Langmuir 2007, 23, 4695-4699
4695
Contact-Line Friction of Liquid Drops on Self-Assembled Monolayers: Chain-Length Effects M. Voue´,*,† R. Rioboo,† M. H. Adao,† J. Conti,† A. I. Bondar,‡ D. A. Ivanov,§ T. D. Blake,† and J. De Coninck† Centre de Recherches en Mode´ lisation Mole´ culaire, UniVersite´ de Mons-Hainaut/Materia NoVa, Parc Initialis, AV. Copernic, 1, B-7000 Mons, Belgium, SerVice de Science des Polyme` res, UniVersite´ Libre de Bruxelles, CP233 BVd du Triomphe, B-1050 Bruxelles, Belgium, Institut de Chimie des Surfaces et Interfaces de Mulhouse, BP 2488, 15 rue Jean Starckyn, F-8057 Mulhouse Cedex, France ReceiVed October 2, 2006. In Final Form: February 27, 2007 The static and dynamic wetting properties of self-assembled alkanethiol monolayers of increasing chain length were studied. The molecular-kinetic theory of wetting was used to interpret the dynamic contact angle data and evaluate the contact-line friction on the microscopic scale. Although the surfaces had a similar static wettability, the coefficient of contact-line friction ζ0 increased linearly with alkyl chain length. This result supports the hypothesis of energy dissipation due to a local deformation of the nanometer-thick layer at the contact line.
During the past 20 years or so, many researchers have become interested in the wetting characteristics of materials in dynamic processes.1,2 Different mechanisms have been proposed to explain the observed phenomena, usually on the basis of either hydrodynamic theories (refs 3 and 4 and references cited therein) or the so-called molecular-kinetic theory (MKT).5,6 These different approaches have been compared for several experimental systems.2,7-9 When considering the spreading of liquid drops on planar surfaces, the power laws that describe the relaxation of the contact angle and the growth of the contact radius, though different for each model, are sufficiently similar to make it difficult to distinguish which mechanism might be at work. Nevertheless, recent investigations of other geometries (cylindrical pore10 and fiber11,12) have shed new light on this question. The MKT provides a description of the moving contact line in terms of a stress-modified activated rate process.5,6 At equilibrium, the molecules at the contact-line jump from one potential well on the substrate to another at a frequency of K0. The length of these jumps is λ. When disturbed, the displacement of the contact line occurs at speed V given by
[
]
γ(cos θ0 - cos θ) dR V) ) 2K0λ sinh dt nkBT
γ is the liquid surface tension, θ0 and θ are the equilibrium and dynamic contact angles, respectively, n is the surface density of interaction sites (potential wells), usually approximated by λ-2, and kB and T have their usual meanings. For a small drop of constant volume (low vapor pressure liquids and nonporous substrates), the speed V is also related to the dynamic contact angle thought the spherical cap approximation. This gives a linked set of partial differential equations that can be solved numerically and fitted to data to obtain values of K0 and λ. For low values of the argument of the sinh function, eq 1 can be linearized:
V)
3 dR K0λ ) γ(cos θ0 - cos θ) dt kBT
Equation 2 shows that V is proportional to the out-of-balance surface tension force γ(cos θ0 - cos θ). The factor
ζ0 )
(1)
where R is the radius of the drop in contact with the solid substrate, * Corresponding author. E-mail:
[email protected]. † Universite ´ de Mons-Hainaut. ‡ Universite ´ Libre de Bruxelles. § Institut de Chimie des Surfaces et Interfaces de Mulhouse. (1) De Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827-863. (2) Blake, T. D. J. Colloid Interface Sci. 2006, 299, 1-13. (3) Cox, R. G. J. Fluid Mech. 1986, 168, 169-194. (4) Kistler, S. F. In Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; p 311. (5) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421-423. (6) Blake, T. D. In Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; p 251. (7) Petrov, P. G.; Petrov, J. G. Langmuir 1992, 8, 1762-1767. (8) De Ruijter, M. J.; De Coninck, J.; Oshanin, G. Langmuir 1999, 15, 22092216. (9) Petrov, J. G.; Ralston, J.; Schneemilch, M.; Hayes, R. A. Langmuir 2003, 19, 2895-2801. (10) Martic, G.; Gentner, F.; Seveno, D.; De Coninck, J.; Blake, T. D. J. Colloid Interface Sci. 2004, 270, 171-179. (11) Seveno, D.; De Coninck, J. Langmuir 2004, 20, 737-742. (12) Vega, M. J.; Seveno, D.; Lemaur, G.; Adao, M. H.; De Coninck, J. Langmuir 2005, 21, 9584-9590.
(2)
kBT
(3)
K0λ3
has the physical dimensions of a friction coefficient.13 It describes the friction of the liquid molecules on the solid substrate per unit length of the contact line and so is referred to as the contact-line friction. Recently, Blake and De Coninck14 have shown that ζ0 can be related to the viscosity of the liquid η and the exponential of the reversible work of adhesion γ(1 + cos θ0)
ζ0 )
ηVL λ3
exp
[
]
γλ2(1 + cos θ0) kBT
(4)
where VL is the molecular volume of the unit of flow. Equation 4 shows the explicit contributions of the dynamic viscosity of the liquid and the solid-liquid interactions to the contact-line friction. (13) De Ruijter, M. J.; Blake, T. D.; De Coninck, J. Langmuir 1999, 15, 7836-7847. (14) Blake, T. D.; De Coninck, J. AdV. Colloid Interface Sci. 2002, 96, 21-36.
10.1021/la062884r CCC: $37.00 © 2007 American Chemical Society Published on Web 03/28/2007
4696 Langmuir, Vol. 23, No. 9, 2007
On soft substrates, the normal component of the liquid surface tension deforms the substrate at the contact line. As the contact line moves, the deformation also moves, thus dissipating energy. For a given driving force, contact-line displacement then occurs at a speed slower than the one measured on a nondeformable surface of similar surface energy and roughness. This phenomenon was identified as visco-elastic braking by Shanahan and coworkers in the early 1990s.15-18 In a previous article,19 we have shown how the thickness of a soft elastomer layer modifies the wetting speed of a liquid drop. This problem has also been theoretically considered by Long and co-workers for elastomeric films20 and grafted polymer layers.21 In ref 19, the thickness of the elastomer layers was in the micrometer range, and no behavior was described for layers thinner than 3 µm. The question we consider here is whether there exists a dissipation of energy due to the deformation of the substrate when the layer thickness lies in the nanometer range. To answer this question, we have studied the spreading of liquid drops on a series of alkanethiol self-assembled monolayers (SAMs) on gold surfaces. The chain length of the alkanethiols was varied from 8 to 18 carbon atoms. Details of the preparation of the SAMs have been described by Semal and co-workers22 and are briefly summarized below. The gold substrates were prepared by epitaxially depositing 500 Å of gold onto silicon (100) wafers (T = 1130 °C, pressure 2 × 10-6 mbar, evaporation rate = 1 Å/s). Secure anchoring of the gold layer to the silicon surface was ensured by first depositing a 30 Å titanium layer. After degreasing by sonication in chloroform and cleaning under UV/ozone, the wafers were immersed for 15 min in ethanol to reduce the oxide layer that appears after UV/ozone exposure and then for 18 h in a grafting solution of 3 mM alkanethiol in ethanol at room temperature (∼21 °C). The length of the alkyl chain was varied from 8 to 18 (i.e., from octyl mercaptan [CH3-(CH2)7-SH] to octadecyl mercaptan [CH3-(CH2)17-SH]). After reaction, the grafted substrates were rinsed with ethanol and kept in that solvent until needed for further use. Only thiols with an even number of carbon atoms were used to avoid the oscillatory behavior of the static contact angle that occurs because of the different orientation of the terminal methyl groups.23 Surfaces prepared in this way will be referred to as Cn surfaces, with n ) 8, 10, 12, 14, 16, and 18. The surfaces were imaged by AFM over an area of 1 × 1 µm2. The resulting profiles provided a check on the quality of the gold-coated substrates, as characterized by its average roughness parameter Ra. The wettability of the surfaces was probed by studying the contact angle relaxation of squalane (Sigma, 99%, 2,6,10,15,19,23-hexamethyltetracosane, C30H62) drops using a custom-built goniometer with a high-speed CMOS camera (Vossku¨hler HCC1000) and synchronized LED flash, allowing image capture at an acquisition rate of 923 images/s. The spatial and depth resolution of the images were 1024 pixels × 512 pixels and 8 bits, respectively. Squalane is a nonpolar, nonvolatile hydrocarbon liquid with a surface tension of γ ) 31.1 mN/m and a viscosity of η ) 35.0 mPa s at a temperature of 21 °C. Drops (12-17 µL) were placed on the surface using an automated syringe, and the time relaxation of the dynamic advancing contact (15) Shanahan, M. E. R.; Carre´, A. Langmuir 1994, 10, 1647-1649. (16) Shanahan, M. E. R.; Carre´, A. Langmuir 1995, 11, 1396-1402. (17) Carre´, A.; Gastel, J. C.; Shanahan, M. E. R. Nature 1996, 379, 432-434. (18) Shanahan, M. E. R.; Carre´, A. Colloids Surf., A 2002, 206, 115-123. (19) Voue´, M.; Rioboo, R.; Bauthier, C.; Conti, J.; Charlot, M.; De Coninck, J. J. Eur. Ceram. Soc. 2003, 23, 2769-2775. (20) Long, D.; Ajdari, A.; Leibler, L. Langmuir 1996, 12, 5221-5230. (21) Long, D.; Ajdari, A.; Leibler, L. Langmuir 1996, 12, 1675-1680. (22) Semal, S.; Bauthier, C.; Voue´, M.; Vanden Eynde, J. J.; Gouttebaron, R.; De Coninck, J. J. Phys. Chem. B 2000, 104, 6225-6232. (23) Gupta, V. K.; Abbott, N. L. Phys. ReV. E 1996, 54, R4540-R4543.
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Figure 1. (a) Representative topographic AFM image (1 × 1 µm2) of the uncoated gold substrate. (b) Same for the C18-grafted surface. The values of the average roughness parameter Ra are given in Table 1. (c) Power spectrum density (PSD) of the uncoated gold surface. Dashed lines represent linear fits of the PSD data. Table 1. Average Roughness Parameter Ra (nm) of Various SAMs as a Function of the Number of Carbon Atoms in the Alkylthiol Molecule ncarb ncarb Ra (nm)
uncoated 0.81
8 0.72
10 0.86
12 0.70
14 0.83
16 0.84
18 0.83
angle θ toward its equilibrium value θ0 was recorded. Additionally, advancing (θa) and receding (θr) contact angles were determined by adding or withdrawing liquid from the drop, with a view to measuring the contact angle hysteresis. Multiple measurements were made on each surface, taking care never to use the same spot twice. Representative AFM images of the bare gold surface and of the C18 surface are shown in Figure 1a,b, respectively. The structure of the surface is clearly apparent. The grain size, estimated from the power spectrum density and assuming an isotropic sample, is about 42 nm (Figure 1c). The topographic structure of the underlying gold layer is preserved after the grafting of the alkanethiol molecules. Within statistical and experimental error, the average roughness parameter Ra is not influenced by the length of the alkanethiol molecules (Table 1) and is about 0.80 nm. These values are comparable to those presented in our previous publication.22 In Figure 2, it is shown that the static contact angles are close to the advancing ones and that they increase slightly (by about 5°) from C8 to C12 before reaching a plateau value at 50° (chains of 12 carbon atoms and higher). The associated error bars are of the order of the symbol size and are not visible in the figure. The receding contact angle follows the same trend (θr = 42°). Thus, as shown in Figure 2 (inset), contact angle hysteresis is more or less constant (at about 7.510°) over the range of chain lengths investigated (C8 to C18). In an article by Gupta and Abbott,23 the intensity of the even-odd effect is about 5°, which is higher than the dispersion of our experimental data and justifies the choice of molecules with an even number of carbons. On the time scale (a few seconds) at which the experiments have been run, the dissolution and/or the penetration of the
Letters
Langmuir, Vol. 23, No. 9, 2007 4697 Table 2. Jump Frequency (K0), Jump Length (λ), and Contact-Line Friction (ζ0) of Squalane Drops Spreading on Alkanethiols Monolayers of Increasing Thickness: Influence of the Length of the Alkanethiol Molecules (ncarb)
Figure 2. Advancing (b), receding (2), and static (4) contact angles of squalane drops as a function of the length of the aliphatic chain grafted onto the gold surface. (Inset) Variations of the contact angle hysteresis with the chain length of the alkanethiol molecules.
Figure 3. Dynamics of the contact angle of a squalane drop on a C10-grafted surface (2) and on a C18-grafted surface (4). The lines correspond to best-fit dynamic contact angles calculated from eq 1. (Values of K0 and λ are given in Table 2.) (Inset) Details of the first 50 ms.
squalane molecules in the alkanethiol upper sublayer can be neglected: the contact angle hysteresis is low (7° on average and in any case less than 10°, Figure 2 inset), and after the initial spreading phenomenon, the contact angle value is stable in time and the equilibrium value is close to the advancing value (Figure 2). This would not have been the case if penetration had occurred. Furthermore, the contact angles for squalane correspond to those reported in our previous article.22 In that article, it was shown that the critical surface tension of the SAMs, γc, was about 20.5 mN/m and corresponded to the surface tension of a fully methylated surface with a high crystalline content. Had the penetration of squalane molecules in the SAM taken place, the critical surface tension would have been higher, corresponding to that of a polyethylene surface (-CH2-):24 γc ≈ 30 mN/m. It is therefore reasonable to consider that the static wetting characteristics of the Cn surfaces do not change significantly on increasing the length of the grafted molecules. Dynamic contact angle relaxation data for the C10 and C18 surfaces are shown in Figure 3 (filled and open triangles, respectively). Except for the C8 surface, for which the contact angles are slightly lower, the dynamic contact angles measured on the remaining C12, C14, and C16 surfaces are distributed between the curves for the C10 and C18 surfaces and have been omitted from the Figure for clarity. Taking into account the contact angle hysteresis and remembering that the static angle may take any (24) Adamson, A. W. Physical Chemistry of Surfaces; Wiley & Sons: New York, 1990.
ncarb
K0 (× 107 Hz)
λ (× 10-10 m)
ζ0 (Pa s)
8 10 12 14 16 18
3.99 ( 0.25 0.79 ( 0.04 1.26 ( 0.09 0.73 ( 0.05 0.63 ( 0.05 0.55 ( 0.04
6.20 ( 0.17 8.61 ( 0.25 7.72 ( 0.14 8.57 ( 0.25 8.96 ( 0.23 8.67 ( 0.22
0.77 ( 0.10 0.82 ( 0.10 0.90 ( 0.11 0.89 ( 0.11 0.93 ( 0.11 1.11 ( 0.16
value between the advancing and receding angles, the asymptotic contact angle at times longer than about 0.5 s is statistically the same for both sets of data. This agrees with the results presented in Figure 2, but whereas these near static angles are not significantly dependent on the length of the alkanethiol chain, the dynamic contact angles measured at shorter times do differ systematically from one surface to another (Figure 3, inset). As we show below, these differences can be interpreted in terms of the contact-line friction. To proceed, eq 1 was used to fit the data to determine the independent values of θ0, K0, and λ. These are shown in Table 2. As previously described,25 the error bars associated with K0 and λ were calculated using a bootstrap method.26 Equation 3 was then used to calculate the contact-line friction ζ0. The values of K0 are consistent with those found by others for low-energy surfaces (e.g., 6.3 × 106 Hz reported by Blake2 for the forced wetting of a polyethylene surface by a 0.104 Pa s aqueous glycerol solution). On more polar surfaces (i.e., modified polyimide surfaces27), a lower value of the jump frequency K0 is measured. As a rule of thumb, we expect, because of the presence of oxygen atoms, the polar component of the surface tension to increase and the interaction with liquids to be stronger. Another point of comparison can be found in the article by Bayer and Megaridis.28 They published a relevant value for a system that is not too dissimilar from ours (octane on Teflon), with the slightly higher value to be expected because of the lower viscosity of the liquid. The λ values reported in Table 2 are in the range of 6.2 to 9.0 Å. Strong and Whitesides29 found that n-alkanethiol molecules adsorbed on a gold(111) substrate had a hexagonal structure, with a S-S spacing of 4.97 Å (i.e., 21.4 Å2 per molecule). Although this spacing is on the same order, it is smaller than the λ values, suggesting that the displacement of liquid molecules at the contact line is rather complex. The link between λ and the structure of the solid also depends on the liquid characteristics. We have shown in earlier work30 that the behavior of a chainlike liquid molecule, such as squalane, on a solid substrate might involve the simultaneous trapping of several atoms of the squalane molecules in the potential wells of the solid substrate and that λ did not exactly correspond to the spacing of the potentials wells. Furthermore, it was shown to be the result of the collective motion of all of the liquid atoms of a single molecule in the potential wells. Another possible source of this discrepancy is the inherent roughness of the gold substrates. Figure 4 shows that the contact-line friction increases linearly with the chain length of the SAMs, even though θ0 is essentially (25) Semal, S.; Voue´, M.; de Ruijter, M.; Dehuit, J.; De Coninck, J. J. Phys. Chem. B 1999, 103, 4854-4861. (26) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1992. (27) Thomas, R. R. Langmuir 2003, 19, 5763-5770. (28) Bayer, I. S.; Megaridis, C. L. J. Fluid Mech., 2006, 558, 415-449. (29) Strong, L.; Whitesides, G. M. Langmuir 1988, 4, 546-558. (30) De Coninck, J.; Voue´, M. Interface Sci. 1997, 5, 141-153.
4698 Langmuir, Vol. 23, No. 9, 2007
Figure 4. Increase of the contact-line friction coefficient ζ0 with the chain length (ncarb). The values of ζ0 and of the associated error are given in Table 2. The plain line corresponds to the linear fit a + bx of the friction coefficients with respect to the number of carbon atoms (a ) 0.563 ( 0.069, b ) 0.026 ( 0.005, and R2 ) 0.935). The slope is statistically different from 0 (P < 0.001). (Inset) Increase of the jump length λ with the chain length (---, with the C10 surface; -, without the C10-surface). In both cases, the slope is statistically different from 0 (P < 0.01).
Figure 5. Correlation between the speed of the contact line and the difference (cos θ0 - cos θ) for the C10 (b) and the C18 (O) surfaces.
constant. The error bars associated with the linear regression coefficients are given in the caption of Figure 4. The average increase of ζ0 per carbon atom is about 26 ( 5 mPa s. Over the range investigated, this result is statistically significant, and the regression line crosses the experimental error bars associated with the ζ0 values. The latter were used as weighting factors in the linear regression. The statistical significance can be deduced from hypothesis tests on the slope of the regression line.31 With a Student’s t value of 4.70 and four degrees of freedom, the result is statistically significant at a probability level of P < 0.001. Furthermore, analyzing all of the subsets of data obtained by removing one point from the whole data set confirms that the significance level is a least 0.01, whatever the discarded point. This definitely confirms the H1 hypothesis: the contact-line friction increases with the number of carbon atoms in the chain. This result also provides evidence that the dynamic wetting behavior of a given liquid on a surface is not determined entirely by its static wettability and that, even for a film thickness in the (31) R Development Core Team. R: A Language and EnVironment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2004. Software available at http://www.R-project.org.
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nanometer range, other energy-dissipation channels, such as the local deformation of the substrate, may have to be taken into account. A comparison of our experimental results with other potentially relevant studies on monolayers is not straightforward. For example, there are both conceptual and physical differences between contact-line friction and the microscale friction coefficient as measured by friction force microscopy (FFM). However, it could be helpful to consider ways in which the theoretical analysis of Long and co-workers mentioned earlier20,21 might shed light on our results. Carpick and Salmeron32 have reviewed fundamental investigations involving FFM. Among the references cited is the work of Green et al.,33 which shows a clear correlation between the friction coefficient determined by FFM and the surface energy measured by contact angle methods. Another interesting study is that of Xiao and co-workers,34 who showed that the friction of an alkylsilane SAM on mica was strongly correlated to the alkyl chain length. The shorter chains exhibited the highest friction, which was interpreted as a consequence of the poor packing of these molecules giving rise to more dissipation. Lio et al.35 and Brewer et al.36 extended the work to thiol films on gold surfaces. The results presented in Figure 4 would appear to be contradictory to these earlier results35-39 because the shorter chains exhibit the lowest contact-line friction. This contradiction is briefly summarized hereafter. As the adsorbate chain length increases, chain mobility decreases, and the packing of the adsorbates becomes more rigid.38 Short-chain SAMs exhibit mobile chain structures containing larger numbers of gauche defects than long-chain SAMs, which may (for greater than approximately 12 carbon atoms) adopt 2D crystalline structures.39 The shorter adsorbates form structures in which the alkyl chains possess significant mobility; the deformation of the alkyl chains is thus easier, leading to greater rates of energy dissipation than is the case for the more ordered long-chain adsorbates. However, one should keep in mind that in our experiments the chain length acts essentially as a dummy variable; of more interest is the packing density,32-39 which in previous work decreased from the shortest chains to the longest ones. To the best of our knowledge, both the chain-length effects and the packing density are linked and cannot be decoupled. In the spreading studies reported here, the role of the packing density is played by the inverse of the square of the jump length λ. Because the contactline friction concerns pairs of solid substrates and liquid molecules, the apparent packing density can somehow be decoupled from the “pure” solid substrate effects. From the FFM point of view, this would correspond to probing the friction with cantilevers having different chemical functions. In the inset of Figure 4, it is shown that the jump frequency λ increases with chain length. This effect is statistically significant (P < 0.01), when taking into account or discarding the experimental data obtained for the C10 surfaces. The apparent packing density, which scales as λ-2, therefore decreases. The surfaces characterized by the smallest (32) Carpick, R. W.; Salmeron, M. Chem. ReV. 1997, 97, 1163-1194. (33) Green, J.-B. D.; McDermott, M. T.; Porter, M. D. J. Phys. Chem. 1995, 99, 10960-10965. (34) Xiao, X.-D.; Hu, J.; Charych, D. H.; Salmeron, M. Langmuir 1996, 12, 235-237. (35) Lio, A.; Charych, D.; Salmeron, M. J. Phys. Chem. B 1997, 101, 38003805. (36) Brewer, N. J.; Beake, B. D.; Legget, G. J. Langmuir 2001, 17, 19701974. (37) McDermott, M. T.; Green, J.-D. B.; Porter, M. D. Langmuir 1997, 13, 2504-2510. (38) Dubois, L. H.; Zegarski, B. R.; Nuzzo, R. G. J. Chem. Phys. 1993, 98, 678-688. (39) Leggett, G. J.; Brewer, N. J.; Chong, K. S. L. Phys. Chem. Chem. Phys. 2005, 7, 1107-1120.
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apparent packing density therefore exhibit the highest friction, as found by Lio35 and Brewer36 using FFM. Clearly, differences exist between friction coefficients obtained from wetting experiments and by FFM. For example, the molecules used to probe friction in the FFM experiments are tightly bound to the cantilever, whereas in the wetting experiments the molecules of the liquid drop are subject only to liquid-liquid interactions. Nevertheless, the similarities are suggestive, and the relationship between the two remains an open question. Let us now consider a possible braking of the drops as a function of the chain length. This concept was introduced by Shanahan and Carre´15-18 and attributed to visco-elastic effects occurring at the triple line, when a liquid drop was spreading on a deformable surface, typically an elastomer. Because of the crystalline structure of the SAMs, the application of this model to our data is somehow questionable but remains interesting because it can evidence a dissipation process at the triple line, which is typically the mechanism deduced from our observations. In a first approach, we tried to compare the behavior of the SAMs with a very thin layer of a deformable material. However, to date, the energy dissipation, due to the visco-elastic properties of the materials or to other factors, has not been studied for layers of nanometer thickness. It is therefore hard to say whether the influence of the deformation is higher for short or long molecules. In particular, the dissipation source could be the local bending of the chains in the vicinity of the contact line and not the vertical stretching of the alkanethiols molecules. None of the articles by Shanahan and Carre´ deal with these kinds of layers. Moreover, to the best of our knowledge, the models of Ajdari and Long, who theoretically considered the dynamics of wetting on thin rubber films20 and on grafted polymer layers,21 have not been used to interpret experimental data. Nevertheless, the comparison between the wetting behavior of polymer brushes and of SAMs remains interesting for further investigations. It is beyond the scope of this article to extract quantitative data concerning the (visco-) elastic parameters of the SAMs, and both the Shanahan and Long models are tentative explanations of our observations. In MKT, only an explicit contribution of the liquid viscosity to the contact-line friction has been evidenced to date. Our data show that dissipation exists, that it is relatively weak, and, because squalane is used throughout all of our experiments, that it concerns some characteristics of the SAMs. The nature of the dissipation process can be discussed. Nevertheless, let us try a semiquantitative application of Shanahan and Carre´’s model
Langmuir, Vol. 23, No. 9, 2007 4699
log[cos θ0 - cos θ] = n log V + log
[
γ 2πGVnO
]
(5)
where V is the speed of the contact line, G is the shear stress modulus, and is a cutoff distance for the elastic behavior of the material. V0 is a characteristic speed defined in such a way that (V/V0)n is the strain energy dissipated during the ridge motion. n is the exponent characteristics of the dissipation. The operational definitions of both and V0 make their practical use difficult, and the only practical information that can be extracted from eq 5 is the characteristic exponent n. Figure 5 represents on a log-log scale our data in a form that is compatible with eq 5. The filled and the open symbols correspond to the C10 and C18 surfaces, respectively. Fitting these data with power laws (eq 5) yields different values for the characteristic exponent: 0.626 ( 0.010 for the C10 surfaces and 0.534 ( 0.016 for the C18 surfaces. Because these two exponents are different, we may conclude that the dissipation is different on both kinds of surfaces. In conclusion, we have examined the wettability of SAMs prepared by grafting alkanethiols molecules of increasing chain length onto gold surfaces. Although the roughness, static contact angles, and contact angle hysteresis are the same for all of the surfaces, we have shown that it is possible to discriminate the different SAMs on the basis of the time relaxation of the advancing contact angle. More precisely, we have found the contact-line friction parameter ζ0 to be linearly correlated with the alkyl chain length of the grafted molecules. Beyond the functional definition of λ, this article sheds new light on the role of this parameter, which can now be related to an effective packing density. The difference in dissipation is also evidenced by the semiquantitative application of Shanahan and Carre´’s model, although the basis of their theory does not directly apply to our surfaces. Complementary molecular dynamics simulations will be run to investigate the influence of the packing density of the solid surface on the spreading of a drop. Acknowledgment. This work is partially supported by the Ministe`re de la Re´gion Wallonne, Belgian Funds for Scientific Research (FNRS), and the European Community (FEDER and Phasing out Program). Thanks are due to J. P. Baland, M. J. Vega, and C. Bauthier for their assistance. LA062884R
