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Langmuir 2006, 22, 2112-2116
Dynamics of Charged Microparticles at Oil-Water Interfaces Chih-yuan Wu, Sowmitri Tarimala, and Lenore L. Dai* Department of Chemical Engineering, Texas Tech UniVersity, MS 3121, Lubbock, Texas 79409 ReceiVed September 23, 2005. In Final Form: December 7, 2005 Solid-stabilized emulsions have been used as a model system to investigate the dynamics of charged microparticles with diameters of 1.1 µm at oil-water interfaces. Using confocal microscopy, we investigated the influences of interfacial curvature, cluster size, and temperature on the diffusion of solid particles. Our work suggests that a highly curved emulsion interface slows the motion of solid particles. This qualitatively supports the theoretical work by Danov et al. (Danov, K. D.; Dimova, R.; Pouligny, B. Phys. Fluids 2000, 12, 2711); however, the interfacial curvature effect decreases with increasing oil-phase viscosity. The diffusion of multiparticle clusters at oil-water interfaces is a strong function of cluster size and oil-phase viscosity and can be quantitatively related to fractal dimension. Finally, we report the influence of temperature and quantify the diffusion activation energy and friction factor of the particles at the investigated oil-water interfaces.
1. Introduction Particle mobility, aggregate structure, and the mechanism of aggregate growth at the 2-D level have been of long-standing fundamental as well as practical interest for diverse physical, chemical, and biological applications.1-7 However, the detailed mechanism of the mobility and aggregation of charged colloidal particles remains unclear. Recently, we have used solid-stabilized emulsions as a new experimental model system to investigate the mobility and in-situ aggregation of charged microparticles at poly(dimethylsiloxane)-water emulsion interfaces.8 We found that the rate of diffusion of the charged particles at the interface is unexpectedly fast and depends strongly on the viscosity of the oil phase.8 This report follows up with further investigation, specifically, on the effect of interfacial curvature on single-particle diffusion, the dynamics of multiparticle clusters, and the influence of temperature on the diffusion at oil-water interfaces. Solid-stabilized emulsions (often referred to as Pickering emulsions and used hereafter), which are composed of droplets of one immiscible liquid in another liquid stabilized by solid particles, were discovered almost a century ago.9 Recently, there has been growing interest in Pickering emulsions because they open new avenues of emulsion stabilization and have numerous practical applications.10-22 Pickering emulsions also provide a (1) Pieranski, P. Phys. ReV. Lett. 1980, 45, 569. (2) Onoda, G. Y. Phys. ReV. Lett. 1985, 55, 226. (3) Robinson, D. J.; Earnshaw, J. C. Phys. ReV. A 1992, 46, 2055. (4) Stankiewicz, J.; Vilchez, M. A. C.; Alvarez, R. H. Phys. ReV. E 1993, 47, 2663. (5) Aveyard, R.; et al. Phys. ReV. Lett. 2002, 88, article number 246102. (6) Vicsek, T.; Family, F. Phys. ReV. Lett. 1984, 52, 1669. (7) Stancik, E. J.; Gavranovic, G. T.; Widenbrant, M. J. O.; Laschitsch, A. T.; Vermant, J.; Fuller, G. G. Faraday Discuss. 2003, 123, 145. (8) Tarimala, S.; Ranabothu, S. R.; Vernetti, J. P.; Dai, L. L. Langmuir 2004, 20, 5171. (9) Pickering, S. U. J. Chem. Soc. 1907, 91, 2001. (10) Tarimala, S.; Dai, L. L. Langmuir 2004, 20, 3492. (11) Dai, L. L.; Sharma, R.; Wu, C. Y. Langmuir 2005, 21, 264. (12) Stancik, E. J.; Fuller, G. G. Langmuir 2004, 20, 4805. (13) Melle, S.; Lask, M.; Fuller, G. G. Langmuir 2005, 21, 2158. (14) Xu, H.; Melle, S.; Golemanov, K.; Fuller, G. Langmuir 2005, 21, 10016. (15) Dinsmore, A. D.; Hsu, M. F.; Nikolaides, M. G.; Marquez, M.; Bausch, A. R.; Weitz, D. A. Science 2002, 298, 1006. (16) Lin, Y.; Skaff, H.; Emrick, T.; Dinsmore, A. D.; Russell, T. P. Science 2003, 299, 226. (17) Dickson, J. L.; Binks, B. P.; Johnston, K. P. Langmuir 2004, 20, 7976. (18) Horozov, T. S.; Aveyard, R.; Clint, J. H.; Neumann, B. Langmuir 2005, 21, 2330. (19) Kralchevsky, P. A.; Ivanov, I. B.; Ananthapadmanabhan, K. P.; Lips, A. Langmuir 2005, 21, 50.
new, convenient, and maybe unique experimental model system for the investigation of particle mobility, aggregation, and the growth mechanism at the liquid-liquid interface.8 In Pickering emulsions, the motion of solid particles into either the water or the oil phase is restricted because of the high desorption energy. For instance, the average Gibbs free energy of desorption is calculated to be 1.43 × 107 kT/particle for poly(dimethylsiloxane)(5 cSt)-in-water Pickering emulsions containing sulfate-treated polystyrene particles of 1 µm.10 The high desorption energy (conventional surfactants only have 10-20 kT/surfactant molecule) indicates that the solid particles strongly adhere to the oil-water interface and that the adsorption is almost irreversible.8,10 Thus, the assembled particles are confined at the oilwater interface and can move only laterally along the droplet contour when the emulsion interface is only partially covered with solid particles. One of the advantages of using Pickering emulsions as a model system for investigating the dynamics of particles at liquidliquid interfaces is the easily changeable interfacial curvature. This can be done by following the mobility of single particles on emulsion droplets with different droplet diameters. Recently, Danov et al.23 have numerically calculated the influence of interfacial curvature on particle motion at liquid-liquid interfaces. They suggest a “recirculation effect” (a finite volume effect), when the ratio of the emulsion droplet radius to the solid particle radius is relatively small. In those cases, the flow inside the droplet is looped and significantly increases the hydrodynamic drag friction that the solid particle experiences.23 Following the Stokes-Einstein equation, D ) kT/f, where D is the diffusion constant and f is the friction coefficient,24 the work from Danov et al.23 suggests that the recirculation effect will lead to a slowing of solid particle motion at liquid-liquid interfaces. In addition, the recirculation effect depends on the location of the particles at the liquid-liquid interface: the deeper in the enclosed phase, (20) Lipowsky, P.; Bowick, M. J.; Meinke, J. H.; Nelson, D. R.; Bausch, A. R. Nat. Mater. 2005, 4, 407. (21) Shah, P. S.; Sigman, M. B.; Stowell, C. A.; Lim, K. T.; Johnston, K. P.; Korgel, B. A. AdV. Mater. 2003, 15, 971. (22) Nobel, P. F.; Cayre, O. J.; Alargova, R. G.; Velev, O. D.; Paunov, V. N. J. Am. Chem. Soc. 2004, 126, 8092. (23) Danov, K. D.; Dimova, R.; Pouligny, B. Phys. Fluids 2000, 12, 2711. (24) van de Ven, T. G. M. Colloidal Hydrodynamics; Academic Press: San Diego, CA, 1989; p 81.
10.1021/la0525978 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/26/2006
Microparticle Dynamics at Oil-Water Interfaces
Langmuir, Vol. 22, No. 5, 2006 2113
increases from 5 to 350 cSt. Brenner and Leal30,31 suggested that the Brownian diffusion of a solid particle at a liquid-liquid interface can be quantified by a modified Stokes-Einstein relationship,
D) Figure 1. In-situ aggregation of 1 µm polystyrene particles at the poly(dimethylsiloxane) (20 cSt)-in-water Pickering emulsion interface.
the larger the effect.23 Obviously, experimental verification is needed for these hypotheses that were generated from numerical simulation. Another important fundamental question is the mobility of multiparticle clusters in two dimension. Meakin, Vicsek, and Family25,26 have shown that the cluster size distribution depends strongly on the diffusion of multiparticle clusters in two and three dimensions. Under the assumption of DN ) D0Nγ, where DN is the diffusion constant of the N-particle cluster, D0 is a constant, N is the number of particles in a cluster, and γ is the diffusivity exponent, their simulation shows that the cluster size distribution goes through a monotonic decay to a bell-shaped curve occurring at a critical γ.25 Our earlier work compared the ambient diffusion constants of a single particle and a five-particle cluster confined at the poly(dimethylsiloxane) (5 cSt)-water emulsion interface. The diffusion of the cluster is significantly hindered compared to that of a single particle (lowered by a factor of 2);8 however, the hindrance in diffusivity is not linearly proportional to the cluster size, which may support the above assumption of the power law dependence. It is also intuitive to ask about the effect of liquid-phase viscosity on the mobility of multiparticle clusters. Particle mobility is closely related to the aggregation and structural formation of solid particles at liquid-liquid interfaces, which are of tremendous interest and are important to various processes. We have successfully observed the in-situ structural formation of solid particles at the oil-water interface, as shown in Figure 1. We hypothesize that the observed structural formation is likely due to diffusion-limited cluster aggregation (DLCA) because every collision of the particles at the oil-water interface leads to the aggregation of particles.8,27,28 Although the fractal dimension is important for understanding the aggregation kinetics and cluster morphology, we were not able to measure the fractal dimension directly because of the relatively small interface area. In three dimension (3-D), the diffusion coefficient of the multiparticle cluster is associated with the fractal dimension through
DN ) D0Nγ ) D0N-1/Df
(1)
where Df is the fractal dimension.3,29 However, because the relationship is derived from a 3-D case, its applicability to a 2-D case is questionable.3 Recently, we have purchased a thermal stage and validated the capability of investigating the effect of temperature on the diffusion of particles at liquid-liquid interfaces. Our previous work8 has shown the relevance of the standard Stokes-Einstein relationship to the diffusion of single particles at poly(dimethylsiloxane)-water interfaces when the viscosity of the oil phase (25) Meakin, P.; Vicsek, T.; Family, F. Phys. ReV. B 1985, 31, 564. (26) Family, F.; Meakin, P.; Vicsek, T. J. Chem. Phys. 1985, 83, 4144. (27) Horvolgyi, Z.; Mate, M.; Zrinyi, M. Colloids Surf., A 1994, 84, 207. (28) Prasad, V.; Trappe, V.; Dinsmore, A. D.; Segre, P. N.; Cipelletti, L.; Weitz, D. A. Faraday Discuss. 2003, 123, 1. (29) Meakin, P.; Family, F. Phys. ReV. A 1988, 38, 2110.
kT fπηa
(2)
where k is the Boltzman constant, T is the temperature, f is a friction factor, η is the liquid viscosity, and a is the radius of the solid particle. “The friction factor, f, is a complicated nonlinear function of the contact angle of the particle and the two liquid viscosities.”32 In this report, we experimentally investigate the effect of temperature on diffusion at liquid-liquid interfaces and extrapolate the friction factor. 2. Experimental Section Oil-in-water type Pickering emulsions containing sulfate-treated polystyrene solid particles were prepared using an ultrasonic processor (Sonics VibraCell, 500 W model). The oil is either poly(dimethylsiloxane) (Rhodorsil Fluid, viscosity of 5 or 20 cSt at 25 °C) or octamethyltrisiloxane (Dow Corning 200 Fluid, viscosity of 1 cSt at 25 °C). Water (HPLC grade, residue after evaporation
