Langmuir 2008, 24, 12369-12374
12369
Dynamical Visualization of “Coffee Stain Phenomenon” in Droplets of Polymer Solution via Fluorescent Microscopy Tadashi Kajiya*, Daisaku Kaneko, and Masao Doi Department of Applied Physics, School of Engineering, The UniVersity of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan ReceiVed June 9, 2008. ReVised Manuscript ReceiVed July 29, 2008 In the drying process of polymer solution droplets, we propose an experimental procedure for visualizing the solute concentration profile by combining the fluorescent microscopy with the lateral profile observation. We have conducted a dynamical observation of the transport process of the solute polymer toward the edge that causes the “coffee stain phenomenon”. We have found that the polymer concentration increases sharply near the edge, while it remains almost constant in the central region until the last stage of drying. The method is useful to understand the dynamical process that occurs near the contact line.
I. Introduction The drying process of polymer solution droplets is an important problem in ink-jet printing technology, which has been a focus of interest as a next-generation production process for microelectronic devices.1,2 An important problem in this technology is how to control the shape of the solute deposited on the substrate after the solution has dried. Various studies have been conducted for the drying process of a droplet on a substrate. Deegan et al.3,4 studied the drying process of colloidal suspension droplets, and they explained the “coffee stain phenomenon”, which involves the formation of ringlike deposits near the edge of the droplet. They explained that the critical factor of the coffee stain phenomenon is the solute transport by the outward flow, which is driven by the combined actions of contact-line pinning and evaporation enhancement of solvent near the contact line. Detailed analysis for the flow field when the contact line is pinned have been conducted by Hu and Larson.5,6 The morphological pattern formed inside the ring, which is closely related to stick-slip motion of contact line, has also been studied in various systems.7-9 The coffee stain effect is also important in polymer solutions, because it is associated with the problem of controlling the thickness profile of polymer films that are made in ink-jet printing. Theoretical analysis has been conducted to predict the final shape by computer simulation.10 Experimentally, de Gans et al.11 showed that the initial contact angle of the droplet is important in regard to controlling the coffee stain phenomenon. The relationship between the initial contact angle and the final shape (1) Shimoda, T.; Kimura, M.; Miyashita, S.; Friend, R. H.; Burroughes, J. H.; Towns, C. R. SID99 DIGEST 1999, 376. (2) Sirringhaus, H.; Kawase, T.; Friend, R. H.; Shimoda, T.; Inbasekaran, M.; Wu, W.; Woo, E. P. Science 2000, 290, 2123. (3) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (4) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. ReV. E 2000, 62, 756. (5) Hua, Hu.; Larson, R. G. Langmuir 2005, 21, 3963. (6) Hua, Hu.; Larson, R. G. Langmuir 2005, 21, 3972. (7) Deegan, R. D. Phys. ReV. E 2000, 61, 475. (8) Maheshwari, S.; Zhang, Lu.; Zhu, Y.; Chang, H. C. Phys. ReV. Lett. 2008, 100, 044503. (9) Zhang, Lu.; Maheshwari, S.; Chang, H. C.; Zhu, Y. Langmuir 2008, 24, 3911. (10) Ozawa, K.; Nishitani, E.; Doi, M. Jpn. J. Appl. Phys. 2005, 44, 4229. (11) de Gans, B. J.; Schubert, U. S. Langmuir 2004, 20, 7789.
was studied in detail by Kajiya et al.12 and Fukai et al.13 The droplet, which was confined by a small bank, was studied by Jung et al.14 Marangoni flow is also considered to be an important factor in regard to controlling the deposit shape. Poulard et al.15 evaluated the effect of Marangoni flow in detail with a certain set of polymer solutions that had different concentration dependences on the surface tension. In these studies, the evaluation was conducted mainly from the surface profile of the droplet and the shape of the final deposit, combined with analytical and numerical calculation. These measurements are not enough to know the state inside the droplet (that is, the flow field and the solute concentration field). These two factors are critical for evaluating the coffee stain effect dynamically. Although the flow field has been measured using the tracer particle method,16,17 the solute concentration field has not been studied. Here, we shall report the first experimental study for the concentration field in the drying droplet. We obtain the concentration field by measuring the fluorescence profile of the solute polymer and the lateral profile of the droplet simultaneously. Our method has affluent possibilities for understanding and controlling the drying process of the polymer solution.
II. Experimental Section A. Materials. The polymer solution consisted of fluorescent polystyrene and anisole (Sigma-Aldrich, USA; boiling point, Tb ) 152-155 °C; viscosity, η ) 1.03 cP). Fluorescent polystyrene was synthesized from the copolymerization of styrene (Junsei, Japan) and 4-acrylamidofluorescein (AAm-F; absorbance ) 463 nm, emission ) 528 nm) into ethanol. The molar ratio for copolymerization is 1:0.003. This ratio was chosen to optimize the requirement of restraining the effect of the absorption of light as low as possible and obtaining the fluorescence intensity profile as clearly as possible. AAm-F was synthesized via the condensation reaction of 4-aminofluorescein (TCI, Japan) with acryloyl chroride (TCI, Japan) into (12) Kajiya, T.; Nishitani, E.; Yamaue, T.; Doi, M. Phys. ReV. E 2006, 73, 011601. (13) Fukai, J.; Ishizuka, H.; Sakai, Y.; Kaneda, M.; Morita, M.; Takahara, A. Int. J. Heat Mass Transfer 2006, 49, 3561. (14) Jung, Y.; Kajiya, T.; Doi, M. Unpublished work. (15) Poulard, C.; Damman, P. Eur. Phys. Lett. 2007, 80, 64001. (16) Hu, H.; Larson, R. G. J. Phys. Chem. B 2006, 110, 7090. (17) Rieger, B.; van den Doel, L. R.; van Vliet, L. J. Phys. ReV. E 2003 68, 036312
10.1021/la8017858 CCC: $40.75 2008 American Chemical Society Published on Web 10/10/2008
12370 Langmuir, Vol. 24, No. 21, 2008
Kajiya et al.
Figure 1. Schematic diagram of the experimental setup used to observe the drying process; the fluorescence intensity profile and lateral profile were observed at the same time.
dehydrated tetrahydrofuran.18 The weight-averaged molecular weight (Mw) of fluorescent polystyrene was 62 kD (as measured by molecular gel permeation chromatography). The substrates were glass slides (Matsunami, Japan). Before use, the glass slides were carefully cleaned with piranha solution (70% H2SO4 + 30% H2O2) and an ultraviolet-ozone (UV-O3) cleaner (Product UV253H, Filgen, Japan). Then, to make the droplet shape appropriate for observation, they were coated with silane-coupling chemicals (3,3,4,4,5,5,6,6,6-nonafluorohexyltrichlorosilane, Shinetsu, Japan). The contact angle of pure anisole on this substrate was ca. 30°. In this surface property, after the droplets of polymer solution started to dry, the contact line was kept pinned until the end of drying, except in the case of very low initial volume fraction (φ < 0.001). B. Experimental Setups. Figure 1 shows the experimental setup. The substrate was set on the inverted microscope (Model IX71, Olympus, Japan), and a droplet of the polymer solution was placed on the substrate with a micropipet. The volume of each droplet was ca. 0.5 µL. The radius of the droplet was ca. 1 mm, and its height was ca. 0.3 mm. The droplet was dried under natural conditions, and the total drying time was 8 ( 1 min. In our experiment, the atmospheric temperature and humidity were ca. 25 °C and 30%, respectively. The light from the mercury lamp was filtered and used for excitation (λ ) 470-490 nm). The emission from the droplet was observed from the bottom through an optical filter (λ ) 515-550 nm). To get a clear image of the entire droplet, both in the horizontal direction and the vertical direction, a low-magnification objective lens was used (magnification ) 4×, with a numerical aperture of N.A. ) 0.16). To minimize the effect of excitation light for drying, the excitation light was illuminated only during the time of picture acquisition with a mechanical shutter. To check the effect of excitation light, the total drying time was compared for the two cases (with and without the excitation light), and there was almost no difference between them. For the observation of the lateral profile, a prism and CCD camera (Model CMOS130-USB2, Fortissimo, Japan) with a magnification lens (Model TS-9 L-CZ8, Fortissimo, Japan) were located on the side of the droplet. White light was used for illumination; it was passed through an optical filter and slit to cut the wavelength of fluorescence measurement. The wavelength of the illumination light was 630-700 nm. (18) Kaneko, D.; Narita, T.; Gong, J. P.; Osada, Y.; Ando, J.; Yamamoto, K.; Onishi, S.; Yaminsky, V. V. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 2808.
Figure 2. Result of the simultaneous measurement of the fluorescence and lateral profiles (φi ) 0.02): (a) sequential pictures of the fluorescence and lateral profiles (t/tf ) 0.10, 0.50, and 0.75) and (b) cross sections of the intensity distribution in different time steps (t/tf ) 0.10, 0.25, 0.50, 0.75, and 0. 95).
From the sequential picture of the lateral view, the radius R and the height at the center h0(t) were measured. The radius of the droplet was smaller than the capillary length (κ-1 ) (γ/Fg)1/2 ≈ 1.9 mm);19 therefore, the shape of the droplet can be approximated to be a spherical cap. Therefore, the volume of the droplet (V) was calculated from R and h0 by
V)
πh0(3R2 + h02) 6
(1)
and the lateral profile of the droplet h(r) was also calculated as
h(r) )
(
)
R2 - h02 h02 + R2 2 - r2 2h0 2h0
(2)
Alternatively, the shape of the final deposit was measured using an optical surface profiler (New View 7000, Zygo, Japan). A threedimensional surface profile of the final deposit was obtained.
III. Results and Discussion A. Fluorescence Observation and Derivation of Volume Fraction. Figure 2 shows the result of simultaneous measurement (the initial volume fraction was φi ) 0.02) of the fluorescence and lateral profiles. Figure 2a shows sequential pictures; the upper picture is the lateral profile, and the lower picture is the fluorescent profile. Figure 2b shows the cross sections of the intensity profile I. For the sake of comparison, position r is normalized by the droplet radius R (rj ) r/R), and time t is normalized by the characteristic evaporation time tf, which was determined as follows. The plot of V vs t indicates that V decreases almost linearly with time until the last stage of drying. We obtained the volume change rate V˙ from the initial slope of the plot of V vs t. The time tf is given by (19) de Gennes, P. G.; Wyart, F. B.; Quere, D. Capillarity and Wetting Phenomena; Springer: New York, 2004.
“Coffee Stain Phenomenon” in Polymer Solution
tf )
V0(1 - φi) V˙
Langmuir, Vol. 24, No. 21, 2008 12371
(3)
where V0 is the initial volume of the droplet and φi is the initial polymer volume fraction. (Notice that tf is not the actual time needed to complete drying. The drying is slowed at the late stage; therefore, the actual drying time is a slightly longer than tf). At an early stage of drying (t/tf ) 0.1), the fluorescence intensity I(r) is highest at the center and the intensity distribution is close to the lateral profile. As drying proceeds (t/tf ) 0.5, 0.75), the intensity near the center decreases and the intensity near the contact line increases, while the lateral profile is still spherical. The intensity profile I(rj) is expected to be proportional to the total amount of polymer existing in the light path of the excitation
Figure 3. Calibration method for confirming the linearity between I(rj) and φ(rj)h(rj): (a) schematic diagram of the setup (the polymer solution is sandwiched by glass plates with a fixed triangle shape, and the intensity profile is observed from the bottom side), (b) dependence of I vs h (φ ) 0.01, 0.05), and (c) dependence of I0 vs φ. For the ease of comparison, each I0 is normalized by I0(0.01).
light, i.e., φ(rj)h(rj). (Here, we have assumed that φ is uniform in the vertical direction.) To confirm this proportionality, the following calibration was conducted. Figure 3a shows the experimental setup for checking the height dependence of intensity. The polymer solution was sandwiched between two glass plates, which forms a rectangular triangle with a bottom length D (expressed in millimeters) and height H (also expressed in millimeters). The fluorescence intensity then
Figure 4. Estimation method of the volume fraction distribution in the horizontal direction from the intensity data. Intensity profile at position jr I(rj) (panel b) is proportional to φ(rj)h(rj). Normalizing I(rj), using the droplet profile hj(rj) ) h/R (panel a), and dividing by a certain constant C, jr yields φ(rj) (panel c).
12372 Langmuir, Vol. 24, No. 21, 2008
was measured as a function of the distance x from the apex. Figure 3b shows the fluorescence intensity I plotted against the height h (here, h ) (H/D)x). Within the range of height relevant in our experiment (i.e., h e 0.3 mm), the intensity increases almost linearly versus the height. From this data, the intensity per unit length of the light path (I0) was calculated and plotted against φ (see Figure 3c). For the sake of comparison, I0 of each φ is normalized by the I0 value of φ ) 0.01. The φ dependence of I0 is almost linear until φ ≈ 0.1. (Note: At high φ values (φ > 0.2), I0 deviates from the linear relation, because of the
Kajiya et al.
absorption of light. Therefore, φ cannot be measured accurately from the intensity at high φ.) These results confirm the linear relationships between I and h, and between I and φ. From the results of I(rj,tj), φ(rj,tj) can be estimated by
φ(r¯,t¯ ) ) C
I(r¯,t¯ ) ¯h(r¯,t¯ )
(4)
where the lateral profile hj(rj,tj) ) h/R is obtained as explained in the Experimental Section, and the constant C is determined from
Figure 5. Profile of φ(rj) in different time steps t/tf, as obtained from the profile of I: (a) φi ) 0.02 and (b) φi ) 0.05.
Figure 6. Time variation of φ near the center of the droplet: (a) φi ) 0.02 and (b) φi ) 0.05. For the sake of comparison, time variations of φ in case the droplet is dried, keeping its φ uniform, is plotted as a dotted line.
Figure 7. (a) Three-dimensional (3D) profile of the final deposit measured by the optical surface profiler (the initial volume fraction is φi ) 0.02). (b) Cross sections of the deposit (φi ) 0.02, 0.05). For the sake of comparison, the horizontal and vertical positions (r, h) are normalized by the radius R.
“Coffee Stain Phenomenon” in Polymer Solution
Langmuir, Vol. 24, No. 21, 2008 12373
Figure 8. Restraint of evaporation and outward flow: (a) diagram of the setup (the droplet is surrounded by the solvent bath, and the system is sealed in a small box; the total drying time of the droplet is ∼3 times longer than that under natural conditions). (b) Cross-sectional profile of the deposit (φi ) 0.02). (c) Cross-sectional profile of the deposit (φi ) 0.05).
Figure 9. Time variation of φcenter in the case of slow evaporation: (a) φi ) 0.02 and (b) φi ) 0.05.
the data taken just after the droplet ejection (i.e., where φ(rj,tj) is equal to the initial volume fraction φi). Figure 4 illustrates the procedure of volume fraction estimation. Here, Figure 4a is the lateral profile of the droplet hj(rj), Figure 4b is the intensity distribution jI(rj), and Figure 4c is the distribution of volume fraction φ(rj,tj), which is obtained from eq 4. B. Discussion of Coffee Stain Phenomenon. Figure 5 shows the time evolution of the volume fraction φ(rj,tj). Here, Figures 5a and b show the results for two initial polymer concentrations (φi ) 0.02 and 0.05). The volume fraction φ shown in Figure 5 exceeds the maximum value of φ ) 1.0. This is because we used eq 4 for all of the concentration regions. In reality, the linear relation between I and φ breaks down at high concentration. Therefore, the value of φ near the contact line should not be taken literally. In both cases of φi ) 0.02 and 0.05, φ becomes quite large in the region near the contact line. This concentrated region is visible even at the early time of drying (t/tf ) 0.1) and grows as drying proceeds. The existence and the growth of the concentrated region clearly demonstrates the polymer transportation toward the contact line due to the outward flow. The amount of polymer transported to the concentrated region is expected to
be larger as the initial polymer concentration increases. Therefore, the concentrated region should grow faster for φi ) 0.05 than for φi ) 0.02. Figure 5 indeed confirms this expectation. To discuss the effect of outward flow more in detail, φ near the center (φcenter) was plotted against t/tf in Figure 6a (for φi ) 0.02) and for Figure 6b (for φi ) 0.05). If one assumes that there is no outward flow and that the polymer concentration remains uniform in the droplet, the time dependence of φ is given by
φ)
φi
( )
φi + (1 - φi) 1 -
t tf
(5)
This is plotted as dotted lines in Figure 6. In contrast, if one assumes that the outward flow is dominant, and that each element in the solution is simply transported by the outward flow, there is no increase of φ, except in the vicinity of the contact line. Our experimental data show that φcenter does not increase until later drying times (t/tf ≈ 0.8). These figures clearly indicate that the strong outward flow transfers most of the polymer in the central region to the edge of the droplet until the last stage of drying. The aforementioned result is consistent with the shape of the final deposit. Figure 7shows the surface profile of the final deposit
12374 Langmuir, Vol. 24, No. 21, 2008
formed after droplet drying. In our droplet, most of the polymer accumulates near the edge (see Figure 7a) and forms a ringlike shape. Figure 7b shows the cross sections. It is seen that the thickness at the center is very small, compared to that at the edge, and that the shape is very different from the original spherical shape. For example, in the case of φ ) 0.02, if there is no advection, hj at the deposit center should be 0.006, which is more than 10 times larger than that of actual central thickness. This also demonstrates the strong effect of the outward flow. C. Dynamics in Slow Evaporation. In the previous section, we have shown that the outward flow removes most of the polymer initially suspended near the center. If the outward flow is slowed, it is expected that solvent evaporation in the center region starts to compete with the flow, and a larger amount of polymer will remain there. To test this idea, we conducted the drying experiment in a covered box with a solvent bath (see Figure 8a). The box and the solvent bath restrain the diffusion of solvent vapor to the atmosphere and reduce the evaporation rate by approximately one-third. Figures 8b and c show the comparison of the profile of the final deposit. It is observed that, in the slow evaporation rate, the width of the ring is broader and the film thickness at the central region is larger than in the case of natural conditions. (This trend is especially clear for φi ) 0.05.) The same trend also can be seen in the time variation of the polymer concentration at the center φcenter Figure 9 shows the plot of φcenter against t/tf in the case of slow evaporation. For the sake of comparison, data in the case of natural conditions and estimated φcenter and in the case of no solute transport (dotted line) are also plotted. In both cases, φcenter starts to increase earlier in the box than under natural conditions and approaches the line of the no-solute-transport case. From this trend, we can also confirm the weakening of the coffee stain phenomenon.
Kajiya et al.
IV. Conclusion In this study, we succeeded to visualize the concentration field in the drying droplets of polymer solution by combining the fluorescence measurement and the lateral profile measurement. We observed that a strong concentrated region is created in the vicinity of the contact line at an early stage, while the polymer concentration in the central region remains almost constant until the late stage of drying. This indicates that the fluid in the central region is removed mainly by the outward flow, not by the evaporation. This explains the fact that polymer film thickness in the central region becomes very small after drying. We also confirmed that the outward flow is subject to the evaporation rate and is weakened when the evaporation is suppressed. In this study, we have focused on the case where the contact line is pinned in the entire drying process. The case that the contact line can move is an important problem and has been studied extensively.20,21 Our method will be a useful tool in understanding the dynamics of the contact line in that case, because we can measure the time evolution of the solute concentration in the vicinity of the contact line. In the future, the method is expected to be combined with the flow field measurement. Acknowledgment. We gratefully thank T. Okuzono, H. Morita, M. Kobayashi, and T. Yamaguchi (Tokyo University) for discussion; we also thank M. Imai, K. Yaegashi, M. Yanagisawa, and Y. Sakuma (Ochanomizu University), and H. Nakamura (Tokyo Metropolitan Industrial Technology Research Institute), as well as H. Matsushita and K. Ishii (Canon Marketing Japan) for their experimental help. LA8017858 (20) Rio, E.; Daerr, A.; Lequeux, F.; Limat, L. Langmuir 2006, 22, 3186. (21) Monteux, C.; Elmaallem, Y.; Narita, T.; Lequeux, F. Eur. Phys. Lett. 2008, 83, 34005.
