Depletion, Adsorption, and Structuring of Sodium Poly(acrylate) at the

Department of Chemistry, Keele University, Staffordshire ST5 5GB, United Kingdom. Received November 2, 1999. In Final Form: February 16, 2000. An atom...
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Depletion, Adsorption, and Structuring of Sodium Poly(acrylate) at the Water-Silica Interface. 1. An Atomic Force Microscopy Force Study A. J. Milling*,† and K. Kendall‡ The Interdisciplinary Research Centre in Polymer Science and Technology, Department of Chemistry, University of Durham, Durham DH1 3LE, United Kingdom, and The Birchall Centre for Inorganic Chemistry and Materials Science, Department of Chemistry, Keele University, Staffordshire ST5 5GB, United Kingdom Received November 2, 1999. In Final Form: February 16, 2000 An atomic force microscope has been used to measure the force between a spherical silica probe and a flat silica surface in the presence of solutions of sodium polyacrylate molecules at pH 7. Two different molecular weight sodium poly(acrylate) samples, of low polydispersity, were used over a wide range of polymer concentrations (0-3.5% w/w). The effects of added simple electrolyte (sodium nitrate) upon the polymer adsorption/depletion behavior were also explored. The measured forces indicate that in the absence of added electrolyte, sodium polyacrylate molecules deplete from the silica-water interface at pH 7, leading to an attractive depletion force at close approach of the surfaces and weak liquidlike structural force oscillations at larger surface separations. These oscillations have a scaling length approximately proportional to cp-0.50, which was independent of polymer molecular weight and in good agreement with the predictions of both scaling theory and computer simulation studies. The depletion layer thickness scaled according to cp-0.6. In 1 × 10-4 M NaNO3 solution, the observed forces where similar to those in the absence of salt at low polymer concentrations, although at higher polymer concentrations the force curves indicated polymer adsorption. Adsorption occurred at a lower polymer concentration for the higher molecular weight polymer sample. At higher polymer concentration, the force oscillations vanished as the polymer solution became homogeneous and the polymer chains presumably entangled.

Introduction Sodium poly(acrylate) (NaPAA) is a relatively simple polyelectrolyte species that has been used with much empirical success both as a steric stabilizer of metal oxide dispersions and as a colloidal flocculant in processes such as paper manufacture and water treatment. In most instances, the mechanism of its interaction with colloidal species and the subsequent effect upon colloidal stability have not been clearly elucidated. In this study we have measured the forces between 5 µm diameter silica spheres attached to atomic force microscope cantilevers and flat silica surfaces in the presence of sodium poly(acrylate) solutions. It is the aim of this paper to outline the forces experienced between silica surfaces in the presence of sodium poly(acrylate) molecules and to relate the observations to some of the interfacial and solution properties of this polyelectrolyte species. We have endeavored to mimic conditions typically found in many metal oxide colloid processing operations. The implications of these studies for colloidal flocculation/phase separation behavior will be discussed elsewhere. At the solvent-solid interface a chemically inert polymer molecule may either adsorb onto or be depleted from the interface. Polymer adsorption is the most commonly observed phenomen, this being reflected in the wealth of literature focusing upon factors such as adsorbed amount and adsorbed layer conformation.1,2 Polymer depletion is a relatively neglected topic. Polymer depletion * To whom correspondence should be addressed. Email: [email protected]. Tel: (44) 0191 3743154. † University of Durham. ‡ Keele University. (1) Napper, D. H. Polymeric Stabilization of colloidal Dispersions; Academic Press: London, 1983.

can have two underlying mechanisms. First, for electrically neutral polymer species the loss of configurational entropy upon adsorption outbalances attractive enthalpic contributions, and therefore adsorption is unfavorable. Second, for polyelectrolyte species interacting with surfaces of the same electrical charge, the Coulombic interaction between the surface and the polymer again ensues that the free energy of adsorption is positive and polymer adsorption is prohibited. In both instances, the depletion of polymers from interfaces has the additional effect that the interfacial solvent molecules (within a so-called “depletion layer”) are at a lower chemical potential relative to the bulk liquid. Overlap of these layers is energetically favorable, and the transfer of solvent to the bulk leads to a weak attractive force between the surfaces. This description is based upon the early theories of Oosawa and Asakura,3,4 Vrij,5 Sperry,6 and Fleer et al.,7 developed for neutral polymer species. Experimental measurement of the neutral polymer depletion force between surfaces8-10 and indirect studies of phenomena such as polymer depletion induced (hard sphere) colloidal phase separation11 have confirmed the (2) Fleer, G. J.; Scheutjens, J. M. H. M.; Cohen-Stuart, M. A.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London, 1993. (3) Asakura, A.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. (4) Asakura, A.; Oosawa, F. J. Polym. Sci. 1958, 33, 183. (5) de Hek, H.; Vrij, A. J. Colloid Interface. Sci. 1979, 70, 592. (6) Sperry, P. R. J. Colloid Interface. Sci. 1982, 87, 375. (7) Fleer, G. J.; Scheutjens, J. M. H. M.; Vincent, B. Polymer Adsorption and Dispersion Stability; ACS Symp. Ser. No. 240; American Chemical Society: Washington, DC, 1984; p 245. (8) Milling, A.; Biggs, S. J. Colloid Interface. Sci. 1995, 170, 604. (9) Kuhl, T. L.; Berman, A. D.; Hui, S. W.; Israelachvili, J. N. Macromolecules 1998, 31, 8258. (10) , Kuhl, T. L.; Berman, A. D.; Hui, S. W.; Israelachvili, J. N. Macromolecules 1998, 31, 8250. (11) Vincent, B.; Edwards, S.; Emmett, S.; Croot, R. Colloids Surf. 1988, 31, 267.

10.1021/la991442v CCC: $19.00 © 2000 American Chemical Society Published on Web 04/21/2000

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essential correctness of this view. With polyelectrolyte solutions, the osmotic pressure is chiefly due to ionic dissolution of the polymer. The depletion force from outside the interstice is counteracted by double-layer interactions within the depleted volume, and the net force is a complex function of the intersticial ionic structure. Both from experimental and theoretical standpoints, depletion of polyelectrolyte species is lesser understood than the case for neutral polymers. As with electrically neutral polymer depletion, indirect phenomenological colloid phase separation studies12-15 have provided initial phenomenological insight. In the first reported direct measurement, an atomic force microscope was used to measure polyelectrolyte-induced depletion and oscillatory forces between silica surfaces in the presence of the strongly ionizing polymer, sodium poly(styrenesulfonate)16 (NaPSS). The findings of this initial atomic force microscopy (AFM) study were subsequently ratified by Walz,17 who used the indirect evanescent wave method developed by Prieve et al.18 An earlier study of interactions due to this polymer (using the surface forces apparatus (SFA))19 indirectly inferred depletion by means of the decay length of the electrical double-layer force between the mica surfaces. However, in the SFA study, the extremely high surface potential of the mica entailed that electrical doublelayer force effectively swamped the much weaker depletion forces. The forces occurring in the presence of solutions of a more weakly ionizing polyelectrolyte species ((poly(acryilic acid) PAAH) have also been examined using AFM by Milling and Vincent.20 In this instance, the polymer simultaneously adsorbs and depletion layers are developed away from the coated surfaces. Prieve et al. latterly found similar behavior for a strongly adsorbing cationic polyelectrolyte species using an evanescent wave method.21 In a recent experimental study of electrically neutral polymer depletion phenomena, the validity of colloid probe AFM measurements has been opined to be invasive in terms of the constrictions arising from attachment of the sphere to the cantilever spring.22 This assumption is groundless for the case of sphere-flat interactions using smooth surfaces. Topics closely related to the polyelectrolyte depletion/ structural force studies have been the depletion and structural forces due to charged surfactant molecules,23-26 colloidal particles,27,28 and the phenomenological related stepwise reduction of thin-film lamellae.29,30 There has been a small body of theoretical development within this field. In earlier theories Hoagland31 considered (12) Rawson, S.; Ryan, K.; Vincent, B. Colloids Surf. 1992, 65, 1. (13) Cawdrey, N. F.; Milling, A. J.; Vincent, B. Colloids Surf., A 1994, 86, 239. (14) Snowden, M. J.; Clegg, S. M.; Williams, P. A.; Robb, I. D. J. Chem. Soc., Faraday Trans. 1991, 87, 2301. (15) Snowden, M. J.; Williams, P. A.; Garvey, M. J.; Robb, I. D. J. Chem. Soc., Faraday Trans. 1994, 166, 160. (16) Milling, A. J. J. Phys. Chem. 1996, 100, 8986. (17) Sharma, A.; Tan, S. N.; Walz, J. Y. J. Colloid Interface. Sci. 1997, 191, 236. (18) Walz, J. Y.; Prieve, D. C. Langmuir 1992, 8, 3073. (19) Marra, J.; Hair, M. L. J. Colloid Interface Sci. 1989, 128, 511. (20) Milling, A. J.; Vincent, B. J. Chem. Soc., Faraday Trans. 1997, 93, 3179. (21) Pagae, E. S.; Tilton, R. D.; Prieve, D. C. Langmuir 1998, 14, 5106. (22) Rudhart, D.; Bechinger, C.; Leiderer, P. Phys. Rev. Lett. 1998, 81, 1330. (23) Parker, J. L.; Richetti, P.; Kekicheff, P.; Sarman, S. Phys. Rev. Lett. 1992, 68, 1955. (24) Kekicheff, P.; Richetti, P. Prog. Colloid Polym. Sci. 1992, 88, 8. (25) Kekicheff, P.; Nalett, F.; Richetti, P. J. Phys. II 1994, 4, 735. (26) Sober, D. L.; Walz, J. Y. Langmuir 1995, 11, 2352. (27) Sharma, A.; Walz, J. Y. J. Chem. Soc., Faraday Trans. 1996, 92, 4997.

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the exclusion of rigid rods from between charged surfaces. The Scheutjens-Fleer (SF)32,3332,33 theory for polymers at interfaces has been extended to incorporate electrical charge effects,34,3534,35 although it would appear that the lattice-based SF theory is currently unable to deal with the subtle complexities of polyelectrolyte behavior. Also Monte Carlo computer simulations36 have been used to explore the conformation of polyelectrolyte species confined between uncharged surfaces. In this study the authors concluded that the structural factors were solely due to segment-segment interactions. Calculations by Yethiraj37 for depleting polyelectrolytes constrained between electrically neutral surfaces have been in agreement with nearly all hitherto experimentally observed features with the notable exception of the force magnitude trends. The model used by Yethiraj predicts that the magnitude of the force oscillations decreases with increasing polymer concentration. In all the experimental studies cited herein, the opposite trend has been observed. Whether the model system envisaged by Yethiraj, i.e., polyelectrolyte nonadsorption at electrically neutral interfaces, can be experimentally realized for aqueous media remains to be seen, and thus this seemingly flawed theory may not be tested without some mitigation. Recently, Walz38 extended hard-sphere solvation theory and used a force balance approach to calculate the depletion force due to small spheres electrostatically excluded from between like-charged surfaces. In contradiction to the findings of ref 36, a Debye-Hu¨ckel based theory, developed by Joanny and Chatellier,39 suggests that at high polymer concentrations, polyelectrolyte molecules (of infinite molecular weight) may form surfaceoriented lamella structures. Sequential depletion of these lamellae gives rise to oscillatory surface forces. For this to occur it was prerequisite that the effective second virial coefficient of the interstitial solution is negative. Recently, Da¨hnert and Huster40 modeled constrained polyelectrolyte molecules, assuming a lamella structure, and using a Poisson-Boltzmann (PB) approach for the interplate ionic distribution, the authors demonstrated the presence of oscillatory forces. Additionally, the authors demonstrated that a Donnan equilibrium41 description for the distribution of ions on either side of a semipermeable membrane is only valid for an uncharged membrane, inferring that for charged surfaces a full PB analysis is required. Calculations by several authors12,14,16,20 have modeled the forces between surfaces in polyelectrolyte solutions by the using an external (attractive) osmotic pressure and an internal (repulsive) electrical double layer interaction. These ad hoc calculations cannot produce oscillatory forces, although long-range electrostatic interactions may give (28) Crocker, J. C.; Matteo, J. A.; Dinsmore, A. D.; Yodh, A. G. Phys. Rev. Lett. 1999, 82, 4352. (29) Asnacios, A.; Espert, A.; Colin, A.; Langevin, D. Phys. Rev. Lett. 1997, 78, 4974. (30) Klitzing, R. V.; Espert, A.; Asnacios, A.; Hellweg, T.; Colin, A.; Langevin, D. Colloids Surf., A 1999, 149, 131. (31) Hoagland, D. A. Macromolecules 1990, 23, 2781. (32) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1979, 83, 1619. (33) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980, 84, 178. (34) Bohmer, M.; Evers, O. A.; Scheutjens, J. M. H. M. Macromolecules 1990, 23, 2288. (35) Dahlgren, M. A. G.; Leermakers, F. A. M. Langmuir 1995, 11, 2996. (36) Carignano, M. A.; Dan, N. Langmuir 1998, 14, 3475 (37) Yethiraj, A. J. Chem. Phys. 1999, 111, 1797. (38) Walz, J. Y.; Sharma, A. J. Colloid Interface Sci. 1994, 168, 485. (39) Chaˆtellier, X.; Joanny, J.-F. J. Phys. II 1996, 6, 1669. (40) Da¨hnert, K.; Huster, D. J. Colloid Interface Sci. (41) Donnan, F. G.; Guggenheim, E. A. Z. Phys. Chem., Abt. A 1932, 162, 346.

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Table 1. Details of the Polymer Samples Used sample

Mn(precursor)/ kg mol-1

Mw/Mn

degree of polymerization

Mn(NaPAA)a/ kg mol-1

NaPAA 33k NaPAA 99k

38.7 132.1

1.15 1.11

305 1040

33.0 99.0

a

Assuming 100% neutralization.

rise to a secondary maximum. “Higher order” virial expansion theories for the partition of small particulate solute species between and beyond an interstice have been shown to give rise to oscillatory forces, the number of force oscillations increasing with the number of virial coefficients used.38,42 While not directly addressing the problem of polymer conformation, these theories clearly demonstrate the importance of long-range electrostatic interactions (both intersolute and solute-surface) in depletion phenomena. More detailed reviews of polymer depletion phenomena may be found elsewhere.2,43,4443,44 Experimental Section Polymer Synthesis. The polymer samples were synthesized by the anionic polymerization of tert-butyl acrylate in tetrahydrofuran (THF), using diphenyl hexyllithium initiation as outlined by Jerome et al.45 to produce poly(tert-butyl acrylate) (PTBA) followed by an acid hydrolysis reaction to yield poly(acrylic acid) (PAAH). The poly(tert-butyl acrylate) polymer samples were purified by precipitation into wet (ca. 5% water w/w) methanol and subsequently characterized by gel-permeation chromatography. The acid hydrolysis of low polydispersity PTBA without cleavage or degradation of the polymer molecules spine has been described in detail elsewhere.46,4746,47 The resultant PAAH was purified by exhaustive dialysis against ultrapure water and was finally isolated by freeze-drying. The molecular weight of the free-acid polymer was calculated using eq 1.

Mn(PAAH) ) Mn(PTBA)

72 128

(1)

The details of the polymer samples used are given in Table 1. Polymer solutions were prepared gravimetrically, and the PAAH solutions were neutralized to pH 7 ((0.05) using aqueous sodium hydroxide. The degree of neutralization was typically ca. 75% at this pH. Dry mass analysis was used to confirm the concentrations of the final NaPAA solutions. The solutions were all maintained at 25 °C for a minimum of 12 h prior to use. AFM Experiments. A Nanoscope “E” (Digital Instruments Ltd) equipped with a fluid cell was used throughout. The AFM laboratory was maintained at a constant 25 °C to avoid thermal drift and associated noise problems. Silicon nitride AFM cantilevers were obtained from Park Instruments Limited. The spring constant of the cantilevers was measured by the resonance method of Cleveland48 and found to be highly consistent for the wafer. Cantilevers with spring constants of ks 0.06 ( 0.005 and 0.03 ( 0.002 N m-1 were used throughout. Silica spheres (kindly gifted by Dr. Franz Grieser, University of Melbourne) of approximately 5-6 µm diameter were purified by first boiling in a hydrogen peroxide solution and then rinsing via several sedimentation/redispersal cycles in pure water and finally in AnalaR ethanol. The probe particles were glued to the tips of the cantilevers using a small amount of either Araldite (Ciba Geigy (42) Mayo, Y.; Cates, M. E.; Lekkerkerker, H. N. W. Physica A., (Amsterdam) 1995, 222, 10. (43) Jenkins, P.; Snowden, M. Adv. Colloid Interface Sci. 1996, 68, 57. (44) Milling, A. J.; Vincent, B. Colloid-Polymer Interactions: from fundamentals to practice; Farantine, R. S., Dubin, P., Eds.; J.Wiley and Sons. (45) Varshney, S. K.; Hautekeer, J. P.; Fayt, R.; Jerome, R.; Teyssie, Ph, Macromolecules 1990, 23, 2618. (46) Cawdrey, N. F. Ph.D. Thesis, University of Bristol, 1992. (47) Kitano, T.; Fujimoto, T.; Nagasawa, M. Polym. J. 1977, 9, 153. (48) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403.

Figure 1. Schematic force curve describing terminology. Ltd) or Epikote resin (Shell). Both gluing operations and probe particle manipulations were performed using a freshly drawn glass whisker attached to a hydraulic micromanipulator. Polished synthetic silica surfaces were purchased from Multilab (Gateshead, U.K.). Contact mode AFM analysis showed these surfaces to be extremely flat and smooth, with a standard deviation of 1 nm over a 1 µm scan length. Prior to use in the AFM, the plates were cleaned by briefly boiling in ammoniacal hydrogen peroxide solution (pH < 9, to avoid etching49), rinsed in copious ultrapure water, and finally blown-dry with a nitrogen jet. The cantilevers were tested prior to the introduction of NaPAA solution by measuring the force between the probe and a silica flat in dilute (1 × 10-4 M NaNO3) as prescribed by Larson et al.50 Polymer solutions were introduced into the AFM wet cell via a syringe, and in most cases, data collection would commence after 15 min. Under conditions where the polymer adsorbs, the force curves where monitored for kinetic effects, although apparently “steady state” force curves would normally be collected within half an hour of introducing the polymer solution. The adsorption behavior was immediately reversible upon flushing the cell with nonadsorbing polymer solutions. Cantilever deflection was monitored using the standard optical technique. Approach speeds in the range 10-75 nm s-1 were used. For these scanner speeds, theory51 suggests that provided the polymer is nonadsorbing, hydrodynamic drainage contributions to the force experienced by the probe will be negligible. Additionally, a small number of long-range scans (using 1-4 µm scanner displacements) were undertaken, confirming the estimated force curve baselines were free from optical contamination artifacts. The raw AFM data were transformed from voltage-scanner displacement form to force-distance using the commercially available AFM analysis software52 based upon the original analysis of Ducker et al.53

Results and Discussion Throughout this study the observed force curves exhibit some generic trends; the salient terminological terms used, namely, the depletion thickness (∆), the correlation length (ξ), the secondary maximum, and the depletion minimum, are all described in Figure 1. Prior to discussing the force-distance data, it is useful to consider some aspects of polyelectrolyte solution properties. The conformational behavior of polyelectrolyte species in bulk solution is still very poorly understood and is a matter of active debate.54 The properties of PE (49) Trau, M.; Murray, B. S.; Grant, K.; Grieser, F. J. Colloid Interface Sci. 1992, 148, 182. (50) Hartley, P. G.; Larson, I.; Scales, P. J. Langmuir 1997, 13, 2207. (51) Chan, D. Y. C.; Horn, R. G. J. Chem. Phys. 1985, 83, 5311. (52) Chan, D. Y. C. Department of Mathematics, University Melbourne, Parkville, Victoria Australia. (53) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (54) Dantzenberg, H.; Jaeger, W.; Ko¨tz, J.; Phillipp, B.; Seidel, Ch.; Stscherbina, D. Polyelectrolytes: C. Hanser: Verlag, Germany, 1994.

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molecules constrained between charged interfaces are even less understood. Factors such as the local pH, the local ionic strength, ionic quenching behavior of the polyelectrolyte chains, and specific surface-polymer interactions have yet to be fully included into contemporary models. However, as outlined by Dobrynin et al.55 and summarized by Scheissel,56 scaling theory for polyelectrolytes facilitates an initial starting point for understanding empirical observations. It is widely accepted that in salt-free, dilute solution, polyelectrolyte molecules assume an extended conformation. The extreme case is an electrostatically stiffened “rigid rod”, although computer simulation studies performed by Stevens and Kremer 57,58 (for many chains) suggest that full extension of a polyectrolyte molecule cannot be realized within physically realistic circumstances. In the present case, we assume that the solvency of the acrylate spine is approximated by “good” conditions, neglecting potential hydrophobic intrachain associations which have been explored by recent scaling theory.59 It is expected that for NaPAA the solvency condition will not be as critical as it is for NaPSS where the strongly hydrophobic phenyl groups have been shown to have considerable effect upon the polymer solubility (e.g., phase separation of NaPSS may be induced by small concentrations of added polyvalent cations60). The experimental force-distance data cover both the dilute and the semidilute regime. To a first approximation, the rigid rod length may be calculated using eq 2

LROD ) Nb

() u fa2

2/7

(2)

where N is the number of monomer units (of length b), u is the ratio of segment length/Bjerrum length (lB ) 0.7 nm for H2O), and fa is the fraction of dissociated monomer units. Using the scaling theory definition, the onset of the salt-free, semidilute regime (C2(rod)*) begins when the precessional volumes of the rods begin to overlap, and as such this condition can be estimated using eq 3.

C2(rod)* ) 4.6 N/πLROD3

(3)

The theory also suggests that at higher concentrations the rods gradually begin to curl up and are more akin to crooked sticks than “rigid rods”. In the presence of added salt, scaling theory predicts that longer chains may be flexible (“wormlike”) in the dilute regime, whereas short chains will remain rigid. Again, this description is at odds with the computor simulations of Stevens and Kremer57,58 who have asserted that the chains are always bent and that the dilute-semidilute transition is better described as occurring when the counterion concentration is equal to the chain concentration. Calculations based on this premise suggest that in the present circumstances, nearly all of our experiments have been performed in the semidilute regime. This latter assertion is questionable as the extremely small ionic strengths encountered in the low polymer concentration regimes are beyond the scope of the mean field Debye-Hu¨ckel description. (55) Dobrynin, A. V.; Colby, R. H.; Rubenstein, M. Macromolecules 1995, 28, 1859. (56) Schiessel, H. Macromolecules 1999, 32, 5673. (57) Stevens, M. J.; Kremer, Phys. Rev. Lett. 1993, 71, 2228. (58) Stevens, M. J.; Kremer, J. Chem. Phys. 1995, 103, 1669. (59) Dobrynin, A. V.; Rubenstein, M. Macromolecules 1999, 32, 915. (60) Olvera de la Cruz, M.; Belloni, L.; Delsant, M. J. Chem. Phys. 195, 103, 5781.

Table 2. Scaling Theory Lengths and Concentration Regimes for the Polymer Samples Used N

L/nm

C*2(rod))/ppm

C*2(salt))/ppm

Rg(saw)/nm

350 1050

53 160

535 58

1118a 124a

5.6 9.2

a

Calculated for 1 × 10-4 M salt.

For scaling theory, the onset of the semidilute regime in the presence of added salt (C2(salt)*) is when the intrablob monomer concentration equals the bulk concentration. Equation 4 describes this situation. In this case B is the ratio of chain contour length/rod length.

(

C2(salt)* 1 +

2Cs faC2(salt)*

)

-3/2

) N -2(B/b)3

(4)

The onset of these regimes have been estimated for NaPAA chains of N ) 350 and 1050, with b ) 0.30 nm, B ) 1.97, and fa was assumed to be 1/5.61,62 The calculated values are presented in Table 2. For comparison, the radius of gyration (Rg) for a random walk conformation has been additionally estimated, using the relationship Rg ) 0.3N1/2 (nm). As with most estimations based on scaling theories, the calculated values cannot be expected to be exact as nondimensional prefactors are neglected. 1. Intersurface Forces in the Absence of Added Electrolyte. Force curves obtained for NaPAA 33k for various polymer concentrations in the absence of (intentionally) added electrolyte are presented in Figure 2. Extremely similar force curves were obtained for NaPAA 99k, although the force oscillations were of slightly longer length scale and slightly lower magnitude for NaPAA 99k. The force curves depicted in Figure 2a-c are for approaching surfaces only, in these concentration ranges there was very little hysteresis in the force curves between approaching and retracting surfaces. The data presented are also “cropped” for purposes of clarity, the higher magnitude forces merely resembling monotonically increasing primary maxima. The concentration range explored is very wide, spanning from the dilute (C2 ) 39 ppm w/w) to the extended semidilute regime of polyelectrolyte solutions at C2 ∼ 3.3% w/w. Generally, the force curves are oscillatory in nature. At the extremely low limits of polymer concentration (e.g., Figure 2a), there are subtle differences in scaling length and force magnitude, between the two polymer samples that do not bear direct comparison. These differences could be ascribed to subtle variance in the degree of neutralization or differing degree of ionic contamination by, for instance, carbon dioxide.62 This apparently defines the limit of experimental sensitivity, which is not so much lower (in terms of polymer concentration) than that cited in evanescent wave studies.21 Notwithstanding these subtleties at low NaPAA concentration, the force-distance behavior due to samples 33k and 99k in the absence of added electrolyte may be commonly described as follows. Starting at a concentration of 39 ppm, there is a very long-range repulsive force, which upon decreasing surface separation passes through a maximum at h ) 110 nm, and then a minimum at h ) 70 nm. With a 4-fold increase in C2 to 158 ppm, the next higher oscillatory force branch has become apparent. Beginning with a minimum at h ) 150 nm, there follows a 3°max at h ) 110 nm and a 3°min at h ) 83 nm. The depletion force begins with the 2°max (61) Konop, A. J.; Colby, R. H. Macromolecules 1999, 32, 2803. (62) Weill, C.; Lachhab, T.; Moucherout, P. J. Phys. II 1993, 3, 927.

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Figure 2. Reduced force curves for a silica sphere interacting with a silica plate at various NaPAA 33k concentrations at pH 7, in the absence of background electrolyte.

at h ) 53 nm, developing a 2°min at h ) 30 nm. In common with earlier studies concerning NaPSS,16 both the depletion layer thickness and the correlation length systematically decrease with increasing polymer concentration and the magnitude of the force oscillation simultaneously increases. At a concentration of 3339 ppm (Figure 3c) there are three attractive force branches, the maximum of the

branch of closest surface approach occurs at a surface separation of ca. 10 nm, prior to the surfaces snapping into contact compliance. Within experimental uncertainty, it would appear that the period length between successive branches (excepting the “depletion branch”) is invariant of bifurcation order for a given polymer concentration. In the absence of added electrolyte and at high polymer

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This approach requires that the probe detachment from the surface is normal, without rolling or slipping over the surface. The estimated adhesion energies for parts d and e of Figure 2 are -2900 and -7950 kT, respectively. Assuming the Derjaguin approximation to be valid (as has been demonstrated for surface force measurements taken in the presence of simple electrolytes63) this would relate to adhesion energies of -43 and -119 kT for interacting spheres of 100 nm radius. Similarly integration of the secondary maximum suggests these spheres would have to pass through an energetic barrier of ca. 6.2 and 9.1 kT prior to reaching the adhesive depletion minimum. Kinetic stabilization has not been observed in colloidal flocculation experiments, although flocculation into a metastable energetic minimum formed at a higher branch order may not be precluded.16,17 The ramifications of these observations with respect colloidal phase stability will be discussed elsewhere.64 Scaling analysis for the depletion layer thickness and the structural correlation length are depicted in Figure 3. The depletion layer thickness has a scaling index of ca. -0.62, in comparison to earlier studies of the “strong” polyelectrolyte, NaPSS,16 and the very weakly dissociated PAAH20 where scaling indices of -0.71 and -0.33 (respectively) were measured. By analogy to theory for the depletion of electrically neutral polymers, ∆ decays more rapidly as the solvency improves (scaling theory66 predicts an exponent of -0.75 for “good” and -0.5 for “theta” solvency conditions, and similarly the model of Vincent67 predicts a faster decay of ∆ with decreasing χ). In Figure 3b the measured oscillatory period length is directly compared to the theoretical prediction of Dobrynin et al.55 using eq 6. The agreement between theory and experiment is very good, although eq 6 is only valid for concentrations >c*. In addition to the scaling rational, the computer simulations of Stevens and Kremer57,58 predict that there is a chain-chain correlation length scale that has a c-1/2 dependency below c*. Figure 3. Summarization of scaling lengths as functions of polymer concentration, for the force curves collected in the absence of added electrolyte. Part a illustrates the surface separation of the secondary maximum, and part b illustrates the structural correlation length. Key: NaPAA 99k, O; NaPAA, 33k b.

concentrations, force curve hysteresis has been observed. Parts d and e of Figure 2 show force curves for both approaching and retracting surfaces (sample NaPAA 33k). At these higher polymer concentrations the attractive depletion force gradient exceeds the force constant of the cantilever spring and the spring “snaps” into its next stable branch position (where dF/dh < 0 and F > 0). Under such circumstances, the form of the force-distance relationship and the magnitude of the attractive force are not sampled. The position of spring stability should also be treated with caution as the rapid “jump” suggests that the local thermodynamic situation may best be described as adiabatic, whereas it is the aim of the experiment to produce isothermal measurements. In these circumstances, examination of the equivalent retraction branch is required. Assuming that local thermal equilibrium to be restored, measurement of the “pull-off” force (FJ) may be used to estimate the energy of adhesion (Wads), using eq 5, i.e., the elastic energy stored in a Hookean spring.

WADS )

FJ2 2k

(5)

ξ ) (B/cb)1/2

(6)

In a previous study it was found that ξ ) c-0.48 for NaPSS.16 In the study of PAAH-mediated forces20 there was a marked absence of structural oscillations. This latter observation being due to reduced intermolecular osmotic stresses (the degree of monomer dissociation was estimated to be ca. 3%). Clearly there is an absence of a universal scaling length for ∆, but scaling indices of higher magnitude are obtained for more highly dissociated polyelectrolyte molecules. This suggests that these species are pushed onto the surface under their own osmotic pressure. For sample NaPAA 33k some of the forcedistance data have been collected in the dilute regime where the polymer is expected to be in a fully extended conformation and there are force oscillations below C2* which are of longer length scale than the estimated stretched rod length. This demonstrates that an isotropic mesh of polyelectrolytes is not solely prerequisite for structural force oscillations as has been suggested.29,30 Several options were discussed for the basis of polyelectrolyte structure factors in de Gennes’ original paper,65 and the paper of Dobrynin et al.53 further elucidates that (63) Cohen, J.; Priel, Z.; Rabin, Y. J. Chem. Phys. 1992, 88, 7111. (64) Christie, G. A.; Carnie, S. L. J. Chem. Phys. 1990, 92, 7761. (65) Milling, A. J. In preparation. (66) de Gennes, P.-G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (67) Vincent, B. Colloids Surf. 1990, 50, 241.

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Figure 4. Reduced force curves for a silica sphere interacting with a silica plate at various NaPAA 99k concentrations at pH 7, in the presence of 1 × 10-4 M NaNO3.

electrostatic forces of a range longer than a finite rod length can lead to osmotically induced structure factors. Additionally, in the semidilute regime, situations where there are three oscillations have been observed, beginning at surface separations shorter in total length than the length of an allegedly rigid rod. Hence for certain circumstances, the conceptual model which includes extended transverse interfacial rods29,30 would seem to be physically unreasonable. The polyelectrolyte molecules must be parallel to the interface in a lamella-like arrangement, either an anisotropic mesh or an isotropic fasciste. It has been stressed that both electrostatic crystal and isotropic mesh correlation lengths both have structural lengths with the dependence ξ∼ c-1/2 and thus it would seem that on the basis of scaling lengths, force measurement techniques are presently unable to distinguish between the available models. 2. Forces in the Presence of Added Electrolyte. It may be expected that the effects of adding electrolyte will be threefold. The bulk osmotic pressure will be reduced (this may be further exacerbated by a decrease in the polymer dissociation constant with increasing salt concentration). The zeta potential of the silica surface will also be reduced in magnitude (as found by electrokinetic measurement in the presence of simple electrolytes).69 And the polyelectrolyte molecule may become flexible. The

former two effects entail that electrostatic interactions (both intra- and intermolecular, and polymer surface) will be reduced both in magnitude and also in length scale (via the Debye length). The theme of chain flexibility represents a divergence in current opinion of polyelectrolyte theory. Molecular dynamics simulation57,58 predicts that chains are flexible for all regimes. Scaling theory asserts that chains become flexible when the Debye length of the bulk electrolyte is equal to the extended rod length (which in most cases is extremely close to the critical overlap concentration). The theory of Odijk70 and Skolnick and Fixman71 maintains that the chains do not become flexible until a somewhat higher polymer concentration (than that predicted by scaling theory) is reached. Figures 4 and 5 illustrate experimental force curves for samples NaPAA 99k and NaPAA 33k obtained with a background electrolyte concentration of 1 × 10-4 M NaNO3 at pH 7. The extended length of NaPAA 33k is approximately the same as the external electrolyte Debye length while for NaPAA 99k the extended rod length greatly exceeds the (68) de Gennes, P.-G.; Pincus, P.; Velasco, R. M.; Brouchard, F. J. Phys II 1976, 37, 1461. (69) Hunter, R. J. Foundations of Colloid Science; Clarendon Press: Oxford, 1989; Vol. 1. (70) Odijk, T. Polymer 1978, 19, 989. (71) Skolnick, J.; Fixman, M. Macromolecules 1977, 10, 944.

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Figure 5. Reduced force curves for a silica sphere interacting with a silica plate at various NaPAA 33k concentrations at pH 7, in the presence of 1 × 10-4 M NaNO3.

Debye length. The force-distance behavior in the presence of either of these two polymer samples is quite different, and both are described in turn. For polymer sample NaPAA 99k, at low polymer concentrations, force oscillations are apparent. However,

these seem to be superimposed upon a long-range weak repulsive force. As the polymer concentration is increased, the force oscillations again decrease in length scale and increase in magnitude but the long-range superimposition becomes slightly attractive. The origin of this “superim-

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force oscillations there is reasonable agreement between theory and experiment. Additionally, at the lower polymer concentrations, ξ is theoretically predicted to be slightly larger in the presence of salt (concentration Cs). This subtlety is also evident in the experimental data.

(

ξ ) b(cb3)-1/2 B1/2 1 +

Figure 6. Summarization of scaling lengths as functions of polymer concentration, for the force curves collected in the presence of 1 × 10-4 M NaNO3. Part a illustrates the surface separation of the secondary maximum, and part b illustrates the structural correlation length. Key: NaPAA 99k, O; NaPAA 33k, b.

posed” long-range force is unclear although a relationship to the whole interstitial ensemble may be suggested. The depletion layer decreases quite rapidly with respect to increasing polymer concentration. This is best illustrated in the scaling analysis in Figure 6a. After the region marked A-B, there is clearly a “jump” in the depletion layer thickness (points B to C). This is the region where the polymer begins to adsorb and this “jump” is the promotion of the second oscillatory force branch to become the depletion branch. The situation is now analogous to the earlier study using a slightly higher molecular weight PAAH sample, where a depletion layer was found beyond an adsorbed layer. After this concentration the primary maximum must be due to a combination of electrostatic and steric components, which are intrinsically coupled for adsorbed polyelectrolyte layers. At still higher polymer concentrations (>5000 ppm) the force oscillations disappear and the intersurface forces are repulsive for all separations. It is surmised that the electrostatic blobs will not have collapsed at these higher concentrations although the flexible chains will have entangled. The scaling analysis55 for the correlation length in the semidilute (added salt) regime is described by eq 7 and is illustrated in Figure 6b. Prior to the disappearance of the

)

2Cs fC2

1/4

(7)

Typical force-distance behavior for sample NaPAA 33k is illustrated in Figure 5. Again there are force oscillations that increase in magnitude and decrease in length scale with respect to increasing polymer concentration. The length-scale behaviors of ∆ and ξ are summarized in parts a and b of Figure 6, respectively. Similarly to sample NaPAA 99k, there is a discontinuity in ∆ versus concentration (Figure 6a points D-E), albeit at a slightly higher concentration. This discontinuity again indicates adsorption of the polymer. Thereafter the behavior as polymer concentration is increased differs slightly than that for the NaPAA 99k sample. The depletion thickness decreases to a value of ca. 5.6 nm at Cp ) 1.57% w/w. The force curves (Figure 4h) illustrate that there is very little change in either ∆ or ξ at these high Cp values. The main effect of increasing polymer concentration is to increase the height of the secondary maximum. The depletion layer vanishes at higher polymer concentration. The behavior of ξ is even more remarkable. In Figure 6b for NaPAA 33k, ξ reaches a plateau value of ca. 12 nm (regions D-E) over nearly a decade in concentration. This plateau value then decreases rapidly at higher concentrations, where the length scales solely remain as residual features in the repulsive force-distance curves. In common with the feature seen for sample NaPAA 99k (ξ ) 18 nm, Figure 6b, region B to C) it may be conjectured that a scaling length of ca. 12 nm represents a basic feature for this polymer system, namely, the onset of polymer entanglement. Qualitatively, for NaPAA 33k the ratio of L/ξ suggests there are approximately five mesh intersections per chain. Similarly, for NaPAA 99k a mesh length of 18 nm represents ca. 7 nodes. This is in accordance with theoretical predictions for entanglement.72 Chain flexibility is obviously a prerequisite for entanglement, and it is not observed for salt-free conditions. Whether the subtle difference in the estimated number of nodes is a free end effect or an artifact introduced by sample polydispersity is uncertain. The onset of these regimes is at approximately 3000 ppm for both polymer samples, and at this concentration, it is estimated that the Debye screening length is around 4 nm, and so the concept of the electrostatic blob would still appear to be valid. The underlying explanation for the protracted plateau in ξ for NaPAA 33k is unclear. At these high concentrations entanglement dynamics between free and adsorbed polymer layers may add a further complication and may partly explain the difference between the two polymer samples. By anology to free solution dynamics, Rouse relaxation times are expected to scale as N3 and thus the chain dynamics of NaPAA 99k would be at least a factor of 30 slower. Hence the oscillatory forces may rapidly disappear for NaPAA 99k while for NaPAA 33k the intersticial viscosity may still be sufficiently low to allow relaxation as the surfaces approach. The difference in the two limiting scaling lengths suggests that this scaling length cannot be related to a reptation tube width, which would be expected to be independent of the degree of polymerization. (72) Kavassalis, T. A.; Noolandi, J. Macromolecules 1989, 22, 2709.

Poly(acrylate) at the Water-Silica Interface

The underlying basis for the adsorption behavior is unclear, although either hydrogen bonding or favorable ion-pair dipole-dipole interactions could be conjectured. Increasing chain flexibility would allow optimal segmentsurface interactions. However, the adsorption cannot be ascribed to the expected “end effect” where the hydrophobic initiator fragment (diphenylhexyl moiety) would promote adsorption inversely with molecular weight. Moreover, at polymer concentrations where the polymer adsorbs (and also where the force oscillations vanish) the inequality faCp . 4Cs is satisfied and thus scaling theory predicts that the polymer behavior should be very similar to that in the salt-free solution. This is clearly not the case and indicates either a weakness in the scaling theory or a further complication due to the silica surfaces’ attendant Stern layers. Conclusions A probe-equipped AFM has been used to study the effects of sodium poly(acrylate) molecules upon the forces between silica surfaces. The polymer led to both depletion and oscillatory “structural” forces between the surfaces; the length scale of both decreased with increasing concentration. In salt-free conditions, at low polymer concentrations these structural forces may be explained by long-range crystal-like ordering of the molecules, and at higher

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polymer concentration, by the formation of a mesh. The length scale of the structural oscillations is in very good agreement with the predictions of scaling theory and computer simulation. The depletion interaction increased with polymer concentration, and the adhesion energy between the surfaces became quite considerable. At polymer concentrations greater than ca. 2% w/w the extremely high solution viscosity prevented further investigation. In the presence of a dilute background electrolyte, the force-distance behavior was extremely modified, mainly due to chain flexibility. At low concentrations, the behavior was similar to that for salt-free conditions. At higher polymer concentration, the polymer was shown to weakly adsorb. Then at higher still concentrations, the chains became entangled and the force oscillations vanished leaving a purely repulsive interaction between the surfaces. For the low and semidilute regimes this behavior is only crudely explained by scaling theory, and there is a subtle discrepancy between the observed correlation lengths and the theoretical predictions. At higher concentrations, scaling theory fails to predict an observed plateau in the force oscillation length scale, although this is not too surprising as this regime is well beyond the dilute, salt-free, reference state of scaling analysis. LA991442V