Langmuir 1995,11, 3075-3082
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Physisorption of Cyclohexane on a SiOdSi Substrate: Evidence of a Wetting Transition above the Triple Point Wolfgang H. Lawnik, Uta D. Goepel, Anja K. Klauk, and Gerhard H. Findenegg" Iwan-N. -Stranski-Institut fur Physikalische und Theoretische Chemie, Technische Universitat Berlin, Strasse des 17. Juni 112, 0-10623 Berlin, Germany Received March 17, 1995. I n Final Form: May 11, 1995@ The physisorption of cyclohexane vapor onto silicon wafers with grossly different oxide layer thicknesses 6 (25 and 570 nm) was studied in the temperature range 15-40 "C by ellipsometry. Isotherms of film thickness d exhibit an extended linear region up to a relative pressureplpo a 0.7, with a small and nearly temperature independent slope ad/a(p/po),indicating weak adsorbate-substrate interactions. Above plpo = 0.7 the isotherms show a pronounced temperature dependence and reveal a wetting transition with a wetting temperature Twnear 20 "C, i.e., ca. 14 K above the triple point of the adsorptive. Above T, the film thickness increases steeply,with values exceeding 20 nm near the saturation pressurepo, as expected for complete wetting. Below T, the film thickness reaches only a few monolayers atpo. In the temperature range just above T, a pronounced hysteresis is observed in pressure quenches near saturation, which is explained by temperature excursions on crossing the prewetting line. The multilayerregime ofthe isotherms above Twwas analyzed in terms of the Frenkel-Halsey-Hill (FHH)equation,ln(plp0)= -(a/kT)d-", where the exponent n is expected to have a value of 3 for nonretarded dispersion force interactions and for sufficiently large d. The present data for the range from above one monolayer up toplpo = 0.95 yield much lower values ( n = 1.65 f 0.2 and 1.0 f 0.2 for wafers with 6 = 25 nm and 570 nm, respectively). These low values of n are consistent with results of theoretical physisorption isotherms obtained by the BornGreen-Yvon theory when the interaction parameters are chosen in a way to reproduce the observed wetting transition. From these results it is concluded that the low values of n found in this study are characteristic for wetting systems just above the wetting transition.
1. Introduction Wetting films on solid surfaces have attracted much attention in the context ofwetting transitions, roughening, surface melting, and surface critical phenomena.l+ Physisorption measurements of vapors on smooth solid substrates provide an experimental access to the study of some of these phenomena. Reflection ellipsometry has been widely employed to determine film thickness isotherms of vapors with submonolayer resolution.6-12 In addition, quartz microbalance techniques13-15 and X-ray reflectivity15-17 have also been used successfully. Complete wetting of a substrate implies that a multilayer adsorbed film grows uniformly over the substrate, ~
Abstract published in Advance ACS Abstracts, J u l y 1, 1995. (1)Pandit, R.;Schick, M.; Wortis, M. Phys. Rev. B 1982,26,5112. (2) Sullivan, D. E.; Telo da Gama, M. M. In Fluid Interfacial Phenomena; Croxton, C. A., Ed.; Wiley: New York, 1986. (3)Dietrich, S.In Phase Transitionsand Critical Phenomena;Domb, C., Lebowitz, J., Eds.; Academic: London, 1988;Vol. 12. (4)Schick, M. In Liquides aux Interfaces;Les Houches 1988 Session XLVIII; Course 9;Charvolin, J., Joanny, J. F., Zinn-Justin, J., Eds.; North-Holland: Amsterdam, 1990. (5) Dash, J. G. In Solvay Conference on Surface Science; Springer Series in Surface Science; de Wette, F. W., Ed.; Springer: Berlin, 1988; Vol. 14. (6)Lawnik, W. H.; Findenegg, G. H. Ber. Bunsen-Ges. Phys. Chem. 1994,98,405. (7)Busscher, H.J.; Kip, G. A. M.; van Silfhout, A,; Arends, J. J. Colloid Interface Sci. 1986,114,307. Chibowski, E.;Holysz, L.; Kip, G. A. M.; van Silfhout, A.; Busscher, H. J . J.Colloid Interface Sci. 1989, 132,54. (8)Gee, M. L.; Healy, T. W.; White, L. R. J. Colloid Interface Sci. 1989,131, 18;1989,133,514;1990,140,450. (9)Volkmann, U.G.; Knorr, K Phys. Rev. B 1993,47,4011. (10)Nham, H. S.; Hess, G. B. Langmuir 1989,5,575.Hess, G.B. In Phase Transitions in Surface Films 2;NATO AS1 Ser., Ser. B 267; D a u b , H., Torzo, G., Lauter, H. J., Fain, S. C., Jr.,Eds.; Plenum: New York, 1991;p 357. (11)Beaglehole, D.; Christenson, H. K. J. Phys. Chem. 1992,96, 3395. Beaglehole, D. Langmuir 1992,8,1033. (12)Levinson, P.;Valignat, M.P.; Fraysse, N.; Cazabat, A. M.; Heslot, F. Thin Solid Films 1993,234, 482. Levinson, P.; Valignat, M. P.; Fraysse, N.; Cazabat, A. M. Colloids Surf. A 1994,85,127. (13)Cheng, E.;Mistura, G.; Lee, H. C.; Chan, M. H. W.; Cole, M. W.; Carraro, C.; Saam, W. F.; Toigo, F. Phys. Rev. Lett. 1993,70, 1854. @
either continuously or layer by layer, and its thickness d diverges as the vapor pressurep approaches the saturation pressure p o . Theories attribute this divergence to the asymptotic behavior of the adsorbate-substrate potential U,,(d) that accounts for the long-range van der Waals interactions between two volume elements ofthe adsorbate (a) and the substrate (s), and the corresponding interactions between volume elements of the bulk adsorbate, viz.,
The parameters C, and C,, contain the number densities of adsorbate and substrate and the pair interaction parameters cBBand caaof the pair potentials uij(r)= where u = 3 for nonretarded van der Waals interactions.18J9 Thermodynamic perturbation theory showsls that if the adsorbed film represents a slab df bulk liquid (or solid) of thickness d in contact with the substrate, its chemical potential p(d) is lower than the bulk chemical potential PO by an increment equal to U,,(d), viz.,
where a = (Cas- C,,) is a weakly temperature-dependent energy density. Complete wetting corresponds to Cas> C,,, i.e., an adhesive adsorbate-substrate energy exceeding the cohesive energy of the adsorbate. This case (a> 0) with u = 3 yields the Frenkel-Halsey-Hill (FHH) (14)Taborek, P.; Rutledge, J. E. Ber. Bunsen-Ges.Phys. Chem. 1994, 98,361;Physica B 1994,197,283. (15)Chiarello, R. P.; Krim, J.; Thompson, C. Surf. Sci. 1994,306, 359. (16)Tidswell, I. M.; Rabedeau, T. A.; Pershan, P. S.; Folkers, J. P.; Baker, M. V.; Whitesides, G. M. Phys. Rev. B 1991,44,10869. (17)Muller-Buschbaum, P.; Tolan, M.; Press, W. X-Ray Study of Wetting Behaviour of CC4 on SiflOO), preprint. (18)Steele, W. A. The Interaction of Gases with Solid Surfaces; Pereamon: Oxford. 1974. (99)Cheng, E.;Cole, M. W. Phys. Rev. B 1988,38,987;Langmuir 1989,5,616.
0743-746319512411-3075$09.00/0 1995 American Chemical Society
3076 Langmuir, Vol. 11, No. 8, 1995
equation when one expresses Ap(d)by the corresponding chemical potentials of the vapor in its ideal gas state, Ap = kT ln(plpo). Incomplete wetting means that the film thickness does not grow beyond some finite value, and droplets (or crystallites) of bulk adsorptive coexist with this film at the saturation pressure. This situation is generally found in systems with relatively weak adsorbate-substrate interactions, but also for strong substrates below the triple point temperature Tt of the Incomplete wetting of strong substrates below Tt is attributed to a structural mismatch between successivelayers of the solidlike film, as strong substrates may impose a higher packing density on the first layer, thus preventing epitaxial growth of the solid. Triple-point wetting, i.e., incomplete wetting at temperatures T < Ttand complete wetting of the substrate by the liquid adsorptive at T L Tt, is thus a signature of the structural incompatibility of thin solid films. Wetting transitions a t temperatures above Tthave been found only recently. In particular, for hydrogen films on rubidium13 and 4He films on cesium14 the so-called prewetting line has been found experimentally by physisorption measurements using a quartz microbalance technique. This prewetting line represents a continuation of a first-order wetting transition into the region of the undersaturated vapor and had been discovered in theoretical Monte Carlo20B21 simulations, and molecular dynamics22simulations long before this experimental verification. The present paper extends a preliminary study6 of the physisorption of several hydrocarbons on thermally oxidized silicon wafers, in which complete wetting had been found'at 30 "C for all liquids studied. However, the remarkably weak and nearly linear dependence of the film thickness on the relative pressure up to plpo 0.7 gave evidence of weak adsorbate-substrate interactions, indicating that some of these systems may have been close to a wetting transition at the experimental temperature. In order to test this possibility we have now studied one of these systems over a wider temperature range. Cyclohexane was chosen as the adsorptive in view of its high triple-point temperature, Tt = 6.320C,23and high cohesive energy density compared with other CSsaturated hydrocarbons. This study indeed reveals a transition from incomplete to complete wetting at a wetting temperature T, ca. 14 K above Tt. In addition, an interesting metastability phenomenon at temperatures near T, was found, indicating that the wett,ing transition represents a first-order transition in this system. We have also studied the influence of the oxide layer thickness of the Si wafer on the film thickness isotherms in the complete wetting regime above T, and used the FHH equation to quantify this influence. Furthermore, we discuss the significance of the low values of the FHH exponent u, which appears to be a characteristic feature of physisorption isotherms on relatively weak substrates. This conjecture is supported by theoretical and simulation studies on the wetting transition. 2. Experimental Section 2.1. Apparatus and Experimental Procedure. Film thickness isotherms were measured by phase modulation ellipsometry. The substrate (SiOdSi wafer) is mounted on a sample holder in the axis of a cylindrical (20)Finn, J. E.; Monson, P.A.Phys. Reu.A 1989,39,6402.Fan, Y.; Monson, P. A. J . Chem. Phys. 1993,99,6897. (21)Kozak, E.;Sokolowski, S. J . Chem. Soc., Faraday Trans. 1991, 87, 3415. (22)Sokolowski, S.;Fischer, J . Phys. Rev. A 1990,4 1 , 6866. (23)Aston, J . G.;Szasz, G. J.; Fink, H. L. J . Am. Chem. Soc. 1943, 65,1035.
Lawnik et al.
100mbar
++
lOOOmbar
,SH
Figure 1. Ellipsometric apparatus in front view (upperpart) and top view (lowerpart). (i)Parts of the adsorption chamber Substrate (S) is mounted on inside the aluminum shells (A): a sample holder (SH) in the axis of a cylindrical glass cell (C) and thermostated by a Peltier element (Pl). (ii) Elements of the ellipsometer with azimuthal angles ai: He-Ne laser (L), polarizer (P), phase modulator (M), analyzer (A), and photo-
multiplier (PM).
glass chamber (90 mm inner diameter, 4 mm wall thickness; see Figure 1). This sample chamber can be evacuated to ca. mbar by means of a turbomolecular pump. Needle valves allow a controlled flow of the vapor into the chamber. Vapor pressure is measured with a precision of 0.15% by a set of capacitance manometers (MKS Baratron, pressure ranges 0-10, 0-100, and 0- 1000 mbar, respectively). The adsorption chamber is thermostated by means of a heating foil and two waterflushed aluminum shells as an outer stage. The sample temperature T is controlled within f 5 mK by means of a Peltier element mounted inside the sample holder; Tis measured using a high-resolution resistance bridge (type F17 by Automatic Systems Laboratories, England). The temperature of the sample is kept ca. 0.05 K lower than the temperature of the walls of the chamber in order to avoid condensation of the vapor on the glass walls. The saturation pressure po(T)is determined in respect to the sample temperature using the Antoine equation. Ellipsometric techniques measure the ratio of the complex amplitude reflection coefficients for light polarized parallel (F,) and perpendicular (FB)to the plane ofincidence. The ellipticity is related to the ellipsometric parameters (phase shift A and azimuth v) by24
Q = i;dFS= tan(v) exp(iA)
(3)
The phase-modulation e l l i ~ s o m e t e consists r~~ of the following optical elements with fixed azimuthal angles ai: The light beam of a 2 mW He-Ne laser (wavelength A. = 632.8nm) first passes through a polarizer with a -45" axis with respect to the plane of incidence. The polarization of the laser beam is changed periodically by a phase modulator (Hinds, Model FS 5 ) with a frequency of 50 kHz and a vertical axis to the plane of incidence. After reflection by the sample, the resulting phase modulation is converted into an intensity modulation by an analyzer with a 45" axis and detected by a combination of a photomultiplier and a lock-in amplifier. The resulting ac signal consists of 50 and 100 kHz components from which the ellipsometric parameters A and 1/, are obtained. For M h e r details see refs 25 and 26. (24)Azzam, R. M.A.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland Amsterdam, paperback ed. 1987. (25)Jasperson, S. N.; Schnatterly, S. E. Rev. Sci. Instrum. 1969,40, 761.
Langmuir, Vol. 11, No. 8, 1995 3077
Physisorption of Cyclohexane on a SiOzlSi Substrate Physisorption isotherms were obtained by the following procedure: First the system was evacuated to a pressure of mbar at an elevated temperature (ca. 70 "C) for several hours. The experimental temperatyre wgs then adjusted, and the ellipsometric parameters A and 1/, of the substrate in vacuum were measured. Vapor was then admitted into the chamber, thus increasing the pressure in steps of a few percent of po. After equilibration the relevant experimental data (ellipsometric signals, pressure, and temperature) were recorded by a computer. Typically, the measurement of a complete isotherm took 10-20 h. Blank measurements with nitrogen gas were made to account for the pressure-dependent birefringence of the glass walls of the sample chamber. This birefringence causes blank values X, of the ellipsometric parameters (X = A, q )which were found to be linear functions of the pressure p of nitrogen gas, i.e., X, = cxp up t o p = 1 bar. 2.2. Data Analysis. The adsorbate film thickness was derived from the measured ellipsometric parameters A and on the basis of a two-slab model, viz., the physisorbed organic film of uniform thickness d and a silicon oxide layer of thickness 6 located between the silicon substrate and the vapor phase. The complex Drude relation was used to compute the parameters A(d) and q(d)for a large set of d values, using the refractive indices of the layers and the experimental parameters (wavelength A0 and angle of incidence of the light beam) as input data. For the present systems (with 6 = 25, 27, and 570 nm) the relation between the film thickness d and the ellipsometric parameters X (X = A, I)) can be represented by
+
d = u,(X - ii', b,(X -
mz
(4)
with a precision of 0.3%ford up to 10 nm. In this range the quadratic term remains much smaller than the linear term. In the computations ofX(d) the refractive index of the physisorbed film was taken to be equal to that of the liquid adsorptive (n = 1.4210 at 30 "C), even for submonolayer films. The justification of this approximation has been confirmed in studies of Smithz7and Bootsma and Meyer.2s Furthermore, it was assumed that the pressure-dependent birefringence of the glass wall (see above) makes an additive contribution to the overall ellipsometric parameters. Accordingly, in eq 4 the qyantityx- Xwas replaced by the net increment 6 X r X - X - X,, withX, = cxp taken from the blank measurements. Due to this procedure, absolute values of the ellipsometric parameters were not required in determining film thickness isotherms. 2.3. Materials. Thermally oxidized silicon wafers obtained from two different sources were used as substrates. These wafer samples had been prepared by oxidation at 800 "C in a gas mixture of equal volume fractions of 0 2 and Nz. Commonly the surface of thermally oxidized wafers has a roughness of only ca. 0.2 nm compared with ca. 0.4 nm for native oxide layers.29 Physisorption studies of water vapor demonstrated the hydrophobicity of the present wafer materials.6 The contact angle for water was not measured but should be similar to the angle determined by Gee et a1.8using heatdehydroxylated quartz, Le., 20-45". The oxide layer thickness of the present samples was redetermined by means of a null ellipsometer (Rudolph Research, Model 43603-200 E) with an accuracy of H . 5 nm. The refractive indices of silicon (n = 3.874 at 30 "C) and silicon oxide ( n (26) Drevillon, B.;Perrin, J.;Marbot, R.; Violet, A,; Dalby, J. L. Rev. Sci.Instrum. 1982, 53, 969. (27) Smith, T. J.Opt. SOC.A m . 1968, 58, 1069. (28) Bootsma, G. A.; Meyer, F. Surf. Sci. 1969, 14, 52. (29) Tang, M.-T.;Evans-Lutterodt, K. W.; Higashi, G. S.; Boone, T. Appl. Phys. Lett. 1993, 62, 3144.
0.0
0.2 0.4 0.6 0.8
1.0
PIP0
Figure 2. Film thickness isotherms for cyclohexane on Si wafers with oxide layer thickness 6 = 27 nm (squares)and 6 = 570 nm (circles) at 30 "C. Inset: Comparison of the experimental data with the curvature predicted by the FHH equation with n = 3 (dashed curve). = 1.468 for 6 = 27 nm and n = 1.457 for 6 = 570 nm at 30 "C) were taken from published data for Si wafers with similar oxide layer thickness.30 Immediately prior to the physisorption experiments, the substrate and the adsorption chamber were cleaned with organic solvents (carbon tetrachloride, methanol) in an ultrasound bath. Cyclohexane of certified grade (GC purity >99.5%, Merck) was used without further purification. Its refractive index at the experimental temperatures was measured by means of an Abbe refractometer with an accuracy of f 2 10-4.
3. Results and Discussion Film thickness isotherms of cyclohexane on two silicon wafers with grossly different oxide layer thicknesses (27 and 570 nm) at 30 "C are presented in Figure 2. In the submonolayer region, up to a relative pressureplpoe 0.7, a nearly linear increase of the film thickness with the vapor pressure is observed. Above plpo = 0.8, the film thickness increases steeply, with values exceeding 20 nm (ca. 40 monolayers) near the saturation pressurepo. This behavior indicates complete wetting at saturation. The temperature dependence of the film thickness isotherms of cyclohexane was studied in the temperature range 15-40 "C on two wafer materials of similar oxide layer thicknesses (25 and 27 nm), but received from two different laboratories. All isotherms exhibit an extended linear region at low coverage, with no significant temperature dependence in d = d(pIpo1, but a strongly temperature-dependent behavior is obtained near the saturation pressure PO: At 25 "C and above, pronounced multilayer adsorption with a film thickness up to 50 nm was detected near PO, indicating complete wetting. At the lowest experimental temperature (15 "C), however, no pronounced increase of the film thickness is observed even at pressures very close topo, as is to be expected for incomplete wetting. Film thickness isotherms at temperatures below 25 "C, obtained on ascending and descending pressure scans, are presented in Figures 3 and 4. At temperatures below 20 "C, reproducible isotherms without any difference between ascending and descending curves were obtained (Figure 3): At the saturation pressurepo, these isotherms end at a finite film thickness with a finite slope. The nominal adsorbate film thickness at saturation increases from 1.7 nm at 15 "C to 7 nm at 17 "C and 15 nm at 19 (30)Jellison, G. E., Jr.; Lowndes, D. H. Appl. Opt. 1985,24, 2948. Jellison, G. E., Jr. Appl. Phys. 1991, 69, 7627.
Lawnik et al.
3078 Langmuir, Vol. 11, No. 8, 1995
i 11 I WI
lo
51 0
0.8
1.o
0.9
PIP,
Figure 3. Film thickness isotherms for cyclohexane on SiOz(25 nm)/Si wafer at temperatures below the wetting temperature;circles and squares represent ascendingcurves;diamonds represent descepding curves. d
I1
c
*
4
2 M l 5t 2
.
n
0
0.8
1.0
0.9
0 0.0
0.2
0.4
0.6 0.8
1.0
PIP,
Figure 4. Adsorptioddesorption hysteresis behavior of film nm)/Si wafer thickness isotherms for cyclohexane on SiO~(25 at temperatures just above the wetting transition. "C. Strong scattering of the reflected light is observed at the saturation pressure, indicating the formation of droplets on the substrate. In the temperature range between 20 and 23 "C, the isotherms exhibit a pronounced adsorptioddesorption hysteresis (Figure 4). The ascending curves (circles) indicate complete wetting behavior: On approaching the saturation pressure, film thicknesses above 10nm, in some cases even above 50 nm, were found. However, on lowering the vapor pressure from PO by a small increment, these thick adsorbate films appear to break down, as illustrated by much steeper descending curves (diamonds). Below, the significance of the findings for the lowcoverage region and the behavior near saturation is discussed in more detail. 3.1. Submonolayer Coverage. In the whole sub5 0.4),the film thickness isotherms monolayer region can be represented within experimental accuracy by d = h,&po
+ do
adsorption on graphite.31 Thus the present substrates represent low-energy surfaces. The nearly linear increase of the film thickness with the vapor pressure extending up to relative pressures p/po = 0.7 (Figure 2) confirms results with similar adsorbents in the literature.7J1J2 While Beaglehole and Christensonll take this behavior as evidence of good surfacehomogeneity of the chemically oxidized silicon wafers used in their study, Levinson et a1.12 suspect that the linearity of the vapor isotherm in the submonolayer region is caused by the presence of a submonolayer film of adsorbed water on the surface of their substrate, a thermally oxidized silicon wafer. The observed dependence of ho on 6 implies that the adsorbate-substrate potential decreases with increasing oxide layer thickness. This effect was attributed to a decrease of the density of silanol groups on the surface. The same tendency was found in chromatographic studies with untreated and heat-dehydroxylated silica32 and alumin~silicate.~~ On the other hand, Gee et a1.8did not observe any difference in the physisorption capacity of given hydrocarbons on hydroxylated and heat-dehydroxylated quartz, but an increasing difference between the two materials was found for adsorptives of increasing polarity (alcohols, water). In part 1ofthis study6 it was shown that the adsorption of water vapor on the thermally oxidized silicon wafers yields isotherms which are linear over the entire pressure range, with a limiting film thickness of only 0.4 0.1 nm (correspondingto less than two statistical layers of water molecules) at saturation pressure. However, the amount of chemisorbed water remaining on the surface after in situ outgassing of the wafers is not known. Although these polar sites may have a somewhat stronger interaction with hydrocarbon molecules than the hydrophobic oxide patches, both kinds of interactions are relatively weak. Furthermore, if the polar sites are significantly smaller than the size of an adsorbate molecule and if they are distributed at random on the surface, the interaction energy experienced by an adsorbed hydrocarbon molecule will vary only slightly as a function of the coordinates parallel to the surface; accordingly, the surface will be energetically nearly homogeneous on a length scale of the adsorbed hydrocarbon molecules. On the other hand, the surface is still disordered and rough on a molecular scale; hence lateral attractive interactions between adsorbed molecules which would cause an S-shape of adsorption isotherms (as in the case of submonolayer films of cyclohexane on graphite)31play no significant role. It is believed that the extended linear region of the adsorption isotherms of hydrocarbon molecules on the present substrates is due to the combination of these two factors: (i)a low-energy surface with a random distribution of small, weakly polar sites of somewhat higher adsorption potential; and (ii)surface roughness on a molecular length scale suppressing attractive lateral interactions in the adsorbed monolayer. 3.2. Wetting Transition and Hysteresis. As outlined above, the steep increase and divergence of the 30 "C film thickness isotherm near saturation shown in Figure 2 is taken as a signature of complete wetting ofthe substrate at vapor/liquid coexistence. This conclusion implies that the film thickness grows in a uniform manner, without breaking up into droplets near saturation. However, ellipsometry measures a mean film thickness averaged over the illuminated spot on the surface and, taken alone, cannot discriminate between uniform and
(5)
where ho = [ad/&dp&p+ is the initial slope of the isotherms and do represents the mean error bar of the film thickness (do = 0.02 nm). For cyclohexane at 30 "C we find ho = 1.0 f 0.4 nm for the wafer with oxide layer thickness 6 = 27 nm, and ho = 0.5 f0.2 nm for the material with 6 = 570 nm. These values are typically 1 order of magnitude lower than the corresponding values for the
(31)Findenegg, G. H.In Fundamentals ofAdsorption; Liapis, A. I., Ed.; AIChE: New York, 1987; Vol. 2,p 53. (32) Milonjic, S.K.; Kopecni, M. M. Chromatographia 1984,29,342. (33)Carrasco-Marin, F.; Domingo-Garcia, M.; Fernandez-Morales, I.; Lopez-Garzon, J. J.Colloid Znterface Sci. 1988,126, 552.
Physisorption of Cyclohexane on a SiOzlSi Substrate
nonuniform films. In this respect this method is equivalent to other integrating techniques like the quartz microbalance. For example, Chiarello et al.15 studied the adsorption of water on gold using a quartz microbalance and obtained isotherms which increase sharply as the saturation pressure of the vapor is approached. X-ray reflectivity measurements performed simultaneously revealed, however, a strongly increasing roughness of the filmlvapor interface near saturation, contrary to expectation for a uniform film, and small droplets of water were seen on the surface at saturation. This case of 'an incompletely wetted substrate demonstrates the possible ambiguity of interpreting global physisorption isotherms without independent information about lateral homogeneity of the film. In the phase modulation ellipsometry used in this study, the dc intensity 10 monitored by the photomultiplier represents a measure of the reflectivity of the film-covered surface (cf. Nham, Hess, ref 10). Above 25 "C,where the film thickness isotherms indicate complete wetting of the substrate, the intensity IO was only a weak function of the film thickness and no significant fluctuations of lo were observed, as to be expected for a film ofuniform thickness. At temperatures below 20 "C, on the other hand, a pronounced reduction of IO and diffise scattering of the light out of the specular beam were observed near saturation, as to be expected if droplets with dimensions comparable to the wavelength or greater appear on the substrate. Thus, phase modulation ellipsometry represents a tool to detect both the mean thickness and the homogeneity of the adsorbed film. From the observations outlined above we conclude that the wetting temperature of the present system is between 20 and 25 "C. In the intermediate temperature range the ellipticity and reflectivity data taken along ascending pressure scans (stepwise increasing vapor pressures) resemble those of complete-wettingisotherms at higher temperatures, but data taken on descending pressure scans exhibit incomplete-wetting features with pronounced light scattering and temperature fluctuations. Either the ascending or the descending curve must represent a metastable state in this region. Instabilities in adsorption isotherms slightly away from the saturation pressure were also observed by Volkmann and Knorr for CFzClz on graphitegnear the triple-point temperature Tt of the adsorptive, which for that system represents the wetting temperature T,: Below Tt the thickness of the solid-like film was found to fluctuate in a quasiperiodic fashion. Both the growth instabilities and the selfsustained oscillations were explained by lateral temperature variations due to the flow of the sublimation heat. Since metastability is a signature of first-order transitions, we infer a first-order wetting transition in the present system. Most of the observed features can be reconciled with such a first-order transition. A first-order wetting transition implies a discontinuous increase of the film thickness along the saturation curve of vaporAiquid coexistence (Ap = 01, from low values do(T) at T IT, to infinity at T 2 T,. It also implies the existence of a prewetting line as a continuation of the surface phase transition into the region of the undersaturated vapor (Ap O).2-4 Such a prewetting line has not been observed in the present work. Tentatively, this may be attributed to the nonideality of our substrate surface and/or the method of stepwise changes ofpressure used in the present work: Heterogeneity or roughness of the surface will blur the stepwise change of the film thickness to be expected as one crosses the prewetting line. In addition, large pressure quenches in the thick-film region above the prewetting line produce pronounced overheating or un-
Langmuir, Vol. 11, No. 8, 1995 3079
T.
Ti
t:
Figure 6. Surface phase diagram of a system with a firstorder wetting transition: The full curve represents the prewetting line;the dashed-dottedcurves represent the corresponding spinodals. The proposed trajectories I and I1 (dashed curves) correspondingto the observed adsorptioddesorption hysteresis are explained in the text.
dercooling effects near saturation which may drive the system into metastable states, as explained below. Consider the phase diagram for a first-order wetting transition shown schematically in Figure 5 where the prewetting line separating the thin-film region from the thick-film region ends in a prewetting critical point. At the prewetting line the film thickness increases discontinuously by an increment Ad(T) = dh(T) - dl(T), which decreases from infinite at T , to 0 at the prewetting critical point at l'&, where dh and dl become identical. For a heterogeneous substrate the step Ad will be smeared out over a finite pressure range and overlaps with the continuation of the film-thickness isotherm in the thickfilm region above the prewetting line. Consider now a pressure increase Ap = pg - P A from a film thickness dA in the thin-film region to a value dg in the thick-film region or vice versa (cf. Figure 5). At temperatures close to T, the increment Ad = dg - dA will be much larger than for an equivalent pressure quench at a higher temperature. Accordingly, overheating or undercooling effects resulting from condensation or evaporation of the vapor will be pronounced near the wetting temperature but not at higher temperatures. Furthermore, we expect a pronounced difference between the process occurring at positive and negative pressure quenches near T,: For a positive quench (Ap > 01,condensation of vapor causes a positive temperature excursion (trajectory I), resulting in a smaller prewetting step and thus a more gradual approach to equilibrium than at the initial temperature. On the other hand, a negative pressure quench starting in the thick-film region close to saturation (point C ) ,where the film thickness isotherm is very steep, will cause strong desorption and thus substantial undercooling of the remaining film; this may drive the system into the thinfilm region even if the final pressure is still in the thickfilm region (point B). As indicated in Figure 5, this path (trajectory 11)may extend into the domain of incomplete wetting and would cause a dewetting of the adsorbed film as is indeed seen along the descending scans of the isotherms between 20 and 25 "C. The fact that trajectory I1 does not end at the equilibrium film thickness dg is meant to indicate that a thin film of thickness d < dg persists as a metastable state in the thick-film region. The importance of metastable states near a first-order wetting transition of multilayer adsorbed films was stressed in recent experimental and theoretical studies,14*34-37 although in these studies metastable states were considered only at or near saturation. For the system 4He/Cs,Taborek and Rutledge14and Dupont-Roc and cow o r k e r ~observed ~~ a metastable thick film below the wetting temperature T, when cooling the wet substrate (34)Nacher, P.J.; Demolder, B.; Dupont-Roc, J. Physica B 1994, 194-196, 975. (35)Bonn, D.;Kellay, H.;Meunier, J.Phys.Reu. Lett. 1994,73,3560. (36)Schick, M.; Taborek, P. Phys. Rev. B 1992,46,7312. (37)Burschka, M. A.;Blossey, R.; Bausch, R. J. Phys. A 1993,26, L1125. Bausch, R.; Blossey, R.; Burschka, M. A. J.Phys. A 1994,27, 1405.
3080 Langmuir, Vol. 11, No. 8, 1995
Lawnik et al.
in equilibrium with bulk liquid. Schick and T a b ~ r e k ~ ~ Au attributed this hysteresis to the kinetics of nucleation of patches of the thin film in a thick-film phase: As the line tension diverges at Tw,38the free energy to form a critical nucleus of thin film in a thick film increases and thus the nucleation rate of a thin film vanishes. An alternative explanation was proposed by Bonn et al.,35who suggested that the anomalously long lifetime of undercooled thick wetting films at vaporlliquid coexistence is related to the location of the spinodals which are also sketched in Figure 5. On the basis of this wetting phase diagram it was argued that overheating of a thin film at coexistence (Ap = 0) means approaching the spinodal where the nucleation d/nm probability of a critical droplet ofthick film becomes unity. Figure 6. Logarithmic plot of film thickness isotherms of Conversely, when a thick film is undercooled along vapor/ cyclohexaneon Si wafers with oxide layer thickness 6 = 27 nm liquid coexistence, one is always far away from the (squares) and 6 = 570 nm (circles) at 30 "C; large symbols represent the data used in the FHH fitting procedure. corresponding spinodal, which does not intersect the bulk coexistence line, and thus the nucleation probability for Table 1. FHH Parameters for Cyclohexane on SiOdSi a critical droplet of thin film is small. This argument Wafers: Influence of the Si02 Layer Thickness S offers an explanation of why the metastability of thick 6=27nm 6 = 570 nm films is more pronounced than for thin films at coexisten~e.~~ fit eq dkT (nm9 exponent n dkT (nmn) exponent n In the present experiment we are considering films away 6a 0.39f 0.06 1.52 f 0.14 0.24 & 0.08 1.01 & 0.28 from bulk coexistence. In this case a pressure quench 6b 0.39 f 0.06 1.61 f 0.13 0.23 f 0.08 1.05 f 0.21 causes changes of film thickness in the one-phase region Table 2. FHH Exponent n for Cyclohexane on SiOdSi of the prewetting phase diagram. As the film thickness Wafers: Influence of the Temperature T grows along trajectory I, the prewetting line will be crossed TPC n (6 = 27 nm) n (6 = 25 nm) at a temperature closer to where the nucleation barrier for a thick film is smaller than at the original 25.0 1.56 f 0.11 1.83 f 0.16 temperature TI. Conversely, a negative pressure quench 30.0 1.61 f 0.13 1.79 f 0.31 from point C in the thick-film region will cause under40.0 1.56 f 0.17 1.71 f 0.26 cooling of the remaining film well below T, if the original increasing error bars on In ldpdp) as one approaches the temperature TI was close to T,. This process may lead saturation pressure PO. to a spontaneous dewetting and droplet condensation of Logarithmic plots of film thickness isotherms are shown the (supersaturated) vapor in the undercooled transient in Figure 6. These isotherms exhibit an approximately state. Temperature equilibration may then proceed in linear region over a range of film thickness d from the thin-film state along trajectory 11. Near T, the somewhat below one monolayer ( d , x 0.53 nmI3l up to ca. prewetting film thickness increment Ad is high, and thus 8 nm. In the fitting procedure based on eq 6a all data the free energy of nucleation of the thick film is large. from d = 0.6 nm up to the highest experimental film Accordingly, the thin film may persist as a metastable thickness were used. The fitting procedure based on the state. logarithmic form (eq 6b) was limited to the data from d In conclusion, a consideration of the wetting phase = 0.6 nm up to relative pressures plpo < 0.95, in view of diagram offers a plausible explanation for the observed the increasing error bars in In ln(pdp) beyond this limit. hysteresis behavior of the film in the region just above the Best-fit values ofthe exponent n and the energy parameter wetting temperature T,, which we expect to be near 20 dkTfor cyclohexane at 30 "C on two wafers with different "C in the present system. oxide layer thickness 6 are listed in Table 1. Table 2 3.3. Statusof the Frenkel-Halsey-Hill Equation. summarizes best-fit values of n for film thickness isoAll film thickness isotherms obtained at and above 25 "C therms of cyclohexane on two different wafers of similar exhibit unlimited multilayer adsorption without hysteroxide layer thickness (6= 26 f 1nm) at three different esis. The multilayer region of these isotherms was temperatures. analyzed in terms of the FHH equation to explore its The values ofthe exponent n for these systems are much applicability to systems near the border from complete to smaller than the theoretical value n = u = 3 expected for incomplete wetting. In the data analysis 'the FHH thick films in the regime of nonretarded van der Waals equation was used in the usual (nonlogarithmic)form and interactions. The pronounced difference between the in logarithmic form, viz., observed behavior and the curvature of an isotherm with n = 3 is illustrated in Figure 2. Among the possible reasons ldplp,) = AplkT = -(a/kT)d-" (6a) for this disagreement we have considered the influence of retarded dispersion forces, the effect of the oxide layer In ln(pdp) = ln(-Ap/kT) = ln(a/kT) - n ln(d) (6b) on the substrate, and the possibility that the low values ofn are caused by the proximity to the wetting transition. The generalized Lifshitz theory of van der Waals interacThe exponent n and the reduced energy density dkTwere tions includes the effects of many-body interactions and treated as adjustable parameters. One severe limitation retardation.lg As shown by D i e t r i ~ hthese , ~ effects can be ofthis analysis arises from the fact that the relevant value represented by the following sum: ofpo cannot be measured directly but has to be estimated from the vapor pressure curve po = f(T) and the temper4 = -&-U - pd-(U+l) ature of the substrate. Furthermore, the uncertainty in (7) the measurement of the vapor pressure, dplp = 0.3%, has to be taken into account. These uncertainties cause where a and , ! Iare independent of d and again u = 3. In the Appendix it is demonstrated that eq 7 results also (38)Indekeu, J. 0. Znt. J . Mod.Phys. B 1994,8, 309. from the consequences of a thin surface layer or a slightly
c,,
Physisorption of Cyclohexane on a SiOzlSi Substrate
-0.6 0
5
10
15
20
25
dlnm Figure 7. Comparison of the plots of eqs 6a and 7with adjusted exponent n = 1.6 (full curve) and with fixed exponent n = 3; the dotted curve represents the one-parameter fit (eq 6a), the dashed curve the two-parameter fit (eq 7); see text.
contaminated substrate if 6ld < 1, where 6 and d represent the thicknesses of the surface layer and the adsorbed film, respectively. A test of eq 7 against the present data is shown in Figure 7. Plots of eqs 6a and 7 are shown for a typical physisorption isotherm of cyclohexane at 30 “C. Using eq 6a with the exponent n as an adjustable parameter (full curve) gives a reasonably good representation of the experimental data. On the other hand, the curves representing eqs 6a and 7 with the exponent n = 3 show significant deviations from the data. Naturally, the one-parameter analysis of the original FHH equation (6a)with n = 3 yields more pronounced discrepancies than the two-parameter analysis of the generalized FHH equation (7). However, neither ofthese theoretical models describes the data with reasonable accuracy. This means that the low value of the FHH exponent n is a signature neither of a crossover from nonretarded to retarded interactions nor of a layered substrate. In the past decades, many experimental studies aiming to test the FHH theory have been made. Here we mention only some experiments with Si wafers as the substrate. In these studies, liquid-gas coexistence (Ap = 0)has been approached either by increasing the vapor pressure at constant temperature or by differentiallyheating the solid substrate relative to the temperature of the liquid reservoir. The physisorption of volatile liquids (cyclohexane, methanol,16and carbon tetrachloride”) on silicon wafers with a thin native oxide layer (6 = 1.6 and 1.0 nm) was studied by X-ray reflectivity measurements along the latter of these two paths. The results were found to be consistent with the generalized FHH equation (7). Isotherms of cyclohexane and octane on thermally oxidized silicon wafers, recorded by ellipsometry, were analyzed by Levinson et a1.12using eq 6a with an effective energy parameter which decreases with increasing oxide layer thickness (see Appendix). The resulting best-fit curves agree with the experimentaldata only in a restricted range of the adsorbate film thickness (1 nm I d 5 3 nm) and relative pressure (0.9 5 plpo 5 0.99). Beaglehole and Christensonll studied the adsorption of organic vapors on gold, mica, and silicon with an oxide layer 6 = 3 nm, using ellipsometry, and found systematic deviations from the predicted FHH exponent. Their isotherms had to be represented by substrate-specific curves for all wetting adsorbates. If the FHH analysis is limited to adsorbate layers above one monolayer and to relative pressures below plpo = 0.95, the film thickness of cyclohexane diverges with an exponent ofapproximately n = 1.5 for the substrate gold and n = 2.3 for the sio2(3nm)/Siwafer on approaching the saturation pressure. From these results of the literature and the present study it appears that for hydrocarbons on silicon wafers the FHH exponent n decreases with increasing oxide layer thickness 6 . Avalue n = 3 was found for the physisorption
Langmuir, Vol. 11, No. 8, 1995 3081
of cyclohexane and methanol,I6 and for carbon tetrachloridell on silicon wafers with a thin native oxide layer (6 = 1.6 and 1.0 nm, respectively). A value n = 2.3 was obtained for cyclohexane isotherms on wafers with a native oxide layer of thickness 6 = 3 nm.” The present study of cyclohexane isotherms on thermally oxidized silicon wafers yields even lower values of the FHH exponent of n = 1.6 f 0.2 for 6 = 27 nm and n = 1.0 f 0.2 for 6 = 570 nm (Table 1). Beaglehole and Christensonll argued that their low values of n for cyclohexane might indicate that the measurements had been performed somewhat below the wetting temperature. Although we would not expect the FHH equation to apply anywhere below the wetting temperature, our results support the idea that the low values of n may be a signature of the complete-wetting regime close to the wetting temperature. It appears that the observed behavior is not limited to a narrow temperature range. From the results in Table 2 it is seen that the best-fit value of n exhibits no significant temperature dependence in the range 25-40 “C for which a mean value ii = 1.7 f 0.2 for the two wafers with 6 FZ 26 nm is obtained. Note, however, that our experimentswere made in a fairly narrow range in terms of reduced temperatures T , = TIT,, viz., 0.54 < T , < 0.57 (T, = 553 K for cyclohexane). No significant change of the analytic form of the film thickness isotherms is seen in this temperature range close to the wetting temperature. 3.4. Theoretical Calculations. The finding of very low values of the FHH exponent n for multilayer adsorbed filmsjust above the wetting temperature is of considerable interest. In order to decide if this behavior occurs only for the present type of systems or if it represents a general feature of systems with weak adsorbate-substrate interactions, we have performed theoretical calculations of the density profiles of physisorption films on the basis of the Born-Green-Yvon (BGY)theory, using the algorithm developed by Fischer and ~ o - w o r k e r s Calculations . ~ ~ ~ ~ ~ of density profiles and adsorption isotherms for a LennardJones fluid on strongly and weakly attractive substrates have been presented in ref 40. In this supplementary study we concentrate on the shape of the adsorption isotherm on the weakly attractive system (referred to as “argodsolid-COz”in the earlier literature20-22) at temperatures where one expects to find the thin-film to thickfilm wetting transition (which had not been searched for in ref 40). The calculations are based on the LennardJones (12, 6) potential for the interaction between gas molecules and a Lennard-Jones (9, 3) function for the adsorbate-substrate potential,
with the “argodsolid-CO2” parameters E,&, = 2.7857 andzdu,, = 0.7823. All relevant quantities are expressed in terms of the LJ parameters (E,,, u,,) of the fluid, for which the critical temperature is estimated as T,* = kTJ E,, = 1.35. Calculated adsorption isotherms for a range of reduced temperatures P = kTlc,, from 0.918 to 1.10 are shown in Figure 8. Qualitatively, these results exhibit features remarkably similar to those of the experimental film thickness isotherms of the present system: a weak, nearly linear increase of the reduced surface concentration I’*= up toplpo x 0.4 and a pronounced temperature dependenceat relative pressuresplpo > 0.8: At the lowest temperature P = 0.918 (corresponding to a reduced temperature T,= PIT,* RZ 0.681, the isotherm reaches a (39)Fischer. J.: Methfessel. M. Phvs. Rev. A 1980.22.2836. (40)Wendland,’M.;Salzmann, S.;Heinbuch, U.;Fischer,’J.Mol.Phys. 1989,67,161.
3082 Langmuir, Vol. 11, No.8, 1995
r-!
2.0
-:m 1 f
t 1.10
0 00 0
1'1
T'
t
i
Lawnik et al.
02
0 918
0 45
06
0.8
1U 0
PIP,
Figure 8. Calculated BGY isotherms for a weakly attractive system (argodsolid COz) near its wetting transition. Inset: Logarithmic plot of the isotherms above the wetting transition at P = 1.00 and 1.10. The break in the r" = 1.00 isotherm represents the prewetting transition.
limiting adsorption r*x 0.5 at saturation, which implies incomplete wetting. At the highest temperature, r" = l.10(Tr%0.815),andatT*= 1.00(Tr%0.74),r*increases sharply for p/po 1, indicating complete wetting. The isotherm at T* = 0.95 (T,x 0.70) appears to be close to the wetting temperature. The multilayer region of the two isotherms in the complete-wetting regime is shown on a double-logarithmic scale as an inset in Figure 8. This graph is analogous to Figure 6. The breakin the T* = 1.00 isotherm represents the prewetting transition from the thin-film to the thickfilm regime which had not been seen in the earlier The multilayer region of these two isotherms was analyzed in terms of the FHH equation 6b with the film thickness d replaced by the adsorption r*. The T* = 1.10isotherm yields an FHH exponent n = 1.2 f 0.1; for the isotherm at T* = 1.00 we obtain n = 1.46 & 0.1 for the thin-film region and n = 1.2 from the two points in the thick-film region. Thus the isotherms calculated on the basis of a (9, 3) adsorbate-substrate potential yield an FHH exponent n very much lower than n = a = 3 in this temperature regime close to the wetting transition, in agreement with the experimental findings of this study. Incidentally, an analysis of BGY isotherms calculated for "argodgraphite" parameters = 9.241, i.e., a strong adsorbate-substrate potential,40 yields the expected exponent n = o for the respective range of the film thickness. Thus the low values of n found for the present system support the conjecture that these low values are a characteristic feature of systems close to the wetting transition. The FHH analysis of the calculated adsorption isotherms was made for relatively thin films and not for the asymptotic regime of thick films, where the predicted n = alaw may still hold. Inspection ofthe calculated density profiles of the adsorbed films shows pronounced layering extending to at least five molecular layers. Since the slab model underlying the FHH theory does not account for this layering effect, we may expect deviations from the FHH behavior to become important if the analysis is not confined to films ofmesoscopic thickness. This is obviously the case between one and two statistical monolayers. In other words, since adsorption on weakly attractive substrates remains rather low up to high relative pressures, the reZatiue increase of the film thickness in the typical FHH regime may be more pronounced than in the case
-
of strongly attractive substrates where the film thickness at the lower end of the FHH regime is already rather high. 4. Conclusions The present study of the adsorption of cyclohexane on thermally oxidized silicon wafers leads to the following main results: (1)The present substrates exhibit a lowenergy surface; this conclusion follows from the low initial slope and the extended linear region of the film thickness isotherms. (2) Complete wetting of the SiO~(25nm)/Si wafer occurs only at temperatures T L 20 "C, i.e., well above the triple-point temperature of the adsorptive (Tt = 6.32 "C). In pressure quenches the first-order wetting transition from incomplete to complete wetting is accompanied by metastable growth modes. (3)An analysis of the physisorption isotherms of the wetting systems in terms of the FHH theory yields values of the exponent n much lower than 3. Model studies in terms of the BGY theory reveal that these low values of n are a signature of physisorption systems on low-energy substrates just above the wetting transition.
Acknowledgment. This work has been supported by the Deutsche Agentur fur Raumfahrtangelegenheiten (DARA)d e r Contract No. 50 W M 9115. A graduate fellowship by the Land Nordrhein-Westfalen for W.H.L. is also gratefully acknowledged. The authors wish to thank J. Fischer, J. 0.Indekeu, and A. Robledo for fruitful discussions and A. M. Cazabat, P. Muller-Buschbaum, and D. Bonn for sending us preprints of refs 12, 17, and 35. Appendix In this Appendix it is shown that the crossover from nonretarded to retarded van der Waals interactions cannot be distinguished from the consequences of a thin surface layer or a slightly contaminated substrate ifd/d < 1,where 6 and d represent the thicknesses of the surface layer and the adsorbed film, respectively. If a substrate (medium 1)is covered by a surface layer (medium 2) of thickness d comparable to the film thickness d , eq 2 is to be replaced by an expression which takes into account the individual layers with their respective interaction energy parameters al and a2:41 Ap = -ae&" = -a&-" - (a, - a&d
+ 6)-"
(All In ref 6 it was shown that for energy ratios (al - az)/az typical for the silicodsilicondioxidesystems of the present study the effective energy parameter ~ f exhibits f a significant dependence on the film thickness d in a range 0.1 5 dld 5 3 but ~ f isf nearly independent of d outside this range. Tidswell et a1.16remarked that for 6/d < 1the quantity (d + 6 ) P may be expanded,
+ 6)-" = d-"(l + 6/d)-"
d-"(l - d d and thus eq A1 can be written as
(d
%
+ ...)
+
Ap = -a&" - a&a2- al)d-(o+l) .., which represents the same relation between the chemical potential Ap and the adsorbate film thickness d as the generalized FHH equation, eq 7:
& = -&-"- pd- (o+l) LA950208B (41)Cazabat, A. M. In Liquides auz Interfaces; Les Houches 1988 Session XLVIII; Course 8; Charvolin, J.,Joanny, J. F., Zinn-Justin, J., Eds.; North-Holland: Amsterdam, 1990.
