Langmuir 1996, 12, 997-1004
997
Monoparticulate Layers of Silanized Glass Spheres at the Water-Air Interface: Particle-Particle and Particle-Subphase Interactions Zolta´n Ho´rvo¨lgyi,1 Sa´ndor Ne´meth,2 and Janos H. Fendler*,2 Department of Physical Chemistry, Technical University of Budapest, H-1111 Budapest, Egry Jo´ zsef utca 20-22, Hungary, and Department of Chemistry, Syracuse University, Syracuse, New York 13244-4100 Received August 22, 1994. In Final Form: October 31, 1995X Silanization has rendered spherical (75 ( 5 µm diameter) glass particles to be weakly (sample A, Θ ) 55°), moderately (sample B, Θ ) 72°), and highly (sample C, Θ ) 90°) hydrophobic. Nonequilibrium surface pressure (Π) vs surface area (A) isotherms have been determined for monoparticulate layers which were prepared from samples A, B, and C at water-air interfaces in a Langmuir film balance. The effect of hydrophobicity on the particle-particle interaction and on the energy (Er) which is necessary for the removal of a particle from the water-air interface (particle-subphase interaction) has been elucidated. Contact cross-sectional areas (CCSA), surface coverages (SC), and collapse energies (Ec), evaluated from Π vs A isotherms, provided semiquantitative information on the structural strength. Monoparticulate layers which were formed from the most hydrophobic glass spheres (sample C) had a structural strength which was almost 5 times greater than that of those which were formed from the least hydrophobic sample (sample A), as revealed by the Ec values which were elucidated for these systems. Long-term stability, determined by time-dependent surface-pressure measurements, was only found for sample C. The energy of a particle-particle contact was calculated, for the strongly cohesive layer of sample C, to be (1.2-1.4) × 10-10 J. The weakly cohesive layer, prepared from sample A, had a 490-nm interparticle distance at the secondary energy minimum and a total repulsive interaction energy in the range of (0.5-1.3) × 10-13 J between two beads at an interparticle distance of 1-200 nm. Values for adhesion work (Wr) were calculated from in situ contact-angle measurements and compared to corresponding Er values which were obtained experimentally by the isotherms. The significant discrepancies between the Wr and Er values which were found for sample A or sample B were rationalized in terms of contact-angle hysteresis, dynamic wetting, and distortion of the electric double layer around the interfacial beads.
Introduction Colloidal particles at liquid-fluid interfaces have significant roles in several important technologies, including oil recovery,3-5 flotation,6,7 (anti)foaming,8-13 and waste-water treatments.14 They have also been used as models for two-dimensional growth,15-25 phase transition,26 and interfacial thermodynamics.3-5,27-30 SignifiX Abstract published in Advance ACS Abstracts, February 1, 1996.
(1) Technical University of Budapest. (2) Syracuse University. (3) Menon, V. B.; Nagarajan, R.; Wasan, D. T. Sep. Sci. Technol. 1987, 22 (12), 2295. (4) Menon, V. B.; Wasan, D. T. Colloids Surfaces 1988, 29, 7. (5) Menon, V. B.; Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1988, 124 (1), 317. (6) Wills, B. A. In Mineral Processing Technology; Hopkins, D. W., Ed.; Int. Ser. Materials Science and Technology, Vol. 41; Pergamon Press: Oxford, 1988; p 457. (7) Fuerstenau, D. W.; Herrera-Urbina, R. In Mineral Separation by Froth Flotation: Surfactant-Based Separation Processes; Scamehorn, J. F., Harwell, J. F., Eds.; Surfactant Sci. Ser., Vol. 33; Marcel Dekker: New York and Basel, 1989; p 259. (8) Garrett, P. R. In Defoaming: Theory and Industrial Applications; Garrett, P. R., Ed.; Surfactant Sci. Ser., Vol. 45; Marcel Dekker: New York, 1993; pp 1-117. (9) Dippenaar, A. Int. J. Miner. Process. 1982, 9, 1. (10) Aveyard, R.; Cooper, P.; Fletcher, P. D. I.; Rutherford, C. E. Langmuir 1993, 9, 604. (11) Tang, F.-Q.; Xiao, Z.; Tang, J.-A.; Jiang, L. J. Colloid Interface Sci. 1989, 131, 498. (12) Kumagai, H.; Torikata, Y.; Yoshimura, H.; Kato, M.; Yano, T. Agric. Biol. Chem. 1991, 55, 1823. (13) Johansson, G.; Pugh, R. J. Int. J. Miner. Process. 1992, 34, 1. (14) Zouboulis, A. I.; Lazaridis, N. K.; Zamboulis, D. Sep. Sci. Technol. 1994, 29 (3), 385. (15) Allain, C.; Jouhier, B. J. Phys. (Paris) Lett. 1983, 44, L-421. (16) Hurd, A. J.; Schaefer, D. W. Phys. Rev. Lett. 1985, 54, 1043. (17) Skjeltorp, A. T. Phys. Rev. Lett. 1987, 58, 1444. (18) Roussel, J.-F.; Camoin, C.; Blanc, R. J. Phys. (Paris) 1989, 50, 3259.
0743-7463/96/2412-0997$12.00/0
cantly, generation of metallic and semiconductor particles and particulate films at aqueous solution-air interfaces has provided an entry to advanced materials.31-33 Investigation of the formation and characterization of these systems with increasing vigor is, therefore, hardly surprising. Determination of surface pressure (Π) vs surface area (A) isotherms of noncohesive monoparticulate layers on aqueous solutions has contributed fruitful information on particle sizes, particle-particle repulsive interactions, and wettabilities.34-38 Information on particle wettability can only be obtained by assuming the identity of Er and (19) Roussel, J.-F.; Camoin, C.; Blanc, R. J. Phys. (Paris) 1989, 50, 3269. (20) Stankiewicz, J. Sixth ECIS Conference (Graz) 1992, Abstract PII-83. (21) Robinson, D. J.; Earnshaw, J. C. Phys. Rev. A 1992, 46 (4), 2045. (22) Robinson, D. J.; Earnshaw, J. C. Phys. Rev. A 1992, 46 (4), 2055. (23) Robinson, D. J.; Earnshaw, J. C. Phys. Rev. A 1992, 46 (4), 2065. (24) Pieranski, P. Phys. Rev. Lett. 1980, 45, 569. (25) Onoda, G. Y. Phys. Rev. Lett. 1985, 55, 226. (26) Armstrong, A. J.; Mockler, R. C.; O’Sullivan, W. J. J. Phys.: Condens. Matter 1989, 1, 1707. (27) Gomm, A. S.; Hauxwell, F.; Moilliet, J. L. In Wetting; S.C.I. Monograph No. 25; Society of Chemical Industry: London, 1967; Vol. 25, p 213. (28) Levine, S.; Bowen, B. D. Colloids Surfaces 1991, 59, 377. (29) Levine, S.; Bowen, B. D. Colloids Surfaces 1992, 65, 273. (30) Levine, S.; Bowen, B. D. Colloids Surfaces A: Physicochem. Eng. Asp. 1993, 70, 33. (31) Fendler, J. H. Membrane-Mimetic Approach to Advanced Materials; Springer-Verlag: Berlin, 1994. (32) Meldrum, F. C.; Kotov, N. A.; Fendler, J. H. J. Phys. Chem. 1994, 98, 4506. (33) Kotov, N. A.; Meldrum, F. C.; Wu, C.; Fendler, J. H. J. Phys. Chem. 1994, 98, 2735. (34) Schuller, H. Kolloid Z. Z. Polym. 1967, 216-217, 380. (35) Sheppard, E.; Tcheurekdjian, N. Kolloid Z. Z. Polym. 1968, 225, 162. (36) Sheppard, E.; Tcheurekdjian, N. J. Colloid Interface Sci. 1968, 28, 481.
© 1996 American Chemical Society
998
Langmuir, Vol. 12, No. 4, 1996
Ho´ rvo¨ lgyi et al.
Wr.39 Er is the work necessary for removal of a particle from the noncohesive layer, obtained from the experimentally determined Π vs A isotherms by
Er ) ΠcAc
(1)
where Πc is the collapse pressure and Ac is the surface area of a particle at the collapse pressure. The adhesion work for a spherical particle, Wr, is defined by
Wr ) γWAR2π(1 ( cos Θ)2
(2)
where R is the radius of the particle, γWA is the water-air interfacial tension (π ) 3.141...), Θ is the characterizing wettability parameter (contact angle), and the ( sign in the parentheses means that the particle moves into the upper (+) or the lower (-) phase. Equations 1 and 2 provide an experimental approach, therefore, for the determination of the wetting (contact angle) of the spherical particles in a monodisperse sample. The contact angle can alternatively be evaluated, even in the absence of information on the radius and density of the spheres, from39
Θ ) arcos ([(Πc2(3)1/2/πγWA)1/2 - 1]
(3)
for monoparticulate layers which are hexagonally closepacked. Equation 3 was subsequently augmented by a repulsion energy term.40 The significance of this term is not clearly understood since the particles can be removed from the liquid-fluid interface during lateral compression, if the repulsive energy just exceeds the value of adhesion work (neglecting the other energy dissipation). Equation 3 was successfully adapted for the determination of contact angles for solid nanometer- and micrometer-sized particles which were floating at aqueous surfactant-air interfaces.41 In spite of these studies,34-41 the effect of particle hydrophobicity on the particle-particle and particlesubphase interaction is incompletely understood. The main purpose of the present work has been to obtain an insight into the collapse phenomenon of monoparticulate layers and to suggest experimental methods for the characterizations of particle-particle and particle-subphase interactions as well as the wettability of solid particles. Silanized glass beads (75-µm diameter) have been used since their hydrophobicity can be easily altered (without using any surfactant) by changing the extent of silylation. The advantages of these relatively large particles are that their behavior on the water surface can be readily visualized and in situ contact-angle determinations can be conveniently performed. Experimental Section Materials. Glass beads (Supelco, 75 ( 5 µm diameter, acidwashed), acetone (EM Science, GR), ethyl alcohol (Pharmco, USP, dehydrated), hexane (Fisher, ACS certified, contains a mixture of isomers), hydrochloric acid (Fisher, ACS Reagent), and trimethylsilyl N,N-dimethylcarbamate (Me3SiC; Fluka, GC grade, purum >98%) were used as received. Water was purified by using a Millipore Milli-Q filtration system provided with a 0.22-µm Millistack filter at the outlet. (37) Doroszkowski, A.; Lambourne, R. J. Polym. Sci., Part C 1971, 34, 253. (38) Garvey, M. J.; Mitchell, D.; Smith, A. L. Colloid Polym. Sci. 1979, 257, 70. (39) Clint, J. H.; Taylor, S. E. Colloids Surfaces 1992, 65, 61. (40) Clint, J. H.; Quirke, N. Colloids Surfaces A: Physicochem. Eng. Asp. 1993, 78, 277. (41) Aveyard, R.; Binks, B. P.; Fletcher, P. D. I.; Rutherford, C. E. Colloids Surfaces A: Physicochem. Eng. Asp. 1994, 83, 89.
Figure 1. Photograph of a monoparticulate layer which was prepared from sample C. The photograph was taken of a glass plate onto which monoparticulate layers had been transferred from the water surface (see the details in the text). Hexagonal ordering in an approximately close packing is clearly seen. Instruments. A commercial Lauda Model P Langmuir Film Balance was used for the determination of surface pressure vs surface area isotherms at room temperature (22 ( 1 °C). The output of the film balance was coupled to a Zenith microcomputer. The maximal and the minimal areas of the trough were 600 and 75 cm2, respectively. Images of the light reflected from the beads were observed through an Olympus PM-10-M microscope which was coupled to a television monitor and video recorder via an NEC NC-8 CCD color camera. Images for demonstration and wettability analysis were computerized by using a frame grabber and printed, if desired, on an HP LaserJet printer. Visual Observations. The aggregation of the sprinkled particles, their collapse, and their redispersibility were carefully observed visually (see Figure 1). Surface Modification. In order to gain some information about the effect of surface hydrophobicity on the Π-A isotherms, three samples were silylated under different experimental conditions. Sample A was prepared by stirring 3.0 g of the glass beads in a 15 mL hexane solution of Me3SiC (5 × 10-5 vol %) for 5 min at room temperature. Silylation of the glass-bead surface was stopped by the addition of 2 mL of ethyl alcohol. Subsequent to the settling of the silylated beads, the supernatant was removed and the glass beads were rinsed four times with acetone (20 mL) and once with hexane (20 mL) and then dried at room temperature. Samples B and C were prepared by shaking 3.0 g of the glass beads in 25 mL of 1.0 M HCl for 80 min in order to increase the amount of surface silanol groups. Subsequent to removing the acidic solution, the particles were rinsed three times with distilled water (20 mL) and once with acetone (20 mL) and then dried at room temperature. For silylation, the particles were stirred in a 15 mL hexane solution of Me3SiC (0.67 vol %) for 5 min (for sample B) or in a 15 mL hexane solution of Me3SiC (2.33 vol %) for 90 min (for sample C) at room temperature. Silylation was stopped by rinsing the glass beads once with hexane (20 mL), three times with acetone (20 mL), and finally with hexane (20 mL) and then drying at room temperature. Wettability Measurements. The wettability of samples A, B, and C was measured by two different methods. In method Ia, one ca. 10 µL water drop was formed on the center of a microscope slide, and then a small amount of glass beads was sprinkled around the liquid patch. A microscope cover slide was then pressed onto the liquid drop whereby the particles were collected at the liquid-air boundary layer. The beads in the boundary layer were photographed from the top. The extent of immersion into liquid was directly proportional to the wetting angle formed on the beads (method Ia).42 In some cases, the wetting angle (measured via the liquid phase) was also determined gonio-
Monoparticulate Layers of Silanized Glass Spheres
Langmuir, Vol. 12, No. 4, 1996 999
Figure 2. Goniometrical method for determining the contact angle (Θ) between two plane parallel microscope slides. W ) water phase, A ) air phase. The dark line is an optical effect due to the curved liquid-air interface. metrically by fitting straight lines at the contour of the glass bead and liquid-air interface at the point of the three-phase contact (method Ib, Figure 2). Method II provides an in situ study of wettability. A reflectional optical microscope, at a relatively high magnification (10 × 80), was used to view the spherical particles floating at the liquid-air interface from the top, focusing (i) on the contour of the three-phase-contact circle (Figure 3a) and (ii) on the contour of the whole bead (Figure 3b). Measuring the radius of the threephase-contact circle (x) and the whole sphere (y), the wetting angle (Θ) can be approximated by geometrical considerations: Θ ) arcsin(x/y) if the effect of gravity on bead immersion is neglected.43 A similar method was described previously in a reverse situation in which particles were on the bottom of a liquid drop.44 Unfortunately, method II cannot be used at a wetting angle of 90° or greater and it introduces significant errors in the range 80-90°, due to the great steepness of the arc sinus function in this region. On the other hand, at a contact angle smaller than 80°, wetting can be determined equally well by either method I or method II. Surface Area-Surface Pressure Measurements. Prior to spreading the silylated glass beads, the liquid surface was cleaned several times by sweeping it with a Teflon barrier. The subphase was deemed to be clean when the surface pressure increase was less than 0.2 mN m-1 upon compression to onetwentieth of the original area. Samples A, B, and C (600 mg) were carefully sprinkled onto the water surface by using a spatula. The surface area (A) was calculated by assuming a particle density of 2.5 × 103 kg m-3 (also see Appendix A). The whole compression-expansion cycle was usually recorded, and each measurement was repeated three to five times. In certain cases, five compression-expansion cycles were performed consecutively (taking approximately 1 h) in order to assess hysteresis. Surface compressions and expansions were carried out at a rate of 15 cm2 min-1 (minimum rate of the film balance). The sprinkled particles were allowed to aggregate for 5 min prior to compression. Contact cross-sectional areas (CCSA), which are defined analogously to head-group area for molecules, were determined by drawing a tangent to the steep part of the Π-A isotherm (also see Figure 4a). Surface coverages (SC; i.e., the percentage of the total surface area which was covered by the floating particles)45 were also calculated for the first compression isotherms (also see Appendix B). (42) Ho´rvo¨lgyi, Z.; Csalava´ri, R. XXIII International Symposium on Colouristics, Balatonsze´plak, Hungary 1991, Abstract No. 9. (43) Princen, H. M. In Surface and Colloid Science, Vol. 2. The Equilibrium Shape of Interfaces, Drops and Bubbles. Rigid and Deformable Particles at Interfaces; Matijevic, E., Ed.; Wiley-Interscience: New York, 1969; p 1. (44) Tschaljovska, S. D.; Aleksandrova, L. B. Chem. Technol. 1978, 30, 301. (45) Ho´rvo¨lgyi, Z.; Ne´meth, S.; Fendler, J. H. Colloids Surfaces A: Physicochem. Eng. Asp. 1993, 71, 327.
c
Figure 3. (a) Contour of the three-phase-contact circle formed on a floating glass sphere at the water-air interface. (b) Contour of the same sphere floating at the water-air interface. (c) Schematics which were used for calculating the water contact angle. x ) the radius of the three-phase-contact circle and y ) the radius of the glass sphere. S ) solid phase, W ) water phase. Investigations of the time dependence of surface pressure (close to the collapse state), subsequent to the fifth compressionexpansion cycle, provided information on the stability of layers. The collapse of solid monoparticulate layers is not a real collapse phenomenon (e.g., surface pressure does not drop to zero at this point). Above a certain surface pressure, creasing of monolayers is observable,45 which takes place in a relatively wide (10-15 mN m-1) surface pressure range; hence, it is not easy to establish the exact collapse pressure, Πc. The method of assigning Πc values34 is illustrated in Figure 4a. The collapse energy,34 Ec, was calculated by
Ec )
∫
Ac
A∞
Π(A) dA
(4)
where A∞ is the area for a particle at which the surface pressure does not exceed the zero value and Ac is the area for a particle at Πc (see Figure 4a). The energy which was necessary to remove a particle from the layer (Er) was also calculated by eq 2. For comparison, the adhesion work (Wr) for the different systems was determined (see eq 1) by using the in situ determined contact angles (Θ ) 90°, Θ ) 72°, Θ ) 55°; also see Table 1). The waterair interfacial tension was assumed to be 72 mN m-1, and 37.5 µm was considered as the average particle radius.
1000 Langmuir, Vol. 12, No. 4, 1996
Ho´ rvo¨ lgyi et al. Table 1. Contact Angles (Θ, deg) of Water on Particles of Samples A, B, and Ca sample A
sample B
sample C
method Ia (between slides) 52 ( 3 (32) 69 ( 4 (10) method Ib (between slides) 59 ( 6 (56) 90 ( 2 (20) method II (for floating 55 ( 2 (27) 72 ( 2 (25) particle) a
Figure 4. (a) The first compression curves obtained for the layers of sample A (A), sample B (B), and sample C (C). Πc ) critical (collapse) surface pressure; CCSA ) contact crosssectional area; Ac ) surface area at the collapse surface pressure. (b) Repeated compression curves (1c going to 5c) of a layer of sample C. (c) Repeated compression curves (1c going to 5c) of a layer of sample B. The value of A in the most close-packed hexagonal arrangement of the beads: 4871 µm2/bead (SC ) 90.7%). Contact angles from the isotherms were also calculated by eq 3 or, in some cases, by eqs 1 and 2. For the calculation of Wr and contact angles, the direction of particle motion was assessed by visual observation. The effect of gravitation can be neglected for particles in the size range43 which was investigated in the present work.
Results Wettability of Samples. Water contact angles of samples A, B, and C are collected in Table 1. Increasing
The number of measurements is given in parentheses.
the extent of silanation and, hence, increasing the hydrophobicities on going from sample A to sample C resulted, as expected, in progressively larger contact angles. The relatively small differences between the contact angles obtained for a given sample demonstrates the reliability of the methods which were employed. Visual Observations. Sprinkling solid samples A, B, and C onto the liquid subphase surface resulted in the initial formation of well-separated particles. Subsequently, prevailing long-range capillary interactions46 and short-range colloid forces facilitated the interfacial association of beads. The more hydrophobic sample C tended to form two-dimensional aggregates looser than its less hydrophobic counterparts (B and A), as was observed previously.47,48 Compression of the aggregates resulted, in every case, in the formation of contiguous monoparticulate layers approaching a close-packed, hexagonal ordering of particles (even in the case of the highest hydrophobic system) in the vicinity of the collapse (see Figure 1 and compare it with the SC data in Table 2). Monoparticulate layers formed from sample C could be transferred onto solid supports (typically untreated glass microscope slides) by a simple “horizontal-immersion and lift-up” technique (see Figure 1). Conversely, “running away” of the particles precluded the transfer of sample A. As was observed previously,45 monoparticulate layers, prepared from the lower hydrophobic samples (A and B), could be redispersed into small domains during expansion. Domains of sample B had a stringy (presumably fractallike) structure which reorganized into a more compact form in 2-3 min. Upon compression, the partially waterwettable particles (sample A) were pushed irreversibly into the water phase and ended up in the bottom of the trough. On the other hand, collapse of sample C layer manifested in the formation of a whitish multilayer (especially in the vicinity of the moving barrier), as was expected for a situation in which particles transferred from the interface into the air phase. Creasing was often observed for sample B at several points on the monolayer, and particles were not found on the bottom of the trough. Unexpectedly, white folds were sometimes observed during the collapse of compressed layers prepared from sample B, indicating the transfer of some beads into air. Surface Area vs Surface Pressure Isotherms. Typical surface pressure vs surface area isotherms for samples A, B, and C are illustrated in Figures 4 and 5. The effect of surface hydrophobicity on the compression isotherms can be seen in Figure 4a. The influence of repeated compressions on the compression curves and on the hysteresis phenomenon are demonstrated in Figures 4b,c and 5, respectively. Repeated compression curves of sample C (Figure 4b) and sample B (Figure 4c), subsequent to the breakdown of the long-range and short-range structure of the monolayers, indicated that particles could not be removed irreversibly from the water-air interface (46) Chan, D. Y. C.; Henry, J. D., Jr.; White, L. R. J. Colloid Interface Sci. 1981, 79, 410. (47) Ho´rvo¨lgyi, Z.; Medveczky, G.; Zrı´nyi, M. Colloids Surfaces 1991, 60, 79. (48) Ho´rvo¨lgyi, Z.; Ma´te´, M.; Zrı´nyi, M. Colloids Surfaces A: Physicochem. Eng. Asp. 1994, 84, 207.
Monoparticulate Layers of Silanized Glass Spheres
Langmuir, Vol. 12, No. 4, 1996 1001
Figure 6. Time dependence of surface pressure (close to the collapse) of samples B (2) and C (b). Table 3. Parameters Evaluated for Monoparticulate Layers Prepared from Samples A, B, and C sample A
sample B
sample C
Πc, Er,b J/particle Wr,c J/particle
65.3 ( 1.3 2.8 × 10-10 5.8 × 10-11
69.8 ( 0.4 3.6 × 10-10 3.2 × 10-10
contact angles from the isotherms, deg
ΘAd ) 90.0
66.9 ( 2.5 3.3 × 10-10 (V) 1.5 × 10-10 (v) 5.5 × 10-10 ΘAd ) 90.7 ΘRe ) 89.3
mJ/m2 a
Figure 5. Hysteresis phenomenon for the first (big hysteresis) (Figure 5a) and the fifth (small hysteresis) (Figure 5b) compression-expansion cycle of a layer of sample C. The dotted lines indicate the expansion isotherms. Table 2. Contact Cross-Sectional Area, Surface Coverage and Collapse Energy Values for Samples A, B, and C CCSA, µm2/bead SC, %, at CCSA Ec, J/particle
sample A
sample B
sample C
4936 90.3 ( 2.9 (>91%)b 1.74 × 10-11
5437 81.2 ( 4.1 (>91%)b 3.20 × 10-11
6849 (5228)a 64.5 ( 0.5 (84.5 ( 2.5)b 8.02 × 10-11
a The surface area which was calculated at the collapse pressure is shown in parentheses. b Surface coverage values at the collapse pressure.
even in the collapse. In the case of sample A, as a consequence of repeated compressions, the isotherms moved step-by-step to smaller surface areas due to particle loss into the subphase. Hysteresis (characterized by the extent of the area between the compression and expansion curves) became smaller during repeated compressionexpansion cycles (Figure 5a,b), which showed the irreversible structure formation from highly hydrophobic beads due to their lateral compression. CCSA, SC, and Ec values calculated for the first compression curves are given in Table 2. Typical stability measurements for samples B and C are shown in Figure 6. Similar behavior was observed for sample A (not shown) as for sample B. It should be noted that layers prepared from sample C were found to be stable even at low (e.g., 22 mN m-1) surface pressure. Values of the collapse pressure and adhesion work (the energy which is necessary to remove a particle from the monolayer) and contact angles, determined by eq 3 for samples A, B, and C, are collected in Table 3. An advancing contact
ΘRe ) 88.1 ΘRf ) 86.3
a The values of collapse pressure. b The energy which is necessary to remove a particle from the interface. c The calculated adhesion work (Wr) for the down (V) and up (v) particle motion. d Advancing contact angles determined from the isotherms from eq 3. e Receding contact angles determined from the isotherms from eq 3. f Receding contact angle determined from the isotherms from eqs 1 and 2.
angle was supposed for particles which moved into the water (sample A), while particles prepared in sample C came to the air phase, manifesting in a receding contact angle. Both advancing and receding contact angles and the corresponding “up” and “down” Wr values were calculated for sample B. Discussion In the following section the effect of hydrophobicity on the particle-particle interaction (firstly) and on the particle-subphase interaction (secondly) will be discussed. In this latter part the instability measurements will also be analyzed. Finally, the results obtained for sample C will be evaluated separately. Effect of Particle Hydrophobicity on the Structural Strength (Particle-Particle Interaction). Aggregation of the hydrophobic silanized glass spheres (sample C) is believed to lead to the formation of a cohesive layer on the water surface.47,48 A high degree of hydrophobicity renders these particles to be in direct contact with each other in the air phase (Θ > 90°) or in the water phase (Θ < 90°). In contrast, intimate particle-to-particle contact in sample A is diminished by double layer and hydration repulsions between the particles. Apparently, the prevailing long-range capillary attractions46 can only form a weakly cohesive layer in sample A. Visual observations and surface pressure vs surface area isotherm determinations, as well as the elucidated CCSA and the more informative SC data (Table 2), are in full accord with the relationship postulated between particle hydrophobicity and structural strength of the monoparticulate layer.45,47,48 That is the higher the particle hydrophobicity, the greater the structural strength of the monoparticulate layer. Calculated collapse energies (Ec values in Table 2)
1002 Langmuir, Vol. 12, No. 4, 1996
Ho´ rvo¨ lgyi et al.
are in accord with this assumption. The energy, necessary to compress the most hydrophobic glass spheres (sample C) into a close-packed hexagonal array, is almost 5 times greater than that required for the compression of the least hydrophobic (sample A) particles (Table 2). The enhanced particle-particle contacts (“bonds”) during compression of sample C leads to an increasing surface pressure. The presence of strong particle-particle “bonds” in sample C is also demonstrated by the 84.5% surface coverage at collapse (Table 2; SC value in brackets), a value below that expected for a hexagonally close-packed layer of glass spheres (90.7%). At this surface coverage, the energy necessary to break up the lateral particle-particle contacts in the plane of interface (concerning one particle) is greater than that which is necessary to remove one sphere from the layer (Er). From the Er value, we can approximate the energy of a particle-particle contact. Assuming a particle coordination number of 5 or 6 at the collapse, adhesion energies of (1.2 or 1.4) × 10-10 J/particle-particle contact can be obtained (see Appendix C). Normalizing the above values of interaction energies by R2 (where R is 37.5 µm), results in 85-100 mJ m-2 as “shearing” adhesion energy. (This value should be compared with the pull-off energy, 130-140 mJ m-2, obtained previously for similarly hydrophobic silanized glass surfaces49.) The relatively high CCSA value of layers prepared from sample B indicates cohesive layer formation, but the close-packed ordering of spheres also takes place below the collapse pressure. Thus, at the collapse, significant Born repulsion can exist and the particle-particle adhesion energy cannot be calculated by the above manner. However, it is supposed that for cohesive monoparticulate layers every point of the isotherm is related to the particle-particle adhesion energy (Πc-Ac can be replaced by any Π-A pairs in the calculation), hence for sample B (at A ) Ac/sample C) 39-46 mJ m-2 values can be assessed. The basis of this calculation is that during an imagined, infinitely short step by step compression all particle-particle connections rearrange in the homogeneous monoparticulate layer. Considering the weakly cohesive nature of monoparticulate layers of sample A, we can write the measurable surface pressure as the sum of the noncohesive (Πnc) and cohesive (Πc) terms:
Π ) Πnc + Πc
(5)
Π begins to increase rapidly at the value of CCSA and it is thought that, from this point, Πnc gives the main contribution to its value. Considering the hexagonal arrangement of beads during this stage of compression, one can calculate the particle-particle distance (H) by
H ) 2[(A/6 tan 30°)1/2 - R]
(6)
Taking the value of 37.5 µm for R and A ) CCSA, we can get a value of about 490 nm for H at the contact crosssectional area, which is considered as the particle-particle distance at the secondary minimum of their interaction energy. This value is in satisfactory agreement with that reported previously for very similar, silanized glass beads (Θ(Young) ) 41° and a bead radius of 34 µm) which were floating at the water-air interface.48 This previous calculation, based on a modified DLVO theory by considering capillary interactions,46 led to a secondary potential energy minimum at 100 nm to 1 µm interparticle distance (Figure 7). We can approximate the (repulsive) total interparticle energies (Erep) from the Π-A isotherms at interparticle (49) Parker, J. L., P. M. Claesson, Langmuir 1994, 10 (3), 635.
Figure 7. Total (colloid and capillary) interparticle energies calculated for silanized glass spheres of similar sizes and wettabilities.48
distances smaller than H(CCSA) as follows:
Erep(A) ) Π′(A)(CCSA - A)/(2 × 3)
(7)
where Π′(A) values represent the fitted line whose intersection with the horizontal axes provides CCSA (Figure 4a). The factor (3) comes from the hexagonal arrangement of beads. This approximation rests upon the linearity of Π-A isotherms in this region (Figure 4a) and on the negligible contribution of Πnc to Π at A > CCSA. For an ideal noncohesive layer, the exact calculation37 would be
Erep(AH) )
∫AA Π(A) dA H
∞
(8)
where AH is the area at which the total interparticle energy has been calculated. The resultant values, (0.5-1.3) × 10-13 J, in the range of 1-200 nm interparticle distances are much greater than those calculated in terms of DLVO theory augmented with the capillary interaction (10-1610-15 J).48 This very great repulsion energy includes both hydrodynamic and hydration effects50 and is a manifestation of the extreme stability of interfacial colloids.51 It also confirms the previous results which were obtained by the measurement of the “effective” interfacial tension in a different way (sessile-drop method).52 These observations substantiate the proposed hydrophobicity-dependent restructuring of interfacial aggregates which are composed of similarly sized, silanized glass beads.47,48 Effect of Particle Hydrophobicity on ParticleSubphase Interaction (Comparison of Measured and Calculated Contact Angles). The most important result is that surface hydrophobicity only influence slightly Er (Table 3) which can be calculated by the isotherms (eq 1) and of which equality to adhesion work, Wr, was supposed previously. The comparison of Wr with Er also led to interesting result. Satisfactory agreement between Wr and Er was only found for layers prepared from sample C. Appreciable differences between Wr and Er for the layers prepared from the less hydrophobic glass spheres (samples A and B) indicate the contribution of energies other than static wetting. Accordingly to the above findings, satisfactory agreement between the contact angles determined by the different methods was only obtained for sample C (Tables 1 and 3). It has been postulated39-41 that eq 3 is valid provided the liquid(50) Derjaguin, B. V.; Churaev, N. V. Colloid Surfaces 1989, 41, 223. (51) Robinson, D. J.; Earnshaw, J. C. Langmuir 1993, 9, 1436. (52) Levine, S.; Bowen, B. D.; Partridge, S. J. Colloid Surfaces 1989, 38, 345.
Monoparticulate Layers of Silanized Glass Spheres
Langmuir, Vol. 12, No. 4, 1996 1003
fluid interface is not curved around the floating particles. It means that particle size should be below about 3 µm. In our case it has only theoretical significance because for much larger particles (those used in the present experiments) the inclination of liquid-fluid interface from the plain is only 0.02-0.04°(!) directly at the bead surface (also see Appendix D and Figure 8). Connected with this, the maximum values of capillary interaction energy are in the range of -10-15 to -10-16 J,46,53 and as can be seen, they are lower by some orders of magnitude than the Er values (see Table 3). So, neither the slightly curved liquid-fluid interface nor the capillary interaction can be responsible for the observed discrepancies. It should be noted that methods I and II (in Table 1) can only provide values for the advancing wetting angle but not for the critical value which forms immediately prior to the beginning of the three-phase-contact line motion. There may be a strong fluctuation of the liquid-air interface due to the trapping the silanized glass spheres, which probably results in a lower (close to Young’s)54 value of the wetting angle. (The capillary forces supply significant kinetic energy for the beads during their trapping which, due to the elasticity of water-air interface, leads to an oscillation of the particles.) However, on a particle which is moving from the interface down or up, the critical (the largest advancing or the smallest receding) angle can readily form. It means that larger (advancing) or smaller (receding) contact angles should be obtained from the isotherms, rather than from the direct contact-angle measurements. In the case of silylated, smooth glass surfaces, the water contact-angle hysteresis can reach a value of 20-25°,47,48 but this effect cannot be responsible alone for the observed differences. In the following section, we present (plausible) explanations of the obtained results sequentially. Dynamic Contact Angles and Their Relaxation: The Instability of Monoparticulate Layers (Sample A and B). The observed instability of the layers, prepared from sample A and B, indicates the need for considering the dynamics of Er. There can be two reasons for this instability. First, the instability may be caused by the structural rearrangement of the layer. Such a rearrangement is unlikely since, in the range of 60-65 mN m-1 surface pressure, the layer of sample A and B is entirely close-packed (see Table 2 and Figure 4a). Second, contact angles are likely to be dynamic.55 The dynamic contactangle relaxation is a well-known phenomenon from the literature. Relaxation of ΘA after halting a water-airsolid contact line advancing at 3 mm min-1 can result in a 7° decrease during 30 min.56 Supposing a row-by-row removal of particles during their compression, the relationship between the average velocity of the three-phasecontact line (V) and the linear rate of compression (l) for spherical particles (Θ < 90°) can be described by
V ) lπΘ/360°
(9)
(In the case of Θ > 90°, V ) lπ(180° - Θ)/360° can be derived.) At a linear compressional rate of 1 cm min-1, at Θ ) 55° and Θ ) 72° (Table 1), we can get 4.8 and 6.3 mm min-1 as the average velocities of the three-phasecontact lines for layers prepared from sample A and B. This makes the instability of these systems understand(53) Paunov, V. N.; Kralchevsky, P. A.; Denkov, N. D.; Nagayama, K. J. Colloid Interface Sci. 1993, 157, 100. (54) Wolfram, E.; Faust, R. In Wetting, Spreading and Adhesion; Padday, J. F., Ed.; Academic Press: London, 1978; p 213. (55) Blake, T. D. Dynamic Contact Angles and Wetting Kinetics: Wettability; Berg, J. C., Ed.; Surfactant Sci. Ser., Vol. 49; Marcel Dekker: New York, 1993; p 251. (56) Elliott, G. E. P.; Riddiford, A. C. Nature 1962, 195, 795.
able. Taking into account the surface pressure drop during the relaxation (10 mN m-1, see Figure 6), the corrected contact angle is 82° for sample A which still seems to be too large and requires the consideration of an additional contribution to the energy term of the sample A particles. For sample B, this calculation leads to an incorrect result because the experimentally determined Er value (3.3 × 10-10 J/particle) involves the effect of extraordinary (“up and down”) particle removal (compare the calculated values of the adhesion work with Er in Table 3). Electrostatic Trapping of Charged Colloids at the Electrolyte-Dielectric Interface57 (Sample A and B). It is fruitful to consider the electrostatic trapping of charged colloids at the electrolyte-dielectric interface. Displacement of the ion cloud surrounding a charged colloid in the hemisphere, as the particle comes to the electrolytedielectric interface, is assumed to be energetically favored.57,58 A particle just below the water surface can be considered to be in an electrostatic energy minimum. Depending on the surface charge, the absolute value of the energy minimum can exceed the value of adhesion work (Wr) for micron-sized particles.57 Since, particles of sample A were pushed entirely through the energetically favored situation into the water phase, Er can be written as
Er ) Wr + Wrel + Wel
(10)
where Wrel and Wel represent the formation of dynamic contact angles and the electrostatic phenomenon, respectively. Conversely, the particles of sample B could not be pushed into the bulk phase which may indicate the common effect of wetting, electrostatic and adhesion forces. It should be remembered that repeated compressions of smaller (3 ( 1 µm diameter) silica beads, silanized to similar extents (Θ ≈ 70°), did not lead to a limiting Π-A curve.45 Apparently, the smaller particles could be irreversibly removed from the interface into the water phase, as expected, since the absolute depth of the electrostatic energy well, relative to the bulk, changes with the particle size as R4.57 The contribution of Wel to Er is likely to be negligible for the smaller silica particles,45 and consequently, they can be irreversibly removed from the interface. Although, the electrostatic effect can provide a possible explanation of observed discrepancies, further experimental evidences are necessary for an improved interpretation. Satisfactory Agreement between the Measured and Calculated Contact Angles (Sample C). Although a satisfactory agreement was obtained between the measured and calculated contact angles for the most hydrophobic sample (Tables 1 and 3), the value of the critical receding contact angle, 88.1°, was found to be somewhat higher than expected. A similar behavior has been reported for layers prepared from surfactantstabilized silica particles.41 The origin of this discrepancy lies in the hysteresis of the contact angle which is included neither in eq 3 nor in the definition of adhesion work (eq 2). Substituting Πc ) γWA into eq 3 allowed the calculation of critical advancing (ΘA) and receding (ΘR) contact angles, which formed during the “down” and “up” particle motion, as 92.9° and 87.1°, respectively. Our inability to realize a contact angle hysteresis greater than 5.8° (the difference between the two critical contact angles) at around an equilibrious contact angle of 90° is hardly surprising. (57) Earnshaw, J. C. J. Phys. D: Appl. Phys. 1986, 19, 1863. (58) Stillinger, F. H. J. Chem. Phys. 1961, 35, 1584. (59) In the abstract of ref 45, the correct values of the contact angles are 90° ( 4° and 70° ( 4°.
1004 Langmuir, Vol. 12, No. 4, 1996
Greater hysteresis than this could only be achieved at a negative “effective” interfacial tension29 (i.e., Πc would be greater than γWA!). A somewhat more realistic value of ΘR ) 86.3° was calculated from the Er values (by eqs 1 and 2 which, unlike eq 3 do not require a hexagonal close packing of the particles), even though the hysteresis was neglected. The stability of layers, prepared from sample C, during the removal of particles from the interface was quite remarkable (Figure 6). It can be related to the lack of contact-line-velocity dependence of the receding contact angles which was observed, previously.60 A decrease of receding water contact angles with an increasing rate of the three-phase-contact line was found to be negligible in the velocity range of 0.1-5.0 mm s-1.60 No difference was found between the static and dynamic receding contact angles, while the change in advancing contact angles exceeded 10° in the velocity range which was investigated.60 This may be the reason for the lack of relaxation in the monoparticulate film, prepared from sample C, when the particles move into the air phase and the receding contact angle remains at the static value. It should be noted that the stability of the layers, observed at a relatively low surface pressure value (e.g., at 22 mN m-1), indicates that the cohesion (structural strength) of the layers can also be responsible for the lack of instability. These arguments suggest that a stable monoparticulate layer, at any surface pressure after a nonequilibrium compression, always indicates the presence of very hydrophobic particles. Conclusion The development of two general experimental approaches is considered to be the major accomplishment of the present work. First, a method has been provided for determining interparticle distances in their secondary interaction energy minimum and total (repulsive) energies for weakly cohesive monoparticulate layers. Second, a technique has been suggested for the determination of particle-particle “shearing” adhesion energy for strongly cohesive layers. Monoparticulate layers which were prepared from spherical glass particles, silanized to low (sample A), medium (sample B), and high (sample C) degrees, have served as models to test the proposed approaches. More specifically, interparticle distances between particles of sample A in their secondary interaction energy minimum have been assessed to be 490 nm. This distance is in fair agreement with that calculated by the DLVO theory, augmented by capillary interaction (see Figure 7). However, the calculated repulsive energies (Erep ) (0.5-1.3)) × 10-13 J) between these particles is some 2 orders of magnitude greater than expected (10-16-10-15 J). This discrepancy is incompletely understood at present. The particle-particle adhesion energy was calculated for the strongly cohesive layer of sample C to be (1.2-1.4) × 10-10 J, of which normalized values are 85-100 mJ m-2. In addition, particle-water (subphase) interactions have been examined by comparing the energy which is necessary for particle removal from the layer, Er, determined experimentally by Π vs A isotherms, with its theoretical value, adhesion work (Wr), determined by in situ contact-angle measurements. Satisfactory agreement between Er and Wr was obtained for the layers which were prepared from sample C. Significant discrepancies between Er and Wr for the layers which were prepared from (60) Kiss, E Ä .; Go¨lander, C.-G. Colloids Surfaces 1991, 58, 263.
Ho´ rvo¨ lgyi et al.
Figure 8. Schematic draw for the representation of the inclination angle (R). Θ is the “perturbed” contact angle and R′ is the radius of three-phase-contact circle. The dotted line through the sphere indicates the three-phase-contact line.
samples A and B were rationalized in terms of contactangle hysteresis, dynamic wetting, and distortion of the electric double layer around the interfacial particles. Acknowledgment. Support of this work by grants from the National Science Foundation (U.S.; to J.H.F.), OTKA (F4216; Hungary; to Z.H.), and the Istva´n Sze´chenyi Foundation (Hungary; to Z.H.) is gratefully acknowledged. Appendix A The calculation of the surface area (A)
A ) T/N
(11)
where T is the actual area in the film balance, and N is the number of all particles.
N ) (m/F)/(4R3π/3),
(12)
where m is the mass of the sample spread onto water surface, and F is the particle density. Appendix B The calculation of the surface coverage (SC):
SC ) 100(R2π/A)
(13)
Appendix C The calculation of the lateral (shearing) adhesion energy of particles (Ep-p)
Ep-p ) 2Er/k
(14)
where k is the coordination number of a bead. Appendix D The calculation of the inclination angle (R) of liquidfluid interface directly at the bead surface (see Figure 8).
R ) arcsin{(G - Fb)/(2R′πγWA)}
(15)
where G is the gravitation force for a bead, Fb is the buoyancy force due to the bead immersion into water, and R′ is the radius of three-phase-contact circle. γWA was assumed to be 72 mN m-1, for the densities of glass and water, the values of 2.5 × 103 and 103 kg m-3 were taken, respectively. The density of air was neglected. For R′ ) 0.765 (it means a value of 50° for “unperturbed” contact angle, Θ′/dΘ-R/) and for R′ ) R (Θ′ ) 90°) one can get from eq 15 for R, 0.036° and 0.015°, respectively. Although, for Fb determination an unperturbed (plane) water-air interface was considered, the error of calculation can only be some percents (neglecting entirely the effect of Fb we can get 0.018° for R (Θ′ ) 90°)). LA940658O
