Examination of Adsorbed Oleate Layers at a Fluorite Surface by

Langmuir 1997, 13, 1345-1351

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Examination of Adsorbed Oleate Layers at a Fluorite Surface by Contact Angle Measurements and FT-IR/IRS Spectroscopy† Jaroslaw Drelich,* Woo-Hyuk Jang, and Jan D. Miller Department of Metallurgical Engineering, University of Utah, WBB 412, Salt Lake City, Utah 84112 Received January 2, 1996. In Final Form: May 16, 1996X Molecular layers of oleate at a fluorite crystal surface were prepared by spontaneous adsorption from alkaline aqueous solutions of sodium oleate. The adsorption density of such oleate layers was determined by Fourier transform infrared internal reflection spectroscopy (FT-IR/IRS). Advancing and receding contact angles were measured for water drops on these carboxylate layers using the sessile-drop technique. The effect of surface heterogeneity (as established by the extent of oleate adsorption) on contact angle hysteresis for varying drop size is demonstrated. It was observed that both the contact angle hysteresis and contact angle/drop size relationship depend on the extent of deviation of the adsorbed layer from an ideal wellorganized monolayer. Experimental results support the position that it is of particular importance to examine both the advancing and receding contact angles with varying drop size whenever the sessile-drop technique is used to describe the nature of heterogeneous surfaces, including those prepared by adsorption of organic molecules. It was also found that the advancing contact angles for water drops are essentially the same for an equivalent level of adsorption of oleate and stearate at a fluorite surface.

Introduction Fluorite (CaF2) is an important mineral for the chemical industry and serves as the main source of fluorine. Worldwide fluorite separation from mined ore is realized with one or two of the following methods: gravity separation, heavy media separation, and/or froth flotation.1 Froth flotation is particularly recommended for the recovery of a high-grade concentrate. Fluorite is a hydrophilic mineral, and the use of hydrophobic surfactants (collectors) is required for flotation.1,2 Among these, tallow oil fatty acids, which are mixtures of various unsaturated fatty acids, particularly oleic acid, are very efficient in alkaline solutions (pH 8.5-10.0) and at elevated temperature (from 40 °C to over 90 °C).1,2 Significant research progress has been made to explain the mechanisms for adsorption of carboxylates at a fluorite surface,3-15 as well as to quantify the extent of carboxylate † Presented at the 2nd International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids organized in Zakopane (Poland) and Levoca (Slovakia) on September 4-10, 1995 (a part of the presentation entitled Contact Angle Measurements for Heterogeneous Surfaces Composed of Adsorbed Organic Mono- and Submono-Layers). * E-mail: [email protected]. Phone: (801) 581-7460. Fax: (801) 581-4937. X Abstract published in Advance ACS Abstracts, July 15, 1996.

(1) Musson, G. H.; Fowler, W. W. in SME Mineral Processing Handbook; Weiss, N. L., Ed.; SME/AIME: Littleton, CO, 1985; Chapter 23, pp 3-8. (2) Fuerstenau, M. C.; Miller, J. D.; Kuhn, M. C. Chemistry of Flotation; SME/AIME: Littleton, CO, 1985; pp 20-21. (3) Peck, A.; Wadsworth, M. E. In Proceedings of the Seventh International Mineral Processing Congress; Arbiter, N. N., Ed.; Gordon and Breach: New York, 1965; pp 259-67. (4) Miller, J. D.; Misra, M. Proceedings of the International Conference on Mineral Science Technology; Laughton, L. F., Ed.; The Council for Minerals Technology: Johannesburg, South Africa, 1984; Vol. 1, pp 259-68. (5) Miller, J. D.; Wadsworth, M. E.; Misra, M.; Hu, J. S. In Principles of Mineral Flotation: The Wark Symposium; Jones, M. H., Woodcock, J. T., Eds.; Australian Institute Of Mining and Metallurgy: Parkville, Australia, 1984; pp 31-42. (6) Hu, J. S.; Misra, M.; Miller, J. D. Int. J. Miner. Process. 1986, 18, 57. (7) Hu, J. S.; Misra, M.; Miller, J. D. Int. J. Miner. Process. 1986, 18, 73. (8) Hu, J. S. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1986.

S0743-7463(96)00010-8 CCC: $14.00

adsorption under various experimental conditions.6,11,14-20 The flotation chemistry of fluorite in fatty acid solutions is now better understood; however, not all surface chemistry aspects have been examined and explained. For example, it has been resolved that (a) at low equilibrium oleate concentrations the oleate monolayer is formed at the fluorite surface by chemisorption of the carboxylate groups with surface calcium sites, whereas (b) calcium oleate precipitates on the fluorite surface at concentrations of calcium and oleate that exceed the solubility product constant for calcium oleate. Although the amount of adsorbed collectors determines the hydrophobicity of the mineral surface and its flotation response, not much work has been done to examine the wetting properties of such carboxylate films at fluorite surfaces. Janczuk et al.21 showed that different cleaning and drying procedures for fluorite plates affect their wetting properties. In consecutive papers published by the same research group, the effect of adsorbed oleate22 and adsorbed dodecyl sulfate23 on the fluorite surface free energy was demonstrated. In both these studies, however, quantita(9) Miller, J. D.; Hu, J. S.; Jin, R. Colloids Surf. 1989, 42, 71. (10) Finkelstein, N. P. Trans. Inst. Min. Metall. 1989, 98, C157. (11) Kellar, J. J. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1991. (12) Kellar, J. J.; Young, C. A.; Knutson, K.; Miller, J. D. J. Colloid Interface Sci. 1991, 144, 381. (13) Rao, K. H.; Cases, J. M.; De Donato, P.; Forssberg, K. S. E. J. Colloid Interface Sci. 1991, 145, 314. (14) Young, C. A.; Miller, J. D. 122nd Annual SME Meeting, Reno, Nevada, February 15-18, 1993; SME/AIME: Littleton, CO, 1993; Preprint No. 93-224. (15) Free, M. L. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1994. (16) Hall, P. G.; Lovell, V. M.; Finkelstein, N. P. Trans. Faraday Soc. 1977, 66, 1520. (17) Marinakis, K. I.; Shergold, H. L. Int. J. Miner. Process. 1985, 14, 161. (18) Kellar, J. J.; Cross, W. M.; Miller, J. D. Appl. Spectrosc. 1989, 43, 1456. (19) Jang, W.-H. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1994. (20) Jang, W.-H.; Miller, J. D. Langmuir 1993, 9, 3159. (21) Janczuk, B.; Bruque, J. M.; Gonzalez-Martin, M. L.; Moreno del Pozo, J. Colloids Surf., A 1993, 75, 163. (22) Janczuk, B.; Gonzalez-Martin, M. L.; Bruque, J. M.; Moreno del Pozo, J. Appl. Surf. Sci. 1993, 72, 201. (23) Janczuk, B.; Gonzalez-Martin, M. L.; Bruque, J. M. Appl. Surf. Sci. 1994, 81, 95.

© 1997 American Chemical Society

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tive analysis of organic species at the fluorite surface was not carried out. We demonstrated in previous reports that contact angle measurements are very sensitive to any changes in structure and stability of the carboxylate films at both fluorite and calcite surfaces.19,24,25 It was found that closely packed well-ordered stearate monolayers, similar to those of transferred Langmuir-Blodgett films, can be formed at fluorite surfaces by spontaneous adsorption from aqueous solutions.19,24,25 Unfortunately, these are the only contributions reporting both the wetting properties and adsorption density of carboxylates at a fluorite surface. Further research effort needs to be conducted in order to explore the fundamentals of fluorite flotation and to find out if well-organized organic monolayers at the fluorite surface are equivalent to deposited Langmuir-Blodgett films. Fourier transform infrared internal reflection spectroscopy (FT-IR/IRS) has been found to be a powerful technique for the examination of froth flotation systems.11,12,14,15,18-20,26 A new theoretical background which was developed in recent years11,26,27 allows for the calculation of collector adsorption densities at mineral surfaces from FT-IR/IRS absorbance data (see the Experimental Procedure section for details). This approach was used in our previous studies19,24,25 to examine the adsorption density of Langmuir-Blodgett monolayers and adsorbed mono- and submonolayers of carboxylates at fluorite and calcite crystals. Also, in this contribution, the carboxylate layers at fluorite are examined with two analytical techniques, goniometry and FT-IR/IRS, and a variation of the wetting properties of the fluorite surface as modified with oleate is demonstrated. Although the two basic goals of this study are (a) exploration of the fundamentals of fluorite flotation systems and (b) wetting characterization of “model” heterogeneous surfaces, as established by the extent of oleate adsorption, it should be recognized that the successful preparation of wellorganized films at fluorite crystals may lead to new applications and the development of advanced materials. Experimental Procedure Materials and Reagents. Fluorite was purchased from Optovac Inc., as a single-crystal parallelepiped internal reflection element (IRE) with dimensions of 51 × 10 × 2 mm3 and an acute angle of 73°. Before each experiment, the fluorite crystal was washed with acetone, dried, and cleaned from organic contaminants in a Tegal Co. plasma chemistry reactor (Plasmod model) with argon plasma for 60 min. Sodium oleate (CH3(CH2)7CHdCH(CH2)7COONa) with purity greater than 99% from Sigma Chemical Co. was used in all experiments as received. A Milli-Q water system, supplied with distilled water, provided high-purity water with a resistivity of +18 MS and surface tension of 72.4 ( 0.2 mN/m at 21 °C. The pH of this water remained at pH 5.8 ( 0.1 after equilibration with the atmosphere. Other chemicals used in the experiments included reagent grade sodium hydroxide (NaOH) and spectrograde acetone (CH3COCH3) from Mallinckrodt, Inc. Adsorption of Oleate at Fluorite. The fluorite crystal (IRE) was immersed into 1 × 10-6 to 1 × 10-4 M aqueous solutions of sodium oleate of pH 9.5 ( 0.1. The pH of the aqueous phase was adjusted and kept at a constant level with 1-5 M NaOH solution. The mineral crystal remained immersed in the sodium oleate solution for 2-16 h. The beaker was covered with (24) Jang, W.-H.; Drelich, J.; Miller, J. D. 124th Annual SME Meeting, Denver, CO, March 6-9, 1995; SME/AIME: Littleton, CO, 1995; Preprint No. 95-96. (25) Jang, W.-H.; Drelich, J.; Miller, J. D. Langmuir 1995, 11, 3491. (26) Sperline, R. P.; Muralidharan, S.; Freiser, H. Langmuir 1987, 3, 198. (27) Miller, J. D.; Kellar, J. J. In Challenges in Mineral Processing; Sastry, K. V., Fuerstenau, M. C., Eds.; SME/AIME: Littleton, CO, 1989; pp 109-129.

Drelich et al. aluminum foil to minimize absorption of carbon dioxide from the laboratory atmosphere by the solution. No agitation was applied. Solutions with varying sodium oleate concentration were used, and different reaction times were maintained in subsequent experiments in order to change experimental conditions for adsorption of oleate by fluorite. In this way, adsorbed layers of varying oleate adsorption density were obtained. At the end of the experiment, a stream of pure water was introduced into the beaker and the reaction solution was diluted at least 500-1000 times to avoid deposition of oleate at the fluorite surface when the crystal was removed from solution. The fluorite crystal was additionally washed with water and dried in a vacuum. The dried crystal was analyzed spectroscopically to determine the amount of adsorbed oleate. FT-IR/IRS Analysis. Fourier transform infrared internal reflection spectroscopy (FT-IR/IRS) experiments were conducted with a Bio-Rad Digilab Division FTS-40 FT-IR spectrometer equipped with a liquid-nitrogen-cooled mercury cadmium telluride (MCT) detector. The spectrometer was purged with dry air supplied by a Balston 75-60 air dryer. Digilab software, version 4.45, was used for spectral manipulation with the SPC 3200 data station. An internal reflection cell with a variable angle holder (a twin-parallel mirror reflection 320 internal reflection accessory, Harrick Scientific) was used to measure the FT-IR/IRS spectra. The dial reading of the variable-angle holder was adjusted to satisfy the condition for total internal reflection inside the IRE. The intensity of the infrared beam internally reflected through the IRE was maximized by adjusting the mirrors of the variable-angle holder. After alignment of the IRE, the spectrometer was purged with dry air for at least 30 min before a background spectrum of the clean IRE was collected in order to minimize possible interferences from water vapor. The IRE was taken for the adsorption experiment in order to prepare an oleate layer (see previous section). The fluorite crystal (IRE) with the adsorbed oleate layer was repositioned in the instrument holder for ex-situ internal reflection experiments. Absorbance spectra of the adsorbed layers were ratioed against the background spectra of a clean IRE. All the spectra were the result of 1024 co-added scans at a resolution of 8 cm-1. The adsorption density of oleate at the fluorite surface was calculated from the FT-IR/IRS adsorption density equation26 (see also refs 11, 18, 20, and 27-29)

Γ)

(A/N) - Cbde 1000(2de/dp)

(1)

which for ex-situ measurements, i.e., for the dried sample in the environment of nitrogen, is reduced to the following expression:

Γ)

A/N 1000(2de/dp)

(2)

where Γ is the adsorption density of oleate at the fluorite surface (mol cm-2), A is the integrated absorbance for oleate molecules at the fluorite surface (cm-1), N is the number of internal reflections in the fluorite crystal,  is the molar absorptivity of the collector (oleate) (l cm-2 mol-1), dp is the depth of penetration (cm), de is the effective thickness of the sample (cm), and Cb is the bulk concentration of active compounds in the solution (for ex-situ FT-IR/IRS measurements Cb ) 0). The parameters N, de, and dp were calculated from the optical constants of the system: wavelength in the absorbance region, refractive indices of the IRE and air, and incident angle for internal reflection. The molar absorptivity was determined from transmission experiments using the Beer-Lambert equation. The absorbance was calculated from the FT-IR/IRS spectrum for each sample individually by integrating the peaks which appear for CH2 and CH3 stretching frequencies over a range of wavelength numbers between 3032 and 2802 cm-2. All details for the above calculations have been presented in previous contributions.11,18,20,27-29 (28) Kellar, J. J.; Cross, W. N.; Miller, J. D. Sep. Sci. Technol. 1990, 25, 2133. (29) Free, M. L.; Jang, W.-H.; Miller, J. D. Colloids Surf., A 1994, 93, 127.

Adsorbed Oleate Layers at a Fluorite Surface Contact Angle Measurements. After spectroscopic examination, the adsorbed oleate layer at the fluorite crystal surface was analyzed with respect to wetting properties using the sessiledrop technique. Fluorite was placed in a glass chamber which was partially filled with water used in contact angle measurements in order to minimize water evaporation from the drop and saturate the surrounding environment with water vapor. A water drop was introduced onto the sample surface through a microsyringe, and the needle remained in contact with the drop. The three-phase contact line of the water drop was made to advance or retreat by adding or withdrawing a small volume of water, and the advancing and receding contact angles, respectively, were measured after 20-40 s using an NRL goniometer (Rame´Hart, Inc.). The contact angles were measured with an accuracy of 1-2° for varying drop sizes. The supporting stage of the instrument is movable and calibrated in 0.02 mm divisions. This allowed for accurate measurements of the drop base diameter. The contact angle measurements were carried out for a water drop whose volume was gradually increased (advancing contact angle measurements) and next decreased (receding contact angle measurements). In selected preliminary tests the contact angle/ drop size relationships were examined at 2-3 different sites on the fluorite crystal surface. It was found from these tests that contact angles were reproducible in a range of (1-3° for large drops (5-8 mm base diameter), and thus, the rest of the experiments were limited to contact angle measurements at one site on the fluorite surface. The contact angles were measured at both sides of each drop size, and the average values are reported.

Results and Discussion Adsorption Density of Oleate at the Fluorite Surface. When the fluorite crystal was immersed in the 1 × 10-6 to 1 × 10-4 M aqueous sodium oleate solution (pH 9.5 ( 0.1) from 2 to 16 h, oleate was adsorbed. Although the mechanism of reaction between the carboxylate species and the fluorite surface is not completely understood, it is well documented that carboxylates chemisorb to the surface calcium sites during formation of the first monolayer.3,10-12,15,19 Formation of “multilayers”, which happens at moderate and high carboxylate concentration and/or at high pH values, is attributed to an uncontrolled precipitation of calcium dioleate and attachment of oleate colloids at the fluorite surface.11,12,15,19 A variation of the experimental conditions, i.e., concentration of sodium oleate in the solution and adsorption time, allowed for a different amount of oleate to be adsorbed in each experiment, from 0.6 to 9.8 µmol/m2. A comparison of the adsorption density values for monolayers of stearic and oleic acids which were established from π-A isotherms for Langmuir-Blodgett films and those evaluated with the FT-IR/IRS technique showed that the values determined spectroscopically are slightly overestimated, by ∼10%.19,20 The adsorption density of a uniform oleate LB monolayer at the fluorite surface corresponds to a value of around 6.2 µmol/m2, as demonstrated from Langmuir-Blodgett experiments.20 In this regard, oleate layers at the fluorite surface with an adsorption density between 0.6 and 9.8 µmol/m2, as prepared in this study, formed a submonolayer, a monolayer, and more than a monolayer. Such a variation in coverage provided an excellent model of surface heterogeneity with varying wetting characteristics. Many researchers have focused their attention on similar systems, especially in recent years (see ref 30 for a review of past work), but unfortunately a complete description of these systems with regard to the amount of adsorbed species at the solid surface is often not available. (30) Ulman, A. An Introduction to Ultrathin Organic Films from Langmuir-Blodgett to Self-Assembly; Academic Press, Inc.: London, 1991.

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Figure 1. Peak frequency change of the asymmetric C-H stretching mode of the CH2 group with increasing adsorption density of oleate at a fluorite surface. Open circles indicate the experimental data obtained in this work, and filled triangles represent the data from ref 12. The original isotherm from ref 12 has been reconstructed using a correction factor of 2.3, based upon sampling area considerations (see ref 29 for details).

The lowest adsorption density of oleate at the fluorite surface was found to be 0.6 µmol/m2, which corresponds to about 10% surface coverage. The contact angle data for surfaces with an oleate adsorption density of less than 10% of a monolayer were irreproducible. Fluorite surface contamination was difficult to eliminate completely with our experimental procedures, which included washing, drying, and FT-IR/IRS and contact angle measurements. Organic contaminants particularly affected the results of FT-IR/IRS measurements for samples with a surface coverage of less than 10% of a monolayer, and thus, the experimental data for these systems are not reported in this paper due to the uncertainty in the results. The highest adsorption density value reported in this contribution is 9.8 µmol/m2, which corresponds to about 1.6 oleate layers. It was our intention to compare the wetting characteristics for two heterogeneous systems, submonolayer coverage and coverage exceeding a monolayer. Unfortunately, the formation of a double layer of oleate, with uniform structure, at the fluorite crystal was unsuccessful in this research program, and properties of such organic films could not be compared with those of films having monolayer coverage. Conformation of Hydrocarbon Chain for Oleate at a Fluorite Surface. Shifts occurring in the IR peak positions for stretching modes of the alkyl groups (30502800 cm-1) indicate a conformational change for organic species adsorbed at a solid surface.12 Such changes in the band position for oleate chemisorbed at a fluorite surface were reported by Kellar et al.11,12 Also, similar shifts in the peak positions for the C-H stretching modes for oleate at a fluorite surface were observed in this study. Shown in Figure 1 is the frequency change of the asymmetric C-H stretching mode of the CH2 groups as obtained in this contribution. For comparison, Figure 1 also shows the experimental data of Kellar et al.12 There is excellent agreement between our experimental data and those reported in the previous contribution although different experimental conditions for the FT-IR/IRS measurements were used. This work was done using the ex-situ FT-IR/ IRS technique, in which a dried fluorite crystal with adsorbed oleate was surrounded by apolar gas (nitrogen). Kellar et al. carried out in-situ FT-IR/IRS measurements with the fluorite crystal immersed in a polar liquid (D2O). As is shown in Figure 1, the characteristic peak for the asymmetric C-H stretching mode for adsorbed oleate (31) Umemura, J.; Mantsch, H. H.; Cameron, D. G. J. Colloid Interface Sci. 1981, 83, 558. (32) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559.

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Figure 2. Advancing contact angle data for water drops at a fluorite surface with different levels of oleate adsorption. Numbers indicate the adsorption density of oleate at the fluorite surface in micromoles per square meter.

molecules is centered at 2926-2924 cm-1 for adsorption density less than about 2 µmol/m2. The frequency value for this peak shifts smoothly to 2920-2918 cm-1 with increased adsorption density of oleate at the fluorite surface and a monolayer structure approaching that of a complete monolayer (6.2 µmol/m2).20 Specifically, it appears from Figure 1 that a minimum in the peak frequency value for the oleate layer is located between 6.0 and 7.0 µmol/m2. At higher adsorption densities (from 7 to almost 10 µmol/m2) a shift of the band to 2921 ( 1 cm-1 is observed. The shifts in the peak position presented in Figure 1 indicate changes in the state of the hydrocarbon chain at the fluorite surface. According to the previous studies,12,30-32 the higher peak frequencies (2926-2924 cm-1) may be attributed to the gauche state of adsorbed oleate molecules at the fluorite surface whereas the lowest peak frequencies (2920-2918 cm-1) may describe the trans state of the more condensed monolayer. Of course, a transition state(s) certainly exists between gauche and trans states for oleate submonolayers. It is speculated that when oleate forms more than one monolayer at the fluorite surface (adsorption density from about 7 to 10 µmol/m2), the band position is affected by both trans molecular arrangement of the first monolayer and lessorganized molecules physically adsorbed onto the first monolayer. This may explain why only a slight shift in the peak frequency was observed for adsorption densities between 6 and 10 µmol/m2 (see Figure 1). Advancing Contact Angle/Drop Size Relationship for Water Drops. It was found in our previous studies that both advancing and receding contact angles may vary with drop (bubble) volume during contact angle measurements using the sessile-drop or captive-bubble technique, and this phenomenon appears important especially for the solid surfaces with either chemical or mechanical heterogeneities.33,34 In this regard, it was postulated that there is a need for the examination of contact angle hysteresis with varying drop (bubble) size whenever the sessile-drop and captive-bubble techniques are used.33,34 The contact angle data for several systems indicate that examination of the relationship between contact angle and drop (bubble) size is an important way to obtain more information about the quality and stability of a solid surface.24,25,33-35 This new concept, proposed in our research group, was also adopted in this study, and the contact angle/drop size relationships for both advancing and receding contact angles were determined for most of the oleate-fluorite systems. The advancing contact angle data for varying water drop sizes are presented in Figure 2. Although several other examples for the contact angle/ (33) Drelich, J.; Miller, J. D.; Good, R. J. J. Colloid Interface Sci. 1996, 179, 37. (34) Drelich, J. J. Adhes., in press. (35) Good, R. J.; Koo, M. N. J. Colloid Interface Sci. 1979, 71, 283.

Drelich et al.

drop (bubble) size relationships were already reported in the literature,24,25,33-39 the explanation of the mechanisms influencing the contact angle variation with drop (bubble) size is incomplete, mostly due to a limited knowledge of the solid surface structure used in these experiments. Surface topography, size, distribution, and the chemistry of surface components are only poorly reported for the systems which have been examined, and most characterization is limited to micron-sized surface features. Also, in this contribution, the surface characteristics are limited to the spectroscopic examination of the amount of oleate present at the fluorite surface. Our analytical tools did not allow us, at the present time, to detect the distribution and size of organic species (heterogeneities) at the surface of fluorite. In agreement with our previous experimental data,24,25,33 only a small effect of drop size was observed on the advancing contact angle (see Figure 2). The advancing contact angle increased 2-6° for a range of drop base diameters from 1-2 to 6.5-8 mm. Although both surface heterogeneity and roughness may affect the contact angle changes for varying drop size,33,34 the former is believed to be the major factor in our systems. The fluorite crystals used in our experiments had surface roughness features, the height of which varied from 100 to 500 Å, as determined independently by atomic force microscopy. A change in contact angle with drop size was systematically analyzed in previous contributions.33-39 It is now accepted that some of the three-phase systems can be described by the modified Young’s equation including the line-tension term:40-42

γSV - γSL ) γLV cos θ +

γSLV r

(3)

where γSV, γSL, and γLV are the interfacial tensions at the solid-vapor, solid-liquid, and liquid-vapor interfaces, respectively; γSLV is the line tension; and r is the drop (bubble) base radius. The modified Young’s equation predicts the linear correlation between the cosine of the contact angle and the reciprocal of the drop base radius as follows:

cos θ ) cos θ∞ -

γSLV γLVr

θ ) θ∞ for r f ∞

(4)

The above equations are only applicable to three-phase systems with homogeneous, rigid, smooth, flat, and stable solid surfaces and, thus, are not useful for the interpretation of the wetting characteristics of heterogeneous surfaces. In our particular case of a two-component heterogeneous surface, the hydrophilic fluorite is covered with hydrophobic oleate species. This heterogeneity, which at the present time has not been defined regarding the size and distribution of hydrophobic/hydrophilic sites, affected a contortion of the water drop edge on contact with the solid surface. The contortion of the three-phase contact line was observed in our systems but not examined analytically. (36) Drelich, J.; Miller, J. D. Colloids Surf. 1992, 69, 35. (37) Drelich, J.; Miller, J. D. Part. Sci. Technol. 1992, 10, 1. (38) Drelich, J.; Miller, J. D.; Hupka, J. J. Colloid Interface Sci. 1993, 155, 379. (39) Drelich, J.; Miller, J. D. J. Colloid Interface Sci. 1994, 164, 252. (40) Vesselovsky, W. S.; Pertzov, W. N. J. Phys. Chem. USSR 1936, 8, 5. (41) Boruvka, L.; Neumann, A. W. J. Chem. Phys. 1977, 66, 5464. (42) Pethica, B. A. J. Colloid Interface Sci. 1977, 62, 567.

Adsorbed Oleate Layers at a Fluorite Surface

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The shape of a drop base may differ significantly between two drops placed at different locations of the solid surface which has a nonuniform distribution and size of the heterogeneous features. This effect, which may be important for many nonideal systems, is neglected in our considerations because the contact angle data were reproducible ((1-3°) when measured at different locations on the fluorite surface, particularly for large drops (5-8 mm base diameter). They indicate that the heterogeneity pattern over the entire fluorite surface was rather uniform. Because, for almost all samples examined, contortion of the water drop base was observed, it is believed at submonolayer coverage that the chemisorbed carboxylate species are “uniformly” distributed as isolated aggregates (patches), probably consisting of at least several molecules per aggregate. Similar models for the adsorbed layers on mineral surfaces have already been analyzed in the literature by other authors.43-48 Of course, surface sites with individually chemisorbed molecules can not be ignored in such a fluorite surface model. Unfortunately, the overall picture for the oleate-fluorite surface structure could not be resolved on the basis of the experimental data presented in this contribution. Contortion of the three-phase contact line which appears for a liquid drop at heterogeneous surfaces may have an impact on the contact angle/drop size relationship.33,34 When solid surface heterogeneities propagate distortions of the circular drop base, such that the radii of curvature of the three-phase line are locally micron-sized or less, the linear excess energy (line tension) might be a significant factor in the thermodynamics of the sessiledrop behavior.37,49-52 However, such a situation does not explain the variation in contact angle with drop size in our system. A recent theoretical analysis of the effect of contortion of the three-phase contact line on the contact angle hysteresis for varying drop volume indicates that contact angles may change with decreasing drop size.33-35,53 This was explained to be due to a strong effect of energy barriers on contact angle which varies with changes in drop size. For a simplified interpretation of contact angle data for varying drop volumes at nonideal surfaces, the concept of pseudo-line tension was proposed by Good and Koo35 and adapted in the literature as follows:37,38

cos θ ) cos θ∞ -

γ*SLV γLVr

(5)

where γ*SLV is the pseudo-line tension and r is the drop base radius. Figure 3 illustrates the data from Figure 2 expressed as the cosine of the advancing contact angle and the reciprocal of the drop base radius. For most of the systems, there is a linear relationship between cos θ and 1/r over (43) Gaudin, A. M.; Fuerstenau, D. W. Trans. Am. Inst. Min., Metall. Pet. Eng. 1955, 202, 66. (44) Somasundaran, P.; Fuerstenau, D. W. J. Phys. Chem. 1966, 70, 90. (45) Goujon, G.; Cases, J. M.; Mutaftschiev, B. J. Colloid Interface Sci. 1976, 56, 587. (46) Levitz, P. J. Phys. Chem. 1986, 90, 1302. (47) Somasundaran, P.; Kunjappu, J. T.; Kumar, Ch. V.; Turro, N. J.; Barton, J. K. Langmuir 1989, 5, 215. (48) Lajtar, L.; Narkiewicz-Michalek, J.; Rudzinski, W.; Partyka, S. Langmuir 1994, 10, 3754. (49) Drelich, J.; Miller, J. D. Langmuir 1993, 9, 619. (50) Drelich, J. Ph.D. Dissertation, University of Utah, Salt Lake City, UT, 1993. (51) Drelich, J.; Miller, J. D.; Kumar, A.; Whitesides, G. M. Colloids Surf., A 1994, 93, 1. (52) Drelich, J.; Wilbur, J. L.; Miller, J. D.; Whitesides, G. M. Langmuir 1996, 12, 1913. (53) Marmur, A. J. Colloid Interface Sci. 1994, 168, 40.

Figure 3. Advancing contact angle data from Figure 2 presented as cosine of the contact angle vs reciprocal of the drop base radius. Numbers indicate the adsorption density of oleate at the fluorite surface in micromoles per square meter.

Figure 4. Pseudo-line tension variation with increasing adsorption density of oleate at a fluorite surface. Markers indicate the standard error associated with the calculated pseudo-line tension values.

the range of drop sizes examined. There are a few contact angle data for large drops (drop base diameter, D > 5.5-6 mm) at oleate adsorption densities of 2.5 and 4.4 µmol/m2 which deviate from the linear dependence. The pseudo-line tension values calculated from the linear cos θ vs 1/r relationship are presented in Figure 4.54 There is a significant change in the pseudo-line tension value with increasing adsorption density of oleate, from about 1 µJ/m to 6 µJ/m (based on average values). A maximum pseudo-line tension value is located between adsorption densities of 2.5 and 4 µmol/m2. The pseudoline tension value approaches “zero”55 for homogeneous states, i.e., a clean fluorite surface and a well-organized oleate monolayer (Figure 4). Note that a similar pseudoline tension relationship was obtained for methylated quartz plates when contact angle measurements were performed with the dynamic captive-bubble technique.36,50 Receding Contact Angle/Drop Size Relationship for Water Drops. Also, the receding contact angles were measured for varying water drop size and the results are (54) The contact angle data which deviated significantly from the linear cos θ vs 1/r relationship were eliminated from the calculation of pseudo-line tension values. The pseudo-line tension values were calculated using a linear regression analysis. The coefficient of determination for our systems was found to be R2 ) 0.5-0.8, indicating a poor linear association between cos θ and 1/r, and this accounts for the large standard errors for the pseudo-line tension values (Figure 4). (55) In a more detailed analysis of this phenomenon it should be said that the pseudo-line tension value approaches a line tension value. The line tension value is expected to be at least two orders of magnitude smaller than the pseudo-line tension values reported in this contribution. For more details on the line tension phenomenon, see refs 37-39, 42, and 56-60. (56) Drelich, J. Colloids Surf., A in press. (57) Ivanov, I. B.; Toshev, B. V.; Radoev, B. P. In Wetting, Spreading and Adhesion; Padday, J. F., Ed.; Academic Press: London, 1978; pp 37-112. (58) Toshev, B. V.; Platikanov, D.; Scheludko, A. Langmuir 1988, 4, 489. (59) Scheludko, A. D. J. Colloid Interface Sci. 1985, 104, 471. (60) Exerova, D.; Kashchiev, D.; Platikanov, D.; Toshev, B. V. Adv. Colloid Interface Sci. 1994, 49, 303.

1350 Langmuir, Vol. 13, No. 5, 1997

Figure 5. Receding contact angle data for water drops at a fluorite surface with different levels of oleate adsorption. Numbers indicate the adsorption density for oleate at the fluorite surface in micromoles per square meter.

presented in Figure 5. There are two distinctly different contact angle/drop size relationships. When the adsorption density of oleate at the fluorite surface was less than 4.5 µmol/m2, there was only a small change in the receding contact angle (0-4°) with drop size and the receding contact angle eventually increased with increasing drop base diameter (Figure 5). The receding contact angle decreased 30-70° with a decrease in drop base diameter from 6.5-7.5 to 1-3 mm when the adsorption density of oleate at the fluorite surface reached values which are close to that of a transferred Langmuir-Blodgett monolayer (6.2 µmol/m2).20 It is believed that hydrophilic sites of small dimensions act as energy barriers, strongly hold the receding water, and also induce a significant and irregular distortion of the drop base. The corrugation of the three-phase contact line and the contortion of the drop surface were enlarged compared to those observed for the advancing contact angles. This is because hydrophilic sites present much deeper energy barriers to overcome for receding water than do hydrophobic sites for advancing water. It was observed for small adsorption densities, 1.3 µmol/ m2 and less, that the receding contact angle always corresponds to that for a clean fluorite surface, about 0°, no matter how big the water drop was. In this regard, the formation of a stable water film at a slightly contaminated fluorite surface is still possible and flotation of fluorite particles will not occur. Only at increased levels of adsorption density (2.2 µmol/m2 and more, in examined systems) was the receding contact angle found to be greater than zero (Figure 5). As long as the adsorption density was less than 4.5 µmol/m2, little change in the receding contact angle (24°) with drop size was observed (Figure 5). The effect of drop size on receding contact angle was comparable to that observed for the advancing contact angle. This indicates that in both cases, for receding and advancing conditions, the contortion of the three-phase contact line would occur to a similar extent. However, it should be remembered that the fractional areas of the hydrophilic and hydrophobic sites in the vicinity of the receding water edge always differ from that for the advancing water edge, at heterogeneous surfaces. As is generally known, the advancing contact angle is more sensitive to hydrophobic sites whereas the receding contact angle is more affected by the hydrophilic part of the heterogeneous surface. When the adsorption density of oleate at the fluorite surface approached the monolayer adsorption density, or exceeded it, the receding contact angle decreased 30-70° with decreasing drop size, starting from a certain critical drop size (Figure 5). Only strong hydrophilic sites (or mechanical barriers33,34) at the solid surface could promote such receding contact angle/drop size relationships as reported in Figure 5 for adsorption densities of 6.0, 7.4,

Drelich et al.

Figure 6. Contact angle hysteresis for water drops (6-7 mm in drop base diameter) at a oleate-fluorite surface as a function of adsorption density of oleate at the fluorite surface.

and 9.3 µmol/m2. When the monolayer is incomplete, there are small uncovered areas of the fluorite surface with hydrophilic properties. Also, at the submonolayer level the excess oleate begins to form the next layer(s) (reverse hemimicelle, admicelle, etc.), which has been shown spectroscopically11,12,15,19 to consist of calcium dioleate, as typically would be prepared by precipitation from solution. This surface precipitate has a reduced level of hydrophobicity, and the hydrophilic characteristics of exposed head groups result in the interaction with water through hydrogen bonding and act as energy barriers against the moving water drop edge. Contact Angle Hysteresis. As presented in this and previous contributions,33-35 the effect of drop size on contact angle can be significant and any contact angle measurements with the sessile-drop and captive-bubble techniques should be well specified with regard to drop (bubble) size. In this contribution, contact angle hysteresis is reported for a drop base diameter from 6 to 8 mm, the value which is close to the upper limit of drop size analyzed in this study. The contact angles remained constant in this range of drop size or changed by only 1-3°. Of course, as is clear from Figures 2 and 5, a correlation between the contact angle hysteresis and adsorption density will be different for small drops (1-3 mm drop base diameter) than for large drops (6-8 mm drop base diameter) mainly due to a difference in the receding contact angle. An analysis of contact angle hysteresis for small drops may lead to incorrect conclusions. Even a small number of strongly hydrophilic sites at the solid surface may cause a large hysteresis in contact angle, particularly for small drops. Already this phenomenon was mentioned in the previous sections. It was observed in our laboratory that contact angles for liquid drops at heterogeneous surfaces are poorly reproduced for small drops. For example, in this study, the receding contact angles were very reproducible ((1-3°) for large drops (6-8 mm base diameter) whereas the reproducibility decreased to (3-6° for small drops (1-3 mm base diameter) when contact angle measurements were repeated at different sites of the fluorite crystal. In this regard, the analysis of contact angle hysteresis is based on the more reproducible contact angle data for large drops (6-8 mm base diameter). The advancing and receding contact angles and contact angle hysteresis with respect to the adsorption density of oleate at a fluorite surface are presented in Figure 6. As expected, the contact angle hysteresis is smallest for those systems approaching a homogeneous state, i.e. clean fluorite or uniform oleate monolayer. Note that the advancing and receding contact angles for water drops at a clean fluorite surface were found to be 3-5° and 0°, respectively. An analysis of the experimental contact angle data for the 6-8 mm drop base diameter indicates that the maximum contact angle hysteresis (about 60°) appears

Adsorbed Oleate Layers at a Fluorite Surface

for an oleate adsorption density of about 4 µmol/m2 (between 3.5 and 4.5 µmol/m2). This means that adsorbed oleate creates the most heterogeneous state when the adsorption density reaches a value from 3.5 to 4.5 µmol/ m2. This finding is in close agreement with our pseudoline tension data from Figure 4, which suggest that the most heterogeneous surface is that with an oleate adsorption density of 2.5-4.0 µmol/m2. It is also interesting to recognize that a similar contact angle hysteresis (5560°) appeared for the oleate adsorption density of 9.8 µmol/ m2. If the value of 6.2 µmol/m2 is accepted as the adsorption density of a well-packed monolayer, it follows that the value of 9.8 µmol/m2 corresponds to the adsorption density of 3.6 µmol/m2 for the second layer. This value is again in the range of 3.5-4.5 µmol/m2, which we attributed to the most heterogeneous structure of the oleate-fluorite system for the first chemisorbed layer. Unfortunately, no other systems with adsorption density larger than 9.8 µmol/m2 were analyzed in this study and it could not be resolved if more heterogeneous two-component surfaces could be created by oleate species at fluorite surface(s). On the other hand, it should be mentioned that although the contact angle hysteresis was found to be similar for both states with adsorption densities of about 4 and 10 µmol/m2, the advancing and receding contact angles were quite different (Figure 6). The advancing and receding contact angles were 25-30° larger for 9.8 µmol/m2 than those for 4.4 µmol/m2. This should not be surprising because the wetting properties of fluorite and carboxylic groups,61 both serving as hydrophilic sites (fluorite for an adsorption density of 4.4 µmol/m2 and carboxylate groups for an adsorption density of 9.8 µmol/m2) could differ. Also, the distribution and size of hydrophilic sites could differ for these two cases. In this regard, the agreement between contact angle hysteresis for both systems under consideration may be a coincidence. This aspect should receive more attention in future research. Comparison with Stearate Layers. Another important observation with regard to the advancing contact angles was made in this study. It was found that the advancing contact angle data for large water drops (drop base diameter between 6 and 8 mm) are essentially the same for an equivalent level of adsorption of oleate and stearate at a fluorite surface (Figure 7, the experimental data for stearate layers were presented in our previous contributions19,24,25). Similar advancing contact angles suggest that the distribution of organic species and orientation of the hydrocarbon chain at fluorite-air and fluorite-water interfaces, during the contact angle measurements, are similar in both systems. For example, it was found for adsorbed stearate layers at a fluorite surface that the adsorption density from about 1 × 10-10 to 8 × 10-10 mol/cm2 does not have any effect on the molecular orientation and that the hydrocarbon chain of the stearate is oriented 21-23° from the surface normal.19,62 A similar scenario regarding the effect of adsorption density on hydrocarbon chain (or its part) orientation is thus expected for oleate films. (61) We speculate here that the second layer(s) (reverse hemimicelle, admicelle, etc.) is physically adsorbed to the first monolayer through hydrocarbon chain association with carboxylic groups oriented into the environment. (62) Jang, W.-H.; Miller, J. D. J. Phys. Chem. 1995, 99, 10272.

Langmuir, Vol. 13, No. 5, 1997 1351

Figure 7. Advancing contact angles for water drops (6-7 mm in drop base diameter) on a carboxylate-fluorite surface as a function of adsorption density for the case of oleate and stearate surfactants.

Summary and Conclusions Molecular layers of oleate at a fluorite crystal surface with variable adsorption density were formed in alkaline aqueous solutions of sodium oleate. These organic films served in this study as model surfaces with varying surface heterogeneity. The effect of fluorite surface heterogeneity, as established by the extent of oleate adsorption, on contact angle is demonstrated. It is shown that both the contact angle hysteresis and contact angle/drop size relationship depend on the degree of deviation of the adsorbed layer structure from that of a well-organized monolayer. Experimental data support our previous position33,34 that it is of particular importance to examine both the advancing and receding contact angles with varying drop size whenever the sessile-drop technique (or captive-bubble technique as well) is used to describe the quality of solid surfaces, including those prepared by adsorption of organic molecules from aqueous solutions. Although it seems that the distribution of the oleate over the entire fluorite surface is quite uniform, the contact angle data suggest that oleate species adsorbed may form aggregates (patches) during the formation of both the first and second layer. First, a contortion of the three-phase contact line was observed during contact angle measurements. Second, the contact angle hysteresis and pseudoline tension value changed with varying adsorption density. The most heterogeneous oleate-fluorite surface was created when the adsorption density of oleate reached a value from 3.5 to 4.5 µmol/m2 (56-73% of a monolayer), under which condition the contact angle hysteresis was as much as 60°, and the pseudo-line tension was found to be about 6 µJ/m. Both the contact angle hysteresis and pseudo-line tension decreased significantly (contact angle hysteresis decreased to 10-12°, and pseudo-line tension decreased to about 2 µJ/m, for the fluorite surface with about 97% of an oleate monolayer) when the first chemisorbed oleate layer approached a monolayer structure. Acknowledgment. This work was financially supported by the DOE Basic Sciences Division, Grant No. DE-FG-03-93ER14315, and by the NSF, Grant No. CTS9215421, which is gratefully appreciated. LA9600107