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Langmuir 2006, 22, 4936-4945
Control over Colloidal Aggregation in Monolayers of Latex Particles at the Oil-Water Interface Sven Reynaert, Paula Moldenaers, and Jan Vermant* Department of Chemical Engineering, K.U. LeuVen, W. de Croylaan 46, B-3001 LeuVen, Belgium ReceiVed January 6, 2006. In Final Form: March 24, 2006 The controlled generation of 2D aggregate networks is studied experimentally using micrometer-sized polystyrene latex particles attached to the oil-water interface. Starting from an initially crystalline monolayer, appropriate combinations of carefully added electrolyte and surfactant enable control over both the fractal dimension and the kinetics of aggregation. Remarkably, the colloidal crystals formed upon first spreading remain stable, even for days, when substantial amounts of electrolyte are added to the aqueous phase. Pressure-area isotherms reveal a slow time evolution of the electrostatic dipole-dipole interaction. When the electrostatic interaction has been sufficiently weakened, aggregation proceeds in well-defined, reproducible manner. The aggregation process is analyzed using quantitative video microscopy. The evolution of the cluster size distribution and its moments is characterized, and static and dynamic scaling exponents are derived to identify the nature of the aggregation process. In the range of concentrations studied here, the kinetics all agree with a “fast”, diffusion-limited cluster type of aggregation. However, the fractal dimension strongly depends on the composition of the aqueous subphase. Rather dense structures are found when only electrolyte is used, whereas more open structures are obtained when even small amounts of surfactant are added. It is suggested that this structural dependency is related to the effect of surfactant on the contact angle and its consequences for the anisotropic nature of the capillary interactions.
Introduction The controlled assembly of particles at fluid interfaces is a subject that has received considerable attention recently, especially because of applications in a variety of disciplines. These include emulsion and food science,1 flotation technology,2 biomedicine,3 and materials science.4 These applications emerge because colloidal particles have the tendency to become irreversibly trapped at liquid-air and liquid-liquid interfaces by the effects of interfacial tension and because the particles can affect the mobility of the interface.5,6 Particle-laden interfaces are very often used because of their capability of stabilizing incompatible materials such as water-oil mixtures against coalescence, resulting in the so-called Pickering emulsions.7 Yet, foams8,9 and even polymer blends10 can also be stabilized by the presence of particles at the interface, and novel colloidal capsules called colloidosomes can be engineered.3 The energy with which small particles are attached to the interface is proportional to the interfacial tension between the two liquids and the particle radius squared and is dependent on the contact angle.5 Most of the applications of particles at interfaces are derived from the effects of the particles on the dynamics and mobility of the interface. It has been suggested that the particles need to pack very densely or even become “jammed”11,12 in order to obtain a rigid particle-laden interface. However, Vignati et al.13 * To whom correspondence should be addressed. E-mail: jan.vermant@ cit.kuleuven.be. (1) Horne, D. S. Curr. Opin. Colloid Interface Sci. 1996, 1, 752. (2) Nguyen, A. V.; Schulze, H. J. Colloidal Science of Flotation; Marcel Dekker: New York, 2003. (3) Dinsmore, A. D.; Ming Hsu, F.; Nikolaides, M. G.; Marquez, M.; Bausch, A. R.; Weitz, D. A. Science 2002, 298, 1006. (4) Wubben, T.; Odenbach, S. Colloids Surf., A 2005, 266, 207. (5) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21. (6) Stancik, E. J.; Fuller, G. G. Langmuir 2004, 20, 4805. (7) Pickering, S. U. J. Chem. Soc. 1907, 91, 2001. (8) Velikov, K. P.; Durst, F.; Velev, O. D. Langmuir 1998, 14, 1148. (9) Sethumadhavan, G. N.; Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 2001, 240, 105. (10) Vermant, J.; Cioccolo, G.; Golapan Nair, K.; Moldenaers, P. Rheol. Acta 2004, 43, 529.
showed that no straightforward relation exists between the extent of particle interfacial adsorption and emulsion macroscopic stability; stable emulsions can be obtained even with relatively low droplet surface coverage. Midmore showed, using flocculated model silica particles, that stabilizing the emulsion required a minimal particle surface coverage of 0.29, corresponding to a percolation threshold for the aggregation of monodisperse spheres in 2D.13 This suggests that more open aggregated structures may play an important role in solid stabilized emulsions. By tailoring the interparticle interactions, a large variety of structures can indeed be generated by particles at interfaces. The structures observed range from colloidal crystals,15 over foamlike structures,16-18 to aggregated structures.19-21 The crystalline monolayers and their dynamics have received the most attention.22-24 The crystalline organization typically occurs because the electrostatic repulsion between charged particles is greatly enhanced at a water-low dielectric medium interface, as was recognized early on by Pieranski.15 A repulsive interaction with the characteristics of a dipole-dipole interaction acting through the low dielectric material is observed. Whereas Hurd25 originally suggested that this dipole-dipole interaction arises (11) Stradfort, K.; Adhikari, R.; Pagonabarraga, I.; Desplat, J. C.; Cates, M. E. Science 2005, 309, 2198. (12) Giermanska-Kahn, J.; Laine, V.; Arditty, S.; Schmitt, V.; Leal-Calderon, F. Langmuir 2005, 21, 4316. (13) Midmore, B. R. Colloids Surf., A 1998, 132, 257. (14) Vignati, E.; Piazza, R.; Lockhart, T. P. Langmuir 2003, 19, 6650. (15) Pieranski, P. Phys. ReV. Lett. 1980, 45, 569. (16) Ghezzi, F.; Earnshaw, J. C. J. Phys.: Condens. Matter 1997, 9, L517. (17) Ghezzi, F.; Earnshaw, J. C.; Finnis, M. J. Colloid Interface Sci. 2001, 238, 433. (18) Stamou, D.; Duschl, C.; Johannsmann, D. Phys. ReV. E 2000, 62, 5263. (19) Robinson, D. J.; Earnshaw, J. C. Phys. ReV. A 1992, 46, 2045. (20) Robinson, D. J.; Earnshaw, J. C. Phys. ReV. A 1992, 46, 2055. (21) Robinson, D. J.; Earnshaw, J. C. Phys. ReV. A 1992, 46, 2065. (22) Stancik, E. J.; Widenbrant, M. J. O.; Laschitsch, A. T.; Vermant, J.; Fuller, G. G. Langmuir 2002, 18, 4372. (23) Stancik, E. J.; Gavranovic, G. T.; Widenbrant, M. J. O.; Laschitsch, A. T.; Vermant, J.; Fuller, G. G. Faraday Discuss. 2003, 123, 145. (24) Stancik, E. J.; Hawkinson, A. L.; Vermant, J.; Fuller, G. G. J. Rheol. 2004, 48, 159. (25) Hurd, A. J. J. Phys. A 1985, 18, 1055.
10.1021/la060052n CCC: $33.50 © 2006 American Chemical Society Published on Web 04/29/2006
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because of an asymmetry in the double layers, Aveyard et al.26 demonstrated that the mechanism is somewhat more subtle. They suggested that a small number of unscreened charges, possibly arising from dissociated groups at the particle surface, are present. The force acting between the particles can be calculated as a function of the interparticle distance R using Stillingers approach,27 where the charges in the oil phase are represented by a point charge qoil located a distance ζ above the oil-water interface
F≈
6q2oilσ2 4πoil0R4
(1)
where 0 is the permittivity of free space and oil is the relative dielectric constant of oil. Direct measurements by Aveyard et al.28 demonstrated that the measured force is independent of the ionic strength of the aqueous phase and indeed decays as R-4. Some issues, however, remain as the inferred degree of dissociation that produces qoil ranges from 0.033%28 up to 1%26 for the same type of particles, depending on the measurement technique used. Yet the charge-dipole character and the remarkable independence of the ionic strength are essential features that have been clearly established. The exact nature of the attractive part is still the subject of debate. For micrometer-sized particles at oil-water interfaces, the van der Waals interaction is significant and will act at a distance corresponding to the order of the particle radius for polymeric particles at the oil-water interface.29 Experiments, however, reveal longer-ranged lateral attractive interactions, even in charged systems, that are due to capillary forces.15-17,30,31 When a particle is attached to the boundary between water and a nonpolar fluid, it can be subjected to the action of a normal force that will then deform the interface. The lateral capillary interactions subsequently arise because of the overlap of the menisci formed around two particles residing at the interface. When the normal force is caused by an external field as is the case for gravity, the interaction is well understood and is shown to be long-ranged.32,33 However internal fields can also create a distortion of the interface, such as the dipolar electric field of the particles. This yields a local force imbalance due to the Maxwell stress tensor.30,34 Some controversy arose with respect to the range and sign of this electrocapillary interaction.30,31,34-38 The emerging picture seems to be that in mechanically isolated systems the interaction is short-ranged.39,40 Medium-ranged flotation-like forces may arise in the presence of even very weak (26) Aveyard, R.; Clint, J. H.; Nees, D.; Paunov, V. N. Langmuir 2002, 16, 1969. (27) Stillinger, F. H. J. Chem. Phys. 1961, 35, 1584. (28) Aveyard, R.; Binks, B. P.; Clint, J. H.; Fletcher, P. D. I.; Horozov, T. S.; Neumann, B.; Paunov, V. N.; Annesley, J.; Botchway, S. W.; Nees, D.; Parker, A. W.; Ward, A. D.; Burgess, A. N. Phys. ReV. Lett. 2002, 88, 246102. (29) Derjaguin, B. V. Theory of Stability of Colloids and Thin Films; Consultants Bureau: New York, 1989. (30) Nikolaides, M. G.; Bausch, M. G.; Hsu, M. F.; Dinsmore, A. D.; Brenner, M. P.; Weitz, D. A. Nature 2002, 420, 299. (31) Nikolaides, M. G.; Bausch, M. G.; Hsu, M. F.; Dinsmore, A. D.; Brenner, M. P.; Weitz, D. A. Nature 2003, 424, 1014. (32) Kralchevsky, P. A.; Nagayama, K. Particles at Fluids Interfaces and Membranes: Attachment of Colloid Particles and Proteins to Interfaces and Formation of Two-Dimensional Arrays; Elsevier: Amsterdam, 2001. (33) Kralchevsky, P. A.; Nagayama, K. AdV. Colloid Interface Sci. 2000, 85, 145. (34) Danov, K. D.; Kralchevsky, P. A.; Boneva, M. P. Langmuir 2004, 20, 6139. (35) Megen, M.; Aizenberg, J. Nature 2003, 424, 1014. (36) Foret, L.; Wurger, A. Phys. ReV. Lett. 2004, 92, 058302. (37) Wurger, A.; Foret, L. J. Phys. Chem. B 2005, 109, 16435. (38) Oettel, M.; Dominguez, A.; Dietrich, S Phys. ReV. E 2005, 71, 051401. (39) Oettel, M; Dominguez, A; Dietrich, S Langmuir 2006, 22, 846. (40) Danov, K. D.; Krachlevsky, P. A. Langmuir 2006, 22, 848
external electric fields or in systems where the local electrostatic force imbalance around a particle acts over distances large compared to the interparticle distance.36-38,40 In this respect, the presence of charges in the oil phase with long screening lengths might again play an important role. Last but not least, interfacial deformations can arise because of particle wetting properties; the resulting “immersion” capillary forces can be operative even between very small particles.33 These capillary interactions depend on the shape of the meniscus and aspects such as particle roughness and particle or agglomerate shape. The interaction can be repulsive or attractive depending on the relative orientations of the interface deformations.18 This also implies that when doublets or irregular aggregates are formed the resulting capillary interactions will no longer be isotropic.41,42 The magnitude of any capillary interaction is proportional to the value of the interfacial tension. The wetting properties of the particles also play an important role, especially where the anisotropy of the capillary interaction is concerned.42 Despite the complex electrostatic and especially capillary interactions that occur between particles at interfaces, Earnshaw and Robinson19-21 successfully used the salt-induced aggregation of latex beads at the air-water interface as a model experiment to study aggregation for comparison with computer simulations and scaling predictions.43-46 In the present work, the structure and kinetics of the aggregation of particles suspended at an oilwater interface will be studied by monitoring the fractal dimension and the cluster size distribution and its moments, respectively. The goal of this work is to generate interfaces with well-controlled structures for an oil-water system and to elucidate the role of the addition of salt and surfactants to the structure formation of planar monolayers. The relative complexity of the interparticle forces will be more pronounced for the particles at the oil-water interface when compared to that reported in earlier studies of Earnshaw and Robinson at the air-water interface because of increased sensitivity of the latex particle wettability to the addition of electrolyte and surfactant. Despite this complexity, it will be shown that 2D percolated particulate networks with controlled structures that could offer tailored rheological properties and interfacial rigidity can be generated. Hence by analogy to 3D weakly aggregated suspensions, which are used as rheological agents,47 interfaces that control aggregate structures can be designed. Controlled interfacial structure and rheology could play a key role in the intelligent design of water-oil Pickering emulsions. In the present work, monodisperse sulfonated polystyrene particles are used as a model system, as in numerous recent studies rendering a comparison with the literature date possible (e.g., refs 22-24, 26, and 28). Changes in electrostatic repulsion are monitored by measuring and analyzing the pressure area isotherms. To analyze the structure and kinetics of aggregation, quantitative video microscopy is used. Furthermore, the kinetics are analyzed using scaling arguments for the evolution of the cluster size distribution and its moments and will be briefly reviewed in the next section. Kinetics of Aggregation: Scaling Theory. Various theoretical approaches have been used to study the kinetics of aggregating dispersions. These include approaches based on the Smoluchowski equation, population balances,48 and simulations.46 (41) Fournier, J. B.; Galatola, P. Phys. ReV. E 2002, 65, 031601. (42) Vassileva, N. D.; van den Ende, D.; Mugele, F.; Melllema, J. Langmuir 2005, 21, 11190 (43) Vicsek, T.; Family, F. Phys. ReV. Lett. 1984, 52, 1669. (44) Vicsek, T. Phys. ReV. Lett. 1984, 53, 2281. (45) Kolb, M. Phys. ReV. Lett. 1984, 53, 1653. (46) Family, F.; Meakin, P.; Vicsek, T. J. Chem. Phys. 1985, 83, 4144. (47) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999.
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Following the approach by Earnshaw and Robinson,20 scaling laws for the cluster size distribution and its moments will be used to classify the type of aggregation regime occurring. The two most likely regimes are the diffusion-limited cluster aggregation regime (DLCA) and the reaction-limited cluster aggregation (RLCA) regime. In the DLCA regime, the essential features are that particles and clusters diffuse freely at a constant, size-independent speed and aggregate irreversibly on first contact. The time spent by a particle before it aggregates is hence fully governed by Brownian motion. The RLCA regime differs only in that the sticking probability is smaller than 1. The time evolution of the cluster size distribution can be used as a dynamic fingerprint of the aggregation mechanism. For example, in the DLCA regime the cluster size distribution is expected to be a monotonic decreasing function of the cluster size. However, in the RLCA regime the aggregate size distribution is expected to be bell-shaped with a distinct maximum at nonzero size.20,46 For the DLCA regime, the power law dependence of the number of particles in a cluster (ns) on cluster size (s) and time (t) can be expressed as20
ns(t) ≈ t-ωs-τh
() s tz
(2)
where the cutoff function h(s/tz) is equal to 1 for s/tz , 1 and h(s/tz) , 1 for s/tz . 1. The scaling exponents ω, τ, and z are linked by a constitutive relation:
ω ) (2 - τ)z
(3)
To determine these exponents in a unique way, it is useful to consider the moments of the cluster size distribution. The weightaveraged cluster size S(t) is defined as
S(t) )
∑s s2ns(s, t) ∑s
(4) ns(s, t)
Substituting eq 2 and using eq 3 yields
ns(t) S(t)2 ≈ F
() s tz
(5)
which implies that when ns(t) S(t)2 is plotted as a function of s(t) a master curve should be obtained when the system is in the fast-aggregation, DLCA, regime. Additional information is contained in the time evolution of the total number of clusters (Ntot), which should decrease as aggregation proceeds as
Ntot ≈ τ-z
if τ < 1
Ntot ≈ τ-ω
if τ > 1
(6)
Likewise, the mean cluster size S(t)rel should increase with time as tz. Hence measurements of ns(s, t), S(t), and N(t) enable a determination of the aggregation regime and allow for a full determination of the kinetics. Apart from kinetic aspects, the aggregation regime is normally also reflected in the structural aspects. Typically, aggregate networks are fractal in nature, and the different regimes are characterized by a unique fractal dimension. For the 2D case, (48) Friedlander, S. Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics, 2nd ed.; Oxford University Press: New York, 2000.
the fractal dimension for the DLCA case is expected to be 1.44 ( 0.04 for a system confined to two dimensions, as was confirmed by experiments and computer simulations.49,50 Because the RLCA regime implies that reorganizations of the structure can occur, it leads to a denser structure with a fractal dimensions of 1.55 ( 0.03 for a 2D suspension.19 However, it will be argued in the present work that the fractal dimension alone is not a sufficient indicator of the aggregation mechanism in the specific case of particles at the oil-water interface. Materials and Methods An oil-water interface was created using n-decane (Acros Organics, 99+%) and deionized, bidistilled water. Prior to use, polar components were removed from decane using adsorption onto aluminum oxide powder (Acros Chemical, acidic activated, particle size 100-500 µm). Isopropyl alcohol (IPA, VWR Prolabo, 99+%) was used as a solvent aiding in the spreading of the particles when injected at the interface. Surfactant-free, sulfonated polystyrene particles (-9.1 µC/m2 and 3.1 ( 0.2 µm diameter) were obtained from Interfacial Dynamics Corporation as aqueous dispersions containing 8 wt % particles. The suspensions were diluted using a ratio of 1 volume of particles/4 volumes of IPA/5 volumes of bidistilled water. Bright-field microscopy experiments (Olympus BX51WI fixed-stage microscope) on a planar interface were carried out on samples in a glass Petri dish. The latter was equipped with a small access port below the liquid-liquid interface to allow the injection of substances using a Hamilton precision syringe without having to go through the interface. To ensure a straight surface up to the walls of the dish between the water subphase and the decane top phase, the top part of the walls of the Petri dish was rendered hydrophobic using a silanization reaction using a 5% dimethylchlorosilane in heptane solution to ensure pinning of the contact line. The dish was covered and sealed to prevent evaporation and convection because they can induce the formation of dense aggregates. Bright-field microscopy was used to monitor the aggregation in situ and as a function of time using high-resolution CCD cameras (i.e., 1000 pixels × 1000 pixels, 12-bit cooled CCD camera connected to a frame grabber (C-8800-21, Hamamatsu) and a 1344 pixels × 1000 pixels, 12-bit IEEE 1394-based digital camera (ORCA-285, Hamamatsu). Image analysis was carried out using the object-based particle identification routines from Crocker and Grier,51 which were adapted for usage on flocculated systems by Hoekstra et al.52 In these routines, the particles are identified by a combination of a local brightness intensity criterion and additional conditions based on Voronoi spaces and the radius of gyration of the objects. Using an objective with a magnification of 20× (NA ) 0.32) in combination with the CCD cameras, the particle diameter corresponds to 10 pixels, and more than adequate positional resolution is obtained. The largest aggregate sizes that could be visualized in the field of view typically contained 1000 particles. A large number of images were taken corresponding to each instant in time or condition to arrive at a minimum of 2 × 105 particles counted for each data point, independent of surface coverage. Further increasing the number of particles in the data set did not significantly improve the results for cluster size distribution and fractal dimension. For some systems, surface pressure-area isotherms were obtained using a liquid-liquid Langmuir trough made out of Teflon and equipped with a analytical film balance (KSV instruments, Finland, maximal through area 172 cm2). The trough is computer-controlled, and two symmetric moving Delrin barriers define the interfacial area. The surface pressure (π) is measured using the Wilhelmy plate method, with the orientation of the plate parallel to the moving barriers. With this setup, the π-A isotherms were recorded for various “ages” of the monolayer (i.e., at distinct times after injection of the (49) Moncho-Jorda, A.; Martinez-Lopez, F.; Hidalgo-Alvarez, R. J. Colloid Interface Sci. 2002, 249, 405. (50) Sorenson, C. M.; Roberts, G. C. J. Colloid Interface Sci. 1997, 186, 447. (51) Crocker, J. C.; Grier, D. G. J. Colloid Interface Sci. 1996, 179, 298. (52) Hoekstra, H.; Vermant, J.; Mewis, J. Langmuir 2003, 19, 9134.
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Figure 1. Effect of SDS concentration on the interfacial tension of a water-decane interface for a salt-free aqueous subphase and a subphase containing 0.25 M NaCl.
Figure 2. Effect of SDS concentration on the contact angle on a polystyrene cast film for air-water and oil-water interfaces and for an oil-water interface with the aqueous phase containing 0.25 M NaCl. salt into the subphase). Prior to every compression, a fresh monolayer was made and allowed to age under the effect of electrolyte, and the pressure-area isotherm was then measured. The use of a fresh sample was required to avoid the formation of irreversible aggregates that can be formed upon strong compression of the monolayer.29 As mentioned in the Introduction, the wetting properties and the magnitude of the interfacial tension play an important role in determining the interactions between the particles at interfaces. To vary these parameters, the effects of small amounts of an ionic surfactant, sodium dodecylsuplhate (SDS, Sigma-Aldrich 98+%), in combination with significant amounts of a monovalent salt, NaCl, were used. The interfacial tension was measured using the pendant drop technique with a goniometer (CAM 200, KSV Instruments, Finland), and the results are given in Figure 1. As expected, adding both SDS and salt tends to lower the value of the interfacial tension from about 50 to below 10 mN/M. To evaluate the changes in the contact angle, a film was cast from the dispersions containing the particles following a procedure outlined by Stancik and Fuller.53 A water droplet is gently placed on the PS film, and a decane environment is then generated around the droplet. The results are given in Figure 2. Somewhat surprisingly, when SDS is added to the system the contact angle at the water-decane interface increases. Following the procedure by Stancik and Fuller,53 contact line (53) Stancik, E. J.; Fuller, G. G. Langmuir 2004, 20, 4805.
Figure 3. Bright-field microscopy images of different microstructures in the colloidal monolayers. (a) Colloidal crystal at a waterdecane interface. (b) Typical example of an aggregated monolayer on a subphase to which 0.5 M NaCl was added. (c) Coexistence of charged aggregates and crystalline ordering on a subphase already containing 0.25 M NaCl before spreading. The scale bar corresponds to 100 µm. hysteresis was checked by measuring the contact angle for the reverse system of an oil drop in water, and good agreement was found, as is shown in Figure 2. It should also be pointed put that no time dependence of the contact angle was observed over the course of several hours. The contact angle is determined by the Young equation: cos θ )
Γso - Γsw Γow
The addition of SDS will lower Γow, as is shown in Figure 1. SDS will also adsorb onto the polystyrene surface in the range of concentrations used,54 thereby lowering Γsw. Provided that SDS can (54) Shi-Yow Lin, Chengdi Dong, Tien-Jung Hsu, Ching-Tien HsuDdt Colloids Surf., A 2002, 196, 189.
4940 Langmuir, Vol. 22, No. 11, 2006
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Figure 4. Time evolution of an aggregating monolayer at a decane-(water + 0.25 M NaCl) interface. (a) Crystal obtained immediately after spreading and salt injection (t ) 0 h). (b) Onset of aggregation (t ≈ 330 h). (c) Aggregation (t ≈ 480 h). (d) Percolation (t ≈ 550 h). come into contact and adsorb onto the PS surface that will be exposed to the oil phase, Γso will also be lowered. In the contact angle experiments on planar substrates, this is the case. For this to occur on the particles at the oil-water interface, this implies that they should rotate. The observed increase in the contact angle implies that the particles trapped at the water-oil interface will be pushed further into the oil phase upon addition of SDS. Destabilization of a Stable Monolayer. When the polystyrene particles are injected at the oil-water interface, a stable colloidal crystal is formed within seconds after spreading the dispersions. When sufficient care is taken in rinsing the decane and with the appropriate composition of the spreading solvent, a structure free of aggregates can be obtained, as is shown in Figure 3a. Without the additon of electrolyte, the crystal structure remains stable for over 900 h (>1 month), which was the longest time scale accessed by our experiments. Following the strategy of Earnshaw and Robinson,19 aggregation was induced by adding a strong electrolyte solution directly to the subphase using a monovalent salt (NaCl) in concentrations ranging between 0.25 and 0.5 M. The monolayer remained stable for an unexpectedly long time, but eventually aggregation is observed to set in. An example of an aggregated structure is shown in Figure 3b. Interestingly, it was observed that when the particles were spread on a subphase with the salt being present before the injection of the spreading suspension a monolayer is obtained where crystalline ordered colloids and aggregates coexists (Figure 3c). The distance between the aggregates and the crystals suggests that the aggregates are charged. In all experiments presented here, the surface coverage was varied between 0.1 and 0.25. Effect of a Monovalent Salt. When salt is added to the subphase of a stable crystalline monolayer, aggregation is observed after a long induction period. Excerpts from typical micrographs obtained as shown in Figure 4 reveal the subsequent evolution as a function of time. Figure 4b shows how the aggregates start out more or less linear and become branched when they grow as in Figure 4c. Eventually, only a limited number of aggregates remain in the field of view, and eventually percolation occurs as in Figure 4d. A reference experiment was run at the same time on a system without salt to ensure that the aggregation was not caused by evaporation or
Figure 5. Logarithm of the total cluster size as a function of the logarithm of the radius of gyration of the aggregates. The slope of the regression fit is 1.58 ( 0.02 for log Rg > 1.4. contamination effects. This sample was subjected to the same environmental conditions and showed no distinct aggregation. The fractal dimension of the aggregates was characterized using the method of the radius of gyration.19 A power-law relationship exists between the number of particles in an aggregate N, the radius of gyration (Rg) of the aggregates, and the fractal dimension Df, which is given by N ) aRgDf
(7)
where a is a numerical prefactor. An example of the relation between the number of particles and the radius of gyration of the aggregates is shown in Figure 5 for the series of images shown in Figure 4. The size of the flocs is plotted logarithmically as a function of the logarithm of the radius of gyration. For every aggregate size, the mean radius of gyration and variance (∼5%) were calculated, and a linear
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Figure 6. π-A isotherms for monolayers of PS particles on a water-decane interface for different ages of the monolayer (i.e., after injection of electrolyte to a total concentration of 0.25 M NaCl). The inset shows the degree of dissociated groups R as a function of aging time. Table 1. Concentration of Salt in the Aqueous Phase C[M], Surface Coverage (Φ), Induction Time (tIND), Fractal Dimension (Df), and Static and Dynamic Exponents τ and ω, z for Experiments Where NaCl Is Added to the Subphase C[M]
φ
tIND (h)
0.50 0.50 0.25
0.25 0.13 0.25
45 125 280
Df
τ
ω
Figure 7. Cluster size distribution as a function of cluster size for different instants in time for particles at a decane-(water + 0.25 M NaCl) interface. The solid line tangent to the data set has a slope of -2. of the dipole-dipole repulsion force in eq 1, the surface pressure can be calculated as a function of surface coverage, and an analytical expression is obtained26 Π(x) )
z
1.58 ( 0.02 1.5 ( 0.1 1.6 ( 0.1 2.8 ( 0.2 1.58 ( 0.03 1.5 ( 0.1 1.8 ( 0.1 2.9 ( 0.1 1.58 ( 0.02 1.5 ( 0.1 4.3 ( 0.1 7.1 ( 0.3
regression analysis gives the fractal dimension as the slope The experimental value for the salt-destabilized monolayer equals 1.58 ( 0.02. This value was observed to be independent of the electrolyte concentration and surface coverage. The difference in surface concentration affects only the proportionality constant a in eq 7. The overall scaling relationship breaks down for aggregates containing fewer than 20 particles (corresponding to a log Rg value of 1.4). To verify the accuracy of the radius of gyration method, the results obtained were compared to the sandbox method for selected images.19 The two methods yielded identical results up to the second digit after the decimal. The induction time was long, and typical values corresponding to several days were found, as is shown in Table 1. However, it turned out to be difficult to obtain reproducible values of this induction time. It was very dependent on the details of the preparation of the monolayer. It could be noted, for example, that adding more IPA to the spreading dispersion decreases the induction time. It is possible that this is related to the fact that IPA improves the solubility of water in decane, resulting in increased polarity of the oil phase and a decreased screening length of the charges in the oil phase. To investigate the origin of the surprisingly long induction time (Table 1), the time evolution of the repulsive electrostatic interaction was studied by measuring the compression isotherms in a Langmuir through. To this end, a initially dilute particle monolayer is deposited onto a 0.25 M NaCl water-decane interface, and the π-A isotherms are recorded as a function of the time after the addition of salt to the subphase. For every isotherm, a pristine water-decane interface was prepared, and particles were spread using exactly the same conditions. It was verified by visual observation before each compression experiment that the monolayer was still stable. Figure 6 shows the isotherms at different instants after salt injection (i.e., 0, 2, 19, and 115 h after injection). The decrease of the maximum in surface pressure implies that as time proceeds the system becomes less repulsive yet the intrinsic shape of the isotherms remains the same. Equation 1 predicts the interaction force to be independent of electrolyte concentration, however, assuming that the fraction of dissociated groups in the oil phase remains constant. On the basis
q2oil 2x30R3x3/2
[
1-
]
1 + (1 + 4β/x)1/2 1 + ln 2 (1 + 4β/x)1/2
(8)
with x)
A Ah
β)
σ2 R2
qoil ) 2πR2σR(1 + cos σ) σ)
R(3 + cos θ) 2
The particles are treated as point charges of magnitude qoil placed a height ζ from the water surface, and x is the reduced Langmuir through area. The isotherms could be fitted quite accurately with the expression above, while leaving the degree of surface dissociation (R) as a fitting parameter with σ being the maximal surface charge density. R displays a monotonic decrease as a function of time as is shown in the inset of Figure 6. This suggests that the repulsion retains its dipole-dipole character but that an equivalent number of dissociated groups diminish as the system ages as a function of time. No straightforward time dependence is observed; rather, the behavior is subdiffusive. At a certain instant in time, however, attractive forces will take over, and compression of the monolayer on longer time scales will result in the formation of a significant number of aggregates, which invalidates the use of eq 8. Aggregation Kinetics in the Presence of Salt. After the induction period, aggregation was observed to set in in a regular and reproducible manner, and its kinetics could be analyzed. Figure 7 shows the number of clusters of a given size as a function of size at different instants in time during the aggregation process for a monolayer with a surface coverage of 0.25 and a salt concentration of 0.25 M NaCl in the subphase. The curves all display a monotonic decrease in the number density of clusters as a function of size, the distribution shifting to larger cluster sizes with time. A remarkable feature of the experimental data is that a common tangent could be drawn. Computer simulations reveal that this tangent should have a slope of -2,46 which agrees well with the experimental data. To test whether the kinetics fall into the DLCA regime, the cluster size distributions were rescaled by the weight-average size squared,
4942 Langmuir, Vol. 22, No. 11, 2006
Figure 8. Rescaled cluster size distribution as a function of rescaled cluster size for the data of Figure 7 and two additional experiments: a decane-(water + 0.5 M NaCl) interface with surface coverages of 0.13 and 0.25, respectively.
Figure 9. Number density of the clusters at a decane-(water + 0.25 M NaCl) interface as a function of the logarithm of time. Three distinct regions can be identified as discussed in the text. as is shown in Figure 8. In agreement with eq 5, all data could be collapsed onto a common functional form. Moreover, all results of experiments with different amounts of salt in the subphase and experiments for different surface coverage could be scaled in the same manner and are also included in Figure 8. In the regime where s/tz , 1, a unique value of the static exponent τ of 1.5 ( 0.1 could be found describing all three experiments, which agrees with the values reported for τ from simulations in the regime where the sticking probablility is close to 1.46 Because τ > 1, the scaling relations predict Ntot to be a decreasing power law function of time with ω as the exponent.20 Figure 9 reveals three regions in the behavior of Ntot as a function of time: during the initial stages of aggregation, most of the interactions occur between individual particles or between particles and other aggregates. The second regime corresponds to the situation where a large number of small aggregates are formed and subsequently cluster-cluster aggregation sets in. This is the region where the scaling laws should apply (zone 2). Eventually, the systems grow beyond the field of view or percolate (zone 3). In zone 2, dynamic exponent z could be determined from the evolution of the weight-average cluster size as a function of time, an example of which is given in Figure 10. The results for three sets of experiments corresponding to different surface coverages or salt concentrations are given in Table 1. The induction time is smaller and the aggregation process is faster when the subphase contains a higher concentration of NaCl and when the surface coverage is higher. For a given salt concentration, a unique set of parameters was found independently of the surface coverage. The packing fraction seems only to affect
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Figure 10. Evolution of the size-averaged cluster size as a function of the logarithm of time for three experiments with different combinations of electrolyte concentration and surface coverage. the onset time of the dynamic scaling regime, although this was not investigated in detail. The overall kinetics are hence consistent with a “fast”, DLCAlike aggregation regime. Microscopic observations of collisions revealed that the particles indeed stick on contact and do not reorganize thereafter. However, some additional comments are in order. First, the fractal dimensions included in Table 1 reveal a dense structure, the fractal dimension corresponding more to what is expected for an RLCA type of aggregation. Also, dynamic exponents ω and z in Table 1 depend on the salt concentration, whereas the surface coverage has essentially no effect. The latter agrees with the assumption that the surface diffusivity of the clusters is size-independent and agrees with the observations of Robinson and Earnshaw at the air-water interface.20 The dynamic exponent for the lower salt concentration is higher (i.e., 7.1 compared to 2.8). This dependence suggests that although the system is in a fast aggregation regime there might be a weak dependence of the sticking probability on the salt concentration.20 The control of the electrostatic and capillary interactions by the addition of salt will be discussed below. Effects of Surfactant and Salt. The main contribution of the effect of the addition of salt is to slowly weaken electrostatic interactions. In contrast, the addition of small amounts of surfactant can be expected to modify most dominantly the capillary interactions more strongly because the addition of surfactant changes both the interfacial tension (Figure 1) and, more importantly, the wetting properties of the particles (Figure 2), pushing the particles more into the oil phase as the amount of surfactant is increased. A modified Petri dish was used so that the surfactant could be gently added to the subphase without having to pass through the interface and homogeneously diffuse into the subphase, avoiding surface pressure gradients. The addition of even tiny amounts of SDS is observed to have pronounced effects on both the structure and the time scales of aggregation. The structure becomes more open, as can be seen from a snapshot of a typical aggregate in Figure 11. From the evolution of the number of particles as a function of the radius of gyration in Figure 12, a fractal dimension of 1.47 ( 0.03 is obtained, independent of SDS concentration in the range studied. At SDS concentrations lower than 0.1 mM, the spreading of the SDS on the interface no longer occurred in a homogeneous way. Aggregation occurred at distinct places at the interface while others remained stable. At SDS concentrations above 0.1 mM, the structure was always open with a fractal dimension equal to 1.46 (Table 2), and no continuous variation of fractal dimensions was observed. The induction times are also greatly reduced upon the addition of surfactant. For example, for an experiment containing only 0.25 M NaCl in the aqueous phase the induction time is on average 280 h. However, adding as little as 0.1 mM SDS reduces this induction
Colloidal Aggregation at the Oil-Water Interface
Langmuir, Vol. 22, No. 11, 2006 4943 except for the experiment at the highest surfactant concentration, the experiments are all consistent with simulations in the regime where the sticking probability is close to 1 as τ > 1. No clear trends could be observed in the values of the dynamic exponents, suggesting that the combined effect of salt and surfactant on the overall interaction potential is nontrivial. The values obtained for the dynamic exponents are, however, in the range of those for simulations of aggregating systems in 2D.44 Remarkably, the addition of SDS alone does not lead to pronounced particle aggregation over prolonged periods of time. The particle layer undergoes a transition from a highly ordered crystalline phase to a melted phase, but no aggregation occurs. This indicates that not only a change in wetting conditions is required to speed up the aggregation kinetics but also an interplay of changes in electrostatics and wetting determines the structure and the kinetics of the aggregation.
Discussion Figure 11. Micrograph of an aggregate obtained at a decane(water + 0.5 mM SDS + 0.5 M NaCl) interface. The scale bar corresponds to 100 µm.
Figure 12. Logarithm of the total cluster size at a decane-(water + 0.1 mM SDS + 0.25 M NaCl) interface as a function of the logarithm of the radius of gyration of the aggregates. The slope of the regression fit is 1.47 ( 0.03 for log Rg > 1.3. Table 2. Concentration of SDS and Salt in the Aqueous Phase C[M], Surface Coverage (Φ), Induction Time (tIND), Fractal Dimension (Df), and Static and Dynamic Exponents τ and ω, z for Experiments Where Both SDS and NaCl Are Added to the Subphase CSDS[mM] + CNaCl[M]
φ
tIND (min)
Df
τ
ω
z
0.5 + 0 0.5 + 0.1 0.5 + 0.3 0.5 + 0.5 0.1 + 0.25 0.9 + 0.3
0.04 0.1 0.05 0.11 0.08 0.08
>6000 330 275 40 1000 290
1.44 ( 0.04 1.45 ( 0.03 1.46 ( 0.03 1.47 ( 0.03 1.46 ( 0.04
1.1 ( 0.1 1.2 ( 0.1 1.7 ( 0.1 1.49 ( 0.05 0.9 ( 0.1
2.8 ( 0.3 2.1 ( 0.1 0.5 ( 0.1 3.7 ( 0.4 2.7 ( 0.2
3.4 ( 0.4 3.0 ( 0.1 1.3 ( 0.1 4.9 ( 0.5 2.8 ( 0.5
period to a mere 17 h. Increasing the SDS and salt concentrations reduces these induction time even further as is shown in Table 2. After the induction time, aggregation is again observed to set in in a consistent and reproducible manner. The evolution of the cluster size distribution is reminiscent of what was observed for the systems containing only NaCl in the subphase. A monotonically decreasing number of clusters as a function of cluster size is obtained at all times (data not shown here), and the data could again be scaled by the same scaling relations. The scaling exponents obtained by analyzing the data in the same manner as indicated above are summarized in Table 2. The static exponent τ determines the growth of the number of clusters and varies between 0.9 and 1.7. Hence,
The aggregation of initially crystalline monolayers can be controlled by the addition of electrolyte and surfactant because both the electrostatic and capillary interactions are altered. Compared to 3D suspensions, some remarkable differences arise that are related to the specific nature of these interface-specific interactions. First, the colloidal crystals remain stable for a surprisingly long period after the addition of a strong electrolyte to the aqueous phase, which is due to an unexpectedly slow evolution of the electrostatic interaction. Second, although the kinetics in the present experiments are consistent with a fast aggregation mechanism in all cases studied here, the density of the structure as characterized by the fractal dimension varies strongly. This can be rationalized by the anisotropy of the capillary interaction and its dependence on wetting conditions as will be discussed below. Pressure-area isotherms at different instants in time after addition of the electrolyte demonstrate that the repulsion retains its dipole-dipole character. They were analyzed by assuming that an equivalent number of dissociated surface groups decrease as a function of time. A monotonic decay of this equivalent fraction was observed, as shown in the inset of Figure 6. The decrease in electrostatic interactions could have different origins. The diffusion of water along the solid-oil interface has been observed in studies on the washing of oil from solid plates by Krachlevsky et al.55 For hydrophilic silica, this is accompanied by a gradual decrease in the contact angle. When the particles are pushed further down into the water phase, again the electrostatic interaction will decrease as was nicely demonstrated by Horozov et al.56-58 However, the experiments by Krachlevsky et al.55 were performed on hydrophilic glass plates, and the formation of a swollen silica “gel” layer was invoked to rationalize the unexpected diffusion. Such a layer will not be formed for the hydrophobic PS surfaces. Moreover, we did not observe any evolution of the contact angle in our contact angle experiments over time periods where R evolves most strongly. Alternatively, the surface diffusion of water molecules is also responsible for the gradual removal of water patches from the oil-particle interface and has an effect on the contact angle. Finally, impurities in the SDS or hydrolysis of the SDS59 could be responsible for the slow evolution of R. (55) Kralchevsky, P. A.; Danov, K. D.; Kolev, V. L.; Gurkov, T. D.; Temelska, M. I.; Brenn, G. Ind. Eng. Chem. Res. 2005, 44, 1309. (56) Horozov, T. S.; Aveyard, R.; Clint, J. H.; Binks, B. P. Langmuir 2003, 19, 2822. (57) Horozov, T. S.; Aveyard, R; Clint, J. H.; Neumann, B. Langmuir 2005, 21, 7407. (58) Horozov, T. S.; Binks, B. P. Colloids Surf., A 2005, 267, 64. (59) Hunter, R. J. Foundations of Colloid Science, 2nd ed.; Oxford University Press: New York, 2001.
4944 Langmuir, Vol. 22, No. 11, 2006
When the electrostatic interaction has been sufficiently weakened, aggregation is observed to set in. The overall kinetics are in agreement with a predominantly fast aggregation mechanism because a monotonic decrease in the cluster size distribution as a function of cluster size is observed at all times and the scaling relations for the moment of the distributions tend to the DLCA regime as was shown in Figures 7-9 and using the scaling analysis for the static and dynamic exponents (Table 1). The dynamic scaling exponents are also on the same order of magnitude as compared to earlier computer simulations44,60 for sticking probalities close to 1. However, the observed structural features seem to be in apparent contradiction because the fractal dimension is much higher than what is expected for the DLCA regime; rather, it is closer to what is expected for the RLCA regime. Earlier aggregation studies by Robinson and Earnshaw19-21 on 1 µm sulfonated polystyrene latex beads at a water-air interface always yielded consistent results between the kinetics and the obtained structures. At low electrolyte concentrations, Earnshaw and Robinson obtained RLCA structures and bell-shaped cluster size distribution curves. At higher concentrations, the DLCA regime was obtained. In agreement with the present observations, an induction time of several hours was obtained, despite the fact that their particles are less charged (4 ( 0.4 µC/m2) compared to the particles used in the present work. However, this lower surface charge has as the disadvantage that Earnshaw and Robinson could never obtain an initial structure free of aggregates, the latter being created during particle spreading. The presence of these initial clusters will affect the subsequent measurements and evolution of the cluster size distribution, yet how this affects the scaling analysis is not completely clear. Therefore, in the present experiments particles with higher surface charges were selected to make sure that particles start out as individual particles. Yet, an even more important difference between the experiments at the air-water and oil-water interfaces concerns the contact angle of the particles and its sensitivity to the addition of electrolyte and surfactant. For the air-water interface, particles are wetted nearly neutrally, with the contact angle being close to 90° (see Figure 2) and the effects of surfactant and salt being small. However, for the oil-water interface, the contact angle is closer to 130°, implying that the particles intersect the interface below their midplane, the height of the particle above the interface equalling about 2/3 of the diameter. For individual particles, this does not play a major role. However, for the complex-shaped aggregates, the effect of the contact angle is more important. For particles with a contact angle of 130°, the contact line at the edge of a particle cluster will undulate in a complex manner, and anisotropic capillary interactions will arise.18,42 The calculations by Stamou and Duschl show that the effects of such contact line undulations are very pronounced. The interaction energy becomes greater than the thermal energy kT for undulation amplitudes of only a few angstroms.61 The relative strength of the capillary interactions is the main determinant of the observed fast aggregation regime. The capillary interaction will depend on the local curvature around an aggregate. A particle will be attracted most to point where the gradient of curvature is largest and will be repelled from regions where the curvature of the interface is not compatible with the deformation caused by the approaching particle.18 When particles in an aggregate are touching, their contact point will not necessarily coincide with the interface. Rather, this will depend on the wetting conditions. When the range of the deformation (60) Meakin, P.; Vicsek, T.; Family, F. Phys. ReV. B 1985, 31, 564. (61) Lucassen, J. Colloids Surf. 1992, 65, 131.
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of the meniscus, which is controlled by the capillary length, and the distance between the particles at the interface are of the same order of magnitude, pronounced anisotropy in the capillary interaction can be expected. For example, Figure 6 in the paper by Stamou and Duschl18 clearly shows that the curvature of the meniscus of two interacting particles has two local minima occurring on either side of the doublet. The minimum closest to a particle corresponds to an attractive local minimum, and the probability for a third particle to approach the doublet is higher at this point. This argument can easily be extended to morecomplex-shaped aggregates (e.g., ref 42), and particles will have the highest probability of attaching to a side of an aggregate where contact line undulations are most pronounced. Hence, the anisotropy in the probability will lead to a densification of the aggregates. Consequently, the anisotropy of the capillary interaction rationalizes the fact that despite the DLCA type of kinetics a fairly dense structure is observed for systems containing only electrolyte in the subphase. However, because the details of the capillary interaction depend on the contact angle and the magnitude of the surface tension this will be changed when wetting conditions are altered. For a doublet, the position of the minimum in curvature has been shown to depend on the particle contact angle and shifts progressively outward when the contact angle differs more strongly from neutral wetting.18 The effect of SDS addition to the system containing PS particles on the overall capillary interaction and the anisotropic nature hereof is twofold. First, because of the change in contact angle the distance between the particles at the fluid-fluid interface increases; in our case, it goes from a130 ) 1.1 µm for a contact angle of 130° (Figure 2) to a distance of a168 ) 2.45 µm for a contact angle of 168° (Figure 2). Second, adding SDS changes the interfacial tension from 50 to 8 mN/m in the case of 1 mM SDS and 0.25 M NaCl (Figure 1). This changes the dimensionless capillary length from qa ) 0.0025 to 0.0012. The effects of changes in wetting conditions and surface tension on the resulting lateral capillary interaction will hence render the interaction less anisotropic and weaker. The effect of the initial contact angle on the electrostatic interactions is less pronounced. The calculations by Horozov et al.57 show that the electrostatic interaction energy will be altered only slightly when the contact angle is changed from 130 to 160°. Lowering the contact angle will decrease the electrostatic interaction more strongly. There might also be an effect on the electrodipping force. The combined effect and especially the more isotropic nature of the capillary forces rationalize the fact that the structure obtained after aggregation for systems containing the surfactant in the aqueous phase leads to a more open structure with a fractal dimension consistent with a DLCA system. For the systems at the airwater interface studied by Earnshaw and Robinson, the contact angle is close to 90°, and in this case, more isotropic interactions are expected, in agreement with the observations of Earnshaw and Robinson.19-21 The SDS concentration also has an effect on the stability of the monolayersthe kinetics speed up, and the induction time is reduced (Table 2). Hence, not only the wetting properties of the particles change but also the electrostatics are clearly modified. Possibly this is due to adsorption of the SDS on the particle surface, possible changes in the contact angle,56 or contaminations due to the SDS. For example, dodecyl alcohol is formed by the hydrolysis of SDS,59 which might dissolve in the oil phase and reduce the electrostatic screening lengths. Despite the difficulties in knowing the mechanism from our indirect measurements, it can be concluded from the decrease in induction time that the electrostatic interaction becomes effectively more screened. Direct
Colloidal Aggregation at the Oil-Water Interface
measurements of interaction forces using optical tweezers will be presented elsewhere. The experimental results in this work demonstrate that it is possible to control the aggregate structure of 2D suspensions at an oil-water interface using combinations of electrolyte and surfactant. The control of the structure at a planar interface could provide a road map to design emulsions with controlled stability. However, results in Figure 3c and the nontrivial effects of combinations of salt and SDS indicate that generating droplet interfaces with controlled structures is nontrivial and the optimal formulation strategy for Pickering emulsions containing salt and surfactant could be very subtle.
Conclusions Control over the aggregate structure of a particle monolayer was achieved by destabilizing an initially crystalline monolayer of colloidal particles. Dense and open structures with similar kinetics scaling behavior could be obtained by altering the composition of the aqueous subphase. The addition of a monovalent salt induces a slow aggregation of latex particles
Langmuir, Vol. 22, No. 11, 2006 4945
and yields a rather dense structure. The aggregation is induced because of a very slow reduction of the electrostatic repulsion and the occurrence of lateral capillary interactions that are dependent on the shape of the aggregates and the wetting properties of the particles. However, adding tiny amounts of an ionic surfactant to the electrolyte results in a more open final structure and faster aggregation kinetics. The obtained results allow one to generate interfaces with tailored structures that should differ in mechanical or rheological interfacial properties. Acknowledgment. We thank Professors Jan Fransaer (K.U. Leuven) and Eric Furst (University of Delaware) for stimulating discussions. We acknowledge financial support from the Bijzonder Onderzoeksfonds K.U.Leuven (GOA 2003/06) and a research program of the Research Foundation - Flanders (FWO - Vlaanderen, project G.00469.05). This work was performed in the framework of a network of excellence SOFTCOMP (EU-6th framework). LA060052N
