Nanoroughness Impact on Liquid–Liquid Displacement - The Journal

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Nanoroughness Impact on Liquid−Liquid Displacement Melanie Ramiasa, John Ralston,* Renate Fetzer,† and Rossen Sedev Ian Wark Research Institute, University of South Australia, Mawson Lakes, South Australia 5095, Australia ABSTRACT: The influence of surface nanoroughness on the static and dynamic behavior of a solid−water−dodecane contact line is investigated. Surface roughness is found to affect the substrate static and dynamic wettability for rootmean-square roughnesses below 7 nm. The kinetics of liquid− liquid displacement is slowed down drastically by the nanoroughness. Nevertheless, contact line motion is found to be governed by a thermally activated process. This process is not based on a pure molecular adsorption−desorption mechanism. Instead, two different nanoscale local displacements mechanisms occurring in the vicinity of the contact line may account for the thermally activated dynamics: we suggest that both molecular adsorption−desorption processes and contact line pinning on nanodefects play significant roles in controlling water displacement by dodecane on surfaces which are rough at the nanoscale.

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INTRODUCTION The partial wetting of ideal solid surfaces by simple liquids is reasonably well-understood. In contrast, our understanding of the wetting processes of surfaces which are not perfectly homogeneous, smooth, and inert is still rudimentary. Natural and artificial surfaces endowed with a specially designed topography present interesting wetting properties.1 Driven by an increasing interest toward superhydrophobic surfaces,2 there has been a strong focus on how the static wetting state is influenced by roughness,3 despite the fact that in many technical fields it is the motion of a complex liquid front across such microtextured surfaces which controls the fate of industrial processes.4,5 Thus, it is of practical interest to understand the mechanisms which drive the dynamic wetting of such nonideal surfaces. For generality’s sake we focus on the displacement of a liquid on a rough surface for the case where the surrounding fluid is another immiscible liquid. In this way, the viscosity of both fluids is accounted for and the results may then be extended to other systems when one can neglect the viscosity of one of the fluids, e.g., water/air/solid system. We deal with the spontaneous displacement of water by a dodecane droplet on nanorough surfaces. The nanoscale features on the rough surfaces are obtained by depositing spherical silica nanoparticles on smooth glass substrates. We investigate the influence of nanoparticle coverage on the dynamics of liquid−liquid displacement. The inherent wettability of the substrate is kept constant, as is the pair of liquids, which have a viscosity ratio of 1.5. Fast video microscopy was used to record the motion of the contact line as the dodecane drop displaces the surrounding water. From the dimension of the dewetted area as it expands as a function of time, we extract both the instantaneous dynamic contact angle and the contact © 2012 American Chemical Society

line velocity. These data for the various nanorough substrates are analyzed and used to critically assess dynamic wetting models. The correlation between the model microscopic parameters obtained and the topographic properties of the surface is discussed. Further, we address the role of nanoroughness in determining the energy dissipation mechanisms occurring at the three-phase contact line.

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DYNAMIC WETTING MODELS In the system studied, capillary driven flow governs the motion of the three phase contact line as two immiscible liquid phases displace one another on a flat solid surface.6 The dodecane droplets do not exceed 300 μm in diameter, and the corresponding Bond number is small (B = ΔρgR02/γ ∼ 5 × 10−3); thus gravity can be neglected.7 The driving force for the wetting process is the out of balance interfacial tension Fw = γ(cos θ0 − cos θD(U ))

(1)

where γ is the interfacial tension between the two fluids, θ0 is the static contact angle, and θD(U) is the velocity-dependent dynamic contact angle. Two different approaches have been developed to describe contact line dynamics in fluid−fluid displacement. The distinction is the origin of the main source of energy dissipation occurring as the three-phase contact line moves across the surface. In the molecular kinetic theory the only channel of dissipation is considered to be thermally activated displacements taking place in the immediate vicinity of the contact line, while viscous friction in the bulk liquid is neglected.8 On the Received: December 13, 2011 Revised: April 4, 2012 Published: April 25, 2012 10934

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contrary, in the hydrodynamic model, the interaction between the solid surface and the fluid phase is not taken into account and energy dissipation is solely ascribed to viscous flow.9,10 Molecular Kinetic Theory. Based on Eyring’s activated rate theory,11 the molecular kinetic theory states that the thermal activity is responsible for the constant back and forth motion of “elements” (originally molecules) at the contact line. The equilibrium frequency, K0, of these local fluctuations can be formulated as a function of the activation free energy, ΔG0*12 K0 =

⎛ −ΔG 0* ⎞ kBT exp⎜ ⎟ h ⎝ NAkBT ⎠

Using eqs 7 and 8, the contact line friction coefficient in the case of the linear approximation can be written as a function of the fluid viscosities and volumes of unit flow ξ12 =

(2)

ξ12 =

(3)

(4)

On the contrary, if the argument of the sinh is much smaller than unity, eq 3 becomes U=

γ(cos θ0 − cos θD)K 0λ 3 1 = Fw kBT ξ

(5)

where the contact line friction coefficient ζ = kBT/K0λ3 quantifies the energy dissipation in the three-phase zone. Revisions to the original molecular kinetic theory have been proposed in order to take into account the viscosity of the fluid phases. Blake first suggested an amended version of eq 2 based on a free energy approach.13 The total activation free energy of wetting is split into three components consisting of surface and viscous contributions of the two fluid phases 1 and 2: ΔGS*, ΔGv1*, and ΔGv2*, respectively. Since the activation free energy of the viscous components are directly related to the viscosity, η, and the volume of unit flow, ν, of the fluid phases11

ηi =

⎛ ΔG vi* ⎞ h exp⎜ ⎟ vi ⎝ NAkBT ⎠

(6)

this approach leads to K0 =

⎛ −ΔG S* ⎞ hkBT exp⎜ ⎟ η1v1η2v2 ⎝ NAkBT ⎠

(η1 + η2)v λ3

⎛ γλ 2(1 + cos θ ) ⎞ 0,1 ⎟⎟ exp⎜⎜ kBT ⎝ ⎠

(10)

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(7)

MATERIALS AND METHODS In the wetting experiments, the contact liquids were ultrapure deionized water, with a resistivity better than 18 MΩ cm and dodecane (99%); the latter was used as received from SigmaAldrich (Sydney Australia). The dodecane−water interfacial tension was 51.8 mN m−1 at 25 °C. The viscosities of water and dodecane measured at 25 °C are respectively 0.89 and 1.34 cP.

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Blake and De Coninck further assumed that the specific activation free energy of wetting, ΔgS* = ΔGS*/λ2NA, can be equated to the reversible work of adhesion, Wa, between the solid and the fluid under consideration in the presence of the other fluid phase, i.e. Δg S* ∼ Wa = γ(1 + cos θ0)

(9)

In eq 10, it is assumed that the volume of unit flow, ν, and the displacement length, λ, are the same for both fluids. Equations 9 and 10 both predict a straight line of positive slope when plotting the logarithm of the friction coefficient, scaled by the sum or the product of the fluid viscosities, ln(ζ/ (η1 + η2)) and ln(ζ/(η1η2)), respectively, as a function of the work of adhesion of the advancing fluid. From the slope and the intercept of the linear fits, the parameters λ and ν can be extracted. Hydrodynamic Approach. To describe the viscous dissipation, Cox10 developed a hydrodynamic model relating the contact line velocity to the dynamic contact angle, based on the assumption that the local microscopic contact angle can be equated to the equilibrium contact angle and allowing the liquid front to slip in a region of size Ls close to the contact line. A simplified version of this model has been derived and used for dodecane−water displacement in ref 16. We have shown previously16,17 that both hydrodynamic and molecular kinetic models seem to provide reasonable descriptions of the dynamic dewetting of various substrate and fluid systems in two distinct velocity regimes. The hydrodynamic theory captures the early and fast stage of the dewetting for small contact angles of the receding fluid, while the molecular kinetic theory describes the slow end of the motion as the dynamic contact angle of the receding fluid converges toward its static value. However, in the experiments discussed here, as the roughness of the substrate increases, the number of experimental data points available in the high-velocity stage of the process decreases substantially. Interpreting the experimental data with the hydrodynamic model was not valid, simply due to the fact that roughness slows the dewetting process so much that very few high velocity data points are available. The ensuing discussion is therefore based on assessing the applicability or otherwise of the molecular kinetic theory.

where λ is the displacement distance between surface sites (or neighboring potential wells). Where the argument of the sinh is large, eq 3 simplifies to ⎡ γ(cos θ − cos θ )λ 2 ⎤ 0 D ⎥ U = K 0λ exp⎢ 2 k T ⎦ ⎣ B

hλ 3

⎛ γλ 2(1 + cos θ ) ⎞ 0,1 ⎟⎟ exp⎜⎜ k T ⎝ ⎠ B

where θ0,1 is the static contact angle of the fluid phase under consideration. In our previous publication we proposed a different approach to compare the friction coefficient with the work of adhesion, based on a force balance analysis. Assuming that the contact line motion driving force Fw is balanced by the sum of the friction force contribution from each fluid,15 then

where kB and h are the Boltzmann and Planck constant, respectively, and NA is Avogadro’s number. The work provided by the out of balance interfacial tension overcomes the energy barrier to local displacement, so that the overall velocity of the contact line, U, can then be written as8 ⎡ γ(cos θ − cos θ )λ 2 ⎤ 0 D ⎥ U = 2K 0λ sinh⎢ 2kBT ⎦ ⎣

η1v1η2v2

(8) 10935

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Sample Preparation and Characterization. Nanorough substrates were prepared by depositing spherical silica nanoparticles on smooth microscope glass slides. To ensure a controlled chemistry of the substrate, the nanorough surfaces were coated with a silane layer. As the topography of the substrate was varied by changing the nanoparticle surface coverage, the silane layer on top of the asperities remained the same on all samples. This guaranteed that the influence of roughness modification was studied, rather than any chemical change. Nanoparticle Deposition. Bare glass slides were carefully cleaned using the following procedure. The plates were sonicated in ethanol for 15 min, rinsed with ethanol and water, dried under a nitrogen flow, and washed in piranha solution (sulfuric acid 98% and hydrogen peroxide 1:3) for 2 h. The glass slides were then thoroughly rinsed with Milli-Q water, dried under a nitrogen flow, and plasma cleaned for 2 min. The surfaces were then completely wetted by water, as shown in separate experiments. Immediately after plasma cleaning, the activated smooth and clean glass plates were immersed in a 2 wt % solution of aminopropyltriethoxysilane (APTES, 97%, Sigma-Aldrich, Sydney Australia) in anhydrous toluene in a glovebag under a nitrogen atmosphere. The plates remained immersed in the solution for 2 h in order to allow a complete self-assembled monolayer to form.18 The slides were rinsed with clean toluene and then sonicated in clean toluene for 5 min in order to remove any excess of APTES from the surface. When these APTES-coated glass slides are in contact with water, their surface is positively charged. The APTEScoated substrates were subsequently dipped into an aqueous nanoparticle suspension using an automated dip coater. The speed of immersion and emersion were precisely controlled in order to control the nanoparticle attachment density at the required amount. A suspension of bare negatively charged silica nanoparticles purchased from Nissan Chemical was used to control the substrate nanoroughness. The nanoparticle size ranges from 10 to 20 nm in diameter. The solution concentration was varied from 0.02 to 0.1 mg/mL at pH 7.5 ± 0.2, reduced from pH 9 in the original solution with dilute hydrochloric acid, in order to tune the number of nanoparticles attaching to the smooth substrate. The attachment of the nanoparticle onto the substrate is influenced by electrostatic interactions between the charged nanoparticles and the oppositely charged substrate as well as by capillary entrainment.19 After dipping, the substrate was again rinsed copiously with Milli-Q water and dried under a nitrogen flow. Finally, the nanorough substrates were baked in an oven at 150 °C for 20 h so as to gently anchor the nanoparticles to the glass substrate. In the last step of the surface tailoring process, in order to control the chemistry of the surface, a new self-assembled monolayer of APTES was deposited on top of the nanoparticles, following the same procedure as before but reducing the sonication time to 1 min and the time spent in piranha solution to 30 min. The nanorough substrates obtained in this way were characterized both chemically and physically, as described below. Static Wettability. Static contact angle measurements on the various substrates were performed via a captive bubble setup. Before each experiment the substrate of interest was sonicated in ethanol for 1 min, rinsed with ethanol and then Milli-Q water, and dried under a nitrogen flow. It was then immersed at the midpoint, facing down, in a glass cell filled with Milli-Q water. A droplet of dodecane was produced by a U-shaped

needle and brought into contact with the substrate from below. The dodecane drop volume was varied in a controlled way by adding or withdrawing a small quantity of dodecane, enabling the receding and advancing contact angle of the water displaced by the oil droplet to be measured. The contact angles were measured on more than five different spots on each sample in order to test the uniformity of the surface. All surfaces generated reproducible static contact angle data. The receding water/dodecane contact angle on a smooth APTES layer (rms 0.015.24 In the present system studied, at velocities below 0.05 m/s, We is less than 0.0005. For each individual drop, the volume, V, of the drop was calculated from the drop diameter, optically measured for the first images recorded before film rupture. The radius R of the contact area was obtained from the subsequent images as a function of time, with t0 set when the film ruptures. The first derivative of the contact area radius, R, with respect to time, dR/dt, gives the velocity of the three phase contact line, U. To avoid the large scatter of velocity data in the late stage of droplet spreading, a rational function of degree three was fitted to the radii data and the time derivative of the best fit was taken. Assuming that the droplet remains as a spherical cap shape during the spreading process, the instantaneous dynamic water contact angle was calculated using the geometrical relationship

we expect the dynamics of the wetting to be influenced by the state preferentially adopted by the system at rest. The Wenzel factor is determined experimentally from AFM images as described in the following section. It is used to characterize the substrate topography, together with the average root-mean-square (rms) value, defined as hrms =

1 ΔR

∫R

R +ΔR

h2 dR′

(13)

where h is the height (or depth) of the asperities, and the integration is performed over all positions R′, from the beginning of the scan at position R to its completion at R + ΔR. The nanoparticle surface coverage (lateral density) is defined as dNp =

covered area total area

(14)

Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). The physical properties of the substrate were investigated by AFM and SEM measurements. Imaging of the surface was performed under ambient conditions using tapping mode atomic force microscopy (Asylum Research MFP-3D). 2 × 2 μm2 scan size images were used to determine the rms roughness and the Wenzel factor using standard procedures. Larger scan size images (20 × 20 μm2) were analyzed to confirm the homogeneity of the nanoparticle deposition on the samples. Although a few larger aggregates were present, we observed a random attachment of individual nanoparticles on the smooth glass slides at submonolayer coverage, which was homogeneous overall for the whole substrate (Figure 1). Cross sections of the AFM images

⎤1/3 ⎛ 3V ⎞1/3⎡ sin 3 θ ⎜ ⎟ R= ⎢ ⎥ ⎝ π ⎠ ⎣ 2 + 3 cos θ − cos3 θ ⎦

Figure 1. AFM images for smooth and nanorough samples obtained with different surface coverages. The height scale is 30 nm for all images. 10937

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APTES coating. In all the positive ion spectra for APTEScoated substrates, signals ascribed to the aminated fragments C2H6N+(m/z = 44.05), CH4N+ (m/z = 30.03), and CNH2+ (m/z = 28.02) were detected.25 These signals were present in the same proportion on both smooth and nanorough samples, but not on the bare glass reference. Very small levels of tin species were present in the APTES-coated samples, which suggest a good coverage of the glass surface. The results from the SIMS are conclusive, too. CN (m/z = 26) and CNO (m/z = 44) signals give a good indication of the APTES coating. ToF-SIMS mapping images of the CN and CNO signals show a homogeneous distribution of these species over the 500 × 500 μm2 area analyzed. The chemistry of the surface was therefore the same for both smooth and nanorough samples coated with APTES. Surface Roughness. The results obtained from the roughness analysis are shown in Table 1. Following the controlled experimental protocol described above, tuned nanoparticle deposition is achieved with a coverage ranging from 0 to 82%, increasing in an almost linear fashion. From the AFM images it appears that the nanoparticles mainly form submonolayers on the smooth surfaces. However, on the most densely covered substrate, one can occasionally observe a particle sitting on top of other ones. These rather scarce stacking events lead to greater roughness than what is achievable from simple monolayers. The rms roughness and the Wenzel factor generally increase with nanoparticle coverage, as anticipated. Interestingly, however, this increase is not linear: both quantities present a local maximum around 40% coverage. We discuss the possible reasons for this in the next section. Further it is important to note that using spherical particles to produce the surface asperities results in the formation of overhangs. This was confirmed by the SEM images. Because the AFM tip cannot penetrate underneath the overhangs, the AFM images cannot reproduce the exact topography, resulting in deviations between real topography and AFM data. As we neglected the effects of the undercut areas in our calculations of the roughness factors, these values should be regarded as minimum quantities. Static Wetting. The results obtained from the static contact angle measurements are reported in Figure 2. The advancing and receding water−dodecane contact angles are plotted as a

Side-view experiments confirmed that the calculated dynamic contact angles coincide with the one observed visually. Every single drop of dodecane displacing water as it spreads on the solid surface sample provides a set of data. On each type of surface, the spreading of many drops (three droplets or more) are recorded on various spots of the substrate using different frame rates in order to confirm the reproducibility of the measurements.

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RESULTS We present results obtained from several sets of experiments obtained for various nanorough substrates; for typical AFM images see Figure 1. Precise adjustments in the preparation of the substrate described earlier enabled the nanoparticle surface coverage to be varied from 25 to 82% (Table 1). Furthermore, a smooth surface coated with an APTES layer under the exact same conditions as the nanorough substrates was used as a reference. Table 1. Nanoparticle Coverage (%), Substrate Roughness (RMS), and Wenzel Factors for Smooth and Nanorough Surfaces surface type smooth rough

nanoparticle coverage (%) 0 27 31 39 41 52 71 75 82

± ± ± ± ± ± ± ±

3 2 1 5 5 2 1 3

rms (nm) 1.0 4.1 5.6 5.8 5.3 4.6 5.7 5.6 6.3

± ± ± ± ± ± ± ± ±

0.3 0.6 0.5 0.6 0.1 0.5 0.1 0.1 0.6

Wenzel factor 1.000 1.04 1.07 1.14 1.17 1.09 1.12 1.18 1.19

± ± ± ± ± ± ± ± ±

0.001 0.02 0.01 0.02 0.05 0.01 0.01 0.04 0.03

Surface Chemistry. The successful deposition of the APTES layer was confirmed in the XPS survey scan by the presence of the N 1s peak at ∼400 eV, which is characteristic of the silane.18 On the bare glass slide, the N 1s signal was not present. The atomic compositions of the APTES layer on both smooth and nanorough samples were indistinguishable. ToF SIMS analysis was performed to further characterize these surfaces and also verified the successful deposition of the

Figure 2. Advancing and receding contact angle of water plotted as a function of (a) the Wenzel factor and (b) the nanoparticle surface coverage as % of the total area. The Wenzel prediction, eq 12, is represented with the blue line. The error bars represent the standard deviations obtained from the contact angle measurements on at least five different areas of the substrates. 10938

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Figure 3. Hysteresis of the static contact angle for the nanorough surfaces as a function of (a) the surface Wenzel factor and (b) the percentage of area covered by the nanoparticles.

function of (a) the Wenzel roughness factor and (b) the nanoparticle surface coverage. The water/dodecane receding contact angle, θr,W, on a smooth APTES coated surface is 54 ± 4°. θr,W decreases as the nanoparticle coverage and Wenzel factor increase. This is in qualitative agreement with the Wenzel prediction of eq 12 (represented by the blue line in Figure 2a, for θY approximated to θ0,r), from which a decrease in the receding contact angle is expected as the roughness increases. However, the theoretical prediction underestimates the contact angle decay. The decrease observed experimentally is much more pronounced than expected from eq 12. The receding contact angle of water decreases by more than 30° for Wenzel factors ranging from 1 to 1.20, although these surfaces are fairly smooth, with rms roughness values less than 7 nm. Further, Figure 2b clearly shows that over the nanoscale of roughness investigated here the receding water/dodecane contact angle decreases as the number of nanoparticles present on the surface increases. In contrast, the values obtained for the advancing contact angle of water, measured as some dodecane is withdrawn from the dodecane drop, do not increase monotonically but pass through a maximum around r = 1.15, corresponding to 40% surface coverage. As a result, the static contact angle displays a maximum in hysteresis, as shown in Figure 3. The contact angle hysteresis on the smooth surfaces is about 20°. On the nanorough surfaces the hysteresis is even greater, with a maximum of 65° for r ∼ 1.15. This large hysteresis suggests that pinning of the contact line or, perhaps, liquid trapping occurs. These phenomena were not directly observable from the top view recordings. However, the abrupt change in slope for the Wenzel factor occurring at r = 1.15 and the maximum in hysteresis observed suggest that the wetting state below and above 40% coverage may be different. Dynamic Wetting. θr,w as a Function of Time. The dynamic contact angle of the receding water displaced by dodecane on increasingly nanorough surfaces is shown in Figure 4 as a function of time. Note that the oscillatory behavior of the data originate from instrumental artifacts (illumination fluctuates in intensity) and not from any real effect. On all substrates, smooth and nanorough, the dynamic contact angle of water first increases rapidly and then plateaus

Figure 4. Variation of dynamic receding water contact angles with time on nanorough surfaces.

at a quasi-static value. The slope of the curve indicates the velocity of the three-phase contact line at each point. As the roughness increases in relation to surface coverage, the motion of the contact line slows. The values obtained for the quasistatic angles are in good qualitative agreement with those obtained from the static study. However, in the time frame of the recording, the receding water contact angle does not quite reach the static value but is slightly less. This difference is enhanced on the roughest substrates where the static values are up to 15° larger than the plateau values. Molecular Kinetic Theory Fits. The experimental values of the cosine of the dynamic contact angle, cos θD(U), are plotted as a function of the velocity of the contact line, U. These data sets were fitted with the full MKT, eq 3, using a nonlinear curve fitting tool from the software Origin 7, based on the method of least-squares regression. The parameters θ0MKT, λ, and K0 were set as free fitting parameters. The best fits of the experimental data obtained from the spreading of dodecane drops displacing water on various samples are given in Figure 5. The plots are presented on a logarithmic scale for the velocity in order to judge the quality of the fits in the lowvelocity regime. For the smooth samples the first few data points from the high-velocity regime were neglected in order to fit the data. The motion of the contact line slows down 10939

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θ0MKT), λ increases up to more than 3 nm and K0 decreases down to about 0.03 MHz.

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DISCUSSION Static Wetting. Among the vast number of questions raised regarding the influence of surface roughness on wettability, one of the most fundamental asks “what magnitude of roughness affects the process?”. Several studies report that this occurs at a critical defect size of 100 nm, below which the liquid is insensitive to the defect.26−28 The static wetting result presented here showed clearly that, for the liquid−liquid system investigated, rms roughness as small as 7 nm has a nonnegligible effect on the static wettability of the surface. The size of the nanoparticles used to produce the nanorough surfaces ranges from 10 to 20 nm in diameter. As the particles form submonolayer coverages, with occasional nanoparticle superimposition on the surfaces with the highest coverage, the maximum defect height is expected to be between 20 and 40 nm, most certainly less than 100 nm (Figure 1). For this small scale roughness we observed a definite dependence for both advancing and receding contact angles on the nanoparticle density (Figure 2). The water/dodecane receding contact angle decreased as the nanoroughness increased. From these results it appears that for liquid−liquid systems (1) nanoscale roughness should not be neglected in static wetting studies, (2) the density of the nanoparticles, just like their size, is a crucial parameter in defining a surface topography, and (3) for the surfaces studied here the nanoroughness enhances the substrate hydrophilicity. Over the wide range of nanoparticle coverages investigated (0−82%), we observed that the static contact angle exhibits a maximum in hysteresis. This behavior was reported for solid− liquid−vapor systems as early as 1964 in the experimental work of Johnson and Dettre.22 The latter revealed that the contact angle hysteresis increases for weakly rough surfaces, before passing through a maximum and then decreases as the roughness was further increased. Analogous behavior was later found for both microscopic29 and nanoscopic defects.30,31 For microscopic surface roughness, the maximum in hysteresis has been attributed to composite wetting. More specifically, the formation of small air bubbles inside the surface asperities is believed to be responsible for a transition between Wenzel and Cassie wetting states.32 As nanobubble formation is also possible,33 a composite wetting transition could theoretically

Figure 5. Cosine of the experimental water/dodecane receding dynamic contact angle on increasingly nanorough surfaces as a function of the three-phase contact line velocity. The solid lines show the Origin fits of eq 3 to the experimental data in the low velocity regime (U < 2 × 10−2 m/s).

markedly on the nanorough surfaces. Even with the very high frame rates used to capture the liquid−liquid displacement only very limited data were able to be acquired in the high-velocity regime. This is especially the case for the rougher samples. We therefore focus on the slow end of the motion, below 0.01 m/s where the molecular kinetic theory applies. The MKT qualitatively captures the experimental data trend. In the velocity range just below about 0.01 m/s the experimental data follow exponential behavior, in good agreement with the predictions of the molecular kinetic theory for large arguments, presented in eq 4. MKT Parameters. The MKT parameters λ and K0 obtained from these fits are represented in Figure 6 as a function of the static receding contact angle of water, θ0MKT, the third parameter obtained from the corresponding MKT fit. Each data point shown represents the average of at least three experiments performed on the respective sample (e.g., three drops spreading on a different position on the same substrate). The numerical values obtained for both λ and K0 are of the same order of magnitude as results reported in the literature (see ref 15 and table therein). The length of local displacement obtained for the smooth surfaces (open black squares) falls within 1 and 2 nm, and the frequency of the jumps, K0, is of the order of 1−10 MHz. As the roughness increases (decreasing

Figure 6. Model parameters λ and K0 from the best fit of the molecular kinetic theory to the low-velocity regime, for all data sets on smooth and nanorough surfaces as a function of the final contact angle. 10940

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Figure 7. Dependence of the contact line friction coefficient normalized by the sum or the product of the fluid viscosities on the work of adhesion of the advancing liquid phase.

Over the whole range of θ0MKT, the length of local displacement, λ, increases from 1 nm on smooth samples to more than 3 nm on the roughest surfaces, while the displacement rate K0 decreases from 1 MHz down to 0.01 MHz on the roughest surfaces. The molecules at the three phase contact line are more strongly held as the nanoroughness increases. We note that in our previous experiments for dodecane displacing water on smooth samples15 the values obtained for λ were found to increase with θ0MKT (i.e., increasing substrate hydrophobicity) while those of K0 were decreasing. The opposite trend found for these nanorough surfaces suggests that dynamic liquid−liquid displacement may be governed by different mechanisms in the two cases, as will be discussed in the next section. Contact Line Friction. From the best fit of the molecular kinetic theory, we evaluated the contact line friction coefficient ζ for the nanorough surfaces. In order to compare these values with the theoretical predictions of eqs 9 and 10, we plot, in Figure 7, the logarithm of the friction coefficient normalized by the product and the sum of the fluid viscosities, as a function of )) the apparent work of adhesion Wa* = γ(1 + cos(180° − θMKT 0 of the advancing dodecane phase.15,17 Note that the apparent work of adhesion reflects the influence of roughness on the static contact angle but does not measure the inherent wettability of the surfaces, which is the same for all smooth and nanorough APTES surfaces investigated. The experimental data cannot be fitted with a straight line of positive slope as expected from eqs 9 and 10. Both friction models fail to predict the behavior on nanorough surfaces. One explanation could be that the specific activation free energy of wetting, ΔgS*, cannot be equated to the apparent work of adhesion in the case of nanorough surface but only to the inherent work of adhesion, eq 8. Further, for both eqs 9 and 10 to predict a straight line, the length of the local contact line displacement λ has to be constant. If this assumption holds for smooth surfaces, our present results on nanorough surfaces show a strong change in λ over a rather narrow range of contact angles (50° to 15°). If the λ is allowed to vary with the work of adhesion of the advancing phase, then no straight line is predicted for the dependence of ln ζ on Wa by eqs 9 and 10. Possible Mechanisms. The exponential variation of the contact line velocity with the cosine of the dynamic contact angle indicates that the dynamics is thermally activated (Figures

also explain the maximum in hysteresis for nanodefects. Another possible explanation for this behavior is the collective pinning on multiple defects. While for low surface coverage individual surface defects act as single pinning sites, it has been argued that, as their concentration increases, the pinning of the contact line on multiple defects may cancel out the pinning efficiency of the defects and result in a decrease in contact angle hysteresis.30 By analogy with superhydrophobicty in liquid−vapor systems, where air is trapped beneath a water droplet, in the system studied here, the decrease in hysteresis at high surface coverage could be attributed to water being trapped in the gaps as the dodecane displaces the bulk of the water. Thus, the packing of the nanoparticles on the substrate could be responsible for a transition between two distinct wetting configurations, i.e., the Wenzel state at low surface coverage (below 40%) and the Cassie state for densely packed surfaces. However, no optical evidence of liquid trapping was found for these surfaces. The increase in potential pinning sites as the nanoparticle surface coverage increases could also contribute to the variation of the contact angle hysteresis. However, the scatter of the water/dodecane advancing contact angle values hints that the wetting state on these elaborate surfaces is, at the very least, complex and probably governed by multiple factors. We further discuss the possible effect of contact line pinning on nanodefects in the dynamic wetting analysis below. Dynamic Wetting. Despite the fact that the original MKT does not take into account surface roughness or the viscosity of both fluids, it still captures the trend followed by the dynamic contact angle of water displaced by dodecane for contact line velocities below 0.01 m/s (Figure 5). MKT Parameters. The static contact angle obtained from the MKT fit, θ0MKT, decreases from 50° on smooth surfaces down to 15° on the roughest substrates. The parameter θ0MKT reflects the overall “Wenzel” roughness of the sample on the exact same spot where the dynamic contact angles were measured. The values of θ0MKT obtained from the fits are in good qualitative agreement with the static contact angle study. However, we noticed that θ0MKT is systematically slightly smaller than the static contact angle. This could be a consequence of a quasistatic motion of the contact line continuing after the recording ends and/or that the very slow end of the contact line motion does not optimally follow the trend predicted by the molecular kinetic model. 10941

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Figure 8. Normalized activation free energy is compared to the affinity of dodecane (orange line) and water (blue line) for the surface and the energy of static contact angle hysteresis (red symbols).

nanorough surfaces with the work of adhesion replaced by the apparent work of adhesion, influenced by the surface roughness. However, a systematic deviation is observed. One can see from Figure 8 that the experimental results are consistently above the affinity of dodecane for the substrate. Viscous contributions to the activation free energy of wetting might be responsible for this deviation. Furthermore, the activation energy is of the same order as the hysteresis energy. The hysteresis energy has been calculated from the static contact angle measurements presented in Figure 2, for every single surface, as H = γ(cos θadv − cos θrec)37 and is represented by the open red symbols in Figure 8. Although the hysteresis energy exhibits a maximum around a final receding water contact angle of 40°, the activation energy values do not show a maximum. The transition in wetting state observed in the hysteresis data is not transferred to the dynamic behavior. A simple explanation for this could be that the transition in wetting state observed in the static measurement was mainly due to the values of the advancing contact angle of water, e.g., a receding dodecane drop. Yet, the dynamic experiment only investigates water receding as the dodecane displaces it. From the static receding water contact angle measurement, we observed a steady consistent trend without indication of a transition, which correspond to that observed in the dynamic results. The influence of static contact angle hysteresis on this system could be further investigated by studying the opposite direction of flow, that is, a drop of water displacing dodecane. Overall, neither the apparent dodecane affinity for the substrate nor the hysteresis energy alone fully correlates with the experimental data. Instead, it seems that the experimental values are roughly distributed in between hysteresis energy and dodecane affinity. A possible explanation is that the thermally activated processes occurring at the contact line in the system studied are influenced by at least two distinct mechanisms. The interaction between the advancing fluid (dodecane) and the hydrophilic surface appears to be as influential as the nanodefects hindering the free motion of the contact line.

4 and 5). Thus, the mechanism controlling the motion of the contact line may be evaluated in terms of thermally activated elementary jumps in the immediate vicinity of the contact line. In many previous studies of simple liquids partially wetting a planar rigid surface, it has been found that the energy barrier of the local displacement can be ascribed to molecular adsorption and desorption processes, which correlate quite well with the work of adhesion. In such cases the displacement length is found to be in the angstrom range, not exceeding 1 nm (see ref 15 and references herein). In the present experiment, the changes in parameters observed as only the nanoroughness of the sample is modified while the surface chemistry remains the same suggest that the chemical affinities between the two fluids and the surface do not solely govern the local displacements at the contact line. Indeed, the λ values obtained for the nanorough samples range from 1.5 to 3 nm, as the nanoroughness increases. This is not consistent with a true molecular mechanism. More recent studies involving rough or deformable surfaces reported larger values for λ of the order of tens of nanometers for very slow contact line motions (below10−3 m/s).34−36 One plausible interpretation for these longer displacement lengths is that the pinning of the contact line on single defects of mesoscopic size controls the activated dynamics in the slow motion range. In this interpretation, the energy barrier which needs to be overcome to induce contact line motion is the energy involved in the attachment of the interface to the surface nanodefects. Thus, the wetting activation energy should scale like the pinning energy, which may be estimated by the static contact angle hysteresis. However, the numerical values of λ found in this present case are about 1 order of magnitude smaller than the defect size. Thus, it appears unlikely that the nanoparticles act as single pinning sites for the contact line. In Figure 8, values of the specific activation free energy Δg0* =ΔG0*/λ2NA obtained from the present experiments via eq 2 are presented, together with previous results obtained for smooth thiol coated surfaces of different hydrophobicity.15 As discussed in our previous publication,16 the affinity of dodecane for the solid substrate is the equivalent, for liquid− liquid systems, to the work of adhesion. The new results on nanorough surfaces confirm that the activation energy of the dodecane displacing water follows qualitatively the same trend as the apparent, roughness-affected affinity of dodecane for the substrate. This suggests that eq 8 may hold not only for smooth surfaces and the inherent work of adhesion but also for

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SUMMARY The dynamics of the water−dodecane contact line motion has been investigated on a range of nanorough surfaces. A controlled nanoparticle deposition method was used in order to finely tune the surface nanotopography while keeping its chemistry unchanged. The size of the nanodefects produced in 10942

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(11) Glasstone, S.; Laidler, K. J.; Eyring, H. J. The Theory of Rate Process; McGraw-Hill: New York, 1941. (12) Cherry, B. W.; Holmes, C. M. J. Colloid Interfacial Sci. 1969, 29, 174. (13) Blake, T. D. Dynamic Contact Angles and Wetting Kinetics. In Wettability; Berg, J., Ed.; Marcel Dekker Inc.: New York, 1993; p 251. (14) Blake, T. D.; De Coninck, J. J. Adv. Colloid Interface Sci. 2002, 96, 21. (15) Ramiasa, M.; Ralston, J.; Fetzer, R.; Sedev, R. J. Phys. Chem. C 2011, 115, 24975. (16) Fetzer, R.; Ramiasa, M.; Ralston, J. Langmuir 2009, 25, 8069. (17) Fetzer, R.; Ralston, J. J. Phys. Chem. C 2010, 114, 12675. (18) Kim, J.; Seidler, P.; Wan, L. S.; Fill, C. J. Colloid Interface Sci. 2009, 329, 114. (19) Aizenberg, J.; Braun, P. V.; Wiltzius, P. Phys. Rev. Lett. 2000, 84, 2997. (20) Wenzel, R. N. J. Phys. Colloid Chem. 1949, 53, 1466. (21) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (22) Johnson Rulon, E.; Dettre Robert, H. Contact Angle Hysteresis. In Contact Angle, Wettability, and Adhesion; American Chemical Society: Washington, DC, 1964; Vol. 43, p 112. (23) Horcas, I. Rev. Sci. Instrum. 2007, 78, 013705. (24) Hoffman, R. L. J. Colloid Interface Sci. 1975, 50, 228. (25) Killian, M. S.; Wagener, V.; Schmuki, P.; Virtanen, S. Langmuir 2010, 26, 12044. (26) Extrand, C. W. J. Colloid Interface Sci. 2002, 248, 136. (27) Eick, J. D.; Good, R. J.; Neumann, A. W. J. Colloid Interface Sci. 1975, 53, 235. (28) Huh, C.; Mason, S. G. J. Colloid Interface Sci. 1977, 60, 11. (29) V., D. J.; Chatain, D.; Rivollet, I.; Eustathopoulos, N. J. Chim. Phys. Phys.-Chim. Biol. 1990, 87, 1623. (30) Ramos, S. M. M.; Charlaix, E.; Benyagoub, A.; Toulemonde, M. Phys. Rev. E 2003, 67, 031604. (31) Ramos, S.; Tanguy, A. Eur. Phys. J. E: Soft Matter Biol. Phys. 2006, 19, 433. (32) Bico, J.; Tordeux, C.; Quere, D. Europhys. Lett. 2001, 55, 214. (33) James, R. T. S.; Detlef, L. J. Phys.: Condens. Matter 2011, 23, 133001. (34) Rolley, E.; Guthmann, C. Phys. Rev. Lett. 2007, 98, 166105. (35) Petrov, J. G.; Ralston, J.; Schneemilch, M.; Hayes, R. A. Langmuir 2003, 19, 2795. (36) Prevost, A.; Rolley, E.; Guthmann, C. Phys. Rev. Lett. 1999, 83, 348. (37) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Rev. Mod. Phys. 2009, 81, 739.

this way remained in the range 10 to 20 nm in height while their lateral density was varied between 0 and 82% coverage of the smooth glass surface (Figure 1). We found that both static and dynamic wetting processes are affected by the nanoroughness, which rms roughness is below 7 nm. The static receding water/dodecane contact angle on the smooth control sample is 54°. The static contact angle analysis reveals that the surface hydrophilicity is enhanced by the nanoroughness (Figure 2). Further, the static contact angle passes through a maximum of hysteresis as the nanoparticle coverage is increased from 0 to 82% (Figure 3). This behavior may be explained by the effect of the contact line anchorage on multiple interacting pinning sites. This hypothesis is further fostered by the dynamic dewetting results where we found that the thermally activated process governing the contact line motion is unlikely to be a pure adsorption−desorption mechanism. Indeed, beyond significantly slowing down the overall spreading process (Figure 4), the nanoroughness of the surface appears to also deeply impact on the core mechanism governing the local displacements occurring in the vicinity of the contact line. The good fit of the experimental data with the molecular kinetic model support that the motion is thermally activated on all the surfaces investigated here (Figure 5). However, the values found for the contact line friction on the nanorough surfaces do not support the hypothesis of a genuine molecular adsorption−desorption mechanism (Figure 7). Comparison of the free activation energy of dewetting with both the liquid’s apparent affinity for the substrates, defined by the static contact angle on the nanorough surfaces, and the hysteresis energy (Figure 8) reveals that as a first approximation, the hysteresis describes the experimental data at least as well as the dodecane affinity for the substrate. This result suggests that on the nanorough substrates studied the contact line motion local displacement is likely to be governed by two different mechanisms simultaneously, namely adsorption−desorption processes and contact line pinning on nanodefects, both thermally activated.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Fax: + 61 (0)8 8302 3683; Tel: + 61 (0)8 8302 3066. Present Address †

Karlsruhe Institute of Technology, 76021, Karlsruhe, Germany. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Australian Research Council is gratefully acknowledged. REFERENCES

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