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Effect of Surface Hydrophobicity on Critical Pinning Concentration of Nanoparticles To Trigger the Coffee Ring Formation during the Evaporation Process of Sessile Drops of Nanofluids Shih-Yao Lin, Kai-Chieh Yang, and Li-Jen Chen* Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan ABSTRACT: The evaporation process of sessile drops of water/nanofluid on hydrophilic/hydrophobic surfaces was observed experimentally. The evaporation process of nanofluid drops generally consists of four stages in the following sequence: (1) the constant contact radius mode, (2) the constant contact angle mode, (3) the mixed mode, and (4) the second pinned mode. The contact angle of nanofluid drops at the occurrence of the second pinning is consistently lower than the receding contact angle of the surface. The critical pinning concentration, at which the contact line is pinned again to initiate the second pinned mode, is independent of the initial concentration of silica nanoparticles. The critical pinning concentration increases along with the surface hydrophobicity, which can be identified by the receding contact angle of the surface. The critical pinning concentration is linearly dependent on the receding contact angle. It is interesting to find out that there exists a critical receding contact angle of 33° in this study. A droplet of nanofluid containing silica nanoparticles placed on self-assembled silane monolayer coated silicon wafer with its receding contact angle smaller than the critical receding contact angle (33°) would always pin immediately to trigger the coffee ring formation.

1. INTRODUCTION Wetting behavior plays an important role in nature and technology. Biological and industrial applications are highly relevant to the interaction between liquid and solid surfaces.1,2 More recently, evaporation, asymmetric wetting, pinning, spreading, and contact line dynamics have been extensively studied so as to improve related applications, such as inkjet printing, lab-on-a-chip, microfluidics, and so on.3,4 Evaporation is the escaping of liquid from the droplet surface. This leads to a variation in the contact angle, contact line, or combination of both. In 1977, Picknett and Bexon5 investigated the evolution of sessile droplet evaporation and were able to distinguish the three modes of evaporation: constant contact area (or constant contact radius, CCR) mode, constant contact angle (CCA) mode, and mixed mode. In the CCR mode, the solid/liquid interface area remains constant while the contact angle decreases. In the CCA mode, the contact angle remains constant while the contact line is moving. Usually, evaporation begins with the CCR mode until the receding contact angle is reached, and then the CCA mode takes over. Toward the end of evaporation, the process is characterized as the mixed mode, where both contact radius and contact angle decrease simultaneously. Picknett and Bexon5 also worked on the evaporation rate by mass profile which had a good agreement with theoretical calculations. BourgèsMonnier and Shanahan6 studied the evaporation of water droplets deposited on polyethylene and epoxy resin surfaces. They measured the evolution of drop height, contact angle, and contact radius in the evaporation process and proposed a model © 2015 American Chemical Society

to determine the diffusion coefficient of the vapor in air. The evaporation process was further classified into four stages: saturated, CCR, CCA, and mixed modes.6 McHale and co-workers7−11 studied the evaporation process of sessile droplets on various solid surfaces, including flat and pattern surfaces. They found that, for flat surfaces, the CCR mode dominates when the initial contact angle is less than 90° and the CCA mode dominates when the initial contact angle is larger than 90°. They attributed the CCA mode to the local saturated vapor near the contact line. Many researchers have studied the evaporation rate of sessile drops on solid surfaces and found that the rate is different from that of spherical droplets.5,6,12,13 Theoretically, the decrease in the volume of the sessile droplet in the CCR mode is linearly related to evaporation time while the volume evolution in the CCA mode follows a power law. Kulinich and Farzaneh14 studied the evaporation process of sessile droplets on superhydrophobic surface and pointed out the contact angle hysteresis is the main factor. The evaporation process of a sessile drop on a highhysteresis surface follows the CCR mode, and in contrast, that of a low-hysteresis surface follows the CCA mode. Recently, the evaporation of sessile water drops on soft surfaces has been examined. It was found that contact angle hysteresis is higher and total evaporation time is shorter for the softer surfaces.15−17 Received: September 21, 2014 Revised: January 23, 2015 Published: January 25, 2015 3050

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Water was purified by double distillation and then followed by a PURELAB Maxima Series (ELGA Labwater) purification system with the resistivity always better than 18.2 MΩ·cm. First of all, we mixed ethanol and water and kept them in a sonication bath (Branson, model 1510) for 10 min. A prescribed amount of TEOS was added for hydrolysis for 20 min. Then, ammonium hydroxide was added as a catalyst to promote the condensation reaction for another 60 min to get the white turbid (nanoparticles) solution. All the experiments described above were performed in the sonication bath in the presence of ice to keep the temperature at 0 °C. Finally, the suspended nanoparticles were separated by centrifugation (15 000 rpm, 10 min) and then rinsed three times by ethanol. The particle size was examined by a particle size analyzer (Nano-ZS, Malvern), and the shape of the nanoparticles was determined by a scanning electron microscope (SEM) (NanoSEM, Nova). 2.2. Preparation of Homogeneous Surfaces of Different Hydrophobicities. The homogeneous surfaces were prepared by coating silicon wafers (100) with methyltrichlorosilane (MTS) (Fluka, 98%), propyltrichlorosilane (PTS) (Acros, 98%), octadecyltrichlorosilane (OTS) (Aldrich, 90+ %), or 3-(phenylamino)propyltrimethoxysilane (PTMS) (Alfa Aesar, 96%) to form a self-assembled monolayer (SAM). All the chemicals were used as received. First, the substrate silicon wafers were cut into pieces of 2 × 2 cm2 and cleaned by immersion in a piranha solution (a 7:3 mixture (v/v) of 98% sulfuric acid (Merck, 95−97%) and 30% hydrogen peroxide (Merck, 30%)) at 120 °C for 30 min, rinsed with clean water, and blown dry with nitrogen. To modify the surface of the substrate, the wafers were first exposed to steam for about 30 s until a water film was formed on the surface. The wafers were then blown dry with nitrogen. Isooctane (Merck, 99%) was purified via filtration through a column of anhydrous aluminum oxide (Merck) and then used as a solvent to prepare the organosilane solutions. The water content of isooctane was 10 ppm, measured by Karl Fischer titration. Solutions of 0.5 wt % organosilane in isooctane were prepared in a glovebag (SigmaAldrich) filled with dry nitrogen to exclude traces of water in the surrounding atmosphere. The substrates were also placed into the glovebag and dipped into the organosilane solutions for appropriate deposition time at room temperature. The immersion time was 24 h for MTS, PTS, and OTS solutions and 48 h for PTMS solutions to ensure the formation of a complete self-assembled monolayer. The substrates were then rinsed with dichloromethane and chloroform and finally stored in water. 2.3. Evaporation. For all the evaporation experiments, the temperature and relative humidity in an advanced environment chamber (Ramé-hart, model 100-26-TH) were set at 30.0 ± 0.1 °C and 50 ± 1%, respectively. After the humidity and temperature of the environment chamber reached equilibrium, a 3 μL droplet was placed on the prepared substrates in the advanced environment chamber. The dynamic behavior during evaporation process along both side and top view of the droplet were recorded simultaneously by a handmade enhanced videomicroscopy system incorporated with a digital image analysis. The frame rate of the solid-state charge coupled device camera (Point Gray, Canada) was set at 2 frame/s to record the evaporation process. The images of side view were used to obtain information on contact angles and contact radii by digital image analysis. Every condition was repeated at least three times to ensure reproducibility.

Besides being phase change material, colloidal nanosuspensions or nanofluids (i.e., suspensions of nanosized particles) have been explored for its potential in production of better-quality nanoscale particles. It is commonly observed that during the evaporation of nanofluids a ring-like deposit of particles develops at the edge of the droplet. This phenomenon, known as the coffee ring effect, usually occurs whenever drops containing nonvolatile solutes evaporate on a solid surface. Deegan and co-workers18−20 explained and proposed a physical model of the coffee ring phenomenon. They found that when a sessile droplet is pinned on the surface, a radially outward capillary flow occurs and carries the particles toward the edge of the droplet. The particles deposit and lead to a ring-like residue. Deegan19 also demonstrated that the existence of particles may enhance the pinning of the contact line. The physics of outward capillary flow within liquid droplets was further investigated by Fisher et al.21 and Hu and Larson.22,23 They described the flow by using lubrication theory and the numerical method. Maenosono et al.24 studied the growth process of an array comprising colloidal semiconductor nanoparticles and found that the ring width depends on the particle volume fraction. The influences of property of particle25−29 and the ambient environment of droplets25,29,30 upon deposition have also been widely studied. Evaporation of nanofluid droplets on different solid substrates is much more complicated owing to the interactions among substrate, liquid, and particles. Uno et al.31 explored the stain patterns after the evaporation of nanofluid droplets on hydrophilic and hydrophobic surfaces. They observed that the dispersed particles on hydrophobic surface are swept and gathered at the center of the contact area. Nguyen et al.32 studied the evaporation evolution and residual depositions on smooth hydrophobic surfaces. They found that the contact line would pin at a second time, called the “late pinned mode”, and the size of deposits is strongly dependent on the surface hydrophobicity. The deposit left on the hydrophobic surface during drying process is highly related to the occurrence of the second pinning of evaporating droplets. The mechanism of this process is not fully understood and still needs be further explored. The purpose of this study is to clarify the evaporation process of sessile drops of nanofluids and deposit formation on different hydrophobic surfaces and the effect of initial nanoparticle concentration on ring formation. In this study, we performed experiments on evaporation evolution of water/nanofluid droplets on surfaces of different hydrophobicities. It is found that the contact angle of nanofluid droplets on a given surface right at the occurrence of the second pinning is consistently smaller than the receding contact angle of the surface. The critical pinning concentration, at which the second pinning occurs, on a given surface is rather a constant and independent of initial concentration of silica nanoparticles. Moreover, the critical pinning concentration is highly related to the surface hydrophobicity. The relationship between the critical pinning concentration and the receding contact angle will be carefully examined and discussed.

2. EXPERIMENTAL PROCEDURE 2.1. Preparation of Silica Nanoparticles. Uniform-sized silicon dioxide nanoparticles were prepared by closely following the sol−gel process proposed by Rao et al.33 Ammonia hydroxide (Acros, 28−30%), tetraethyl orthosilicate (TEOS) (Merck), and ethanol (Merck, 99.9%) were used as received. 3051

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The Journal of Physical Chemistry C 2.4. Advancing/Receding Contact Angle Measurement by Using the Embedded Needle Method. The advancing/receding contact angles of water droplets were measured by a homemade enhanced video microscopy system incorporating digital image analysis. Initially, the prepared substrate was placed in the environmental chamber (Ramé-hart Instrument Co.), and a needle was positioned inside the chamber. A syringe pump (model NE-1000, NEW ERA) was utilized to generate a water droplet on the substrate. After the drop-forming step, water was continuously and slowly injected into (or sucked from) the droplet at a rate of 3.0 μL/min. The evolution of the water droplet was recorded simultaneously by the enhanced video-microscopy system. The experimental details can be found in our previous studies.34−36 The initial volume of a water droplet was fixed at 3 μL for the advancing/ receding contact angle measurements. The advancing/receding contact angles were measured at more than three different positions on each substrate.

3. RESULTS AND DISCUSSION In this study, the substrates of different hydrophobicities were prepared by coating silicon wafer with four different organosilanes: MTS, PTS, OTS, and PTMS. Table 1 reports the Figure 1. Evolution of contact angle and diameter of water droplet during evaporation process. The blue, purple, green, and red lines represent the respectively OTS (1), PTS (2), MTS (3), and PTMS (4) coated substrates. Two blue dashed vertical lines are used to separate the regions of CCR, CCA, and mixed mode for the evaporation process on the OTS coated substrate.

Table 1. Advancing and Receding Contact Angles (deg) of Water on Substrates Coated by Four Different Organosilanes: OTS, PTS, MTS, and PTMS by embedded needle measurement surface OTS PTS MTS PTMS

θadv 108 105 110 70

± ± ± ±

θrec 3 2 1 2

89 81 68 47

± ± ± ±

2 1 2 1

by evaporation θinitial

θCCA,start

θCCA,end

103 99 101 67

93 81 72 52

87 77 68 47

decreased, and the contact line was pinned. Once the receding contact angle was reached, the contact line started to move, and the constant contact angle (CCA) mode took over. At the end of evaporation process, both contact radius and contact angle decreased simultaneously, and this is called the mixed mode. We compared the receding contact angle determined from the embedded needle method to that determined from the evaporation in the CCA mode, as listed in Table 1. Note that the contact angle in the CCA mode does not remain exactly constant but fluctuates slightly as time proceeds. Consequently, there exhibits many receding contact angles in the CCA mode. Thus, θCCA,start denotes the contact angle at the beginning of the CCA mode and θCCA,end represents the contact angle at the end of CCA mode. Overall, the range of receding contact angles in the CCA mode has a good agreement with the receding contact angle (θrec) determined by the embedded needle method, as reported in Table 1. The evaporation rate varies in substrates with different surface hydrophobicities. The initial volume of a water droplet was fixed at 3 μL. Assume the water droplet sitting on homogeneous surface is a spherical cap; as a consequence, different contact angles result in different surface areas of a liquid droplet. A higher contact angle leads to less area contact with the ambient. The contact angle of a water drop on the OTS coated surface is always higher than the others; as a consequence, it is evaporate rate is the slowest. 3.2. Evolution of Evaporation of a Water Droplet Containing Silicon Dioxide Nanoparticles on Hydrophobic Surfaces. The SEM image of nanoparticles, as shown in Figure 2a, illustrates that silicon dioxide nanoparticles are spherical in shape. The particle size analyzer (Nano-ZS, Malvern) was applied to determine the particle size distribution

advancing/receding contact angles of these substrates determined by the embedded needle method. Note that the advancing contact angle is rather close to one another for the MTS, PTS, and OTS coated substrates. On the other hand, the surface hydrophobicity can be distinguished by the receding contact angle. The receding contact angle slightly increases with increasing chain lengths for methyl-terminated alkylsiloxane monolayer MTS, PTS, and OTS coated substrates that is attributed to the progressive ordering of alkyl chain conformation (such as defects, tilt angle of alkyl chain, coverage, etc.) along with an increase in alkyl chain length. In addition, the receding contact angle of the PTMS coated substrate is even smaller than that of the PTS coated substrate due to the difference of chemical nature between phenylaminoterminated and methyl-terminated end groups. Therefore, the receding contact angle of these substrates is in the order of θrec(OTS) > θrec(PTS) > θrec(MTS) > θrec(PTMS).37−39 3.1. Evolution of Evaporation Process of a Pure Water Droplet on Surfaces of Different Hydrophobicities. Figure 1 shows the evolution of contact angle and contact diameter during the evaporation process of a water droplet of 3 μL on four different surfaces under the condition of a constant relative humidity (50%) and temperature (30 °C). Initially, the contact angles of drops on these surfaces, as the θinitial reported in Table 1, were rather close to, but slightly smaller than, their advancing contact angles. The evaporation process started with the constant contact radius (CCR) mode: the contact angle 3052

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Figure 3. Evolution of the contact angle and contact radius of nanofluid droplets containing different initial concentration of silica nanoparticles on the OTS coated substrate during evaporation process. The blue (1), purple (2), green (3), and red (4) lines represent the initial concentrations of nanofluid droplets with respectively 0, 0.5, 1.0, and 5.0 wt % nanoparticles.

Figure 2. (a) SEM image of silica nanoparticles. (b) Particle size distribution of silica nanoparticles determined by dynamic light scattering.

of silica nanoparticles, as illustrated in Figure 2b. The average diameter of these nanoparticles was 408 ± 119 nm. Here, the evaporation of a 3 μL nanofluid droplet deposited on the OTS, PTS, and MTS coated surfaces was experimentally performed at constant relative humidity (50%) and temperature (30 °C). Figures 3, 4, and 5 show the variation of contact angle and diameter of nanofluid droplets containing 0, 0.5, 1.0, and 5.0 wt % silica nanoparticles on the OTS, PTS, and MTS coated surfaces, respectively, as a function of time during the evaporation process. Because the initial drop volume was fixed, the droplets of higher initial nanoparticle concentration possessed less water; as a consequence, those droplets evaporated faster than pure water droplets. It is interesting to find out that the receding contact angle observed in the CCA mode during the evaporation process of nanofluid drops almost coincides with that of pure water drops. Note that even though the initial nanoparticle concentration was as high as 5.0 wt % (red line in Figure 3), the existence of nanoparticles did not affect the contact angle of drops substantially. The evaporation process of nanofluid droplets was similar to that of pure water droplets to exhibit sequentially three modes: CCR → CCA→ mixed mode. Nevertheless, the three-phase contact line was pinned again in the mixed mode at the end of the evaporation process of nanofluid drops, and a deposit was left behind on the surface after the water drop dried out. We will come back to discuss the effect of initial nanoparticle concentration on deposits on different surfaces in section 3.3. To further discuss the evaporation mechanism of nanofluid droplets on these hydrophobic surfaces, the evolutions of evaporation process of nanofluid droplets containing 1 wt % silica nanoparticle on the MTS coated surface along with side and top view image are demonstrated in Figure 6. Both the variation of contact angles on the left- and right-hand side (θleft and θright) and diameter are plotted in Figure 6. The evolution

Figure 4. Evolution of the contact angle and contact radius of nanofluid droplets containing different initial concentration of silica nanoparticles on the PTS coated substrate during evaporation process. The blue (1), purple (2), green (3), and red (4) lines represent the initial concentrations of nanofluid droplets with respectively 0, 0.5, 1.0, and 5.0 wt % nanoparticles.

of contact angle on the left-hand side (blue line) almost coincides with that of right-hand side (green line) throughout 3053

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grabbed from the evolution videos. The evaporation process involved four distinctive modes: CCR mode (A → B), CCA mode (B → C), mixed mode (C → D), and second pinned mode (D → E). Deegan et al. found that when a nanofluid droplet sits on solid surface, the contact line would be pinned during the whole evaporation process, and a capillary flow from the interior is formed to replenish the liquid that evaporating from the edge of droplet.18 However, when a nanofluid droplet is placed on a hydrophobic surface, the contact line pinning (the CCR mode) does not last for the whole evaporation process (only A → B). The evaporation is then followed by the CCA mode (B → C). Then the evaporation process would exhibit a transition from the CCA mode to the mixed mode (C → D), in which both the contact angle and contact diameter decrease simultaneously. In the later stage of evaporation (the mixed mode), an additional three-phase contact line pinning was observed and coined as the second pinned mode (D → E in Figure 6), which is to be distinguished from the first pinned (CCR) mode. This finding is consistent with that of Nguyen et al.,32 who named the “late pinned mode” instead. The beginning of the second pinning of contact line is marked as the time D in Figure 6. It should be pointed out that Nguyen et al.32 observed that the evaporation process of nanofluid drops (0.5 μL) on hydrophobic surfaces is composed of three stages: CCR, CCA, and the second pinned mode without the mixed mode (see Figure 7 in ref 32). Note that the duration of the mixed mode might be too short to be identified for evaporating a nanofluid drop of 0.5 μL. In addition, Nguyen et al.32 found that adding nanoparticles would prolong the duration of CCR mode (see Figure 8 in ref 32). In contrast to our results, as

Figure 5. Evolution of the contact angle and contact radius of nanofluid droplets containing different initial concentration of silica nanoparticles on the MTS coated substrate during evaporation process. The blue (1), purple (2), green (3), and red (4) lines represent the initial concentrations of nanofluid droplets with respectively 0, 0.5, 1.0, and 5.0 wt % nanoparticles.

the whole evaporation process. The images from top and side views at time A, B, C, D, and E marked in Figure 6 were

Figure 6. Evaporation process of a nanofluid droplet containing 1.0 wt % silica nanoparticle on the MTS coated substrate. Blue and green lines are referred to contact angle at the respectively left- and right-hand side, and yellow line represents contact diameter. The top and side view images at time A, B, C, D, and E are shown in the second and third row, respectively. The evaporation mechanism can be split into four modes sequentially: CCR mode (A → B), CCA mode (B → C), mixed mode (C → D), and second pinned mode (D → E). The second pinning starts at point D. At the end of evaporation process (E), a ring-like deposit is left. 3054

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Figure 7. Evolution of top (upper row) and side (lower row) view images of 1.0 wt % SiO2 nanoparticle droplet evaporating on the MTS coated surface during the second pinned mode (D → E). Part (a) refers to the beginning point D of the second pinning. During the half of this process, as illustrated in part (b), it was clearly observed that the particles moved radically toward the edge of the droplet. A ring-like structure is left behind after drying out (part (c)).

shown in Figures 3−5, adding nanoparticles would shorten the duration of CCR mode. The second pinned mode is observed not only on the MTS coated surface (see Figures 5 and 6) but also on the PTS and OTS coated surfaces (see Figures 3 and 4). In addition, the second pinned mode observed on these surfaces is consistently transited from the mixed mode. That is, this second pinned mode occurs right after the mixed mode. The contact diameter remains constant, and the contact angle decreases in the second pinned mode until the water completely dries out. The contact angle at the occurrence of the second pinned mode, as the time D in Figure 6, is always lower than the receding contact angle of the surface. Figure 7 shows the optical top view images of the evolution of evaporation of a nanofluid droplet containing 1 wt % SiO2 nanoparticles on the MTS coated surface in the second pinned mode. At the very end of this evaporation process, it was clearly observed in Figure 7b that the nanoparticles were moving radically toward the edge of the droplet in the second pinned mode. 3.3. Residual Deposits of Nanoparticles and the Effect of Initial Nanoparticle Concentration on Coffee Ring Formation. The nanoparticle deposits formed by evaporating 3 μL nanofluid droplets at different initial nanoparticle concentrations on the MTS, PTS, and OTS coated surfaces are shown in Figure 8. These ring-like deposits appeared after the water completely dried out. For a given initial concentration of nanoparticles, the diameter of residual deposits on different surfaces was different; for instance, the diameter of deposit on the MTS coated surface was larger than that of the PTS and OTS coated surfaces, as the pinning diameters reported in Table 2. This is mainly because in the evaporation process the second pinning of a nanofluid droplet on the MTS coated surface with the smaller receding contact angle occurs earlier than that of the PTS and OTS coated surfaces. The methyl group (−CH3) is the functional end group exposed to air for these three (MTS, PTS, and OTS coated) surfaces. However, the alkyl chain length increases with a decrease in surface energy according to the receding contact angle reported in Table 1. Consequently, while the nanoparticles flow radically toward the contact line during the evaporation, nanoparticles are more likely to be adsorbed onto the MTS coated surface with a relatively higher surface energy. Note that not all of the nanoparticles would be carried to the edge of the ring. Some nanoparticles are deposited in the center of the ring, resulting in a formation of thin film of nanoparticles.

Figure 8. Residual deposits formed by evaporating 3 μL nanofluid droplets of different initial concentrations of nanoparticles (0.5, 1.0 and 5.0%) on the MTS, PTS, and OTS coated surfaces. For a given initial nanoparticle concentration, the diameter of residual deposits on different surfaces is different. A larger initial concentration leads to a larger deposit. The scale bar is 500 μm.

Table 2. Contact Angle, Contact Diameter, and Pinning Concentration Observed Right at the Occurrence of the Second Pinning on the MTS, PTS, and OTS Coated Surfaces

surface MTS

PTS

OTS

initial concn (wt %) 0.5 1.0 5.0 0.5 1.0 5.0 0.5 1.0 5.0

(4)a (3) (3) (3) (3) (3) (3) (3) (3)

pinning contact angle (deg) 64 64 64 70 72 72 64 71 78

± ± ± ± ± ± ± ± ±

4 4 4 2 4 2 4 2 1

pinning diam (μm) 877 1072 1749 717 916 1496 723 858 1343

± ± ± ± ± ± ± ± ±

35 23 63 29 53 48 49 34 18

pinning concn (wt %) 17.0 18.0 19.8 24.1 23.4 26.8 28.6 28.8 31.0

± ± ± ± ± ± ± ± ±

1.6 1.6 2.1 2.8 2.1 0.8 2.4 1.2 1.0

critical pinning concn (wt %) 18.3 ± 1.5

24.8 ± 1.8

29.2 ± 1.6

a

The number in parentheses refers to the number of experimental data for each initial nanoparticle concentration.

When a nanofluid droplet evaporates, the nanoparticle concentration in the droplet increases along with evaporation process due to the nonvolatile nanoparticles. It is interesting to explore the effect of initial concentration of nanoparticles on the pinning concentration where the three-phase contact line 3055

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Figure 9. (a) Schematic illustration of determination of the pinning point, as the point D shown in Figure 6, appeared in the evaporation process of 1.0 wt % nanoparticle droplet on the MTS coated surface. The pinning point is determined by the intersection of the linear fitted line (black solid line) and the pinning diameter (black dashed line). The variation of contact diameter, normalized by the initial contact diameter d0, as a function of nanoparticle concentration during the evaporation process of nanofluid droplets of different initial concentrations on the MTS (b), PTS (c), and OTS (d) coated surfaces. The blue (1), green (2), and yellow (3) lines represent the initial concentrations of droplets of respectively 0.5, 1.0, and 5.0 wt %. The symbol triangle stands for the pinning point determined by the method defined in part (a).

To examine this pinning point (or concentration) more carefully, the experiments of evaporation process of nanofluid droplets on each surface were performed at least three times for each initial concentration of nanoparticles. The variations of contact diameter, normalized by the initial contact diameter d0, as a function of weight percentage of nanoparticles in nanofluid droplets are illustrated in Figures 9b, 9c, and 9d for the evaporation process of nanofluid droplets at different initial concentrations on the MTS, PTS, and OTS coated surfaces, respectively. The symbol red triangle, shown in Figure 9, stands for the pinning concentration determined by the method mentioned above. Note that the red triangle in Figure 9 represents a transition point beyond which the contact line starts to pin and the contact diameter becomes constant. Table 2 also reports the pinning conditions, including the pinning concentration, contact angle, and contact diameter right at the pinning point, for different initial concentrations of nanoparticles. Despite different initial concentrations, the contact angle right at the pinning point is consistently lower than the receding contact angle of substrates, as listed in Table 1. Higher initial concentration leads to higher pinning diameter, as expected. It is interesting to observe that the pinning concentration for each surface, as listed in Table 2, is independent of the initial concentration of nanoparticles within the experimental error. That is, the critical pinning concentrations of the MTS, PTS, and OTS coated surfaces are 18.3, 24.8, and 29.2 wt %, respectively, as listed in Table 2, resulting from the average over the pinning concentrations determined at different initial concentrations. Note that the critical pinning concentration increases along with the surface hydrophobicity, which can be distinguished from the receding contact angle. Figure 10 demonstrates that the critical pinning concentration is linearly dependent on the receding contact angle of the surface. Note

starts the second pinning to trigger the evaporation process into the second pinned mode. In other words, the pinning concentration is the nanoparticle concentration in nanofluid droplets right at the transition point from the mixed mode to the second pinned mode during the evaporation process, such as the concentration at the time D in Figure 6. Figure 9a demonstrates the enlargement of contact diameter versus time plot near the transition point D in Figure 6. Around 300 data points of contact diameter around the pinning moment, before the contact diameter levels off, are chosen and linearly fitted, as the black solid line shown in Figure 9a. The pinning point D is then determined by the intersection of this linear fitted line (black solid line) and the black dashed horizontal line of constant diameter after pinning, as shown in Figure 9a. Once the pinning point D is identified, the contact angle and contact diameter at this pinning point can be determined from the video image. In addition, the pinning concentration can be further evaluated. First of all, the initial density of nanofluid was calculated by assuming the ideal mixing of the volume of water and silica nanoparticles. The volume of the droplet at the beginning was directly determined from the side-view image by numerical integration of the drop profile and assuming that the droplet was composed of symmetrical disks. The total mass of the droplet was then evaluated from the initial density and drop volume. The total mass of nanoparticles in the droplet could be determined from its initial concentration and was fixed throughout the evaporation process due to the nonvolatile nanoparticles. The silica nanoparticle concentration in the droplet during the evaporation process can be determined accordingly. Thus, the pinning concentration right at the pinning point D (Figure 6) can be identified and evaluated as well. 3056

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nanoparticles at different initial concentrations of nanoparticles. For the evaporation process of a nanofluid droplet with 5 wt % nanoparticles, the CCA and mixed modes were skipped and the pinning and deposit started immediately whenever the droplet was placed on the PTMS coated surface. In other words, the critical pinning concentration of the PTMS coated surface is lower than 5 wt %. In the cases of initial concentrations of 0.5 and 1 wt % nanoparticles, the moment of the pinning cannot be well identified because the pinning was not symmetrical. Some particles were adsorbed on the PTMS surface while some were not, causing many thorns to form on the edge of the droplet, as illustrated in Figure 11. It may be attributed to the fact that silicon dioxide particles are more likely to be adsorbed onto the surface rather than to be driven by the internal flow of droplet during evaporation since the PTMS coated surface was a rather hydrophilic surface. Besides, the prolonged immersion time (48 h) of preparing the PTMS coated surface may introduce some defects randomly distributed on the surface and lead to random pinning. Note that the critical pinning concentration can be determined based on image analysis of side view of drop profile throughout the whole evaporation process by assuming a symmetrical drop conformation. We could get a successful experiment of evaporation with a symmetrical drop conformation on the PTMS surfaces throughout the evaporation process at a probability of about less than 10%. The critical pinning concentration of the PTMS coated surface (48 h immersion time) is approximately 4.7 wt %, which is consistent with the linear correlation of the critical pinning concentration and the receding contact angle, as illustrated in Figure 10. We also prepared the PTMS coated surface with a shorter reaction time to get more hydrophilic surfaces. The advancing and receding contact angles for the PTMS coated surface with 12 h reaction time were measured by the embedded needle method and found to be respectively 70 ± 3° and 23 ± 1°, as listed in Table 3. Note that this receding contact angle (23°) of the PTMS coated surface with 12 h reaction time is much lower than that of the long reaction time (24 and 48 h) PTMS coated surface (47°), especially lower than the critical receding contact angle 33°, as estimated in Figure 10. That implies the nanofluid

Figure 10. Relationship of the critical pinning concentration and the receding contact angle. Blue circles refer to the OTS, PTS, and MTS coated surfaces and brown triangles represent the PTMS coated surface prepared by two different reaction times: 48 and 12 h. The blue solid line is the linear fitted curve of the critical pinning concentration, and the receding contact angle of the OTS, PTS, and MTS coated surfaces and blue dashed line is simply the extension of this curve.

that the extrapolation of this linear line to the x-axis results a critical receding contact angle of 33°, as shown in Figure 10. That implies as long as the receding contact angle of a surface is lower than 33°, nanofluid droplets of silica nanoparticles of 408 nm in diameter would always pin immediately and exhibit residual deposit (coffee ring) after water drying out under the condition of 30 °C and 50% relative humidity. In other words, a nanofluid drop containing silica nanoparticles is always selfpinning19 on a self-assembled silane monolayer coated substrate with a receding contact angle lower than 33°. 3.4. Residual Deposits of Nanoparticles on the PTMS Coated Surface. A more hydrophilic surface, the PTMS coated surface, is further utilized to verify the relationship between the receding contact angle and the critical pinning concentration shown in Figure 10. However, the situation of coffee ring formation is more complicated for the evaporation process of a nanofluid droplet on the PTMS coated surface. Figure 11 shows the patterns of residual deposits of

Figure 11. Evolution of appearance (top view images) of nanofluid droplets with initial concentration (a) 0.5, (b) 1.0, and (c) 5.0 wt % during the evaporation process on the PTMS coated surface prepared by 48 h immersion time. The pinning for the systems of 0.5 and 1.0 wt % is not symmetry and irregular. For the system of 5.0 wt %, the pinning occurred at the very beginning of the evaporation process. The scale bar is 500 μm. 3057

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fails and the size of residual deposit reduces dramatically, as shown in Figure 12a. As a consequence, there exists a threshold nanoparticle concentration (in between 0.0001 and 0.00001 wt %), above which the contact line pinning (self-pinning) is enhanced to trigger the coffee ring formation.

Table 3. Dependence of the Advancing/Receding Contact Angles (deg) of the PTMS Coated Surface on the Reaction Time timea 10 min 30 min 1h 12 h 24 h 48 h a

θadv

33 70 69 70

18 22 ±2 ±3 ±1 ±2

θrec

8 23 47 47

± ± ± ±

4 5 1 1 1 1

4. CONCLUSIONS The evolutions of evaporation processes of water/nanofluid droplets on homogeneous surfaces with different hydrophobicities exhibit a similar mechanism. Evaporation of sessile drops generally starts with the constant contact radius mode followed by the constant contact angle mode when the receding contact angle is reached and then the mixed mode toward the end. For the nanofluid droplets, an additional three-phase contact line pinning is observed at the end of the mixed mode, the second pinned mode takes over until the droplet dries out, and a ring-like deposit is left behind. It is interesting to observe that the contact angle of nanofluid droplets right at the occurrence of the second pinning is consistently smaller than the receding contact angle of the surface. Higher initial concentration of nanoparticles leads to larger residual deposits. As for a given initial nanoparticle concentration, the diameter of residual deposits on different surfaces is somehow related to the surface hydrophobicity. The critical pinning concentrations of the MTS, PTS, OTS, and PTMS coated surfaces were carefully determined and found independent of initial nanoparticle concentration. The critical pinning concentrations of these surfaces are in the order of PTMS < MTS < PTS < OTS. The critical pinning concentration linearly depends on the receding contact angle, as illustrated in Figure 10.

The reaction time to prepare the PTMS coated surface.

droplets would pin immediately on this PTMS coated surface (12 h) to trigger the coffee ring formation. Droplets containing different initial nanoparticle concentrations were deposited on this PTMS coated surface (12 h reaction time) to observe the residual deposits. Figure 12



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.-J.C.). Notes

The authors declare no competing financial interest.



Figure 12. Initial and final images during the evaporation process of drops containing eight different initial concentrations of silica nanoparticles: (a) 0.00001, (b) 0.0001, (c) 0.001, (d) 0.01, (e) 0.1, (f) 0.5, (g) 1.0, and (h) 5.0 wt % on the PTMS coated surface prepared by 12 h immersion time. The pinning occurred at the very beginning of the evaporation process, even the initial concentration of nanoparticles as low as 0.0001 wt %.

ACKNOWLEDGMENTS This work was supported by the Ministry of Science and Technology of Taiwan.



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