ARTICLE pubs.acs.org/Langmuir
Comparison of the Relaxation of Sessile Drops Driven by Harmonic and Stochastic Mechanical Excitations F. J. Montes Ruiz-Cabello, M. A. Rodríguez-Valverde,* and M. A. Cabrerizo-Vílchez Biocolloid and Fluid Physics Group, Department of Applied Physics, University of Granada, Campus de Fuentenueva, E-18071 Granada, Spain ABSTRACT: Currently, there is no conclusive evidence regarding the global equilibrium condition of vibrated drops. However, it is well-known that vibration of sessile drops effectively reduces the contact angle hysteresis. In this work, applying a recent methodology for evaluating the most-stable contact angle, we examined the impact of the type of excitation signal (random signal versus periodical signal) on the values of the most-stable contact angle for polymer surfaces. Using harmonic signals, the oscillation frequency affected the postvibration contact angle. Instead, the white noise signal enabled sessile drops to relax regardless of their initial configuration. In spite of that, the values of most-stable contact angle obtained with different signals mostly agreed. We concluded that not only the amount of relaxation can be important for relaxing a sessile drop but also the rate of relaxation. Together with receding contact angle, most-stable contact angle, measured with the proposed methodology, was able to capture the thermodynamic changes of “wetted” polymer surfaces.
1. INTRODUCTION One of the current challenges in the studies of wetting phenomena is the measure of the most stable contact angle (MSCA). By definition, this contact angle corresponds to the drop configuration, for a given volume, with the lowest free energy. Consequently, the MSCA is the only contact angle closely related with the surface energy of chemically homogeneous surfaces or else the average surface energy of chemically heterogeneous surfaces. In spite of the relevance of the MSCA, most experimental studies in wetting are based on the advancing contact angle (ACA) and the receding contact angle (RCA). These contact angles are readily identifiable and measurable. Moreover, the affinity between a liquid and a solid surface is better described by the ACA and RCA values, rather than the MSCA value, because the adhesion forces depend on the former angles,1 accordingly. However, it is very common to estimate the surface energy of solids from the ACA values2,3 (and occasionally from the RCA values). This approximation can produce misleading results, especially on rough surfaces.4 Several authors have used the forced relaxation of drops and menisci to attain the stable configuration of the global minimum energy (GME).5 10 Unfortunately, it is a nontrivial task to ensure that a sessile drop is actually at the GME configuration, after being vibrated. Unlike the ACA or RCA configurations, there is no experimental way to identify that a system attains the GME configuration. The axisymmetric shape of vibrated drops is often used as a necessary (but not sufficient) condition to recognize the GME configuration.8 For real surfaces, the energy barriers surrounding the GME configuration in the free energy curve are higher than far from the GME configuration. For this reason, if the vibration does not provide energy enough to the drop, this may be trapped in a metastable configuration close to r 2011 American Chemical Society
the GME configuration, but without a clear physical meaning.11 The same situation would happen if the drop were overexcited due to an energy excess. Recently, we presented a novel methodology for evaluating the MSCA, invoking its operative definition: the contact angle of the drop configuration with the lowest susceptibility to perturbations.10 In this methodology, we form several stable drops with identical volume but different contact angles belonging to the observable hysteresis range. Next, we monitor the postvibration response of each metastable configuration to find the changeless configuration (i.e., the MSCA). The effectiveness of vibrations in changing contact angles is still an open question. Excitation modes of the liquid vapor interface and contact line, threshold amplitude (nonlinear effects), atomization, etc. are points to take into account for achieving the optimum drop relaxation using vibrations.5,12 To the best of our knowledge, little attention has been given to the type of excitation signal (waveform) for relaxing drops.13 As Mettu and Chaudhury reported,14 we have also found that the contact angle measured just after sinusoidal vibration may depend on the input frequency. Instead, Mettu and Chaudhury applied successfully a stochastic signal (white noise) for relaxing sessile drops.14 Drop relaxation with stochastic excitation is more readily performed because, except for the signal amplitude, it does not require one to select any input frequency. The aim of this work is to analyze the effect of the excitation signal on the MSCA values obtained with the methodology described above. This study was performed with two types of Received: March 22, 2011 Revised: May 27, 2011 Published: June 24, 2011 8748
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Langmuir signals: harmonic (sine wave) and stochastic (white noise), on different polymer surfaces. Second, we examined the effect of drop volume on the MSCA values.
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Table 1. Arithmetic Roughness (Ra), Root-Mean-Square Roughness (Rq), and Advancing and Receding Contact Angles (ACA and RCA) of the Polymer Surfaces Employed in This Worka polymer
2. EXPERIMENTAL SECTION We employed six polymer surfaces [polystyrene PS, poly(ethylene terephthalate) PET, poly(methyl methacrylate) PMMA, polycarbonate PC, polypropylene PP, and poly(tetrafluoroethylene) PTFE], as supplied by Goodfellow. The roughness parameters were measured with a white-light confocal profiler (model Plμ, Sensofar) over a scan-area of 196.7 196.7 μm2 at 50. The surfaces were drilled with a 2 mmdiameter hole. All of the surfaces were degreased with aqueous detergent solution and next, sonicated in ethanol for 5 min (except for PMMA). Finally, they were plentifully rinsed with distillate water and dried at room temperature, properly covered. First, the ACA and RCA values of each surface were measured using the sessile drop method and the lowrate dynamic contact angle technique.15 For each experiment, an amount of Milli-Q water (up to 200 μL) was dispensed to the surface from below with a microinjector (Hamilton ML500) at 2 μL/s. For receding mode, the same amount of liquid was removed at the same flow rate. For several polymer surfaces, we observed that the RCA values were not stable, decreasing as the drop volume was lower. This apparent dependence of RCA on volume was reproducible and it was even found for greater initial volumes of drop (300 400 μL). This effect has been widely reported in the literature for polymer surfaces16 (see Figure 4 in the work of Pierce et al.17). However, its possible explanation (surface swelling, liquid sorption/retention on the surface, etc.) is out of the scope of this paper. Since the contact angle of receding drops (i.e., moving contact lines) changed with the drop size, we selected as RCA the contact angle when the drop volume reached 150 μL, and this angle was averaged over at least three runs on each surface. We used this same procedure for measuring the ACA values, although the contact angle of advancing drops was constant over a wide volume range for all the polymer surfaces used in this work. It is worth highlighting that the ACA value estimated this way agreed with the contact angle averaged over those regions where the three-phase contact line was advancing. To measure the MSCA, we monitored the response of several water drops of known volume V0 and different initial contact angles to mechanical vibrations following the procedure described in a recent work.10 “Seed” sessile drops, with volume arbitrarily greater than V0, were dispensed with the microinjector at 2 μL/s. Next, an amount of liquid was sucked at the same flow rate to each seed drop in order to reach the target volume V0. Following this procedure, we were able to form drops of the identical volume but with different contact angle (θ0) within the practical hysteresis range. As the volume removed from the drop was greater, the initial contact angle θ0 decreased from the ACA value up to the RCA value. Once the initial contact angle was measured, the system was vibrated with a mechanical driver (PASCO SF-9324) controlled by a computer. The input vibration function was generated by the software GoldWave. The actual amplitude of the vibrating platform was measured with a high-speed camera (Phantom Miro 4). Special attention was given to avoid drop atomization and bursting.18 After vibration, the contact angle was measured (this route was reported as the appropriate one for measuring the MSCA19) and the unsigned deviation of contact angle was plotted in terms of the initial contact angle. The MSCA was identified by finding the initial metastable configuration with null variation in contact angle after vibration. We employed two kinds of excitation signal: a harmonic signal (sine function) and a stochastic signal (white noise function). Both signals were implemented with the software GoldWave. The input parameters of the sine function were amplitude and frequency, although we confirmed that the amplitude was not relevant above a threshold value where the contact line oscillated. The resonance frequency of each sessile drop, with known values of
Ra (μm)
Rq (μm)
ACA (deg)
RCA (deg) 35.0 ( 1.2
PMMA
0.009 ( 0.005
0.025 ( 0.009
69.8 ( 1.5
PET
0.013 ( 0.004
0.016 ( 0.005
77.8 ( 1.3
32 ( 2
PS
0.0120 ( 0.0014
0.018 ( 0.005
89.5 ( 1.5
63.8 ( 1.8
PP
0.024 ( 0.003
0.031 ( 0.003
102.3 ( 1.2
76.1 ( 1.3
1.0 ( 0.2
1.3 ( 0.3
123 ( 2
84.5 ( 1.5
0.014 ( 0.002
0.018 ( 0.003
85.8 ( 1.0
45.0 ( 1.0
PTFE PC a
The values of ACA and RCA were measured for a water drop volume of 150 μL.
Figure 1. Difference between the vibrated contact angle and the initial contact angle of 150 μL water drops on a PET surface as a function of the initial contact angle employing sinusoidal (circles) and stochastic (triangles) vibrations. The obtained most-stable contact angles were 53.0 ( 1.5° and 53.0 ( 1.0°, respectively. The ACA and RCA values obtained by low-rate dynamic contact angle experiments are shown with vertical continuous lines and the average angle of ACA and RCA and the corresponding angle from the average cosine with vertical dotted lines. volume, initial contact angle, liquid surface tension, and density, was calculated by applying the method of Strani and Sabetta.20 Although this numerical method was originally developed for pinned contact lines, it was validated by Yamakita et al.13 for oscillating contact lines at low acceleration amplitudes. For the white noise function, the signal amplitude was optimized by setting the lowest sampling rate at 1000 samples per second.
3. RESULTS The values of roughness parameters (Ra and Rq) and the values of ACA and RCA, from the low-rate dynamic contact angle experiments, for 150 μL water drops are collected in Table 1. All of the employed surfaces, except for PTFE, were assumed to be smooth. However, we observed relatively high contact angle hysteresis. This observation is commonly reported in wetting studies with “smooth” polymer surfaces.15,21 8749
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Figure 2. Difference between the vibrated contact angle and the initial contact angle of 150 μL water drops on a PMMA surface as a function of the initial contact angle employing stochastic (triangles) and sinusoidal vibrations (circles). The obtained most stable contact angles were 54.0 ( 1.0° and 48.0 ( 1.0°, respectively. The ACA and RCA values obtained by low-rate dynamic contact angle experiments are shown with vertical continuous lines and the average angle of ACA and RCA and the corresponding angle from the average cosine with vertical dotted lines.
Table 2. Most-Stable Contact Angles (θMS) Measured Using Harmonic and Stochastic Signals, Arithmetic Average of the Advancing and Receding Contact Angles (Average 1) and Angle of the Average Cosine (Average 2) for the Polymer Surfaces Studied in This Worka θMS (deg) surface
harmonic
stochastic
average 1 (deg)
average 2 (deg)
PMMA
48.0 ( 1.0
54.0 ( 1.0
52.4 ( 1.2
53.9 ( 1.2
PET
53.0 ( 1.5
53.0 ( 1.0
54.8 ( 1.3
55.5 ( 1.3
PS PP
73.1 ( 1.5 89.4 ( 1.5
72.3 ( 1.5 87.5 ( 1.5
76.5 ( 1.5 89.2 ( 1.5
77.0 ( 1.5 88.4 ( 1.5
107.3 ( 1.5
108.1 ( 1.1
103.5 ( 1.7
102.7 ( 1.7
58.5 ( 1.0
66.1 ( 1.1
65.4 ( 1.0
67.4 ( 1.0
PTFE PC a
Figure 3. Values of ACA and RCA in terms of the drop volume (upper graph) and contact radius in advancing and receding modes in terms of the drop volume (lower graph) for a PC sample. The values were averaged over three experimental runs. The continuous straight lines are the linear fits of ACA and RCA as a function of drop volume. In the upper graph, we also plot the MSCA values (solid circles), obtained by relaxing with white noise water drops on the same PC sample, and the average line of ACA and RCA in terms of the drop volume.
The bold numbers correspond to those θMS values in good agreement.
In Figure 1, we present the graphical method to assess the MSCA for the PET surface, using harmonic and stochastic excitation signals. For this particular case, we observed a very good agreement between the MSCA values provided with both signals. In the graph of Figure 1, we also show the ACA and RCA values referred to 150 μL drops on the same PET surface (see Table 1). We calculated the average of ACA and RCA and the average of their corresponding cosines. These averages are usually proposed in literature as empirical estimates of the MSCA.22 25 For the case of the PET surface, we observed that the two average angles disagreed with the measured MSCA. However, the results found with the PET surface were not general. In Figure 2, we present the results of the PMMA surface. In this case, we measured different values of MSCA for each excitation signal, but the MSCA value reproduced with the
stochastic signal agreed with the arithmetic average of the values of ACA and RCA. In Table 2, we compile the MSCA values and the average contact angles for the polymer surfaces. It is worth highlighting that the MSCA values summarized in Table 2 were obtained by relaxing 150 μL water drops. The MSCA measured using the stochastic and harmonic signals mostly agreed, except for the PC and PMMA surfaces. We observed on these two surfaces that, after the sinusoidal vibration, the sessile drops revealed a noticeable asymmetry. As mentioned in the Introduction, we observed in general that the contact angle measured after the sinusoidal vibration depended on the oscillation frequency and so on the initial contact angle. However, the contact angle observed after the white noise was mostly independent of the previous configuration of the drop. 8750
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surface, but we found disagreement for the PTFE surface. In this last case, the average line systematically underestimated the MSCA value, probably due to the roughness of the PTFE sample (hydrophobic material). However, in both cases, the average line described the same trend for the MSCA values as the drop volume changed.
Figure 4. Values of ACA and RCA in terms of the drop volume (upper graph) and contact radius in advancing and receding modes in terms of the drop volume (lower graph) for a PTFE sample. The values were averaged over three experimental runs. The continuous straight lines are the linear fits of ACA and RCA as a function of drop volume. In the upper graph, we also plot the MSCA values (solid circles), obtained by relaxing with white noise water drops on the same PTFE sample, and the average line of ACA and RCA in terms of the drop volume.
Next, we studied the dependence of the MSCA on the drop volume. For this study, we excited sessile drops with the white noise signal on two polymer surfaces: PC and PTFE. In Figures 3 and 4, we plot the MSCA values in terms of the drop volume for the PC and PTFE samples, respectively. Moreover, we displayed the corresponding values of ACA and RCA, measured in low-rate dynamic contact angle experiments, as the drop volume changed. It is possible to check in Figures 3 and 4 that the three-phase contact lines were actually moving forward or back, accordingly. As mentioned in section 2, we found that the contact angle of receding drops on the PC surface was not stable. Due to this effect, like guide lines, we also draw in Figures 3 and 4 the corresponding best-fit straight lines of low-rate dynamic contact angles (ACA and RCA) as a function of drop volume. We compared the MSCA values with the average line of the two linear fittings of ACA and RCA. We observed a good agreement between the average line and the MSCA values for the PC
4. DISCUSSION In this work, we measured the values of MSCA of water sessile drops on different polymeric surfaces using a novel methodology based on the drop relaxation induced by mechanical vibration. We examined the roles of excitation signal (harmonic vs stochastic) and drop volume on the MSCA values. We were able to measure the MSCA monitoring the behavior of sessile drops of same volume but different contact angle within the hysteresis range. Most of the previous works in the literature7,8,12,26,27 were focused on the study of postvibration drops regardless of their initial state. This approach is based on the assumption that vibrations, being applied properly, remove the previous history of drops. However, the complete removal of the system history is hardly accomplishable and noticeable. In our approach, rather than identifying the MSCA as the contact angle measured just after vibration, we focused on the initial contact angle with the lowest perturbation after drop excitation. The complete mitigation of contact angle hysteresis is wellestablished as a necessary (not sufficient) condition for identifying the GME configuration. As shown in Table 2, we found that the MSCA values obtained with our methodology were mostly independent of the type of excitation signal within the experimental error. This observation was reported by Yamakita et al.13 However, we found that, whereas the previous history of the system was apparently erased when using harmonic vibrations, the contact angle measured after periodical vibration was dependent on the input frequency. This artifact causes a residual history dependence of the relaxed system. For the PMMA and PC surfaces, the vibrated drops were systematically deformed after the harmonic excitation, which violates a necessary condition7 for identifying the GME configuration. Otherwise, sessile drops subjected to stochastic relaxation were generally symmetric, even on the PMMA and PC surfaces. The drop relaxation occurs over a time scale determined by the particular vibration signal. Hence, random force acting on a sessile drop can excite their “fast” modes instead of the “slow” modes, as in a damped harmonic oscillator driven by sinusoidal force. Since the steady response of a damped harmonic oscillator with external noise usually dominates the transient one, a rapid, initial relaxation is produced rather than a long time relaxation. We also measured the values of ACA and RCA on the polymer surfaces using low-rate dynamic contact angle experiments. However, we did not find any correlation between the MSCA and the ACA and RCA values. Instead, we found that the wellknown rule of the average of ACA and RCA28 was consistent with our results of MSCA. We observed size dependence in the RCA results of several polymer surfaces, such as in Figure 3. This observation cannot be attributable to line tension effects because it was reproduced for a volume range where these effects are negligible.29 Surprisingly, as shown in Figure 3, we found that the MSCA was also dependent on the drop volume. In fact, although we did not find any theoretical proof for this observation, the MSCA scales with drop volume with similar slope than the arithmetic average of ACA and RCA (Figures 3 and 4). This 8751
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Langmuir result suggests that the size dependence of RCA found in several polymers might reveal a thermodynamic change rather than a kinetic artifact (i.e., time of liquid solid contact). Further work should be addressed to validate this effect.
5. CONCLUSIONS The most relevant conclusions of this work are summarized as follows: (1) We have validated with polymer surfaces a new methodology for evaluating the MSCA using mechanical vibration. We identified, within the contact angle hysteresis range, the MSCA as the contact angle of the changeless sessile drop, i.e., with null variation in contact angle, after forced relaxation. (2) We observed that the type of vibration signal did not affect the MSCA values measured with the methodology described above. However, we found it more suitable to use stochastic (white noise) signals rather than harmonic (sine wave) signals. Stochastic excitation did not need to predict previously the resonance frequency of each sessile drop, which depends on the initial contact angle, volume, surface tension, density, and oscillation mode. Furthermore, stochastic excitation more easily removed the previous history of the system so that contact angle hysteresis was completely mitigated. This property enables one to estimate directly the MSCA value as the postvibration contact angle, regardless of the initial contact angle. (3) Although we did not find any correlation between ACA and RCA with MSCA for the polymer surfaces used in this work, the MSCA described the same trend as for the arithmetic average of ACA and RCA as the drop volume was changed. Like RCA, MSCA was able to reveal possible thermodynamic alterations onto polymer surfaces due to liquid contact. ’ AUTHOR INFORMATION Corresponding Author
*Tel: (34) 958-24-00-25. Fax: (34) 958-24-32-14. E-mail: marodri@ ugr.es.
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(6) Della Volpe, C.; Brugnara, M.; Maniglio, D.; Siboni, S.; Wangdu, T., In Contact Angle, Wettability and Adhesion; Mittal, K. L., Ed.; VSP: Boston, 2006; Vol. 4, p 79. (7) Della Volpe, C.; Maniglio, D.; Siboni, S.; Morra, M. Oil Gas Sci. Technol. Rev. IFP 2001, 56 (1), 9–22. (8) Meiron, T. S.; Marmur, A.; Saguy, I. S. J. Colloid Interface Sci. 2004, 274 (2), 637–644. (9) Noblin, X.; Buguin, A.; Brochard-Wyart, F. Eur. Phys. J. Special Topics 2009, 166 (1), 7–10. (10) Rodríguez-Valverde, M. A.; Montes Ruiz-Cabello, F. J.; Cabrerizo-Vílchez, M. Soft Matter 2011, 7, 53–56. (11) Long, J.; Chen, P. Adv. Colloid Interface Sci. 2006, 127 (2), 55–66. (12) Andrieu, C.; Sykes, C.; Brochard, F. Langmuir 1994, 10, 2077–2080. (13) Yamakita, S.; Matsui, Y.; Shiokawa, S. Jpn. J. Appl. Phys. 1999, 38, 3127–3130. (14) Mettu, S.; Chaudhury, M. K. Langmuir 2008, 24 (19), 10833–10837. (15) Rodríguez-Valverde, M. A.; Montes Ruiz-Cabello, F. J.; GeaJodar, P. M.; Kamusewitz, H.; Cabrerizo-Vílchez, M. A. Colloids Surf., A 2010, 365 (1 3), 21–27. (16) Tavana, H.; Neumann, A. W. Colloids Surf., A 2006, 282, 256–262. (17) Pierce, E.; Carmona, F. J.; Amirfazli, A. Colloids Surf., A 2008, 323 (1 3), 73–82. (18) James, A. J.; Smith, M.; Glezer, A. J. Fluid Mech. 2003, 476, 29–62. (19) Nadkarni, G. D.; Garoff, S. Langmuir 1994, 10 (5), 1618–1623. (20) Strani, M.; Sabetta, F. J. Fluid Mech. 1984, 141, 233–247. (21) Extrand, C. W.; Kumagai, Y. J. Colloid Interface Sci. 1997, 191 (2), 378–383. (22) Marmur, A. Adv. Colloid Interface Sci. 1994, 50, 121–141. (23) He, B.; Lee, J.; Patankar, N. A. Colloids Surf., A 2004, 248 (1 3), 101–104. (24) Li, W.; Amirfazli, A. J. Colloid Interface Sci. 2005, 292 (1), 195–201. (25) Vedantam, S.; Panchagnula, M. V. J. Colloid Interface Sci. 2008, 321 (2), 393–400. (26) Della Volpe, C.; Maniglio, D.; Morra, M.; Siboni, S. Colloids Surf., A 2002, 206 (1 3), 47–67. (27) Cwikel, D.; Zhao, Q.; Liu, C.; Su, X.; Marmur, A. Langmuir 2010, 26 (19), 15289–15294. (28) Marmur, A. Soft Matter 2006, 2 (1), 12–17. (29) Drelich, J. J. Adhes. 1997, 63 (1 3), 31–51.
’ ACKNOWLEDGMENT This research work has been supported by the “Ministry of Science and Innovation“ (project MAT2010-14800) and by the “Junta de Andalucía” (projects P07-FQM-02517, P08-FQM4325 and P09-FQM-4698). Authors thank to Dr. Juan Antonio Holgado-Terriza, programmer of the software Dinaten and Contacto used for contact angle measurements. ’ REFERENCES (1) Gao, L. C.; McCarthy, T. J. Langmuir 2008, 24 (17), 9183–9188. (2) Tavana, H.; Jehnichen, D.; Grundke, K.; Hair, M. L.; Neumann, A. W. Adv. Colloid Interface Sci. 2007, 134 (35), 236–248. (3) Kwok, D. Y.; Lam, C. N. C.; Li, A.; Zhu, K.; Wu, R.; Neumann, A. W. Polym. Eng. Sci. 1998, 38 (10), 1675–1684. (4) Kwok, D. Y.; Neumann, A. W. Adv. Colloid Interface Sci. 1999, 81 (3), 167–249. (5) Decker, E. L.; Garoff, S. Langmuir 1996, 12 (8), 2100–2110. 8752
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