Interaction Forces between Two Hard Surfaces in Particle-Containing

Feb 4, 2004 - The interaction forces between two hard surfaces in the presence of particle-containing aqueous systems were measured with an atomic for...
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Langmuir 2004, 20, 1953-1962

1953

Interaction Forces between Two Hard Surfaces in Particle-Containing Aqueous Systems Cathy E. McNamee,*,† Yoshinobu Tsujii,‡ Hiroyuki Ohshima,§ and Mutsuo Matsumoto‡ Organic and Macromolecular Chemistry, OC3, The University of Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan, and Faculty of Pharmaceutical Sciences, Science University of Tokyo, 2641 Yamazaki, Noda, Chiba 278-8510, Japan Received September 24, 2003. In Final Form: January 2, 2004

The interaction forces between two hard surfaces in the presence of particle-containing aqueous systems were measured with an atomic force microscope. Bare silica and sodium dodecyl sulfate (SDS)-modified paraffin were used for the surfaces. SDS micelles and colloidal silica were used for the particles. Increasing the number of micelles between two silica surfaces increased the number and magnitude of the oscillations. The effect of the compression speed was seen only with fast speeds g3420 nm s-1, probably because of a hydrodynamic force. The decay length of the observed electrostatic repulsion decreased with a SDS concentration increase, as a result of an increase in the number of free ions above the critical micelle concentration resulting from a finite dissociation of ions from the surfactant. The effect of using a silica particle instead of a micelle did not show any measurable differences in the oscillations of the force curves. The effect of using an asymmetric system (silica-solution-SDS-modified paraffin) instead of a symmetric system (silica-solution-silica) showed differences only in the Derjaguin-Landau-Verway-Overbeek forces. In all cases, the forces could be explained well by a summation of an electrostatic, van der Waals, and a structural force.

1. Introduction Colloidal solutions are important in industrial and medical applications. For example, periodic structures fabricated from colloids have been used as colloidal inks,1 advanced ceramics,2-3 sensors,4 and cosmetics. The forces of a particle-containing system must be studied and understood to utilize their unique structuring ability. This will allow the improvement and extension of their possible applications. The forces in a particle-containing solution can be affected by the presence of polymers or surfactants, the number and size of particles present, the type of surface, the solution properties, and external factors. The presence of nonadsorbing macromolecules in a particle-containing system can cause particle flocculation. Asakura and Oosawa5,6 proposed that the flocculation was due to a depletion-attractive force, which results from the differential osmotic pressure that exists when the separation between two particles is less than the radius of gyration of the macromolecule. Since then, a long-range attractive force has been directly measured in the presence of a nonadsorbing polymer, when the distance between two particles or surfaces is less than the radius of gyration of a polymer.7-11 This attraction was shown by Sober and * To whom correspondence should be sent. Tel.: +49 731 502289. Fax: +49 731 5022883. E-mail address: cathy.mcnamee@ chemie.uni-ulm.de. † The University of Ulm. ‡ Kyoto University. § Science University of Tokyo. (1) Smay, J. E.; Cesarano, J.; Lewis, J. A. Langmuir 2002, 18, 5429. (2) Lewis, J. A. J. Am. Ceram. Soc. 2000, 83, 10, 2341. (3) Tohver, V.; Smay, J. E.; Bream, A.; Braun, P. V.; Lewis, J. A. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 8950. (4) Allahverdi, M.; Danforth, S. C.; Jafari, M.; Safari, A. J. Eur. Ceram. Soc. 2001, 21, 1485. (5) Asakura, S.; Oosawa, F. J. Chem. Phys. 1954, 22, 1255. (6) Asakura, S.; Oosawa, F. J. Polym. Sci. 1958, 33, 183.

Walz12 not to be limited to polymers, when they measured an attractive depletion force for cetyltrimethylammonium bromide (CTAB) micelles between a colloidal polystyrene latex sphere and a flat plate and their separation was less than the size of the CTAB micelle. The number and size of the particles or molecules have been shown to affect their intermolecular forces through their structuring ability. Horn and Israelachvili13 and Christenson and Horn14 showed that oscillation forces exist between two molecularly smooth solid surfaces separated by a nonpolar liquid and that the spacial periodicity of the oscillations equals the size of the liquid molecules. These oscillations occur when there is a change in the liquid density at the surfaces when they approach each other15 due to the change in the packing of the liquid molecules. Nikolov and Wason showed by reflected light microinterferometry that the thickness of foam films formed from micellar solutions of sodium n-alkyl sulfates or from latex particles16,17 changed with regular stepwise jump transitions, resulting in a number of metastable equilibria for the film. This stratification of thin films was explained as a layer-by-layer thinning of ordered structures of (7) Milling, A.; Biggs, S. J. Colloid Interface Sci. 1995, 170, 604. (8) Pagac, E. S.; Tilton, R. D.; Prieve, D. C. Langmuir 1998, 14, 5106. (9) Ruths, M.; Yoshizawa, H.; Fetters, L. J.; Israelachvili, J. N. Macromolecules 1996, 29, 7193. (10) Kuhl, T. L.; Berman, A. D.; Hui, S. W.; Israelachvili, J. N. Macromolecules 1998, 31, 8250. (11) Kuhl, T. L.; Berman, A. D.; Hui, S. W.; Israelachvili, J. N. Macromolecules 1998, 31, 8258. (12) Sober, D. L.; Walz, J. Y. Langmuir 1995, 11, 2352. (13) Horn, R. G.; Israelachvili, J. N. J. Chem. Phys. 1981, 75, 1400. (14) Christenson, H. K.; Horn, R. G. Chem. Scr. 1985, 25, 37. (15) Israelachvili, J. Intermolecular & Surface Forces; Academic Press: London, 1994; p 265. (16) Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1989, 133, 1. (17) Basheva, E. S.; Danov, K. D.; Kralchevsky, P. A. Langmuir 1997, 13, 4332.

10.1021/la0357763 CCC: $27.50 © 2004 American Chemical Society Published on Web 02/04/2004

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micelles or colloids. Richetti and Kekicheff18 measured with the surface force apparatus the forces between two mica surfaces in the presence of CTAB micelles. At low CTAB concentrations, double layer forces resulting from dissociated counterions and free CTA+ ions were observed. At high CTAB concentrations, the repulsions were reduced and an oscillatory force profile with a spacial period corresponding to the size of the micelle was measured. This suggested a particle number and geometrical dependence on the structural force. A solution of sodium poly(styrenesulfonate),19 and similarly a solution of sodium poly(acrylate),20 has been observed by the atomic force microscope (AFM) to give structural forces, in addition to depletion forces, when contained between two silica surfaces. As the concentration of the polymer increased, the size and number of the oscillations increased. The presence of positively charged micelles effects the interaction force between two hard, negatively charged surfaces through the introduction of a depletion attraction and the presence of oscillations. The number of micelles is proportional to the number and magnitude of the oscillations.12,21 The effect of negatively charged micelles on the interaction force between two hard, negatively charged surfaces has not been studied experimentally before in terms of their number and the charge of the surfaces. Additionally, the effect of the particle type on the structural forces has not been investigated before. The effect of the surface properties on the forces has been well-studied for the case of mica or silica in aqueous solutions.22,23 There have also been numerous AFM studies that measured the interactions between oil-water24 and solid-water interfaces.25-33 However, the forces originating from an emulsion surface are not well-known. Emulsions are metastable colloids that are made by dispersing one immiscible fluid into another in the presence of surface-active agents.34 Electrostatic repulsive forces have been measured35 between two emulsion droplets, when the concentration of surface-active agents is below their critical micelle concentration (cmc). Above the cmc, repulsive steric forces have been observed between emulsion droplets stabilized with Tween 20 and proteins due to the micellar condensation on the droplet surface.36 A depletion-attractive force and oscillatory (18) Richetti, P.; Kekicheff, P. Phys. Rev. Lett. 1993, 68, 1951. (19) Milling, A. J. J. Phys. Chem. 1996, 100, 8986. (20) Milling, A. J.; Kendall, K. Langmuir 2000, 16, 5106. (21) Sharma, A.; Walz, J. Y. J. Chem. Soc., Faraday Trans. 1996, 92, 4997. (22) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature 1991, 353, 239. (23) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975. (24) Hartley, P. G.; Grieser, F.; Mulvaney, P.; Stevens, G. W. Langmuir 1999, 15, 7282. (25) Atkin, R.; Craig, V. S. J.; Wanless, E. J.; Biggs, S. J. Phys. Chem. B 2003, 107, 2978. (26) Biggs, S.; Burns, J. L.; Yan, Y.; Jameson, G. J.; Jenkins, P. Langmuir 2000, 16, 9242. (27) Atkin, R.; Craig, V. S. J.; Biggs, S. Langmuir 2001, 17, 6155. (28) Webber, G. B.; Wanless, E. J.; Armes, S. P.; Baines, F. L.; Biggs, S. Langmuir 2001, 17, 5551. (29) Woodward, N. C.; Snowden, M. J.; Chowdhry, B. Z.; Jenkins, P.; Larson, I. Langmuir 2002, 18, 2089. (30) McNamee, C. E.; Matsumoto, M.; Hartley, P. G.; Mulvaney, P.; Tsujii, Y.; Nakahara, M. Langmuir 2002, 17, 6220. (31) Nespolo, S. A.; Chan, D. Y. C.; Grieser, F.; Hartley, P. G.; Stevens, G. W. Langmuir 2003, 19, 2124. (32) Fleming, B. D.; Wanless, E. J.; Biggs, S. Langmuir 1999, 15, 8719. (33) Notley, S. M.; Biggs, S.; Craig, V. S. J. Macromolecules 2003, 36, 2903. (34) Leal-Calderon, F.; Poulin, P. Curr. Opin. Colloid Interface Sci. 1999, 4, 223. (35) Philip, J.; Prakash, G.; Kalanasundaram, P.; Mondain-Monval, O. Langmuir 2002, 18, 4625.

McNamee et al.

structural forces have also been obtained for a thin aqueous film sandwiched between two oil phases and stabilized by an anionic surfactant, that is, an emulsion film in the presence of micelles.37 There has still not, however, been a study into the form of the force between an emulsion surface and a silica particle in the absence and presence of micelles. The properties of the solution can also affect the forces in a particle-containing solution. Milling19 measured with an AFM the interaction forces between two silica surfaces in the presence of aqueous solutions of poly(styrenesulfonate). A pH change at the same high polyelectrolyte concentration changed the magnitude of the electrostatic repulsive force and the position of onset of the depletion force. This was reckoned to decrease the electrostatic repulsions between the surfaces and the particles, thereby affecting the depletion-force position. Biggs and others38 showed that a short-ranged electrostatic repulsion exists between two charged hard surfaces in the presence of a globulelike polyelectrolyte, followed then by a decaying oscillation at larger separations. It is, however, still not well-understood how the surface charge of the two surfaces affects the structural forces caused by the structuring of micelles. The speed of interaction of two macroscopic surfaces in the presence of particles was predicted by Overbeek39 to affect the interaction forces. No systematic study exists to date that shows how the interaction speed affects the structural and other forces. In this study, we investigate for the first time the effect of the symmetry of the system on the surface forces. In the first part of this research, we studied the forces between two negatively charged silica surfaces, as a function of sodium dodecyl sulfate (SDS) concentration, solution pH, and compression speed. In the second part, we studied the effect of using silica particles instead of micelles on the interaction forces. In the final part, we studied the forces between an emulsion-modeled surface and a silica surface in the presence of SDS micelles. This allowed us to comment on the effect of an asymmetric system and the effect of an emulsion surface on the forces. 2. Experimental Section 2-1. Materials. The following electrolytes and surfactants were used in this study: NaOH (Aldrich, 99.99% purity), HCl (Aldrich, 99.99% purity), NaNO3 (Aldrich, 99.995% purity), LiNO3 (Aldrich, 99.99% purity), SDS (cmc ) 8 mM,16 Sigma, >99% purity). Dodecane (99% purity) was obtained from Nacalai Tesque. Paraffin with a melting point of approximately 40 °C was used. The aqueous solutions were prepared using doubly distilled water passed through a reverse osmosis membrane and an ionexchange resin. The polished silica substrates for the AFM measurements were purchased from Nipponchikagaku, Ltd., Japan. The silica particles (Snowtex brand, Nissan Chemical Engineering Co.) for the dispersions had a radius of 10 nm. The silica particles (Ube Nittoh Kagaku, Japan) for the probe in the AFM measurements were prepared by a sol-gel method and had a radius of 5 µm. 2-2. Sample Preparation. 2-2-1. SDS-Modified Paraffin Surface. A 1.5-cm2 glass square was hydrophobized with approximately 30% dimethyldichlorosilane (Wako Chemicals) in hexane (high purity, Nacalai Tesque) for 10 min, rinsed with hexane, then with distilled water, and dried. It was subsequently placed on a heating plate (∼45 °C), and several droplets of melted paraffin were placed on the hydrophobized silica. The plate was (36) Dimitrova, T. D.; Leal-Calderon, F. Langmuir 1999, 15, 8813. (37) Marinova, K. G.; Gurkov, T. D.; Dimitrova, T. D.; Alargova, R. G.; Smith, D. Langmuir 1998, 14, 2011. (38) Biggs, S.; Dagastine, R. R.; Prieve, C. J. Phys. Chem. B 2002, 106, 11557. (39) Overbeek, J. Th. G. J. Colloid Interface Sci. 1977, 58, 408.

Particle-Containing Aqueous Systems then removed from the heating plate and placed in approximately 2 mL of 100 mM SDS, after the paraffin hardened. The paraffin and glass plate in SDS solution were placed on the hot plate again (∼45 °C) and left there for approximately 15 min to allow the SDS to adsorb into the paraffin. The SDS-modified paraffin was then allowed to cool and harden again, before use in the force measurements. 2-3. Surface Force Measurement Technique. 2-3-1. Preparation. The preparation of a cantilever with an attached silica particle was as follows: The silica particles for the probe were cleaned by dispersing them in a 15% H2O2 solution for 24 h and ultrafiltered more than 20 times with distilled water. They were then further ultrafiltered with pure ethanol several times and kept in ethanol in a glass vessel. The silica particles in ethanol were subsequently spread on a cleaned glass slide plate. The tip end of the micropyramid of a V-shaped cantilever (Olympus Optical Co., Ltd.) was glued using 5-min curing epoxy resin (Araldite, Ciba-Geigy Japan, Ltd.), and then a single silica particle from the glass plate was transferred onto the tip end. The silica probe was cleaned before setting up and commencing an AFM experiment in a 1 part 31% H2O2, 1 part 28% NH3, and 2 parts distilled water solution for 5 min and then rinsed with distilled water. The spring constant (k) of the cantilever (k ) 0.68 N/m) was determined by the method of Cleveland et al.40 and was within (10% of the spring constant supplied by the manufacturer. The silica plates were cleaned prior to a force experiment by soaking them in a 1:1 solution of concentrated H2SO4 (Wako Pure Chemical Industries, guaranteed grade) and concentrated HNO3 (Nacalai Tesque, guaranteed grade) for 24 h. They were then transferred into a 1 part 31% H2O2 (Santoku Chemical Industries, guaranteed grade), 1 part 28% NH3 (Nacalai Tesque, guaranteed grade), and 2 parts distilled water solution for another 24 h and then rinsed with copious amounts of distilled water. AFM images showed the absence of detectable contamination on the silica surfaces and a surface roughness of 0.35 nm over 25 µm2. The surface of a 1.5-cm2 glass square and the probe silica particle were hydrophobized with approximately 30% dimethyldichlorosilane (Wako Chemicals) in hexane (high purity, Nacalai Tesque) for 10 min and then washed with hexane and then with distilled water. 2-3-2. Measurements. The surface forces between a silica substrate and a silica particle in solution were measured at room temperature (approximately 25 °C) as a function of their separation distance using an AFM (Seiko Instruments, Inc., SPA400). The piezo actuator (Seiko Instruments, Inc., PZT FS20A, z-scan size, 20 µm) was calibrated and its nonlinearity compensated as described elsewhere.41 The forces between a substrate and a silica probe in surfactant solutions were measured using a circular Teflon liquid cell, which was placed on the piezo actuator. In the case of the silica-particlecontaining solutions, the liquid cell was not used. Instead, the substrate was directly attached to the piezo actuator and a drop of the solution was placed on the substrate and also on the silica probe particle. The absence of particle-containing liquid above the cantilever reduced the scattering of the AFM laser beam, which occurs because of the difference between the refractive index of the silica particles and that of the water. The force measurements in this study were all performed according to the method of Ducker and others.22 Briefly, the cantilever with the silica probe fixed on the cantilever holder was positioned in solution to face the substrate. The change in the deflection of the cantilever (∆x) was measured as a function of the piezo displacement, using the differential intensity of the reflection of the laser beam off the cantilever onto a split photodiode. The force (F) was calculated from Hooke’s law, F ) k∆x, where k is the spring constant of the cantilever. Because the radius of the silica probe (R) was always much greater than the separation distance, the force was normalized to the (40) Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403. (41) Yamamoto, S.; Ejaz, M.; Tsujii, Y.; Matsumoto, M.; Fukuda, T. Macromolecules 2000, 33, 5602.

Langmuir, Vol. 20, No. 5, 2004 1955 interaction free energy (Gf) by the Derjaguin approximation:

F/R ) 2πGf

(1)

Zero separation was defined from the position of the onset of the linear compliance region in the force profile, which was due to the further compression of both surfaces after contact was made. The surface separation, D, was estimated from the displacement of the substrate relative to this constant compliance region. The zero force position between the surfaces was defined from the baseline of no deflection of the silica probe cantilever at large probe-substrate separations. 2-4. Elementary Analysis of the Silica-Particle-Containing Solution. A solution containing 41% silica particles was ultrafiltered using a Millipore UFP2 THK24 filter. It was then diluted with Millipore water to give a 4.1% silica solution. The elementary analysis method of high-resolution inductively coupled plasma spectroscopy was then utilized to determine the types and numbers of ions in the solution.

3. Theory 3-1. Force Theory. There are two main forces evident in colloid-containing solutions. These are the van der Waals force, FVDW, and the electrostatic force, FEL. According to the Derjaguin-Landau-Verway-Overbeek (DLVO) theory,42,43 the total force, FTOT, within a system can be represented by the summation of these two forces:

FTOT ) FEL + FVDW

(2)

Additional forces, however, have been observed for particle- or macromole-containing solutions. The depletion force has been observed as an attraction when the separation between two surfaces containing a solution with a high bulk concentration of polymers with a large coil radius8-11,19,20 or solutions containing particles12 is less than the diameter of the substance.44 Asakura and Oosawa5 explained this attraction as an osmotic pressure phenomenon that occurs as a result of the lower number density of particles or polymer between the two surfaces compared to that in the bulk solution. At appropriate larger surface separations, the particles or macromolecules12,19,20,45-51 can arrange into structured layers between the two surfaces. As the surface separation changes, the particle packing changes, causing changes in the liquid density. A structural force44 that oscillates with the separation distance is the result. Both the depletion and the structural force occur as a direct result of the particles between two surfaces. It is, therefore, convenient to represent both of these forces by one expression. Kralchevsky and Denkov46 proposed an analytical expression for a particles containing liquid confined between two flat plates or for liquid films. The expression for the interaction free energy, Gf(D), accounts for both the depletion force and the structural force through (42) Derjaguin, B. V.; Landau, L. Acta Physicochim. USSR 1941, 14, 633. (43) Verway, E. J. W.; Overbeek, J. Th. G. The Theory of the Stability of Lyophobic Colloids; Elsevier Publishing Co.: Amsterdam, 1948; p 102. (44) Israelachvili, J. Intermolecular & Surface Forces; Academic Press: London, 1994. (45) Sharma, A.; Tan, S. N.; Walz, J. Y. J. Colloid Interface Sci. 1997, 190, 392. (46) Kralchevsky, P. A.; Denkov, N. D. Chem. Phys. Lett. 1995, 240, 385. (47) Ohshima, H.; Healy, T. W.; White, L. R. J. Colloid Interface Sci. 1982, 89, 484. (48) Ohshima, H. In Electrical Phenomena at Interfaces; Ohshima, H., Furusawa, K., Eds.; Marcel Dekker: New York, 1988; p 3. (49) Pashley, R. M.; Ninham, B. W. J. Phys. Chem. 1987, 91, 2902. (50) Nikolov, A. D.; Kralchevsky, P. A.; Ivanov, I. B.; Wasan, D. T. J. Colloid Interface Sci. 1989, 133, 13. (51) Usui, S. J. Colloid Interface Sci. 1973, 44, 107.

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McNamee et al.

the osmotic pressure and the geometric packing of the particles, respectively; see eqs 3 and 4:

Gf(D) )

1

( )]

2

2π sin

Gf(D) )

[ ( )

P0d1 exp[(d3/d12d2) - (h/d2)] d1 2πD cos d2 d1 4π2 + (d /d )2 2πD d1

for D g d (3)

[ ( )

P0d1 exp[(d3/d12d2) - (d/d2)] d1 2πd cos d2 d1 4π2 + (d /d )2

2π sin

( )] 2πd d1

1

2

- P0(d - D)

for 0 e D e d (4)

where D is the separation distance and d is the size of the particle. P0 is the particle osmotic pressure and is given by

P0 )

6φ 1 + φ + φ2 - φ3 kT πd3 (1 - φ)3

(5)

where φ is the volume fraction. The parameters that take into account the packing of the particles between the two surfaces are d1 and d2. These are defined as

d1 ) d[x(2/3) + 0.237 28∆φ + 0.633 00(∆φ)2] (6) and

d2 ) d

63 - 0.420 32) (0.486 ∆φ

(7)

Table 1. Calculated Parameters for the Forces in a Symmetric System of Two Silica Surfaces in SDS Solutionsa concd SDS (mM)

Ccalc1 (mM)

1/κ1 (nm)

Ccalc2 (mM)

0.1 8 100 210 500 (pH 7.4) 500 (pH 4.3) 1000 (pH 7.2) 1000 (pH 3.7)

0.1 8 8.2 8.2 8.2 8.2 8.2 8.2

30.6 3.42 3.42 3.42 3.42 3.42 3.42 3.42

0.1 30.6 0 0 0 8 3.42 11.56 47.6 0 26.56 1.88 8.56 75.0 0.24 48.56 1.39 7.58 87.1 0.32 106.56 0.94 6.67 104.3 0.44 106.56 0.94 6.67 104.3 0.44 206.56 0.67 6.15 121 0.60 206.56 0.67 6.15 121 0.60

1/κ2 (nm)

dcalc2 (nm)

∆φ ≡

π -φ 3x2

(8)

In the case of micelles, the particle size is given by the effective diameter of a micelle,18 dcalc:

dcalc ) 2(R + 1/κ)

(9)

The 1/κ term is the Debye length and takes into account the thickness of the counterion atmosphere around the micelle. If the radius of the two approaching surfaces is much greater than the separation distance, as is in the case of the AFM measurements here, then the combined structural and depletion forces, FOS, can be obtained from eqs 3 or 4 by application of the Derjaguin approximation. The DLVO theory can be extended to include other force types, such as the oscillation force, FOS, by their summation. This can be expressed by a general equation

FTOT )

∑i Fi

(10)

where Fi are the force components. In the case of a structural and depletion force, FOS, coexisting with an electrical and a van der Waals force, the total force can be supposed to be

FTOT ) FEL + FVDW + FOS

(11)

3-2. Calculation of the Volume Fraction of Micelles. The number of micelles in a solution increases with an increase of the surfactant concentration above its

φcalc2

a Concd SDS, C calc1, 1/κ1, Ccalc2, 1/κ2, dcalc2, Nag, and φcalc2 are the concentration of SDS used, the concentration of free ions assuming all ions above the cmc are involved with the micelles, the Debye length calculated from Ccalc1, the concentration of free ions calculated by eq A1 assuming a micellar ionization of 0.2, the Debye length calculated from Ccalc2, the effective diameter of the SDS micelles calculated from eq 9 and Ccalc2, the aggregation number of the SDS micelle calculated by eq 13, and the volume fraction of the SDS micelles calculated from eq 14 using dcalc2 and Nag.

cmc. The number of micelles (NM) in 1000 mL of solution can be calculated by

NM ) (C* - Ccmc)NA/Nag

(12)

where C*, Ccmc, NA, and Nag are the total concentration of surfactant ions, the cmc, Avogadro’s number, and the aggregation number, respectively. The aggregation number, Nag, of SDS increases as the concentration of SDS is increased above its cmc.52 Its value can be computed with the following equation:52

Nag ) β1 + β2(C*)1/4

with

Nag

(13)

where β1 and β2 are constants of 16 molecules and 105 molecules/M1/4, respectively, and C* is the concentration of SDS in M. The calculated values of Nag for the SDS concentrations used in this experiment are listed in Table 1. To calculate the volume fraction of the micelles, their geometry must be known. SDS is a spherical micelle with a radius of approximately 2.4 nm at relatively low ionic strengths.16 It has been reported to become cylindrical though in the presence of 600 mM NaCl,53 when the aggregation number becomes 1000. Because the highest aggregation number here is ,1000, it is assumed that the micelles are either spherical (for low concentrations up to 500 mM) or possibly wormlike (for the high concentration of 1000 mM). We assume here for simplicity that the volume of a wormlike micelle is approximately the same as that of NM closely packed spherically shaped micelles. Thus, the volume fraction of the SDS micelles (φ) is calculated by multiplying the volume of one spherical micelle by the number of micelles:

φ ) NM(4/3)πR3

(14)

where R is the radius of the micelle. 4. Results and Discussion In this study, we measured the forces in a symmetric and in an asymmetric system. For the symmetric systems, we measured the forces between two silica surfaces in the (52) Bales, B. L.; Almgren, M. J. Phys. Chem. 1995, 99, 15153. (53) Israelachvili, J. Intermolecular & Surface Forces; Academic Press: London, 1994; p 374.

Particle-Containing Aqueous Systems

Figure 1. Effect of increasing the SDS concentration from 0.1 to 100 mM on the interaction forces between two bare silica surfaces at pH 6.8. The concentrations and measuring velocities of the SDS solutions are, 4, 0.1 mM and 30.6 nm s-1; O, 8 mM and 34.2 nm s-1; and, 0, 100 mM and 26.7 nm-1. The inset shows the best fits to the force curves for each of the SDS concentrations using the summation of an electrostatic force component using the constant charge model, assuming the identical surface potentials of 55, 33, and 29 mV interacting in 0.12, 6, and 30 mM 1:1 electrolyte solution, respectively, and a van der Waals force component using the nonretarded Hamaker constant of 1.2 × 10-20 J.

presence of (i) SDS micelles and in the presence of (ii) silica particles. For the asymmetric system, we measured the forces between a SDS-modified paraffin surface (an emulsion-modeled surface) and a silica surface in the presence of SDS micelles. 4-1. Forces in Symmetric Systems. 4-1-1. Forces between Two Silica Surfaces in SDS Solutions. Figure 1 shows an example of the compression F/R versus D curves for pH 6.8 solutions of 0.1 (below cmc), 8 (at cmc), and 100 (above cmc) mM SDS between two negatively charged silica surfaces, measured with a compression velocity of 30.5 ( 5.3 nm s-1. These concentrations were still low enough that only an electrostatic repulsive force without detectable oscillations was apparent at all surface separations. The magnitude of the electrostatic forces decreased with an increase in the surfactant concentration. These force profiles were independent of the speed of the compression force mode, which was varied from 3618 nm s-1 to 6 nm s-1 (speeds corresponding to compression times of 0.5-30 s). The decay lengths, 1/κexp, of the forces in Figure 1 were determined from the plot of log(F/R) versus D (inset). Figure 2 shows the effect of further increasing the SDS concentration to 210, 500, and 1000 mM on the compression force profiles between two silica surfaces, when the solution was maintained at pH 7. The average compression velocity of the AFM for the force measurements was 47.5 ( 12.1 nm s-1. This rate was slow enough to measure the equilibrium forces between the two surfaces as a function of the distance because the forces did not vary with slower compression velocities. Oscillations were observed for each of these SDS concentrations. The inset of Figure 2 shows the enlargement of the force curves so that the oscillations can be seen more clearly. In the case of 210 mM SDS, weak oscillations were superimposed on a long-ranged weak repulsive force. When the SDS concentration was increased to 500 and 1000 mM SDS, the strength and range of the long-range repulsion significantly decreased. The number and strength of the oscillations increased when the SDS concentration was increased from 500 to 1000 mM. The separation distance at which the first oscillation maximum commenced also decreased with an increase in the SDS concentration. The decay lengths were determined by plotting log(F/R) versus

Langmuir, Vol. 20, No. 5, 2004 1957

Figure 2. Effect of increasing the SDS concentration from 210 to 1000 mM on the interaction forces between two bare silica surfaces at pH 7. The concentrations and measuring velocities of the SDS solutions are, 3, 210 mM and 18.6 nm s-1; O, 500 mM and 21.3 nm s-1; and, b, 1000 mM and 18.1 nm s-1. The solid, dotted, and dashed lines show the best fits to the force curves for 210, 500, and 1000 mM SDS using the summation of an electrical force component using a constant charge model, assuming identical surface potentials of 28, 25, and 25 mV interacting in 40, 100, and 155 mM 1:1 electrolyte solution; a van der Waals force component using a nonretarded Hamaker constant of 1.2 × 10-20 J; an oscillatory structural force component (using only eq 3) with volume fractions of 0.23, 0.3, and 0.4, and experimental effective micellar diameters of 6.5, 5.8, and 6.0 nm. The dashed-dotted line shows the effect of using both eq 3 and eq 4 for the oscillatory force on the fitting. The inset shows an enlargement of the forces so that the oscillations can be seen better. The arrows indicate the position of the depletion attraction.

Figure 3. Decompression force curves between two silica surfaces in, 0, 8 mM SDS; 4, 100 mM SDS; ], 210 mM SDS; O, 500 mM SDS; and, 1, 1000 mM SDS.

D (not shown). The surface potentials of the force curves in Figures 2 and 3 were determined by fitting the experimental force curves with the summation of an electrostatic force, which was calculated using the nonlinear solution of Ohshima and others47 with the constant charge boundary condition, a van der Waals attraction, which was computed using the Hamaker constant of 1.2 × 10-20 J for a silica-water-silica system,30,54 and an oscillatory structural force component of Kralchevsky and Denkov46 (only for SDS concentrations g 210 mM). The equation for the structural forces was used only for large separations until separations equivalent to the size of the colloids (i.e., only eq 3 was used) were reached. The inclusion of the depletion force gave a much larger depletion attraction than was measured (compare the fit for the force curve of 1000 mM SDS in Figure 3 when both eq 3 and eq 4 and when only eq 3 was used). The surface potentials (Ψ0), concentration of ions (Cexp), and volume (54) Rabinovich, Y. I.; Yoon, R.-H. Langmuir 1994, 10, 1903.

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Table 2. Fitting Parameters for the Forces in a Symmetric System of Two Silica Surfaces in SDS Solutionsa concd SDS (mM)

Ψ0 (mV)

1/κexp (nm)

Cexp (mM)

σ (µC m-2)

0.1 8 100 210 500 (pH 7.4) 500 (pH 4.3) 1000 (pH 7.2) 1000 (pH 3.7)

55 33 29 28 25 0 25 0

27.9 3.42 1.77 1.53 0.97

0.12 6 30 40 100

52.8 200 386 429 600

155

747

0.78

dexp (nm)

φexp

6.5 6 5.8 6.1 6.0

0.23 0.26 0.3 0.38 0.4

a Concd SDS, Ψ , 1/κ 0 exp, Cexp, σ, dexp, and φexp are the concentration of SDS used, experimental decay length, the actual concentration of free ions in solution determined experimentally, the surface charge density, the size of the particles that gives the same value as that of the special dimensions of the oscillations as obtained from the curve fitting, and the experimental volume fraction of micelles obtained by the curve fitting, respectively.

fractions (φexp) that were determined for each SDS concentration are shown in Table 2. The decay length values give the actual concentration of ions in solution.The 0.1 mM SDS gave a decay length that was within 9% of the theoretical Debye length48 of 30.6 nm at 298 K for a 0.1 mM 1:1 electrolyte aqueous solution; see Tables 1 and 2. The fact that the experimental ionic concentration of 0.12 mM is, within error, the same as the predicted value is expected because this SDS concentration is well below the cmc. The experimental decay lengths for 8 (cmc) and 100 (above cmc) mM SDS were the same and 48% smaller, respectively, than the Debye length calculated for an 8 mM 1:1 electrolyte aqueous solution. The experimental decay length continued to decrease with an increase in concentration from 210 to 1000 mM SDS. These results indicate an increase in the ionic strength of the solution above the cmc. This was not anticipated because, according to the phase separation model, the concentration of the free surfactant molecules should be constant at and above the cmc.55 The similar observation of an ion concentration increase with increased surfactant concentration above the cmc has been reported by Bossev and others56 and Pashley and Ninham.49 Pashley and Ninham explained the increase in counterion concentration as being a result of a finite ion dissociation of the surfactant. The increase in ion concentration with a SDS concentration above the cmc in our experiment may, therefore, be due to the dissociation of the sodium counterion from the dodecyl sulfate. Quina and Toscano57 showed that the concentration of nonbound sodium counterions can be calculated by assuming the degree of micellar ionization to be 0.2; see Appendix 1. Comparison of the Debye length (1/κ2) of this calculated ionic strength (Ccalc2) with the experimentally determined ones give agreements within 0, 5.9, 10.1, 3.2, and 16.4% for 8, 100, 210, 500, and 1000 mM SDS, respectively; see Tables 1 and 2. Information on the character of the silica surfaces can be obtained from the variation of the surface potential and surface charge density, σ, with the SDS concentration. The magnitude of the surface potential of 55 mV obtained with 0.1 mM SDS agrees with the surface potential of -55 mV for the surface force of 0.1 mM NaNO3 measured between two bare silica surfaces and the zeta potential of (55) Myers, D. Surfaces, Interfaces, and Colloids Principles and Applications; VCH: New York, 1991; p 309. (56) Bossev, D. P.; Matsumoto, M.; Nakahara, M. J. Phys. Chem. B. 1999, 103, 8251. (57) Quina, F. H.; Toscano, V. G. J. Phys. Chem. 1977, 81 (18), 1750.

-54 mV.30 We can, therefore, conclude that there is no specific adsorption of the SDS co-ions onto the negatively charged silica at this concentration. The surface potential, however, decreases successively when the concentration of SDS is increased to 8 and then to 500 mM. A further increase in SDS concentration to 1000 mM does not change the magnitude of the surface potential. This trend may be due to an electrostatic adsorption of the dissociated sodium cations to the negatively charged silica surface, where a saturation in the adsorption of the sodium ions occurs at 500 mM. However, calculation of the charge density of the systems58 shows an increase in σ with an increase in the SDS concentration from 0 to 1000 mM (see Table 1), instead of the expected σ decrease that would accompany an electrostatic adsorption of Na ions. Because the surface charge in an aqueous solvent may also be acquired by the dissociation of the silica surface groups, this result may be explained by an increased dissociation of the silanol groups on the silica surface, with an increase in the SDS concentration. The period of the oscillation in a force curve is determined by the size of the particle, which is equivalent to the effective diameter of a micelle. Ccalc2 was used for 1/κ (1/κ2) to calculate the effective diameter (dcalc2) for each SDS solution; see Table 1. The diameter of the particle (dexp), obtained by fitting the oscillatory structural force theory to our experimental force results, is shown in Table 2 to be within 14% of the calculated effective diameter of SDS for the concentrations studied here. The volume fractions predicted from eq 13 for pH 7 were within 28, 48, and 37% of the volume fractions determined experimentally by curve-fitting the oscillatory structural force theory for 210, 500, and 1000 mM SDS, respectively. A depletion attraction is not clearly seen in the compression force curves shown in Figure 2. However, its presence is clearly visible in the decompression force curves, shown in Figure 3. Here, the attraction at small separations is seen to increase with an increase in the number of micelles, as is expected. The depletion in the compression force curves (shown by the arrows in the inset) is not clearly seen in Figure 2 because of the presence of a repulsion at small separations. The onset of the repulsion is seen to begin at shorter separations as the SDS concentration increases. This suggests an electronic or steric origin. An electronic repulsion could exist as a result of a repulsion between the SDS micelles and the silica surfaces. Biggs and others38 have reported observing a repulsion between a charged surface and a charged wormlike-shaped macromolecule. A steric force can result from a silica gel, which has been observed on the surface of silica in aqueous solutions.59 Alternatively, it could be due to ions adsorbed on the silica surface. The discrepancy between the theory and the experiment at short separations could be a result of this additional repulsion not being accounted for in eq 11. We can test if the repulsive force at short separations is electrical in origin by varying the pH of the solution to between pH 3.5 and pH 4; this is the pH that gives the isoelectric point of silica.60 If the forces are due to the charge on the silica surface, then no short-range force should be observed. The effect of the surface charge of the (58) Usui, S. In Electrical Phenomena at Interfaces Fundamentals, Measurements, and Applications; Kitahara, A., Watanabe, A., Eds.; Marcel Dekker: New York, 1984; p 28. (59) Vigil, G.; Xu, Z.; Steinberg, S.; Israelachvili, J. J. Colloid Interface Sci. 1994, 165 (2), 367. (60) McNamee, C. E.; Matsumoto, M.; Hartley, P. G.; Nakahara, M. Colloids Surf., A 2001, 193, 175.

Particle-Containing Aqueous Systems

Figure 4. Effect of changing the surface potential of the two silica surfaces on the interaction forces between two silica surfaces in a 500 and in a 1000 mM SDS solution by changing the solution pH. The concentration, pH, and measuring velocity of the SDS solutions are, 0, 500 mM at pH 4.3 and 25.6 nm s-1 (Figure 6A); 9, 500 mM at pH 7.4 and 21.3 nm s-1 (Figure 6A); O, 1000 mM at pH 3.7 and 25.6 nm s-1 (Figure 6B); and, b, 1000 mM at pH 7.2 and 18.1 nm s-1 (Figure 6B). The best fits to the force curves for each of the SDS concentrations were obtained by using the summation of an electrostatic force component using a constant charge model assuming identical surface potentials; a van der Waals force, using a nonretarded Hamaker constant of 1.2 × 10-20 J; and an oscillation structural force component (using only eq 3). The surface potentials and volume fractions for 500 mM SDS at pH 4.3, 500 mM SDS at pH 7.4, 1000 mM SDS at pH 3.7, and 1000 mM SDS at pH 7.2 are 0, 25, 0, and 25 mV, respectively, and 0.3, 0.26, 0.4, and 0.38, respectively.

silica substrates on the force was investigated in 500 mM and in 1000 mM SDS. The compression forces in 500 mM SDS that were measured at pH 7.4 and at pH 4.3 are shown in Figure 4A, and the compression forces in 1000 mM SDS that were measured at pH 7.2 and at pH 3.7 are shown in Figure 4B. In both the 500 mM and the 1000 mM SDS cases, the strong repulsion at short separation that was seen with a high surface potential is no longer present at low or negligible silica surface potentials. The repulsive force measured at 1000 mM SDS at high pH extended to several nanometer, although there is only a subnanometer Debye length. Thus, the repulsive force observed for 210, 500, and 1000 mM SDS cannot be characterized as repulsion solely electrostatic in origin. Rather, it is probably due to a combination of both an electrostatic force and a steric force. The magnitude of the oscillation at the smallest separation increased significantly for both 500 and 1000 nm SDS at low pH, that is, at low or negligible substrate surface potential, compared to that at high pH, that is, with a highly negative surface potential. The ability to see the structural force at low pH and, therefore, in the absence of the repulsive force shows that the total force must be a summation of both the electrostatic, steric, and structural forces. The short-ranged repulsions seen in Figure 2 were fitted with a conventional electrostatic, van der Waals, and structural force. Table 1 shows the variation in the surface potentials, decay lengths, and SDS concentrations. The position of the first oscillation maximum is also seen in Figure 4 to shift to smaller separations when the SDS concentration is increased and the pH is decreased. Milling19 measured the effect of a pH change of a 4000 ppm solution of the polyelectrolyte of sodium poly(styrenesulfonate) on the forces between two silica surfaces. Milling reported that the onset of the first oscillation maximum decreased with a pH decrease. This was explained by a weaker electrostatic repulsion between

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Figure 5. Effect of the compression speed on the interaction forces between two silica surfaces at pH 7 in the presence of 1000 mM SDS. The speeds and corresponding apparent compression times are, 0, 6.0 nm s-1, 30 s; 4, 18.1 nm s-1, 5 s; 9, 120.6 nm s-1, 1.5 s; and, b, 3618.6 nm s-1, 0.05 s.

the polymer coil and the silica surface compared to the osmotic pressure pushing the polymer to the interface, resulting in a collapse of the depletion layer under the osmotic pressure. Increasing the pH caused the depletion thickness to increase because of the stronger electrostatic repulsion between the surfaces and the polymer coils. The repulsion between the micelles and the silica surfaces and the repulsion between the micelles themselves must cause the micelles to form organized layers at a specific spacing.44 Thus, the greater the repulsion, the greater the spacing will be and, therefore, the larger the separation will be where the first maximum commences. The effect of the compression velocity on the force curves with oscillations is shown in Figure 5. In the case of 1000 mM SDS at pH 7.2, the oscillations in the force curve are clear and sharp for the slow measuring times from 6.0 nm s-1 to and including 121 nm s-1. However, when the faster measuring time of 3420 nm s-1 was used, the oscillations became smoothed out and nonsharp. When two surfaces approach each other very fast, the hydrodynamic force probably acts to force the particles out from between the two surfaces. Overbeek39 also suggested that the speed of collision of the particles may affect the interactions between colloid particles. 4-1-2. Forces between Two Silica Surfaces in SilicaParticle-Containing Solutions. The interaction forces between two silica surfaces in pH 8 aqueous solutions of silica particles with volume fractions (φ) of 0.01, 0.30, and 0.40 and measured at a compression speed 60 ( 10 nm s-1 are shown in Figure 6. The force is repulsive with no oscillations for φ ) 0.01. The oscillations, however, become visible as φ is increased to 0.30 and 0.40. The inset of Figure 6 shows the same plot enlarged to see the oscillations more clearly. The solid and dotted arrows point out these oscillations for the φ ) 0.30 and 0.40 cases, respectively. The repulsions observed may be either electrostatic or steric in origin. An electrostatic force would result if ions were present in the solution. A steric force could result if a layer of silica adsorbed on one or both of the surfaces. The possibility of an electrostatic force can be investigated by determining the experimental ionic strength and comparing that with an elemental analysis of the ions present in the solution in which the particles were kept. The decay length, which can give the ionic strength, is obtained by the slope of the plot of log(F/R) versus D (not shown). Table 3 shows that the ionic concentration is 0.6 ( 0.1 mM, regardless of the volume fraction of silica used. This suggests that ions are present in the silica

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Figure 6. Effect of increasing the number of silica particles on the interaction forces between two silica surfaces in silicaparticle-containing solutions. The volume fractions and measuring velocities of the silica-particle-containing solutions are, 4, 0.01 and 55.5 nm s-1; b, 0.30 and 75.1 nm-1; and O, 0.40 and 91.6 nm s-1. The dotted, solid, and dashed lines show the best fits to the force curves for the solutions with volume fractions of 0.01, 0.30, and 0.40, respectively. The best fits were obtained using the summation of an electrostatic force component using the constant charge model, assuming the identical surface potentials of 27, 26, and 31 mV, respectively, interacting in 0.5, 0.7, and 0.6 mM 1:1 electrolyte solution, respectively; a van der Waals force component using a nonretarded Hamaker constant of 1.2 × 10-20 J; and an oscillatory structural force component (using only eq 3) with the volume fractions of 0, 0.30, and 0.35, respectively. The inset shows an enlargement of the forces. The solid and dotted lines point to the oscillations in the solutions with volume fractions of 0.30 and 0.40, respectively. The dashed line points to the position where a layer of silica may be squeezed out between the two surfaces. Table 3. Fitting Parameters for the Forces in a Symmetric System of Two Silica Surfaces in Aqueous Solutions of 10-nm-Diameter Silica Particlesa φused

Ψ0 (mV)

1/κexp (nm)

Cexp (mM)

dcalc (nm)

φexp

0.01 0.30 0.40

27 26 31

13.7 11.6 12.5

0.5 0.7 0.6

10 10

0.30 0.35

a φ used, Ψ0, 1/κexp, Cexp, dcalc, and φexp are the volume density of silica particles used, the surface potential of the silica surfaces, the experimental decay length, the actual concentration of free ions in solution determined experimentally, the diameter of silica particles that gives the same value as that of the special dimensions of the oscillations as obtained from the curve fitting, and the experimental volume fraction of particles obtained by the curve fitting, respectively.

Table 4. Elemental Analysis Results: Concentrations of Compounds in an Aqueous Solution of 10-nm-Diameter Silica Particles compound concentration (mM) compound concentration (mM) P As Cd Pb Cr Cu

2.78 × 10-2 6.36 × 10-3 2.58 × 10-4 6.86 × 10-3 9.62 × 10-4 2.19 × 10-3

Ni Fe Mn Zn Se

1.28 × 10-3 2.26 × 10-3 1.82 × 10-4 1.48 × 10-3 1.42 × 10-3

sample. Table 4 shows the elemental analysis results of all the ions found present in the silica-particle-containing solution. Phosphorus, a high-valent ion, was present in the largest concentration, which was only 0.028 mM (corresponding to a Debye length of 47.3 nm). This concentration is too low to account for the ionic concentration obtained in the force measurements. The ions contributing to the measured ionic concentrations are probably, therefore, the OH- ions that resulted from the preparation of the silica particles. It should also be noted

that no silicate species were detected in the solution, showing the negligible solubility of the silica particles in these systems. In this experiment, we could not determine definitely whether a layer of silica adsorbed onto the substrate or probe. However, we can see an oscillation for the 40% system at the small separation of 2 nm (see the dashed arrow in Figure 6). This may be a depletion force, resulting from the squeezing out of a layer of silica adsorbed on the two surfaces as the surface separation decreased. Because the effect of higher valence ions on the force curves can be neglected, the force curves could be fitted with the summation of an electrostatic force between two identical surfaces using the constant-surface-charge boundary condition for a 1:1 electrolyte, a van der Waals force using the Hamaker constant of 1.2 × 10-20 J, and an oscillatory structural force using eq 3. The resulting effective diameter and the volume fraction of the particles are shown in Table 3. The volume fractions of the particle solutions determined by the curve fitting were within 12.5% of the actual volume fractions. The surface potentials do not vary much with an increase in the volume fraction of the particle solutions. Therefore, there is not an increase in the ion adsorption at the silica surfaces and there are no acid-base reactions at the silica surfaces. This is understandable because no additional ions were added to the particle solution and also the pH of the solution was unchanged. The spatial dimension of the oscillations corresponded exactly to the size of the silica particles. The presence of the decay length around the hard particle, caused by the free ions in solution, did not need to be taken into account. This was different for the micelle case. Both the forces for the hard particles case and those for the soft particles contain an electrostatic, a van der Waals, and an oscillation structural force component. The oscillations, however, are larger and seen more clearly with the SDS micelles. This may be a result of the much smaller extent of the repulsive force for the SDS case than that for the silica particles case. Measuring the silica sample at a pH that gives the isoelectric point of silica would let us see the oscillations with the silica particles easier because the electrostatic repulsion contribution would be significantly decreased or removed. Additionally, theory tells us that the magnitude of the oscillation maximum decreases with an increase in the particle diameter, if samples with the same volume fraction of particles are compared. The diameter of the silica particles was greater than that of the SDS micelle. Using either smaller silica particles or a higher volume fraction of silica particles would produce, in theory, oscillations with maxima of the same magnitude as those measured for SDS. However, it is difficult to purchase a monodisperse solution of silica particles with a diameter 50% as a result of the scattering of the laser beam from the particles. Additionally, a small scattering of the laser beam due to the different refractive index of the silica particles compared to that of the aqueous solution would smear the oscillations. Although the major properties of the force profiles are unchanged by changing the hardness of the sample, it is difficult to conclude if any small differences in the oscillations changed. The effect of varying the compression velocity on the forces was also investigated. A faster speed caused the oscillations in the forces to become more smooth and nonsharp (figure not shown). Again, this can be thought to be a hydrodynamic force effect.

Particle-Containing Aqueous Systems

Figure 7. Effect of increasing the SDS concentration from 8 to 100 mM on the interaction forces between a bare silica surface and a SDS-modified paraffin surface at pH 7. The concentrations and measuring velocities of the SDS solutions are, O, 8 mM and 41.5 nm s-1 and, 0, 100 mM and 38.3 nm-1. The inset shows the best fits to the force curves for each of the SDS concentrations. They were obtained using the summation of an electrostatic force component using the constant charge model, assuming the surface potentials of 33 and 29 mV for the silica surface and the surface potentials of 24 and 22 mV for the SDS-modified paraffin surface, interacting in 6 and 30 mM 1:1 electrolyte solution, respectively, and a van der Waals force component using a nonretarded Hamaker constant of 0.7 × 10-20 J.

4-2. Forces in an Asymmetric System. 4-2-1. Forces between a Bare Silica and a SDS-Modified Paraffin Surface in SDS Solutions. Solid paraffin, which has a low melting point, can be easily liquified when it is heated in hot water. If surfactant is also present, then the paraffin surface may be modified through surfactant adsorption, if the paraffin is caused by melting to be in a liquid state. The force measurement of a dissimilar double layer interaction is possible after cooling the modified paraffin to a solid before it is setup as the substrate. The system of bare silica and paraffin modified with SDS may also be a good surface model to study the interaction force between a solid and emulsion particles. The interaction forces between an emulsion particle and a hard particle, such as silica, in the presence of additional particles is otherwise difficult to measure experimentally. The Hamaker constant of the silica-aqueous solutionsolid SDS-modified paraffin surface was estimated as 7 × 10-21 J. This value was obtained by measuring the force (not shown) between a silica surface and a SDS-modified paraffin surface in the highly concentrated solution of 500 mM NaNO3 and by fitting the experimental curve with the van der Waals equation. The high concentration of NaNO3 used ensured that the Debye length was small enough that the electrostatic double layer contribution was minimal. The resulting compression interaction forces between the silica particle and the SDS-modified paraffin for 8.2 and 100 mM SDS that were measured at a compression speed of 39.9 ( 2.3 nm s-1 are shown in Figure 7. These concentrations are low enough to allow only purely electrostatic repulsive forces with no oscillations to be observed. The strength of the repulsion decreased with an increase in the SDS concentration. The inset of Figure 7 shows the plot of log(F/R) versus D, the slope of which gives the decay lengths. When the concentration of SDS was increased to 210, 500, and 1000 mM, oscillations could be observed when the slow measuring compression speed of 37.6 ( 3.3 nm s-1 was used; see Figure 8. The inset of Figure 8 shows an enlargement of the plot, allowing the oscillations to be seen more clearly. Oscillations are

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Figure 8. Effect of increasing the SDS concentration from 210 to 1000 mM on the interaction forces between a bare silica surface and a SDS-modified paraffin surface at pH 7. The concentrations and measuring velocities of the SDS solutions are, ., 210 mM and 40.5 nm s-1; b, 500 mM and 38.3 nm s-1; and, 3, 1000 mM and 34.0 nm s-1. The solid, dashed, and dotted lines show the best fits to the force curves for 210, 500, and 1000 mM SDS, respectively. They were obtained using the summation of an electrical force component using the constant charge model, assuming the surface potentials of 28, 25, and 25 mV, respectively, for the silica surface, and the surface potentials of 22, 23, and 23 mV, respectively, for the SDSmodified paraffin surface interacting in 40, 100, and 155 mM 1:1 electrolyte solution, respectively; a van der Waals force component using a nonretarded Hamaker constant of 0.7 × 10-20 J; an oscillatory structural force component (using only eq 3) with the volume fractions of 0.23, 0.30, and 0.35; and experimental effective micellar diameters of 6.5, 6, and 5.3 nm, respectively. The inset shows an enlargement of the forces so that the oscillations can be seen better.

observed to start at distances 4, 3, and 1 nm prior to the obvious electrostatic repulsive force for 210, 500, and 1000 mM SDS. The number and strength of the oscillations increased with a SDS concentration increase. The slope of the plot of log(F/R) versus D (not shown) gave the decay lengths. The force curves for 8.2, 100, 210, 500, and 1000 mM SDS were fitted with the calculated resultant of the electrostatic force between two dissimilar surfaces using the constant-surface-charge boundary condition,45 the van der Waals force using the Hamaker constant of 7 × 10-21 J, and the oscillatory structural force from eq 3. The resulting surface potentials, concentration of ions, volume fractions, and diameter of particles are shown in Table 5. The volume fractions predicted from eq 14 were within 32 and 42% of the volume fractions determined from the curve fitting for 500 and 1000 mM SDS, respectively. The diameter of the particles (dexp) determined from curve fitting was within 14% of that calculated from the effective particle diameter. The effect of measuring the forces with faster speeds was to smooth the oscillations and make them nonsharp. This can again be thought to be the result of the hydrodynamic force at a high compression speed. Table 5 shows that the concentration of ions in solution, the dissociated Na ions, increases with a SDS concentration increase. The surface potential of the SDS-modified paraffin surface is effectively unchanged when the SDS concentration is increased from 8.2 to 1000 mM. This can be understood by the inability of the SDS-modified paraffin surface to dissociate. The decrease in the surface potential of the silica probe can again be thought to be due to an increased dissociation of the silanol groups with a SDS concentration increase. The decrease in potential of the bare silica surface and the modified paraffin surface with the SDS concentration

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Table 5. Fitting Parameters for the Forces in an Asymmetric System of a Silica Surface and a SDS-Modified Paraffin Surface in the Presence of SDSa concd SDS (mM)

Ccalc2 (mM)

1/κ2 (nm)

dcalc2 (nm)

φcalc2

Ψ0SiO2 (mV)

Ψ0par (mV)

1/κexp (nm)

Cexp (mM)

dexp (nm)

φexp

8 100 210 500 (pH 7.4) 1000 (pH 7.2)

8 26.56 48.56 106.56 206.56

3.42 1.88 1.39 0.94 0.67

11.56 8.56 7.58 6.67 6.15

0 0.24 0.32 0.44 0.60

33 29 28 25 25

24 22 22 23 23

3.95 1.77 1.53 0.97 0.78

6 30 40 100 155

6.5 6.0 5.3

0.23 0.30 0.35

a Concd SDS, C calc2, 1/κ2, dcalc2, φcalc2, Ψ0SiO2, Ψ0par, 1/κexp, Cexp, dexp, and φexp are the concentration of SDS used, the concentration of free ions calculated by eq A1 assuming a micellar ionization of 0.2, the Debye length calculated from Ccalc2, the effective diameter of the SDS micelles calculated from eq 9 and Ccalc2, the volume fraction of the SDS micelles calculated from eq 14 using dcalc2 and Nag, the surface potential of the silica surface, the surface potential of the SDS-modified paraffin surface, the experimental decay length, the actual concentration of free ions in solution determined experimentally, the size of the particles that gives the same value as that of the special dimensions of the oscillations as obtained from the curve fitting, and the experimental volume fraction of micelles obtained by the curve fitting, respectively.

reduces the electrostatic repulsion between the surfaces and between the SDS micelles and the surfaces. The repulsion that is seen superimposed on the oscillatory force is probably due to an electrostatic force and a steric force. The former is due to the electrostatic repulsion between the two charged surfaces and between a surface and the SDS micelles. The latter may be due to a silica gel layer or a layer of adsorbed ions on the silica particle probe. The high SDS concentration of 1000 mM has only a subnanometer Debye length. Therefore, that repulsion is probably primarily due to a steric repulsion. The repulsion in the force curves is seen to decrease with an increased SDS concentration. This would cause the micelles to form organized layers at a smaller specific spacing, shifting the onset of oscillations to lower separations. The always-present repulsion, however, means that the modeled emulsion droplet will not adhere to the charged hard surface. This is different to the adhesion that can occur between two emulsion droplets61-63 that possibly occurs via a van der Waals or hydrophobic attraction. This difference may be due to the hydrophilicity of the silica surface and the hydrophobicity of the paraffin surface; a hydrophobic interaction would not exist in such a system. 4-3. Comparison of Forces in Symmetric and in Asymmetric Systems. Comparing the results obtained with the asymmetric system of the silica-SDS-SDSmodified paraffin and the symmetric system of the silicaSDS-silica allows us to comment on the effect of symmetry on the interaction forces. In both cases, an electrostatic repulsive force was observed, the range of which decreased with a SDS concentration increase. Its origin was thought to be due to the Na ions that dissociated from the dodecyl sulfate. This, however, caused no differences to be observed in the oscillations between the symmetric surfaces and between the asymmertric surfaces. In both cases, the oscillations increased in size and in magnitude with a SDS concentration increase above 210 mM. Also, in both cases, a repulsive force was observed at separations less than the size of a SDS micelle. This repulsion was explained by a repulsion between the silica or SDS(61) Leal-Calderon, F.; Poulin, P. Curr. Opin. Colloid Interface Sci. 1999, 4, 223. (62) Poulin, P.; Bibette, J. Phys. Rev. Lett. 1997, 79, 3290. (63) Aronson, M. P.; Princen, H. M. Nature 1980, 286, 370.

modified paraffin surface and the micelles or a steric force. Thus, the effect of using a symmetric system compared to a nonsymmetric system appears to affect only the DLVO forces because of differences in their surface potentials. 5. Conclusions In this study, we saw that the number and magnitude of oscillations increases with the number of particles between two surfaces. There also appears to be an electrostatic repulsion between the surfaces and the particles. The effect of using a particle instead of a micelle did not show any measurable effect on the forces. Additionally, the effect of using an asymmetric system instead of a symmetric system appears only to affect the DLVO forces and not the appearance of the structural force. The compression speed affects the forces only when high particle volume fractions and high compression speeds were used, probably as a result of a hydrodynamic force. All the forces in this study could be fitted well by using a summation of an electrostatic, van der Waals, and oscillatory structural force. Acknowledgment. This study has been indebted to the Science Promotion Grant 10640558 of the Ministry of Education, Japan, and to the Humboldt Foundation, Germany. We are also grateful to Prof. Peter Kralchevsky (Sofia University, Bulgaria) for invaluable discussions concerning this research. Appendix 1. Calculation of the Ionic Strength of SDS above the cmc. If we assume that the Na cations bind to SDS micelles with a micellar ionization (R) of 0.2 in water at T ) 25 °C, then the ionic strength (Ccalc2) of SDS above the cmc can be calculated via

Ccalc2 ) cmc + R(C* - cmc)

(A1)

where C* is the concentration of SDS.64 LA0357763 (64) Bales, B. L.; Almgren, M. J. Phys. Chem. 1995, 99, 15153.