Evaporation of Sessile Droplets of Dilute Aqueous Solutions

Sep 18, 2008 - Samsung Electronics Co., Ltd., San #16 Banwol-Dong, Hwasung-City, ... Although the initial contact angles of the droplets were not sign...
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Langmuir 2008, 24, 11442-11450

Evaporation of Sessile Droplets of Dilute Aqueous Solutions Containing Sodium n-Alkylates from Polymer Surfaces: Influences of Alkyl Length and Concentration of Solute Jung-Hoon Kim,† Sung Il Ahn,† Jae Hyun Kim,‡ Jong Soo Kim,| Kilwon Cho,| Jin Chul Jung,† Taihyun Chang,§ Moonhor Ree,§ and Wang-Cheol Zin*,† Department of Materials Science and Engineering, Department of Chemical Engineering, Department of Chemistry, and Polymer Research Institute, Pohang UniVersity of Science and Technology, Pohang 790-784, Korea, and Manufacturing Technology Team 1, Memory DiVision, Semiconductor Business, Samsung Electronics Co., Ltd., San #16 Banwol-Dong, Hwasung-City, Gyeonggi-Do 445-701, Korea ReceiVed May 26, 2008. ReVised Manuscript ReceiVed July 18, 2008 The evaporation of sessile droplets placed on polymer surfaces was studied by microscopic observation of the changes in shape of aqueous solution droplets in which the alkyl lengths and the initial concentrations of sodium n-alkylates were varied. Although the initial contact angles of the droplets were not significantly different, the evaporation process varied significantly with the alkyl length of the sodium n-alkylate employed. For the sodium dodecanoate (C12), showing the highest surface activity, the concentration was found to have a significant effect on the evaporation process of the droplets. In the evaporation of water droplets, variations in the three distinct stages were caused by the different concentration of solutes distributed near or at the air/water interface. It is revealed that the concentration of droplet solute near the air/water interface requires not only solvent evaporation but also some affinity of the solute for the interface. The initial C12 concentration-dependence of the evaporation of C12 solution droplets is discussed with particular emphasis on the sudden spreading or sudden contraction of the contact area near the end of evaporation. It is suggested that the cluster formation by C12 molecules at the air/liquid interface during the evaporation causes Marangoni instability in an evaporating droplet, and the clusters are expected to move dynamically, depending on the droplet concentration of C12, from the droplet center to the contact line and vice versa, showing Marangoni flow along the air/water interface.

1. Introduction The evaporation phenomenon of droplets plays an important role in many applications. Over the past several decades, the evaporation of sessile droplets has been extensively studied because of its scientific interest and implication on everyday life.1-11 In recent years, the ink-jet printing is regarded as an emerging key technology for a fabrication method in many applications such as microarrays of biomaterials,12,13 templates for microlenses,14 self-assembled colloidal particles,15 and electronic devices.16-19 For these applications, controlling the thickness distribution of deposited solutes on a substrate after the evaporation of a sessile droplet, caused by an evaporationdriven flow, is crucially important. To understand the pattern of * Corresponding author. Tel.: +82-54-279-2136. Fax: +82-54-279-2399. E-mail: [email protected]. † Department of Materials Science and Engineering, Pohang University of Science and Technology. ‡ Samsung Electronics Co., Ltd. § Department of Chemistry, Pohang University of Science and Technology. | Department of Chemical Engineering, Pohang University of Science and Technology.

(1) Picknett, R. G.; Bexon, R. J. Colloid Interface Sci. 1977, 61, 336. (2) Birdi, K. S.; Vu, D. T. J. Phys. Chem. 1989, 93, 3702. (3) Birdi, K. S.; Vu, D. T. J. Adhesion Sci. Technol. 1993, 7, 485. (4) Bourge`s-Monnier, C.; Shanahan, M. E. R. Langmuir 1995, 11, 2820. (5) Rowan, S. M.; Newton, M. I.; McHale, G. J. Phys. Chem. 1995, 99, 13268. (6) Erbil, H. Y.; Meric, R. A. J. Phys. Chem. B 1997, 101, 6867. (7) McHale, G.; Rowan, S. M.; Newton, M. I.; Banerjee, M. K. J. Phys. Chem. B 1998, 102, 1964. (8) Erbil, H. Y.; McHale, G.; Rowan, S. M.; Newton, M. I. Langmuir 1999, 15, 7378. (9) Erbil, H. Y.; McHale, G.; Newton, M. I. Langmuir 2002, 18, 2636. (10) Shanahan, M. E. R. Langmuir 2002, 18, 7763. (11) Arcamone, J.; Dujardin, E.; Rius, G.; Pe´rez-Murano, F.; Ondarc¸uhu, T. J. Phys. Chem. B 2007, 111, 13020. (12) Laurell, T.; Nilsson, J.; Marko-Varga, G. Anal. Chem. 2005, 77, 264A. (13) Dugas, V.; Broutin, J.; Souteyrand, E. Langmuir 2005, 21, 9130.

residual solutes formed on a substrate after the evaporation of a droplet, the evaporation-driven microfluid flow in evaporating droplets has been numerically analyzed20-22 and experimentally studied.23-25 The formation of the remaining solute in a ringlike pattern on a substrate after evaporation is quantitatively explained by outward microfluid flow in an evaporating droplet when the contact line is pinned during the evaporation.26,27 In our previous work, we found that the nature of microfluid flow during the last stage of the evaporation process can provide an understanding of the pattern of drying stains seen after the evaporation of droplets from surfaces.28 Early in 1977, Picknett and Bexon distinguished two modes of evaporation of sessile droplets from solid surfaces.1 These (14) Bonaccurso, E.; Butt, H. -J.; Hankeln, B.; Niesenhaus, B.; Graf, K. Appl. Phys. Lett. 2005, 86, 124101. (15) He, J.; Zhang, Q.; Gupta, S.; Emrick, T.; Russell, T. P.; Thiyagarajan, P. Small 2007, 3, 1214. (16) Sirringhaus, H.; Kawase, T.; Friend, R. H.; Shimoda, T.; Inbasekaran, M.; Wu, W.; Woo, E. P. Science 2000, 290, 2123. (17) Kawase, T.; Sirringhaus, H.; Friend, R. H.; Shimoda, T. AdV. Mater. 2001, 13, 1601. (18) Kawase, T.; Shimoda, T.; Newsome, C.; Sirringhaus, H.; Friend, R. H. Thin Solid Films 2003, 438-439, 279. (19) Cheng, K.; Yang, M. -H.; Chiu, W. W. W.; Huang, C. -Y.; Chang, J.; Ying, T. -F.; Yang, Y. Macromol. Rapid Commun. 2005, 26, 247. (20) Fischer, B. J. Langmuir 2002, 18, 60. (21) Hu, H.; Larson, R. G. Langmuir 2005, 21, 3963. (22) Hu, H.; Larson, R. G. Langmuir 2005, 21, 3972. (23) Hu, H.; Larson, R. G. J. Phys. Chem. B 2006, 110, 7090. (24) Kang, K. H.; Lee, S. J.; Lee, C. M.; Kang, I. S. Meas. Sci. Technol. 2004, 15, 1104. (25) Ko, S. H.; Lee, H.; Kang, K. H. Langmuir 2008, 24, 1094. (26) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 829. (27) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. ReV. E 2000, 62, 756. (28) Kim, J.-H.; Ahn, S. I.; Kim, J. H.; Zin, W.-C. Langmuir 2007, 23, 6163.

10.1021/la801609d CCC: $40.75  2008 American Chemical Society Published on Web 09/18/2008

EVaporation of Sessile Droplets on Polymer Surfaces

were the “constant contact area mode” in which the contact area remained unchanged while the contact angle decreased, and the “constant contact angle mode” in which the contact angle did not change while the contact area decreased. These authors also observed a “mixed mode” in which both the contact angle and the contact area changed irregularly, but they did not discuss the origin of this mode. Many other research groups have observed that the evaporation of water droplets usually occurs in three distinct stages, namely the constant contact area mode, followed by the constant contact angle mode, and then the mixed mode in which both contact angle and contact area are decreased.7,28-32 In this mixed mode, the direction of microfluid flow was found to be outward, resulting in circular ring-like stains on surfaces after evaporation. The cause of the outward microfluid flow in the mixed mode is Marangoni instability which arises from the chance emergence of a local concentration gradient, along the surface, in a water droplet. Unintentional surfactant contamination of water is thought to be significant in induction of the mixed mode near the end of evaporation.28 The effects of surfactants on the evaporation of droplets and the patterns of stains seen after evaporation have been extensively studied in recent years to develop new techniques and strategies for microfabrication and self-assembly processes.33-35 These studies have shown that surfactants can be used to alter flow fields and deposition patterns from evaporating aqueous droplets. Despite the considerable progress, most previous work has focused on evaporative flow field behavior and residual patterns after the evaporation of droplets with small contact angles,33-36 or on the wetting phenomena exhibited by droplets placed on substrates.37-39 Some such tests feature the constant contact area evaporative mode only.33,34 Others explore only a mixed mode (in which the contact angle decreases while the contact area increases).37-39 The emergence of only the constant contact area mode in evaporation of the droplets arises more quickly for a droplet of small contact angle than for a droplet of large contact angle because the solute piling and solidification process takes place much more quickly in a droplet of small contact angle than in a droplet of large contact angle.40 The emergence of only the mixed mode in evaporation of the droplets arises because a high initial concentration of surfactant may lower the relative surface tension of liquid in the three phases of solid, liquid, and vapor.37 Therefore, it is expected that the evaporation of a droplet with a large contact angle and a sufficiently low concentration of surfactant may be a quite complex process, as noted in the three distinct evaporative stages of a water droplet. With a large contact angle and a sufficiently dilute surfactant concentration, however, any correlation between the evaporation behavior of a droplet and the resulting residual stain pattern is not yet fully understood because of the complexities of evaporation. It may be expected that a sufficiently low surfactant concentration in a droplet placed on a surface with a large contact angle will significantly affect (29) Uno, K.; Hayashi, K.; Hayashi, T.; Ito, K.; Kitano, H. Colloid Polym. Sci. 1998, 276, 810. (30) Fang, X.; Li, B.; Petersen, E.; Ji, Y.; Sokolov, J. C.; Rafailovich, M. H. J. Phys. Chem. B 2005, 109, 20554. (31) Fang, X.; Li, B.; Sokolov, J. C.; Rafailovich, M. H.; Gewaily, D. Appl. Phys. Lett. 2005, 87, 094103. (32) Fukai, J.; Ishizuka, H.; Sakai, Y.; Kaneda, M.; Morita, M.; TakanaraA., Int. J. Heat. Mass Transfer 2006, 49, 3561. (33) Nguyen, V. X.; Stebe, K. J. Phys. ReV. Lett. 2002, 88, 164501. (34) Truskett, V. N.; Stebe, K. J. Langmuir 2003, 19, 8271. (35) Cui, L.; Li, B.; Han, Y. Langmuir 2007, 23, 3349. (36) Pierce, S. M.; Chan, K. B.; Zhu, H. J. Agric. Food Chem. 2008, 56, 213. (37) de Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827. (38) Nikolov, A. D.; Wasan, D. T.; Chengara, A.; Koczo, K.; Policello, G. A.; Kolossvary, I. AdV. Colloid Interface Sci. 2002, 96, 325. (39) Chengara, A.; Nikolov, A.; Wasan, D. Colloids Surf., A 2002, 206, 31. (40) Kajiya, T.; Nishitani, E.; Yamaue, T.; Doi, M. Phys. ReV. E 2006, 73, 011601.

Langmuir, Vol. 24, No. 20, 2008 11443 Table 1. Characteristics of the Solutes Employed in This Study abbreviation C3 C6 C10 C12

full name sodium sodium sodium sodium

chemical formula

propionate hexanoate decanoate dodecanoate

C3H5O2Na C6H11O2Na C10H19O2Na C12H23O2Na

transitions near the end of evaporation, and the resulting stain pattern due to the continuous loss of solvent by evaporation leads to an increase in droplet surfactant concentration. In addition, stains formed from the evaporation of droplets with large contact angles and very soluble components need to be further researched for the development of ink-jet printing technology. To understand the correlation between the evaporation process of a droplet and the resulting stain, it is necessary to investigate solute behavior in an evaporating droplet. The aim of the present study, therefore, is to describe the evaporation processes of aqueous solution droplets in detail and to understand solute behavior in evaporating droplets placed on surfaces with large contact angles in order to explore residual stain patterns. We conducted microscopic observations of changes in the shapes and weights of water (DI) and aqueous solution droplets placed on two different hydrophobic polymer surfaces. The sessile droplets employed in this study were DI and aqueous solutions of sodium n-alkylates of four different alkyl lengths (C3, C6, C10, and C12) with the equally controlled initial concentrations, and aqueous solutions of sodium dodecanoate (C12) of different initial concentrations. Here, we report our experimental results and show the patterns of stains formed on the polymer surfaces after the evaporation of each droplet type. The evaporation process of droplets and the solute behavior in droplets during the evaporation are discussed with reference to both the new data and previous studies.

2. Experimental Section 2.1. Materials. Polymer films were coated onto native oxide layers of Si wafers (100). The Si wafers were cleaned by immersion in an H2SO4:H2O2 (7:3) solution for 20 min at 90 °C, and then rinsed with deionized water (DI). Two films with different hydrophobic properties were used: poly(methyl methacrylate) (Mw/Mn ) 1.09, Mw ) 21 600 g/mol) and poly(R-methyl styrene) (Mw/Mn ) 1.11, Mw ) 24 400 g/mol), both purchased from Pressure Chemicals. The films prepared from poly(methyl methacrylate) and poly(R-methyl styrene) are denoted as PMMA and PAMS, respectively. Both PMMA and PAMS were prepared by spin coating from 1 wt % solutions of toluene at a speed of 2000 rpm for about 60 s. To ensure that the samples had flat surfaces, and that solvent had been eliminated, samples were annealed for 3 h at 40 °C above bulk Tg under vacuum. By atomic force microscopy (Multimode, Digital Instruments), both PMMA and PAMS were found to have smooth and flat surfaces with 3-4 Å rms roughness. The thicknesses of annealed PMMA and PAMS were found to be about 29-31 nm by ellipsometry (VASE, J. A. Woollam Co.). Aqueous solutions were prepared by diluting sodium n-alkylates, purchased from Sigma-Aldrich, with DI (18.2 MΩ/cm, Millipore) to obtain the desired concentrations shown in the text, and solutions were shaken at least for 24 h. The sodium n-alkylates used are listed in Table 1. 2.2. Methods. To minimize gas-borne particles in the experimental environment, a transparent chamber with inside dimensions of 12 cm × 12.5 cm × 17 cm with a small hole sitting on a microbalance with a sensitivity of ( 10 µg (XS-105, Mettler Toledo) was used to observe weight losses and shape changes of water droplets on polymer surfaces during the evaporation. To ensure constant relative humidity and gas flow during experiments, dry nitrogen was pumped into the chamber at a constant rate of 2 mL/min. The constant slow nitrogen flow prevented the gas phase saturation by water

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Figure 1. Representative images of an evaporating DI droplet and sodium n-alkylate-containing aqueous solution droplets from PAMS surfaces. (a) A DI droplet with the initial weight of 3.62 mg; (b) a C3 solution droplet with the initial weight of 3.37 mg; (c) a C6 solution droplet with the initial weight of 3.24 mg; (d) a C10 solution droplet with the initial weight of 3.49 mg; (e) a C12 solution droplet with the initial weight of 3.56 mg. The times represent elapsed times after droplet deposition. The scale bar in each image is 1 mm.

vapor and yet caused only a very small degree of gas convection because the rate of flow was very low in comparison with the total chamber volume. The temperature and the relative humidity in the chamber were held approximately constant at 19-21 °C and 17-20%, respectively. Before each experiment, the balance pan was completely dried, and the balance was calibrated at room temperature to permit equilibration with the environment. A quantity of DI or aqueous solutions of sodium n-alkylates in the weight range 2.31-5.44 mg were deposited as sessile drops from a micropipette onto fresh polymer surfaces, and changes in droplet shapes and weight losses of droplets were simultaneously recorded. To observe changes in shapes of droplets during the evaporation, fine images of droplets were acquired along an axis parallel to the surfaces of the thin films. A 100 mm macro lens and a digital camera (R-7D, Konica Minolta) with a 6 megapixel charge-coupled device were used, employing a fluorescent backlight. The lens was focused on droplets when the droplets were deposited. Imaging was started immediately, and images were collected automatically at intervals of 30 s. Balance weights were similarly recorded. After all images had been acquired, digital analysis was performed to determine the contact radius (R) and height at the center (h) of each droplet, as determined by droplet reflection on the polymer surface, using both in-house and Photoshop 7.0 software. The contact angle of each droplet was calculated by the formula θ ) 2 arctan(h/R), with the use of a spherical cap model. The radius and height were transformed into real dimensions using a ruler scale; the ruler was placed above deposited droplets and was also imaged. The stains formed on polymer surfaces after the evaporation of droplets were observed using optical microscopy (OM, Leitz). The compositions of the formed stains were investigated with the energy-dispersive X-ray analysis (XL30SFEG, Phillips).

3. Results and Discussion 3.1. Influence of Alkyl Length of Solute on Evaporation. First, we studied the effect of alkyl length of dissolved sodium n-alkylates (C3, C6, C10, and C12) on the evaporation of droplets deposited onto both PAMS and PMMA surfaces. The solute concentrations were controlled to similar values (1.0 × 10-3 mol/L for C3 solution, 7.2 × 10-4 mol/L for C6 solution, 5.2 × 10-4 mol/L for C10 solution, and 4.5 × 10-4 mol/L for C12 solution), and droplets of three different sizes were placed on both PAMS and PMMA surfaces. Representative images of an evaporating DI droplet, and droplets with dissolved sodium n-alkylates, from PAMS surfaces are shown in Figure 1. As the evaporation proceeded, the volumes of the droplets decreased

Figure 2. Initial contact angles of DI droplets and sodium n-alkylate solution droplets on PAMS surfaces (b) and PMMA surfaces (O).

continuously with changes in contact area or contact angle or both. The initial contact angles obtained from the averages of three different initial weights of DI droplets and aqueous solution droplets are shown in Figure 2. The initial contact angles of DI droplets on PAMS and PMMA surfaces were 90.4° and 67.8°, respectively. As the alkyl length of sodium n-alkylates in aqueous solution droplets increased, initial contact angles decreased slightly on both PAMS and PMMA surfaces. The initial contact angles of DI droplets on PAMS and PMMA surfaces agreed well with previous results within experimental error.28 As the alkyl length increased from C3 to C12, the amphiphilic properties of the sodium n-alkylates become more important.41 The amphiphilic property of a sodium n-alkylate with a relatively long alkyl length, such as C12, would lower the surface tension of DI resulting in the spread of the contact area. In our experimental range, we found that the initial contact angles of droplets on polymer surfaces were not significantly reduced even in C12 solution droplets because of the dilute solute concentrations employed. As an example of the results obtained, changes in the shapes of DI droplets on the PAMS and PMMA surfaces are shown in Figure 3, as a function of evaporation time, for three different initial weights of DI (from 2.41 mg to 5.28 mg). Regardless of (41) Laughlin, R. G. The Aqueous Phase BehaVior of Surfactants; Academic Press: San Diego, 1994; Chapter 9.

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Figure 3. Shape changes of DI droplets with initial weights of 2.45 mg (9), 3.62 mg (b), and 5.27 mg (2), on PAMS surfaces, and 2.41 mg (0), 3.40 mg (O), and 5.28 mg (4), on PMMA surfaces, as a function of evaporation time: (a) contact angle; (b) contact radius.

Figure 4. Volume loss (O) and weight loss (9) of DI droplets as a function of evaporation time: (a) on PAMS surfaces; (b) on PMMA surfaces.

the magnitude of the initial contact angle and the quantity of DI, the evaporation invariably went through three distinct stages. In the first stage the contact radius of the DI droplet was initially pinned, and the contact angle of the DI droplet decreased linearly. Once the contact angle had attained its receding angle on the PAMS or PMMA surface, the contact radius then began to decrease while the contact angle remained constant. This second stage lasted for a long period during the evaporation. At the end of this stage, the contact angle suddenly decreased and the third stage commenced. Increasing the quantity of DI increased evaporation time and the contact radius of the DI droplet, whereas the initial contact angle and the receding angle varied only with surface properties and were independent of the quantity of DI. These three distinct stages in the evaporation process are the constant contact area mode, the constant contact angle mode, and the mixed mode, as demonstrated in our previous study.28 To check the accuracy of the data shown in Figure 3, we compared the weights of the DI droplets as obtained from the microbalance with volumes calculated from eq 1, under the assumption of a spherical cap model:

V(R, h) )

πh(3R2 + h2) 6

(1)

where R is the contact radius and h is the height at the center of the droplet. As shown in Figure 4, weights and the volume losses of DI droplets varied nonlinearly with evaporation time, and the calculated volumes and measured weights were in agreement throughout the evaporation process within the experimental error. This confirms that the acquired data are of high accuracy, and that the DI droplets all formed spherical caps on PAMS and PMMA surfaces during the evaporation. The applicability of the spherical cap model to the water droplets means that surface tension effects dominate gravity effects under our experimental conditions. To examine the effect of the initial weight of DI on evaporation, the contact angles and the contact radii obtained from Figure 3

Figure 5. Normalized shape changes of DI droplets with initial weights of 2.45 mg (0), 3.62 mg (O), and 5.27 mg (4), on PAMS surfaces (main panel), and 2.41 mg (0), 3.40 mg (O), and 5.28 mg (4), on PMMA surfaces (inset), as a function of normalized evaporation time: (a) contact angle; (b) contact radius.

were normalized by the initial contact angle and initial contact radius, respectively. The normalized results are shown in Figure 5 as a function of evaporation time normalized by final evaporation time. It should be noted that normalized results are mutually superimposed with respect to normalized evaporation time, and

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Figure 7. OM images of stains formed on polymer surfaces: (a-1) from a DI droplet of initial weight 3.62 mg; (a-2 to a-5) from solution droplets with dissolved C3 of initial weight 3.37 mg, C6 with initial weight of 3.24 mg, C10 with initial weight of 3.49 mg, and C12 with initial weight of 3.56 mg, on PAMS surfaces, respectively; (b-1) from a DI droplet with initial weight of 3.40 mg; (b-2 to b-5) from solution droplets with dissolved C3 of initial weight of 3.25 mg, C6 with initial weight of 3.15 mg, C10 with initial weight of 3.48 mg, and C12 with initial weight of 3.47 mg, on PMMA surfaces, respectively.

Figure 6. Normalized shape changes of aqueous solution droplets with dissolved C3 (red), C6 (green), C10 (blue), and C12 (magenta), and of DI droplets (black), with three different initial weights on PAMS surfaces (main panel), and PMMA surfaces (inset), as a function of normalized evaporation time. Data overlapping, which is obtained by the weight normalization for each of droplets containing the same solute, indicates that the evaporation process is independent of the initial weights of droplets in our experimental range. Data from DI, C3, and C6 droplets overlapped each other (see text): (a) contact angle; (b) contact radius.

vary with surface properties. From this result, we conclude that the evaporation process of a DI droplet is independent of the initial quantity of DI in the droplet, in the experimental range studied. Figure 6 shows the weight-normalized results of the evaporation of solute-containing droplet with three different initial weights as a function of normalized evaporation time in comparison with the DI droplet evaporation data shown in Figure 5. As with DI droplets, the weight-normalized results of the evaporation of droplets with each studied solute overlapped in this analysis. Thus, we conclude that the evaporation process varies not only with surface properties but also with the nature of the dissolved solute and is independent of the initial weights of droplets in our experimental range. The normalized results from C3 and C6 solution droplet evaporation on both PAMS and PMMA surfaces are analogous to DI droplet data and consisted of three distinct stages, reflecting the application of the constant contact area mode, the constant contact angle mode, and the mixed mode. In the evaporation process of C10 solution droplets, by contrast, there were four distinct stages: a constant contact area mode, a constant contact angle mode, a mixed mode, and a constant contact area mode once more. As the evaporation of C10 solution droplets proceeded on both PAMS and PMMA surfaces, the durations of the constant contact area mode were almost the same as with DI droplets. However, the durations of the constant contact angle mode shortened slightly than that of DI droplets on both PAMS and PMMA surfaces. In addition, the durations of the mixed mode were prolonged when compared with that of the evaporation of DI droplets on both PAMS and PMMA surfaces. Furthermore, the constant contact area mode is newly and briefly observed as

the last stage of the evaporation process on both PAMS and PMMA surfaces. The evaporation process of C12 solution droplets deviated still more from the evaporative processes of DI droplets and C10 solution droplets. As C12 solution droplets were deposited on the surfaces of both PAMS and PMMA, some spreading of contact areas with decreases in the contact angles of droplets were seen in the initial stages of evaporation. In other words, the constant contact area mode was not immediately apparent. After the brief spreading, the constant contact area mode was noted, and the mixed mode was observed just after the completion of the constant contact area mode. In other words, the constant contact angle mode was not apparent at this time. In the mixed mode, the decay rates of contact angles gradually increased whereas the decay rates of contact radii gradually decreased as the evaporation proceeded. After the mixed mode was over, the dramatic spreading of contact areas with decreases in contact angles suddenly commenced, and the mixed mode was briefly observed later as the last stage of evaporation. We also observed that circular stains formed on both PAMS and PMMA surfaces after the evaporation of droplets. As shown in Figure 7, the solutes were concentrated in specified areas and showed various stain sizes and patterns. The radii of stains formed on polymer surfaces from evaporation of DI droplets corresponded to the observed contact radii of evaporating droplets at the last moments of evaporation. Although we did our best to avoid contamination of DI samples, the ring-like stains are invariably formed on the polymer surfaces as a result of evaporation of DI droplets containing nonvolatile components. We thus confirmed that DI attracted contaminants strongly, and the outward flow inside evaporating DI droplets in the mixed mode resulted in ring-like stains on surfaces after evaporation.28 The main components in the ring-like stain are C, O, and Na which may come from inevitable water contact with the wall of vial or the tip of micropipette in the experimental procedure. From the comparison between volumes of the stains formed on surfaces in Figure 7, the concentration of the contaminants in the DI droplet is expected to be sufficiently lower by two orders than the lowest concentration of C3 employed in our experiments (1.0 × 10-3 mol/L). Also, these contaminants may exist in all solution droplets and equivalently affect the evaporation of droplets studied in this experiment. Although the evaporation of both C3 and C6 solution droplets went through the same stages seen in the evaporation of DI droplets, the morphologies of stains formed from the evaporation of C3 and C6 droplets were quite different from the ring-like stains formed from the evaporation of DI droplets. Instead of yielding ring-like patterns, most C3 and C6 solutes were uniformly distributed in circular stains. The rather

EVaporation of Sessile Droplets on Polymer Surfaces

Figure 8. Schematic diagram of distributions of solutes in the (a) DI droplet, (b) C3, (c) C6, (d) C9, and (e) C12 solution droplets.

complicated evaporation process of C12 solution droplets described above left ring-like stains of large diameters; we will discuss these later in detail. In stains formed from C10 solution droplets, the diameters and morphologies were considered to be intermediate between those of C6 and C12 solution droplet stains, as were evaporation behaviors (see above). From Figure 6, it is evident that different solutes cause different evaporation behaviors. As the hydrophobic alkyl group in the sodium n-alkylates becomes longer to attain C10 and C12, the deviations of droplet evaporation behavior from that of DI droplets was increasingly apparent. It is well-known that the balance between the hydrophobic and hydrophilic properties of solutes is responsible for amphiphilic properties and association behaviors in solutions.41 A rule-of-thumb is that there should be more than 12 hydrocarbons in a chain before an insoluble monolayer is formed.42 If the alkyl chain is shorter than 12 hydrocarbons, the solutes tend to form micelles which are soluble in water. To confirm the above hypothesis, we measured the isotherm curves of surface pressure versus mean molecular area for the sodium n-alkylates studied (Supporting Information). The isotherm surface pressure of C12 (only) increased as the surface area was compressed, which means that only C12 was at the air/water interface in this study as a result of the C12 amphiphilic property. In Figure 8, we show the possible distributions of contaminants in DI droplet and solutes in solution droplets placed on a polymer surface. In DI droplets containing only contaminants, the contaminants are thought to be placed at the air/water interface in droplets. This conjecture is reasonable because the solutes placed on the air/water interface are responsible for Marangoni instability in evaporating droplets caused by concentration gradient of solutes. Therefore, the contaminants would have a long alkyl chain of more than 12 hydrocarbons in a chain and act as surfactants in the droplets. In C3 and C6 solution droplets, C3 and C6 are thought to be uniformly distributed because the short alkyl group balanced against the polar headgroup has but low affinity for the air/water interface. These uniformly distributed solutes would interact with each other inside the evaporating droplets, and finally remained as the stain with the dot-like pattern on the polymer surfaces as shown in Figure 7 after the evaporation. The contaminants in C3 and C6 droplets would also be placed at the air/water interface in the droplets in a manner simlar to that with DI droplets and cause the Marangoni instability in evaporating droplets instead of C3 and C6 which are uniformly distributed in droplets. Almost the same concentration of contaminants at the air/water interface in the droplets causes the similar evaporation process for DI, C3, and C6 droplets. In C12 solution droplets, C12 tends to accumulate mainly at the air/water interface because of an amphiphilic property. Because these different distributions of solutes in droplets are reasonable, we conclude that the different evaporation behaviors shown in Figure 6 are caused by the different concentration of solutes near or at (42) Martelet, C.; Jaffrezic-Renault, N.; Hou, Y.; Errachid, A.; Bessueille, F. In Applied Scanning Probe Method VII; Bhushan, B., Fuchs, H., Eds.; SpringerVerlag: Heidelberg, Germany, 2007.

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the air/water interface in droplets, and solutes concentrated near or at the air/water interface have an effect on the evaporation behavior. In C10 solution droplets, it is expected that most C10 is concentrated near the air/water interface because the evaporation goes through four distinct stages which are thought to be intermediate between C6 and C12 solution droplet evaporation behavior. In C10 and C12 droplets, the effect of contaminants is negligible because the concentration of contaminants is very low in contrast to the concentration of C10 and C12 accumulated near or at the air/water interface. The evaporation behavior of C10 solution droplets is quite similar to previously reported results using polymer solution droplets.40 Kajiya and co-workers reported that dimples in concentrated solutions are created by a buckling phenomenon of the soft elastic phase near the surface of a droplet. The reason given for the increase in the polymer concentration near the air/droplet interface was solvent evaporation. From our data, we suggest that the increase in the solute concentration near the air/droplet interface requires not only a solvent evaporation but also some solute affinity for the air/droplet interface. 3.2. Influence of Concentration of C12 on Evaporation. Next, we explored the effect of concentration of C12 on the evaporation of C12 solution droplets deposited onto both PAMS and PMMA surfaces. The concentrations of C12 solution were controlled between 4.5 × 10-5 and 4.5 × 10-4 mol/L, and C12 solution droplets of approximately the same initial weights were deposited onto PAMS and PMMA surfaces. Representative images of C12 solution droplets evaporating from a PAMS surface is shown in Figure 9. As the evaporation proceeded, the volumes of C12 solution droplets continuously decreased with changes in contact areas or contact angles or both. The initial contact angles of the C12 solution droplets shown in Figure 9 are plotted as a function of initial C12 concentrations in Figure 10. As the initial concentration of C12 in droplets increased, initial contact angles decreased slightly on both PAMS and PMMA surfaces. Because C12 has an amphiphilic property sufficient to lower the surface tension of water, it is natural that the contact angle should decrease as the initial concentration of C12 in droplets increased. In this experimental range, we also confirmed that the initial contact angles of C12 solution droplets on both PAMS and PMMA surfaces did not change significantly with concentration, as only dilute solutions were employed. To compare the evaporation behaviors of droplets, as performed above to generate Figure 6, the normalized data from C12 solution droplets are shown in Figure 11 as a function of normalized evaporation time and compared with DI droplet data on both PAMS and PMMA surfaces with initial DI weights of 3.62 mg and 3.40 mg (data from Figure 5). In the evaporation of C12 solution droplets with initial C12 concentrations of 4.5 × 10-5 and 2.2 × 10-4 mol/L from both PAMS and PMMA surfaces, the initial stage was the constant contact area mode as in an evaporating DI droplet, and the duration in that mode prolonged slightly as the initial concentration of C12 increased. As mentioned above, the initial stage in the evaporation of C12 solution droplets with an initial C12 concentration of 4.5 × 10-4 mol/L on both PAMS and PMMA surfaces was the mixed mode in which the contact angle decreased while the contact area increased. Once the initial contact angles of the droplets after the deposition attained the characteristic contact angles on PAMS or PMMA surfaces, the constant contact area mode appeared. Regardless of the initial concentration of C12 in C12 solution droplets, the mixed mode was observed just after the constant contact area mode. This differed from DI droplet evaporation, where the constant contact angle mode was seen at this stage. In the mixed

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Figure 9. Representative images of evaporating C12 solution droplets on PAMS surfaces: (a) a droplet with initial C12 concentration of 4.5 × 10-5 mol/L and initial weight of 3.56 mg; (b) a droplet with initial C12 concentration of 2.2 × 10-4 mol/L and initial weight of 3.57 mg; (c) a droplet with initial C12 concentration of 4.5 × 10-4 mol/L and initial weight of 3.65 mg. The times represent elapsed times after deposition. The scale bars are 1 mm.

Figure 10. Initial contact angles of C12 solution droplets on PAMS surfaces (b) and PMMA surfaces (O) as a function of initial concentrations of C12. The solid and dashed lines represent the initial contact angles of DI droplets on PAMS and PMMA surfaces, respectively. The error bars obtained by multiple measurements of DI droplets and C12 solution droplets with the initial concentration of 4.5 × 10-4 mol/L indicate that the size of error bars is smaller than that of symbols. Other data are obtained by single measurement for each of droplets on the surfaces.

mode of evaporation of C12 solution droplets, the decay rate of the contact angle gradually increased, whereas the decay rate of the contact radius gradually decreased as the evaporation proceeded. It is important to note that the contact areas of droplets on both PAMS and PMMA surfaces either dramatically contracted, or suddenly spread, depending on the initial concentration of C12, after the mixed mode phase was over. When the contraction of contact area in evaporating C12 solution droplets with the initial C12 concentration of 4.5 × 10-5 mol/L occurred on either PAMS or PMMA surfaces, contact angles quickly increased, or fluctuated, respectively. However, when the spreading of contact area in evaporating C12 solution droplets with initial C12 concentrations of 2.2 × 10-4 and 4.5 × 10-4 mol/L occurred on either PAMS or PMMA surfaces, contact angles decreased more drastically than was seen when the mixed mode was operative. After the completion of sudden contraction or sudden spreading in the contact areas of evaporating droplets, the mixed mode, during which both contact area and contact angle decreased, was observed as the final stage in evaporation independent of the initial concentration of C12. The radii of stains formed on polymer surfaces from evaporation of C12 solution droplets with the initial concentrations not only of 4.5 × 10-5 mol/L but also of 2.2 × 10-4 and 4.5 × 10-4 mol/L corresponded to the extent of the sudden contraction and the maxima of spreading, respectively, of evaporating droplets. It is clear that the evaporation behaviors of C12 solution droplets changed drastically with variations in the initial concentration

Figure 11. Normalized shape changes of C12 solution droplets with initial C12 concentration of 4.5 × 10-5 mol/L (O), 2.2 × 10-4 mol/L (4), and 4.5 × 10-4 mol/L (3), compared with changes in DI droplets (0), on PAMS surfaces (main panels), and on PMMA surfaces (insets), as a function of normalized evaporation time: (a) contact angle; (b) contact radius. The arrows indicate the radii of the circular stains formed on each polymer surface.

of C12. Because C12 accumulates mainly at the air/water interface in C12 solution droplets, we conclude that the evaporation behavior depends on the concentration of solutes accumulated at this interface. The increase (with C12 concentration) in the duration in the initial stage (the constant contact area mode) occurs because the receding angles of the droplets fall as the initial concentration of C12 rises from 0 to 2.2 × 10-4 mol/L, as demonstrated previously.43 The emergence of spreading in the contact area as the initial stage in evaporation of C12 solution droplets with an initial concentration of 4.5 × 10-4 mol/L is caused by a reduction in the surface tension of the droplet. When the contact angles of the droplets attain equilibrium on PAMS or PMMA surfaces, as determined by the thermodynamic states of the three boundary (43) Eckmann, D. M.; Cavanagh, D. P.; Branger, A. B. J. Colloid Interface Sci. 2001, 242, 386.

EVaporation of Sessile Droplets on Polymer Surfaces

Figure 12. OM images of stains formed on polymer surfaces: (a-1 to a-3) from C12 solution droplets with the initial concentration of 4.5 × 10-5 mol/L and the initial weight of 3.56 mg, with the initial concentration of 2.2 × 10-4 mol/L and the initial weight of 3.57 mg, and with the initial concentration of 4.5 × 10-4 mol/L and the initial weight of 3.65 mg, on PAMS surfaces; (b-1 to b-3) from C12 solution droplets with the initial concentration of 4.5 × 10-5 mol/L and the initial weight of 3.44 mg, with the initial concentration of 2.2 × 10-4 mol/L and the initial weight of 3.45 mg, and with the initial concentration of 4.5 × 10-4 mol/L and the initial weight of 3.54 mg, on PMMA surfaces.

phases (solid/liquid/vapor), the spreading stops and the contact line is pinned. Because the concentration of C12 increases continuously as droplets evaporate, it is reasonable to suggest that the receding angle decreases continuously. Thus, the appearance of the mixed evaporative mode after the constant contact area mode, and the gradual increase in the decay rate of the contact angle are comparable to the use of the constant contact angle mode and the mixed mode, respectively, in DI droplet evaporation. To the best of our knowledge, the sudden commencement of the contraction or the spreading of droplet contact area after the use of the mixed mode in evaporation has not previously been discussed. The Marangoni instability caused by the inhomogeneous distribution of C12 at the droplet air/water interface is considered to be a significant cause of the sudden contraction or the sudden spreading in evaporation. To suppress the local surface tension gradient in an evaporating droplet, a microfluid flow would be generated mainly along the droplet surface, as reported in previous studies.22,23 Because water has a high surface tension, and because C12 may act as a surfactant to lower the surface tension, the direction of microfluid flow will be from regions where C12 is concentrated to areas where C12 is dilute, along the surface of an evaporating droplet. It is thus expected that a contraction will occur when the distribution of C12 at the air/water interface is more concentrated near the contact line than in the center of a droplet, whereas spreading will occur in the reverse situation. The sudden contraction or the sudden spreading of contact area in evaporating C12 solution droplets near the end of evaporation would result in different patterns of stains on both PAMS and PMMA surfaces after the evaporation is complete. As shown in Figure 12, the diameters of perimeters, and the morphologies, of C12 in circular stains differed, depending on the initial concentration of C12 in C12 solution droplets. From the C12 solution droplets with initial concentrations of 4.5 × 10-5 mol/L, which experienced the contraction of contact areas before completion of evaporation, irregularly aggregated C12 within weak circular perimeters with diameters of about 1.3-1.4 mm were found on both PAMS and PMMA surfaces. However, from C12 solution droplets with initial concentrations of 2.2 × 10-4 and 4.5 × 10-4 mol/L, which experienced the spreading of contact areas before completing the evaporation, C12 was mostly concentrated at the circle perimeters, and diameters of about 2.4-2.9 mm were observed on both PAMS and PMMA surfaces. The different C12 behavior, depending on the initial concentration of C12 in the evaporating the droplet, is responsible for

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the different evaporation process of C12 solution droplets. Because it is not easy to directly observe the solute behavior and the microfluid flow in the evaporating droplet, we speculated the solute behavior and the direction of microfluid flow in the droplets during the evaporation. One possible explanation for the initial concentration dependence of spreading or contraction in the evaporation of C12 solution droplets involves both C12 concentrations and Marangoni instability in evaporating droplets, as schematically shown in Figure 13. In C12 solution droplets, C12 accumulates mainly at the air/water interface and would be uniformly distributed along the surfaces of droplets deposited onto the polymer surfaces. As the evaporation proceeds, C12 would form a cluster at the center of the droplet surface because C12 has sufficient alkyl length to show this behavior,44 and the center of the droplet is the most probable site for cluster formation. The clustering of C12 at the center of the surface of the evaporating droplet is adequate to account for the increase in the decay rate of contact angle after the constant contact area mode phase because the cluster formed at the center of the droplet generates Marangoni instability responsible for the drastic reduction in contact angle during the mixed mode observed after the constant contact area mode. The Marangoni instability would cause an outward C12 flow along the surface of the evaporating droplet to suppress the local gradient of surface tension. As a result of this flow, some of the cluster composed of C12 would move from the center to near the contact line in the evaporating droplet. At that time, if the concentration of C12 in the droplet has not reached the sufficient concentration for wetting, the sudden contracting of contact area would occur because of emergence of Marangoni inward flow caused by increased concentration of C12 near the contact line. By the inward flow along the surface of the droplet, the cluster would move toward the center of the droplet again. If the concentration reaches a sufficient threshold for wetting, however, a spreading of contact area would occur because of the lowered surface tension of the droplet. The outward flow caused by Marangoni instability would be enhanced by the spreading and would accelerate the spreading of the contact area. This explanation of spreading is consistent with previous studies.38,39 By the outward flow along the surface of the droplet, most of the cluster is expected to move toward the contact line and adhere to the polymer surfaces. The different stain patterns showing irregularly aggregated C12 within weak circular perimeters or mostly concentrated C12 at circular perimeters on polymer surfaces are thought to result from these different behaviors of C12 during the contracting and spreading before the completion of evaporation of C12 solution droplets. On the basis of this understanding, we can describe the contaminants behavior in an evaporating DI droplet. In DI droplets, the clustering of contaminants at the center of droplet to generate Marangoni instability requires a lot of removal of the water in DI droplets by evaporation because of the extremely low concentration of contaminants at the air/ water interface. In the mixed mode, the caused Marangoni outward flow along the surface of the evaporating droplet would carry the contaminants to around the contact line of droplet. After the emergence of Marangoni outward flow, the short lifetime of the droplet would prevent the emergence of Marangoni inward flow. As the evaporation is completed, the contaminants concentrated at the contact line of droplet would adhere to polymer surfaces, and form a stain in ring-like pattern. Further study about the adsorption dynamics of a surfactant from a droplet onto the surface as completing the evaporation is still required. (44) Vysotsky, Y. B.; Bryantsev, V. S.; Fainerman, V. B.; Vollhardt, D. J. Phys. Chem. B 2002, 106, 11285.

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Figure 13. Schematic diagrams of the evaporation process of DI droplet and C12 solution droplets on a substrate and the formation of drying stains: (a-1) the constant contact area mode; (a-2) the constant contact angle mode; (a-3) the mixed mode in which both contact angle and contact area decrease; (a-4) the formation of stain in which contaminants are mostly concentrated at a small circular perimeter by evaporation of a DI droplet; (b-1) the constant contact area mode; (b-2, b-3, and b-5) the mixed modes in which both contact angle and contact area decrease; (b-4) the mixed mode in which the contact angle increases while the contact area decreases; (b-6) the formation of stain with irregularly aggregated pattern by the evaporation of a droplet with the initial C12 concentration of 4.5 × 10-5 mol/L; (c-1) the mixed mode in which the contact angle decreases while the contact area increases; (c-2) the constant contact area mode; (c-3, c-4, and c-6) the mixed modes in which both contact angles and contact areas decrease; (c-5) the mixed mode in which the contact angle decreases while the contact area increases; (c-7) the formation of stain in which C12 is mostly concentrated at a large circular perimeter, from the evaporation of a C12 solution with the initial concentration of 4.5 × 10-4 mol/L. In C12 solution droplets, the contaminants are omitted from the diagrams due to the extremely low concentration compared to the concentration of C12. γ+ and γrepresent the locally increased and decreased region in surface tension of the evaporating droplets, respectively. The arrow marks represent the direction of generated Marangoni flow along the surface of the droplets.

4. Conclusion We have studied the effects of the alkyl lengths of sodium n-alkylates, and the initial concentration of C12 showing the highest surface activity on the evaporation of sessile droplets, and the morphology of resulting stains, using two different hydrophobic polymer surfaces on which the droplets may have large contact angles. It was shown that, although initial contact angles did not significantly change, the evaporation processes differed considerably with variations in the alkyl length of sodium n-alkylates (C3, C6, C10, and C12) and the initial concentration of C12 in droplets. By varying the alkyl length, it is found that the deviation of evaporation processes in aqueous solution droplets from those of DI droplets is caused by the different concentration of solutes distributed near or at the air/water interface. As revealed by solvent evaporation studies, the increase in the solute concentration near or at the air/droplet interface requires not only a solvent evaporation but also some solute affinity for the air/droplet interface. By varying the initial concentration of C12, the sudden contraction or the sudden spreading of contact areas in evaporating C12 solution droplets near the end of evaporation was observed, and the patterns of resulting stains differed. It is suggested that the formation of a C12 cluster at the air/water interface during evaporation causes Marangoni instability in an evaporating droplet, and the formed cluster dynamically moves, depending on the concentration of C12 in the droplet, from the

center to the contact line and vice versa by Marangoni flow along the air/water interface. The proposed dynamic behavior of C12 in evaporating C12 solution droplets can be consistently applied to understand the evaporation process of DI droplet showing the three distinct stages. Therefore, when the sudden appearance of the mixed mode near the end of evaporation is observed, it may be expected that some dilute solutes (unavoidable contaminants) will be nonuniformly distributed and will show the dynamic behavior near or at the air/water interface of the evaporating droplet. From this study, it is confirmed that the addition of surfactant to a droplet is an efficient way to control the evaporation behavior and the stain morphology. This systematic study affords a fundamental understanding of the complex evaporation of sessile droplets with large contact angles and the resulting stain patterns, and it may have applications in the ink-jet printing technology. Acknowledgment. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-005-J01301). We also appreciate the financial support and helpful advices from Samsung Electronics Co., Ltd. Supporting Information Available: Isotherm curves of surface pressure versus mean molecular area for sodium n-alkylates studied. This material is available free of charge via the Internet at http://pubs.acs.org. LA801609D