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Ellipsometric Study of the Wetting of Air/Water Interfaces with Hexane, Heptane, and Octane from Saturated Alkane Vapors Thomas Pfohl, Helmuth Mo¨hwald, and Hans Riegler* Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin/Adlershof, Germany Received April 28, 1997. In Final Form: July 1, 1998 Ellipsometric investigations of alkane adsorption from saturated alkane vapor show that hexane and heptane wet the air/water interface with a closed ultrathin film of molecular thickness that is topped with droplets of micrometer dimensions. Octane adsorbs only in a submonolayer film. Brewster angle microscopy and the analysis of the time evolution of the ellipsometric signal of the hexane and heptane adsorption reveal phase transitions; i.e., the alkane films are below their critical temperatures. In the course of the adsorption first the formation of a monolayer with low (gaseous) molecular density is observed. Then a first-order phase transition to a condensed molecular packing occurs. After completion of this condensed monolayer, another transition is observed, either from the molecules lying flat to orienting themselves upright or from a mono- to a bilayer. Depending on the molecular orientation, the molecular packing density in the condensed films is either approximately the same as the liquid bulk density (if the molecules are oriented upright) or it is about 120% of the liquid bulk density (if the molecules lie flat). Ultimately the mono- and/or bilayer is topped with droplets of several micrometers diameter.
I. Introduction Wetting is an important process in many technological and biotechnological areas. Therefore it is not surprising that there exists a large amount of literature on this topic.1,2 However, this literature in many ways is controversial, as the nature of the underlying forces is not fully understood. An especially simple model system, still with technical relevance, is the water surface in contact with alkanes. Some work has been reported on this system for alkanes (CnH2n+2 ) Cn) with n g 4. Measurements of the surface tension of the water surface in contact with the saturated alkane vapors and the visual observation of alkane lenses indicate for 5 < n < 8 the coexistence of an ultrathin film with lenses.3-5 For n > 8 the general finding is partial wetting; i.e., the alkanes form lenses without a thin film in between. These findings are explained through a subtle balance between short range and long range forces.6,7 This balance is for instance revealed by the observation of a temperature induced (critical) wetting transition of pentane on water at 53 °C by Ragil et al.8 This transition is explained through the change of the sign of the Hamaker constant at 53 °C due to the overcompensation of the negative, approximately temperature independent, zero-frequency contribution by the positive, temperature dependent, dispersion force component. An analogous critical wetting transition has just recently been observed by some of the authors of this paper for octane at the interface between an aqueous (1) Dietrich, S. Phase Transistions and Critical Phenomena; Domb, C., Lebowitz, J., Eds.; Academic Press: London, 1988; Vol. 12. (2) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (3) Johnson, R. E.; Dettre, R. H. J. Colloid Interface Sci. 1966, 21, 610. (4) Del Cerro, C.; Jameson, G. J. J. Colloid Interface Sci. 1980, 78, 362. (5) Hauxwell, F.; Ottewill, R. H. J. Colloid Interface Sci. 1970, 34, 473. (6) Brochart-Wyart, F.; J.-M. et al. Langmuir 1991, 7, 335. (7) Hirasaki, G. J. Contact Angle, Wettability and Adhesion; Mittal, K. L. Ed.; VSP: Utrecht, 1993; p 183. (8) Ragil, K.; et al. Phys. Rev. Lett. 1996, 77, 532.
glucose solution and air saturated with octane vapor.9 In this case the Hamaker constant was changed by variation of the glucose concentration. The critical wetting scenario presented for pentane and octane requires additionally to the long-range forces shortrange force components that favor wetting. These short range forces are mainly responsible for the ultrathin films indirectly proposed in the above mentioned earlier papers from visual observation and surface tension data for alkanes of six to eight C-atoms at room temperature. In the following we will present quantitative data on the time evolution and equilibrium coverages of these alkanes and derive details about the molecular ordering in these molecularly thin films. II. Material and Methods II.1. Substances. The water was purified with a Milli-Q system (18.2 MΩ/cm). The n-alkanes hexane (C6), heptane (C7), and octane (C8) were obtained from Sigma (purity 99+%). For further purification the alkanes were passed through a column, of which the lower half was packed with 35-70 mesh chromatographic-grade silica gel (Fluka) and the upper half with chromatographic-grade aluminum oxide (Fluka, pH 9.5 ( 0.2). This treatment was repeated until the interfacial tension of the alkane/water bulk interface did not change for at least 20 min. II.2. Instrumentation. The setup for the ellipsometric measurements is depicted in Figure 1. The phase-modulated beam (λ ) 6328 Å) hits the water surface at the Brewster angle ΦB ) 53.1°. Under these conditions the imaginary part of the measured reflectivities r ) rp/rs equals the ellipticity Fj (rp, rs are the amplitudes of p- and s-polarized waves). In the results we present ∆Fj, the difference between the ellipticity of the bare and a film-covered water surface.10 The time resolution of the ellipsometer (Beaglehole Instruments, Wellington, New Zealand) is better than 20 ms, and the beam area is about 1 mm2. The water surface (area ≈ 7 cm2) is contained in a gastight glass cell, which is kept in a thermostated ((0.1 K) container. At the beginning of an experiment a sufficiently large alkane (9) Pfohl, T.; Riegler, H. Submitted for publication in Phys. Rev. Lett. (10) Beaglehole, D. Physica 1980, 100B, 163.
S0743-7463(97)00430-7 CCC: $15.00 © 1998 American Chemical Society Published on Web 08/15/1998
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( )( )
a - 1 b + 2 Fa ) Fb a + 2 b - 1
Figure 1. Experimental setup of the ellipsometric experiment. reservoir (drop) is placed at the bottom of the glass cell (not in contact with the water surface) to adjust a saturated alkane vapor pressure. Then the compartment is sealed and the ellipsometric signal recording is started. For the Brewster angle microscopic observation (Nanofilm Technology, Go¨ttingen, FRG) the vapor pressure was kept saturated in a plastic container. The experiments were performed at room temperature, and the images were electronically corrected for image distortion due to observation at an oblique angle. II.3. Data Analysis. Within the Drude model ∆Fj is related to the dielectric constants of the two adjacent bulk phases, 1 and 2, and to the dielectric constant in the vicinity of the interface, (z) (which is assumed to vary only normal to the interface). According to ref 10, one obtains (λ ) wavelength of the measurement beam)
∆Fj )
π x1 + 2 λ 1 - 2
∫
+∞
-∞
dz
((z) - 1)((z) - 2) (z)
(1)
If the interfacial profile of (z) is assumed rectangular, i.e., if it can be replaced by an interfacial dielectric slab with thickness d and isotropic dielectric constant , eq 1 reduces to
∆Fj )
π x1 + 2 ( - 1)( - 2) d λ 1 - 2
( )
(2)
(3)
with NA ) Avogadro’s constant, M ) molecular mass, and R ) polarizability. Equation 3 can be transformed into Fa/Fb, the ratio between densities Fa and Fb, as function of the corresponding dielectric constants (11) Bootsma, G. A.; Meyer, F. Surf. Sci. 1969, 14, 52.
Through eqs 3 and 3a information on the molecular packing is obtained from the ellipsometric data. According to eqs 2 and 3 ∆Fj will be positive in the beginning of the adsorption because 1 < < 2 at low densities. Later, at higher densities, ∆Fj may become negative if the alkane density gets high enough in the adsorbed layer. Between, when ) 2, the ellipticity is zero. Concomitant with the density the film thickness may grow. According to eq 2 this affects only the magnitude of ∆Fj, not its sign. For T < Tc, at a certain packing density and/or vapor pressure, a phase transition from the low-density gaseous phase to a condensed phase will occur. The film will become heterogeneous with domains of condensed alkane in a gaseous matrix. For the gaseous phase < 2; hence ∆Fj > 0. For the condensed alkane phase (which may be, for instance, liquidlike) is larger than both, 2 and 1; hence ∆Fj of the condensed phase is negative. What is the measured ellipticity? If the condensed domains are much smaller than λ, ellipsometry will “see” only an arithmetic mean of the local of the low density and of the condensed phase, each weighted with the corresponding area fractions. In this case the resulting ellipticity ∆Fj varies with increasing alkane surface coverage Θ similar to that for T > Tc. The situation is different if the condensed domains are larger than λ. Then one obtains a ∆Fj, which is the arithmetic mean of the local ∆Fj weighted with the corresponding area fractions. The two different scenarios for the variation of the ellipticity ∆Fj as function of the alkane surface coverage Θ are shown in Figure 2. For simplicity it is assumed that the film thickness is constant up to a completely condensed monolayer. The dotted line without kink at the surface coverage Θml* shows ∆Fj for T > Tc and for T < Tc if the surface heterogeneities (condensed domains) are smaller than λ. The ellipticity increases continuously to a maximum value ∆Fjmax. Then it decreases, is zero when ) 2, and finally becomes negative. At ∆Fjmax the dielectric constant of the alkane film, ∆Fjmax, is given by 2
∂∆Fj π x1 + 2 (∆Fjmax - 12) ) d)0 ∂ λ (1 - 2) ∆Fj 2
(4)
∆Fjmax ) x12
(5)
max
This is a good approximation for thin insoluble layers at interfaces. For an alkane film on water we have an especially informative situation since the dielectric constant of the film can be either between that of air (1 ) 1.000) and the adjacent bulk water (2 ) 1.777), or larger, depending on the molecular packing of the alkane. Thus, with variation of the molecular packing in the course of the adsorption, one obtains according to eq 2 a very specific behavior of the ellipticity including possible changes of its sign. This can be used to derive extra information on the opto-geometrical parameters of the layer as discussed in the following adsorption scenarios. During the build-up of the vapor saturation, different adsorption schemes are feasible. If the temperature T is above the critical temperature of the alkane film, Tc, the packing density will continuously grow up to its maximum. The dielectric constant increases with the packing density according to the Clausius-Mossotti relation:11
4πNA R -1 )F +2 3M 4π0
(3a)
hence
With eq 2 this leads to a film thickness d∆Fjmax at ∆Fjmax
d∆Fjmax )
∆Fjmaxλ (1 - 2) x12 π x1 + 2 (x12 - 1)(x12 - 2)
(6)
which is for the interface air/water (∆Fjmax(a/w) ) 1.333)
d∆Fjmax ) 8470 ∆Fjmax (Å)
(6a)
From eq 2 it is apparent that if d increases with increasing , then the maximum ∆Fjmax* is shifted to ∆Fjmax > (12)1/2. According to eq 6 this means that d∆Fjmax is also shifted to larger values. Irrespective of the details of the variation of the film thickness as function of the dielectric constant between 1 and 2, one can show that the maximum of ∆Fj is always at the minimum of the thickness d(). For any fixed ∆Fj, eq 2 can be written as
d() f() ) const
(7)
∂d() ∂f() ∂ {d() f()} ) f() + d() )0 ∂ ∂ ∂
(8)
hence
thus,
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Figure 2. Schematic of the variation of the ellipticity, ∆Fj, the molecular ordering, and the profile of the dielectric constant as function of the surface coverage, θ, for temperatures above and below the critical temperature. For T > Tc (dotted line) the ellipticity increases continuously without a kink to ∆Fjmax and then decreases continuously. For T < Tc (solid line) the ellipticity has its maximum with a kink at ∆Fjmax* and θml*, which marks the first-order phase transition from a gaseous monolayer to a monolayer with varying degrees of coexistence of gaseous and condensed phases. The second kink at ∆Fjml and θml respectively, is at the transition from a monolayer to a multilayer. Alternatively the second kink may be attributed to a transition between a monolayer with molecules lying flat and a monolayer with molecules oriented upright (not shown in the schematic molecular ordering).
if:
∂f() ) 0, ∂
then
∂d() )0 ∂
(9)
The result of eq 9 is evident in the plots of Figure 6. For T < Tc and large domains, one first observes, like for T > Tc, a positive, smoothly increasing ∆Fj due to the continuously increasing (low) molecular density. Then, at a surface coverage Θml*, corresponding to ∆Fjmax*, the phase transition causes a kink in the ellipticity. Further increase of Θ keeps the of both the low-density packing and the condensed phase and the corresponding local ellipticities constant. However, the observed ∆Fj decreases linearly from the positive ∆Fjmax* to the negative ∆Fml at Θml, the coverage at which the monolayer is completely condensed, because the area fractions of the different phases change according to the lever rule. Any further increase of Θ is then assumed to start multilayer formation at constant , which causes a further decrease of ∆Fj with yet another slope. The schematic molecular orderings of Figure 2 show the adsorption scenario for idealized, isotropically shaped molecules. For anisotropically shaped molecules such as alkanes, the scenario might be different because of the additional degrees of freedom. Especially at Θml a transition from a monolayer with the molecules lying at the interface to a monolayer with the molecules oriented upright is quite conceivable.
III. Experimental Results The topology and film formation kinetics are very sensitive to external disturbances. It seems that vibrations or even very small temperature variations cause significant noise and oscillations in the ellipticity. Nevertheless, under favorable experimental conditions, for instance, during weekends, nicely reproducible results could be obtained.
Figure 3. Time development of the ellipsometric signal for hexane and heptane adsorption at the interface between water and saturated alkane vapor (T ) 25 °C). ∆Fjmax* and ∆Fjml have the same meaning as in Figure 2. ∆Fjmle is the equilibrium ellipticity after long adsorption times. Figure 3 shows the time evolution of the ellipsometric signal for hexane/water (a) and heptane/water (b) on a logarithmic time scale. Up to about 104 s (103 s in the case of C7) the behavior resembles the variations of the ellipticity with a change of the sign, which are schematically shown in Figure 2. For a comparison one has to take into account that Figure 2 displays the ellipticity as a function of the surface coverage, whereas the experimental data of Figure 3 show ∆Fj as a function of time, which will probably not be linearly proportional to the adsorbed amount of alkane! At the beginning of the adsorption one observes a positive increase of ∆Fj. After reaching a maximum (within typically 100s), ∆Fj decreases to negative values. After a few minutes this decrease pauses for some time (typically hours). Then the signal decreases further, often accompanied by fluctuations, and finally ends in a presumably stable signal (note the logarithmic time scale!) at ∆Fjmle. The experimentally observed maximum positive ellipticities and the first (negative) plateau values are identified with ∆Fjmax* and ∆Fjml, respectively, of the scheme of Figure 2. This attribution will be vindicated later. Figure 4 shows the time evolution of the ellipticity of the system octane/water. Only positive ellipticities are observed, with a maximum ∆Fjmax*. Figure 5 presents Brewster angle microscopy images that were recorded during an adsorption experiment from hexane vapor analogous to the experiments with the conventional ellipsometer. In Figure 5a one clearly observes the typical foamlike structures reminiscent of a gas/liquid coexistence. After some time the surface gets more homogeneous, and eventually small droplets appear as depicted in Figure 5b. Although the Brewster angle microscopic experiment was not simultaneously monitored by the conventional ellipsometry, the time development of the observed structural changes suggests that Figure 5a depicts an adsorbed monolayer in its gas/liquid coexistence and Figure 5b shows a closed ultrathin film with macroscopic (compared to molecular dimensions) droplets. The nucleation of such droplets may cause the fluctuations in ∆Fj before it settles to its equilibrium
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Figure 4. Time development of the ellipsometric signal for octane adsorption at the interface between water and saturated octane vapor (T ) 25 °C). ∆Fjmax* has the same meaning as in Figure 2. value ∆Fjmle. If the droplets are large enough, they are barely detected with conventional ellipsometry because their curved top surface scatters the measurement beam in all directions. According to eq 2 the ellipsometric data can be translated into combinations of d and , respectively d and the refractive index n. In Figures 6 and 7 such combinations are presented for the maximum positive ellipticities, ∆Fjmax*, the ellipticities of the first plateau, ∆Fjml, and the equilibrium ellipticities ∆Fjmle. Indicated on the y-axis are the molecular lengths l0(Cn) and the diameter of an alkyl chain, d0. In Figure 6 the bulk liquid refractive indices of hexane and heptane, nl(C6) and nl(C7),12 are marked on the x-axis. For the ∆Fjmax*, one notes that layer thicknesses close to molecular diameters d0 or lengths l0 mean either refractive indices close to 1 or close to the water value of 1.33. For ∆Fjml and ∆Fjmle (Figure 7) the assignment to combinations of d and n is unambiguous. The thicknesses corresponding to ∆Fjml are about one molecular length if bulk liquid refractive indices are assumed. The film thicknesses corresponding to ∆Fjmle are a few molecular lengths for bulk liquid refractive indices.
IV. Interpretation and Discussion From the dielectric constants and/or refractive indices, the molecular densities were calculated with the Clausius-Mossotti relation (eq 3). This relation is not perfectly correct for molecularly thin films due to the reduced number of polarizable partners compared to the threedimensional case.11 It underestimates the density up to 30% in the case of a monolayer of idealized polarizable, spherical particles; i.e., in reality the film is thicker. Alkane layers are somewhat between this idealized two-dimensional and the three-dimensional case, and the dimensionality effect is significantly less than 30%. Another misinterpretation of the ellipsometric data may originate from the optical anisotropy of the films. If, for instance, the molecules are oriented all-upright in the films, is slightly higher in direction parallel to the molecular axis than normal to it. If this anisotropy is not taken into account, the layer appears thicker than it is in reality. However, even if all molecules are oriented in the same direction, the optical anisotropy is expected to be quite small.13 Because the dimensionality and the anisotropy effects will partially cancel each other, and because they are quite small anyway, in the following the data are interpreted according to the Clausius-Mossotti relation (eq 3) without corrections. In Figures 8 and 9 the thicknesses are plotted as function of the packing densities for ∆Fjmax*, ∆Fjmle, and ∆Fjml. The (12) CRC Handbook of Chemistry and Physics, 75th ed.; CRC Press: Boca Raton, FL, 1995. (13) Paudler, M.; Ruths, J.; Riegler, H. Langmuir 1992, 8 (1), 184.
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packing densities are normalized to the corresponding bulk liquid values, Fl3d, at 25 °C.12 The measurements were performed well below the three-dimensional critical temperature, Tc3d, of all investigated alkanes (Tc3d(C6) ) 507.6 K, Tc3d(C7) ) 539.8 K, Tc3d(C8) ) 568.9 K11). However, according to the twodimensional van der Waals (VdW) equation of state for isotropic, laterally mobile particles, we were above the corresponding two-dimensional critical temperatures, Tc2d, which are either exactly, or close to 0.5Tc3d, depending on the details of the theory.14,15 For anisotropically shaped molecules the mutual orientation of the molecules is important. If the molecules erect each other during condensation, then the theory predicts Tc2d > 0.5Tc3d. If the molecules are lying flat, then Tc2d < 0.5Tc3d. This anisotropy effect can be quite substantial.14 Henceforth, according to the two-dimensional VdW equation of state, in our case Tc ()Tc2d) can be close to 25 °C, and thus one may argue that T > Tc and that the ellipticities identified as ∆Fjmax* are in reality ∆Fjmax (see Figure 2). In this case eq 6a allows the estimation of the corresponding film thicknesses and densities. Thus for all three alkanes one obtains densities of F(∆Fjmax) ≈ 0.43Fl3d (Fl3d ) the three-dimensional liquid bulk phase density at 25 °C) and thicknesses of less than 3 Å. This is significantly less than one molecular diameter (d0 ) 4.5 Å)! In agreement with eq 9 the thicknesses corresponding to ∆Fjmax are the minimum possible thicknesses. These minimum thicknesses are physically not meaningful. Therefore the observed maximum positive values of must be interpreted as ∆Fjmax* and not as ∆Fjmax. This and the observed foam topology (Figure 4) indicate that T < Tc and that there is a phase transition at ∆Fjmax*. For octane the observed maximum ellipticity is probably not identical to ∆Fjmax* as defined in the scheme of Figure 2 because we do not measure a continuous decrease of with ∆Fj longer adsorption times. Nevertheless, it is helpful for the comparison with hexane and heptane to identify the maximum observed ellipticity of octane with ∆Fjmax* and thus with a gaseous state of maximum density at vapor saturation under these experimental conditions. If we assume that the observed maximum positive ∆Fj can be attributed to ∆Fjmax*, then the restriction of eq 9 is not valid any more because ∂d()/∂ is not defined at ∆Fjmax*. Any combination of density and thickness is allowed, except for d < 4.5 Å, the molecular diameter. Consequently, the ∆Fjmax* values correspond to either very low or nearly liquid bulk densities. Let us first analyze the low density alternative. If we assume that T < Tc, we can estimate with a simple VdW approach based on bulk data12 the maximum gaseous phase density at the verge of the gaseous/liquid-phase transition for the three-dimensional case. Thus we obtain for T ) 25 °C: F/Fl3d(C6) ) 1.3%, F/Fl3d(C7) ) 0.9%, F/Fl3d(C8) ) 0.6%. If we assume the same densities for the alkane layers at ∆Fjmax* (Figure 8), we get thicknesses of about 50 Å for all three adsorbed alkanes. Simulations show that for the low-density films measurable changes in the real part of the coefficient of reflectivity could be expected only for thicknesses of more than 200 Å. Hence, at first sight, we cannot exclude 50 Å thick films with densities corresponding to bulk material under equivalent conditions. If we assume monolayer thickness (d ) l0(Cn)) at ∆Fjmax*, we obtain F/Fl3d(C6, d ) l0(C6)) ) 6.1%, F/Fl3d(C7, d ) l0(C7)) ) 4.5%, F/Fl3d(C8,d ) l0(C8)) ) 2.8%. For all three alkanes this is about four to five times the corresponding maximum three-dimensional gaseous (14) De Boer, J. H. Adv. Catal. 1956, 3, 18. (15) Hill, T. L. J. Chem. Phys. 1946, 14 (7), 441.
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Figure 5. Brewster angle microscopy images of the adsorption of hexane from a saturated vapor pressure onto pure water at the beginning of the experiment (a) and after about 1 h (b).
Figure 6. Alkane layer thickness as function of the refractive index for the ellipticities ∆Fjmax*. Also shown are the molecular lengths, l0(Cn), the molecular diameter d0, and the refractive index (12)0.25 corresponding to the minimum film thicknesses.
density. If we assume the minimum allowed thickness of one molecular diameter (all molecules lying flat), d0, then the densities are for all three alkanes about 10-12 times higher than those of the corresponding bulk states. For the high-density branch of the plot of Figure 8 we obtain about 80% of the three-dimensional liquid bulk density for film thicknesses between one molecular diameter and less than 50 Å (above which we would have measured a change in the real part of the coefficient of reflectivity for these densities). Due to the nature of the time evolution of the adsorption process with respect to the ellipsometric signal, the high density interpretation is obsolete for the following reasons. The ellipticity has always a positive maximum for some between 1 and 2 (see Figure 2 or eq 2). We can assume that after the sealing of our compartment, the surface coverage is continuously increasing up to its maximum value. The surface coverage is a function of the film thickness and of the packing density (which, of course, is related to ). Both, the molecular packing density and the thickness will each either increase or remain at least constant during the adsorption experi-
Figure 7. Alkane layer thickness as function of the refractive index for the ellipticities ∆Fjml and the equilibrium ellipticities ∆Fjmle. Also shown are the bulk refractive indices of hexane (nl(C6)) and heptane (nl(C7)), their molecular lengths, l0(C6) and l0(C7), and the molecular diameter d0.
ment. Therefore, the maximum possible density corresponding to the observed ∆Fjmax* is the one that (1) matches the thinnest film possible (in our case d0) and (2) is the lowest of all possible densities fitting this film thickness. In other words, before we could observe the ∆Fjmax* originating from the high, nearly liquidlike density, we will observe the same ∆Fjmax* caused by the lower density because its corresponding lower surface coverage will “occur first” and because there is a minimum film thickness, which does not allow “bypass” of the lower density ∆Fjmax* with a thinner film. The plots of thickness vs density for ∆Fjml and ∆Fmle are depicted in Figure 9. For thicknesses of one (two) molecular length(s) the densities corresponding to ∆Fjmax*(∆Fmle) quite exactly ((5%) match the bulk liquid values Fl3d. For film thicknesses of one (two) molecular diameters (d0) the densities are only slightly (10-20%) higher. If densities less than Fl3d are considered, thicknesses of substantially more than one molecular length must be assumed. The maximum thickness conceivable is about
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Figure 8. Alkane layer thickness for ellipticities ∆Fjmax as function of the densities F normalized to the corresponding bulk densities Fl3d. Also shown are the molecular lengths, l0(Cn), and the molecular diameter d0.
Figure 9. Alkane layer thickness for ellipticities ∆Fjml and ∆Fjmle as function of the densities F normalized to the corresponding bulk densities Fl3d. Also shown are the molecular lengths, l0(Cn), and the molecular diameter d0.
50 Å, beyond which a change in the real part of the coefficient of ellipticity would have been observed. Hence, from the ellipticities without additional assumptions film thicknesses between 5 and 50 Å are conceivable. The densities are in any case approximately those of a liquid condensed bulk phase ( > 2!). There are reasons to favor monolayer and/or bilayer thicknesses. The remarkable stepwise change of the ellipticities at ∆Fjml and ∆Fmle recommends monolayer and/ or bilayer formation at these ellipticties. This implies thicknesses of either d0 or l0(Cn); i.e., the molecules are either lying flat or standing upright. At ∆Fjml multilayers of molecules that lie flat or stand upright (or a mixture of both) seem unlikely because the thickness at ∆Fjmle is about twice of that at ∆Fjml and thus the steps would indicate multilayer/multilayer transitions. Why should these multilayer/multilayer transitions be so conspicuous in the adsorption behavior whereas monolayer/multilayer steps, which should also occur in the course of adsorption, are hidden? On the other hand, a transition at ∆Fjml from monolayers with the alkanes lying flat to monolayers with the molecules oriented all upright is quite conceivable. According to Figure 9 the density would barely change for such a transition. V. Summary and Conclusions The ellipsometric data and the Brewster angle microscopy observations indicate that hexane and heptane form
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molecularly thin films at the interface between water and air saturated with alkane vapor. A detailed analysis of the time evolution of the ellipsometric signal in the course of the adsorption reveals a phase transition from a low density, gaseous-like, to a condensed phase. This is in agreement with foamlike structures observed with Brewster angle microscopy during the adsorption. If we accept the argumentation above and identify the stepwise changes of the ellipticity at ∆Fjml with mono-/ monolayer or mono-/bilayer transitions of molecules that lie flat or stand upright, then we can conclude that the molecular packing densities at the verge of the phase transition (i.e., corresponding to ∆Fjmax*) are 5 to 10 times higher in the films than in the bulk at the gaseous/liquid phase transition at the same temperature. This holds, because if the densities in the film and in the bulk were the same, then the film thickness would largely exceed one molecular length. However, such thicknesses appear unlikely because the thickness of the condensed part of the film at the coexistence of low density and condensed phase is very likely only about one molecular length or less (see argumentation above). Even thicknesses corresponding to one molecular length seem barely realistic for the low density phase, due to entropic reasons as a consequence of the low molecular density. Densities matching thicknesses of molecular length and the ellipticities measured at the phase transition correspond to lateral distances of about 5 molecular diameters. Hence, if the molecules were oriented upright, they would be quite isolated and their lateral interactions would be weak. Only a much stronger affinity of the methyl end segments to the water subphase compared to that of the methylene middle segments could energetically overcome the tendency to tilt.16 Alternatively, one may consider several layers of molecules lying flat at the interface. However, it appears not very plausible that in the course of increasing alkane coverage first bilayers or trilayers of gaseous-like density adsorb and that then, at the same thickness, a transition to a condensed monolayer (molecules upright) or multilayer (molecules lying) occurs. A decrease of the thickness at the transition from the low to the high density phase is even more unlikely. Henceforth it appears most reasonable that the molecules in the low-density film are lying flat at the interface forming one monolayer (d ) d0). The corresponding, somewhat higher density compared to the analogous three-dimensional case indicates a significant decrease of the critical temperature for the monolayer compared to the bulk. This agrees well with theoretical considerations.15 However, the decrease is not as low as expected for an idealized two-dimensional VdW system, which predicts for all alkanes investigated critical temperatures below the measurement temperature and thus a dissappearance of the phase transitions. A critical temperature somewhere between the bulk value and the idealized two-dimensional system is quite plausible if, for instance, the molecules erect each other during condensation.14 The suggested alkane densities of the low-density state at the verge of the transition to the condensed state may also be compared to those of Langmuir monolayers under comparable conditions. For instance, for pentadecanoic acid at 20 °C in the liquid/gaseous coexistence, the area per molecule in the gaseous state is about 1500 Å2, in the liquid condensed state it is about 45 Å2.17 Hence the molecular density in the gaseous state is about 3% of that (16) Schlangen, L. J. M.; Koopal, L. K. Langmuir 1996, 12 (7), 1863. (17) Stine, K. J.; et al. Phys. Rev. A 1990, 41 (12), 6884.
Wetting of Air/Water Interfaces
of the liquid state, which fits quite well the suggested scenario for the alkane films. The stepwise change of the ellipticity in the condensed phase and densities comparable to or slightly higher than the bulk values suggest either monolayers or, for the equilibrium adsorption, at most bilayers of molecules that are either lying flat or standing upright. Alternatively the second step in the ellipticities may be attributed to a transition within a monolayer from lying to uprightoriented molecules. Films thicker than monolayers and bilayers necessitate densities less than the bulk values. Besides that the stepwise changes in the ellipticities would have to be attributed to multilayer/multilayer transitions there are reasons that recommend increased densities in ultrathin films compared to bulk density values. The initial spreading coefficients of hexane and heptane on water are positive. The final spreading coefficients are negative.18-20 For octane both values are very close to zero. Obviously, at least for hexane and heptane, shortrange interactions favor wetting. Long-range VdW interactions favor nonwetting for hexane and longer homologes. This follows from the initial spreading coefficients, the limited film thicknesses, and the Hamaker constants.8,9,21,22 We may assume that the short-range contribution of the interactions can be described by a shortrange Cahn-type gradient theory.23,24 According to this theory the interfacial density will be higher than the bulk density if the short-range interactions favor wetting. (18) Takii, T.; Mori, Y. H. J. Colloid Interface Sci. 1993, 161, 31. (19) Akatsu, S.; Yoshigiwa, H.; Mori, Y. H. J. Colloid Interface Sci. 1995, 172, 335. (20) Johnson, R. E.; Dettre, R. H. J. Colloid Interface Sci. 1966, 21, 610. (21) Hough, D. B.; White, L. R. Adv. Colloid Interface Sci. 1980, 14, 3. (22) Israelachvili, J. Intermolecular & Surface Forces; Academic Press: London, 1976. (23) Cahn, J. W. J. Chem. Phys. 1977, 66 (8), 3667.
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In summary, there are several, quite similar adsorption sequences/steps conceivable for hexane and heptane under the presented conditions: (1) a low-density monolayer, followed by (2) a condensed monolayer, and finally ending as (3) a condensed monolayer or bilayer. In the condensed phase the molecules may be oriented either parallel or normal to the interface with possible transitions from lying to upright but not vice versa. In the condensed phase an upright orientation may be considered as energetically more favorable than the orientation parallel to the interface because of a possible higher affinity of the methyl endgroups compared to the methylene groups to the water.16 It seems however very unlikely that this extra energetic contribution can overcome the entropic cost and orient the molecules upright in the low-density phase. If the scenario with the phase transition is correct, one should observe a kink in the adsorption isotherm at the phase transition. Hitherto this has never been observed unambiguosly for these systems, although transitions from monolayers to multilayers can be derived from isotherms of comparable systems.25 In our case the phase transition occurs only minutes after sealing of the measurement cell. It is unclear to which relative alkane vapor pressure this corresponds. It could be close to saturation, and thus kinks in the adsorption isotherms might be barely measurable. Clearly further investigations are necessary on this subject. Acknowledgment. We thank Gerd Weidemann and Dr. Vollhardt for the generous support with the Brewster angle microscopy. LA970430B (24) Ragil, K.; Bonn, D.; Broseta, D.; Meunier, J. J. Chem. Phys. 1996, 105, 5160. (25) Baumer, D.; Findenegg, G. H. J. Colloid Interface Sci. 1982, 85 (1), 118.
