pubs.acs.org/Langmuir © 2009 American Chemical Society
Evaporation Dynamics of Microdroplets on Self-Assembled Monolayers of Dialkyl Disulfides )
Guangfen Li,† Susana Moreno Flores,‡ Chandrasekhar Vavilala,§ Michael Schmittel,§,^ and Karlheinz Graf*, ,^ †
)
College of Material Science and Chemical Engineering, Tianjin Polytechnic University, Chenglinzhuang Road 63, 300160 Tianjin, P. R. China, ‡CIC BiomaGUNE - Biosurfaces unit, Paseo Miram on 182, E-20009 San Sebasti an, Spain, §Organische Chemie I, Universit€ at Siegen, Adolf-Reichwein-Strasse 2, D-57068 Siegen, Germany, Lehrstuhlvertretung Physikalische Chemie, University of Siegen, Adolf-Reichwein-Strasse, D-57068 Siegen, Germany, and ^Research Center for Micro- and Nanochemistry and -Engineering, FB 8, Chemie/Biologie, University of Siegen, Adolf-Reichwein-Strasse, D-57068 Siegen, Germany Received April 22, 2009. Revised Manuscript Received September 8, 2009 We present a study of the static wettability and evaporation dynamics of sessile microdroplets of water on selfassembled monolayers (SAMs) prepared with unsymmetric dialkyl disulfides CH3-(CH2)11+m-S-S-(CH2)11-OH (m = 0, ( 2, ( 4, ( 6) on gold-covered mica. The advancing and receding contact angles decrease linearly with increasing hydrophilicity of the SAM. The latter was changed either via the molar ratio or via the chain length of the hydroxyl-terminated alkyl chains in the monolayer. In contrast to SAMs made of thiols, the contact angle hysteresis was 10 for all disulfides, irrespective of their chain lengths. During evaporation of single droplets, a transition from pinning to constant contact angle mode was observed. The transition time between the modes increases with the surface hydrophilicity, leading to longer pinning. This way, the time for complete droplet evaporation decreases by ∼30% owing to the fact that during pinning the overall droplet area stays large for a longer time. For single droplets the measured total evaporation times agree well with the calculated ones, showing the validity of the standard evaporation model for both evaporation modes. In contrast to the results for single droplets, many droplets with different initial volumes show a power-law dependence on the total evaporation time with an exponent different from 1.5 as expected from the standard model. For disulfides with m 6¼ 0, the exponent is in the range of 1.40-1.47 increasing with the surface hydrophilicity. For the SAMs with m = 0 the exponent increases up to 1.61 for the most hydrophilic surface. We explain this deviation from the standard evaporation model with the presence of a liquid precursor film around the droplet, which either enhances or decelerates evaporation. Our results suggest that SAMs of dialkyl disulfides offer the possibility to tune the wettability of gold surfaces in a more controlled way than thiols do.
1. Introduction The study of microdroplet evaporation has been a vigorous field of research for decades owing to its relevance for different applications as for instance in sprays and compression-ignition engines,1-3 inkjet printing,4 and meteorology.5 Recent research utilizes evaporation of sessile droplets on solid substrates to investigate or enhance ordering processes in more complex liquids or in solids related to application. Examples are the proper deposition of DNA in microarrays,6,7 the formation of assemblies of particles with long-range order,8-11 or the structuring of *Corresponding author. E-mail:
[email protected]. Phone: + +49 (0)271/740-2803. Fax number: ++49 (0)271/740-2805. (1) Arcoumanis, C.; Bae, C.; Crookes, R.; Kinoshita, E. Fuel 2008, 87, 1014– 1030. (2) Gelfand, B. E. Prog. Energy Combust. Sci. 1996, 22, 201–265. (3) Hartranft, T. J.; Settles, G. S. Atomization Sprays 2003, 13, 191–221. (4) Calvert, P. Chem. Mater. 2001, 13, 3299–3305. (5) Whiteman, C. D. Mountain Meteorology: Fundamentals and Applications; Oxford University Press: New York, 2000. (6) Blossey, R.; Bosio, A. Langmuir 2002, 18, 2952–2954. (7) Heim, T.; Preuss, S.; Gerstmayer, B.; Bosio, A.; Blossey, R. J. Phys.: Condens. Matter 2005, 17, S703–S716. (8) Kuncicky, D. M.; Velev, O. D. Langmuir 2008, 24, 1371–1380. (9) Deegan, R. D. Phys. Rev. E 2000, 61, 475–485. (10) Chang, S. T.; Velev, O. D. Langmuir 2006, 22, 1459–1468. (11) Fustin, C.-A.; Glasser, G.; Spiess, H. W.; Jonas, U. Langmuir 2004, 20, 9114–9123.
13438 DOI: 10.1021/la901422v
polymer surfaces by inkjet etching with solvent droplets.12-17 In all these examples, the evaporation plays a crucial role for the performance of the experiment. Therefore, a basic understanding of the evaporation process is desired. Principally, the evaporation of a droplet from a solid support proceeds in two different evaporation modes (Figure 1). For contact angles >90 degrees, the droplet usually evaporates at a constant contact angle (CCA) but decreasing contact radius, called the CCA mode. For contact angles 10
ð4Þ
β ¼ ð1 - cos θ0 Þ2 3 ð2 þ cos θ0 Þ
ð5Þ
Multiplying with ttotal/100 is required to plot the droplet volume versus t/ttotal in %. With D = 2.4 10-5 m2/s, M = 18 g/mol, R = 8.3145 J/K/mol, T = 298.15 K (25 C), F = 1 g/mL, ΔP = 1585 Pa at 50% relative humidity, a ≈ 360 μm, ttotal = 130 and 58.48 s, θ0 = 110 and 33.14 for the hydrophobic and hydrophilic surface, respectively, we obtain C = 1.19 103 μm2 and 5.94 104 μm3/1.13 for the methyl- and hydroxyl-terminated thiol SAMs, respectively. Despite the respective deviations of 11 and 33%, these values are in excellent agreement with the fit, considering that the treatment is only valid for pure CCA or CCR modes. This is not strictly fulfilled in the measurement. The quantitative agreement of the constants and the exponents with theory confirms that the evaporation of single droplets can be described with the standard evaporation model. 3.3. Total Evaporation Time for Single Droplets. More detailed information can be derived if the total evaporation time ttotal is analyzed, here for droplets with initial volumes of 5 nL (Figure 8). Since for experimental reason it is difficult to set the initial volume to a desired value with high precision, we derived the total evaporation time from a multidroplet experiment (see Figure 10 below). There, the evaporation times were measured for different initial volumes for each system. A fit to the data provided the total evaporation time for 5 nL droplets with high accuracy. The total evaporation time decreases with increasing the SAM’s hydrophilicity, when the composition or the chain length is changed (Figure 8). For a quantitative comparison, the total evaporation times can be calculated from eq 1 with C given either by eq 2 or 3, depending on the evaporation mode. After setting V = 0 and rearranging the corresponding equations, we obtain for the CCA mode (p = 1.5) 3 π 1=3 β1=3 FRT 2=3 ttotal ¼ 3 f 3 DMΔP 3 V0 ðnon-pinnedÞ 4π 3
ð6Þ
sinðθ0 =RÞ FRT V0 ðpinnedÞ f ðθ0 =RÞ 3 2πaDMΔP 3
ð7Þ
For droplets that evaporate exclusively in the CCA or CCR mode, we obtain 29.4 or 18 s, respectively, on the methylated and the hydroxylated SAM surfaces. These values are in excellent agreement with the actually measured ones. This quantitative agreement of the total evaporation times with theory shows again that the evaporation of single droplets can be described with the standard evaporation model. Langmuir 2009, 25(23), 13438–13447
The decreasing evaporation time for the SAM with increasing hydrophilicity can be understood on the basis of the observed increased tendency of droplet pinning. The longer the droplet stays pinned, the longer the overall area of the droplet remains large. This leads to an overall higher evaporation rate and thus a shorter evaporation time. As a confirmation, the curves show the mirrored characteristics of the transition time between CCR and CCA mode in Figure 6. For example, the lower evaporation time of the disulfide with m = 4 is related to the maximum of the same sample in Figure 6. This relation between pinning and evaporation time can be illustrated if the area As of the droplet surface is divided by V2/3. This ratio reflects the actual area of the sessile droplet divided by the area of a virtual spherical droplet with the same volume as that of the sessile droplet. With60 As ¼
2πa2 πa3 βðθÞ and V ¼ 1 þ cos θ 3 sin3 θ
ð8Þ
we obtain for the area ratio As/V2/3 As =V 2=3 ¼
and for the CCR mode (p = 1) ttotal ≈
Figure 8. The total evaporation time for 5 nL droplets on SAM surfaces versus the (a) molar ratio of hydroxyl- and methylterminated alkyl chains in the SAM and the (b) relative chain length m in the disulfides as defined in Figure 2. The evaporation times were determined from the fits in Figure 10 for reason of comparability.
≈
2 3 32=3 3 π1=3
ð1 -cos θÞ1=3 ð2 þ cos θÞ2=3 6:09
ð1 -cos θÞ
1=3
ð2 þ cos θÞ2=3
ð9Þ
It is reasonable to plot the area ratio versus the evaporation time because, according to eq 6, ttotal V02/3 for the CCA mode. The same dependence holds for the CCR mode as well if the exact solution is derived (eq 7 is a linear approximation only). For more details, see eq 12 in ref 28. If As/V2/3 is plotted versus the (60) Erbil, H. Y. J. Phys. Chem. B 1998, 102, 9234–9238.
DOI: 10.1021/la901422v
13445
Article
Li et al.
Figure 9. The ratio of the actual droplet surface and the volume2/3 versus the normalized evaporation time. For clarity, the curves of two samples were omitted (m = (2). The numbers x and y in CxCyOH indicate the numbers of CH2/CH3 groups in the methyl- or the hydroxyl-terminated alkyl chain of the disulfides, respectively.
normalized evaporation time, characteristic curves for each SAM system are obtained (Figure 9). For the nonpinning pure hydrophobic surface, the plot is nearly horizontal except for the very end of the evaporation. In contrast, the pure hydrophilic hydroxylated SAM with nearly permanent pinning increases from the very beginning. For all other systems the area ratios lie between the two extremes. A closer look shows that the sequence of the area ratio curves roughly follows the data for the total evaporation time (for clarity, not all curves are shown). For example, the area ratios for the SAMs with m = -4 and -6 coincide, and these systems actually exhibit nearly the same total evaporation time. On the other hand, the extraordinarily high area ratio for the hydroxylated SAM shows the shortest evaporation time. Thus, the area ratio according to eq 9 can be taken as a rough measure for the total evaporation time. However, two characteristics of the curve are important. A higher ratio of As/V2/3 is indicative of a higher hydrophilicity and kinks in the curves reflect pinning. The higher is the area ratio and the later appears the kink, the shorter is the time for complete evaporation. A longer pinning enhances the evaporation despite a relatively low hydrophilicity, as it can be seen for the disulfide with m = 4 for which the curve lies above that one for m = 6. This result is in agreement with findings from other groups.34 3.4. Deviation from the Standard Evaporation Model. So far, the analysis of the evaporation rate of single sessile droplets was based on the standard evaporation model. It claims that the total evaporation time of a sessile droplet is proportional to V2/3 for both, the CCA and the CCR mode. A deviation from this model is found if log V0 for different initial volumes of the deposited droplet is plotted versus log ttotal and fitted linearly, thus providing a scaling exponent according to log V0 p log ttotal (Figure 10). For the methylated SAM, p = 1.47, which is close to the expected value of 1.5 for the standard evaporation model. However, with increasing hydrophilicity the exponent increases to p ≈ 1.61 for the SAMs with m = 0. The SAMs with m 6¼ 0 show exponents lower than 1.5, increasing by trend from ∼1.40 to ∼1.47 with increasing length of the hydroxyl-terminated chain. Since pinning cannot be the cause for the deviation of the exponent, as pointed out in the last chapter, a different evaporation model must be considered. The exponent in the above equation changes if evaporation through a flat water film is assumed. Such a water film with a radius of up to a few millimeters is likely to occur, especially for hydrophilic surfaces as a precursor film in front of the droplet some milliseconds to seconds after (61) Alteraifi, A. M.; Sasa, B. J. J. Adhes. Sci. Technol. 2006, 20, 1333–1343. (62) Drelich, J.; Chibowska, D. Langmuir 2005, 21, 7733–7738.
13446 DOI: 10.1021/la901422v
Figure 10. Initial droplet volume V0 in nL versus the total evaporation time ttotal in seconds (log-log plot) for droplet evaporation on thiol and disulfide SAM surfaces. The straight lines are fits to the data with a power law of the form V0 tptotal. The slopes from the fit are shown in the log-log plots for each system and represent the exponents of the power law. The total evaporation times for microdroplets with a volume of 5 nL plotted in Figure 8 are obtained from the fit equation. The numbers x and y in CxCyOH indicate the numbers of CH2/CH3 groups in the methyl- or the hydroxyl-terminated alkyl chain of the disulfides, respectively.
deposition.31,61,62 To derive a relation for the time-dependence of the volume, we apply the first Fickian law on the evaporation through a flat water surface J¼
dn dc ¼D Adt dx
ð10Þ
J is the flux of n moles of evaporating molecules per area of the water film per time dt under the concentration gradient dc/dx in the air. The flux is negative because the concentration of water molecules in the air decreases with the distance from the water surface. dc/dx can be assumed constant for a flat water film, and eq 10 can easily be integrated resulting in V ¼ V0 -
M dc AD t F dx
ð11Þ
after converting the molar amount n into a volume of the water film according to n = FV/M. From eq 11 we obtain V0 ttotal. Since the exponent is lower than that for the evaporation through the curved droplet surface (V0 t1.5 total), the observed lower exponent for the curved SAMs with m ¼ 6 0 might be explained with evaporation through a precursor film. The more hydrophilic is the surface, the more pronounced the evaporation through the precursor film should be. Thus, a decrease of the exponent is expected with increasing hydrophilicity. However, the opposite is observed for our samples. This observation can be explained tentatively if the limited size of the precursor film is considered. At the edge of such a film the evaporation rate is increased. Accordingly, for complete wetting of water on mica with contact angles close to 0 degree an increased evaporation rate dV/dt (ttotal - t)0.65 was measured.63 (63) Poulard, C.; Guena, G.; Cazabat, A. M. J. Phys.: Condens. Matter 2005, 17, S4213–S4227.
Langmuir 2009, 25(23), 13438–13447
Li et al.
Article
Figure 11. Schematic of the refined evaporation model as obtained from the deviation of the exponents in Figure 10 from 1.5, the value expected for the standard model. We suggest that part of the evaporation proceeds through the center (V0 t1total) or the rim of a precursor 1.5 film (V0 t1.65 total) in contact with the water droplet (V0 ttotal). The evaporation rate through the droplet surface is nonuniform.
Integration provides V0 t1.65 total and therefore an increased exponent if a thin limited precursor film is assumed. As a confirmation, the value is close to the one we observed for the most hydrophilic hydroxylated sample. The suggestion for an enhanced evaporation through a liquid precursor film is physically reasonable because the increased tendency of pinning on the more hydrophilic surfaces leads to an increased flux of liquid to the rim of the droplet.64,65 Additionally, an enhanced evaporation was found for water droplets on swollen polyelectrolyte films, which is comparable to the situation in a precursor film.66 Therefore, we suggest an evaporation model as illustrated in Figure 11. The droplet evaporates mainly through a spherical cap according to a scaling law V0 tptotal with p ≈ 1.5. This is observed for the methylated hydrophobic gold surface. For SAMs with m 6¼ 0, p is lower than 1.5 because of a precursor film in front of the droplet. Since the contact angle for those SAMs is higher than that for the hydroxyl-terminated SAM, this film evaporates mainly through its surface. Thereby, the flexible alkyl chains keep the water film. In contrast, the hydrophilic SAMs with m = 0 and xOH = 0.5 and 1 show an exponent p higher than 1.5. This is because the precursor film is more extended after initial droplet deposition owing to the decreased contact angle and a missing influence from flexible alkyl chains. Thus, the evaporation in the precursor film is increasingly influenced by the evaporation rate at its edge the more hydrophilic the surface is. Since the hydrophilicity of the SAMs also increases with increasing length of the hydroxylterminated alkyl chain, the same trend is observed for the SAMs with m ¼ 6 0 as a confirmation. Thus, evaporation through the droplet surface and the precursor film is probable for SAMs made of unsymmetric dialkyl disulfides.
4. Summary and Conclusion We studied the static wettability and the evaporation dynamics of sessile water droplets with low Bond (Bo) numbers on SAMs on gold. As SAMs we used methyl- or hydroxyl-terminated thiols or unsymmetric dialkyl disulfides with different alkyl chains lengths, one of which was terminated with a hydroxyl and the other terminated with a methyl group. We showed that the static contact angle decreases linearly with increasing molar ratio or with increasing length of the hydroxyl-terminated alkyl chains in the monolayer. A comparison of the cosine of the advanced contact angles with the Cassie-Baxter relation was consistent with the assumption of 1:1 hydrated hydroxyl groups in the SAM surface. The contact angle on the hydrophilic and the hydrophobic thiol SAMs were obtained as a limiting value from (64) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827–829. (65) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. Rev. E 2000, 62, 756–765. (66) H€anni-Ciunel, K.; Findenegg, G. H.; von Klitzing, R. Soft Mater. 2007, 5, 61–73.
Langmuir 2009, 25(23), 13438–13447
the extrapolation of the contact angles of the dialkyl disulfides for the case of one vanishing alkyl chain. While the contact angle hysteresis depended on the molar ratio of the OH-terminated alkyl chains in the monolayer, it was constant at ∼10 if the relative length of the two alkyl chains in the disulfides was changed. The surface roughness was excluded as the reason for this observation. Thus, SAMs of dialkyl disulfides offer the possibility to effectively tune the surface wettability without the need for a thorough control of the monolayer composition during formation and without changing the surface sensitivity to imperfections, as necessary for thiols. During the evaporation of the sessile droplets, all possible evaporation modes were observed. The initially pinned droplet evaporated with constant contact angle after a time, which was characteristic for the SAM used. With increasing surface hydrophilicity, the droplet stayed pinned longer and thus its surface area stayed large longer, whether controlled via the molar ratio or the length of the hydroxyl-terminated alkyl chain in the monolayer. As a consequence, the time for complete evaporation decreased. Since the total evaporation time depends on the initial droplet volume to a power of 2/3, the time-dependence of the actual droplet area compared to volume2/3 is a good measure for it. On the basis of the good agreement between measured and calculated total evaporation times, we show that the evaporation of droplets on SAMs of dialkyl disulfides can be described with the standard evaporation model for all evaporation modes, including pinning. In contrast, by measuring the time for the complete evaporation of many droplets with different initial volumes, we found a deviation from the standard evaporation model. The initial droplet volume depends on the total evaporation time with a power of p. We found p ≈ 1.5 for the methyl-terminated SAM, as expected for the standard evaporation model. For the more hydrophilic SAMs, p increased to 1.61, while it was lower than 1.5 for all disulfide SAMs with different alkyl chain lengths. We tentatively explain this result with a liquid precursor film around the sessile droplet. This idea leads to a modified evaporation model, in which part of the liquid evaporates through the surface or the edge of the precursor film depending on the surface hydrophilicity and the relative alkyl chain length in the disulfides. Our results provide evidence that by chemical modification of gold surfaces with dialkyl disulfides containing different alkyl chain lengths and terminating functional groups, the static wettability and the evaporation rate can be tuned in a more controlled way compared to mixtures of thiols. The low tendency of water for pinning on SAMs made of disulfides suggests them as interesting candidates to minimize wetting artifacts as, e.g., in microfluidic systems. In addition we have shown that from a multidroplet analysis the total evaporation time can be determined with higher precision than from experiments on single droplets alone. This way it was possible to detect a deviation from the standard evaporation model. Acknowledgment. Andreas Best and Norbert H€ohn are acknowledged for their technical support. Helpful discussions with Huayna Cerqueira Streit, Prof. Steffen Hardt, Prof. Friedhelm Sch€onfeld, Prof. Holger Sch€ onherr, and Dr. R€udiger Berger are acknowledged. The authors thank Prof. Edward Bormashenko from Ariel University, Israel, for hints to helpful literature. This work was supported by the Deutsche Forschungsgemeinschaft (GR 2003/2 - FOR 516 and SCHM 647/14 - FOR 516), the Nature Science Foundation of Tianjin (No. 08JCYBJC26300), and the Max Planck Society. DOI: 10.1021/la901422v
13447
