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Observations of Capillary Forces between Fluorocarbon Surfaces in Vapors of Various Liquids Satomi Ohnishi* and Vassili V. Yaminsky Department of Applied Mathematics, Research School of Physical Sciences & Engineering, Australian National University, Canberra, A.C.T. 0200, Australia, and National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, 305-8565, Japan Received July 9, 2001. In Final Form: May 10, 2002 Forces between the fluorocarbon monolayer surfaces were measured in the process of vapor saturation with the interfacial gauge. In vapors of ethanol or chloroform, for both liquids contact angles to the surface are finite (51° and 65°, respectively), the forces on approach showed long-range attraction, of which the range increased with time. These force profiles agree with the theory of capillary bridging mainly by constant volume meniscus. In the vapor of perfluorohexane, force profiles of a similar type as in the vapors of ethanol and chloroform were observed at the beginning of exposure to the vapor, while later the interaction changed to that for the meniscus in equilibrium with the vapor. After exposure of the surfaces to the vapor for more than 1 h and separating apart, discontinuous curves with an abrupt jump-in at 25 nm were observed on the following approach. Since perfluorohexane wets the fluorocarbon surface, the condensate spreads over the surfaces after breaking the meniscus. The force discontinuity is explained by the coalescence of two wetting films of perfluorohexane with a thickness of 8 nm. By fitting the measured force curves with theoretical forms, the condensate volumes and the acting values of relative vapor pressure were estimated and changes with time were considered.
Introduction Capillary condensation is a well-known phenomenon observed in our daily life and influences many physical properties such as adhesion and friction. This is mainly because an attractive force is induced by formation of a condensate bridging the surfaces.1-3 Molecular and macroscopic aspects of the vapor adsorption and condensation enhanced in confined space were studied over decades by methods of chemical kinetics and thermodynamics. The most recent studies have been carried out with the surface force apparatus (SFA) using inorganic crystalline surfaces, typically mica, in vapors of liquids which fully wet the surfaces.4-11 In this study, we present the results of dynamic force measurements between the fluorocarbon surfaces with the interfacial gauge (IG) in vapors of several volatile organic liquids showing different wettability of the fluorocarbon surface. We utilized the well-characterized fluorocarbon surfaces that are “robust” and smooth Langmuir-Blodgett type monolayers chemically grafted to the hydroxylated glass substrate (with a mean rough* To whom correspondence should be addressed. E-mail:
[email protected]. Telephone: +61-2-6125-4692. Fax: +612-6125-0732. (1) Crassous, J.; Charlaix, E.; Gayvallet, H.; Loubet, J.-L. Langmuir 1993, 9, 1995. (2) Yaminsky, V. V. Langmuir 1997, 13, 2. (3) Blomberg, E.; Claesson, P. M.; Wa¨rnheim, T. Colloids Surf., A 1999, 159, 149. (4) Sabisky, E. S.; Anderson, C. H. Phys. Rev. 1973, A7, 790. (5) Fisher, L. R.; Israelachvili, J. N. J. Colloid Interface Sci. 1981, 80, 528. (6) Christenson, H. K. J. Colloid Interface Sci. 1988, 121, 170. Christenson, H. K. Phys. Rev. Lett. 1994, 73, 1821. (7) Crassous, J.; Charlaix, E.; Loubet, J.-L. Europhys. Lett. 1994, 28, 37. (8) Aveyard, R.; Clint, J. H.; Ness, D. J. Chem. Soc., Faraday Trans. 1997, 93, 4409. Aveyard, R.; Clint, J. H.; Paunov, V. N.; Ness, D. Phys. Chem. Chem. Phys. 1999, 1, 155. (9) Curry, J. E.; Christenson, H. K. Langmuir 1996, 12, 5729. (10) Kohonen, M. M.; Maeda, N.; Christenson, H. K. Phys. Rev. Lett. 1999, 82, 4667. (11) Qiao, Y.; Christenson, H. K. Phys. Rev. Lett. 1999, 83, 1371. Maeda, N.; Christenson, H. K. Colloids Surf., A 1999, 159, 135. Maeda, N.; Kohonen, M. M.; Christenson, H. K. Phys. Rev. E 1999 61, 7239. Kohonen, M. M.; Christenson, H. K. Langmuir 2000, 16, 7285.
ness of ∼0.14 nm).12,13 The preparation of the fluorocarbon monolayer and its chemical characterization and physical properties were reported previously.13,14 We consider the condensation kinetics in relation to the evolution of force profiles in complex situation of changing vapor saturation and the surface dynamics. The results of the force measurements are explained by the theory of capillary bridging. The volume of condensation and the relative vapor pressure are estimated by fitting measured force profiles with theoretical equations. We also briefly discuss the interplay of changing boundary conditions of vapor diffusion, liquid evaporation, and film drainage in relation to the dynamic conditions of the measurements. Materials and Methods Materials. The Pyrex glass rods (2 mm diameter) and plates were treated in a propane-oxygen flame and used as substrates to deposit fluorocarbon monolayer. The substrates for force measurements with the IG, glass spheres about 4 mm diameter were obtained by melting the end of a rod. The flame-polished glass plates were used for contact angle measurements by the Whilhelmy balance method. These fused glass surfaces (the molten spheres and plates) showed complete wetting by water, indicating hydroxylation and cleanness of the surfaces. Reagents for chemical modification of the surfaces, heptadecafluoro(1,1,2,2,tetrahydrodecyl)triethoxysilane (Gelest Inc.) and nitric acid, were used without further purification. Chloroform (ACS grade, Aldrich), ethanol (CSR Australia), and n-perfluorohaxane (Fluka AG, Bushs SG, Switzerland) were distilled under nitrogen. Phosphorus pentoxide (P2O5) (Fluka AG, Bushs SG, Switzerland) was used as a drying agent. The water was distilled and processed through a Millipore UHQ unit. Surface Preparation. The fluorocarbon monolayers were prepared as described previously.13,14 The pH of the subphase was adjusted to 2 with nitric acid, and a 3 mM chloroform solution of heptadecafluoro(1,1,2,2,-tetrahydrodecyl)triethoxysilane was spread over the surface. The fluorocarbon monolayer at the air(12) Wood, J.; Sharma, R. Langmuir 1994, 10, 2307. (13) Ohnishi, S.; Ishida, T.; Yaminsky, V. V.; Christenson, H. K. Langmuir 2000, 16, 2722. (14) Ohnishi, S.; Yaminsky, V. V.; Christenson, H. K. Langmuir 2000, 16, 8360.
10.1021/la011052k CCC: $22.00 © 2002 American Chemical Society Published on Web 06/21/2002
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Figure 1. Measured forces on approach in ethanol vapor (a), chloroform vapor (b), and perfluorohexane vapor (c, d) at various exposure time of the surfaces to the vapors. In (a), the points at the distance from 0 to 200 nm were taken at 1 point per second (1 p/s) at 12 and 15 min, 2 p/s at 30 min, 5 p/s at 80 min, and 10 p/s at 120 min. In (b), the points were taken at 5 p/s for 0-100 nm at 10 min, 10 p/s for 0-130 nm at 25 min, 10 p/s for 0-160 nm at 35 min, 15 p/s for 0-180 nm at 60 min, and 15 p/s for 0-250 nm at 120 min. In (c) and (d), the points were taken at 1 p/s at 1 min, 1 p/s at 5 min, 2 p/s at 10 min, 5 p/s at 20 min, and 10 p/s at 35-90 min. Measurements were continued over most of this time (period 1.5-3 min, distance amplitude 0.5-2 µm). water interface was maintained at 10 mN/m for 30 min and then transferred onto the fused glass substrate by retraction at constant speed (5 mm/min). The Langmuir-Blodgett fluorocarbon film thus transferred onto the glass was annealed in an atmosphere of dry nitrogen at 100 °C for 2 h after the deposition. Force Measurements. Forces were measured with the IG.15 This instrument permits the measurement of forces in function of separation between two smooth surfaces. One of the surfaces was connected to the rigid base of the instrument and the other was mounted on the free end of the piezoelectric cantilever spring (a bimorph) that acts as the force/spring deflection sensor. The base of the spring is connected to a motorized micro-translation stage allowing moving the surfaces with respect to each other to adjust their initial separation. A magnetic force transducer with a magnet attached to the cantilever allows fine separation control by bending the spring in a range of up to several micrometers.15 The spring deflection under the effects of attraction and repulsion and abrupt inward and outward “jumps” occurring at the onset of spring instabilities were monitored with a computer. Forces were calculated from the measured spring deflection and the known cantilever spring constant (258 N/m). The speed at which the surfaces approach and separate was varied from 3 to 35 nm/s. The distance of maximum separation was varied from 0.5 to 2 µm by changing the amplitude of triangle (15) Yaminsky, V. V.; Ninham, B. W.; Stewart, A. M. Langmuir 1996, 12, 836; Yaminsky, V.; Jones, C.; Yaminsky, F.; Ninham, B. W. Langmuir 1996, 12, 3531.
wave of the electric current passing through the coil of the magnetic transducer. Dynamic conditions for the measurements were varied to cover the entire range of the interaction observed between the surfaces by changing period of one measurement, amplitude, and the initial separation. The radii of curvature of the molten Pyrex glass spheres were measured with a microscope with a travelling reticule (estimated error (0.02 mm). The surfaces were installed in the chamber (100 cm3) of the IG with the drying agent. The force measurements were started immediately after the drying agent was replaced with the liquid and continued for 3 h. Contact angles were measured at room temperature by the Whilhelmy balance method.
Results The forces in air dried with P2O5 showed a van der Waals (vdW) attraction with a jump-into contact from 7 nm as we reported previously.14 After the P2O5 was replaced for a volatile organic liquid, we observed that the range of attractive forces immediately started increasing. Figure 1 shows how the force curves on approach change with time for each organic liquid vapor. In ethanol vapor the range of attraction successively increased with time and exceeded 500 nm in about 1 h, while after 2 h the force profile did not change much (Figure 1a). The way force profiles evolved with time was not sensitive, at least as long as the meniscus does not break,
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to either the contact duration or the time of separation. This was studied by changing period (from 1 to 3 min) with various combinations of surface speeds (3-25 nm/s) and maximum distances of separation (500-2000 nm). The observed force profiles did not critically depend on these dynamic measurement conditions. This suggests that the dominant factor that causes the range of attraction to increase is the rise of relative vapor pressure in the chamber. At the beginning of the measurements, the relative vapor pressure is low but increases and reaches condensation-evaporation equilibrium in about 2 h. Therefore the observed attraction can be attributed to capillary bridging forces changing with time, as can be explained by the condensate growth in the narrow gap between the surfaces. In chloroform vapor the attraction range initially increased with time faster than that in ethanol vapor, over the time up to 35 min (Figure 1b). However, at around 40-50 min, the increase in the range of the attraction slowed. Force curves measured at this time showed strong dependence on dynamic conditions such as the period of one run. That is, while in measurements with a period less than 1 min, the attraction was longer-range than that observed at 35 min, a shorter-range attraction than that at 35 min was observed with one measurement taking more than 2 min. At about 60 min after introducing chloroform vapor, the observed attraction range was shorter than that at 35 min (filled small circles in Figure 1b). It appears as if the force curves “temporarily” shifted toward smaller distances (to the left in the figure) at 60 min and then started shifting slowly toward larger distances again with time, up to 120 min. As with ethanol vapor, the force profile did not change much after 2 h. The pull-off forces measured on separation (Fs) were 0.32 mN for ethanol and 0.38 mN for chloroform. The values of interfacial energy γ calculated as γ ) Fs/2πR are 26 and 30 mN/m, respectively. The 2πR scaling generally holds for capillary forces at zero distances independent of the conditions.16,24 Both of the adhesion values are about 3 mN/m higher than the surface tension of the corresponding liquid. The critical surface tension of wetting of heptadecafluorocarbon monolayer has been reported as low as 4 mN/m.17 Since ethanol and chloroform have much higher surface tension than that and consequently show a large contact angle to the fluorocarbon surface, the solidsolid attraction across the liquid makes a significant contribution to the adhesion.18 To compare force profiles in the vapors of wetting and partly wetting liquids, we carried out force measurements in the vapor of n-perfluorohexane for which the contact angle to the fluorocarbon surface is less than 1°. The force under the vapor of n-perfluorohexane also changed with time. However, the evolution appeared to be more complicated than that under the vapor of the former two substances. At the beginning of the exposure, the attraction extending in the range with time was similar to that in ethanol and chloroform (Figure 1c), whereas after 35 min of exposure it suddenly changed to shorter-range attraction than that at 20 min (Figure 1d). The force curves in Figure 1d show a weak attraction at larger distances and a steeper attraction over the linear range at smaller distances. The linear part of the curve shows that the gradient of the attraction exceeds the spring constant. (16) Derjaguin, B. V.; Muller, V. M.; Toporov, Y. P. J. Colloid Interface Sci. 1975, 53, 314. (17) Johnson,R. E., Jr.; Dettre, R. H. Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; Chapter 1. (18) Christenson, H. K.; Yaminsky, V. V. Langmuir 1993, 9, 2448.
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After the change of the profile, the liner range gradually increased with time. It is obvious that the transition to the new interaction regime took place between 20 and 35 min. At 20 min, the force curve showed continuous increase in attraction (Figure 1c) when the period of one measurement was less than 2.5 min. However, a different curve was observed that showed a linear range with a slope corresponding to the spring constant from about 40 nm distance to the contact when the period of one measurement was more than 2.5 min (similar to the curve at 35 min in Figure 1d). In contrast to that, at 35 min and later, the force profiles were not affected by changing the period of a measurement and shifted with time again toward the larger distances. Since the time intervals between recorded points are constant (cf. the legends for Figure 1), the speed of the surface during the jump can be calculated. The results show that the jump-in behavior of the surfaces changes with time. In measurement at 35-45 min, the surfaces slightly accelerated by the attraction then decelerated at smaller distances, while at 55-70 min they kept accelerating down to the contact. After 1 h, the force profile practically stopped changing, yet another interaction pattern appeared on the approach by separating the surfaces far apart. When the separation distance exceeded 1.6 µm, discontinuous curves with abrupt jump-in at about 25 nm were observed regardless of the speed of approach (crosses in Figure 1d). It must be noted that the force profiles were similar to those at 70 min in measurements with the maximum separation of less than 1.6 µm. That clearly indicates that 1.6 µm is the critical distance at which the capillary bridge breaks. Since perfluorohexane wets the fluorocarbon surface, the condensate spreads into two films rather than stays in droplets. The jump-in distance of 25 nm is consistent with the condensation theory describing van der Waals coalescence of two wetting films of several nanometer thickness, as discussed in the following section.19 The evolution of the force profile reflects how the condensate between the surfaces grows with time. This is determined by a combination of several physical factors. The parameters responsible for the interaction are the surface tension of the liquid, contact angle to the surface, and the acting relative vapor pressure. In the following section, we analyze the force profiles and discuss the interaction in each liquid vapor. Discussion To estimate the static interaction between the surfaces during the jump, the viscous drag and the inertia should be taken into account.20 The drainage force Fd between two spheres is given by21,22
Fd )
3 πηR2 dD 2 D dt
( )
(1)
where η is the viscosity of the liquid (ethanol, 1.2 cP; chloroform, 0.58 cP; the viscosity of n-hexane,23 0.326 cP, was used as an estimate for n-perfluorohexane), R is the average (harmonic mean in the case of spheres24) radius (19) Derjarguin, B. V.; Churaev, N. V. J. Colloid Interface Sci. 1976, 54, 157. (20) Attard, P.; Schulz, J. C.; Rutland, M. W. Rev. Sci. Instrum. 1998, 69, 3853. (21) Steblin, V. N.; Shchukin, E. D.; Yaminskii, V. V.; Yaminskii, I. V. Kolloidn. Zh. 1991, 53, 684. (22) Chan, D. Y. C.; Horn, R. G. J. Chem. Phys. 1985, 83, 5311. (23) Handbook of Chemistry and Physics, 53rd ed.; Weast, R. C., Ed.; CRC Press: Cleaveland, OH, 1972. (24) Derjaguin, B. V. Kolloidn. Zh. 1934, 69, 155.
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Figure 2. Force curves of the total force acting between the surfaces estimated by subtracting inertia and drainage forces from the measured forces shown in Figure 1. The lines are theoretical curves calculated using eqs 2 and 3 with the experimental parameters.
of the surfaces, and dD/dt is the velocity at the distance D. The inertia was calculated from the acceleration data with the equation of motion, using the inertial mass (about 1 g) evaluated from the resonance frequency and the stiffness of the spring. Figure 2 shows the interaction force between the surfaces after introducing the corrections for Fd and inertia. To examine these force curves under the influence of the meniscus growth in the process of capillary condensation, theoretical profiles for capillary forces were compared with the experimentally obtained force profiles. The capillary bridging force with constant volume of condensation is approximated by14,25
F)
2πRγ cos θ πRD2 1+ V
(
)
(2)
where θ is the contact angle of the meniscus to the surface, γ is the surface tension of the liquid, and V is the volume of the liquid in meniscus bridging the two surfaces. The (25) Yaminsky, V. V. Colloids Surf., A 1999, 159, 181.
known surface tension and measured contact angle of the liquid to the fluorocarbon monolayer were used for the volume calculation by fitting the force curves. The capillary force of a meniscus in chemical equilibrium with the vapor (assuming constant pressure) is given by the Kelvin equation in the Derjaguin approximation as24,26
(
)
F D ) 2πγ cos θ 1 R 2rk cos θ
(3)
where rk is the Kelvin radius of curvature of the meniscus and the term 2rk cos θ is the equilibrium Kelvin height of the meniscus. As shown in Figure 2a, for the ethanol vapor (γ ) 22.8 mN/m, θ ) 51°), the theoretical force profiles with constant condensate volume are in good agreement with the experimental curves. The values of condensate volume estimated by fitting the experimental force curves with eq 2 are shown in the figure. No discontinuity was observed on the experimental curves. This can be explained if either (26) Evans, D. F.; Wennerstro¨m, H. The colloidal domain, 2nd ed.; Wiley-VCH: New York, 1999; Chapter 5.
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the two droplets left on breaking the meniscus do not evaporate by the time of the next approach or the meniscus simply does not break during the measurement. In the measurements with ethanol, continuity of the capillary bridge is maintained when the meniscus is sufficiently large on the scale of separation amplitude (the D < V1/3, from the condition of Rayleigh instability). In addition, even if the capillary bridge splits into droplets by separating the surfaces further apart, the force profiles would not be noticeably changed as long as volumes of the droplets do not change much. The evaporation time depends on volatility of the liquid, relative vapor pressure, and the radius of the droplets in relation to the condensate volume. According to eq 3, the droplets with the contact angle of 51° on each surface coalesce on approach at a distance that is much larger than the distance where the strength of capillary attraction becomes significant, compared to the experimental resolution. In any case, force curves with a measurement period within 3 min in ethanol vapor fit the equation that assumes constant volume of condensation. This shows that the volume of condensation of ethanol is practically constant during one measurement. Under the chloroform vapor good agreement between experimental results and theoretical curves for constant volume of condensation was observed up to 35 min (γ ) 27.1 mN/m, θ ) 65°) (Figure 2b). The range of the attraction in chloroform vapor increases faster than that in ethanol vapor. This is apparently because the saturation vapor pressure of chloroform (173 mmHg at 20 °C) is higher than that of ethanol (44 mmHg at 20 °C). However, after the condensate volume reaches about 5 × 10-11 cm3, the measured force curves start deviating from the theoretical force profile with constant volume. The main features of the force curves observed at 60 min are (1) the attraction range is shorter than at 35 min and (2) the force changes linearly with the distance. The slope of the linear part of the force curve decreases with time, and the attraction range accordingly increases (cf. 60 and 120 min). The observed behavior can be attributed to a transition to the capillary interaction at constant Laplace pressure, from that at constant volume of the meniscus. By fitting the slope in the force profile with the constant pressure equation (eq 3), the values of the Kelvin radius of the condensate rk as the fitting parameter for the profiles at 60 and 120 min were found to be 38 and 72 nm, respectively. Using the values of the apparent Kelvin radius rk, the relative vapor pressure p/ps can be estimated with the Kelvin equation
rk ) -
γυm kT ln(p/ps)
(4)
where T is the temperature, k is Boltzmann’s constant, and υm is the molar volume of the liquid. The thus estimated relative vapor pressure p/ps was about 0.977 at 60 min and 0.988 at 120 min. It appears that the transition from the capillary interaction at constant volume to that at constant pressure occurred as the relative vapor pressure increased closer to saturation. The changes in the force profile by change of period of one run observed between 35 and 60 min suggest an intermediate state of the capillary bridge. The chloroform condensate is practically maintained at constant volume when one measurement takes less than 1 min, but the condensate is maintained at constant pressure, in equilibrium with the surrounding vapor, when one measurement time exceeds 2 min. The interaction in this case changes between the two limiting modes by
changing the dynamic conditions. In the case of ethanol, on the other hand, the condensate volume remains constant even in the measurement for which the period is longer than 2 min. Because the vapor pressure of ethanol is one-third of that of chloroform, the transition to the capillary interaction at constant pressure should take place in a period longer than 3 min in ethanol vapor. Parts c and d of Figure 2 show variations of force curves under the vapor of n-perfluorohexane. The evolution of capillary forces in perfluorohexane vapor proceeded faster than in the vapor of the other two substances. This is consistent with the fact that n-perfluorohexane has the highest saturation vapor pressure (190 mmHg) among the three substances. In addition, unlike the other two liquids, perfluorohexane wets the fluorocarbon surface so that adsorbed vapor films are much thicker. This enables the condensate in the gap to grow by the drainage mechanism of suction of the liquid from the wetting film into the meniscus maintained at negative Laplace pressure. As is the case of the measurements in chloroform vapor, the surfaces exhibited long-range attraction of a meniscus of constant volume over times up to 20 min (γ ) 11.4 mN/m, θ = 0°) (Figure 2c). Subsequently, when the estimated volume of the condensation reached about 3 × 10-11 cm3, the force profiles started changing to that of linear attraction (Figure 2d). Force curves at 35 and 45 min clearly show an abrupt change of attraction at distances between 40 and 60 nm. The linear attraction observed at larger distances can be attributed to capillary force with constant pressure. By fitting these curves with eq 3, the estimated Kelvin radius of the condesate at 35 and 45 min is found to be 24 and 29 nm, which corresponds to the relative vapor pressure p/ps of 0.963 and 0.969. By use of the estimated Kelvin radii, the equilibrium condensate volume for the surfaces at contact is given by V ≈ 2πRrk2, according to the formula of elementary geometry for the volume surrounding the point of contact between two spheres. Theoretical curves for capillary interaction at constant volume of meniscus shown in Figure 2d were calculated using the condensate volume estimated in this way (V ) 2.9 × 10-11 cm3 at p/ps ) 0.963, V ) 4.2 × 10-11 cm3 at p/ps ) 0.969). It has been found that the experimental force profiles at 35 and 45 min agree with the theoretical curves for capillary interaction at constant volume at distances smaller than 50 nm. It should be emphasized that the condensate volume independently derived from the Kelvin radius estimated by fitting the pressure constant equation to the measured force profile at larger distances is consistent with the volume that follows as a fitting parameter for the force profile in the range of smaller distances. Thus, the force profiles at 35 and 45 min are self-consistent, and the constant volume regime conforms to the Kelvin condition. From these results, one can conclude that these force curves show a transition between the two modes of attraction. It is caused in this case not by changing relative vapor pressure but by changing separation. That is, capillary interaction at constant pressure observed at separations larger than 50 nm changes closer to that at constant volume at separations less than 50 nm. This implies that at the smaller distances the condensate maintains the volume rather than equilibrates with the surrounding vapor. This tendency is also observed in chloroform vapor. In Figure 2b, forces measured at 60 and 120 min deviate at distances around 50 nm from the linear dependence for the capillary force with constant pressure. The measured forces at around 50 nm are better described by the constant volume
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equation. The transition from the interaction at constant pressure to that at constant volume in chloroform vapor is less pronounced due to the lower saturation pressure and the large contact angle of chloroform. In perfluorohexane vapor, the transition is sharper than that in chloroform because of the higher intensity of the mass exchange according to the higher volatility and wettability. It occurs at smaller condensate volumes and lower vapor pressures than the one observed in chloroform vapor. At 55 and 70 min the force profiles agree with the capillary force at constant pressure. The estimated Kelvin radius has grown by that time to about 50 nm, showing that the relative vapor pressure p/ps has increased to 0.982. The liquid films in coexistence with the meniscus are accordingly thicker. The equilibration is more rapid when the relative vapor pressure is higher, and consequently capillary force profiles of constant pressure are observed. As mentioned in the Results section, for the 1 h and longer times of exposure to the perfluorohexane vapor, the capillary bridge breaks and spreads into the wetting films when the surfaces are separated to distances larger than 1.6 µm. With the estimated Kelvin radius at 70 min, the condensate volume at which the bridge breaks is estimated to be 1.3 × 10-10 cm3. By approximating the bridge by a cylinder, the calculated neck diameter of the bridge at the point when it breaks in the mode of interaction without changing the volume is less than 10 µm. In dynamic measurements the meniscus readily passes the critical Kelvin distance of chemical instability while it remains mechanically stable up to the distance of the Rayleigh instability. Only when the neck diameter of the meniscus thinning on separation becomes comparable to the width of the widening gap does the capillary bridge lose mechanical stability.27 After the capillary bridge breaks, coalescence of the two wetting films is theoretically expected at a surface-tosurface distance of about one-third of the thickness of the films.19 The instability that gives discontinuity of the force curve (at 90 min in Figure 1d) at about 25 nm can thus be ascribed to coalescence of perfluorohexane films of an average thickness of 8 nm. For the films to grow to such thickness,9,28 the relative vapor pressure of perfluorohexane according to the theory has to be 0.9998, assumimg a value of the Hamaker constant of the order of 10-20 J (precise value is not critical).29 Due to the high saturation vapor pressure and small contact angle, it should be easier to bring the vapor closer to saturation. We have demonstrated that the volume of condensation and relative vapor pressure can be reasonably estimated through dynamic measurement of capillary forces. Capillary condensation takes place when contact angle θ of the liquid to the surface is 0° e θ < 90°. Contact angle of water to the fluorocarbon surface is larger than 90°.14 Under the water vapor, no long-range attraction was observed because nonwetting liquid does not form capillary condensate. Figure 3 gives a summary of estimated values of volume of condensation and relative vapor pressure in vapors of ethanol, chloroform, and perfluorohexane. It is noted that the effective values of p/ps obtained on the basis of the experimental force curves increase consistently with time. Condensates of liquids having higher vapor pressure grow faster. The figure also shows that higher relative vapor pressure is attained faster. For completely wetting liquids (27) Dyson, D. C. Prog. Surf. Membr. Sci. 1978, 12, 479. (28) Beaglehole, D.; Christenson, H. K. J. Phys. Chem. 1992, 96, 3395. (29) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, CA, 1992.
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Figure 3. The estimated volume of condensation (a) and relative vapor pressure (b), as a function of time. The points represent data of ethanol (open circles), chloroform (filled diamonds), and perfluorohexane (open triangles). The data represented as light symbols (four triangles at 30-70 min and a filled diamond at 60 min) show the values of condensate volume estimated from Kelvin radii.
the rate is higher because the condensate growth is assisted by the film drainage. When the liquid has a low vapor pressure and large contact angle to the surface, force curves attributed to interaction at constant volume of the condensate were mainly observed. In contrast, in the vapor of a liquid that has high vapor pressure and a small contact angle to the surface, the measured force curves exhibited mainly profiles of capillary force with constant pressure. The capillary condensates tend to interact at constant volume under low relative vapor pressure while their volumes are small but interact at constant pressure in the vapor close to saturation. The transition from interaction at constant volume to that at constant pressure was observed with decreasing the speed while the relative vapor pressure was increasing. Conclusion In the vapor approaching saturation, capillary forces due to condensation of liquid between the surfaces were observed in successive measurements, for liquids that have contact angles 0° e θ < 90° with the surface. The volume of condensation and the relative vapor pressure were estimated by fitting the measured force curve with theoretical equations for the capillary attraction by a meniscus of constant volume and of constant Laplace
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pressure. We have investigated the complicated evolution of the force profiles with time and interpreted the results based on the theory of capillary condensation. We have demonstrated that surface force measurements with the interfacial gauge can be utilized to measure volumes of condensation, rates of condensate growth, critical coalescence distances and bridge elongation, and droplet evaporation times. Further measurement of capillary force and mathematical predictions regarding capillary bridging are currently underway.30-32 We consider implications of (30) Iwamatsu, M.; Horii, K. J. Colloid Interface Sci. 1996, 182, 400.
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these results in the context of hydrophobic force measurements separately.33 Acknowledgment. We thank H. K. Christenson for discussions and comments and acknowledge technical assistance from T. Sawkins and A. Hyde. LA011052K (31) Concus, P.; Finn, R. Phys. Fluids 1998, 10, 39. (32) Lowry, B. J. J. Colloid Interface Sci. 2000, 224, 28. (33) Yaminsky, V. V.; Ohnishi, S.; Ninham, B. W. Handbook of Surfaces and Interfaces of Materials; Nalwa, H. S., Ed.; Academic Press: New York, 2001; Vol. 4, Chapter 3.
