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Drop Retention Force as a Function of Resting Time Rafael Tadmor,* Kumud Chaurasia, Preeti S. Yadav, Aisha Leh, Prashant Bahadur, Lan Dang, and Wesley R. Hoffer Department of Chemical Engineering, Lamar UniVersity, Beaumont, Texas 77710 ReceiVed August 9, 2007. ReVised Manuscript ReceiVed March 25, 2008 The force, f, required to slide a drop on a surface is shown to be a growing function of the time, t, that the drop waited resting on the surface prior to the commencement of sliding. In this first report on the resting time effect, we demonstrate the existence of this phenomenon in different systems, which suggests that this phenomenon is general. We show that df/dt is never negative. The shorter the resting times, the higher df/dt is. As the resting time increases, df/dt decreases toward zero (plateau) as t f ∞. The increase in the force, ∆f, due to the resting time effect (i.e., f(t f ∞) – f(t f 0)) correlates well with the vertical component of the liquid-vapor surface tension, and we attribute this phenomenon to the corrugation of the surface by the drop due to this unsatisfied normal component of Young’s equation.
Introduction Young’s equation1 describes the thermodynamic equilibrium2–4 contact angle, θ0, as a function of the interfacial tensions (all of which can thus be calculated5) between liquid and solid, liquid and vapor, and solid and vapor: γSL, γ, and γSV respectively
γSL + γ cos θ0 ) γSV
(1)
The modified Young’s equation (introduced originally in 19366) can be obtained by minimizing the sum of surface energies and the line energy, k (also known as line tension), associated with the three phase contact line7–15
k ) γ(cos θ - cos θ0)r
(2)
where θ is the apparent contact angle, θ0 is Young’s equilibrium contact angle defined in eq 1, and r is the drop radius. Different orders of magnitude for k obtained by different investigators (i.e., refs 16–21) resulted in some controversy in the literature. Eventually, it was realized that k may describe two different phenomena.22 One is a very weak thermodynamic line tension, which is more significant for smaller drops or smaller length scales, and although weak (on the order of ∼10-10 N) was * Corresponding author. E-mail:
[email protected]. (1) Young, T. Philos. Trans. R. Soc. London, Ser. A 1805, 95, 65. (2) Safran, S. A. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes; Addison-Wesley Publishing Company: Reading, MA, 1994. (3) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces; John Wiley and Sons: New York, 1997. (4) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, 1991. (5) (a) Chibowski, E.; Terpilowski, K. J. Colloid Interface Sci. 2008, 319, 505. (b) Terpilowski, K.; Holysz, L.; Chibowski, E. J. Colloid Interface Sci. 2008, 319, 514. (6) (a) Vesselovsky, V. S.; Pertzov, V. N. Zh. Fiz. Khim. 1936, 8. (b) Toshev, B. V.; Platikanov, D.; Scheludko, A. Langmuir 1987, 4, 489. (7) Boruvka, L.; Neumann, A. W. J. Chem. Phys. 1977, 66, 5464. (8) (a) Gretz, R. D. J. Chem. Phys. 1966, 45, 3160. (b) Gretz, R. D. Surf. Sci. 1966, 5, 239. (9) Tadmor, R. Surf. Sci. 2008, 602, L108. (10) Milchev, A. I.; Milchev, A. A. Europhys. Lett. 2001, 56, 695. (11) Pethica, B. A. J. Colloid Interface Sci. 1977, 62, 567. (12) Sheludko, A. Colloid J. USSR 1986, 48, 917. (13) Tadmor, R. Langmuir 2004, 20, 7659. (14) Marmur, A. J. Colloid Interface Sci. 1997, 186, 462. (15) Shapiro, B.; Moon, H.; Garrell, R. L.; Kim, C. J. J. Appl. Phys. 2003, 93, 5794. (16) Drelich, J.; Wilbur, J. L.; Miller, J. D.; Whitesides, G. M. Langmuir 1996, 12, 1913. (17) Drelich, J. Pol. J. Chem. 1997, 71, 525.
Figure 1. Various dimensions and parameters used in the measurement.
successfully measured for various systems.18,21 In macroscopic drops, however, a pinned contact line gives rise to another line energy on the order of ∼10-6 N, which overshadows the weak line tension. The terms line energy and line tension follow de Gennes et al.’s terminology.23 Unlike the line tension, which gives rise to a decrease of θ0 with r when both θ0 and r are small,18 the line energy gives rise to contact angle hysteresis around θ0 at large θ0 and r values.13 This paper addresses macroscopic drops with large θ0 values. Apparently, macroscopic drops pose a greater challenge than microscopic drops/thin films since for the latter case there are equations that can predict experimental results,24–28 which is not the case for macroscopic drops. The additional complexity of macroscopic drop problems is related in part to the resting time effect, which is presented here for the first time. We tested this time effect only for macroscopic drops, and we believe that for high surface energy substrates (such as hydrophilic surfaces) where the drops form very small contact angles, a time effect phenomenon may be too small to be observed. (18) Wang, J. Y.; Betelu, S.; Law, B. M. Phys. ReV. Lett. 1999, 83, 3677. (19) Amirfazli, D. Y.; Kwok, J.; Gaydos, N. A. W. J. Colloid Interface Sci. 1998, 1, 205. (20) Li, D.; Neumann, A. W. Colloids Surf. 1990, 43, 195. (21) Pompe, T.; Herminghaus, S. Phys. ReV. Lett. 2000, 85, 1930. (22) Amirfazli, A.; Neumann, A. W. AdV. Colloid Interface Sci. 2004, 110, 121. (23) de Gennes, P. G. Brochard-Wyart, F.; Quere, D. Capillary and Wetting Phenomena Drops, Bubbles, Pearls, WaVes; Springer-Verlag: Berlin, 2003. (24) Kemps, J. A. L.; Bhattacharjee, S. Langmuir 2005, 21, 11710. (25) Sabin, J.; Prieto, G.; Messina, P. V.; Ruso, J. M.; Hidalgo-Alvarez, R.; Sarmiento, M. Langmuir 2005, 21, 10968. (26) Hirasaki, G. J. J. Adhes. Sci. Technol. 1993, 7, 285. (27) Tadmor, R. J. Phys.: Condens. Matter 2001, 13, 195. (28) Tadmor, R.; Klein, J. J. Colloid Interface Sci. 2002, 247, 321.
10.1021/la7040696 CCC: $40.75 2008 American Chemical Society Published on Web 08/02/2008
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The previous discussion was based on energy minimization. Another approach based on force analysis views k (line energy per unit length) as a force preventing the drop from advancing or receding. Here, k has a direction opposite to the advancing or receding directions. On the basis of this approach, one can relate the line energy associated with the advancing to that associated with the receding angle and consequently obtain θ0 as a function of θA and θR (the maximal advancing and minimal receding angles, respectively).13 Similarly, the force per unit length retaining a drop on a tilted surface should be proportional to
force/unit length ∼ (cos θR - cos θ0) - (cos θA - cos θ0) ) (cos θR - cos θA) (3a) Indeed, Dussan29 and Furmidge30 proved this. Dussan used fluid dynamic considerations, and Furmidge used energy considerations supported by experimental data. Specifically, they wrote the retention force, f, as
f ) γ(cos θR - cos θA) w
(3b)
where w is the drop width (e.g., for spherical drops, w ) 2r). The analogy to line energy is now straightforward; namely, for an axisymmetric drop
kR - kA f f ) ) w 2r 2r
(4a)
or (for the same particular case)
f ) kR - kA
(4b)
Equation 4a hints as to why in all the graphs we use force/unit length, and not just force. Equation 4b shows that k is associated with the retention force. Yet, the physical origin of the line energy of macroscopic drops is still not clear. What physical phenomena are responsible for k? In this paper, we show that k and f change with the resting time, and based on this and other supporting evidences, we propose that the line energy is induced by some gradual deformation of the surface. We qualitatively explain this deformation as being induced by the unsatisfied normal component of the liquid-vapor surface tension. To the best of our knowledge, there is no report that aims at studying the change of the retention force as a function of the time the drop rests on the surface. Yet, there are literature manifestations for a time effect in experiments of dynamic cycling of drops. For example, a careful study by Lam et al.31 shows a clear correlation between the time a surface has been in contact with a drop and the dynamic contact angles (advancing and receding). Moreover, the existence of a correlation between the time the drop rests on the surface and the force required to slide it is noted by Furmidge,30who writes: “the Velocity of the drop tended to increase once it had cleared the area on which it had originally rested. The magnitude of this effect depended on the length of time that the drop had remained stationary on the surface”. To bypass this effect, Furmidge made measurements on drops as they were sliding far from the area on which they originally rested, where their velocity became constant and small. We, on the other hand, emphasize this time effect and therefore consider the force required to set the drop in motion, which is (29) Dussan, E. B. J. Fluid Mech. 1985, 151, 1. (30) Furmidge, C. G. L. J. Colloid Sci. 1962, 17, 309. (31) Lam, C. N. C.; Ko, R. H. Y.; Yu, L. M. Y.; Ng, A.; Li, D.; Hair, M. L.; Neumann, A. W. J. Colloid Interface Sci. 2001, 243, 208.
just as the drop began moving and is still in the area on which it originally rested.
Experimental Procedures Measurements. In each experiment, we placed a liquid drop of a given volume on a solid surface using a microsyringe prescribed reading (errors of 0.1 µL). We verified that the drop looked perfectly symmetric when it was placed on the surface, and the picture of the as-placed drop was used to calculate the drop’s volume, V, which matched its prescribed volume. The error of our measured volume ranged from 0.05 µL for the smallest drops to 1 µL for the largest drops, matching the accuracy of our microsyringe at a volume of 2 µL. We then waited various periods of time before beginning to tilt the surface. Oil drops did not change in volume or shape in any way we could detect. The evaporation of water drops was suppressed using above-saturation humidity conditions. These were achieved by adding many satellite drops that were only a bit smaller than the drop we measured. Being smaller, they evaporated faster and suppressed the evaporation of the drop that was considered for the experiment rather efficiently. The volume measurements of water drops were performed just prior to tilting to further reduce errors associated with the suppressed evaporation that took place. The tilting continued until the drop began to slide, at which point the lengths a and b (Figure 1) were measured and the tilt angle R deduced. By “began to slide”, we refer to the first motion of the drop’s front (which is the first thing to budge). Qualitatively, the same phenomenon happens when the rear side moves (at which point the entire drop moves). The lateral retention force, f, was calculated as
f ) FVg sin R
(5)
where F is the density of the drop liquid, V is the drop volume, and g the gravitational acceleration. Rather than f, we plotted f/V1/3, which normalizes the forces with respect to different drop sizes (see equation 5.3 in ref 29). The resulting error in f/V1/3 is (0.15 mN/m. The error in the angle measurements was (1°. All experiments were performed in a dust-free laminar flow hood (Terra Universal, ULPA filters). This type of hood filters particles larger than 30 nm. Materials. Some surfaces were covered with surfactants and others not. Surfactant coverage was performed by self-assembly32 of the ionic surfactant octadecyl trimethylammonium+ (OTA+) on ionic surfaces of either mica or glass and removing the excess surfactant with distilled water. This is a standard procedure to achieve surfactant covered surfaces (see, e.g., refs 28 and 33–35). Briefly, OTA+ was dissolved in water from OTA-bromide to OTA+ and Br– ions. Clean surfaces were immersed in a 0.4 mg/mL water solution of the surfactants. The surfaces were withdrawn dry following rinsing in pure water. Glass surfaces were sonicated in acetone and then in ethanol, washed with ethanol, dried in a dust-free laminar flow hood, and then rinsed with water prior to immersion in the surfactant solution. Mica surfaces were cleaved from both sides prior to immersion. OTA+ is known to form a stable rigid smooth monolayer of 10 ( 3 Å on mica,33 as measured by surface force balance and by other techniques, which neutralizes most of the negative charges on the mica surface.35 Note that in refs 33–35 OTA is called STAI where the S stands for stearicsthe acid derivative of OTA (OTA is not related to OTAI from ref 33). In this paper, we adopt the more modern nomenclature, hence OTA. Three kinds of Teflon surfaces were used, and as was shown by Geil et al.,36 Teflon surfaces of different preparations are rather (32) Ulman, A. An Introduction to Ultrathin Organic Films; Academic Press: San Diego, 1991. (33) Tadmor, R.; Rosensweig, R. E.; Frey, J.; Klein, J. Langmuir 2000, 16, 9117. (34) (a) Raviv, U.; Giasson, S.; Frey, J.; Klein, J. J. Phys.: Condens. Matter 2002, 14, 9275. (b) Tadmor, R.; Chen, N. H.; Israelachvili, J. Macromolecules 2003, 36, 9519. (35) Kampf, N.; Gohy, J. F.; Jerome, R.; Klein, J. J. Polym. Sci., Part B: Polym. Phys. 2005, 43, 193. (36) Geil, P. H.; Yang, J.; Williams, R. A.; Petersen, K. L.; Long, T.-C.; Xu, P. AdV. Polym. Sci. 2005, 180, 89.
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different surfaces. One was a 1.6 mm thick board (item #45446 bought from U.S. Plastic Corp.), the other was a thin tape used for domestic sealing (PTFE Thread Sealant Tape bought from Taega Technologies), and the third was a Teflon coating from 3M Novec electronic coating (fluoroaliphatic polymer, 3M ID No. 98-02122993-9 using an EGC 1700 solution). The first was sonicated and then rinsed with water, the second was stretched on a glass slide as received, and the third was used as coating for silicon wafers practicing the following coating procedure: Silicon was placed in piranha solution (70% H2SO4 and 30% H2O2 aqueous solution) overnight at 25 °C. Then, it was washed with water and dipped in the EGC 1700 solution for 80 s and withdrawn. Submerging and withdrawing were performed at 0.5 mm/min. To check if any of the experimental observations depended on purity, occasionally identical chemicals of different purities were used, or the same drop was used for a few experiments (repositioned aged drops). They always produced the same experimental behavior (within the scatter), suggesting that the experimental findings are not related to material purity. Three sources were used for water: our laboratory distilled water (Barnstead Nanopure Purification specific conductance (25 °C) e0.7 × 10-6 Ω-1 cm-1), water from Aldrich (ACS reagent: heavy metals e0.01 ppm, silicate e0.01 ppm, and specific conductance (25 °C) e2 × 10-6 Ω-1 cm-1), and distilled water from a local supplier (distillated, microfiltered, and ozonated by Pure Deep Well). Hexadecane and OTA-Br were purchased from Aldrich. Two kinds of hexadecane purities were used: 99%+ and 99% (Aldrich highest purities for this substance). None of the hexadecane impurities was found to be surface active on OTA.33 Tetradecane was purchased from Fluka with a purity of g99.5% (the highest available).
Lateral Retention Force versus Rest Time Figure 2 shows the lateral force, f, required to set drops in motion (calculated from eq 5) as a function of the time, t, the drops had been resting on the surfaces from the moment they were placed on the surface until the moment the drops’ front edge moved, for seven different systems noted in panels a-g. In these different systems, we see the same general phenomenon: the retention force, f, required for the onset of motion of a drop on a surface is a growing function of the time, t, that the drop rests on the surface prior to sliding and either reaches a plateau after some time or clearly approaches a plateau (i.e., df/dt g 0 and d2f/dt2 e 0 (defined for t g 0)). For short rest periods, f increases more rapidly with t so that lim df/dt ) tf0 (df/dt)max, but this positive derivative decreases as the rest period 2 2 becomes longer (i.e., d f/dt < 0) until, after long rest periods, f reaches a plateau (lim df/dt ) lim d2f/dt2 ) 0). tf∞
tf∞
The same phenomenon was also observed with hexadecane drops on OTA covered silicon wafers (Virginia semiconductors) pretreated with piranha and for hexadecane drops on a Teflon board (both are preliminary results and are not shown). We also learn from Figure 2 that the three systems in which the liquid drops were water show a much higher increase in f/V1/3 as compared to the four systems in which the liquid drops were oils (hexadecane or tetradecane). This is in accordance with the much higher surface tension of water as compared to that of oil. A third important observation is regarding the relaxation time. When the substrate was the rather soft material, Teflon, then full relaxation did not occur even after 2 hours. On the other hand, the two other surfaces, which are much more rigid, reached a complete relaxation within 10-15 min. The correlation between surface rigidity and relaxation time suggests that the process involves surface deformation. The correlation between the surface tension and the size of the retention-force-increase suggests that the surface tension induces this deformation of the substrate surface. Thus, these findings insinuate the idea that the unsatisfied
Figure 2. Lateral force, f, required to set drops in motion on surfaces as a function of the time, t, that the drops had been resting on them prior to sliding. The force is normalized by a unit length (V is the drop volume). The inset in panel d expands the shorter times of that panel. The curves are guides to the eye. V1/3 ranges were (a) 2.7-3.6, (b) 1.5-2.8, (c) 1.4-1.5, (d) 1.4-1.7, (e) 3.1-3.5, (f) 2.2-2.5, and (g) 1.4-1.6 mm. The Teflon surfaces in (a) and (f) were the tape and the EGC 1700, respectively. t ) 0 is the first time the drop became stationary on the surface, which is almost immediately (milliseconds) after it was placed on the surface.
normal component of Young’s equation may be responsible for this time effect. Thus, the unsatisfied normal component, which itself is constant with time, slowly deforms the surface. Further evidence for surface deformation using AFM or other scanning techniques is much desired but poses a very challenging task: when the surfaces are rough (e.g., Teflon), it is difficult to distinguish a small ridge from other structures, and when they are smoother (e.g., OTA covered mica), their deformation is expected to be mainly elastic as we explain in the next paragraph. Yet another difficulty, is to enlarge an unknown location of a 1 nm scale three phase contact line. However, it is known that capillary forces are strong enough to deform rigid surfaces,37 and more than that, a study by Sheiko et al.38 showed that surface tension forces are strong enough not only to induce intermolecular motions in solids but even break chemical bonds.38 While this was observed for rather thin drops, note that the surface tension (37) Fan, J.-G.; Zhao, Y. P. Langmuir 2006, 22, 3662. (38) Sheiko, S. S.; Sun, F. C.; Randall, A.; Shirvanyants, D.; Rubinstein, M.; Lee, H.-I.; Matyjaszewski, K. Nature (London, U.K.) 2006, 440, 191.
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Table 1 system
θAPa
γ (mN/m)
HD/OTA covered glass HD/OTA covered mica HD/Teflon coating TD/OTA covered mica water/Teflon tape water/OTA covered glass water/OTA covered mica
23.5 35 58 29 123.6 67.2 74
27.1 27.1 27.1 26.15 72 72 72
γ⊥ (γ sin θAP)
∆f/V1/3 (mN/m)
10.8 15.5 23 12.7 60 66.4 69.2
1.5 3 10 2 33 26 27
a γ⊥ denotes the unsatisfied normal component of Young’s equation. ∆f/V1/3 denotes the increase in force per unit length due to the resting time effect and was estimated from Figure 2. γ denotes the liquid surface tension, and the as-placed47 contact angle, θAP, denotes the contact angle of the drop when it was resting on the planar surface. θAP did not change as long as the surface was not tilted.
associated with bulk drops should be either similar or stronger.39 Later on we bring some evidences that more than the topographic deformation, it is the related changes in the surface chemistry that influence the retention force. We mention later other possible mechanisms associated with time effects, but the next paragraph discusses a correlation that other mechanisms cannot explain. Assuming surface deformation,9 the nature of the deformation (plastic, elastic, or a combination of the two (viscoelastic)) depends on the surface. Subsequent drops placed on previously used OTA covered surfaces gave results that were similar to those with fresh OTA covered surfaces, suggesting that the time effect seen for that surface was mainly elastic. On the other hand, Teflon or EGC 1700 covered surfaces seem to age such that subsequent drops usually did not reproduce well the forces associated with the first few drops. Regardless of the deformation type (plastic or elastic or viscoelastic), the deformation is expected to increase with the time that the drop rests on the surface and eventually reaches a plateau. The rather slow relaxation time (minutes) is in agreement with other relaxation times reported in the literature.40 In that case, one expects not just a correlation between the surface tension, γ, and the retention force increase, ∆f, but rather the normal component of the surface tension,9 γ⊥, (i.e., γ sin θ). The calculated values of the normal components for the systems studied here are shown in Table 1. Table 1 shows that relating ∆f/V1/3 to γ⊥ rather than just γ sharpens the correlation: considering for example the two OTA covered glass surfaces, the water/hexadecane γ⊥ ratio of 66.4 to 10.8 mN/m is roughly double that of 72 to 27.1 mN/m and hence closer to the ∆f/V1/3 ratios of those systems. Additionally, it seems to explain the difference between the three hexadecane (HD) drop systems: the one with the smaller contact angle indeed has a smaller ∆f/V1/3 value, and the others align correspondingly as well. Also, the tetradecane versus hexadecane ratios of ∆f/V1/3 to γ⊥ correlate better than their ∆f/V1/3 to γ ratios. On the other hand, the much smaller relative difference between the two water systems: water/OTA covered glass and water/Teflon, seems to be in the wrong direction (the Teflon case has a smaller γ⊥ value but higher ∆f/V1/3 value). Yet, this is in agreement with our perception of the problem because the higher ∆f/V1/3 value corresponds to the much softer Teflon surface that can yield larger deformations for the same pulling force. The deformation of OTA covered mica is mainly limited to the OTA monolayer, while the Teflon deformation has a much larger depth potential. A recent theoretical study9 also suggests that the change in retention force with time is induced by the deformation of the surface along the three phase contact line conjugated by the (39) Tadmor, R.; Pepper, K. G. Langmuir 2008, 24, 3185.
associated surface chemistry changes. This deformation is proportional to the Laplace pressure and is pulling the surface up in the direction of the unsatisfied normal component of Young’s equation.9 In this case, one may expect the phenomenon to be more pronounced for softer materials than for harder materials, and indeed, our data demonstrate this. Additionally, such deformation is clearly observed for very soft materials (see, e.g., Extrand and Kumagai,41) and was studied in some detail for moving drops by Shanahan and co-workers,42 yet for rather hard (more regular) materials, this was not studied. One may expect then that in very hard surfaces, the phenomenon will not be observed at all since extrapolating the observations in ref 41 should result in a very small deformation. Yet, beyond the increase in the topographical roughness (assuming its effect on the force is small), there are also molecular realignment changes9,43,44 that will have a significant effect on the force9,28,45 because of the different intermolecular interactions associated with those deformations. For example, refs 43 and 44 show that identical surface molecules of different orientations, correspond to significant contact angle differences. This can be further enhanced in cases when nanometric scale deformations are easier than their macroscopic analogues.48 Indeed, we were unable to find a system whose rigidity prevented the time effect. Another reason that makes such a system not easy to find is that most very hard surfaces (like metals) have a very high surface energy. Even inert metals such as gold and platinum have a very high surface energy and therefore are wetted by most if not all liquids.46 The theoretical connection between surface rigidity and surface tension lies in the fact that both result from intermolecular forces as described in Israelachvili’s book:4 materials with higher intermolecular attraction (like all metals) have therefore a higher surface tension than materials with low intermolecular attraction (like oils). Solids, and especially the more rigid solids, are characterized by high intermolecular attraction, and this makes finite contact angle systems very difficult to find for these cases: most liquids will wet them completely. An exception to this may be nonmultimolecular materials (like diamond). All the previous discussion was regarding the front edge motion of the drop. The rear edge moves at a slightly higher force, and for optical reasons, its onset of motion is slightly more difficult to accurately determine since its contact angle is smaller and hence the moving rear edge is thinner. However, the phenomenon exists also for the rear edge. Some data regarding the rear edge are shown in a previous paper.49 Other parameters that are often used to explain various interfacial phenomena effects include: intercalation of liquid (40) Tadmor, R.; Janik, J.; Klein, J.; Fetters, L. Phy. ReV. Lett. 2003, 91, 115503. (41) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1996, 184, 191. (42) (a) Shanahan, M. E. R.; Carre, A. Compt. Rend. Acad. Sci., Ser. IV 2000, 1, 263. (b) Shanahan, M. E. R.; de Gennes, P. G. Compt. Rend. Acad. Sci., Ser. II 1986, 302, 517. (c) Carre, A.; Gastel, J. C.; Shanahan, M. E. R. Nature (London, U.K.) 1996, 379, 432. (43) Heng, J. Y. Y.; Bismarck, A.; Lee, A. F.; Wilson, K.; Williams, D. R. Langmuir 2006, 22, 2760. (44) Yasuda, T.; Miyama, M.; Yasuda, H. Langmuir 1992, 8, 1425. (45) Yadav, P. S.; Dupre, D.; Tadmor, R.; Park, J. S.; Katoshevski, D. Surf. Sci. 2007, 601, 4582. (46) Bewig, K. W.; Zisman, W. A. J. Phys. Chem. 1965, 69, 4238. (47) Tadmor, R.; Yadav, P. S. J. Colloid Interface Sci. 2008, 317, 241. (48) Alcantar, N. A.; Park, C.; Pan, J. M.; Israelachvili, J. N. Acta Mater. 2003, 51, 31. (49) Yadav, P. S.; Bahadur, P.; Tadmor, R.; Chaurasia, K.; Leh, A. Langmuir 2008, 24, 3181.
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Figure 3. Maximal advancing and simultaneous corresponding receding contact angles just prior to motion of the advancing edge of a hexane drop on Teflon (EGC 1700) covered silicon surface vs the time the drop rested on the surface.
molecules in the surfactant layer (although not in our system50), effects associated with surface roughness such as the dissolution of the air entrapped between the solid and the liquid, the concentration at the triple line of impurities contained in the liquids or on the surfaces if the liquid slightly evaporates, slow spreading of precursor films, and penetration of liquid into a porous substrate. While these parameters can still have some influence on the time effect reported here, they cannot explain the correlation of the retention-force-difference to the unsatisfied normal component of the surface tension or the agreement between the time scales of the force changes and the surface rigidities. These appear, experimentally, to support a surface deformation mechanism. Note that the time effect reported here is observed regardless of the previously stated parameters. For example, this phenomenon is observed regardless of roughness: we sometimes use the same surfaces (i.e., the roughness is the same) but different liquids, and we observe a time effect that is correlated with the unsatisfied normal component of Young’s equation. If we change the surfaces, the roughness must change as well; still, the increase in the retention force with resting time is correlated to the unsatisfied normal component of Young’s equation. So is the case with other parameters: whether they change or not, the correlation holds. The time variation of the force is associated also with the time variation of the advancing and receding contact angles. Figure 3 shows typical variations: a small variation of the advancing edge and higher variation of the receding edge and a rather large scatter that agrees with the other studies.49,51 Note that just as Figure 2 corresponds to the advancing angle on the verge of motion, so does Figure 3, and hence, the corresponding receding (50) The OTA layer robustness is manifested in measurements performed with hexadecane in ref 33 (cf. Figure 2b within) using the Surface Force Balance (SFB), where no variation of surfactant layer is recorded. Note that in a typical SFB experiment, a single surface is used for ∼1 week, where the surfaces are in contact with hexadecane (and a few such experimental weeks are performed). Thus, the lack of monolayer time changes there is sufficient to assume a lack of monolayer time changes in the present paper, where the waiting times are only fractions of hours. Note also that ref 33 shows that OTA+ is insoluble in hexadecane (where it is termed STAI). OTA is not related to OTAI from ref 33. (51) Nguyen, H. V.; Padmanabhan, S.; Desisto, W. J.; Bose, A. J. Colloid Interface Sci. 1987, 115, 310.
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angle is not the minimal receding angle but rather the receding angle that corresponds to the situation of an advancing edge on the verge of moving. This differs from the onset of motion of the whole drop, which occurs after the receding edge moves. The fact that θA changes much less than θR may seem surprising because it is the advancing edge that we monitor. The reason for this is not completely understood; however, two factors should be considered: (i) Both drop edges influence each other; thus, the change in the receding edge should vary the retention force just as the advancing edge does, and one should consider the entire envelope of liquid–vapor surface. (ii) θA at any given moment corresponds to a higher cosine variation than its corresponding θR value because of its closer proximity to the straight angle and the nature of the cosine function. In summary, we have shown that the lateral force required to initiate a drop motion along a surface toward sliding is a function of the time the drop rests on the surface. We explain this time effect as being induced by the unsatisfied normal component of Young’s equation, γ⊥, which pulls on the surface and thus deforms it in a way that increases the drop–surface attraction along the three phase contact line. Higher attraction corresponds to lower free energy and thus higher retention force. Our results show a correlation between γ⊥ and force increase induced by the time effect. Additionally, there is a correlation between the surface rigidity and the relaxation time associated with the time effect, i.e., how quickly the resting time reaches a plateau. Unlike very soft materials, in rigid surfaces, the ridge along the three phase contact line is not visible but still manifests itself by the increase in retention force. This is possibly due to chemical changes that occur at the three phase contact line, either by moving of functional groups43,44 or by breaking of chemical bonds.38 The surface deformation associated with the harder surfaces that we consider is expected to have a smaller corrugation increase. This is especially true for systems in which the surfaces are covered with a surfactant monolayer: the total possible corrugation depth is predominantly the size of the monolayer. Thus, parameters that conjugate with the topographical changes to the increase in the retention force with time are important to consider. It is known that wetting properties are sensitive to the specific functional groups on the surface, so surfaces of identical chemical nature that orient different functional groups on the surface differ considerably in their wetting properties.28,43,45,47,52 Thus, even a subnanometric distortion could affect significantly the retention force, f. Hence, the theoretical prediction of f is related also to the exact chemical functional groups that became exposed to the surface.28,43,45,47,52 In this connection, see also the work of Extrand relating contact angle hysteresis to surface chemistry.52 Acknowledgment. We are grateful to Mr. David M. Day for vital technical support. Acknowledgement is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the National Science Foundation through Grant DMR-0619458 and for the Research Enhancement Grant (Lamar University) for support of this research. We thank Jianguo Fan for going over the manuscript. LA7040696 (52) Extrand, C. W. J. Colloid Interface Sci. 2002, 248, 136.
