Article pubs.acs.org/Langmuir
Creating Controlled Thickness Gradients in Polymer Thin Films via Flowcoating Raleigh L. Davis,† Sahana Jayaraman,† Paul M. Chaikin,‡ and Richard A. Register*,† †
Department of Chemical and Biological Engineering and Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States ‡ Department of Physics, New York University, New York, New York 10003, United States S Supporting Information *
ABSTRACT: Flowcoating is a popular technique for generating thin (5−200 nm), substrate-supported polymer films. In this process, a reservoir of coating fluid is held between the horizontal substrate and a nearly horizontal blade above the substrate; a film of fluid is drawn out of the reservoir by moving the substrate. Accelerating the substrate produces a film with a thickness gradient, particularly useful for high-throughput measurements where film thickness is an important parameter. The present work compares experimental film thickness profiles with a model based on a Landau−Levich treatment to identify the experimental parameters which govern film thickness. The key parameters are the capillary number and the radius of curvature of the reservoir’s static meniscus, which is set by the blade angle, gap height, solution reservoir volume, and contact angles of the fluid with the blade and substrate. The results show excellent quantitative agreement with the first-principles model; the model thus provides a design approach which allows a user to produce polymer thin films of virtually any desired thickness profile.
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INTRODUCTION Creation of thin ( 10−4) were considered when generating best-fit lines; the cause of, and threshold for, the deviations observed at low Ca will be discussed below. The resulting slopes of the best-fit lines are displayed in the corresponding plots in Figure 4. All four panels show a dependence on Ca close to the predicted 2/3 power; moreover, all four panels are essentially identical, as shown by the “master” curve in the Supporting Information, with a bestfit slope of 0.662 ± 0.006. This provides compelling evidence that, in the range of Ca considered (10−4 < Ca < 10−2.58), the flowcoating process is indeed a Landau−Levich flow and robustly follows the predicted 2/3 dependence. While velocity (∼0.5−20 mm/s) and viscosity (∼0.5−5 cP) were each varied over at least a decade in generating the data of Figure 4, one limitation in this work was the comparatively narrow range over which the solution surface tension could be varied (approximately 20%, by changing solvent). Performing experiments over a wide range of γ is difficult, as most organic solvents have comparable surface tensions. In principle,
The flowcoated films contained negligible quantities of trapped solvent. PS films were flowcoated from toluene at 100 and 200 nm thickness, with the initial thickness measured within an hour of flowcoating; these films were then annealed in air at 150 °C for 30 min, cooled to room temperature, and the thickness remeasured. The 100 nm film showed a thickness decrease of only 0.9%, while the 200 nm film showed a decrease of only 1.6%; analogous spin-coated PS films showed very similar thickness changes following annealing. While these thickness changes represent upper bounds on the minute amount of trapped solvent in the present films, the amount could potentially be larger for solvents of much lower volatility or much stronger affinity for the polymer.
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RESULTS AND DISCUSSION Capillary Number Dependence. Films were deposited from solution (112 kg/mol PS, 1 wt % in toluene) by coating at constant acceleration rates of 0.05, 0.10, 0.50, 1.0, and 5.0 mm/ s2. In addition several films were made with uniform thickness, using a constant U of 0.5, 1.0, 5.0, or 10.0 mm/s. All films were produced with V = 50 μL, G = 200 μm, and α = 7°. Figure 3 shows the dry film thickness tdry plotted vs instantaneous coating velocity U on a log−log scale. A best-fit line to the data yields a slope, m = 0.642 ± 0.009 (± indicates one standard deviation), very close to the 2/3 power dependence predicted by Landau−Levich theory. The precise agreement between the flat (A = 0) and gradient (A ≠ 0) films confirms that instantaneous stage velocity, not stage acceleration, is the relevant control parameter. A wider array of tests was performed by changing the properties of the coating solution: polymer molecular weight and concentration as well as polymer and solvent type (with V, G, and α all still fixed at the previous values). These results are shown in Figure 4. To compare across solutions, the ordinate is 5639
dx.doi.org/10.1021/la501247x | Langmuir 2014, 30, 5637−5644
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Figure 4. Plots showing twet vs Ca, where the coating solutions were varied as follows: (a) PS molecular weight, (b) PS concentration, (c) solvent type, and (d) polymer type. Each plot shows the best-fit line (with slope m and ± indicating one standard deviation) for Ca > 10−4.
the capillary length, equal to γ/ρg, where g is acceleration due to gravity. The rear meniscus height, H, is somewhat ill-defined and difficult to accurately measure in the experimental setup (with an approximate measurement uncertainty of ∼9%). We chose instead to indirectly determine H by approximating the solution reservoir volume as a trapezoidal prism. One can then use simple geometry to compute H from α, G, V, and the blade width, B (here, simply the width of the glass slides used, B = 25 mm). Although held constant up to this point, V, G, and α may each be varied over some range. Therefore, to test the length scale proposed by eq 3, these parameters were adjusted (20 μL < V < 200 μL, 100 μm < G < 400 μm, 5° < α < 10°) and the calculated H and L were applied in the analysis of the measured film thicknesses according to eq 1. For simplicity, these experiments were all done using one solution (1 wt % of 112 kg/mol PS in toluene), so that θ1, θ2, and lcap were not varied. θ1 and θ2 were assumed to equal the static contact angles of pure toluene on silicon with native oxide and on glass, respectively. For both substrates, the contact angle was measured to be θ1 = θ2 = 15 ± 4° and the contact angle hysteresis (difference between advancing and receding contact angles) was found to be less than the measured error. All flat films were produced using U = 10 mm/s, hence Ca was fixed. Figure 5 shows twet/Ca2/3 vs L for films produced using a variety of G, α, and V. If true Landau−Levich flow is observed, these data should describe a line through the origin with a slope equal to c1, the numerical constant predicted to be 1.34. The data in
aqueous solutions could also be employed, but considerable effort must be taken to eliminate even trace levels of surfactants; otherwise, Marangoni effects may strongly affect the film thickness.40 Characteristic Length Scale. In addition to the 2/3 power dependence of film thickness on Ca, Landau−Levich theory predicts that there should exist a characteristic length scale, L, with which the film thickness should scale linearly; this characteristic length scale depends on the coating geometry.39 Perhaps surprisingly, both previous work12 and our own experiments show that the gap height, G, between the blade and the substrate is not a useful predictive length scale in this flow. Instead, the length scale proposed by Le Berre37 and Lau,40 derived by calculating the curvature of the static meniscus and using this to obtain a complete solution to the Landau−Levich flow problem, will be used. Because the lateral pressure gradient in the solution reservoir is zero,37 the radius of curvature in the front and rear menisci can be equated. The rear meniscus height and wetting conditions are typically easier to measure than the curvature; thus, the following expression for the rear meniscus curvature is chosen as the characteristic length scale, L: L=
H cos θ1 + cos θ2 −
H2 2(lcap)2
(3)
where H is the height of the rear meniscus, θ1 and θ2 are the back meniscus wetting angles as shown in Figure 1, and lcap is 5640
dx.doi.org/10.1021/la501247x | Langmuir 2014, 30, 5637−5644
Langmuir
Article
experimentally determined c1 and the predicted value (∼18%) could reflect the method used to evaluate the rear meniscus height H, wherein the reservoir volume was approximated by a trapezoidal prism. This approach likely underpredicts the true H, leading to an apparent increase in the measured value of c1. A further consideration is that H has been assumed constant during coating; however, as coating progresses and solution is drawn out, the reservoir volume, and therefore the back meniscus height, gradually decreases. However, calculations suggest that this effect is small for the films of Figures 2−5 (
