Adsorption Characteristics of Bottle-Brush Polymers on Silica: Effect of

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Langmuir 2008, 24, 5341-5349

5341

Adsorption Characteristics of Bottle-Brush Polymers on Silica: Effect of Side Chain and Charge Density Geoffrey Olanya,†,| Joseph Iruthayaraj,*,†,| Evgeni Poptoshev,†,‡ Ricardas Makuska,§ Ausvydas Vareikis,§ and Per. M. Claesson†,| Department of Chemistry, Surface Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden, BaleV Ltd, P.O. Box 1293, 1000 Sofia, Bulgaria, Department of Polymer Chemistry, Vilnius UniVersity, Naugarduko 24, LT-03225 Vilnius, Lithuania, and YKI, Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden ReceiVed NoVember 29, 2007. ReVised Manuscript ReceiVed February 21, 2008 The adsorption behavior of bottle-brush polymers with different charge/PEO ratio on silica was studied using optical reflectometry and QCM-D. The results obtained under different solution conditions clearly demonstrate the existence of two distinct adsorption mechanisms depending on the ratio of charge/PEO. In the case of low-charge density brush polymers (0-10 mol %), the adsorption occurs predominantly through the PEO side chains. However, the presence of a small amount of charge along the backbone (as low as 2 mol %) increases the adsorption significantly above that of the uncharged bottle-brush polymer in pure water. As the charge density of the brush polymers is increased to 25 mol % or larger the adsorption occurs predominantly through electrostatic interactions. The adsorbed layer structure was studied by measuring the layer dissipation using QCM-D. The adsorbed layer formed by the uncharged brush polymer dissipates only a small amount of energy that indicates that the brush lie along the surface, the scenario in which the maximum number of PEO side chains interact with the surface. The adsorbed layers formed by the low-charge density brush polymers (2-10 mol %) in water are more extended, which results in large energy dissipation, whereas those formed by the high-charge density brush polymers (50-100 mol %) have their backbone relatively flat on the surface and the energy dissipation is again low.

1. Introduction Bottle brush polymers, also known as cylindrical polymer brushes, refer to a class of branched polymeric structures in which the side chains are covalently linked to a linear polymer main chain.1 The graft density, number of side chains per main chain monomer, is an important parameter to assess the chain conformation. Ideally one side chain per main chain monomer renders a cylindrical shape to the molecule. For example the uncharged brush polymer used in this work contains one PEO side chain per methacrylate main chain monomer. The presence of side chains results in large intramolecular excluded volume interactions and as a consequence the backbone flexibility diminishes. It was shown using small-angle X-ray scattering (SAXS) that this polymer adopts rather stiff rodlike conformations.2 Poly(ethylene oxide), also known as poly(ethylene glycol), is a homopolymer of ethylene oxide monomers and one of the most well studied water-soluble polymers both in terms of its solution3–6 and interfacial properties.7–12 It is important within * Corresponding author. E-mail: [email protected] † Royal Institute of Technology. | YKI, Institute for Surface Chemistry. ‡ Balev Ltd. § Vilnius University.

(1) Zhang, M.; Breiner, T.; Mori, H.; Muller, A. Polymer 2003, 44, 1449–58. (2) Dedinaite, A.; Bastardo, L. A.; Oliveira, C. L. P.; Pedersen, J. S.; Claesson, P. M.; Vareikis, A.; Makuska, R. Proc. Baltic Polym. Symp, in press. (3) Kinugasa, S.; Nakahara, H.; Fudagawa, N.; Koga, Y. Macromolecules 1994, 27, 6889. (4) Devanand, K.; Selser, J. C. Nature 1990, 343, 739. (5) Devanand, K.; Selser, J. C. Macromolecules 1991, 24, 5943. (6) Zhou, P.; Brown, W. Macromolecules 1990, 23, 1131. (7) Vanderbeek, G. P.; Stuart, M. A. C.; Cosgrove, T. Langmuir 1991, 7, 327. (8) Wind, B.; Killmann, E. Colloid Polym. Sci. 1998, 276, 903. (9) Mathur, S.; Moudgil, B. M. J. Colloid Interface Sci. 1997, 196(1), 92. (10) Flood, C.; Cosgrove, T.; Howell, I.; Revell, P. Langmuir 2006, 22, 6923. (11) Fu, Z. L.; Santore, M. M. Macromolecules 1998, 31, 7014.

the context of our present work to highlight the salient features of the interfacial properties of poly(ethylene oxide) (PEO) on silica in terms of its adsorption mechanism. Much of the earlier works were aimed at understanding the flocculation-deflocculating behavior of colloidal silica suspensions by water soluble nonionic polymers such as poly(vinyl alcohol)13 and PEO. A substantial work on PEO adsorption on colloidal silica was presented by Rubio and Kitchener.14 Their studies have shown that the adsorption of PEO on silica particles depends crucially on the synthesis route adopted for the preparation of the particles. Specifically, at pH 6 the adsorption was found to be higher on flame silica as compared to precipitated silica. Flame silica, also known as fumed silica, is prepared by flame hydrolysis of silicon tetrachloride in an oxy-hydrogen flame (commercial names: Cabosil from Cabot Corp and Aerosil from Degussa Corp), whereas precipitated silica is synthesized by acidifying sodium silicate solutions using sulfuric acid. It was hypothesized that the two different synthetic routes resulted in silica surfaces with two different surface silanol groups, the surface of flame silica being populated with isolated surface silanol groups whereas that of precipitated silica contained higher density of silanol groups H-bonded to each other. Furthermore, the isolated silanol groups were thought to be the principal adsorption sites for the ether groups of PEO and the adsorption is favored if the regions between these sites are rendered hydrophobic. In the case of flame silica, the hydrophobicity is due to the presence of siloxane rings at the surface. In contrast, on precipitated silica the surface is covered with a high density of silanol groups resulting in substantial hydration which disfavors PEO adsorption. A systematic study of the effect of pH and ionic strength on the adsorption behavior of PEO on Aerosil silica was reported (12) Mubarekyan, E.; Santore, M. M. Macromolecules 2001, 34, 7504. (13) Tadros, T. F. J. Colloid Interface Sci. 1974, 46, 528. (14) Rubio, J.; Kitchener, J. A. J. Colloid Interface Sci. 1976, 57, 132.

10.1021/la703739v CCC: $40.75  2008 American Chemical Society Published on Web 04/19/2008

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by Eremenko et al.15 It was shown that the adsorption of PEO decreased with increase in pH. Interestingly, the effects of pH and ionic strength seem to depend on the adsorbed amount of PEO. At low surface excess (typically around 0.1 mg/m2), the adsorption is practically independent of pH in the range (4-9) whereas at high surface excess (0.4 mg/m2) the adsorption decreases steadily with increasing pH. In general, the adsorption of PEO has shown a very weak dependence on ionic strength at neutral and acidic pH whereas a significant decrease with ionic strength is found at high pH (typically >8). Adsorption studies of PEO on various oxides have shown that the adsorption density depends critically on the point of zero charge (pzc) of the oxides. Oxides such as V2O5, MoO3, and SiO2 (pzc between 0-2) have higher affinity for PEO, whereas oxides such as TiO2, Fe2O3, and MgO (pzc between 4-12) have poor affinity for PEO.9 It has been argued that strong Bronsted acid sites on the surface interact with the ether oxygen of PEO, which is a Lewis base. Recent investigations on the adsorption of PEO on fumed silica using IR spectroscopy have shown that the surface of fumed silica is populated with both isolated (O-H stretching region 3740-3750 cm-1) and H-bonded silanol groups (O-H stretching region 3500-3550 cm-1), and the adsorption of PEO affected approximately 70% of the isolated silanol groups.16 Thus, it can be concluded that PEO interacts with silica primarily through isolated surface silanol groups. Poly(ethylene oxide) plays an important role in a wide array of technological applications primarily due to its efficacy in stabilizing colloidal particles through steric stabilization. Some examples of PEO-based steric dispersants and their applications are PEO lipids used as steric stabilizers for drug-loaded liposomes,17 block copolymers of PEO-PPO-PEO, used in the dispersion of singlewalled carbon nanotubes (SWNT),18 and a triblock dispersant, PEOCOOH-PEO used for stabilizing magnetic nanoparticles such as magnetite (Fe2O3).19 The COOH moiety serves as the anchoring point, as it can form coordination type bonds with Fe3+, and PEO serves as the steric stabilizing unit. Apart from steric stabilization, immobilization of PEO on surfaces is found to decrease nonspecific protein20–22 adsorption and reduce friction between two oxide surfaces in aqueous surrounding.23 The efficacy to reduce protein adsorption and friction and the enhancement of steric stabilization warrants for a high density of PEO chains at the interface, often in the form of a brush structure. These can be formed primarily by two different approaches, either through covalent linkage of PEO to surface groups such as amine24,25 or through adsorption of block/ brush polymers containing PEO chains covalently linked to the anchor block/backbone. The backbone of the brush polymer is made to possess stronger affinity to the surface than the PEO side chains. Poly (L-lysine) grafted with poly(ethylene oxide) is a very good example that illustrates this approach. At physi(15) Eremenko, B. V.; Sergienko, Z. A. Colloid J. USSR 1979, 41, 353. (16) Voronin, E. F.; Gun’ko, V. M.; Guzenko, N. V.; Pakhlov, E. M.; Nosach, L. V.; Leboda, R.; Skubiszewska-Zieba, J.; Malysheva, M. L.; Borysenko, M. V.; Chuiko, A. A. J. Colloid Interface Sci. 2004, 279, 326. (17) Silvander, M. Prog. Colloid Polym. Sci. 2002, 120, 35. (18) Shvartzman-Cohen, R.; Levi-Kalisman, Y.; Nativ-Roth, E.; YerushalmiRozen, R. Langmuir 2004, 20, 6085. (19) Harris, L. A.; Goff, J. D.; Carmichael, A. Y.; Riffle, J. S.; Harburn, J. J.; St Pierre, T. G.; Saunders, M. Chem. Mater. 2003, 15(6), 1367. (20) Unsworth, L.; Sheardown, H.; Brash, J. Biomaterials 2005, 26, 5927. (21) Xu, Z.; Marchant, R. Biomaterials 2000, 21, 1075. (22) Zhou, Y.; Liedberg, B.; Gorochovceva, N. A.; Makuska, R.; Dedinaite, A.; Claesson, P. M. J. Colloid Interface Sci. 2007, 305, 62. (23) Yan, X.; Perry, S.; Nicholas, S.; Pasche, S.; Susan, D. P.; Textor, M.; Lim, M. S. Langmuir 2004, 20, 423. (24) Brink, C.; Oesterberg, E.; Holmberg, K.; Tiberg, F. Colloids Surf. 1992, 66(2), 149–56. (25) Gombotz, W. R.; Guanghui, W.; Hoffman, A. S. J. Appl. Polym. Sci. 37, 91–107.

Olanya et al.

ological pH the cationic backbone,26 poly(L-lysine), adsorbs to different oxide surfaces such as TiO2, Si0.4Ti0.6O2 and Nb2O5 while the uncharged PEO side chains are exposed to the solution.27 The adsorbed layer structure formed due to adsorption of poly(L-lysine)-g-poly(ethylene oxide) has been shown to exhibit good protein repellency and lubrication in aqueous surroundings. In this work, we have studied the adsorption characteristics on silica of a series of bottle-brush polymers, having different PEO/charge ratio along the backbone. One motivation for this work stems from our previous findings that the surface excess of a low-charge density PEO brush, with 2 mol % of the monomers carrying permanent positive charges with the remaining 98% containing poly(ethylene oxide) side chains, decreases significantly in presence of small amount of 1:1 electrolyte at neutral pH28 and by increasing the solution pH at constant ionic strength. The interaction of PEO-brush polymers to silica surfaces occurs through both the PEO side chains and the backbone charges depending on pH and ionic strength of the solution. It will be shown in this study how the interaction of the PEO brush polymer with silica switches from predominantly PEO driven to predominantly electrostatically driven as the PEO/charge ratio of the polymer is increased.

2. Materials and Methods 2.1. Materials. Poly(ethylene glycol) methyl ether methacrylate (PEO45MEMA) (Mn) 2080) supplied by Aldrich as a 50 wt % aqueous solution and methacryloxyethyl trimethylammonium chloride (METAC) provided by Polysciences Inc. as a 70 wt % aqueous solution were used as received. The molecular weight of the poly(ethylene oxide) component (PEO45) of the monomer (PEO45MEMA) is well-defined (polydispersity index 1.1) and equals 2000 g mol-1. Azobisisobutyronitrile (AIBN) from Reachim was recrystallized twice from methanol at room temperature prior to use. 2-Propanol, chloroform, and methanol from Fluka were used without further purification. The series of bottle-brush polymers of varying charge densities used in this work, represented as PEO45MEMA: METAC-X, were synthesized by free-radical copolymerization of PEO45MEMA and METAC monomers in polymerization tubes under nitrogen atmosphere28 using AIBN as the thermal initiator. In the polyelectrolyte representation, “X” denotes the molar percentage of METAC segments, which constitutes the permanently charged segments of the copolymer. The polymerization reaction was carried out for 20 h at 60 °C. The yields of the copolymers were determined gravimetrically based on their dry weight after purification by extensive dialysis. The absence of the characteristic peak in 1H NMR spectra of the dialyzed products in the region δ ) 5-6.5 ppm indicates absence of any double bonds (or absence of any residual monomers) in the copolymers. The composition of the copolymers was calculated through their chlorine content, as determined by argentometric titration. The yields of the copolymers reached ca. 90% irrespective of monomer feed, and the average copolymer composition was very close to the initial monomer feed for all samples (see Table 1). The synthesized PEO45MEMA:METAC-X copolymers have a polydispersity index of around 2-3 (as determined by GPC for selected samples), which is typical for polymers prepared by freeradical polymerization (see Chart 1). Sodium nitrate (NaNO3, AnalaR grade), sodium hydroxide, and hydrochloric acid were all used as received (from Merck). The water was pretreated by a Milli-RO Plus unit and then purified by a Milli-Q plus 185 system and filtered through a 0.2 µm Millipak filter. The resistivity after the treatment (26) Elbert, D. L.; Hubbell, J. A. J. Biomed. Mater. Res 1998, 42, 55. (27) Kenausis, L. G.; Voros, J.; Elbert, D. L.; Huang, N.; Hofer, R.; RuizTaylor, L.; Textor, M.; Hubbell, J. A.; Spencer, N. D. J. Phys. Chem. B 2000, 104, 3298. (28) Iruthayaraj, J.; Poptoshev, E.; Vareikis, A.; Makuska, R.; van der wal, A.; Claesson, P. M. Macromolecules 2005, 38, 6152.

Adsorption Characteristics of Bottle-Brush Polymers on Si

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Table 1. The Copolymers Used in This Studya

brush polymers Poly(PEO45MEMA) PEO45MEMA:METAC-2 PEO45MEMA:METAC-5 PEO45MEMA:METAC-10 PEO45MEMA:METAC-25 PEO45MEMA:METAC-50 PEO45MEMA:METAC-75 Poly(METAC)

ClMETAC METAC (mol %) (weight %) (mol %) in Yield in feed in copolymer copolymer (%) 0 2 5 10 25 50 75 100

0 0.03 0.1 0.20 0.57 1.62 3.93 15.9

0 2.0 5.6 10.6 25.8 51.3 75.0 99.3

92 90 88 92 93 92 95 89

a The columns denote the composition (mol %) of the feed in terms of METAC monomers, chloride content of the copolymer in weight % (and hence the amount of METAC segments in the copolymer). The last column reports the synthesis yields of the various copolymers.

Chart 1. Molecular structures of the PEO45MEMA and METAC segments in the investigated brush polymer series, where X denotes the amount of the charged METAC component (mol %) in the polymer

were determined experimentally using a differential refractometer.31 2.2.1.1. Preparation of Silica Surfaces for Reflectometry. Thermally oxidized silicon wafers were purchased from Wafer Net, Germany. The wafers were cut to required size and conditioned by immersion in a solution mixture of H2O/HCl/H2O2 (65:20:15) at 75-80 °C for 10 min. The plates were then removed and rinsed in Milli-Q water several times before immersion in a solution mixture of H2O/NH3/H2O2 (70: 20:10) at 75-80 °C for another 10 min. Finally, the plates were rinsed with copious amounts of Milli-Q water and stored under absolute ethanol prior to use. The above procedure yielded fully hydrophilic surfaces with the water contact angle being close to zero. 2.2.2. Quartz Crystal Microbalance-Dissipation (QCM-D). QCM-D measurements were performed using a q-sense E4 microbalance. Quartz crystals (AT-cut 5 MHz) coated with 50 nm silica are allowed to oscillate at their resonance frequency in water. The resonance frequency (f) and the dissipation (D) of the crystal are accurately determined as described by Rodahl et al.32 The dissipation is measured by switching off the driving power and monitoring the amplitude decay profile. The amplitude decays as an exponentially damped sinusoidal function with a characteristic decay time (τd). The decay time is related to the dissipation (D) as:

D)

2 ωτd

(2)

The symbol ω represents the angular frequency. Upon adsorption the frequency decreases and the dissipation increases. The change in frequency (∆f) is approximately related to the adsorbed mass by the Sauerbrey equation,

ΓQCM ) -C ×

was 18.2 MΩ-cm, and the total organic carbon content of the water did not exceed 2 ppb. 2.2. Methods. 2.2.1. Optical Reflectometry. The adsorption of the PEO45MEMA:METAC-X brush polymers on thermally oxidized silicon wafers was investigated using optical reflectometry.29 The thermally oxidized silicon wafer consists of a 100 nm thick SiO2 layer, as determined with ellipsometry, on top of a silicon (Si) substrate. Linearly polarized light is reflected at the SiO2/Si-water interface at an angle close to the Brewster angle. The reflected light is split into its parallel and perpendicular polarization components using a beam splitter and their respective intensities, Ip and Is, are recorded via photodiodes. The ratio (Ip/Is) referred to as the signal, is continuously recorded during the experiment. The change in signal (∆S) upon adsorption is related to the surface excess (Γrefl) via

Γrefl )

1 ∆S × As S

(1)

The parameter As, also known as the sensitivity factor (relative change in S per unit surface excess), is determined by treating the system as a two-layer optical model where each layer is characterized by its thickness (t) and refractive index (n): Si (nSi)-SiO2 (nSiO2, tSiO2) -adsorbing layer (nlayer, tlayer)- aqueous medium (nwater) within the framework of the Fresnel reflectivity theory.30 The sensitivity factor also depends on the refractive index increment of the polymer (dn/dc) and these values (29) Dijt, J. C.; Stuart, M. A. C.; Hofman, J. E.; Fleer, G. J. Colloids Surf. 1990, 51, 141. (30) Dijt, J. C.; Stuart, M. A. C.; Fleer, G. J. Macromolecules 1994, 27(12), 3219–3228.

∆f n

(3)

Where ΓQCM is the sensed mass per unit piezoelectrically active area, C is a proportionality constant (0.177 mg/m2) dependent on the material properties of quartz such as its shear modulus and density and n is the overtone number of the oscillation.33 The sensed mass includes the mass of the adsorbing polymer as well as the water trapped at the interface. The dissipation change (∆D) upon adsorption can be qualitatively treated in terms of layer viscoelasticity. A highly viscoelastic layer results in high dissipation change whereas a rigid layer results in low dissipation change. 2.2.2.1. Preparation of QCM Silica Crystals. The silica crystals were treated with 2% Hellmanex (Hellma GmbH) for 30 min followed by rinsing with copious amount of Milli-Q water. The surfaces were left overnight in Milli-Q water before the measurement. The silica surfaces used in all of our experiments (both reflectometry and QCMD) are completely wetted by water suggesting that the surface is fully hydroxylated with no hydrophobic patches due to siloxane rings, and thus it is similar to precipitated colloidal silica.

3. Results In this section, we first present the results obtained with reflectometry followed by a description of the QCM-D results. 3.1. Optical Reflectometry. 3.1.1. Adsorption of PEO45MEMA:METAC-X in Water (pH∼6). PEO45MEMA:METAC-X brush polymers of varying charge densities were adsorbed on silica from 10 ppm aqueous solutions at different solution conditions. Figure 1a consists of four curves, each representing the adsorbed mass versus charge density of the brush polymers for a specific solution condition. Curve 1 shows the adsorbed masses obtained in water (pH ∼ 6). It is clear that the adsorbed mass increases sharply when the charge density of the polymer (31) Naderi, A.; Iruthayaraj, J.; Vareikis, A.; Makuska, R.; Claesson, P. M. Langmuir 2007, 23, 12222. (32) Rodahl, M.; Hook, F.; Krozer, A.; Brzezinski, P.; Kasemo, B. ReV. Sci. Instrum. 1995, 66, 3924. (33) Ho¨o¨k, F.; Kasemo, B. Springer Ser. Chem. Sens. Biosens. 2007, 5, 425.

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Figure 2. Adsorbed mass of PEO45MEMA:METAC-X plotted as a function of pH at constant ionic strength (10 mM), Uncharged brush polymer (9); 2% charged (O); 5% charged (0); 10% charged (*); 25% charged (b); 50% charged (2); 75% charged (1); 100% charged (()

Figure 1. (a) Adsorbed amount of PEO45MEMA:METAC-X at different solution conditions. Curve 1: adsorption in water (pH ∼ 6 ). Curve 2: adsorption in presence of 10 mM NaNO3 (pH ∼ 6). Curve 3: adsorption at pH ∼ 2. Curve 4: adsorption at pH ∼ 10 in presence of 10 mM NaNO3. (b) Number of PEO side chains calculated from the adsorbed mass at different solution conditions. Curve 1: adsorption in water (pH ∼ 6). Curve 2: adsorption in presence of 10 mM NaNO3 (pH ∼ 6). Curve 3: adsorption at pH ∼ 2. Curve 4: adsorption at pH ∼ 10 in presence of 10 mM NaNO3. (c) Number of charged segments calculated from the adsorbed mass of PEO45MEMA:METAC-X polymers at different solution conditions: pH 6, water (9); pH 2, 10 mM HCl (∆); pH 6, 10 mM NaNO3 (O); pH 10, 10 mM NaNO3 (0).

is increased from 0 to 2 mol %. Thereafter, the adsorbed mass decreases as the charge density of the backbone increases from 2 to 100 mol %, which largely is due to the progressive decrease in the PEO side chain density. However, the decreasing trend shows different regimes depending on the charge density of the brush polymers. First the decrease in adsorption exhibited by the brush polymers containing up to 10 mol % of charged segments is very small as compared to the change observed when moving from 10 to 25 mol % charge density. The decrease in the adsorbed

mass levels off between 25 and 50 mol % followed by a linear decline between 50 and 100 mol %. Figure 1b, which shows the amount of PEO in the adsorbed layer, provides a similar picture of the adsorption as Figure 1a. The number of charged groups on the surface, as shown in Figure 1c, increases monotonically with increasing polymer charge density except at pH 2 where a maximum is achieved for PEO45MEMA:METAC-75. 3.1.2. Effect of Surface Charge Variation at Constant Ionic Strength. Curves 2-4 in Figure 1a compares the adsorbed masses of the PEO45MEMA:METAC-X series at constant ionic strength at pH 2 (Curve 3), pH 6 (Curve 2), and pH 10 (Curve 4). These data are also shown in Figure 2 as a function of pH, which clearly shows two distinct patterns of the adsorption behavior of the PEO45MEMA:METAC-X polymers. The adsorption decreases with increasing surface charge density (i.e., increasing pH) in the case of brush polymers containing up to 10 mol % of charged segments. In the case of 25 and 50 mol % of charged segments, the adsorption increases from pH 2 to pH 6, followed by a small decrease in the adsorption as the pH is increased further to 10. In the case of 75 and 100 mol % charge density, the adsorption increases between pH 2 and pH 6, but no significant change is observed between pH 6 and pH 10. 3.1.3. Effect of Ionic Strength on Adsorption of PEO45 MEMA:METAC-X The effect of ionic strength on the adsorbed mass of the PEO45MEMA:METAC-X polymers in water (pH ∼ 6) is illustrated in Curves 1 and 2 in Figure 1a. The adsorbed mass of the brush polymers containing up to 10 mol % of charged segments decreases significantly in presence of 10 mM 1:1 electrolyte. On the contrary, from 25 mol % onward the adsorbed mass increases with increasing ionic strength. 3.1.4. Effect of Ionic Strength and pH on Preadsorbed PEO45MEMA:METAC-X Layers on Silica. In these experiments, PEO45MEMA:METAC-X polymers were initially adsorbed from 10 ppm salt-free solution (pH ∼ 6). In the subsequent steps, the adsorbed layer was thoroughly rinsed with Milli-Q water (pH ∼ 6) followed by rinsing with NaNO3 solutions of increasing concentrations of 0.1, 1, and 10 mM. The amount of polymer left on the surface after rinsing with 1 and 10 mM NaNO3 along with the adsorbed mass prior to rinsing is shown in Figure 3. It is evident that the brush polymers containing up to 10 mol % charge density desorb significantly in presence of 10 mM NaNO3, and the effect is substantially reduced at higher charge densities. Brush polymers with 5 mol % charge density and below desorb significantly even in 1 mM NaNO3.

Adsorption Characteristics of Bottle-Brush Polymers on Si

Figure 3. Adsorbed mass of PEO45MEMA:METAC-X in water (squares) adsorbed from 10 ppm solution; adsorbed mass left on the surface after rinsing with 1 mM NaNO3 (triangles) and 10 mM NaNO3 (circles).

Figure 4. Percentage of PEO45MEMA:METAC-X polymer removed from the silica surface after rinsing with 0.1 mM NaOH (empty squares) and 0.1 mM NaNO3 (filled triangles). The polymers were initially ˜ 6). adsorbed from 10 ppm solution in water (pH

Similarly, the effect of pH on the preadsorbed layers was studied by first rinsing with 0.1 mM NaNO3 (pH ∼ 6). In the second step, the layer was rinsed with 0.1 mM NaOH (pH ∼ 10). The percentage of polymers removed from the surface after rinsing with 0.1 mM NaNO3 and 0.1 mM NaOH is shown in Figure 4. The brush polymers in the low-charge density region (2-5 mol %) readily desorb as the solution pH is increased from 6 to 10. This effect decreases significantly with increasing polymer charge density, and essentially no desorption is observed for the polymers with 25 mol % or higher charge density. 3.2. Quartz Crystal Microbalance-Dissipation (QCM-D). The change in frequency and the change in dissipation due to adsorption of the PEO45MEMA:METAC-X polymers on a QCM silica crystal was measured in water (pH ∼ 6). The polymer concentration was 10 ppm, that is, the same as in the reflectometry measurements. The measured frequency change is used to calculate the sensed mass using the Sauerbrey model (eq 3). The Sauerbrey model is valid in the case of thin nondissipating layer that is clearly a simplified model for the description of the adsorbed polymer layer in solution. A better approximation is the Johannsmann model34 in which the adsorbed layer is modeled as a thick dissipating layer. In the present case, both of these models provide similar results for the sensed mass and the hydrodynamic thickness (Figures 5 and 6). A full viscoelastic modeling of the QCM results, comparing the different models, (34) Johannsmann, D. Macromol. Chem. Phys 1999, 200, 501–516.

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Figure 5. Sensed mass using Sauerbrey (ΓQCM, filled circles), Sensed mass using Johannsmann (unfilled circles), and adsorbed mass (Γrefl, unfilled squares) as a function of polymer charge density. The PEO45MEMA:METAC-X polymers were adsorbed from a 10 ppm solution (pH∼6) with no added salt. Note the different Y-scales.

Figure 6. Effective hydrodynamic thickness calculated using the Sauerbrey equation (deff, unfilled squares) and using the Johannsmann model (unfilled circles), and water content (filled circles) of PEO45MEMA: METAC-X layers on silica in water (pH ∼ 6) with no added salt, plotted as a function of polymer charge density. The polymer concentration was 10 ppm.

will be presented in a forthcoming publication. Figure 5 shows the sensed mass, calculated using Sauerbrey and Johannsmann model, and the adsorbed mass obtained through optical reflectometry as a function of the polymer charge density. Figure 6 shows the hydrodynamic thickness calculated from both the models.35,36 3.2.1. EffectiVe Hydrodynamic Thickness, Dissipation, and Water Content. From the sensed mass, calculated from the QCM-D response (ΓQCM), the adsorbed mass, calculated from the optical response (Γrefl), and the bulk density of the polymer (Fpolymer),31 it is possible to calculate the effective hydrodynamic thickness of the adsorbed layer (deff) as shown in eq 437

deff )

(

ΓQCM

)

(

Γrefl Γrefl Fpolymer × + Fwater × 1 ΓQCM ΓQCM

)

(4)

The effective hydrodynamic thickness (deff) of the adsorbed layer is a measure of the layer extension that in turn can be (35) Granstaff, V. E.; Martin, S. J. J. Appl. Phys. 1994, 75, 1319. (36) Voinova, M. V.; Rodahl, M.; Jonson, M.; Kasemo, B. Phys. Scr. 1999, 59, 391. (37) Hook, F.; Kasemo, B.; Nylander, T.; Fant, C.; Sott, K.; Elwing, H. Anal. Chem. 2001, 73, 5796.

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Figure 7. Adsorbed mass (Γrefl, unfilled squares) and dissipation change (filled circles) due to adsorption of PEO45MEMA:METAC-X polymers in water (pH ∼ 6) with no added salt, plotted as a function of polymer charge density. The polymer concentration was 10 ppm.

interpreted in terms of layer structure. The above equation is based on a shear model that assumes that all material in the distance range of 0 to deff oscillates with the crystal and thus contributes fully to the true sensed mass, whereas the material located further away from the surface does not oscillate with the crystal and does not contribute to the sensed mass. The sensed mass obtained from QCM-D includes contributions from both the adsorbed species and the solvent. The QCM thickness is thus influenced by the amount of water that oscillates with the crystal, and this quantity is an unknown function of the segment density profile. Nevertheless, the water content of the layer can be calculated from the difference between the sensed mass and the adsorbed mass as

% water )

ΓQCM - Γrefl × 100 ΓQCM

(5)

The effective hydrodynamic thickness calculated using eq 4 and the water content in the layer for the PEO45MEMA: METAC-X polymers are reported in Figure 6. Dissipation, as measured by QCM-D, can be considered as a consequence of the relaxation of the oscillatory motion imposed on the adsorbed layer. Dissipation changes can be understood as the interplay between different time-scales; the time taken by the adsorbed layer to relax and thus move in phase with the crystal (τR), the measured decay time of the oscillation (τd), and the time period of oscillation of the quartz crystal (τq). If τR e τq (rigid layer) then the τd will be the same both in presence and absence of the adsorbed layer and in this case the dissipation change will be zero. If τR > τq (slow relaxing layer), then the τd in the presence of the adsorbed layer will be smaller than the decay time of the bare crystal and the dissipation will increase. Thus, a slow relaxing layer will dampen the crystal oscillation more efficiently than a fast relaxing one. The change in dissipation due to adsorption of the PEO45MEMA:METAC-X polymers is compared with the adsorbed mass obtained by reflectometry in Figure 7. Notice that for polymers with 10 mol % of charges or more the dissipation falls much quicker with respect to polymer charge density than the adsorbed mass.

4. Discussions The adsorption of PEO45MEMA:METAC-X brush polymers on silica exhibits some interesting characteristics, which are summarized below:

(1) The adsorbed mass and layer dissipation obtained in water depends strongly on the polymer charge and side-chain density as illustrated in Figure 7. (2) The low-charge density brush polymers (X ) 2-10 mol %) adsorb in significantly higher amounts than the uncharged brush in water (pH ∼ 6). (3) The adsorption of low-charge density brush polymers (X ) 2-10 mol %) (Figure 1a, curves 1 and 2) decreases significantly with a small increase in the ionic strength of the solution. The effect is significantly larger than for linear polyelectrolytes of comparable charge density. The adsorption of brush polymers with higher charge densities increases with ionic strength. (4) The adsorption of the low-charge density brush polymers (X ) 2-10 mol %) decreases with increasing pH at constant ionic strength whereas the adsorption of the high-charge density brush polymers (X ) 25-75) increases (Figure 2). On the basis of these observations we will discuss and draw conclusions about how the adsorption mechanism and layer structure depends on the bottle-brush polymer architecture and the silica surface charge density. 4.1. Adsorption of Brush Polymers (PEO45MEMA: METAC-X) in Water. 4.1.1. Adsorption of PEO45MEMA: METAC-X (X ) 50-100 mol %). The adsorbed mass increases linearly with decreasing charge density from 100 to 50 mol % (Figure 1a, curve 1). This is solely due to the increased number of PEO side chains because the total number of backbone segments in the adsorbed layer, calculated using the adsorbed mass and the average segment weight, remains constant in this regime, indicating that the backbone conformation remains unaffected. It is well known that the 100% charged polyelectrolyte in the absence of inert salt adsorbs in a flat conformation.38,39 Our data suggest that the backbone remains flat on the surface as long as the polyelectrolyte charge density is above 50 mol %, and thus the PEO side-chain density is below 50 mol %. This suggests that the adsorption of PEO45MEMA:METAC-X (X ) 50-100 mol %) is mainly electrostatically driven. A further support for a flat backbone conformation comes from the relatively low energy dissipation in this charge density range (Figure 7). We note that the dissipation increases slightly when the polymer charge density is decreased from 100 to 50 mol %. The reason is that it is only the backbone that assumes a flat conformation at the interface whereas many of the PEO side chains form tails, and it is the shearing of these tails that give rise to the increased dissipation. The low hydrodynamic thickness, shown in Figure 6, supports the structural model proposed above, and it is also consistent with recent force measurements.40 4.1.2. Adsorption of PEO45MEMA:METAC-X (X ) 50-25 mol %). The adsorbed mass as a function of polymer charge density (Figure 1a, curve 1) nearly plateaus between PEO45MEMA:METAC-50 and PEO45MEMA:METAC-25. The decreased charge density and the increased steric repulsion between the PEO side chains counteract adsorption. We conclude that the steric repulsion between the PEO side chains has reached a sufficient strength to limit the adsorption, and the number of backbone segments in the layer is consequently lower for PEO45MEMA:METAC-25 than for PEO45MEMA:METAC-50. We note that the dissipation is significantly higher for the layer of PEO45MEMA:METAC-25 as compared to that formed by PEO45MEMA:METAC-50, providing further support to the suggestion that in the former case the backbone no longer resides flat at the interface. (38) Rojas, O.; Ernstsson, M.; Neuman, R.; Claesson, P. Langmuir 2002, 18, 1604–1612. (39) Fleer, G. J.; Stuart, C. M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces Chapter 7; Chapman & Hall: London, 1993.

Adsorption Characteristics of Bottle-Brush Polymers on Si

4.1.3. Adsorption of PEO45MEMA:METAC-X (X ) 25-2 mol %). With further decrease in charge density of the brush polymer, the steric repulsion between the side chains becomes larger and the electrostatic driving force becomes smaller. Both these factors oppose the formation of a flat backbone structure. In this region the number of backbone segments in the layer is close to constant but the adsorbed mass due to the increased number of PEO-side chains in the molecular architecture increases significantly with decreasing polymer charge density; see curve 1 in Figure 1a. We note that the dissipation value and the hydrodynamic thickness are significantly larger in this low-charge density regime than at high polymer charge densities, which demonstrates that more extended layers are formed by the low-charge density polymers. It is thus clear that the adsorbed layer undergoes a drastic structural change as the charge density of the brush polymer is decreased below 25 mol %. The data shown in Figure 2 demonstrate that the adsorbed mass decreases significantly with increasing surface charge density in the case of PEO45MEMA:METAC-X (X ) 2-10 mol %). This is a typical behavior of linear PEO on silica15 and suggests that the main driving force for adsorption of PEO45MEMA:METAC-X (X ) 2-10 mol %) on silica is due to PEO-surface interactions. On the basis of the above discussions, the series of bottlebrush polymers, PEO45MEMA:METAC-X, can be broadly classified into two groups according to their adsorption properties on silica: (1) low-charge density brush (X ) 2-10 mol %) (mainly PEO-driven adsorption) and (2) high-charge density brush (X ) 25-100 mol %) (mainly electrostatically driven adsorption). 4.1.4. Small Amount of Charge along the Polymer Backbone Changes the Adsorbed Layer Structure. The adsorbed amount of the uncharged bottle-brush polymer, poly(PEO45MEMA), in water (pH ∼ 6) is significantly smaller than that of PEO45MEMA: METAC-2. This is interesting considering that both the uncharged and the 2 mol % charged brush polymers share similar conformation in solution. SANS and SAXS data have revealed that both polymers adopt rather stiff rodlike conformations in dilute solution2,41 with a cross section radius of gyration (Rc,g) of 32.5 Å. The interaction between poly(PEO45MEMA) and silica can occur only through the PEO side chains. Thus, the adsorbed layer formed by the uncharged brush can be envisaged as rods lying along the surface to maximize the interaction between PEO and the surface silanol groups. The hydrodynamic thickness of the uncharged brush polymer as calculated from the QCM-D sensed mass is 3.7 nm, which is close to the Rc,g of the brush polymer. This supports the idea that the polymer lie with its backbone along the surface. Although many of the PEO side chains interact with the surface, some of them must for geometrical reasons be extended into solution. When the polymer architecture is changed by introducing some charged segments along the backbone (2-10 mol %), the drive for a close proximity between the backbone charges and the charged surface forces the layer structure to change and more extended structures are formed, as evidenced by the large increase in dissipation and hydrodynamic thickness caused by the introduction of a small amount charges in the polymer structure. In summary, the proposed change in layer structure with polymer architecture can be understood by considering the interplay between strong electrostatic segment-surface interactions (40) Pettersson, T.; Naderi, A.; Makuska, R.; Claesson, P. M. Langmuir 2007, 24(7), 3336–3347. (41) Bastardo, L. A.; Iruthayaraj, J.; Lundin, M.; Dedinaite, A.; Vareikis, A.; Makuska, R.; van der Wal, A.; Furo, I.; Garamus, V. M.; Claesson, P. M. J. Colloid Interface Sci. 2007, 312, 21.

Langmuir, Vol. 24, No. 10, 2008 5347

Figure 8. Schematic representation of the adsorbed layer structure formed by brush polymers of varying architecture. Table 2. Surface charge density calculated based on the titration data provided by Bolt43 a electrolyte surface % of total % of isolated concentration charge density surface silanol surface silanol pH mM (σ) mC/m2 dissociated dissociated 2 6 10

10 10 10

0 12.8 135

0 1.6 16.7

0 8 88

a The data correspond to commercial Ludox silica sol of particle radius 15 nm and specific surface area 180 m2/g.

and weaker PEO-surface interactions. The proposed evolution of the layer structure with polymer charge density is depicted in Figure 8. 4.2. Effect of Ionic Strength on the Adsorption 4.2.1. LowCharge Density Brush Polymers (X ) 0-10 mol %). The results presented in Figure 1a (curve 2) show that presence of 1:1 electrolyte decreases the adsorption significantly in the case of low-charge density brush polymers (X ) 2-10 mol %). Furthermore, the concentration of electrolyte required to achieve desorption of this magnitude is much lower than observed for typical linear polyelectrolytes. For instance, it requires only 10 mM of 1:1 electrolyte to reduce the surface excess of low-charge density brush polymers by 80%, whereas the same amount of salt has very little effect in the case of linear AM-MAPTAC (acrylamide-methylaminopropyl trimethyl ammonium chloride) polyelectrolytes of comparable charge density on silica.42 This indicates that the salt effect exhibited by the low-charge density brush polymers cannot be explained by screening of electrostatic interactions. This is emphasized by the observation that the adsorption of the uncharged brush polymer also decrease in presence of salt. To understand this strong effect of salt, we have to consider the charging mechanism of silica, which is detailed in Appendix 1. The dissociation of surface silanol groups increases with pH and with ionic strength. The reason for the increase with ionic strength is the enhanced screening of the repulsion between the charged surface groups (see Appendix 1). The increase in silica surface charge density thus results in decreased adsorption of the uncharged brush and of the low-charge density cationic brushes. If the adsorption was primarily driven by electrostatic polymersurface attraction, the opposite trend, increase in adsorption with increase in electrolyte concentration, would be expected. On the other hand, the affinity between PEO and silica decreases with increasing degree of ionization of the silanol groups.15 Thus, we conclude that changes in PEO-surface interactions explain the effect of ionic strength on the adsorption of the uncharged bottle brush and of PEO45MEMA:METAC-X (X ) 2-10 mol %). As shown in Table 2, at pH 6 in the presence of 10 mM salt about 8% of the surface silanol groups are ionized and our results show that this is sufficient to cause a significant reduction in the affinity between PEO and the surface. Finally, we note that the amount adsorbed at a given ionic strength is the same as the amount remaining on the surface after rinsing the preadsorbed layer (formed in water) with a solution of this ionic strength. Thus, the end result is independent of the (42) Shubin, V.; Linse, P. J. Phys. Chem. 1995, 99, 1285.

5348 Langmuir, Vol. 24, No. 10, 2008

experimental pathway, indicating that the data reflect the equilibrium situation. 4.2.2. High-Charge Density Brush Polymers (X ) 25-100 mol %). In the case of high-charge density brush polymers, the adsorbed mass increases in presence of 1:1 electrolyte, which is due to the increased surface charge density of silica. This demonstrates that the adsorption is predominantly electrostatically driven and the PEO-silica affinity is of secondary importance when 25 mol % or more of the segments in the polymer are cationic. 4.3. Effect of pH at Constant Ionic Strength. 4.3.1. LowCharge Density Brush Polymers (X ) 0-10 mol %). For the low-charge density brush polymers (X ) 0-10 mol %) the adsorption decreases steeply with increasing solution pH at constant ionic strength; see Figure 2. A similar behavior, decreasing adsorption with increasing pH, is also observed for linear poly(ethylene oxide) on a fully hydroxylated silica.14 Thus, again we find that the predominant interaction of the brush polymers containing up to 10 mol % charged segments with the silica surface occurs through the PEO side chains. 4.3.2. Nature of the PEO Interaction with Silica. It is commonly stated that PEO adsorbs to silica due to hydrogen bonding with surface silanol groups. It is thus to be expected that the PEO-surface affinity should decrease with increasing surface charge density. The results in Table 2 indicate that less than 20% of the surface silanol groups are deprotonated at pH 10, and our data show that this is sufficient to prevent the adsorption of the uncharged and the low-charge density brush polymers. It may appear surprising that such a small reduction in the surface silanol population can completely prevent adsorption. However, if it is the isolated silanol groups that are the primary hydrogen-bonding centers, as can be rationalized by the fact that they can form hydrogen bonds without breaking already existing intrasurface bonds, it turns out that about 90% of the isolated surface silanol groups are dissociated at pH 10. This could certainly have a serious impact on the hydrogen-bonding ability between PEO and the silica surface and rationalize the lack of adsorption found in this study. Finally, we note that although H-bonds form between the ether groups of PEO and the surface silanol groups,16 it is more appropriate to describe the PEO-silica affinity as a consequence of the change in free energy due to several related processes: the breaking of water-silanol H-bonds, dehydration of PEO segments, formation of new water-water H-bonds, and formation of PEO-silanol hydrogen bonds. 4.3.4. High-Charge Density Brush Polymers (X ) 25-100 mol %). In the case of PEO45MEMA:METAC-25, PEO45MEMA: METAC-50, and PEO45MEMA:METAC-75, the adsorption increases with increasing surface charge density. This can unambiguously be attributed to the electrostatic attraction between the positively charged METAC segments and the negatively charged surface sites. The polymers in the charge density region between 25-100 mol % adsorb also at pH 2 when the silica surface is uncharged. At first, it might appear that the adsorption is only due to the affinity between the PEO side chains and the surface. However, one cannot completely neglect the interaction between the charged segments and the surface because even the 100% charged polyelectrolyte shows a limited adsorption at pH 2. It has been shown through experiments44 and theoretical modeling45 that the surface charge density of charge-regulating surfaces such as silica increases due to the presence of adsorbed polyelectrolytes. Thus, the presence of cationic-charged segments (43) Bolt, G. H. J. Phys. Chem. 1957, 61, 1166. (44) Samoshina, Y.; Nylander, T.; Shubin, V.; Bauer, R.; Eskilsson, K. Langmuir 2005, 21, 5872. (45) Shubin, V.; Linse, P. Macromolecules 1997, 30, 5944.

Olanya et al. Table 3. Adsorbed Mass (Γ) in the Presence and Absence of Salt on a Planar Hydrophilic Silica Surface PEO architecture

Γ mg-2 No salt

Γ mg-2 10 mM NaNO3

brush linear

0.70 0.56

0.25 0.23

at the interface induce ionization of surface silanol groups, and this provides an electrostatic driving force for adsorption. 4.4. Salt Effects on PEO Adsorption. Adsorption of linear PEO on Aerosil silica (fumed silica) is not affected by the addition of monovalent ions at neutral pH,15 whereas the adsorption increases in the case of BINDZIL silica.10 Clearly the nature of the silica surface, affected by the method of preparation, strongly affects the adsorption behavior of linear PEO. We have shown that the adsorption of the uncharged brush polymer, poly (PEO45MEMA) decreases significantly in presence of small amount of electrolyte. To elucidate if this effect is peculiar to the brush-type architecture, we also studied the adsorption of linear PEO of comparable molecular weight (500 000 g mol-1) with reflectometry. It was found (Table 3) that both linear and brush-type PEO polymers show similar behavior, a decrease in adsorption with increasing electrolyte concentration. Hence, the reported salt effect appears to be general for PEO-based polymers and not due to the specific polymer architecture.

5. Conclusions The adsorption behavior of bottle-brush polymers containing different charge/PEO ratio on silica was studied using optical reflectometry and QCM-D. It is concluded that the adsorption of brush polymers, depending on the ratio of charge to PEO along the backbone, is due to two distinct mechanisms. In case of low-charge density brush polymers (X ) 0-10 mol %), the adsorption occurs predominantly through the PEO side chains. This conclusion is based on the experimental observation that the adsorbed mass decreases with increase in surface charge density. Nevertheless, the presence of a small amount of charges increases the adsorption significantly and results in the formation of more loops and tails. As the charge density of the brush polymers is increased to 25 mol % or larger, the adsorption occurs predominantly through electrostatic interactions. This conclusion is based on the observation that the adsorbed mass increases with increasing surface charge density. The adsorbed layers formed by the high-charge density brush polymers (X ) 50-100 mol %) in pure water (pH ∼ 6) in the absence of 1:1 electrolyte have the backbone flat on the surface. However, the side chains form tails that contribute to the small increase in the dissipation with increasing PEO content of the polymer in this composition regime. The adsorbed layers formed by the low-charge density brush polymers (X ) 2-10 mol %) in water (pH ∼ 6) in the absence of 1:1 electrolyte consist of loops and tails formed by the backbone that in turn results in large dissipation. Thus, the layers in this charge density regime are the most extended ones. The adsorbed layer of the uncharged brush polymer dissipates considerably less energy which indicates that the brush lie parallel to the surface in agreement with the hydrodynamic QCM thickness. The water content of the PEO containing layers is in all cases high; about 80% of the mass sensed by QCM is due to hydrodynamically coupled water. In contrast, the water content of the poly(METAC) layer is only about 50%.

Adsorption Characteristics of Bottle-Brush Polymers on Si

Langmuir, Vol. 24, No. 10, 2008 5349

Appendix 1. Charging Mechanism of the Silica Surface

increases with increasing salt concentration and pH. This has been confirmed experimentally in several studies.47,48 The charging mechanism of silica in presence of salt has recently been included in the extended self-consistent field (SCF) model to describe the surface charge density of the substrate both in absence and presence of adsorbing polyelectrolyte.45 The existence of two types of silanol groups at the planar silica/water interface, having pKa values of 4.5 and 8.5 with surface population of 19 and 81%, respectively, was reported by a second harmonic generation (SHG)49 investigation. The silica surface used in the SHG study was a fused silica prism that was cleaned with methanol, sodium hydroxide, and a mixture of concentrated HNO3 and HCl. The silanol group with lower pKa value was assigned to the isolated silanol. Potentiometric and deuterium exchange with mass spectrometry studies report that a fully hydroxylated silica surface contains 4-5 Si-OH50 per nm2. We calculated the surface charge densities of silica at pH 2, pH 6 in 10 mM 1:1electrolyte, and pH 10 in 10 mM 1:1 electrolyte based on the titration data given by Bolt.43 The percentage of dissociated silanol groups can be calculated from the total number of surface silanol groups (5 per nm2) and the surface charge density. It is further possible to calculate the percentage of charged isolated surface silanol groups by considering the fraction of isolated silanol groups and the ratio of the equilibrium constants of the two types of silanols. The values obtained are provided in Table 2. The values reported in this table depend critically on the number of silanol groups and the fraction of isolated silanol groups. The trends are, however, generally correct as can also be shown by solving eqs A1-A3 iteratively until self-consistency is achieved.

The surface of silica is populated with silanol groups (Si-OH) and these groups establish equilibrium with water by means of surface ionization as shown below. Ka

SiOH T SiO- + H+ The equilibrium constant, Ka, is defined as

Kai )

[SiO-]i · [H+]s [SiOH]i

and

Kag )

[SiO-]g · [H+]s [SiOH]g (A1)

Where the superscripts “i” and “g” stands for the isolated and geminal silanol groups. The concentration of hydronium ions at the interface [H3O+], is related to that in the bulk [H3O+] through the Boltzmann distribution law

( )

[H3O+]s ) [H3O+]b × exp

-eψ0 kT

(A2)

The symbols Ψ0, k, T, and e represent the surface potential, Boltzmann constant, temperature and the elementary charge, respectively. The surface charge density is given by46

( )

σ0 ) -e[[SiO-]i + [SiO-]g] ) (8ε0εrkTc)1⁄2 × sin h

eψ0 2kT (A3)

The product 0r denotes the static permittivity of the dielectric medium and c is the salt concentration. By solving eqs A1-A3 iteratively, it can readily be shown that the surface charge density (46) Evans, F.; Wennerstro¨m, H. The Colloidal Domain; 2nd ed.; 1999; p 134–35.

LA703739V (47) Allen, L. H.; Matijevic, E. J. Colloid Interface Sci. 1970, 33(3), 421–30. (48) Dove, P. M.; Craven, C. M. Geochim. Cosmochim. Acta 2005, 69(21), 4963–4970. (49) Ong, S. W.; Zhao, X. L.; Eisenthal, K. B. Chem. Phys. Lett. 1992, 191, 327. (50) Zhuravlev, L. T. Langmuir 1987, 3, 316.