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Dewetting of a droplet induced by the adsorption of surfactants on a glass substrate† Cite this: Soft Matter, 2014, 10, 5597

Y. Takenaka,*ab Y. Suminoc and T. Ohzonoa The dewetting of a surfactant droplet, induced by the adsorption of surfactants on a hydrophilic glass substrate, was observed experimentally. After being dropped onto the substrate, the droplet began shrinking and the speed of shrinkage increases with the surfactant concentration. We explained this dynamics, which is known as reactive dewetting, semi-quantitatively by expanding a simple theoretical model originally proposed and discussed qualitatively by M. E. R. Shanahan and P.-G. de Gennes [Startup of a reactive droplet, C. R. Acad. Sci. Paris, 1997, 324, 261–268]. In addition, for the surfactant droplet

Received 13th April 2014 Accepted 15th May 2014

with a concentration near or higher than the critical micelle concentration (CMC), we found that it maintains a large final contact area compared with that in the case of the low surfactant concentration.

DOI: 10.1039/c4sm00798k

We discussed this phenomenon by taking the decrease in the vapor–liquid and solid–liquid interfacial tensions into consideration.

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1. Introduction Wetting/dewetting of a droplet on a substrate is relevant for various industrial applications such as ink-jet printing and pesticide spraying. Two distinctive processes, occurring on different time scales, are observed during the wetting/dewetting of a droplet. One is the behavior observed when the droplet impacts the substrate surface (microseconds to several milliseconds). This behavior has been actively studied using a highspeed camera and numerical simulation.1–13 The other process is the relatively slower wetting/dewetting process (sub-milliseconds to several hours) that reects the interaction between the droplet and the substrate.14–21 In some cases, the translational motion of droplets induced by that interaction was reported.22–25 For droplets of pure liquids, which contain no chemicals interacting with the substrate surface, the contact angle of the droplet on the ideal at surface relaxes to the equilibrium value qE determined by Young's equation: gSG  gSL ¼ g cos qE

(1)

where gSG, gSL, and g are the surface tension between a solid– vapor interface, a solid–liquid interface, and a liquid–vapor interface, respectively. In the actual case, however, contact angle hysteresis exists because of the chemical and/or physical defects

a

Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8565, Japan. E-mail: [email protected]

b

PRESTO, JST, Kawaguchi, Saitama 322-0012, Japan

c

Department of Applied Physics, Faculty of Science, Tokyo University of Science, Tokyo 125-8585, Japan † Electronic supplementary 10.1039/c4sm00798k

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on the surface and qE is in a range between qA and qR, where qA and qR are advancing and receding angles, respectively. When a droplet contains chemicals such as surfactants that interact with the substrate surface, the relaxation dynamics becomes more complex. In this case, the surface energy of the substrate increases/decreases successively because of the adsorption of surfactants onto the substrate. When adsorption occurs over a time scale comparable with the time scale of droplet motion, gSG(t) and gSL(t) vary as a function of time t; in addition, the instantaneous “equilibrium contact angle” qE(t), which transiently satises the Young's equation at time t, changes over time. Such droplet motion, induced through a temporal change in surface tension, is oen called reactive wetting/dewetting. In the case of reactive wetting/dewetting, we have to consider the coupling between the time-dependent chemical reaction and droplet motion by adopting the effects of hydrodynamics. Some reports have focused on the dynamics of a reactive droplet accompanied by a chemical reaction between the surfactant molecules and the substrate. Yaminsky et al. observed the dewetting of droplets containing simple organic ions on a mica substrate.26 Shanahan et al. presented a theoretical model for the reactive dewetting of a droplet containing chemicals that react with the substrate surface.27 However, there has been no quantitative analysis for the reactive dewetting of a droplet that considers the effects of hydrodynamics. In this study, we experimentally observed the shrinking of a reactive surfactant droplet (105 to 104 M) on a hydrophilic glass substrate. We analyzed the dynamics of the reactive droplet semi-quantitatively based on Shanahan's model.27 Different dynamics were also shown for droplets with a high surfactant concentration (103 M).

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2.

Paper

Experimental

The experimental setup is shown in Fig. 1. We dropped 10 mL of a surfactant solution onto a glass substrate from a xed height of 20  5 mm using a pipette (Nichipet EX, Nichiryo, Japan). The time point at which the contact area (post the impact) stopped spreading was taken as t ¼ 0; we then monitored the shrinkage of the droplet at t > 0. The evolution of the contact area between the droplet and the substrate with time was observed for 100 s using a digital video camera recorder (Handycam; Sony DCRHC62, Japan) at 30 frames per second. Hexadecyltrimethylammonium bromide (HTAB; C16H33(CH3)3NBr, Tokyo Chemical Industry, Japan) at different concentrations ranging from 1.0  105 to 1.0  104 M was used as the cationic surfactant. This range of concentration is below the critical micelle concentration (CMC) of HTAB,28 which is approximately 103 M at 25  C. Each glass substrate (micro cover glass, Matsunami, Japan) was baked in air at 500  C for 10 min and was used aer cooling to room temperature. The baked glass substrate should be freshly prepared before each experiment to minimize contamination from air.29 Aer observing the dewetting for 5 min, we measured the contact angle of the droplet (DM-301, Kyowa, Japan). In addition, to examine the effects of evaporation, the weight of each surfactant droplet (with different surfactant concentrations) was also monitored during the experiment using a precision balance (ASP114, As One, Japan).

3.

Results

Time evolution of the contact area A between the droplet of the surfactant solution and the glass substrate is shown in Fig. 2a and b. Representative snapshots of the time evolution from one sample are also shown. Fig. 2a shows that the speed with which droplets shrink increases with the surfactant concentration. However, the resulting sizes of contact area A are almost the

Time evolution of the contact area A of droplets on glass substrates. (a) Short and (b) long term data are shown. The surfactant concentrations of the sample are (A) 1.0  105 M, (B) 2.0  105 M, (C) 3.0  105 M, (D) 5.0  105 M, and (E) 1.0  104 M. The speed of shrinkage increases along with the surfactant concentration. After 100 s, all droplets show a similar diameter. The representative camera images of the contact areas are shown at the bottom. The images are converted into black and white, in which the white area represents the contact area. Fig. 2

same (20 mm2) aer 100 s regardless of the surfactant concentration. To conrm that the volume remains constant, we measured the initial weight of each droplet and found that all of them had approximately the same weight, i.e., 10  1.3 mg. We then monitored the temporal change in the droplet weight and found that it remained constant over 100 s. The effects of evaporation were therefore ignored during the experiments.

4. Discussion 4.1

Fig. 1

Schematic illustration of the experimental setup.

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Theoretical modelling

Our theoretical model is based on that originally proposed by Shanahan27 et al. Briey, the researchers created a theoretical model for the reactive dewetting of a droplet, which is induced by the adsorption of chemicals within the droplet, by taking the viscosity dissipation at the contact line into consideration. In

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the following parts of this sub-section, we analyzed the time evolution of the contact area between the droplet and the substrate using Shanahan et al.'s model. In addition, the unknown parameter k (rate constant of adsorption) was determined by tting the experimentally obtained time-dependent contact area under the condition t  1 s, although Shanahan et al. did not obtain the value of k. Using the estimated parameter k, the experimental results were reproduced semiquantitatively. In the present experiment, an HTAB droplet showed slow shrinkage on a glass substrate. The shrinkage was induced by the adsorption of surfactants onto the substrate. The droplet contained cationic surfactants, whereas the glass substrate had a negative charge from baking at high temperature.30 Thus, hydrophilic head-groups of the surfactants begin to bind tightly to the glass substrate via a coulombic interaction aer the droplet is dropped onto the substrate. The adsorption of the surfactants continued to form a single Langmuir-type layer,31–33 gradually modifying the wettability of the substrate. This was expressed by the temporal changes in the surface tensions gSG(t) and gSL(t) in Young's equation eqn (1). The difference in the interfacial tensions before and aer the adsorption of surfactants can be addressed using a certain time-dependent function f(t) as follows: (gSG  gSL)t  (gSG  gSL) ¼ g1f(t)

(2)

where g1 is a proportional constant. It would be reasonable to regard f(t) as an adsorption ratio of the surfactants at a certain time t on the glass substrate. Thus, we next consider the adsorption kinetics of surfactants on a glass substrate. Assuming rst-order adsorption kinetics and that the desorption of surfactants from the glass substrate can be ignored, we can then obtain the following differential equation regarding f(t): dfðtÞ ¼ kcð1  fðtÞÞ; dt

(3)

where k and c are the rate constant of adsorption and the surfactant concentration, respectively. Here, the number of surfactant molecules in the droplet is assumed to be large enough and the surfactant concentration inside the droplet can be regarded as a constant c, even aer the adsorption of surfactants occurs. By taking the initial condition into account, i.e., f(t ¼ 0) ¼ 0, Eqn (3) can be solved as follows: f(t) ¼ 1  ekct.

(4)

During the adsorption of the surfactants on the substrate, eqn (1) at time t corresponds to (gSG  gSL)t ¼ g cos qE(t),

(5)

where qE(t) is the “equilibrium contact angle” at time t. As we mentioned before, the contact angle hysteresis would exist in

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the present experiments, and thus in this paper, the “equilibrium contact angle” means the time-dependent receding contact angle because we analyze only the retraction process of droplets. From eqn (1), (2), (4) and (5), we can derive  g  cos qE ðtÞ ¼ cos qE  1 1  ekct : (6) g Eqn (6) represents the process in which qE(t) relaxes to the 1 nal equilibrium contact angle with the time constant . The kc hydrophilicity/hydrophobicity of the substrate, which is reected by the contact angle qE(t), changes as determined by the degree of adsorption of surfactants on the substrate. Let us consider the reactive dewetting of the surfactant droplet on a hydrophilic glass substrate. Aer a droplet is set onto a substrate, the contact angle q starts relaxing towards the “equilibrium contact angle” qE(t) because the glass surface becomes gradually hydrophobic as a result of surfactant adsorption. The fringe speed of a droplet, dx/dt, can be discussed in the context of viscosity dissipation, in which the force required for the droplet to recede, driven by the difference between qE(t) and q, balances with the viscous drag. During the initial stages of droplet shrinking, the contact angle can be assumed to be q  1 and dx/dt can then be derived34 as dx q ¼ gðcos qE ðtÞ  cos qÞ; dt 3hl

(7)

where q, h, and l are the contact angle at time t, the viscosity of a droplet, and a logarithm factor, respectively. Since the volume of a droplet is constant, assuming a spherical-cap shape, the volume of droplet V can be written as Vz

pqx3 ; 4

(8)

when q  1. According to eqn (8), parameter x is uniquely determined by parameter q. Instead of q, we therefore made a theoretical model of the time dependence for radius x and area A of the contact area, which were obtained directly from the present experiments. Hereaer, we consider the reactive dewetting of a droplet described by eqn (7). When t  1 s, we can solve eqn (7). Moreover, using the obtained equation, we can estimate the rate constant k by tting the experimental results of the time evolution of the contact area. When t  1 s is not satised, we cannot solve eqn (7), and we therefore calculate it numerically for the long-term behavior of x. Firstly, t  1 s is considered. Upon the onset of droplet shrinkage, we can set q  1 because the droplet is widely and thinly spread. By inserting (8) into (7) and expanding q to the rst order, the following equations are derived: dx t z G 3 dt x 4V g1 kc G¼ : 3phl

(9)

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According to eqn (9), the speed of droplet shrinkage increases with the surfactant concentration because the time constant G increases with the surfactant concentration, c. This tendency also appears in the experimental results (Fig. 2). Eqn (9) can be solved, yielding  1=4 2G x z x0 1  4 t2 : (10) x0 This relationship can be rewritten as that of the contact area A, i.e., ! p2 G 2 A z A0 1  2 t ; (11) A0 where the following approximation is used, p2 Gt2  1: A0 2

(12)

Here, x0 and A0 are the initial (t ¼ 0, i.e., at the onset of the shrinkage) radius and area of contact, respectively. We can estimate the value of k by tting the experimentally obtained time-dependent contact area with eqn (11) under the condition of t  1 s. To do so, the value of g1 should be obtained separately. Parameter g1 can be determined from eqn (6) using t / N. Fig. 3 shows that the contact angle, qE(t / N), is approximately 60 . The contact angle, qE, which corresponds to that of water on the baked glass, is 0 (data not shown). We therefore obtain 1 g1 z g: 2

(13)

The value of G is obtained by tting the experimental curves (Fig. 2a) with eqn (11). Using feasible values for the parameters,34 i.e., h ¼ 0.8  103 Pa s, g ¼ 7.2  102 N m1, V ¼ 1.0  108 m3, l z 20, and the separately obtained g1, we can estimate k from eqn (9). The value of h is set as the viscosity of pure water for the sake of simplicity as the order of magnitude seems to be the same. Fig. 4 shows the calculated values for k. When the surfactant concentration is much lower than the CMC, the rate constant k should remain unchanged and in actuality it is approximately 103. The value of k does not change even if the

Fig. 3 Contact angles qE(t / N) of droplets with different surfactant concentrations c after 100 s from the onset of the shrinkage.

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Fig. 4 Estimated values of k for different surfactant concentrations. k shows almost a constant value of 103 except in the case that the surfactant concentration is 1.0  104 M.

time range of the tting is modulated. It is therefore almost constant except when the surfactant concentration is 1.0  104 M. The increase in k at 1.0  104 M can be accounted for the collective adsorption caused by micellization of the surfactant near the CMC. In the following discussion, we set k ¼ 103 for simplicity. To discuss the long-term change in the contact area, we expand q to a second order without the condition t  1 s. By inserting (8) into (7), we obtain ) (    2   dx 1 4V g 4V 1 1 kct z ; (14)  g1 1  e  dt 3hl px3 2 p x6 xI 6 which cannot be solved analytically. Here, we numerically calculate eqn (14). The results in which x is converted into A are shown in Fig. 5. The shrinking speed of the droplets increases with the surfactant concentration, as shown in Fig. 5. This tendency was also observed in the experimental results (Fig. 2a). By comparing the dynamics shown in Fig. 2a and 5, we nd a semiquantitative relationship, demonstrating the validity of the

Fig. 5 Long-term changes in the contact area A of droplets for different surfactant concentrations are numerically simulated using eqn (14). The surfactant concentrations are (A) 1.0  105 M, (B) 2.0  105 M, (C) 3.0  105 M, (D) 5.0  105 M, and (E) 1.0  104 M. The parameters used are V ¼ 1.0  108 m3, g ¼ 7.2  102 N m1, g1 ¼ 3.6  102 N m1, k ¼ 103, h ¼ 0.8103 Pa s, and l z 20. For simplicity, we used the surface tension of pure water for the droplet g.

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present simple theoretical model as the mechanism of reactive dewetting of a droplet, induced by the adsorption of surfactants on a glass substrate. One reason19–21,35 for the difference in the timescale of the experiments (Fig. 2a) and simulation (Fig. 5) may be because the parameter values such as surface tension g were simply set with those for pure water. Actually, the decrease in the surface tension shows the decrease in the shrinking speed of droplets in the simulation (Fig. S1†).36,37 Another factor ignored in the model is the effect of the contact-line pinning. In the present case, physical and/or chemical defects (e.g. the inhomogeneity of adsorbent density) would exist. When the contact line encounters the inhomogeneous spot, it will be pinned if the interaction between the defect and the liquid is strong enough. Finally the pinning is released with enough force. The energy dissipation to release the pinning will retard the contact-line motion in the dewetting process.34

4.2 When the surfactant concentration inside the droplet is high (near the CMC of 1.0  103 M) As shown in the previous section, the time evolution of the contact area at surfactant concentrations less than 1.0  104 M can be semi-quantitatively reproduced using a simple

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theoretical model. Here, we show the result obtained for surfactant concentrations higher than 2.0  104 M. As shown in Fig. 6, the contact areas are almost constant; i.e., shrinkage was not observed. The resulting contact areas (aer 100 s from the onset of the shrinkage) are 1.5 times larger than those shown in Fig. 2a. The large nal contact area may be due to the following reasons (here, the effect of viscosity is less important38). One possible reason is the drastic decrease in the vapor–liquid surface tension g above the CMC.36,37 Another is the decrease in the solid–liquid interfacial tension, gSL, owing to the adsorption of surfactants onto the glass surface at concentrations above the CMC.30–33,39 Near and above the CMC, surfactants adsorb on the surface as a bilayer, while they adsorb as a monolayer when the concentration is quite lower than the CMC.30 Both of them can lead to an increase in the spreading parameter and to a large contact area under the nal conditions.

5.

Conclusions

We observed the reactive dewetting of a droplet, induced by the adsorption of surfactants, on a glass substrate. At surfactant concentrations lower than 1.0  104 M, the surfactant droplet on a glass substrate started shrinking. The shrinkage was driven by the adsorption of surfactants on the surface of the substrate. The speed with which the droplets shrunk increased with the surfactant concentration. A simple theoretical model based on the viscosity dissipation of a thin liquid-lm was expanded so that the present experimental results can be reproduced semiquantitatively. At surfactant concentrations higher than 2.0  104 M, the droplets showed no shrinkage and maintained a large contact area. The increase in the nal contact area might be caused by the decrease in surface tension at the vapor–liquid interface and a qualitative change in the adsorbed structure of the surfactants on the glass surface near the CMC. These results can be useful for controlling the contact area or the thickness of liquid lms made of droplets containing adsorbates to a substrate. Such a control technique can help with such processes as ink-jet printing for exible electronics and pesticide spraying on the leaves of agricultural crops.

Acknowledgements The authors thank Ms Chikako Sekiguchi for her experimental support. This work was partly supported by the fundamental research fund of AIST.

Notes and references

Fig. 6 Time evolutions of contact area A of droplets with a high surfactant concentration (near the CMC) on the glass substrate. (a) Short and (b) long term data are shown. The surfactant concentrations of the sample are (A) 1.0  103 M, (B) 1.0  102 M, and (C) 2.0  104 M. When the surfactant concentration is 2.0  104 M, we can observe the initial shrinkage, which might be reproduced by the present theoretical model; however, the detailed kinetics is too fast to be analyzed.

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Dewetting of a droplet induced by the adsorption of surfactants on a glass substrate.

The dewetting of a surfactant droplet, induced by the adsorption of surfactants on a hydrophilic glass substrate, was observed experimentally. After b...
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