Langmuir 1996, 12, 5729-5735
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Adsorption, Wetting, and Capillary Condensation of Nonpolar Fluids in Mica Slits Joan E. Curry Department of Soil, Water and Environmental Science, University of Arizona, Tucson, Arizona 85721
Hugo K. Christenson* Department of Applied Mathematics, Research School of Physical Sciences, Australian National University, Canberra, ACT 0200, Australia Received June 3, 1996. In Final Form: August 12, 1996X The adsorption behavior of n-pentane and cyclohexane in mica slits at room temperature has been studied as a function of chemical potential and gap width with multiple-beam interferometry. The measured film thicknesses close to saturation for large slit widths (effectively isolated surfaces) range up to 7 nm with n-pentane (at a relative vapor pressure of 0.9996) and 3 nm with cyclohexane (at a relative vapor pressure of 0.995). The thickness of these adsorbed wetting films is slightly larger than that predicted by van der Waals theory. The difference may be accounted for by thermal fluctuations of the adsorbed liquid-vapor interface. At smaller slit widths a capillary condensation transition occurs as the slit fills up with liquid. The separation at which this occurs is in good agreement with a film-thickening mechanism due to van der Waals forces across the gap only for the thickest films (t g 6 nm). For thinner films the capillary condensation transition occurs at larger than expected slit widths, and the deviations are large for t e 3 nm. We speculate that these larger-than-expected condensation separations are related to a fluctuation-enhanced film thickness in this regime. The work demonstrates the utility of measurements in a system consisting of a single slit-pore, without the complications of polydispersity and connectivity of pore networks. The results show that vapor adsorption isotherms can be measured with multiple-beam interferometry, i.e., in the surface force apparatus.
Introduction The state and thickness of films adsorbed from vapor to solid surfaces depend on the forces between the substrate and the adsorbing species (adsorbate), as well as interactions between the adsorbate molecules.1-3 Above the roughening temperature any layering transitions found at low temperatures, in the vicinity of and below the triple point, are smoothed out as thermal fluctuations affect the interface between the adsorbed film and the vapor. Theory then predicts that the film thickness in the limit of large separations is given by the Lifshitz theory.4 This continuum description assumes that the film thickness is determined by the interaction between the solid substrate and vapor across a liquid-like film. It also ignores thermal fluctuations of the thickness of the adsorbed film. The force can be calculated from the dielectric properties of bulk matter. This disjoining pressure Πt can be expressed in terms of a Hamaker function A123(t), which in the general case is a function of film thickness t, as
Πt ) -
A123(t) 6πt3
(1)
The subscripts 1, 2, and 3 denote the solid substrate, the liquid in the film, and the vapor phase, respectively. In the limit of small t the Hamaker function becomes a * Author to whom correspondence should be addressed: fax, 616-249 0732; e-mail,
[email protected]. X Abstract published in Advance ACS Abstracts, October 15, 1996. (1) Steele, W. A. The Interaction of Gases with Solid Surfaces; Pergamon: Oxford, 1974. (2) Dash, J. G. Films on Solid Surfaces; Academic Press: New York, 1975. (3) Dietrich, S. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic: London, 1988, Vol. 12. (4) Dzyaloshinskii, I. E.; Lifshitz, E. M.; Pitaevskii, L. P. Adv. Phys. 1961, 10, 165.
S0743-7463(96)00538-0 CCC: $12.00
constant and the disjoining pressure should show a characteristic t-3 behavior. For most simple liquids on most solid substrates the Hamaker constant is negative and hence the disjoining pressure is positive. The disjoining pressure Πt may be related to the chemical potential µ or relative vapor pressure p/p0 of the adsorbing species by
Πt ) - µ(t,T) ) -
kT ln[p/p0] vm
(2)
where vm is the molecular volume of the adsorbate. A repulsive force across the adsorbed layer means that the film thickens without bounds as saturation (coexistence) is approached. This is wetting of the substrate by the adsorbed film, and it is equivalent to the condition of a zero contact angle of the liquid on the substrate. Many experiments have been carried out to test the validity of these theoretical concepts. Very good agreement with the Lifshitz theory has been found in the case of liquid helium films on CaF2 or SrF2 crystals5 and for liquid films of nitrogen and inert gases at low temperatures.6 At higher temperatures, however, the situation has often been less clear.6-8 There are often complications caused by roughness of the substrate and contamination of the surface, which lead to thicker than expected films. The need for scrupulous cleanliness and the very high accuracy required in the control of the chemical potential (temperature and pressure) have hampered quite a few experiments. Muscovite mica is an ideal substrate for vapor adsorption worksit is molecularly smooth and inert and has (5) Sabisky, E. S.; Anderson, C. H. Phys. Rev. 1973, A7, 790. (6) Panella, V.; Chiarello, R.; Krim, J. Phys. Rev. Lett. 1996, 76, 3606. (7) Blake, T. D. J. Chem. Soc., Faraday Trans. 1 1975, 71, 192. (8) Gee, M. L.; Healy, T. W.; White, L. R. J. Colloid Interface Sci. 1989, 131, 18.
© 1996 American Chemical Society
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been extensively studied in connnection with direct force measurements.9,10 A novel ellipsometric technique has recently allowed measurements of adsorption isotherms of nonpolar liquids on mica at room temperature, and the results were compared to the Lifshitz theory of van der Waals forces.11-13 It was found that theory underestimates the thickness of adsorbed films in the range of relative vapor pressures up to 0.99, but chemical potentials closer to coexistence were not studied. For monolayer and submonolayer coverage the adsorbed films were on average thinner than those predicted by the Lifshitz theory. Lifshitz theory predicts that the thickness of a cyclohexane film on mica at a relative vapor pressure of 0.974 should be about 1.2 nm, in contrast to the 1.8 nm which was found in the above study.13 This is in the vapor pressure regime of the largest deviations from theory. Such discrepancies between experiment and a continuum theory are perhaps not surprisingsat 1.2 nm the film is only 2 molecular diameters thick. For comparison, the measurements on He films referred to above gave agreement for films four molecular diameters or thicker.5 A possible complication in the case of mica is the presence of a thin (monomolecular?) film of adsorbed water on the air-cleaved mica surfaces used in the experiments.14 This means that the effective Hamaker constant would be slightly different from that calculated on the basis of dielectric data for mica alone. The presence of the adsorbed water film might actually lead to an effectively greater surface homogeneity and thus explain partly the linear shape of the isotherms at low pressure.13 It is unlikely, however, to be able to account for an increased adsorption at any separation. The surface force apparatus (SFA)15,16 is in principle capable of yielding information on the thickness of adsorbed films via the refractive index. By measuring the refractive index of the medium between the two mica surfaces and their separation, it is possible to deduce the adsorbed film thickness per surface. The main problem is one of accuracy, which is much less than that achievable by, for example, ellipsometry. On the other hand, the SFA permits the investigation of conditions between two surfaces, and in particular capillary condensation. Capillary condensation takes place when the bulk vapor-liquid transition is shifted by the proximity of two surfaces. A slit of width H will support a stable liquid phase at a lower chemical potential than in bulk. This is described classically by the Kelvin equation, which gives the equilibrium condition for the hypothetical case of no direct interactions (i.e., no vapor adsorption at an isolated solid surface). Then
γvm/r ) kT ln[p/p0]
(3)
where γ is the surface energy of the vapor-liquid interface (9) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1991. (10) Christenson, H. K. In Modern Approaches to Wettability: Theory and Applications; Schrader, M. E., Loeb, G., Eds.; Plenum Press: New York, 1992; p 29. (11) Beaglehole, D.; Radlinska, E. Z.; Ninham, B. W.; Christenson, H. K. Phys. Rev. Lett. 1991, 66, 2084. (12) Beaglehole, D.; Radlinska, E. Z.; Ninham, B. W.; Christenson, H. K. Langmuir 1991, 7, 1843. (13) Beaglehole, D.; Christenson, H. K. J. Phys. Chem. 1992, 96, 3395. (14) Christenson, H. K. J. Phys. Chem. 1993, 97, 12034. (15) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans.1 1978, 74, 975. (16) Parker, J. L.; Christenson, H. K.; Ninham, B. W. Rev. Sci. Instrum. 1989, 60, 3135.
Figure 1. Diagram of capillary condensation hysteresis, based on theoretical expectations and in semiquantitative accord with experimental findings for p/p0 close to unity. On approach the surfaces pass into the metastable vapor region when H ) 2r + 3t (thick solid line), where r is the Kelvin radius and t is the adsorbed film thickness. The dashed line is defined by twice the Kelvin radius; i.e., the effect of adsorption is neglected. Condensation occurs when H equals the spinodal curve, defined by eq 9 in the film-thickening model. On separation, liquid persists until capillary evaporation takes place at the equilibrium transition to vapor.
and r is the principal radius of curvature of the interface. In a slit,
1/r ) 2 cos θ/H
(4)
where θ is the contact angle of the liquid on the substrate. In all cases considered here θ ) 0 and cos θ ) 1. The Kelvin equation can thus be expressed without explicitly including a liquid-vapor interface.17 In a real case there is usually an adsorbed film of thickness t on the surfaces, and this modifies the equation by replacing H with H 3t.18 The validity of the Kelvin equation (eq 3) was studied by Fisher and Israelachvili19 using the SFA, and they found good agreement for radii of curvature larger than 4 nm. The actual formation of the condensate was not studied, nor the mechanism giving rise to the vapor-liquid transition. It is obvious that the transition will not occur in a very wide slit even arbitrarily close to coexistence, and some explicit mechanism that leads to the filling up of the slit must be invoked. There is thus a hysteresis associated with capillary condensation, even in a single slit-pore. On approach of two surfaces the vapor phase is metastable at separations below the equilibrium transition line given by the Kelvin equation with the correction for the adsorbed film (eqs 3 and 4, see Figure 1). The capillary condensation transition occurs at separations which define a spinodal for the gas-liquid transition.20 On separation of the surfaces the condensate (17) Evans, R.; Marini Bettolo Marconi, U.; Tarazona, P. J. Chem. Phys. 1986, 84, 2376. (18) Derjaguin, B. V.; Churaev, N. V. J. Colloid Interface Sci. 1976, 54, 157. (19) Fisher, L. R.; Israelachvili, J. N. J. Colloid Interface Sci. 1981, 80, 528. (20) Evans, R. In Capillarity Today, Lecture Notes in Physics; Petre´, G., Sanfeld, A., Eds.; Springer Verlag: Berlin, 1991; Vol. 386.
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or the liquid phase remains stable out to the equilibrium transition line, where capillary evaporation takes place. One of us has recently shown21 that for thick adsorbed films (t > 5 nm) the formation of a condensate is consistent with a film coalescence model originally advanced by Derjaguin and Churaev.18 According to this model, the capillary condensation transition involves the coalescence of adsorbed films through the action of van der Waals forces between the opposing surfaces and their adsorbed films. These experiments were carried out with tert-butyl alcohol as the condensing liquid, but no attempt was made to measure the actual vapor pressure or chemical potential of the tert-butyl alcohol. This is not necessary for a comparison with theory, as the film-thickening model predicts a relationship between t and H, without direct involvement of µ. Similar results have also been obtained by Crassous et al., although they concluded that the film thickening model was accurate down to film thicknesses of 2 nm.22 Earlier, it was shown how measurements of the equilibrium Kelvin radius of the condensate formed between mica surfaces could be used to provide an in situ measurement of the relative vapor pressure.23,24 It thus seemed natural to combine the two approaches by studying the adsorbed film thickness of vapors on mica surfaces as they are brought together. The separation at which capillary condensation occurs can be measured and the chemical potential (p/p0) determined by measuring the radius of curvature of the condensate with the surfaces in contact. In this manner all the relevant information is obtained in one measurement, and in what follows we present an investigation of the adsorption of n-pentane and cyclohexane on isolated surfaces and in slits. Experimental Section The measurements were performed using a modified21,23 Mark IV surface forces apparatus16 (see Figure 2) with the lower of the two surfaces attached to a very rigid support (spring constant k ≈ 3 × 105 N m-1). Coarse surface separation was controlled directly with a dc motor on the translation stage attached to the lower surface, and fine control was achieved with a piezoelectric device (total range 1.6 µm) attached to the upper surface. The mica (Mica Supplies Ltd., U.K.) which had been cleaved into molecularly flat sheets (2-6 µm thick) and then back silvered, was glued to cylindrically polished silica disks using an epoxy resin (Epon 1004, Shell Chemical Co.). The interferometer formed by the back-silvered surfaces transmits only certain, discrete wavelengths which are passed through a diffraction grating and observed as fringes of equal chromatic order at the exit slit of the spectrometer. A video camera (Dage MTI) was used to monitor the experiment in real time and to record the fringes for quantitative analysis after the experiment using a video micrometer (Colorado, model 305). The temperature of the measuring chamber was monitored with a thermistor, and the measurements were carried out in a temperature-controlled laboratory at 22 ( 0.2 °C. The apparatus was cleaned with ethanol and assembled in a laminar flow cabinet. A small dish filled with the drying agent phosphorus pentoxide was placed in the bottom of the chamber just before it was sealed. The chamber was then flushed with nitrogen for a minimum of 30 min before starting the experiment. The inward jump due to van der Waals forces and contact between the mica surfaces were measured in nitrogen, and the refractive index of the nitrogen medium was checked. After introduction of vapor (see below) at least 15 min was allowed for equilibration, and the surfaces were then brought toward each other slowly. At the condensation separation the surfaces were pulled together (21) Christenson, H. K. Phys. Rev. Lett. 1994, 73, 1821. (22) Crassous, J.; Charlaix, E.; Loubet, J.-L. Europhys. Lett. 1994, 28, 37. (23) Christenson, H. K.; Yaminsky, V. V. Langmuir 1993, 9, 2448. (24) Wanless, E. J.; Christenson, H. K. J. Chem. Phys. 1994, 101, 4260.
Figure 2. Schematic diagram of experimental setup. White light is passed through a number of heat filters and is allowed to impinge on two facing, back-silvered mica surfaces in a crossed-cylinder configuration. This interferometer transmits only discrete wavelengths which may be resolved in a spectrometer. The wavelengths provide information on the surface separation and the refractive index of the medium between the mica surfaces. The surface separation is controlled with a translation stage and a piezoelectric cylinder. The chamber may contain a reservoir of bulk material and a drying agent. For methods of vapor pressure control, see text. by the negative pressure in the liquid bridge (see Figure 3). They were left in contact until the annular condensate that forms around the contact area reached its maximum size, which was taken to be the point at which no further condensate growth was detected. The condensate size was monitored on the video screen as a break in the fringes due to a discontinuous change in the refractive index at the interface between the liquid condensate and the surrounding vapor. The size of the condensate is related to the curvature of the vapor-condensed liquid interface. Referring to Figure 3, the total curvature of the interface can be approximated as
1 1 1 1 ) + ≈ r r1 r2 r1
(5)
The relative vapor pressure can then be calculated from the Kelvin equation (eq 3). The surfaces were separated to a large distance (micrometers), the condensate was allowed to evaporate, and the approach process was repeated several times. When sufficient measurements were recorded, the surfaces were separated (≈100 µm) and the chamber was flushed with nitrogen to remove all traces of the vapor. The inward jump and contact in nitrogen were then examined to ensure that the system was free from contamination. The cycle was repeated for the next relative vapor pressure. The duration of each experiment varied from a few days to a week. The p/p0 was changed by three methods. Firstly, the amount of liquid injected into the chamber (volume ≈ 300 mL) can be
5732 Langmuir, Vol. 12, No. 23, 1996
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Figure 3. A schematic cross section of the surfaces (in the equivalent sphere-on-a-flat configuration) showing the surfaces far apart in vapor (top), and the formation of a bridge of condensed liquid at the capillary condensation separation Hc (middle), whereupon the surfaces are pulled into contact (bottom). The radius of curvature of the vapor-liquid interface of the capillary-condensed annulus is used to determine the relative vapor pressure. Typically, 20 e r2 e 50 µm and 10 e r1 e 500 nm, so that 1/r ≈ 1/r1. The diameter of the flattened contact zone a0 is of the order of 40 µm. variedsthis only gives very coarse control and cannot be used to get closer to saturation than p/p0 ≈ 0.90-0.95. Secondly, it was found that very slow absorption of vapor by the drying agent due to capillary condensation between the grains in the powder led to an effective p/p0 below saturation during the absorption process. In this manner, injection of an excess amount of liquid relative to that required to saturate the chamber would give a p/p0 in the range 0.95-0.999, which was constant for many hours. During this time several reproducible measurements as detailed above could be carried out. Finally, the temperature of the surfaces could be varied by removing one or more of the normally three heat-absorbing filters placed between the light source and the chamber (Figure 2). This would cause the effective relative vapor pressure at the surfaces to be decreased. Similarly, dimming the light source with all three heat filters in place enables relative vapor pressures very close to saturation (0.9996 for n-pentane) to be investigated). The upper limit in the relative vapor pressure is largely due to the very long times required for growth of an equilibrium condensate close to saturationsat the upper limit it is about 2 h. We emphasize that although the control of the vapor pressure is somewhat arbitrary, the actual vapor pressure is measured with great accuracy and reproducibility between successive measurements under exactly the same conditions. We conducted measurements for vapor pressures from zero to near saturation but were unable to quantitatively measure the vapor pressure in the chamber below ∼0.7 since the size of the condensate was too small to be accurately determined from the fringes. All experimental data on the inward jump separations, the refractive indices of the medium between the surfaces, and the size of the condensates were obtained directly from the video image. Errors in the measurements due to nonlinearity of the video camera were minimized by calibrating the dispersion of the video screen in the vicinity of the measurements. The pentane was HPLC grade from Sigma-Aldrich and the cyclohexane was analytical grade from BDH. Both were used without further purification.
Results The refractive index of the medium between the surfaces, n, is related to the thickness t of the films on the surfaces by the relation
t)
H(n - 1) 2(nf - 1)
(6)
Figure 4. Interferometrically determined film thickness t as a function of relative vapor pressure p/p0 for cyclohexane (open symbols) and n-pentane (filled symbols) adsorbed from vapor on mica at 22 °C. The different symbols are the results of separate experiments with different mica sheets. The solid line is the film thickness predicted by the Lifshitz theory. On this scale the difference between the predictions for pentane and cyclohexane is negligible.
where nf is the refractive index of the film. It is assumed that the thickness of the adsorbed film is equal on each surface and nf is equal to the refractive index of the bulk liquid. The values used were n ) 1.3575 for n-pentane and n ) 1.4266 for cyclohexane. Additionally, we assume that the system may be treated as a three-layer interferometer (mica-medium-mica), whereas, strictly, it is a five-layer system. Calculations by Clarkson25 using the multilayer matrix method26 have shown that for small surface separations (H < 100 nm) the three-layer approximation gives results that are within experimental error equal to those of the five-layer system. The equilibrium film thickness for each approach was taken as an average of several measurements for at least five different surface separations prior to capillary condensation. The measurements were confined to separations less than 100 nm. Distortion in the video image for larger separations, as the fringes get close to the edge of the field of view, makes those measurements unreliable. Also, the three-layer interferometer approximation becomes successively less accurate at separations greater than 100 nm. The standard deviation of the average film thicknesses was typically (0.5 nm, resulting from uncertainties in the measured refractive indices. The experimentally measured condensate size is converted to relative vapor pressure using the Kelvin equation (eq 3) with 2r ) H - 3t, where t is the experimentally determined film thickness per surface. Note, however, that inclusion of the correction term t is only important for p/p0 < 0.8, for which few measurements were made. The film thickness as a function of relative vapor pressure is shown on a linear scale in Figure 4, with the unfilled symbols the results of two series of measurements with cyclohexane and the filled symbols two experiments with n-pentane. The theoretical film thickness calculated from the Lifshitz theory (including retardation) is plotted as (25) Clarkson, M. T. Unpublished results. (26) Clarkson, M. T. J. Phys. 1989, D22, 475.
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under the same conditions was t ) 6.8 nm and p/p0 ) 0.9996), and the thickest cyclohexane film was 3.1 ( 0.3 nm at p/p0 ) 0.9949. The difference in the highest achieved vapor pressure reflects at least partly the slower condensate growth found with cyclohexane, due to its lower absolute vapor pressure at 22 °C. Also, at a given relative vapor pressure the equilibrium condensate is larger for cyclohexane than for n-pentane. The surfaces were not left in contact for more than a few hours, for fear of surface damage due to large compressive forces. This puts an effective upper limit to the size of condensates that may be investigated. The van der Waals expression for the disjoining pressure in a thin film given by eq 1 must be modified when there are two interacting films. As previously outlined, for the interaction of two film-covered surfaces18,21,24,27,28
-Π(H,t) ) Figure 5. Disjoining pressure Π as a function of film thickness t for cyclohexane films adsorbed on mica. The two sets of open symbols are the results of two separate series of measurements using interferometry to measure the film thickness (this work) and the filled circles are the results of ellipsometry measurements taken from ref 13. The solid line is the theoretically expected results assuming that the disjoining pressure is given by a retarded van der Waals interaction across the adsorbed film. The calculations were based on dielectric data for bulk cyclohexane and were taken from ref 13.
A123 A232 kT ln[p/p0] ) + 3 vm 6πt 6π(H - 2t)3 A123 6π(H - t)3
(7)
where A232 is the Hamaker constant for the material in the adsorbed film (subscript 2) interacting across vacuum or vapor (subscript 3). Effects of retardation are neglected, so that A123(t) ) A123, etc. The film loses its stability and coalesces when dΠ(H,t)/dt ) 0. This gives
A123 4
2t
A232 +
A123 4
(H - 2t)
-
2(H - t)4
)0
(8)
This may be solved analytically if the last term is neglected, to give
tc )
Figure 6. Disjoining pressure Π as a function of film thickness t for n-pentane films adsorbed on mica. The two sets of open symbols are results from interferometry, and the filled circles are the results of ellipsometry measurements.13 The solid line is the theoretically expected results from Lifshitz theory, based on dielectric data for bulk n-pentane.13
the solid line. The predictions for n-pentane and cyclohexane are virtually indistinguishable on the scale of the figure. The p/p0 values may be converted to disjoining pressure with eq 2, and the results are plotted as a function of film thickness t in Figures 5 (cyclohexane) and 6 (n-pentane). The different symbols are the results of two separate experiments with different mica sheets for each vapor. The results of recent ellipsometry studies by Beaglehole and Christenson13 are shown as filled circles, and the solid lines are the results expected from the Lifshitz theory.13 The thickest n-pentane film measured was 7.6 ( 0.5 nm at p/p0 ) 0.9996 (the average of three measurements
Hc 2 + (-2A232/A123)1/4
(9)
The condensation separation Hc as a function of the film thickness tc has been plotted in Figure 7. Note that no experimentally significant change in t with H could be detected and therefore t ≈ tc in this study. The n-pentane results (open points) show on average a slightly larger condensation separation than cyclohexane (filled points) for a given film thickness. The straight lines show the results of the complete solution to eq 8 for cyclohexane (upper line) and n-pentane (lower line). The approximate solution (eq 8) for cyclohexane is indicated by the dashed linesas can be seen it practically coincides with the full solution. The equilibrium transition, given by the Kelvin equation (eq 3 and eq 4), is shown as the curve on the left side. For the thickest n-pentane films (tc > 6 nm) agreement with van der Waals theory is good. As the film thickness decreases, the condensation separations are increasingly larger than theory predicts, and in the limit of very thin films (tc < 2 nm) the agreement is very poor. In all cases the jumps are within error much smaller than the equilibrium transition for a given film thickness. Discussion The adsorption isotherms for n-pentane and cyclohexane on mica show such a steeply increasing film thickness near saturation that a linear plot as in Figure 4 does not permit anything other than very general conclusions about (27) Forcada, M. L. J. Chem. Phys. 1993, 98, 639. (28) Iwamatsu, M.; Horii, K. J. Colloid Interface Sci., in press.
5734 Langmuir, Vol. 12, No. 23, 1996
Figure 7. The condensation separation (Hc) for cyclohexane (filled symbols) and n-pentane (open symbols) as a function of the critical film thickness (tc). The different symbols are the results of separate experiments. The condensation separation was measured from the recorded fringes of equal chromatic order. The film thickness was calculated from the measured refractive index of the medium between the surfaces according to eq 6. The straight lines are the predictions of the film coalescence model (full solution to eq 8) for cyclohexane (upper solid line) and n-pentane (lower solid line). The dashed line is the approximate solution (eq 9) for cyclohexane, and the curve near the y-axis is the expected equilibrium transition according to a modified Kelvin equation, eq 3 and eq 4. The condensation separation deviates most strongly from the expectations of the film coalescence model (eq 8) for small film thicknesses.
the film thicknesses near coexistence. Given the error in film thickness of (0.5 nm, the measured isotherms seem close to the theoretically expected results for film thicknesses below 2 nm. When the isotherms are converted to disjoining pressure and presented on double logarithmic plots, as in Figures 5 and 6, more useful comparisons may be made. Both the cyclohexane and the n-pentane isotherms show on average slightly larger adsorption than Lifshitz theory. There is good agreement with the ellipsometry results for cyclohexane, but not for n-pentane. The thicker films here measured with cyclohexane are undoubtedly a result of approaching saturation more closely, 0.995 as against 0.987 in ref 13. Because of the comparatively large error in the interferometry measurements, we cannot draw any conclusions about the behavior of the isotherms for average film thicknesses below 1 nm, which includes the submonolayer region where no measurements were made. The disagreement between the ellipsometry results for n-pentane and those presented here can only be attributed to the presence of contamination in the former measurements, as was discussed in ref 13. The maximum film thickness found here, 7 nm at 0.9996, is slightly larger than that predicted by the Lifshitz theory (5.5 nm). It is uncertain whether or not the difference in maximum film thickness measured with cyclohexane and n-pentane is the result of a significant difference in the wetting behavior of the two liquids on mica or merely a result of the factors discussed in the results section (i.e., slower growth of condensates for cyclohexane which precluded measurements at relative vapor pressures as high as for n-pentane. At a given p/p0, the measured film thicknesses are in fact within error equal up to p/p0 ≈ 0.995. The surface energy of n-pentane (16 mJ m-2) is lower than that of cyclohexane (25 mJ m-2) and this would of course favour wetting by n-pentane if the mica-liquid interactions
Curry and Christenson
were similar. Mica is a high-energy surface14 and this fact alone might favour wetting for both cyclohexane and n-pentane. However, the mica is undoubtedly covered with a monolayer of strongly adsorbed water and the shortrange interactions involved may not be simple. The question of the wetting of bulk water by simple hydrocarbons has been the subject of much uncertainty due to the subtle nature of the interactions involved. Nevertheless, it is clear from this work that the main reason such thick films have not been measured previously 11,13, 23 on mica was that the relative vapor pressure was not high enough. Note that in ref 24 a 4.4 ( 0.9 nm thick film of ethanol on mica was found at p/p0 ) 0.995. If p/p0 were maintained even closer than 0.995 to saturation it is very likely that even thicker films would be found with cyclohexane on mica. Very thick films are more easily detected with pentane because it is easier to accurately bring the vapor pressure sufficiently close to saturation. Both the cyclohexane and the n-pentane isotherms show slightly greater adsorption than that predicted by Lifshitz theory. In this regard they are similar not only to ellipsometrically determined isotherms of various vapors (excluding n-pentane discussed above) on mica but also to a great many isotherms on smooth substrates at room temperature, such as n-decane on alumina7 and alkanes on Aerosil.29 Mecke and Krim30 have recently shown how this feature may be explained by allowing for thermal fluctuations in the thickness of the adsorbed films. Such fluctuations are not accounted for by Lifshitz theory, but suppression of these fluctuations by the proximity of the solid surface leads to an increase in the average film thickness for liquid films of intermediate thickness (110 molecular layers). For thicker films the effect becomes unimportant due to the increasing distance between the liquid-vapor and the solid-liquid interface. Very good agreement30 was obtained between ellipsometrically determined adsorption isotherms of cyclohexane on mica11 using reasonable parameters (an interfacial width of 0.49 nm and a monolayer thickness of 0.545 nm). Inclusion of fluctuations is thus very likely to lead to better agreement in the present case as well. The maximum thickness of the adsorbed cyclohexane film is about 6 statistical layers, and of the pentane film up to about 15. The elongated shape and flexibility of the pentane molecule make this number uncertain - it would depend upon the molecular orientation in the adsorbed film and to what extent it differs from bulk. The surface force apparatus and similar devices constitute perhaps the most direct experimental tool for investigating phase behavior in confined geometries. In particular, most experimental information on the capillary condensation transition comes from such measurements. Previous studies of this transition have found good agreement with the film-thickening model for tert-butyl alcohol,21 but only for film thicknesses >5 nm. This result appears to hold for pentane as well, but for cyclohexane (where t e 3.1 nm) no agreement was found. The lack of agreement for thinner adsorbed films is not surprising in view of the underestimate of the film thickness that Lifshitz theory gives in this regime. The results obtained here for cyclohexane and n-pentane are very similar to the tert-butyl alcohol measurements from ref 21. If displayed on the same plot, no clear trend is evident. This is to be expected in view of the similarity of the Hamaker constants and the insensitivity of eq 8 to the precise values of these constants. This is easily seen (29) Schlangen, L. J. M.; Koopal, L. K.; Cohen Stuart, M. A.; Lyklema, J. Langmuir 1995, 11, 1705. (30) Mecke, K. R.: Krim, J. Phys. Rev. 1996, B53, 2073.
Adsorption in Mica Slits
from the approximate solution, eq 9. Similarly, the effects of retardation would not be very significant, since a more or less equal decrease in both A232 and A123 would be cancelled out. It is uncertain whether or not the slightly larger condensation separations found with n-pentane, on average, are significant. This is the opposite to the predictions of the model (see Figure 7) and more accurate measurements are needed to be able to answer this question. The only obvious difference between these results and those of ref 21 is in the magnitude of the maximum film thickness and condensation separation. Much larger film thicknesses were obtained with tert-butyl alcohol. The main reason is probably that the thickest films with tertbutyl alcohol were obtained by equilibrating with the light off and then rapidly measuring the film thickness during approach.21 This evidently made it possible to approach saturation more closely than here. Unfortunately, this strategy does not permit the actual p/p0 to be determined. We may speculate on the importance of fluctuations of the liquid-vapor interface for the capillary condensation transition. In the same manner as these fluctuations lead to thicker adsorbed films in the intermediate thickness regime, they would also cause the transition to occur for larger than expected surface separations. The film coalescence model does not take into account the filmthickening caused by thermal fluctuations or any additional effect on the transition above and beyond that caused by the larger average film thickness. This might at least partly account for the significantly greater than expected condensation separations for adsorbed films thinner than 5 or 6 nm. Above this film thickness it is
Langmuir, Vol. 12, No. 23, 1996 5735
expected that fluctuations would have only minor importance in thickening the adsorbed films.30 The results thus show on average slightly thicker films than Lifshitz theory predicts for both n-pentane and cyclohexane on mica at p/p0 g 0.97. This is consistent with the findings of many other experiments on liquidlike films adsorbed to smooth solids.7,8,29 The experimental error does not permit any conclusions for lower vapor pressures. The formation of capillary condensates between mica surfaces is well described by a film-thickening mechanism due to van der Waals forces that neglects fluctuations for the thickest films of n-pentane (t g 6 nm, at p/p0 g 0.999). For thinner films of both cyclohexane and n-pentane the condensation transition occurs at larger separations than the model predicts. The deviations are substantial for thin (t < 3 nm) adsorbed films. This is consistent with the results of a recent investigation of capillary condensation of tert-butyl alcohol in mica slits,21 where agreement was found for t > 5 nm, although the vapor pressure was not determined. Acknowledgment. This work has been supported in part by the USDOE under Grant No. DE-FG02-85ER6 0310. M. T. Clarkson is thanked for performing calculations to check our approximations. K. R. Mecke is thanked for calling our attention to ref 30 and for helpful correspondence, and M. Iwamatsu is thanked for sending a preprint of ref 28. LA960538B
