Langmuir 1998, 14, 6501-6504
6501
Eliminating Surface Pressure Gradient Effects in Contact Angle Determination of Nano- and Microparticles Using a Film Balance Marianna Ma´te´,† Janos H. Fendler,‡ Jeremy J. Ramsden,§ Jo´zsef Szalma,| and Zolta´n Ho´rvo¨lgyi*,† Department of Physical Chemistry, Technical University of Budapest, H-1521 Budapest, Hungary, CAMP, Clarkson University, Potsdam, New York 13699-5814, Biozentrum, University of Basel, CH-4056 Basel, Switzerland, and Department of Physical Chemistry, Lora´ nd Eo¨ tvo¨ s University, H-1117 Budapest, Pa´ zma´ ny Pe´ ter Se´ ta´ ny 2, Hungary Received December 8, 1997. In Final Form: June 26, 1998 The surface pressure vs surface area isotherms of monoparticulate layers determined using Langmuir and Wilhelmy film balances depend nontrivially on the amount of spread particles. It is inferred that a surface pressure gradient across the spread particle layers is responsible. An extrapolation procedure for determining correct values of the contact angles is described.
Introduction
cos θ ) ([{(2(3)1/2 πc)/(πγLV)}1/2 - 1]
Monoparticulate layers at water-air interfaces, like the monomolecular films of insoluble surfactants, can be formed by spreading the particles onto the water surface from volatile organic dispersions (e.g., refs 1 and 2). Surface pressure (π) vs surface area (A) isotherms can be determined for monoparticulate layers by means of Langmuir or Wilhelmy film balances.1-2 Upon compressing the layers, collapse takes place at a certain pressure πc, at which the particles are forced out of the water-air interface. Beyond this point, it may be presumed that the work done on the system is entirely channeled into the removal of particles from the interface.1 The removal energy (Er) for one particle can be written as the product
Er ) πcAc
(1)
where Ac is the area per particle at collapse. (For the calculation of Ac, one has to know the particle size and density.) On the basis of the supposed equality of Er to the adhesion work,1,3 the collapse pressure can be related to the water-air contact angles (θ) for monodisperse and spherical particles according to
πcAc ) γLV r2 π[1 ( cos θ]2
(2)
where γLV is the water-air surface tension and r is the particle radius. If a particle is removed from the interface into the upper phase, then the cosine in the brackets is taken positive and θ signifies receding contact angle; if it moves into the lower phase, it is taken negative (advancing contact angle). For the closest packed (hexagonal) arrangement of monodisperse and spherical particles at collapse, the contact angle can be calculated using a simpler expression:1 †
Technical University of Budapest. Clarkson University. § University of Basel. | Lora ´ nd Eo¨tvo¨s University. ‡
(1) Clint, J. H.; Taylor, S. E. Colloids Surf. 1992, 65, 61. (2) Ho´rvo¨lgyi, Z.; Ne´meth, S.; Fendler, J. H. Colloids Surf. A: Physicochem. Eng. Asp. 1993, 71, 327. (3) Ho´rvo¨lgyi, Z.; Ne´meth, S.; Fendler, J. H. Langmuir 1996, 12, 2 (4), 997.
(3)
The choice of sign before the brackets is made as for eq 2. In this case, the contact angle can be determined without knowing the particle size and density. The physical background of this contact angle determination method is discussed in detail in ref 1. Contact angles calculated from eqs 2 and 3 accurately reflect the intrinsic water contact angle only when no complicating circumstances, such as a surface pressure gradient across the spread particle layer, occur. Recently, contact angles for hydrophobic particles (forced out of the interface into the air) have been determined by eq 2 or 3 from Langmuir3 and Wilhelmy4 film balance experiments. In every case, a higher than expected receding value was obtained. These findings and other observations led us to propose the existence of a surface pressure gradient along the cohesive layer, which can make contact angle determinations using eq 2 or 3 problematical. Such a surface pressure gradient was previously demonstrated for insoluble macromolecular films by simultaneously measuring the surface pressures at two different places in the layer.5-7 Particle wettability has a crucial role in several industrial processes (e.g., froth flotation8) and in producing various colloidal systems (foams,9 Pickering emulsions10) of practical significance. Hence, knowledge of particle hydrophobicity is indispensable for planning effective technologies and for the advantageous exploitation of colloidal materials. Furthermore, partially wettable nanoparticles can form particulate films at aqueous solution-air interfaces, which can be transferred onto solid supports by the Langmuir-Blodgett technique, (4) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; Rutherford, C. E.; Colloids Surf. A: Physicochem. Eng. Asp. 1994, 83, 89. (5) Peng, J. B.; Barnes, G. T. Langmuir 1990, 6, 578. (6) Peng, J. B.; Barnes, G. T. Langmuir 1991, 7, 1749. (7) Peng, J. B.; Barnes, G. T.; Abraham, B. M. Langmuir 1993, 9, 3574. (8) Fuerstenau, D. W.; Herrera-Urbina, R. In Mineral Separation by Froth Flotation: Surfactant-Based Separation Processes; Scamehorn, J. F., Harwell, J. F., Eds.; Surfactant Science Series, Vol. 33; Marcel Dekker: New York and Basel, 1989; p 259. (9) Aveyard, R.; Cooper, P.; Fletcher, P. D. I.; Rutherford, C. E. Langmuir 1993, 9, 604. (10) Menon, V. B.; Nikolov, A. D.; Wasan, D. T. J. J. Colloid Interface Sci. 1988, 124 (1), 317.
10.1021/la971344e CCC: $15.00 © 1998 American Chemical Society Published on Web 10/02/1998
6502 Langmuir, Vol. 14, No. 22, 1998
Ma´ te´ et al.
Table 1. Characteristic Parameters (Particle Sizes and Contact Angles) of the Model Particles Used particle glass spheres silica spheres Cab-O-Sil M5b
particle size (diameter)
contact anglea with water, deg
75 ( 5 µm 3 ( 1 µm 10 ( 1 µm 10 nma 10 nma
≈90 ≈90 ≈90 ≈90 ≈45
a See “Methods and Instruments” for a description of the method of estimation. b Primary particles.
providing an entry to advanced materials.11 In this procedure, the presence of a surface pressure gradient along the Langmuir film can lead to nonhomogeneous (defective) layer formation on the solids. The investigation of such surface pressure gradients can result in improved layer formation on solid supports. In this work, we determine the collapse pressures and collapse areas of nano- and microparticulate layers for different amounts of spread hydrophobic particles in order to investigate possible effects of surface pressure gradients. We discuss the consequences of a pressure gradient and present an extrapolation method for the correct determination of contact angles from the π-A isotherms that eliminates the surface pressure gradient effect in the calculations. Calculated contact angles of microparticles were compared with the values obtained experimentally by a microscopic method. Experimental Section Materials. Spherical glass microparticles (diameter: 75 ( 5 µm, Supelco), spherical silica microparticles (diameters: 3 ( 1 and 10 ( 1 µm, Spherisorb), silica nanoparticles (Cab-O-Sil M5, Fluka; the diameter of the primary particles is about 10 nm according to SAXS measurements, but they form small aggregates whose size depends on the polarities of the dispersion phase and of the particle surface), hexane (ACS, Fisher; a mixture of hexane isomers), and trimethylsilyl-N,N-dimethylcarbamate (purum, ∼97% (GC), Fluka) were used as received. Water was purified using a Millipore Milli Q filtration system provided with a 0.22 µm Millistack filter at the outlet. Methods and Instruments. The surfaces of the solid particles were rendered hydrophobic by silylation.3 Any excess silylating agent was always removed from the samples by continuous distillation (for the nanoparticles) or by a simple drying procedure (for the microparticles).3 The wettability of the larger (75 µm diameter) microparticles was characterized by equilibrium (Young12) water contact angles, which were measured on the beads by a microscopic method.3 The wettability of the smaller micro- and nanoparticles was assessed on the basis of experiments in which the same silylating conditions were applied to macroscopic glass surfaces. For comparison, the silica nanoparticles were also silylated to a lower hydrophobicity. The particle properties used in the experiments are summarized in Table 1. The water contact angles of the hydrophobic particles investigated were found to be around 90°. For the weakly hydrophobic silica nanoparticles the water contact angle was assessed to be around 45°. Surface pressure vs surface area isotherms were determined using a Langmuir film balance (Lauda Model P) for the nanoparticles and a laboratory-built Wilhelmy film balance for the microparticles. Note that the distance between the moving barrier and the surface pressure meter is significant in the film balances used in the experiments. The layers were compressed at a rate of 22 cm2 min-1.
Results and Discussion Surface Pressure Gradient along the Particulate Layer. Visual Observations. Creasing of the particu(11) Fendler, J. H.; Meldrum, F. C. Adv. Mater. 1995, 7, 607.
Figure 1. (a) Surface pressure π vs surface area A isotherms obtained from different amounts (800, 1000, and 1200 mg from left to right) of spread hydrophobic glass beads (diameter: 75 µm). The extrapolation procedure for the determination of πc and Ac is also shown. (b) Surface pressure vs surface area isotherms obtained from different amounts (31.5, 42.5, 63.7, 74.4, 85.0, and 106.2 mg from left to right) of spread hydrophobic silica spheres (diameter: 10 µm).
late layers (an indication of the collapsed state) always begins at the moving barrier for hydrophobic particles. This means that the real value of the collapse pressure can only be measured in the vicinity of the moving barrier for such particles. The effect was not observed for layers composed of weakly hydrophobic particles, in which creasing takes place simultaneously at several points in the layer. Mass Dependence of Collapse Pressure. Surface pressure vs surface area isotherms obtained for hydrophobic silica particles (3 and 10 µm diameter, and CabO-Sil nanoparticles) and glass microparticles (75 µm diameter) are depicted in Figures 1-3. The extrapolation procedure for the precise determination of πc and Ac is shown in Figure 1a. The collapse pressures show a significant decrease with increasing amounts of spread particles. As the amount of spread particles decreases, the zone of collapse (in the vicinity of the moving barrier) moves closer to the surface pressure meter (platinum plate), and hence the measured collapse pressures become more realistic. It should be noted that the weakly hydrophobic silica nanoparticles also reveal a dependence of collapse pressure on the amount of spread particles (Figure 2b). Thermodynamic Nonsense During Expansion. Complete compression-expansion cycles, obtained on a (12) Wolfram, E.; Faust, R. In Wetting, Spreading and Adhesion; Padday, J. F., Ed.; Academic Press: London, 1978; p 213.
Nano- and Microparticle Contact Angle Determination
Langmuir, Vol. 14, No. 22, 1998 6503 Table 2. Collapse Pressure (πc), Collapse Area for All Particles (Ac-total), Collapse Area for a Single Particle (Ac), Energy (Er) Necessary for Removing a Particle from the Water-Air Interface, and Receding Contact Angle (θR) at Different Amounts of Spread Particles for Hydrophobic Silica Spheres of Diameter 3 µm amt of spread πc, Ac-total, Ac, θR, particles/mg mN m-1 cm2 µm2/particle Er, pJ degree 9.4 12.5 18.7 25.0 31.2 37.5
46.1 38.5 32.8 26.1 34.4 13.2
44.8 73.4 92.5 130.1 130.7 202.3
11.6 14.2 12 12.6 10.1 13.1
53 55 39 33 35 17
88.6 87.8 92.5 101.3 99.9 114.6
Table 3. Collapse Pressure (πc), Collapse Area for All Particles (Ac-total), Collapse Area for a Single Particle (Ac), Energy (Er) Necessary for Removing a Particle from the Water-Air Interface, and Receding Contact Angle (θR) at Different Amounts of Spread Particles for Hydrophobic Silica Spheres of Diameter 10 µm
Figure 2. (a) Surface pressure vs surface area isotherms obtained from different amounts (0.5, 0.8, 1.1, 1.6, and 2.1 mg from left to right) of spread hydrophobic silica (Cab-O-Sil) nanoparticles. (b) Surface pressure vs surface area isotherms obtained from different amounts (3.2, 5.6, and 8.1 mg from left to right) of spread weakly hydrophobic silica (Cab-O-Sil) nanoparticles.
Figure 3. Compression-expansion cycles obtained for hydrophobic silica spheres (3 µm) at two different spread amounts: solid line, 18.3 mg; dashed line, 25.0 mg.
Wilhelmy film balance for the 3 µm hydrophobic silica spheres, are shown in Figure 3. The areas enclosed by the hysteresis loops are negative! The surface pressure remains essentially constant at the beginning of the expansion. Its value begins to decrease only when the particulate layer becomes entirely smooth (as observed visually) in the vicinity of the moving barrier. A similar effect was previously found for cohesive particle layers using a Langmuir film balance.2
amt of spread particles, mg
π c, mN m-1
Ac-total, cm2
Ac, µm2/particle
Er, pJ
θR, deg
31.9 42.5 63.7 74.3 85.0 106.2
40.5 29.4 30.7 26.4 20.8 15.4
42.5 76.4 92.5 115.2 151.0 177.8
119.3 160.8 130.0 138.6 158.9 148.0
4.8 4.7 4.0 3.6 3.1 2.7
94.3 94.9 96.3 101.3 103.6 111.2
The above findings can be plausibly interpreted in terms of a significant surface pressure gradient along the cohesive layer, as previously found in insoluble macromolecular films.5-7 These effects should not be considered as the consequence of film balance type (Langmuir or Wilhelmy); they were observed whenever we studied hydrophobic particle layers. Both our earlier3 and present investigations showed that the surface pressure is rather stable in time for hydrophobic particles. Upon halting the moving barrier, it remains practically constant for several hours. To obtain direct evidence for the surface pressure gradient, we simultaneously measured the surface pressure at two different points in the layer by using hydrophobic silica nanoparticles (Cab-O-Sil M5). One of the Wilhelmy plates (A) was positioned close to the moving barrier while the other (B) was placed some distance away. The distance between A and B was 8 cm. When the layer was compressed to the collapse state (i.e., noticeable creasing in the vicinity of the moving barrier) and the moving barrier was halted, the surface pressure was found to be 3.7 mN m-1 higher at the moving barrier than at the other point during the first few seconds after halting, confirming the supposition of a surface pressure gradient. A subsequent slow increase of the pressure difference (up to 15 mN/m) was observed during the first hour, indicating a significantly higher value of the real collapse surface pressure. Consequences of the Surface Pressure Gradient. A Method for Calculating Correct Values of the Receding Contact Angles from Surface Pressure vs Surface Area Isotherms. We determined the collapse pressure (πc) and the collapse area (Ac) for all the systems investigated and calculated the energy (Er) necessary for particle removal from the water-air interface and hence the receding contact angles using eqs 1 and 2 (Tables 2 and 3). The dependence of the receding contact angle on the layer area at collapse, which is proportional to the number of particles spread, is given in Figure 4 for the silica microparticles. As can be seen, the receding contact angle decreases almost linearly with the decreasing
6504 Langmuir, Vol. 14, No. 22, 1998
Figure 4. Dependence of receding contact angles (θR) on the collapse area for silica particles with diameters 3 and 10 µm. The determination of the intrinsic contact angle by the extrapolation of the contact angle data obtained from the different amounts of spread particles is also depicted.
amount of particles and a characteristic (”intrinsic”) contact angle can be determined by extrapolating to the compressed area equal to the pressure sensor position along the length of the trough multiplied by the width of the trough. If the moving barrier and the sensor were at the same place, the sensor would measure the real surface pressure; this ideal situation can be reached by the extrapolation procedure. The extrapolated values, 80° and 88°, are reasonable for these surfaces (which are characterized by a Young (equilibrium) contact angle of 90°). Therefore, by measuring the relevant parameters (πc and Ac) for different amounts of spread particles and
Ma´ te´ et al.
extrapolating the calculated receding contact angles to a characteristic area (equal to zero for the Langmuir film balance), we have a convenient method for the correct determination of contact angles of hydrophobic particles. The surface pressure gradient is also important for the larger beads (75 µm diameter, Figure 1a). In this case, the cohesion of the layer, despite the smaller number of particle-particle contacts per unit area of trough surface, is also responsible for an inhomogeneous surface pressure distribution. Origin of Surface Pressure Gradient. The main reason for the surface pressure gradient is the cohesiveness of the particulate layer. The hydrophobic particles can strongly attract each other due to the hydrophobic and van der Waals (dispersion) forces.2,3 The applied surface pressure (by the moving barrier) cannot propagate immediately along the layer because the rupture of particleparticle contacts is hindered by the cohesive interactions between the particles. We can deduce a slight surface pressure gradient even for the weakly hydrophobic particles, suggesting that elevated surface viscosity may also contribute to this phenomenon. Acknowledgment. This work was supported by the Hungarian Cultural Ministry (Z.H.), the Hungarian National Scientific Foundation for Research (OTKA T023080), and the U.S. National Science Foundation (J.H.F.). We thank the Swiss Federal Ministry for Foreign Affairs (through the program of scientific cooperation with central and eastern European countries managed by the Swiss National Science Foundation) for providing further financial support. We also thank Dr. Attila Bo´ta for the SAXS measurements. LA971344E
