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J. Phys. Chem. 1996, 100, 8986-8993
Depletion and Structuring of Sodium Poly(styrenesulfonate) at the Silica-Water Interface A. J. Milling† The AdVanced Mineral Products Research Centre, School of Chemistry, The UniVersity of Melbourne, ParkVille, Victoria 3052, Australia ReceiVed: October 19, 1995; In Final Form: February 26, 1996X
An atomic force microscope has been used to study the interaction forces between spherical silica particles (of radius 3-6 µm) and a planar silica surface mediated by aqueous solutions of sodium poly(styrenesulfonate). The experimental parameters explored were the free polymer molecular weight and concentration, the background electrolyte concentration, and pH. Force-distance curves displayed a short-range repulsion due to overlap of opposing electrical double layers and then a minimum due to depletion of the polymer. In some instances, at further surface separations, oscillatory forces indicative of polymer coil structuring were observed for both approaching and retracting surfaces.
Introduction The use of polyelectrolytes to modify the interactions between colloidal particles is important in many applications such as in dewatering processes, soil conditioning, and paper manufacture. The chief focus of interest has been the flocculation of particles to form nondilatent sediments using mutually adsorbing polymers to induce bridging flocculation of particles. The effect of nonadsorbing (depleting) polymers upon colloidal stability has received somewhat less attention, and in turn studies reporting on polyelectrolyte depletion are less common than those of depletion of uncharged polymers.1-3 Depletion of polymer coils from interfaces occurs when the net segmental adsorption energy is insufficient to balance the configurational entropy loss upon adsorption of the polymer molecule.4 For a polyelectrolyte molecule approaching an interface of the same charge sign there is a repulsive electrostatic contribution to the segmental adsorption energy.3 The depletion of polymers from surfaces leads to the formation of depletion layers (of thickness ∆) of increased solvent chemical potential (µ01) relative to the bulk free polymer solution (chemical potential µ1) so there exists a negative disjoining pressure between the interface and the bulk solution. Overlap of adjacent depletion layers transfers solvent to the bulk solution and is thus energetically favorable, as recognized by Oosawa and Asakura5,6 (OA theory). The attractive depletion interaction energy was thus described as the product of the overlap volume and the chemical potential of solvent molecules in the depletion layers (relative to those in the bulk polymer solution). Initially, the depletion thickness was identified with the radius of gyration of the dissolved polymer coil5,6 although subsequent theories7-9 for neutral polymers have recognized that ∆ decreases with increasing free polymer concentration. A working definition of the depletion thickness was provided by Fleer et al.7 (SFV model), who demonstrated, using a meanfield approach for polymers at interfaces,10,11 that for intersurface separations of 2∆ or less the interstice is devoid of polymer molecules, and as such the depletion force (Fdepletion) between a plate and a sphere (of radius a) as a function of separation (h) may be described by eq 1 † Present address: School of Chemistry, Keele University, Keele, Staffs ST5 5BG, UK. X Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(95)03095-4 CCC: $12.00
Fdepletion ) π
( ) µ1 - µ01 ν01
(h + 2a)(h - 2∆)
(1)
where (µ1 - µ01)/ν01 is the osmotic pressure of the polymer solution, ν01 being the molecular volume of the solvent. It should be noted that for close approach of surfaces with thin depletion layers eq 1 is approximately linear. For polyelectrolyte solutions the osmotic pressure may be directly measured or estimated from, for instance, eq 2
µ1 - µ01 ν01
)
RTc2 4A2cs + Ac
(2)
where R is the gas constant, T is the temperature, c is the concentration of monomer units, cs is the concentration of added salt, and A is the average number of monomer units between uncondensed charges along the polymer chain. Development of a theory for the depletion of polyelectrolytes from interfaces has been somewhat slow, although selfconsistent-field calculations12,13 (based on the ScheutjensFleer10,11 model) have been made for polyelectrolytes interacting with both neutral and charged solid-solution interfaces. These calculations were mainly concerned with generating polymer volume fraction profiles, and the mean field (in planes parallel to the interface) assumed by the model ignores specific multiplebody interactions. Hoagland14 has examined the case of rodlike polyelectrolytes interacting with like-charged surfaces; the calculations, which are pertinent for dilute solutions of strongly stretched polyions, show that the depletion thickness increases with increasing surface potential, increasing rod length, and decreasing ionic strength. Generally, experimental studies of polymer depletion have been limited to indirect methods, such as particulate flocculation studies. Other studies have included the estimation of the depletion layer thickness by methods such as an evanescent wave technique,15 1H nuclear magnetic resonance spectroscopy,16 neutron reflectivity,17 and electrophoresis.18 The contact depletion interaction energy has been estimated rheologically19,20 and also by the strength of adhesion of vesicles.21 Recently, there has been a renewal of interest in depletion phenomena using newly developed techniques to study depletion forces: an atomic force microscope (AFM) has been used to directly measure the depletion force between two stearlyated silica © 1996 American Chemical Society
NaPSS at the Silica-Water Interface surfaces mediated by cyclohexane solutions of poly(dimethylsiloxane)22 (PDMS), the surface force apparatus (SFA) has been used to study the forces between surfactant bilayers adsorbed onto mica due to micellar solutions,23,24 and an evanescent wave technique25 has been used to study the forces between a large latex sphere and a flat plate, again mediated by micellar solutions.26 The studies of forces between surfaces mediated by the micellar solutions also demonstrated structural forces that became increasingly apparent as the micelle concentration increased. The formation of ordered structures in (bulk) solutions of polyelectrolyte molecules27,28 and sulfonated latices29,30 has been extensively studied by Ise and co-workers; additionally, there are other reports of colloidal crystals formed from charged latices.31-33 The observation of ordered structures suggests that the summation of pairwise interaction forces will be insufficient in describing the interfacial properties of polyelectrolyte solutions. The problem of many multiple-body interactions and attendant structural forces has been investigated by Wasan and co-workers,34,35 who have studied stepwise thinning of films formed from micellar solutions and subsequently modeled the ordering and drainage of thin films of hardsphere particles between two solid surfaces using Monte Carlo simulations. Attard36 has also demonstrated that multiple-body interactions in heterogeneous (bimodal) hard-sphere fluids leads to the formation of structured and depleted (solute) layers. The effect of depletion of sodium poly(styrenesulfonate) (NaPSS) from aqueous-solid interfaces has been studied by several authors by means of dispersion stability experiments,37-40 utilizing both silica and polymer latices. Additionally, measurements made by Marra and Hair41 using an SFA42 inferred depletion of NaPSS from the water-mica interface although, in this instance, electrical double-layer repulsions were of sufficient magnitude to swamp the relatively weak depletion interaction between the surfaces. This study presents direct force data that confirms the depletion of NaPSS from the silicawater interface and also demonstrates the presence of structural forces between the surfaces due to polymer molecules. Experimental Section All AFM experiments were performed using a Nanoscope III instrument (Digital Instruments). All water used in the experiments was Milli-Q grade, and electrolyte solutions were prepared using “AnalaR” grade NaNO3 (BDH). The NaPSS samples used were obtained from Pressure Chemicals Ltd. and from Polymer Laboratories; the supplier quoted molecular weights were 200 000 and 46 100 (respectively denoted P1 and P2 hereafter), and both samples had a polydispersity index (Mw/ Mn) less than 1.1. Sample P2 was extensively dialyzed against Milli-Q water. Silica spheres were obtained from Allied Signal, and polished silica plates were purchased from H. A. Groiss Ltd. AFM imaging of the plates gave a typical surface roughness of 2 nm for a 1 µm2 scan size. Prior to use the plates were initially soaked in 2 M HNO3 and then, after washing with copious H2O, boiled in ammoniacal hydrogen peroxide as described by Grieser et al.43 Silica spheres (of 4-6 µm radius) were glued to the tips of AFM cantilevers (Digital Instruments) using Epikote 1004 resin (Shell) as the adhesive, as outlined by Ducker et al.44 Such cantilevers with attached colloid spheres will hereafter be referred to as colloid probes. In a typical AFM experiment, the force, F(h), is measured as a function of the surface separation (h) between the colloid probe and the flat plate. In all cases, forces are recorded via a split photodiode as deflections of the cantilever probe as the plate is continuously scanned to and away from it. Following the description of Ducker et al.,44 the surfaces were considered to be in contact
J. Phys. Chem., Vol. 100, No. 21, 1996 8987 when the output of the diode became a linear function of the sample displacement; zero force was defined as when displacement of the surface caused zero deflection of the cantilever. From estimation of these two limits, force-distance curves may be constructed. In all the experiments reported here 200 µm long Si3N4 cantilevers were used. Calibration of the cantilever spring constant using the method of Cleveland et al.45 gave a value of 0.074 ( 0.02 N m-1. Polymer solutions were prepared gravimetrically in screw-top vials, and the pH of these solutions was adjusted prior to use with small aliquots of NaOH or HNO3. For the force-distance experiments polymer solutions were introduced into the AFM liquid cell via a syringe and allowed to equilibrate for a 1/4 h prior to acquisition of data. Identical force-distance data were collected in instances where longer solution incubation times were allowed (ca. 6 h). Forcedistance scans were made for a series of scanning frequencies from 0.05 to 2 Hz and for scan ranges of 100-750 nm both in the presence and in the absence of free, dissolved polymer. In these circumstances the slow approach speed of the colloid probe to the silica plate ensured that hydrodynamic drainage forces, as examined by Chan and Horn,46 are negligible. Data acquired were fully reversible with respect to solution conditions. In the Results section of this paper, for reasons of clarity, experimental force-distance curves are shown for approaching surfaces only. With the exception of instances where the (attractive) force gradient was sufficient to cause a “snap-in” to the flat surface upon aproach, identical force-distance curves were obtained on separation of the surfaces. Under conditions where a “snap-in” was observed there appeared to be a very small increase in the adhesion force indicated by a small increase in the “pull-off” jump distance upon retraction of the surfaces; however, upon reattaining separations where the cantilever spring was stable, approaching and retracting force curves were perfectly superimposable. Results and Discussion In all the experiments performed in this study the solution pH was always maintained above the isoelectric point of silica (2-3 pH units) so that both the silica and the polymer molecules had a net negative charge, and thus there were repulsive electrostatic interactions between the opposing silica surfaces, the silica surfaces, and the polymer molecules (causing depletion) and also between the polymer molecules. At close approach of the surfaces the total force between the surfaces will be a summation of depletion, van der Waals (VDW), and electrical double-layer interactions (EDL). The screening length of the EDL force is determined by a Donnan equilibrium established between the polymer-free interstice and the bulk solution. For larger surface separations there are additional forces due to the mutual repulsion between polymer coils. This repulsion leads to structuring of the polymer molecules as schematically illustrated in Figure 1. Increasing compression of the polymeric crystal leads to a positive disjoining pressure between the surfaces relative to the bulk, until at a sufficiently high pressure the crystal relaxes by shedding a lattice layer to the bulk, leading to a negative disjoining pressure. Continued approach of the surfaces thus leads to the observed force oscillations. The magnitude of the force oscillations increases as the surfaces approach due to increasing ordering of the polymer molecules between the interfaces and an increase in the relative (both positive and negative) disjoining pressure between the intersurface region and the bulk. Considering the shedding of each layer as a quasi-depletion process, simple geometric and osmotic considerations suggest that the maximum positive disjoining pressure upon removal of a layer is propor-
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Figure 1. Schematic representation of interactions between polyelectrolyte molecules and surfaces. The diagram depicts polymer-polymer correlation (ξ) distances and also polymer-surface depletion layers (shaded).
tional to n/(2∆ + (n - 1)ξ) - C and the minimum disjoining pressure is proportional to (n - 1)/(2∆ + nξ) - C, where n is the number of lattice layers and C ) n/(2∆ + nξ); i.e., the relative disjoining pressure oscillations increase as n decreases. For n ) 0, there is no polymer between the surfaces, and a true depletion force will be observedsthe negative disjoining pressure is solely due to the osmotic pressure of the polymer solution. Depletion layers at the solid-solution interface are also indicated in Figure 1. The electric field interactions between the surface and a polymer molecule will not be the same as for the interactions between polymer molecules, and as such the depletion layer thickness near the surface will not display the same scaling length behavior as for the structural forces in the bulk solution. Effect of Polymer Concentration. Experimental results for sample P1 at a solution pH of 5.5-6 in the absence of added electrolyte and varying polymer concentrations are illustrated in Figure 2. Similar results were obtained for sample P2 for a pH range 4.5-5 and are illustrated in Figure 3. In each instance the forces at large surface separations are oscillatory, and at close approach of the surfaces there is a attractive depletion force and an electrostatic repulsion between the silica surfaces. The magnitude of the oscillatory forces and the periodic length are greater for sample P1, as is the depletion attraction for a given polymer concentration (up to ca. 7000 ppm). The periodic length of the oscillations decreases with increasing polymer concentration, as does the decay length of the electrical doublelayer interactions. The observed effects upon increasing the free polymer concentration may be rationalized as follows: the electrical double-layer interactions between the silica surfaces (at close approach) are reduced because the Donnan equilibrium that is established between the surfaces leads to an increase in the interstitial ionic strength; the gradient of the depletion force (eq 3) increases due to the increasing osmotic pressure of the polymer solution and, to a lesser extent, a decrease in the depletion layer thickness; the magnitude of the oscillatory forces increases and their period length decreases as the force gradient between the polymer molecules increases (so that they appear “harder”). In circumstances where a large sphere and a weak spring are used, it is found that at higher polymer concentrations, greater than ca. 1000 ppm, the depletion force gradient can exceed the spring constant of the colloid probe used, and the spring becomes unstable and “snaps in” towards the surface.
( )
∂Fdepletion µ1 - µ01 (a + h - ∆) ) 2π ∂h ν01
(3)
For both polymer samples, increasing the concentration beyond
Figure 2. Reduced force versus surface separation curves for a silica sphere (of radius 4.7 µm) interacting with a flat silica plate at various NaPSS (molecular weight 200 000) concentrations (as indicated) in the absence of added electrolyte. The pH was maintained in the range 5.56.0.
ca. 5000 ppm resulted in the magnitude of the oscillations decreasing with increasing polymer concentration; the periodic length continued to decrease and the depletion force steadily decreased, vanishing upon attaining a concentration of about 7000 ppm for P1 and 15 000 ppm for P2 (see Figure 3c). This may be due to the decrease in the length scale of the depletion interaction producing problems due to surface roughness of the colloid probe and the flat surface, or the effect is a genuine disappearance of the depletion force, i.e., depletion restabilization7,8 in which the models suggest the depletion thickness
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Figure 4. Plot of log(polymer concentration/ppm) versus log(scaling length/nm) for the polymer-polymer correlation distance ξ (samples P1 and P2 as indicated) in the absence of background electrolyte. Both lines follow the scaling law ξ ) kCp-0.48 with respective values of k being 1334 and 1127. Also shown is the position of the apex of the secondary maximum (onset of the depletion interaction) as a function of surface separation for sample P1 for which the scaling law ∆ ) 2744Cp-0.71 is obeyed.
Figure 3. Reduced force versus surface separation curves for a silica sphere (of radius 4.7 µm) interacting with a flat silica plate at various NaPSS (molecular weight 46 100) concentrations (as indicated) in the absence of added electrolyte. The pH was maintained in the range 4.55.0.
tends to zero (as opposed to the “depletion stabilization” predicted by Napper47,48 in which dispersion stability at higher polymer concentration is attributed to an energetic (kinetic) barrier to flocculation). Figure 3 shows the depletion attraction disappearing as the position of 20max moves toward lower surface separations with increasing polymer concentration. The presence of the structural oscillations is not necessarily in accordance with Napper’s prediction of an energetic barrier prior to entrance into a depletion minima; his calculations were for uncharged polymer molecules, as opposed to polyelectrolytes. An AFM study22 of the effects of PDMS solutions on the forces between
hard surfaces did not show any such barrier. Experimentally, it has been observed that dispersions flocculated using NaPSS may restabilize with respect to increasing free-polymer dosage.37 The same study also made the observation that samples only flocculated if agitated, quiescent samples remain apparently stable. This observation also provides evidence for the presence of an energetic barrier to depletion flocculation of particles by NaPSS due to structural forces. At higher polymer concentrations the tertiary force minima observed experimentally may be of sufficiently depth to allow aggregation of particles and might explain observations such as the formation of a gel-like solid phase upon adding a relatively high NaPSS dosage (beyond that where the depletion thickness has decreased to effectively zero) to a “Ludox” silica dispersion.40 The periodicity of the structural oscillations was measured for both NaPSS samples at various polymer concentrations. Figure 4 illustrates the scaling length, ξ, as a function of the polymer concentration (Cp) for both polymer samples. The scaling exponent of -0.48 suggests that force oscillations are essentially electrostatic in origin. Scaling theories of polyelectrolyte solutions49-51 predict that in the dilute regime and at low background salt concentrations polymer molecules repel each other electrostatically with length scales proportional to the Debye screening length of the solution (i.e., the inverse square root of the polymer concentration). In the semidilute regime the radius of the polymer coils scales according to Cp-1/4 (although the electrostatic blob correlation length still scales as Cp-1/2). If the polymer molecules were considered to be ordered in a space-filling, nonintermixing latex, the expected scaling law would be ξ ) Cp-1/3; this is clearly not so. The fact that the preexponent term is only slightly larger for the higher molecular weight polymer sample demonstrates that ξ is only weakly dependent upon the physical size of the solvated polymer coil (also suggesting that polydispersity will not have a large effect in the observed forces). Simple calculations also show that the scaling volume per polymer molecule is nonspacefilling, although Ise et al.36 have shown that while void structures are formed in the bulk of latex dispersions, the structure at isolated silica surfaces remained relatively random. It is tentatively proposed that the observed force periodicity produced by compression of the interstitial polymer may reflect more upon the bulk behavior than that at an isolated surface.
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Figure 5. Reduced force versus surface separation curves for a silica sphere (of radius 4.7 µm) interacting with a flat silica plate at an NaPSS (molecular weight 200 000) concentration of 4000 ppm at different solution pH values. The data were collected in the absence of added electrolyte.
The onset of the depletion attraction in the force curves is preceded by a secondary maximum (20max) as the surfaces approach; the relationship between the 20max and the function of polymer concentration is additionally described in Figure 4 for sample P1 (solution conditions as per Figure 2). Again it appears that this follows a simple scaling relationship of exponent H(20max) ) Cp-0.71. The 20max scaling exponent decreased slightly with decreasing pH values (the lowest estimated value being 0.61 at pH 4). The 20max, by analogy with the SFV7 theory for neutral polymers, may be considered to be equivalent to 2∆. Unfortunately, there has been no scaling analysis made for polyelectrolyte depletion from a charged interface, although in the instance of neutral polymers under conditions of good and athermal solvencies, scaling exponents of -3/4 and -1/2 are predicted,9 respectively. Figure 4 additionally illustrates that, within experimental uncertainty, the depletion layer thickness is always less than half of the polymer-polymer correlation length. Effect of pH. The principal effect of changing the pH of the solution is upon the zeta potential of the silica surfaces; the effects on the charge of the polyelectrolyte will be mimimal for the pH range spanned (sulfonic acid groups being strong proton donors). Figure 5 illustrates the effect of increasing the pH of a solution of P1 at a concentration of 4000 ppm. At a pH of 3.5 and a bulk ionic strength of approximately 0.01 M, the zeta potential of the silica will be quite low (ca. -15 mV52), and the repulsion between the polymer coil and the surface will be quite weak and of short decay length (due to the interfacial Donnan equilibrium) relative to the osmotic pressure pushing
the coil toward the interface. This effect causes the depletion layer to collapse under the osmotic pressure of the polymer solution in a manner analogous to the description of Vincent8 for neutral polymer coils, where the depletion thickness is determined by a balance of osmotic and elastic restoring forces. Increasing the pH to 4.7 causes a stronger electrostatic repulsion between the surfaces, and the polymer coils and the depletion interaction become apparent, albeit at a short range. Further increases in pH increase the depletion thickness via this mechanism, until at a pH of ca 6.5 the pseudoplateau value of the silica zeta potential-pH isotherm is attained,52 and further increases in the pH make negligible difference to the spatial position of the secondary maximum. It is interesting to note that the depletion force only produces an energetic minimum for conditions of pH > 6 at this polymer concentration. The periodicity of the structural forces observed (Figure 5) are constant, reinforcing the supposition that the charge of the polyelectrolyte is relatively insensitive to pH. Effect of Added Salt. Intuitively, it would be expected that the ionic strength of the solution should effect both the range and the magnitude of all the electrostatic interactions. Figure 6 shows the force curves obtained for a free polymer concentration of 750 ppm (Mn 200 000) in the presence of varying amounts of added NaNO3. Equation 2 describes the reduction in the osmotic pressure with respect to increasing electrolyte concentration and also shows that this effect is more pronounced at the lower free polymer concentrations. Thus, it would be expected that increasing the electrolyte concentration will reduce the magnitude of the structural forces and also reduce the
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Figure 6. Reduced force versus surface separation curves for a silica sphere (of radius 4.3 µm) interacting with a flat silica plate at an NaPSS (molecular weight 200 000) concentration of 750 ppm in the presence of varying background electrolyte concentrations (as indicated). The solution pH was maintained between 5.8 and 5.6.
depletion interaction. These trends were observed for both polymer samples at various polymer concentrations until at an electrolyte concentration of ca. 0.01 M only surface-surface double-layer interactions were observable. As stated, the reduction of the depletion interaction is due to the increase of the osmotic pressure between the surfaces and subsequent reduction of the net disjoining pressure between the capillary and the bulk solution; it does not necessarily mean the depletion thickness is effected (although some calculations12 predict that the depletion thickness increases with respect to ionic strength!). A suprising observation is that, for ionic strengths where the structural forces are still discernible from background noise, their periodicity is hardly altered, suggesting that the Debye screening length for polyelectrolytes is only weakly dependent upon salt concentration, as predicted by computor simulations of polyelectrolyte solutions.53,54 Model Calculations. While the OA theory is insufficient in describing the observed structural oscillations, the depletion, van der Waals, and EDL interactions at close approach of the surfaces can be readily estimated. Figure 7 illustrates the force between a sphere and a plate as a function of surface separation for various solution conditions, the depletion interaction is calculated from eqs 1 and 2, and the electrical double-layer interaction is calculated using a linearized Poisson-Boltzmann expression55 (using the constant surface charge boundary condition); the interstitial ionic strength was estimated from the addition of the dissociated polyelectrolyte ionic strength (i.e. c/A), added electrolyte, and also contributions from dissolved (and dissociated) carbon dioxide (at a concentration of 4 × 10-6 M dm-3 (ref 56). The contribution of dissociated silicic acid
(saturation concentration ca. 2 × 10-3 M dm-3 and pKa ) 10) to the ionic strength will be negligible at pH 7 or less. Equation 2 suggests that trace ionic impurities will have a pronounced effect upon the osmotic pressure of the polymer solutions at the lower polymer concentrations. For the sake of simplicity, it was assumed that the zeta potential of the silica surfaces was in the range -50 to -80 mV, these values being typical for solution conditions of pH 5-7 and electrolyte concentrations 10-2-10-3 M dm-3 (ref 52). The parameters used in the calculations are given in Table 1. The first six curves (a-f) illustrate the effect of increasing the polymer concentration and show an initial increase in the depth of the attractive depletion well and a collapse in the range of the of the EDL interaction between the surfaces with respect to increasing polymer concentration. At higher polymer concentrations it is clear that the depletion interaction becomes increasingly buried within the EDL interaction until finally the total force becomes repulsive, although not monotonically so. Additionally, the heights of the secondary maxima in the calculations are less than those observed experimentally, inferring that interstitial polyelectrolyte (neglected in the calculations) has a strong effect on the observed forces, prior to the entering into attractive depletion well. The last eight curves (g-n) illustrate the effect of added salt upon the total interaction for two different free polymer concentrations; although it is somewhat simplistic to assume that the depletion thickness is independent of added electrolyte, the curves illustrate the reduction of the attractive well with respect to increasing electrolyte concentration. This effect is more pronounced for lower polymer concentrations as indicated by eq 2.
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Figure 7. Calculated reduced force versus surface separation curves for a sphere and a plate under various solution conditions. The depletion thickness was assumed to follow the scaling relationship described in Figure 4, and the counterion condensation parameter, A, was taken to be 5 (ref 51). Zeta potentials, polymer concentrations, osmotic pressure, added electrolyte concentrations, and ionic strength are given in Table 1.
TABLE 1: Input Parameters Used for Figure 7 curve Cp/ppm ∆/nm Cs/mM dm-3 [I]/mM dm-3 Π/Nm-2 ζ/mV a b c, g d, k e f h i j l m n
100 200 500 1000 2000 5000 500 500 500 1000 1000 1000
100 62 30 20 12.5 6.5 30 30 30 20 20 20
0 0 0 0 0 0 0.100 0.500 1.000 0.100 0.500 1.000
0.103 0.199 0.487 0.968 1.923 4.814 0.587 0.978 1.487 1.068 1.468 2.968
187 419 1130 2320 4764 11910 650 96 53 1682 773 461
-80 -75 -70 -65 -60 -55 -70 -65 -60 -65 -55 -50
Direct fitting of theoretical curves to the experimental data was not attempted. Use of the simple theoretical model outlined above would require the use of four principal fitting parameters (surface potential, ionic strength, polymer depletion thickness, and osmotic pressure), of which only the osmotic pressure due to the dissolved polymer is independently measurable, more sophisticated models for the EDL interaction would require even more parameters. As such, this approach would not have been satisfactory. However, the model calculations presented in
Figure 7 lend weight to the the supposition that, for close approach of the surfaces, the forces between the surfaces are indeed due to the superposition of depletion, electrical double layer, and van der Waals forces and are, in view of the parameter sensitivity, in good qualitative agreement with the experimental findings presented in the Results section of this paper. Conclusions The forces between silica surfaces in the presence of NaPSS have been studied using an atomic force microscope. At close approach of the surfaces the force is described by a summation of depletion, van der Waals, and electrical double-layer components. The depletion interaction showed a maximum as a function of polymer concentration, and the depletion thickness decreased with increasing polymer concentration according to a simple scaling relationship. This confirms the essential correctness of both scaling9 and mean-field7 theories for the depletion of polymers from interfaces. The observed forces are in good qualitative agreement with semiempirical calculations. At higher surface separations the force between the surfaces was oscillatory, the amplitude of the oscillations decaying with increasing separation. These oscillations are indicative of
NaPSS at the Silica-Water Interface macrosolute ordering between interfaces. The periodic length of the oscillations also decreased with increasing polymer concentration by a scaling law with exponent of -0.48; this suggests that the polymer molecules are ordered into a quasicrystalline array between the surfaces under the influence of electrostatic forces. Acknowledgment. This work was supported by the Australian Research Council Advanced Mineral Products Research Centre. References and Notes (1) Fleer, G. J.; Scheutjens, J. M. H. M.; Cohen-Stuart, M. A.; Cosgrove,T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London, 1993. (2) Edwards, J.; Emmett, S.; Jones, A.; Vincent, B. Colloids Surf. 1991, 57, 185. (3) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (4) Silberberg, A. J. J. Chem. Phys. 1968, 48, 2835. (5) Asakura, A.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. (6) Asakura, A.; Oosawa, F. J. Polym. Sci. 1958, 33, 183. (7) Fleer, G. J.; Scheutjens, J. M. H. M.; Vincent, B. Polymer Adsorption and Dispersion Stability; ACS Symp. Ser. 1984, 240, 245. (8) Vincent, B. Colloids Surf. 1990, 50, 241. (9) deGennes, P. G. Macromolecules 1981, 14, 1637. (10) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1979, 83, 1619. (11) Scheutjens, J. M. H. M.; Fleer, G. J. J. Phys. Chem. 1980, 84, 178. (12) Bohmer, M. R.; Evers, O. A.; Scheutjens, J. M. H. M. Macromolecules 1990, 23, 2288. (13) Dahlgren, M. A.; Leermakers, F. A. M. Submitted to Langmuir. (14) Hoagland, D. A. Macromolecules 1990, 23, 2781. (15) Ausserre, D.; Hervet, H.; Rondelez, F. Macromolecules 1986, 19, 85. (16) Cosgrove, T.; Obey, T. M.; Ryan, K. Colloids Surf. 1992, 65, 1. (17) Lee, L. T.; Guiselin, O.; Lapp, A.; Farnoux, B.; Penfold, J. Phys. ReV. Lett. 1991, 67, 2838. (18) Krabi, A.; Donath, E. Colloids Surf. (A) 1994, 92, 175. (19) Reynolds, P. A.; Reid, C. A. Langmuir 1991, 7, 89. (20) Prestidge, C.; Tadros, Th. F. Colloids Surf. 1988, 31, 325. (21) Evans, E.; Needham, D. Macromolecules 1988, 21, 1822. (22) Milling, A.; Biggs, S. J. Colloid Interface Sci. 1995, 170, 604. (23) Richetti, P.; Kekicheff, P. Phys. ReV. Lett. 1992, 68, 1951. (24) Richetti, P.; Kekicheff, P. Prog. Colloid. Polym. Sci. 1992, 88, 8. (25) Prieve, D. C.; Frej, N. A. Langmuir 1990, 6, 396.
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