J. Phys. Chem. B 2002, 106, 1703-1708
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Confined Liquids: Solvation Forces in Liquid Alcohols between Solid Surfaces Volker Franz and Hans-Ju1 rgen Butt* Labor fu¨ r Physikalische und Theoretische Chemie, UniVersita¨ t Siegen, 57068 Siegen, Germany ReceiVed: July 5, 2001; In Final Form: NoVember 20, 2001
The force profile between a silicon nitride tip and solid substrates in short linear alcohols (CnH2n+2O, n ) 2-8) has been measured with an atomic force microscope. On a hydrophilic substrate like mica the profile was oscillatory. The period was longer than the length of a single molecule and increased proportional to the chain length. This indicates that the molecules are in a roughly upright position and may form a double-layer. On a hydrophobic substrate the force profiles showed two distinct jumps that are independent of the chain length of the alcohols, indicating that the molecules lie flat on a hydrophobic substrate.
Introduction The structure of a liquid at a solid surface is of fundamental scientific interest and it is important in many industrial applications. Experimentally the liquid structure near surfaces can be analyzed by different methods (e.g., refs 1-3). One powerful method is the measurement of surface force. In such a measurement two solid surfaces are brought into close proximity and the force required to approach them from a large distance to a separation d is measured. For large separations the force between two solid surfaces in a fluid medium can usually be described by continuum theories such as the van der Waals and the electrostatic double-layer theory. At surface separations approaching molecular dimensions continuum theory breaks down and the discrete molecular nature of the liquid molecules has to be taken into account. Several calculations for apolar molecules, such as hard spheres,4-8 Lennard-Jones fluids,9-14 Gay-Berne,15 and lattice models,16,17 show that the fluid density profile normal to a solid surface oscillates about the bulk density with a periodicity of about one molecular diameter close to the surface. Far away from the surface it smoothens out to the bulk density. For liquids confined between two surfaces these density variations lead to a periodic force.18 Periodic forces at small separations were experimentally verified with the surface forces apparatus (SFA). In the SFA the force between two crossed mica cylinders of typically 1 cm radius is measured. During recent years solvation forces were also studied with the atomic force microscope (AFM). Layered liquid structures were indeed observed for nonpolar liquids with a roughly spherical structure such as octamethylcyclotetrasiloxane (OMCTS), cyclohexane,19-23 and toluene.24 Oscillating surface force were also observed in polar liquids such as propylene carbonate25 or acetone.26 Even across water a tendency for a periodic force was observed.27,28 The structure of linear alkanes and alcohols near solid surfaces is of particular interest because of their widespread application. In monodisperse linear alkanes the force oscillates with a periodicity of 4-5 Å, which corresponds to the diameter of an alkane chain.29 These oscillations dominate the interaction for separations up to 2-3 nm. This suggests that the alkanes have * Corresponding author. E-mail:
[email protected]. Phone: +49-271-7404125. Fax: +49-271-7403198.
a tendency toward a parallel orientation near the mica surface. In contrast, branched alkanes or mixtures of different alkanes showed almost no layering.30 Molecular dynamics simulations reproduced the results and support the conclusion.18 Long-chain n-alcohols (CnH2n+2, n ) 8-12) have been systematically investigated with the AFM.23,31 On graphite a layer of 5 Å thickness was observed for all alcohols under investigation. Nakada et al. could obtain an image of a fishbone ordering of the molecules on graphite. This indicates that the molecules orient parallel to the graphite surface. On mica these authors observed two phases. At room temperature they observed an oscillatory force with a periodicity of 8.6 Å for all alcohols with nine carbon atoms or more. Increasing the temperature to 40 °C leads to a double-layer structure of the long-chain alcohols, that are oriented perpendicular to the mica. These findings are consistent with measurements made with a SFA with 1-octanol and 1-undecanol.32 In an alternative approach Morishige et al. have investigated the structure of n-alcohols (CnH2n+2, n ) 3, 6-9) on graphite by X-ray diffraction.33 Consistently with the force measurements and the images they find that the molecules arrange in a herringbone pattern on the graphite surface. They were also able to measure the melting behavior of these two-dimensional smectic-like phases. However, it was impossible to obtain information about the structure of the molecules in layers other than the adsorbed layer directly on the surface. The solvation forces for solutions of methanol, ethanol, and 1-propanol in water have been investigated by Kanda et al.34,35 They find that short n-alcohols tend to form a monolayer of vertically adsorbed molecules on the surface that are replaced by water molecules at increasing water content. In the present work we extend the previous studies of solvation forces to short chain alcohols for a series from ethanol to 1-octanol (CnH2n+2, n ) 2-8). Experimental Section We used alcohols (per analysi grade, for heptanol and octanol for synthesis grade) from Merck, Darmstadt, Germany, without further purification. All alcohols were dried over molecular sieves (LAB, 0.3 nm, Merck) under dry argon for at least 24 h. Mica and highly ordered pyrolytic graphite (HOPG) have been purchased from PLANO, Wetzlar, Germany. They were cleaved immediately before each experiment and exposure to ambient
10.1021/jp012541w CCC: $22.00 © 2002 American Chemical Society Published on Web 01/29/2002
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Figure 1. Normalized force-versus-distance curves (force divided by radius of the tip in 10-3 N/m) for the interaction of a silicon nitride AFM-tip with mica in 1-ethanol, 1-butanol, 1-pentanol, 1-hexanol, 1-heptanol, and 1-octanol. Each force curve is a superposition of ≈10 individual force curves. All force curves except of ethanol were fitted with an exponentially decaying periodic function (eq 4). These fits are shown as continuous lines. In addition, the van der Waals attraction calculated with eq 1 using Hamaker constants given in Table 1 are shown as dotted lines. The insets show weak forces at an enhanced scale.
air was kept as short as possible. The experiments were carried out with a commercial AFM (NanoScope 3, Veeco Instruments, Santa Barbara, CA), equipped with a fluid cell. V-shaped silicon nitride cantilevers (Veeco Instruments, CA, length 200 or 100 µm, width 40 µm, thickness 0.6 µm) were cleaned in a plasma cleaner in oxygen for 8 min at 30 W. As radius of the tip curvature we use an average value of 40 nm as determined previously by transmission electron microscopy.36 Cantilever spring constants were individually determined by moving them against a reference cantilever,37 yielding values in the range of 0.04-0.08 N/m for the long cantilevers and 0.17 N/m for the short ones. In the vertical direction we calibrated the AFM scanner interferometrically.38 In a force measurement, the sample is periodically moved up and down at constant speed by applying a voltage to the piezoelectric translator onto which the sample is mounted while measuring the cantilever deflection. For all measurements with long cantilevers we used an approach velocity of 100 nm/s, while for the short cantilevers the velocity was 50 nm/s. To obtain a force-versus-distance curve (from now on called a “force curve”), cantilever deflection as a function of piezo displacement was recorded. From this, a force curve is calculated by multiplying cantilever deflection with the spring constant of the cantilever to obtain the force. The z-piezo displacement is subtracted from the cantilever deflection to obtain the distance from contact. To resolve as many details of force curves as possible, in a first step we plotted approximately 10 force curves in one graph. To fit the curves with appropriate functions, the data array of all force curves was sorted according to the d-values of the data points. Results and Discussion Force Curves on Mica. Force curves measured with all alcohols showed common features (Figures 1 and 2). In all cases
Figure 2. Normalized force-versus-distance curves for the interaction of a silicon nitride AFM-tip with mica in 1-propanol. The force curve is a superposition of ≈10 individual force curves. They were fitted with an exponentially decaying periodic function (eq 4, continuous line). We measured the force during approach (filled circles) and retraction (open circles). Positive forces are repulsive, negative forces attractive. The van der Waals attraction was calculated with eq 1 using Hamaker constants given in Table 1 (dotted line). The distance DH is indicated as a vertical dashed line. The elastic deformation is fitted to eq 5 (white solid line).
the normalized force, i.e., the force divided by the radius of the tip, is shown. No significant force was observed for distances larger than roughly 4 nm. At closer distance during the approach of the tip several repulsive maxima and subsequent jumps were observed. The series of two (for octanol) or three (for propanol to heptanol) repulsive maxima is presumably a manifestation of the solvation force caused by the ordering of molecules in the gap between the mica and the tip surface. In the following we call the last layer of alcohols removed out of the gap the “inner” layer. It corresponds to the repulsive maximum at the closest distance. At least two outer layers could be identified.
Liquid Alcohols between Solid Surfaces
J. Phys. Chem. B, Vol. 106, No. 7, 2002 1705
TABLE 1: Dielectric Permittivities and the Refractive Indices for the Alcohols Used at 20 °Ca ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol
3
n3
Amica/10-21 J
Agraphite/10-19 J
25.3 20.8 17.8 15.1 13.0 11.8 10.3
1.361 1.385 1.399 1.410 1.418 1.425 1.430
3.3 2.8 2.5 2.3 2.1 2.0 1.9
1.19 1.06 0.98 0.92 0.88 0.84 0.82
a Hamaker constants A were calculated for mica ( ) 5.4, n ) 1 1 1.58441) and graphite interacting with silicon nitride (2 ) 7.4, n2 ) 1.98841) across alcohol.
Determination of zero distance is often a critical step in AFM force measurement. Two observations indicate that after the jump through the inner layer direct contact between the tip and mica surface is established. First, no further jump is observed even when applying a normalized force up to 0.125 N/m. Second, the “contact” part of the force curve is a straight line showing no indications of deformation. Jumps of the tip occur when the gradient of an attractive force on the tip exceeds the spring constant of the AFM cantilever (see, e.g., ref 39). The cantilever jumps until its spring force is balanced by an equally strong repulsive force. The whole region of the attractive force in between cannot be resolved during the approach. However, the attractive force in this regime which is inaccessible during the approach can be probed by retracting the cantilever immediately after the jump has occurred. Experimentally this is realized by a force trigger that is slightly higher than the force at the end point of the jump and lower than the force at which the next jump occurs. This has been carried out for 1-propanol on mica (Figure 2). Comparison with van der Waals Forces. The solvation force was much stronger than the continuum van der Waals attraction. To demonstrate this, we calculated the van der Waals force using a simple theory40 and approximating the geometry of the tip by a sphere of radius R. For distances below 5 nm retarded van der Waals forces can be neglected and the nonretarded van der Waals force is given by
FvdW ) -
AR 12d2
(1)
Here, A is the nonretarded Hamaker constant. The Hamaker constant was calculated with eq 11.8 of ref 40. The material properties enter via the dielectric permittivities at zero frequency of the sample, tip, and medium. For two dielectric solids such as mica, alcohols, and silicon nitride we can use the following expression for the dielectric constant:
(iν) ) 1 +
n2 - 1 1 + V2/νe2
(2)
Here, n is the refractive index of the material in the visible and νe is the main electronic adsorption frequency that is set to 3 × 1015 s-1.40,41 For graphite a different expression for the dielectric constant had to be used to account for the high electric conductivity:
(iν) ) 1 -
νp2 V2
(3)
Here, νp denotes the plasma frequency. For graphite it is 1.87 × 1016 s-1.42 Hamaker constants are listed in Table 1.
TABLE 2: Results Obtained from Fitting Superimposed Force Curves with the Exponentially Decaying Periodic Function (4)a ethanol 1-propanol 1-butanol 1-pentanol 1-hexanol 1-heptanol 1-octanol
σ/nm
∆/nm
ξ/nm
E/GPa
0.95 1.05 1.29 1.35 1.50 1.65
0.35 0.20 0.61 0.45 0.60 0.60
0.39 0.4 0.7 0.65 0.8 0.8
0.05 0.1 0.1 0.1 0.05 0.03 0.01
a Key: σ, phase shift; ξ, decay length of the exponentially decaying periodic function; E, Youngs modulus of the inner layer calculated with eq 5.
Figure 3. Mean jump-in distance D (down triangles), DH, the distance of zero force before the inner force maximum (circles), and the periodicity σ (squares) are shown versus the number of carbon atoms. For comparison the straight solid line shows the length of the corresponding, fully extended alcohol. Lines are guides for the eye. The inset shows a typical histogram of jump-in distances D measured with 1-hexanol at an approaching velocity of 200 nm/s.
When calculating the Hamaker constant, we assume that the molecules are free to rotate. In reality the molecules in the confined space are ordered and not free to orient with respect to an external electric field. Thus, the van der Waals force is probably even smaller than expected from eq 1. Evaluation of Solvation Force. To evaluate solvation forces more quantitatively, superimposed force curves were fitted with an exponentially decaying periodic function (refs 40, p 266, and 43)
F ) F0 cos
(2πσ[d + ∆])e
-d/ξ
(4)
Here, σ is the periodic length which at first approximation can be interpreted as the length of density fluctuations in the confined liquid.10,44,45 The decay of density fluctuations is characterized by the decay length ξ. Equation 4 is strictly valid with ∆ ) 0 only for two plane walls without interaction with the molecules in the liquid and an oscillatory density profile of the liquid between the walls with slowly varying amplitude.16,18,46 In the proximity of a rigid wall, however, the density is discontinuous and not slowly varying. Therefore the phase shift ∆ is introduced as an additional fitting parameter. Results for our measurements are listed in Table 2. The period of the force oscillations increased linearly with increasing chain length of the alcohols (Figure 3). This indicates that the molecules are not oriented parallel to the mica surface but at least partially in an upright position. The period σ is larger than the calculated length of the molecules. At least two possible structures agree with the observations. The first is a bilayer
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Franz and Butt
Figure 5. Illustration of the elastic foundation or ‘mattress’ model.
The elastic layer of thickness h rests on a rigid base and is compressed by a rigid spherical indenter. Using this model the force versus indentation δ can be approximated by
F) Figure 4. Dependence of the height of the inner jump D for 1-propanol on mica on the approach velocity of the tip (solid line, right axis). The dotted curve refers to the left axis and shows the break-through force for 1-propanol on mica.
structure (Figure 7), in which the alcohols are tilted with respect to the surface normal and the hydroxy groups form hydrogen bonds. The tilt angle can be estimated: Taking the length of the alcohol molecules with n carbon atoms to be L ) n‚1.23 + 2.98 Å the estimated thickness of a bilayer is 2L cos Θ. Here, Θ is the tilt angle with respect to the surface normal. Fitting the measured periodicities with this function leads to an average tilt angle to the substrate normal of 49°. For 1-propanol this interpretation fits well with X-ray studies of the bulk liquid structure.47 These X-ray studies revealed a chain structure in which a row of 1-propanol molecules is connected by hydrogen bonds. The carbon tails of the 1-propanol molecules are tilted with respect to the bond plane so that the height of the whole row can be calculated to be 9-10 Å. This agrees with the value of the periodicity for 1-propanol. In the second possible structure the alcohol molecules stand upright. They oscillate around their average position so that the particle density is smeared out and the periodicity of the particle density is increased. The ordering is nematic. The considerable oscillations of the alcohol molecules in the second structure should make hydrogen bonding impossible and the hydroxy groups of the alcohol molecules do not have to point toward each other. With the present experimental evidence we cannot exclude one structural model. Evaluation of the Inner Layer. Several measures exist for the thickness of the inner layer. D is the distance over which the tip jumps through the inner layer. It is equal to the distance of the inner force maximum. DH is the distance at the bottom of the inner force maximum where the force is zero. At this distance no load is applied to the inner layer and it its deformation is minimal. In Figure 3 the mean values of D and DH are shown for all alcohols. To get an impression of the scatter of results obtained from individual force curves, the inset shows a histogram of jump-in distances D obtained in 1-hexanol. Break-through forces and jump-in distances D of all alcohols did not significantly depend on the approaching velocity of the tip. As an example Figure 4 shows results obtained with propanol. In general, D and DH increase with increasing chain length. Since an increasing force compresses the inner layer, the jump distance D is always smaller than the distance DH. We note that DH is close to the periodicity σ of the oscillatory force profile so that the inner layer presumably has the same structure as the outer layers. To account in a more quantitative way for the deformation of the inner layer, we use the elastic foundation or “mattress” model (ref 48, p 104). This model is illustrated in Figure 5.
πERδ2 h
(5)
Here, E is the Youngs modulus of the elastic layer. The indentation δ of the inner layer is calculated from a position where the force applied to the layer is zero. This position, DH, and Young’s moduli were obtained by fitting the inner repulsive force peak with eq 5 (Table 1, Figure 2). We obtained Young’s moduli of 0.01-0.1 GPa. The alcohol layers show an elasticity similar to that of Langmuir-Blodgett bilayers of lipids on mica of typically 0.04-0.07 GPa.49 Reference calculations with the Hertz theory yielded elastic moduli that were by a factor of 4 higher. Since the Hertz theory is only valid for thin layers if the deformation is very small in the layer, it cannot be used for our experiments. The interpretation using an elastic theory should, however, be taken with care. In elastic theory the molecules cannot escape under load which cannot be safely assumed for a layer that is not chemisorbed to the surface. However, the measurements show that alcohols on mica have similar elastic as adsorbed lipid bilayers. The amplitude of the force required to break through the inner layer was low for ethanol, increased with increasing chain length until propanol and then decreased again. We have yet no good explanation for the fact that the solvation force is strongest for propanol. It should, however, not be overinterpreted. Gelb and Lynden-Bell50 showed theoretically that the exact tip shape may have a strong impact on the amplitude of the solvation force. The precise shape of the tip was not determined in our experiments so that it might well be that differences between the tip radii might account for the various amplitudes. Temperature Dependence. All our measurements were made at 22 ( 2 °C. For long-chain alcohols Nakada et al.31 distinguished between a phase at room temperature and at higher temperatures of about 40 °C. At the higher temperature the periodicity depends on the chain length in almost the same way as our measurements at room temperature; the period for the long-chain alcohols from 1-octanol to 1-dodecanol increased by 1.2 Å per carbon atom while we measured 1.5 Å per carbon atom. Note also that Nakada et al. did not observe a flat lying phase for 1-octanol at room temperature. They postulate a transition temperature Tm at which the structure of the alcohol molecules changes from a horizontal to a more upright orientation. This transition temperature depends, like the melting point, on the chain length of the alcohol. Since octanol has a transition temperature below 25 °C, Tm for the shorter n-alcohols is expected to be even lower so that at room temperature only an upright oriented phase should exist. This is what we observed so that the results of Nakada et al. are in good agreement with our measurements. Peculiar Features. Force-curves of three alcohols, ethanol, 1-hexanol, and 1-octanol, showed peculiar features. For ethanol we observed a long-range attractive force which was stronger
Liquid Alcohols between Solid Surfaces
Figure 6. Normalized force-versus-distance curves (force divided by radius of the tip in 10-3 N/m) for the interaction of a silicon nitride AFM-tip with HOPG in 1-propanol and 1-pentanol. Each of the curves represents one single measurement. The dotted and the solid lines denote the van der Waals force for 1-propanol and 1-pentanol, respectively.
than the calculated van der Waals force. It decays roughly exponentially with a decay length of 2.7 nm. If we interpret this repulsion as an electrostatic force according to the DLVO theory this corresponds to a salt concentration of 0.005 mol/L, which might be due to ions dissociated from mica. Only one jump through an inner layer could be identified. The force, at which the jump occurs, varied considerably more than for the other alcohols. This indicates a high degree of disorder in the adsorbed ethanol layer. In the case of 1-hexanol a shoulder before the inner jump was observed. A possible explanation is a rearrangement of the molecules under the pressure of the tip. Similar shoulders have been identified in Monte Carlo simulations of rod-shaped molecules between two walls that interact by a Gay-Berne potential.15 These authors could show that a nematic phase forms in an isotropic liquid phase that is squeezed out layer by layer when the size of the gap between the walls is decreased. Just before the removal of a layer, however, the molecules in the gap tilt which eventually leads to a shoulder in the force profile. With 1-octanol only the inner force peak was clearly resolved. The second repulsive force maximum was less reproducible than with the other alcohols. No third repulsive maximum could be measured. This might indicate that the layering in 1-octanol is less pronounced than in the other alcohols. We would like to stress that the experimental results were sensitive to the presence of water. Measurements in alcohols that were not dried prior to use showed unreproducible force profiles and often only a single jump could be identified. This issue has been previously addressed by Kanda et al.35,34 who carried out detailed measurements in water-alcohol mixtures. They could show that the occurrence of jumps is suppressed if the alcohol weight fraction is decreased from 0.99 to 0.3. Solvation Force on Graphite. Force curves on graphite have been recorded in the same way as on mica. Here, we made measurements only for 1-propanol and 1-pentanol (Figure 6). During the approach there is no interaction at distances larger than 10 nm. The van der Waals attraction on graphite is significantly stronger than on mica. This attractive force leads to a jump of the cantilever toward the surface at a separation of about 2 nm. However, at a distance of roughly 9 Å the repulsive solvation forces starts to dominate and two subsequent jumps are discernible. For 1-propanol the first jump occurs at a force of ≈7 mN/m (separation from contact ≈8 Å) over a distance of 4-5 Å. The second, or “inner”, jump occurs at a force of ≈70 mN/m over a somewhat smaller distance of 3-4 Å. Taking the distance between the zero force at the bottom of a repulsive
J. Phys. Chem. B, Vol. 106, No. 7, 2002 1707
Figure 7. Models for the layering of 1-propanol confined between a spherical tip and mica. The period spacing is 9-10 Å. Hollow circles indicate carbon atoms, and black circles, oxygen. The hydrogen atoms are left out for clarity. (a) The molecules are arranged in the conformation proposed by Mikusinska-Planner.47 (b) Layers of alcohols show nematic order and oscillate about their average positions.
force peak where the deformation of the layer is minimal, we calculate both jump distances to be 4.5 Å. For 1-pentanol the jumps occur at lower forces but the distances are the same as for 1-propanol. The forces at which jumps occur differed considerably between subsequent force curves and in many cases only the inner jump was observed. The large variations between the curves make it impossible to superimpose the force curves because instead of enhancing average features the superposition of dissimilar force curves obscures the details of the individual curves. We observe a constant period of a multiple of the molecular diameter of ≈4.5 Å, independent of the chain length. The measurements indicate that the alcohols are oriented parallel to the surface. These observations confirm the result of others.31,23,33 Conclusions. Solvation forces of linear alcohols (CnH2n+2O, n ) 2-8) between mica and silicon nitride surfaces show a periodicity of n‚1.5 + 2.9 Å. This indicates that the molecules are forming a layered structure in the gap in which they stand at least partially upright. Two different models are proposed. One consists of bilayers of tilted alcohol molecules and the other of a nematic order of the individual molecules. For all alcohols under investigation except of ethanol the double-layer structure extends over at least three periods from the mica substrate into the liquid. Force curves measured on graphite in 1-propanol and 1-pentanol showed a solvation force with two peaks and a spacing of 4.5 Å. This indicates that on graphite n-alcohols show a tendency to align parallel to the surface. This order extends at least over two layers into the liquid. Acknowledgment. We thank K. Graf and F. Schneider for fruitful discussions. We further acknowledge financial support by the Deutsche Forschungsgemeinschaft grant Bu 701/11 (V.F.). References and Notes (1) Lo¨ring, R.; Findenegg, G. H. J. Colloid Interface Sci. 1981, 84, 355-361. (2) Yu, C. J.; Richter, A. G.; Kmetko, J.; Datta, A.; Dutta, P. Europhys. Lett. 2000, 50, 487-493. (3) Doerr, A. K.; Tolan, M.; Seydel, T.; Press: W. Physica B 1998, 248, 263-268. (4) Mitchell, D. J.; Ninham, B. W.; Pailthorpe, A. Chem. Phys. Lett. 1977, 51, 257-260. (5) Snook, I. K.; Henderson, D. J. Chem. Phys. 1978, 68, 2134-2139.
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