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Ind. Eng. Chem. Res. 2010, 49, 8532–8537
Improvement of Wetting Properties of Colloid Silica Binders Maria Morga,† Graz˙yna Para,*,† Zbigniew Adamczyk,† and Aleksander Karwin´ski‡ Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30-239 Cracow, Poland, and Foundry Research Institute, ul. Zakopian´ska 73, 30-418, Cracow, Poland
Wetting properties of colloid silica binders modified by addition of surfactants were investigated. Perfluorononanoic, an anionic surfactant, the nonionic fluorinated surfactant Zonyl FSO-100, the nonionic commercial surfactant Rokafenol, and their mixtures were studied. As a model silica binder, a 30% colloid dispersion of SiO2 in water was used, which was compared with the commercial binder Sizol, also based on colloid silica. The size of particles in these dispersions was determined by dynamic light scattering and by the atomic force microscopy imaging of particles deposited on mica. The zeta potential of particles was measured by microelectrophoresis. The dynamic surface tension and contact angles of binders on a paraffin substrate was determined by drop shape analysis. Our investigations showed that the Zonyl-FSO surfactant and its mixture with Rokafenol effectively reduced the dynamic contact angle to a value of 18°. Such low contact angles represent a significant improvement in comparison with commercial binders. 1. Introduction
2. Experimental Section
The interfacial tension of liquid/liquid or liquid/gas interfaces exerts a significant influence on the kinetics of many technological processes such as emulsification, emulsion coalescence and breakup, tertiary oil recovery from tar sands, extraction, detergency, froth flotation, etc. The interfacial tension also determines the wettability of solid substrates by liquids, which has a major practical significance. For example, an efficient wetting of wax patterns by ceramic slurries produced from silica binders is critical for the investment casting industry in order to reduce the number of faulty parts. This is especially vital in the case of fine pattern details, which are hardly wetted by unmodified binders. Therefore, in order to improve the wetting properties of binders and slurries, various surfactants are added, usually of a nonionic character. However, the presence of a colloid phase of large specific surface area may lead to a partial removal of surfactants due to adsorption, which results in less effective wetting. Despite the major significance of these problems, few systematic studies have been reported in the literature, based on quantitative measurements of surface tension and the contact angles of binders on various interfaces. In our previous work1 we have performed surface tension measurements for silica binders using two model surfactants, SDS (anionic type) and CTAB (cationic type). However, in that work, the contact angle of modified binders on solid substrates, which is a parameter of primary significance, was not determined.
2.1. Materials. In our experimental studies the following surfactants were used: (1) perfluorononanoic, CF3(CF2)7COOH, in 97% purity (Aldrich), average molecular weight 464, hereafter referred to as PFNA, an anionic surfactant; (2) Zonyl FSO-100 (C2H4O)x(CF2)yC2H5FO (Aldrich), average molecular weight 726, a nonionic surfactant; (3) Rokafenol RN8 (produced by the Rokita, Dolny Brzeg, Poland), which is a mixture of compounds synthesized by a nonylphenol/ethylene oxide polycondensation reaction with the number of (OCH2CH2) groups ranging from six to nine, average molecular weight 616, a nonionic surfactant. As binders, the following colloid silica based products were used: (1) Silicon IV oxide, 30% SiO2, a colloidal dispersion in water (Alfa Aesar), referred to as AA. Data given by the manufacturer: solid content in stock solution 50% [w/v], pH ) 10, density F ) 1.4 g/cm3; (2) Sizol, a commercial silica binder produced by the Rudniki factory, Poland. Data given by the manufacturer: solid content in stock solution 30% [w/v], pH ) 9.8, density F ) 1.4 g/cm3. Other materials: Parafilm “M”, Laboratory Film, American National Can, used as a model of a wax pattern substrate. 2.2. Experimental Methods and Procedures. Surface Tension and Contact Angle Measurements. The surface tension measurements were carried out using the drop shape analysis method shown schematically in Figure 1. Our apparatus exploits the video image processing system of a pendant drop for surface tension measurements. This method also enables nonstationary (dynamic) surface tension measurements of sur-
Therefore, the primary aim of this work was to develop efficient methods for a quantitative characterization of wetting properties of silica binders used commonly in the investment casting industry. These methods are based on precise measurements of surface tension and the dynamic contact angles using the drop shape analysis. In this way, an optimum composition and concentration range of surfactants can be specified, enabling the improvement of wetting properties of binders, which was another goal of our work. * To whom correspondence should be addressed. E-mail: ncpara@ cyf-kr.edu.pl. † Polish Academy of Sciences. ‡ Foundry Research Institute.
Figure 1. Experimental apparatus for simultaneous surface tension and contact angle measurements: (1) thermostatic chamber, (2) stalagmometer, (3) quartz capillary, (4) investigated solution, (5) camera, (6) computer, (7) light source.
10.1021/ie100772c 2010 American Chemical Society Published on Web 08/12/2010
Ind. Eng. Chem. Res., Vol. 49, No. 18, 2010
factants over hours time. This is vital in the case of a diluted surfactant solution, where the surface tension varies slowly with time due to diffusion of surfactants to the liquid/air interface. For more concentrated surfactant solutions, the ring method was also used to determine the surface tension, in order to confirm the precision of the drop shape method. On the other hand, the dynamic contact angles of binders on solid substrates were determined from the sessile drop image analysis. The main part of the apparatus, shown in Figure 1, was the quartz-glass stalagmometer (2) made of a quartz capillary (3) of an outer diameter of 0.628 cm, placed in a thermostatic chamber of regulated humidity to prevent drop evaporation during the measurement. The stalagmometer (2) was filled with the solution under investigation. The principle of the method consists of producing the drop and determining its shape on the basis of computer image analysis. Images of the drop were taken by a CCD video camera, equipped with a macro lens (Nikkor 55 mm). The images were digitized in real time by a Matrox Meteor frame grabber card installed on a personal computer. The image processing was performed in C++ using the commercial software library MilLite 4.0 by Matrox.2,3 The experimental drop shape was fitted using a numerical solution of Laplace’s equation, in which the value of surface tension γ was the only unknown parameter.
(
pA - pB ) -γ
1 1 + R1 R2
)
(1)
where pA - pB is the pressure difference inside and outside of the drop, γ is the surface tension, R1, R2 are the radii of curvature at point P. In order to determine contact angles, the stalagmometer was placed over the paraffin surface. A pendant drop detached from the capillary and formed a sessile drop at the paraffin surface, characterized by the advancing contact angle ϑ. The volume of sessile drops was constant, equal to 20 µL. The computer software allowed the determination of the contact angle every 5 s. In order to increase the precision of measurements, the whole setup was situated on an antivibration table. Our method enables the direct measurement of the dynamic surface tension of binders modified by surfactants and simultaneously the dynamic contact angle under the same conditions of temperature and humidity. In this work at least five kinetics measurements of contact angles were performed for each experimental condition. Discrepancy of contact angle measurements was (2°. The surface tension and contact angle measurements were carried out at 295 K. Particle Size and Zeta Potential Measurements. The size of colloidal particles was determined by the dynamic light scattering (DLS), using a Zetasizer Nano ZS Malvern instrument. From the autocorrelation function, the diffusion coefficient D of the silica particles can be calculated. With the value of D, the hydrodynamic radius of the particles RH can be calculated from the Einstein relationship:4,5 D)
kT 6πηRH
(2)
where k is the Boltzmann constant, T is the absolute temperature, η is the viscosity of the solution, and RH is hydrodynamic radius of particles. In the case of nearly spherical particles, the hydrodynamic radius corresponds to the geometrical radius of the particle a. On the other hand, the zeta potential ζ of silica particles was measured in the same device by exploiting the laser Doppler
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Figure 2. Micrograph of the Sizol binder particles deposited on mica modified by adsorption of PEI (AFM picture, scan size 5 × 5 µm).
velocimetry (LDV) principle. The principle of measurement is based on charged particles that are attracted to the oppositely charged electrode, and their velocity is measured and expressed per unit field strength as the electrophoretic mobility µe. With the mobility value, the zeta potential of the particles can be calculated using the Henry-Smoluchowski equation:6,7 ζ)
3η µ 2εF(κa) e
(3)
where ε is the dielectric constant of the silica dispersion, F(κa) is the function of the dimensionless κa parameter, κ-1 ) (εkT/ 8πe2I)1/2 is the double-layer thickness, e is the elementary charge, k is the Boltzmann constant, T is the absolute temperature, I ) 1/2(∑iciz2i ) is the ionic strength of the electrolyte, ci is the ion concentrations in the bulk, and zi is the ion valency. Additionally, the size distribution of silica particles in both binders was checked by topological studies performed with atomic force microscopy (AFM),8 using a Solver Pro device (NT-MDT Co., Moscow, Russia). In order to perform such measurements, silica particle monolayers on mica were produced under diffusion-controlled deposition, according to the procedure applied previously for colloids9-11 or polyelectrolytes.12,13 A dilute (10 ppm, pH ) 6.1 for AA and pH ) 6.1 for Sizol) solution of the binder was used in the deposition experiments. Additionally, the mica surface was modified by preadsorption of a cationic polyelectrolyte, poly(ethylene imine) (PEI),13 in order to convert its surface charge to positive, promoting irreversible attachment of negatively charged silica particles. The deposition time was 15-20 min, which resulted in a rather dilute silica particle monolayer, characterized by a coverage of about 5% (see Figures 2, 3). This allowed the determination of particle size distribution and the average particle size by measurement of the lateral cross-section of the deposited particles. For each binder, statistics from ca. 200 particles were taken. 3. Results and Discussion 3.1. Physicochemical Characteristics of Binders and Surfactants. One of the most important characteristics of the binders is the particle size, which was determined as mentioned via the DLS measurements of the particle diffusion coefficient. From these measurements, it was found that the average hydrodynamic radius of silica particles of the AA binder was
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Figure 3. Micrograph of the AA binder particles deposited on mica modified by adsorption of PEI (AFM picture, scan size 5 × 5 µm).
Figure 4. The dependence of the zeta potential ζ of the silica binders on the ionic strength, pH ) 9.5, T ) 293 K. The points denote experimental values obtained for (1) AA, and (2) Sizol.
Table 1. Physicochemical Characteristics of Silica Binders Used in This Work binder characteristics
SiO2, AA
Sizol
average size DLS [nm] average size AFM [nm] concentration [wt%] density [g/cm3] pH zeta potential [mV] pH ) 9.1; I ) 10-3M surface tension [mN/m] contact angle [deg] binder/paraffin
30 25 30 1.24 9.4 -43 72.4 109
24 17 30 1.22 9.8 -44 32 46
15 nm, which corresponds to an average particle size of 30 nm. In the case of Sizol, the primary particle size was significantly smaller, equal to 24 nm. From AFM measurements, the average particle size for the AA binder (see Figure 2) was determined to be 25 nm, and for the Sizol binder 17 nm (see Figure 3). These values agree approximately with the DLS measurements. The size of the silica particles and other physicochemical data are collected in Table 1. Another important characteristic of the silica suspension is the zeta potential, which is strictly correlated with the uncompensated surface charge of particles.6,7 With the zeta potential of suspensions, their stability can be quantitatively predicted, i.e., tendency to form aggregates,4,14 which usually diminishes the technological properties of a binder. The dependence of the zeta potential of the silica particles of both binders on the ionic strength (regulated by the addition of the NaCl salt) was determined by the microelecotrophoretic measurements as described above. The results of these measurements are plotted in a graphical form in Figure 4 for the ionic strength range of 10-4 to 10-2 M NaCl and a constant pH of 9.5. The zeta potential of both binders was strongly negative, varying between -47 and -40 mV for the above ionic strength range for AA and between -52 and -42 mV for the Sizol binder. Such relatively high negative values suggest that both binders were almost indefinitely stable for this range of ionic strength, which was confirmed by measuring their hydrodynamic radius over a period of a few months. Additionally, the surface tension and contact angles for these unmodified binders were measured. The 30% AA silica exhibited a surface tension of 72.4 mN m-1 (dyn cm-1), which practically coincides with the surface tension of triple distilled water used in our studies. This indicates that the AA silica dispersion was of a high purity, containing no organic contaminants. The contact angle of the AA silica drop on the paraffin
Figure 5. The dependence of the surface tension γ on the molar concentration of aqueous solutions of various surfactants: (1) PFNA (drop shape and the ring method); (2) Rokafenol N8; (3) Zonyl.
surface was 109° (see Table 1). This high value indicates poor wetting of hydrophobic surfaces, being, therefore, unacceptable for use in investment casting. On the other hand, the Sizol binder exhibited a surface tension of 32 mN m-1 (dyn cm-1), which indicates the presence of a significant amount of surfactants. Accordingly, the contact angle of the Sizol drop on the paraffin surface was 46° (see Table 1). Although this value is significantly lower than in the case of AA, it is still too high to promote an efficient wetting of the fine details of wax patterns used in investment casting. These facts indicate unequivocally that modifications of both silica suspensions, by addition of surfactants, are needed in order to produce binders suitable for practical applications. Therefore, surface tension measurements were performed for the surfactants used in this work with the aim to determine the concentration range suitable for practical application. In order to increase the precision of these measurements, the surface tension dependence on time was determined for each surfactant solution. Then, these results were extrapolated to infinite time, as reported in ref 3, which produced equilibrium values of the surface tension. The results of these measurements are shown in Figure 5 in the form of the dependence of the equilibrium surface tension
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Figure 6. The dependence of the surface tension on the molar concentration of PFNA in various solutions: (1) water; (2) AA 30%; (3) Sizol 30%.
on the surfactant concentration varied from 10-6 to 10-2 M. PFNA exhibited the lowest surface activity, since appreciable changes in the surface tension occurred at a surfactant concentration above 10-4 M whereas the Zonyl surfactant was already active at a concentration of about 10-5 M. This significant difference between both surfactants is caused by the ionic character of PFNA, whose adsorption at the liquid/air interface produces a significant electric field that opposes adsorption of other surfactant molecules.3 In the case of nonionic Zonyl surfactant, its adsorption at the liquid/air interface does not produce any electric field; hence, it is more efficient at a lower surfactant concentration range. This behavior was quantitatively described previously for other ionic surfactant systems.3 However, in the case of PFNA, the minimum surface tension was 17 mN m-1 (at a surfactant concentration of 3 × 10-3 M), which is noticeably lower than the minimum value for Zonyl, 25 mN m-1 (at a concentration of 7 × 10-5 M). For concentrations of surfactant higher than these critical values, respectively, the surface tension of these surfactants remains practically constant. The concentration at which this transition occurs is referred to in the literature as the critical micelle concentration (cmc).15,16 The appearance of cmc is typical to pure surfactants. In the case of surfactant mixtures, such as Rokafenol, the cmc cannot be precisely defined, see Figure 5. 3.2. Modifications of Silica Dispersions. As deduced from the surface tension results shown in Figure 5, the fluorinated surfactants studied in this work can be used to effectively reduce the surface tension of silica dispersions. In order to verify this hypothesis, the surface tension of these suspensions in the presence of surfactants and their mixtures was determined as a function of surfactant concentration. In Figure 6 the results obtained in the case of the pure PFNA surfactant are shown. As shown, the effectiveness of this surfactant was, in the case of the AA silica dispersion, even higher than in the case of pure water, for a PFNA concentration range of 10-5 to 10-3 M. Colloidal silica contains electrolyte (NaOH). An increase of electrolyte concentration leads to the reduction of the thickness and potential of the electric double layer at the interface that facilitates additional adsorption of surfactant ions.3 The minimum surface tension of an aqueous solution of PFNA was 17 mN/m and of the AA dispersion in the presence of PFNA was 25 mN/m (at a PFNA concentration of 3 × 10-3 M). In the case of the Sizol dispersion, the effect of the addition of PFNA was less pronounced. Nevertheless, the initial surface tension of pure Sizol, equal to 32 mN m-1,
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Figure 7. The dependence of the surface tension on the molar concentration of Zonyl FSO in various solutions: (1) water; (2) AA 30%; (3) Sizol 30%.
Figure 8. The dependence of the surface tension of AA 30% silica binder on the molar concentration of various surfactants: (1) PFNA; (2) Rokafenol N8; (3) Zonyl; (4) mixture (Zonyl FSO + Rokafenol).
was reduced by the addition of PFNA to the minimum value of 17 mN m-1 (at 3 × 10-3 M PFNA) see Figure 6. Analogous results obtained for Zonyl are shown in Figure 7. In this case, however, the dependence of the surface tension on surfactant concentration was practically the same for both pure water and the AA silica dispersion. Thus, in this case, adsorption of Zonyl on silica particles was practically negligible. Moreover, due to the nonionic nature of this surfactant, there was no influence of the electrolyte contained in colloidal silica. Also, the minimum surface tension of the AA/Zonyl system was practically the same as for pure water, i.e., 26 mN m-1 (at a Zonyl concentration of 7 × 10-5 M). In the case of the Sizol dispersion, the addition of Zonyl exerted a rather limited effect on its surface tension, which was reduced from 32 mN m-1 to a minimum value of 23 mN m-1 (at 3 × 10-5 M Zonyl). The influence of surfactant mixtures on the surface tension of the AA silica dispersions was also studied. The results shown in Figure 8 indicate that the best effect was observed for the Zonyl/Rokafenol mixture in a ratio of 1:1. However, the minimum surface tension of AA and Sizol dispersions was practically the same as that for pure Zonyl, i.e., 22 mN m-1. The surface tension measurements discussed above enable preselection of the most favorable conditions for promoting an efficient wetting of surfaces by silica dispersions. However, a
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Figure 9. The kinetics of contact angle changes of the silica binders on paraffin: (1) AA + Zonyl at a concentration of 1.1 × 10-4 M; (2) Sizol + Zonyl at a concentration of 1.1 × 10-4 M.
precise selection of these parameters becomes feasible only upon determining the contact angles of binder drops on the paraffin surface. In such wetting studies, the kinetics of the contact angle variations as a function of the time are of practical significance. Experiments of this type, involving silica binders, have not been reported previously in the literature. In Figure 9 the dependencies of the contact angle of the AA silica dispersion and the Sizol binder modified by addition of 1.1 × 10-4 M Zonyl on the time are plotted. The initial contact angles were relatively high, 85° for AA and 60° for Sizol. However, they decreased with the measurement time, attaining quasistationary values of 55° for AA solution and 30° for Sizol solution, for a time of 600 s. This effect can probably be explained by re-equilibration of the surfactant concentration distribution within the drop after its placement on the solid paraffin surface. The re-equilibration is realized by surfactant transport from the contact zone of the drop with the paraffin substrate to the liquid/air interface at the periphery of the drop. The relaxation time τ is of the order of a2/D (where a is the drop radius and D is the surfactant diffusion coefficient). For a ) 0.1 cm and D ) 5 × 10-6 cm2 s-1, τ ) 2000 s, which is comparable with the relaxation time observed in our experiments. A similar behavior was observed for other surfactants as well, with the equilibration time fairly independent of the surfactant type. Therefore, we present hereafter the contact angle data attained after 10 min equilibration time only. Accordingly, in Figure 10 the dependence of the equilibrium contact angle of the AA silica dispersion is plotted vs the surfactant concentration. For a low concentration range, 10-6 to 10-4 M, the Rokafenol surfactant most efficiently reduced the contact angle, to a limiting value of about 40°. For this concentration range, PFNA and Zonyl were less effective, probably because of their significant adsorption on the paraffin surface. However, the Zonyl surfactant at higher concentrations, exceeding 10-4 M, induced a more significant decrease in the contact angle than that of Rokafenol, down to a value of 30°. Interestingly, the mixture of Zonyl and Rokafenol was even more efficient, further reducing the contact angle to 18°, which practically means a complete wetting of the paraffin surface by the modified silica drop. Results of analogous measurements performed for the Sizol binder are shown in Figure 11. A significant reduction of the contact angle was induced by Zonyl and PFNA surfactants. In
Figure 10. The dependence of the contact angle of the AA silica binder (on paraffin) on the concentration of various surfactants: (1) PFNA; (2) Zonyl; (3) Rokafenol N8; (4) mixture (Zonyl + Rokafenol N8).
Figure 11. The dependence of the contact angle of Sizol (on paraffin) on the concentration of various surfactants: (1) PFNA; (2) Rokafenol N8; (3) Zonyl.
the case of PFNA, the contact angle as low as 23° was achieved for a relatively high surfactant concentration of 3 × 10-3 M. The contact angles, in the case of Zonyl at a concentration of 10-4 to 5 × 10-4 M, achieve about 20° lower values than that for PFNA. The minimum contact angle value was 15° at a Zonyl concentration of 10-3 M. Contact angles for Rokafenol solutions remain constant, at 44°. This value corresponds to a value of 40° achieved for AA/Rokafenol solution. Hence, these measurements proved unequivocally that the surfactants studied in our work and their mixtures can be used for the major improvement of wetting properties of both pure silica dispersion and a commercial colloid silica binder, used in investment casting. 4. Conclusions An efficient method for quantitative characterization of wetting properties of silica binders was developed, based on precise measurements of surface tension and the dynamic contact angles using drop shape analysis. In this way, an optimum composition and concentration range of surfactants was determined, resulting in significant improvement of the wetting properties of binders used in investment casting.
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Our investigations showed that the fluorinated nonionic surfactant Zonyl FSO and its mixture with Rokafenol effectively reduced the surface tension of colloid silica (AA) and the commercial silica binder to a low value of 20 mN m-1. Because of surfactant adsorption, the dynamic contact angle of binders on paraffin films was decreased, attaining a minimum value of 18° at a bulk surfactant concentration of about 10-3 M (0.07%). Such low contact angles represent a significant improvement in comparison with that of ordinary binders used commonly for producing casting forms in the investment casting industry. Acknowledgment This work was supported by the Polish Ministry of Science and Higher Education (MNiSzW) grant: POIG.01.01.02.-12028/09. Literature Cited (1) Adamczyk, Z.; Para, G.; Karwin´ski, A. Surface Tension of Surfactant Solutions in the Presence of Colloid Silica. Tenside, Surfactants, Deterg. 1998, 38, 261. (2) Para, G.; Jarek, E.; Warszyn´ski, P.; Adamczyk, Z. Effect of Electrolytes on Surface Tension of Ionic Surfactant Solution. Colloids Surf., A 2003, 222, 213. (3) Para, G.; Jarek, E.; Warszyn´ski, P. The Hofmeister Series Effect in Adsorption of Cationic Surfactants s Theoretical Description and Experimental Results. AdV. Colloid Interface Sci. 2006, 122, 39. (4) Adamczyk, Z. Particles at Interfaces, Interactions, Deposition, Structure; Elsevier, Academic Press: Amsterdam, 2006; pp 214-219. (5) Adamczyk, Z.; Sadlej, K.; Wajnryb, E.; Nattich, M.; Ekiel-Jez˙ewska, M. L.; Bławzdziewicz, J. Streaming Potential Studies of Colloid, Polyelectrolyte and Protein Deposition. AdV. Colloid Interface Sci. 2010, 153, 1.
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(6) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: London, 1981. (7) Delgado, A V.; Gonzales-Caballero, F.; Hunter, R. J.; Koopal, L. K.; Lyklema, J. Measurement and Interpretation of Electrokinetic Phenomena. J. Colloid Interface Sci. 2007, 309, 194. (8) Johnson, C. A.; Lenhoff, A. M. Adsorption of Charged Latex Particles on Mica Studied by Atomic Force Microscopy. J. Colloid Interface Sci. 1996, 179, 587. (9) Adamczyk, Z. Kinetics of Diffusion-Controlled Adsorption of Colloid Particles and Proteins. J. Colloid Interface Sci. 2000, 229, 477. (10) Adamczyk, Z.; Szyk, L. Kinetics of Irreversible Adsorption of Latex Particles under Diffusion-Controlled Transport. Langmuir 2000, 16, 5730. (11) Brouwer, E. A. M.; Kooij, E. S.; Wormaester, H.; Poelsema, B. Ionic Strength Dependent Kinetics of Nanocolloid Gold Deposition. Langmuir 2003, 19, 8102. (12) Adamczyk, Z.; Zembala, M.; Michna, A. Polyelectrolyte Adsorption Layers Studied by Streaming Potential and Particle Deposition. J. Colloid Interface Sci. 2006, 303, 353. (13) Adamczyk, Z.; Michna, A.; Szaraniec, M.; Bratek, A.; Barbasz, J. Characterization of Poly(ethylene imine) Layers on Mica by the Streaming Potential and Particle Deposition Methods. J. Colloid Interface Sci. 2007, 313, 86. (14) Elimelech, M.; Gregory, J.; Jia, X.; Williams, R. Particle Deposition and Aggregation: Measurement, Modelling and Simulation; ButterworthHeinemann: Oxford, U.K., 1995. (15) Adamson, A. W. Physical Chemistry of Surfaces; John Wiley and Sons, Inc.: New York, 1990. (16) Miller, C. A.; Neogi, P. Interfacial Phenomena; M. Dekker, Inc.: New York, 1985.
ReceiVed for reView April 14, 2010 ReVised manuscript receiVed July 21, 2010 Accepted July 24, 2010 IE100772C
