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Particles Adsorbed at the Oil-Water Interface: A Theoretical Comparison between Spheres of Uniform Wettability and “Janus” Particles B. P. Binks* and P. D. I. Fletcher* Surfactant & Colloid Group, Department of Chemistry, The University of Hull, Hull HU6 7RX, United Kingdom Received March 5, 2001. In Final Form: May 8, 2001 We consider the adsorption at an oil-water interface of spherical particles of two types. The first type has a homogeneous surface of uniform wettability. The second type, so-called “Janus” particles, has two surface regions of differing wettabilities. Homogeneous particles are strongly surface active but are not amphiphilic, whereas Janus particles are both surface active and amphiphilic. We present calculations to show how the particle amphiphilicity, tuned by variation of either the relative surfaces areas or the different wettabilities of the two surface regions on the particles, influences the strength of particle adsorption. Increasing the amphiphilicity of the particles produces a maximum of a 3-fold increase in surface activity for average contact angles around 90°. Unlike homogeneous surface particles, Janus particles remain strongly surface active for average contact angles approaching either 0 or 180°.
The adsorption of solid particles at either gas-liquid or liquid-liquid interfaces is attracting increasing interest owing to many potential applications in the stabilization of foams and emulsions, respectively. Recently, one of us has described the preparation, stability, and inversion characteristics of novel surfactant-free emulsions containing nanometer-sized silica particles.1,2 The hydrophobicity of the particles, varied by coating them to different extents, is crucial in dictating the type (oil-inwater or water-in-oil) and coalescence stability of the emulsions. Particles of intermediate hydrophobicity are most effective in stabilizing oil or water drops of submicron diameter. Such particles, possessing different ratios of surface hydrophobic and hydrophilic groups, exhibit different wettabilities, but in each case, the wettability is uniform over the particle surface. Uniform, homogeneous particles of intermediate wettability are highly surface active at oil-water interfaces, as evidenced by their ability to stabilize emulsions for periods exceeding several years.1,2 In this theoretical study, we consider the adsorption of spherical particles of two types at the oil-water interface. The first type has a surface of uniform wettability and is characterized by the contact angle between the particle surface and the oil-water interface which is independent of the position of the three phase contact line on the particle surface. As noted above, the value of the contact angle can be controlled by variation of the surface coating of the particle in addition to the chemical nature of the oil and water phases. The second particle type has two different surface regions, designated here as polar and apolar, and is characterized by two contact angles, θA and θP, depending on whether the three phase contact line lies within the apolar or polar surface region of the particle, respectively. The term “Janus” particle was coined originally to denote particles of inhomogeneous wettability for which the areas of the polar and apolar regions were equal.3 However, the apolar and polar area ratio can be variable. * To whom correspondence should be addressed. E-mail:
[email protected] and
[email protected]. (1) Binks, B. P.; Lumsdon, S. O. Langmuir 2000, 16, 2539. (2) Binks, B. P.; Lumsdon, S. O. Langmuir 2000, 16, 8622. (3) Casagrande, C.; Fabre, P.; Raphae¨l, E.; Veyssie´, M. Europhys. Lett. 1989, 9, 251.
Figure 1. Geometry of a Janus particle within an oil-water interface. The relative areas of the polar and apolar particle surface regions are parametrized by the angle R. The immersion depth of the particle in the oil-water interface is parametrized by the angle β.
As shown in Figure 1, the position of the surface boundary between the apolar and polar regions on the particle is denoted by the angle R. Values of R of either 0 or 180° correspond to homogeneous particles, and R ) 90° corresponds to a Janus particle in the original meaning denoting equal areas. In this letter, we will use the term Janus particle in a less restricted sense to denote particles for which R lies between 0 and 180°. Veyssie´ et al.3,4 studied such amphiphilic particles both experimentally and theoretically. There are several reports detailing the preparation of amphiphilic particles. Casagrande et al.,3 using glass spheres of diameter 60 µm, protect one hemisphere with a varnish and chemically treat the other with a silane reagent. The varnish is subsequently dissolved yielding Janus particles. Rossmy5 describes their synthesis either from hollow glass spheres, with the ability to coat the inner and outer surfaces differently, or in situ at an oil-water interface. The use of particle monolayers spread at air-water surfaces or adsorbed at solid-liquid interfaces appears to be a successful way of preparing microspheres with nonuniform coatings.6 A different class of colloidal particles, also termed amphiphilic by the original authors, has been reported by Li et al.,7 in which (4) Ondarc¸ uhu, T.; Fabre, P.; Raphae¨l, E.; Veyssie´, M. J. Phys. France 1990, 51, 1527. (5) Rossmy, G. Prog. Colloid Polym. Sci. 1998, 111, 17. (6) Fujimoto, K.; Nakahama, K.; Shidara, M.; Kawaguchi, H. Langmuir 1999, 15, 4630.
10.1021/la0103315 CCC: $20.00 © 2001 American Chemical Society Published on Web 07/03/2001
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hydrophilic polyacrylamide cores are encapsulated by porous hydrophobic poly(butyl methacrylate) shells. Stable dispersions of such particles can be prepared in both water and oil solvents. In comparing the adsorption of homogeneous particles and Janus particles, it is useful to distinguish between surface activity and amphiphilicity. A surface active species is one which shows a tendency to adsorb at surfaces, whereas an amphiphilic species is one possessing a diblock structure in which the two blocks have different affinities for the solvent(s). Homogeneous particles for which the contact angle with the oil-water interface is around 90° are strongly surface active at this interface but are not amphiphilic. Janus particles are both surface active and amphiphilic. The amphiphilicity of Janus particles can be “tuned” through variation of both the angle R (parametrizing the relative areas of the polar and apolar regions) and the magnitude of the difference between the two contact angles θA and θP. Zero amphiphilicity (corresponding to homogeneous particles) corresponds to either R ) 0 or 180° or (θP - θA) ) 0. Strongest amphiphilicity is expected when R ) 90° and (θP - θA) is 180°. In this letter, we compare calculated free energies of particle desorption from an oil-water interface as the amphiphilicity is tuned from zero to the maximum. Following the work of Ondarc¸ uhu et al.,4 the total surface free energy E for a Janus particle within an oilwater interface as a function of the angle β (characterizing the immersion depth of the particle, Figure 1) is given by
Figure 2. Variation of particle desorption energy with areaweighted average contact angle for particles of radius 10 nm and R ) 90°. The oil-water tension was set to 36 mN m-1. In order of increasing desorption energies, the curves refer to ∆θ of 0 (the homogeneous particle case), 20, 40, 60, and 90°.
The contact angles θA and θP correspond to the equilibrium angles given by Young’s equation.
cos θA )
γ(AW) - γ(AO) γ(OW)
(3)
cos θP )
γ(PW) - γ(PO) γ(OW)
(4)
For β e R
[
E(β) ) 2πR2 γ(AO)(1 + cos R) + γ(PO)(cos β 1 cos R) + γ(PW)(1 - cos β) - γ(OW)(sin2 β) (1) 2
]
The immersion angle β corresponding to the lowest surface energy configuration of the Janus particle depends on the relative magnitudes of R, θA, and θP. The three possibilities are listed below.
For R < θA < θP, then β ) θA
For β g R
[
2
E(β) ) 2πR γ(AO)(1 + cos β) + γ(AW)(cos R 1 cos β) + γ(PW)(1 - cos R) - γ(OW)(sin2 β) (2) 2
]
where R is the particle radius and γ(AO), γ(PO), γ(AW), γ(PW), and γ(OW) are the interfacial energies of the apolar-oil, polar-oil, apolar-water, polar-water, and oil-water interfaces, respectively. Equations 1 and 2 are valid under conditions such that the radius of curvature of the oil-water interface is negligible relative to the particle radius and are applicable to the case of recently reported solid-stabilized emulsions1,2 in which micrometersized liquid drops are coated with nanometer-sized particles. For the case of small particles considered here (of density not too different to that of the bulk oil and water phases), the oil-water interface shape is not significantly deformed by particle buoyancy effects. It is further assumed that the Janus particles are located the “right way round” in the interface, that is, with the apolar region all or mostly in the oil and the polar region all or mostly in the water. In addition, effects of the line tension associated with the liquid-solid perimeter line around the particle (for which theoretical estimates of the order of 10-11 N have been made8) might be envisaged to be significant for nanometer-sized particles. For the purposes of this theoretical study focusing on the role of particle amphiphilicity, we have neglected such line tension effects. (7) Li, H.; Zhao, J.; Ruckenstein, E. Colloids Surf., A 1999, 161, 489. (8) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Oxford University Press: Oxford, 1989; Chapter 8.
For θA < R < θP, then β ) R For θA < θP < R, then β ) θP
(5)
Equations 1 and 2 together with the inequalities in [5] allow the calculation of the minimum surface energy of the adsorbed particle Esurface. The surface energy of the particle located entirely in either the bulk oil (Eoil) or water (Ewater) is given by eqs 1 or 2 with β set to either 0° (for the particle in oil) or 180° (for the particle in water). The surface activity of the particle is calculated as the desorption energy which is defined as the free energy required to desorb the particle from the interface into either the bulk oil or water phase, (Eoil - Esurface) or (Ewater - Esurface), whichever is the lowest. Figure 2 shows the variation of particle desorption energy in units of kT per particle with average contact angle for Janus particles of different values of ∆θ. For this series, R, R, and γ(OW) are set to constant values of 90°, 10 nm, and 36 mN m-1, respectively. For calculations of different selected contact angles, the appropriate combinations of surface energies were obtained by solution of eqs 3 and 4. The average contact angle plotted as the abscissa is weighted by the relative areas of the polar and apolar particle surface regions according to
θaverage )
θA(1 + cos R) + θP(1 - cos R) 2
(6)
For this series at constant R, the particle amphiphilicity is tuned by changing ∆θ (defined as (θP - θA)/2). ∆θ of 0°
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corresponds to a homogeneous particle of zero amphiphilicity. ∆θ ) 90° corresponds to the maximum possible amphiphilicity in which the polar region of the particle is completely wetted by water and the apolar region is completely wetted by oil. For nonzero values of ∆θ and θaverage approaching either 0 or 180°, the individual values of θA and θP necessarily lie outside the range 0-180°. Although such values are not realizable in a practical measurement of contact angle, they still correctly account for an increasing or decreasing affinity for the solid surfaces. The point that liquid-solid adhesion energies can increase beyond the transition point of zero contact angle has been noted by Clint.9 From Figure 2, it can be seen that increasing the particle amphiphilicity through ∆θ increases the strength of particle adsorption up to a maximum of 3-fold for θaverage of 90°. In addition, the Janus particles maintain strong adsorption at average contact angles approaching 0 or 180° where the surface activity of the nonamphiphilic (homogeneous with ∆θ ) 0) particles is low. The calculations of Figure 2 refer to a particle radius of 10 nm and an oil-water interfacial tension of 36 mN m-1, values which correspond to the coated silica particles used in recent studies of the formation and stability of emulsions stabilized by particles alone.1 The desorption energies for different particle radii and interfacial tensions are simply obtained by noting (eqs 1 and 2) that the energy scales in proportion to the product γ(OW)R2. Even for particles of radius 10 nm, the maximum desorption energies are very high, of the order of several thousands of kT. Figure 3 shows corresponding plots for Janus particles with a fixed ∆θ of 40° where the particle amphiphilicity is varied by changing R. The homogeneous (nonamphiphilic) particle case corresponds to R ) 0 or 180°. The desorption energy reaches a maximum at R ) 90°, corresponding to maximum amphiphilicity. For angles R not equal to either 0, 90, or 180°, the curves are asymmetric with one limb having the same shape as for the case of the homogeneous particle. In these limbs of the plots, the solid-liquid perimeter line lies above or below the polarapolar boundary on the particle surface. The shapes of (9) Clint, J. H. Curr. Opin. Colloid Interface Sci. 2001, 6, 28.
Letters
Figure 3. Variation of particle desorption energy with areaweighted average contact angle for particles of radius 10 nm and ∆θ ) 40°. The oil-water tension was set to 36 mN m-1. In order of increasing desorption energies (around θaverage of 90°), the curves refer to R equal to 0 or 180 (the homogeneous particle case), 45, 120, and 90°.
the other limbs of the plots are different to those of the homogeneous particle as a consequence of the “pinning” of the oil-water interface at the apolar-polar boundary, that is, when β ) R. It can be seen that the particles can remain strongly surface active at average contact angles of 0 or 180° in this situation. Two main conclusions may be drawn from this study. First, desorption energies of homogeneous particles may be increased 3-fold by maximizing the amphiphilicity of Janus particles. Second, unlike homogeneous particles, Janus particles retain their strong adsorption even for average contact angles of 0 and 180°. It is expected that Janus particles with either low or high average contact angles will prove to be efficient emulsion stabilizers. Further intriguing possibilities arising with Janus particles adsorbed into thin liquid films and with Janus type particles with more than two different types of surface wettability regions are currently under investigation. LA0103315
