the brush at low pH and low salt concentration has been derived to be4
R≈
(
Rb σ-1(FH+ + Fs) 1 - Rb
)
2/3
(4)
In the model of Zhulina et al.,4 only an average or overall value of R is considered. In more detailed analytical or numerical models, the variation of R throughout the brush [i.e., R(x)] is taken into account.5,6 From the expression just presented, it follows that for a given pH (i.e., a fixed Rb), R decreases with increasing grafting densities. At high grafting densities, R may become low enough for the brush to effectively be a neutral brush. Note that R is predicted to increase with the salt concentration until it evidently reaches its bulk value at high concentrations. As mentioned, the brush thickness is determined by a balance of electrostatic, steric, and conformational forces. In mean-field scaling models, the steric interactions are neglected in the O ˜ sB-regime. The equilibrium brush thickness is a balance between the electrostatic interactions of the charged monomers, which induce stretching, and the conformational entropy of the chain, which opposes stretching. The brush height in the O ˜ sB regime is predicted to scale as4
(
H ∼ Nσ-1/3
)
Rb 1 - Rb
combined contribution of the anchoring and bouy block to π, investigation of power law exponents of π(σ) and subsequent identification of conformational regimes was not possible. The thickness of a polybase brush was investigated with neutron reflectivity by An et al.16 The brush thickness at fixed grafting density was found to increase with increasing pH (i.e., increasing fraction of charged monomers). However, the results were not compared with any scaling law for annealed brushes in the O ˜ sB regime. To our knowledge, experimental evidence of the peculiar features of the O ˜ sB regime (i.e., a maximum in the brush thickness with increasing ionic strength or a decrease in thickness with increasing grafting density) has not been given to date. In previous papers we used polystyrene (PS)-polyethylene-oxide (PEO) block copolymers at an air/water interface to prepare neutral brushes of controlled chain length and grafting density.17-19 As demonstrated by Currie et al.,18 valuable information concerning the conformation of grafted polymers may be obtained from analysis of surface pressure isotherms. In particular, the predicted scaling relationship of π(σ) for neutral brushes (π ∼ σ5/3) was observed experimentally by analyzing such isotherms. We therefore perform similar analyses on the surface pressure isotherms of PS-PAA monolayers to determine the conformation of the grafted PAA chains under various conditions. In addition, we recently reported a novel technique for transferring PS-PAA block copolymers from the air/water interface to a hydrophobically modified Si wafer.12 In this way, weak acidic brushes are prepared at a controlled grafting density. In this paper, the thickness of such PAA brushes on modified Si wafers is measured with ellipsometry as a function of the pH, ionic strength, and grafting density. Using this technique, we can experimentally check the theoretically predicted nonmonotonic behavior of the thickness of an annealed brush.
2/3
(FH+ + Fs)1/3
(5)
Using a simple scaling model, the paradoxal result is obtained that the brush thickness in the O ˜ sB regime may decrease with increasing grafting density or increase with increasing salt concentration. With increasing salt concentration, however, the brush enters the salted brush regime. In this regime, the brush thickness is predicted to decrease with increasing salt concentration (see eq 2). Thus, using simple arguments, the mean-field scaling model of Zhulina et al.4 predicts a maximum in the PAA brush thickness as a function of the ionic strength, provided the pH and grafting density remain constant. Experimental evidence for the brush regimes just presented, however, is scarce. The surface forces between monolayers of anchored PMAA chains were measured by Kurihara and Kunitake.13 It was observed that the repulsive forces between two grafted polymeric monolayers increased with increasing salt concentration. The thickness of NaPSS (quenched) brushes of constant grafting density was investigated experimentally with X-ray reflectometry by Guenoun et al. as a function of the ionic strength.10 They concluded that in the SB regime, H decreases as a function of the ionic strength with the predicted scaling exponent -1/3 (see eq 2). Surface pressure isotherms of block copolymers with a long hydrophobic (polyethylene) and hydrophilic (NaPSS) block were measured by Ahrens et al.15 However, because of the (15) Ahrens, H.; Fo¨rster, S.; Helm, C. A. Macromolecules 1997, 30, 8447.
Materials & Method The PS-PAA block copolymers were synthesized by Polymer Source Inc., Quebec. The investigated block copolymer samples were PS(33)-PAA(368) and PS(36)-PAA(122), and were used as received. The size of the blocks denotes the number of monomers. The reported polydispersities were 1.06 and 1.05, respectively. The block copolymer was first dissolved for 2 days at 60 °C in dioxane, after which toluene was added to obtain a solution of 1 g L-1 in a 60%/40% dioxane/toluene mixture. This mixing of solvents is necessary because PAA does not dissolve in the usual organic spreading solvents, such as pure chloroform or toluene, because of its polarity. With this mix of solvents, the density of the spreading solution is lower than that of water, which facilitates deposition. Also, the solvent is sufficiently hydrophobic to prevent loss during spreading. It must be remarked that aged solutions showed hysteresis in the surface pressure isotherms, which is attributed to slow coagulation of the diblock copolymer. Therefore, only the reversible results of freshly prepared solutions are discussed. Deposition of the polymer solution on the air/water interface in a Teflon Langmuir trough was done with a Hamilton precision microsyringe, after which the toluene was allowed to evaporate for ∼0.5 h. Typically, 50-100 µL of polymer solution was deposited on the trough interface (600-80 cm2). The surface pressure (16) An, S. W.; Thirtle, P. N.; Thomas, R. K.; Baines, F. L.; Billingham, N. C.; Armes, S. P.; Penfold, J. Macromolecules 1999, 32, 2731. (17) Bijsterbosch, H. D.; de Haan, V. O.; de Graaf, A. W.; Mellema, M.; Leermakers, F. A. M.; Cohen Stuart, M. A.; van Well, A. A. Langmuir 1995, 11, 4467. (18) Currie, E. P. K.; Leermakers, F. A. M.; Cohen Stuart, M. A.; Fleer, G. J. Macromolecules 1999, 32, 487. (19) Currie, E. P. K.; Wagemaker, M.; Cohen Stuart, M. A.; van Well, A. A. Macromolecules 1999, 32, 9041.
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measurements were performed with a Teflon Langmuir film balance with a moving barrier. The (de)compression rate was standard 10 mm2 s-1, and the temperature was 296 ( 0.5 K. The surface pressure was measured continuously with a Wilhelmy platinum plate tensiometer. The sensitivity of the tensiometer is 0.02 mN m-1. Several (de)compression isotherms were obtained during each measurement. The subphase consisted of deionized water to which HCl, NaOH, and NaCl (Merck) were added to set the pH and salt concentration at the desired value. The deposited block copolymer layer was stable up to surface pressures of the order 45 mN m-1. Above this surface pressure, polymer was irreversibly lost in the bulk phase. More details on measurement of surface pressure isotherms of block copolymers are given by Bijsterbosch et al.17 It must be noted that it is assumed that no block copolymers are lost directly after deposition (i.e., the surface densities are directly derived from the deposited amount). Currie et al.,19 using neutron reflectivity, showed that this assumption was reasonable for similary deposited PS-PEO. Si wafers coated with PS and PS-PAA were prepared as described by Currie et al.12 and Sieval et al.25 In short, a Si wafer is etched in 5% HF for a few minutes to remove the oxide layer. Subsequently, the wafer is placed for 2 h in a 5% styrene solution in toluene at 150 °C, in a N2 environment under reflux conditions.25,26 The result is a chemically and thermally stable, covalently bonded styrene monolayer on the Si wafer. The thickness of this layer, measured with ellipsometry, is ∼2 nm. A PS layer of ∼65 nm is spin-coated on the modified wafer at 3000 min-1 from a 10 g L-1 solution of PS (43 K) in chloroform and dried with N2. The result is a Si wafer hydrophobized with PS, the optical properties of which are insensitive to changes in pH or ionic strength. This feature is essential because the change in optical properties of PS layers coated with PAA is measured as a function of the pH and ionic strength with ellipsometry. We note that during the grafting reaction a few oligomers may form in the styrene monolayer. Because a PS layer of 65 nm is spincoated on top of the monolayer, these oligomers are of no importance and may even serve to improve the stability of the spin-coated PS layer. PS-PAA monolayers were prepared on a clean H2O subphase in a Langmuir trough as described previously. The PS-PAA block copolymers subsequently were transferred from the air/ water interface to the coated PS layers by the Schaeffer variant of the familiar Langmuir-Blodgett (LB) technique.27 The transfer ratio was close to one. Following this, the wafers were first dried in air to evaporate the water layer on the LB layer, and subsequently heated at 150 °C for 10 min on a heating stage. Immediate heating above 100 °C after dipping resulted in layers that by eye appeared to be damaged. This damage was probably due to the rapid retreat of the water layer. During heating above the glass temperature of PS ((100 °C), the PS blocks of the PSPAA block copolymers diffuse into the spin-coated PS layer.28 After cooling, the PS layer becomes glassy again, and the PS blocks are firmly ‘rooted’ in the PS sublayer. In this manner, the block copolymers are irreversibly fixed at the grafting density at which the LB film is prepared. Without this thermal annealing, the PAA layer is unstable in solutions of high pH (i.e., the PSPAA are pulled from the wafer) as a result of the high electrostatic potential in the PAA layer. The PAA-PS-Si wafers were placed in an optical cell containing a known volume of pure, deionized H2O at a certain pH. After measurement of the ellipsometric parameters ∆ and (20) Forne´s, J. A. Langmuir 1997, 13, 2779. (21) Landau, E. M.; Lifstitz, L. P. Statistical Physics, 3rd ed., Part 1; Pergamon Press: New York, 1980. (22) Birdi, K. S. Lipid and Biopolymer Monolayers at Liquid Interfaces, Plenum Press: New York, 1989. (23) Cao, B. H.; Kim, M. W. Faraday Discuss. 1994, 98, 245. (24) Vilanove, R.; Poupinet, D.; Rondelez, F. Macromolecules 1988, 21, 2880. (25) Sieval, A. B.; Vleeming, V.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 1999, 15, 8288. (26) Sieval, A. B.; Demirel, A. L.; Nissink, J. W. M.; Linford, M. R.; van der Maas, J. H.; de Jeu, J. H.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir, 1998, 14, 1759. (27) Langmuir-Blodgett Films; Roberts, G., Ed.; Plenum Press: New York, 1990. (28) Brandrup, J.; Immergut, E. H. Polymer Handbook, 3rd ed.; Wiley: New York, 1989.
Currie et al. Ψ (vide infra), an amount of a 1 M NaCl solution at identical pH was added. In this manner, a ∆,Ψ curve was obtained for a PAA brush at a given pH and varying ionic strength I.29 Care was taken to maintain the laser beam on the same spot of the Si wafer during measurement of the ∆,Ψ curve to ensure that small lateral inhomogeneities in the spin-coated PS layer would not influence the outcome. The measurements were performed with a Multiskop ellipsometer from Optrel, Germany. The optical cell was obtained from Akzo Nobel and has two planar faces at 20° with respect to the normal. The arms of the ellipsometer were mounted to give an angle of incidence of 70° with respect to the normal. The laser used was a He-Ne laser with a wavelength of 632.8 nm. The measurements were done at room temperature. A brief review of ellipsometry is given; for a throrough treatment we refer to Born and Wolf30 and Tompkins.31 The electric field of a reflected laser beam may be divided into a component polarized parallel to the plane of reflection (p) and a component polarized perpendicular to this plane (s). When a beam in medium R encounters a single R,β interface at an angle φ, part of the beam is reflected at the same angle and part is refracted at an angle φ′, given by Snell’s law (sin φ′ ) sin φnR/ nβ).32 The reflection of both components is expressed by the p,s 30,31 : Fresnel coefficients rRβ p rRβ )
nβ cos φ - nR cos φ′ nβ cos φ + nR cos φ′
s rRβ )
nR cos φ - nβ cos φ′ nR cos φ + nβ cos φ′
(6)
In our case of a coated Si wafer in contact with water, at least two interfaces are to be considered: water-polymer (Rβ) and polymer-Si (βγ). The overall reflection coefficients, taking internal reflection into account, are given as:30,31
Rp )
p + rpβγ exp(-2idp) rRβ p 1 + rRβ rpβγ exp(-2idp)
Rs )
s + rsβγ exp(-2idp) rRβ s 1 + rRβ rsβγ exp(-2idp)
(7) where dp denotes the thickness of the polymer layer, and i ) x-1. In the case that one or more of the media are nondielectric, for instance Si, the complete refractive index n˜ ) n - in′ must be taken into account. We now denote the initial phase difference between the parallel and perpendicular polarized components of the incident beam as δ1. If that of the outgoing, reflected beam is δ2, the overall phase difference that occurs on reflection is
∆ ) δ1 - δ2
(8)
Furthermore, the ratio of the amplitudes of both reflected components is given as
tan Ψ )
|Rp| |Rs|
(9)
Equation 9 can be combined to an overall equation for the reflection of a polarized beam on a surface as follows:
Rp ) tan Ψei∆ Rs
(10)
(29) The ionic strength I of a solution is defined as I ) 1/2∑iFiz2i , where the summation over i is over all electrolyte species, Fi is the density or concentration of each species, and zi is the valence. Note that in our system, I is a sum of the proton concentration and the salt concentration. (30) Born, M.; Wolf, E. Principles of Optics, 5th ed.; Pergamon Press: Oxford, 1975. (31) Tompkins, H. G. A User’s Guide to Ellipsometry; Academic Press: San Diego, 1993. (32) Here we have assumed that both media R and β are dielectrics (i.e., the imaginary part of the refractive index is zero). (33) Be`rard, D. R.; Patey, G. N. J. Chem. Phys. 1992, 97, 4372. (34) Go¨bel, J. G.; Besseling, N. A. M.; Cohen Stuart, M. A.; Poncet, C. J. Colloid Interface Sci. 1999, 209, 129.
Polyacrylic Acid Brushes
Figure 1. The bulk degree of dissociation Rb of PAA as a function of the pH for three salt concentrations.
Figure 2. Surface pressure of PS(33)-PAA(368) (in unit mN m-1) plotted linearly and double-logarithmically (inset) as a function of the area per chain σ-1 (nm2) at pH 4.4 and 0.1 M NaCl. Lines with slopes 0.8 and 1.8 are drawn as an illustration in the inset. The quantities ∆ and Ψ are measured and contain information on the optical properties of the reflecting surface. Using a suitable model to mimic the investigated system, ∆ and Ψ may be transformed into physical parameters, such as the layer thickness and density. We return to this point in the following sections.
Results and Discussion Surface Pressure Isotherms. For reference, a titration curve of PAA consisting of 7000 monomers in a bulk solution of 0.001, 0.01, and 0.1 M KNO3 is given in Figure 1. KNO3 is an indifferent electrolyte, similar to NaCl. The degree of dissociation in the bulk Rb is plotted as a function of the pH and it increases slightly with increasing salt concentration at a given pH. The reason for this increase is the decreasing electrostatic cost of dissociation with increasing ionic strength. If we assume that the titration curve may be characterized by an intrinsic pKa, then this value is ∼5.5 for 0.1 M. For the surface pressure isotherms of the PS-PAA diblock copolymers, we start with the simplest system; that is, relatively weakly charged tethered polyelectrolytes in a solution of high ionic strength. In Figure 2 the surface pressure isotherm of PS(33)-PAA(368) at pH 4.4 and 0.1 M NaCl is plotted as a function of σ-1 (area per molecule, in nm2) on a linear scale. In the inset, the same isotherm is plotted double-logarithmically. Figure 2 demonstrates that two density regimes can be distinguished in the
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Figure 3. Surface pressure of PS(33)-PAA(122) plotted linearly and double-logarithmically (inset) as a function of σ-1 at pH 4.7 and 0.1 M NaCl.
isotherm. At low σ, the surface pressure increases slowly, with a power law exponent between 0.7 and 0.9. At high σ, the surface pressure increases more strongly, with a power law exponent of 1.7-1.9. For clarity, two straight lines are drawn in the inset of Figure 2, with a slope of 0.8 at low σ and of 1.8 at high σ. Although it is difficult to pinpoint the grafting density at which the transition from the low-density to the high-density regime occurs, the crossover density is estimated to be of the order 35 nm2 per molecule. Similar results for a smaller PAA block [i.e., PS(35)PAA(122)] are shown in Figure 3 for pH 4.7 and 0.1 M NaCl. This isotherm has a low density regime with a weak increase in surface pressure, a crossover to a second regime at higher densities with high power law exponent (∼3), and a third regime at very high densities, again with a lower exponent. It must be noted that a slight hysteresis occurs in the isotherms at 0.1 M; the surface pressure increases slightly with increasing number of compression/expansion cycles. This increase in surface pressure excludes the usual cause of hysteresis in irreversibly adsorbed monolayers, namely, loss of material. Evidently, the surface pressure must drop during the loss of adsorbed polymers. The hysteresis only affects the magnitude of the surface pressure; the value of the scaling exponents in the doublelogarithmic plots and the crossover densities are identical. This hysteresis is therefore believed to stem from a slow unfolding of the collapsed PAA block over time after deposition on the air/water interface. In the absence of salt and at low pH, the surface pressure isotherms are markedly different. This difference is most evident for the long PAA chains, as shown in Figure 4. Three distinct regimes may be identified in the doublelogaritmic plot; one at low density with a relatively high power law exponent (1.5-2.5), an intermediate regime with a low exponent (0.3-0.5), and, at high densities, again a regime with a high exponent (1.6-2). These regimes, indicated by dotted lines in the double-logarithmic plot in Figure 4, are observed in the case of no added salt or low salt concentration (10-3 M NaCl) in the pH-regime 3 to 5. The three distinct regimes are also observed in the case of short PAA chains under similar conditions (not shown). At pH values >5.5, the clear distinction between several scaling regimes in the isotherms is lost, both in the case of added salt and in the absence of salt (not shown). For 0.1 M added salt, the distinct difference of a low and high density regime gradually dissappears as the pH exceeds
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Figure 4. Surface pressure isotherms of PS(33)-PAA(368) plotted linearly and double-logarithmically (inset) as a function of σ-1 at pH 4.7 in the absence of salt. Dotted lines are drawn in the inset as a guide to the eye.
5.5. The surface pressure at high densities increases more strongly with increasing σ than at low pH (i.e., the exponents in the double-logarithmic plot are higher), but a single power law cannot be fitted to the data. In the absence of salt, the three distinct regimes in the isotherm disappear as the pH exceeds 5.5. The isotherm at pH 6.5 and no added salt for PS(33)-PAA(368) resembles the isotherm with added salt. There is no regime with a constant well-defined scaling exponent, and the (apparent) exponent increases gradually as the grafting density increases. To interpret the isotherms in Figures 2-4, we first consider the contribution of the PS blocks to the surface pressure isotherms. Because the PS blocks are relatively small and collapsed, they merely act as anchors and do not contribute to the surface pressure at the examined densities. This result was checked by spreading PS homopolymer dissolved in chloroform on an air/water interface and measuring π(σ): the resultant surface pressure is zero until the collapsed PS blocks overlap at high densities. Thus, the measured surface pressure in Figures 2-4 is entirely due to the tethered PAA block. Using Figure 1, the average degree of dissociation of the grafted PAA chains in the pH regime 3.5-5 with 0.1 M inert electrolyte is estimated to be of the order 0.1-0.3. The Debye length of the bulk solution is of the order of 1 nm, so the effect of electrostatic screening is strong. The interactions between the dissociated monomers are therefore limited in range, and the value of R of the grafted chains is close to the bulk value Rb. This experimental regime should correspond with the SB regime proposed in mean-field models.4,5 The degree of dissociation in the SB regime is predicted to remain constant up to high grafting densities at constant pH, due to the excess of inert counterions.4-6 At low grafting densitites (i.e., σ < σ*), mean-field theories predict the tethered PAA chains to have a swollen coil conformation, whereas for σ > σ*, a brush conformation is expected. The crossover density σ* is defined as 1/σ* ≈ 4 πR2G, where RG is the radius of gyration of the grafted chain. The predicted scaling behavior of π as a function of σ in the coil and SB regimes is π ∼ σ and π ∼ σ5/3, respectively. These predicted power laws for π(σ) correlate roughly with the observed regimes in Figure 2. At low grafting densities, the surface pressure is low and increases slowly. This result corresponds to the regime of weakly interacting swollen coils. The fact that the surface pressure increases
Currie et al.
less than proportional with σ (the scaling exponent is 0.70.9) indicates that some conformational organization may take place. At high grafting densities, the tethered PAA chains develop strong intermolecular excluded-volume interactions, which result in a strong increase in π with increasing σ. A power law exponent of 1.7-1.9 is found in this regime, which corresponds roughly with the predicted exponent 5/3 in the SB regime of mean-field models.4 The short PAA chains show a similar SB regime, but the exponent at high σ is higher than that of the long chains. Moreover, the width of the scaling regimes with constant power law exponents is less. This result may be due to the fact that effects due to finite chain lengths, which are not taken into account in mean-field models, are relatively important in the case of short end-grafted chains. This explanation agrees with the results for neutral PEO brushes, where solely long PEO chains (N ) 445, 700) are found to obey the mean-field power laws of H(σ) and π(σ).18 Shorter PEO chains also demonstrated a stronger dependence of π on σ. We may conclude from Figure 2 that the crossover of the tethered PAA(368) chains from a coil to a brush conformation occurs at 1/σ* ≈ 35 nm2. According to meanfield models, the crossover density σ* is given as 1/σ* ≈ 4πR2G ) cN6/5, where c is a numerical prefactor that contains, among others, the effective virial coefficient υeff. Inserting the values for PAA(368) we find that c is ∼0.175. If we use this value to determine the crossover density of PAA(122) under the same conditions, 1/σ* is equal to 9 nm2, which corresponds nicely with the apparent transition density in Figure 3. Such agreement would not be found if the scaling law for the coil size (i.e., RG ∼ N3/5) is strongly disobeyed. Thus, the conformational transition at σ*-1 is believed to be a coil-to-SB transition. Using the same reasoning as just presented, it is tempting to also interpret Figure 4 with the mean-field theory for annealed brushes in the O ˜ sB regime, as the low pH (low R) and zero added salt correspond to the specified theoretical conditions.4,5 According to this mean-field theory, the polymeric monolayer at low σ (regime 1) consists of weakly interacting, charged chains (R ≈ Rb). As σ increases (regime 2), the overall degree of dissociation in the brush decreases (see eq 4). In other words, the chains are effectively neutralized as σ increases. At high σ (regime 3), the brush effectively consists of neutral chains (R ≈ 0), and the scaling relationships for H and π are predicted to be those of neutral brushes. Regime 1 should correspond with the regime at small σ, with the power law exponent of the order 2 in Figure 4; regime 2 should correspond with the intermediate density regime, with power law exponent 0.3; and regime 3 should correspond with the regime at high σ, with an exponent of the order 1.8. As we will demonstrate, this interpretation is too simple because it does not consider adsorption effects of grafted PAA to the air/water interface. Adsorption of the tethered PAA chains at low pH and zero added salt may prevent the occurrence of the O ˜ sB-regime because the PAA chain has a pancake conformation instead of a brush conformation. The consequence is that in this regime, a PAA brush is only obtained at high grafting densities (i.e., when the density is far above the overlap density of pancakes).17,18 To start with, the saturated pressure of PAA homopolymer solutions (11 K and 29 K, 0.01 g L-1 was measured with and without salt. At pH 3 and no added salt, a saturated surface pressure of ∼3.8 m Nm-1 is observed. In contrast, the saturated surface pressure in the pH regime 3-5 and 0.1 M NaCl is approximately zero.
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Figure 5. The renormalized fluctuation density ΥR as a function of the area per chain σ-1 (nm2) for PS-PEO(445) and PS-PAA(368) at pH 4.7 and no added salt. The PEO data are taken from ref 17. The curves are a guide to the eye.
At pH 5.5 and above, the saturated surface pressure is close to zero, both for no added salt and 0.1 M NaCl. Adsorption of grafted PAA chains can be demonstrated more rigorously by considering the two-dimensional (2D) compressibility of the PS-PAA monolayer.20 The compressibility of a monolayer is a measure for the density fluctuations that occur in any given system. The equilibrium fluctuation density in a three-dimensional (3D) system, denoted by Υ, is defined as where Fj denotes the
Υ ) x∆F2 )
x()
-kBTFj2 ∂p V ∂V T
(11)
average particle density and p is the pressure in the system. It is convenient to express the strength of these fluctuations relative to those in ideal systems. The latter are simply Υid ) xFj.21 As we consider a monolayer, the 2D equivalent ΥR of the normalized fluctuation density is
ΥR ≡
Υ ) Υid
x (∂π∂σ) kBT
-1
(12)
where we have used the fact that πid ) kBTσ. Generally speaking, the strength of density fluctuations is the strongest in the proximity of a phase transition. In the case of a first-order phase transition in the monolayer (e.g., an expanded-liquid-to-condensed-liquid transition in surfactant monolayers), (∂π/∂σ) ) 0.22 Equation 12 shows that the strength of the fluctuations diverges during such a first-order phase transition. We now consider the strength of density fluctuations in the PS-PAA and PS-PEO monolayers as a function of the grafting density. As discussed extensively by Bijsterbosch et al.17 and Currie et al.,18 PEO adsorbs strongly to the air/water interface. Thus, at low densities it has a flat (pancake) conformation. As the grafting density increases above a certain overlap density, the chains are pushed out of the interface and a brush is formed. This pancakebrush transition is continuous, the compressibility ΥR is a measure for the abruptness of the transition.18 In Figure 5 ΥR values of PS(38)-PEO(445) and PS(34)-PAA(368) are shown as a function of the area per chain σ-1.35 The lengths of both the anchoring PS blocks, like the hydrophilic PEO and PAA blocks, are comparable. The PS-PAA isotherm was measured at pH 4.7 and no added salt (Figure 4). Evidently, the behavior of ΥR(σ-1)
Figure 6. ΥR as a function of the area per chain σ-1 (nm2) for PS-PAA(368) at pH 4.4 with 0.1 M NaCl and at pH 4.7 with no added salt. The latter curve is the same as in Figure 4.5. The curves through the data points are a guide to the eye.
is qualitatively the same for both polymers: at low σ, the density fluctuations are small; at higher σ, the fluctuations increase; and at high σ, the fluctuations again decrease with increasing σ. This result is consistent with the picture of a pancake-brush transition of tethered chains. If we introduce σc to denote the grafting density at which the maximum in ΥR(σ-1) is found, then the chains are adsorbed at the interface in a pancake conformation for σ,σc. In this regime, the density fluctuations in the monolayer are low because the chains are completely adsorbed. Because the adsorption strength is weaker for PAA compared with PEO, the low surface pressures make the pancake regime of PAA experimentally less accessible than the pancake regime of PEO, which explains the small number of data points of PAA at low σ in Figure 5. If σ ∼ σc, the adsorptiondesorption transition of the grafted chains greatly enhances the fluctuations in the monolayer. For σ.σc, the chains are almost completely desorbed in a brush conformation and the fluctuation strength is small again. When the maximum in ΥR is indeed associated with the adsorption-desorption transition of tethered chains, this maximum at σc should (approximately) occur at the saturated surface pressure of the adsorbing block. In the case of PEO homopolymer, the saturated surface pressure for long chains is known to be 9.8 mN m-1.23 The surface pressure of the PS-PEO(445) diblock copolymer is 9.6 mN m-1 at σc. The surface pressure of PS-PAA(368) at σc at pH 4.7 and no added salt is 3.2 mN m-1. We recall that the surface pressure of solutions of PAA homopolymer in low pH and salt regime was also of the order 3 mN m-1. Thus, a strong correlation is found between ΥR(σ-1) and the adsorption properties of the grafted chains. Naturally, the same analysis for lateral density fluctuations can be performed for PAA at different salt concentrations. In Figure 6 ΥR is plotted for PS-PAA monolayers at pH 4.7 and no salt and at pH 4.4 and 0.1 M NaCl. Clearly, the form of ΥR(σ) with and without added salt differs: at low σ, the fluctuations are large in the case of added salt. This result is attributed to the small increase of π as a function of σ in the coil regime, and the subsequent large density fluctuations. The strength of the fluctuations (35) One may wonder why the data points in Figures 5 and 6 are rather scattered. During measurement of a surface pressure isotherm the area and surface pressure vary with finite increments. This variation is especially important in a regime corresponding with a pseudo-plateau in the isotherm (i.e., a pancake-brush transition).17,18 The numerical derivative of the data may deviate from the overall trend because of these finite steps, resulting in a scattering of points.
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Figure 7. The titration curves of PAA brushes for three areas per chain and 10-3 M ionic strength.
decreases with increasing σ, which corresponds to the increasing monomer density in the grafted layer as the brush regime is approached. There is no maximum in ΥR(σ) in the case of added salt, which indicates that that the adsorption-desorption transition is absent. We can therefore conclude that at relatively low pH and no added salt, grafted PAA chains have a pancake conformation at low σ instead of the theoretically predicted osmotic brush in the O ˜ sB-regime. This pancake conformation is responsible for the high exponent in Figure 4 at low σ. The scaling exponent y in π ∼ σy in the pancake regime is given as y ) 2ν/(2ν - 1) in a 2D system, where the exponent ν characterizes the relationship between the radius of gyration of a chain and its length (i.e., RG ∼ Nν).24 For an ideal 2D self-avoiding walk, ν ) 3/4 (and the surface pressure of flat pancakes should increase as π ∼ σ3.17,24 Our exponent y is closer to 2 than to 3, so a completely flat pancake conformation is unlikely. The high value nevertheless indicates strongly interacting chains in a pancake-like conformation. At high pH, the π(σ) isotherms with and without added salt are observed not to obey a single-power law. This result indicates that the interaction between the grafted chains is not dominated by a single osmotic interaction. In the SB regime, the scaling behavior of π(σ) stems from the dominance of binary monomer-monomer interactions. In the derivation of the scaling laws in the SB regime, the assumption is made that the osmotic pressure in the brush layer is proportional to the difference in total ion concentration in the brush and in the bulk solution.4 This assumption is only valid in the limits of low ion densities; at high densities, the complete virial expansion in terms of ∆Fion must be taken into account. The result of these higher order terms in ∆Fion is that no clear scaling regime for π(σ) is found. Also, at these high densities, osmotic interactions between nondissociated monomers also play a role.36 Thus, the absence of scaling regimes in the π(σ) isotherms at high pH is thought to be the combined result of high charge densities and high monomer densities in the brush. Ellipsometry. We first show the titration isotherms of PAA brushes at low and constant ionic strength I as a function of pH, obtained with reflectometry and presented in ref. 12. The titration curves of PAA at three grafting densitites and ionic strength 10-3 M are shown in Figure 7. All curves commence at pH 3 because of the requirement of constant ionic strength of 10-3 M. It is observed that (36) Abe, T.; Higashi, N.; Niwa, M.; Kurihara, K. Langmuir 1999, 15, 7725.
Currie et al.
Figure 8. The ∆ (in degrees) values as a function of the ionic strength I for 3.9 nm2 per PAA chain at three pH values, plotted semilogarithmically. The dashed curves are drawn as a guide for the eye.
Figure 9. The same as Figure 8 for Ψ.
the titration curves of the grafted PAA chains effectively shift to higher pH values with increasing σ, as the theory of annealed brushes predicts.4-6 The shift in effective pKa value is ∼1.5 units as σ-1 decreases from 18 to 8 nm2. This shift in apparent pKa agrees qualitatively with theoretical models for annealed brushes that predict the (overall) degree of dissociation R to decrease strongly with increasing grafting density σ at constant pH and ionic strength. We now turn toward the ellipsometry results of densely grafted PAA brushes. In Figures 8 and 9, the measured values of ∆ and Ψ are shown as a function of the total ionic strength (this explicitely includes the proton contribution to I) at a relatively high grafting density (3.9 nm2 per PAA chain). As is clear from Figure 9, ∆ and Ψ are relatively insensitive to variations in I at pH 3.0. At higher pH, however, ∆ and Ψ vary significantly and nonmonotonically with increasing I. Evidently, the difference between the ∆,Ψ curves at pH 3.0 and 5.8 reflects a difference in behavior of the grafted PAA layer with increasing ionic strength. In Figure 10 the increase in ∆, denoted as ∆ - ∆0, is shown as a function of the ionic strength for three grafting densities, at a fixed pH of 5.9. The quantity ∆0 is the value of ∆ at zero added salt (i.e., at I ≈ 10-pH). It is clear that the effect of increasing ionic strength on ∆ increases with increasing grafting density. Also, the maximum in ∆ appears to shift to higher ionic strengths with increasing grafting density.
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Figure 10. The increase in ∆ with increasing I for three grafting densities and pH 5.9, plotted semilogarithmically. The dashed curves are drawn as a guide for the eye.
Figure 12. The thickness H of the PAA layer (in nm) plotted semilogarithmically as a function of I for three pH values (σ-1 is 3.9 nm2). The dashed curves are a guide to the eye.
Figure 11. The ∆,Ψ curves calculated with the box model for nPS ) 1.56, dPS ) 60 nm, and three values for nPAA. The modeled PAA thickness is 0-50 nm, with every 3 nm a marker.
Figure 13. The thickness H of the PAA layer (in nm) plotted semilogarithmically as a function of I at pH 4.0 for σ-1 of 8 nm2 (closed squares), 6.2 nm2 (triangles), 3.9 nm2 (open squares), and 2.6 nm2 (circles). The dashed curves are a guide to the eye.
Table 1. Parameters for Modeling Ellipsometry Results31 nSi
nPS
nPS
nPAA
3.885-0.0185i
1.54-1.56
55-65 nm
1.35-1.59
To obtain values for the brush thickness and monomer density from the measured values of ∆ and Ψ, it is necessary to make use of a presupposed model that mimics the investigated system. We used a box model to model the PAA brush; that is, the refractive index, which is coupled to the monomer density, is assumed to be uniform throughout the layer. The values used for the refractive index and thickness of the Si and PS layers are shown in Table 1. In Figure 11 the ∆,Ψ curves, calculated numerically using the box model, are shown as the thickness of the PAA brush increases from 0 (low value of ∆ and Ψ) to 50 nm (high value of ∆ and Ψ). These curves may be interpreted as ‘isodensity’ curves. Experimentally, both the PAA thickness and overall density in the brush are expected to vary with varying ionic strength. This expectation requires that the experimental ∆,Ψ curves cross the numerical ∆,Ψ curves for constant n in Figure 11 with varying ionic strength. In Figure 12 we have plotted the fitted thickness from the data of Figures 8 and 9 as a function of the ionic strength at three pH values. Error bars denote the estimated uncertainty in the fitted value of H. At pH 3.0, the brush thickness is independent of the ionic strength. At higher pH values, the thickness initially increases and
subsequently decreases with increasing ionic strength. This effect is most pronounced for pH 5.8. In Figure 13 the brush thickness is plotted as a function of the ionic strength at pH 4.0 for four grafting densities. The brush thickness is a nonmonotonic function of the ionic strength for all grafting densities. Evidently, the greatest (absolute) increase in thickness is found at the highest grafting density (i.e., 2.6 nm2 per PAA molecule). Using the box model to fit the ellipsometry data, we obtain the thickness and the overall refractive index of the layer. Evidently, the latter is related to the monomer number density F. The overall refractive index in the box model, which depends on the density F, degree of dissociation R, and refractive index of the nondissociated monomer and that of the dissociated monomer plus counterion, can be written as: nPAA ) (1 - Fυ)nH2O + Fυ((1 - R)nCOOH + RnCOO-Na+). The constant υ denotes the ratio of the volume of a monomer and a water molecule, which formally is also a function of R. Because this expression contains at least two unknown parameters (F and R), it is not possibile to determine either F or R unambiguously from the fitted value of nPAA. Nevertheless, it is interesting to examine the overall value of n as a function of I and the pH. In Figure 14 the fitted value of n is shown for the same data as used in Figure 12. At pH 3.0, n is independent of I, which agrees with the constant value of H in Figure 12. The refractive
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Figure 14. The refractive index n of the PAA layer plotted semilogarithmically as a function of I for three pH values (σ-1 is 3.9 nm2). The dashed curves are a guide to the eye.
Figure 15. The data of Figure 13 plotted double-logaritmically. Lines corresponding to scaling exponents of 1/3 (solid line) and 1/10 (dashed line) are plotted as well.
index of the PAA layer at pH 4.0 and 5.8 initially decreases with increasing pH at low ionic strength. This result corresponds with an additional stretching of the PAA brush (see Figure 12). At high ionic strength, however, both the decrease in brush thickness and the increasing co- and counterion density (Cl- and Na+) in the brush result in an increasing value of n with increasing I. Thus, the nonmonotonic behavior of the refractive index of the brush qualitatively mirrors that of the thickness. As already mentioned, a presupposed model is necessary to transform the measured values of ∆ and Ψ into physical parameters. In this respect, the final results obtained by ellipsometry are not unambiguous and must be interpreted with care. To demonstrate that the variation of ∆ and Ψ with varying ionic strength is significant, we have plotted the ∆ and Ψ data in Figures 8-10 and the model calculations in Figure 11. The nonmonotonic trends in H(I) and n(I) do not depend on the values used for the thickness of the spin-coated PS layer and its refractive index. The precise values of H and n, however, do depend on the refractive index and thickness of the spin-coated layer. We have used the simplest possible model to mimic the PAA brush (i.e., the box model). Analytical and numerical self-consistent field (SCF) calculations predict density and counterion distributions throughout the brush.5,6 Because only two parameters are measured with ellipsometry, it is not possible to deal with such density distributions. To determine either the counterion or monomer density distribution, one needs a scattering technique with a high spatial resolution; for instance, neutron or X-ray scattering. Evidently, the most interesting result is the nonmonotonic behavior of H(I). This nonmonotonic behavior stems from the influence of the ionic strength on the electrostatic potential in the grafted layer. In pure deionized water, the Debye length, κ-1, which characterizes the range over which charged entities interact via electrostatic interactions, is of the order of 100 nm. Under such conditions, the overall charge density of the grafted chains in the brush is significantly below Rb (see Figure 7). As the ionic strength increases, the overall charge density on the grafted chains increases, and the brush thickness increases as a result of the enhanced electrostatic interactions. This result corresponds to the O ˜ sB regime as proposed theoretically by Zhulina et al.,4 and Lyatskaya et al.,5 Israe¨ls et al.6 At high ionic strength, R is close to Rb; in this regime, a subsequent increase in ionic strength
merely decreases the strength of the electrostatic interactions between dissociated monomers and the brush thickness decreases. This decrease is characterized by a decrease in the monomeric excluded volume υeff and corresponds with the SB regime.4 The brush thickness in the O ˜ sB-regime is given by eq 5.4 In our experiments, σ and N are fixed, and if Rb is assumed independent of I (Figure 1 shows this assumption to be not completely valid), this expression reduces to H ∼ I1/3 at a given pH. However, if we plot the experimental data of Figure 13 double-logarithmically, we obtain power laws with an exponent close to 0.1 instead of 0.33. This double-logarithmic plot is shown in Figure 15. The same exponent is also found at pH 5.8 (not shown). Thus, the experimental dependence of the brush thickness on the ionic strength in the O ˜ sB-regime is significantly less than predicted theoretically. The difference between the experimentally observed power law exponent and the theoretical exponent predicted for the O ˜ sB-regime is probably due steric interactions. Stated simply, in the case of charged brushes, there are two forces that induce stretching (steric interactions between monomers and electrostatic interactions between dissociated monomers) and one force that opposes stretching (conformational). To obtain a scaling law, either the steric or electrostatic force must be neglected, as was done for the steric force by Zhulina et al. to obtain the scaling behavior for H(I) in the O ˜ sB regime.4 However, if R approaches zero the PAA brush resembles a neutral brush, the height of which is determined by steric interactions and was predicted by Zhulina et al.4 From our ellipsometry results one could conlude that the system is on the boundary of the O ˜ sB regime and a neutral brush because of relative high grafting densities. Thus, the increase in brush thickness with increasing ionic strength in the O ˜ sB-regime is less than given by the aforementioned mean-field scaling law. This result also demonstrates why the predicted decrease in brush thickness at low ionic strength and pH with increasing grafting density is not observed. The underlying reason for this decrease is the decrease in fraction of dissociated monomers with increasing grafting density (see Figure 7). However, in Figure 13, the thickness of the PAA brush increases with increasing grafting density at low ionic strength and pH. It is believed that the steric interactions result in an increase of the brush thickness with increasing grafting density, which corresponds with the behavior of a neutral brush.18
Polyacrylic Acid Brushes
Conclusions In this paper we have investigated the properties of grafted PAA chains at various conditions using surface pressure measurements and ellipsometry. These results are compared with theoretical predictions for the behavior of annealed brushes. Analysis of surface pressure isotherms of PS-PAA at the air/water interface yields information on the conformation of the grafted PAA chains. It is shown that at low pH and high salt concentration, the power law of the surface pressure as a function of the grafting density correponds with the mean-field power law for charged brushes in the salted brush regime (i.e., π ∼ σ5/3) in the case of long chains. Short chains do not follow this power law. This result is similar to that of neutral polymers in the neutral brush regime.18 Analysis of the compressibility of the PS-PAA monolayer demonstrates that the PAA chains adsorb to the interface at low salt concentrations and low pH. This adsorption prevents the occurrence of an osmotic brush regime of annealed chains (O ˜ sB regime) at low densities. Using ellipsometry, the thickness of the grafted PAA layer was measured. The PAA brush thickness is nonmonotonic as a function of the ionic strength at a given pH and grafting density. The extent of (de)swelling increases with increasing pH and grafting density. At pH 3 (far below the pKa of PAA), the brush height is independent of the ionic strength because the fraction of dissociated monomers is close to zero, regardless of the ionic strength. At higher pH, the brush initially swells with increasing ionic strength because of an increasing fraction of charged monomers. At an ionic strength of the order of 0.1 M, the charge density is close to that of a PAA chain in a dilute bulk solution. In this regime, the thickness decreases with increasing ionic strength because of increased screening of electrostatic interactions between charged monomers. The nonmonotonic behavior agrees qualitatively with theoretical predictions of Zhulina et al.,4 Lyatskaya et al.,5 and Israe¨ls et al.6 The mean-field power law of Zhulina et al.4 for the O ˜ sB regime, H ∼ I1/3 at a given pH and σ, is not observed; the measured exponent is ∼0.1. The swelling is therefore less than predicted, which is probably due to steric interactions that are neglected in the analysis ˜ sB regime. Also, theoretically, of Zhulina et al.4 of the O
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the brush thickness is predicted to decrease with increasing grafting density in the O ˜ sB regime, whereas experimentally it is found to increase. Again, the difference is believed to originate from the neglect of steric interactions in the theoretical analysis. One may wonder under which conditions the O ˜ sB regime, as theoretically characterized in the analytical and numerical models, is experimentally accessible. The theoretical models assume the polymers to be grafted to an inert, neutral surface. Because of its chemical structure, the carbon backbone of a polymer is intrinsically hydrophobic. The solubility of polymers is generally due to charged or polar groups on the chain. The grafting of charged chains close to the water/air interface is unfavorable because of dielectric anisotropy.33 Because the dielectric constants of most organic compounds are low compared with that of water, the problems associated with the dielectric anisotropy of the water/air interface are also present for polyacids chemically or physically grafted to a fluid/fluid interface or solid/fluid surface.34 Also, shielding of the carbon backbone from the water phase results in an additional affinity of grafted polyacids for such fluid/ fluid or solid/fluid interfaces. Thus, the occurrence of the O ˜ sB regime for annealed polymers grafted to an apolar surface is, in general, unlikely at low grafting densities, because of adsorption effects that result in a pancake conformation. At grafting densities above the pancake-brush transition, the PAA chains are (partially) desorbed in a brushlike conformation. However, in this regime, the chains are relatively close packed and steric interactions, which are neglected in the analytical models for the O ˜ sB regime, are important. The nonmonotonic dependence of the brush height as a function of the ionic strength, which is indicative for the O ˜ sB regime, is observed experimentally at high grafting densities. The quantitative agreement between the analytical models and experiments, however, is poor, because the chains are stretched by both steric and electrostatic interactions in this grafting regime. Acknowledgment. We thank Marcelo Avena for the PAA titration isotherms. Oleg Borisov is thanked for many useful remarks and discussions. LA991528O
