Selective dip-coating of chemically micropatterned surfaces

Anton A. Darhuber, Sandra M. Troian, Jeffrey M. Davis, Scott M. Miller, and Sigurd Wagner

Citation: Journal of Applied Physics 88, 5119 (2000); doi: 10.1063/1.1317238

View online: http://dx.doi.org/10.1063/1.1317238
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 JOURNAL OF APPLIED PHYSICS VOLUME 88, NUMBER 9 1 NOVEMBER 2000

Selective dip-coating of chemically micropatterned surfaces

Anton A. Darhuber, Sandra M. Troian,a) Jeffrey M. Davis, and Scott M. Miller
Interfacial Science Laboratory, Dept. of Chemical Engineering, Princeton University, Princeton,
New Jersey 08544
Sigurd Wagner
Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544
共Received 11 May 2000; accepted for publication 17 August 2000兲
We characterize the selective deposition of liquid microstructures on chemically heterogeneous
surfaces by means of dip coating processes. The maximum deposited film thickness depends
critically on the speed of withdrawal as well as the pattern size, geometry, and angular orientation.
For vertically oriented hydrophilic strips, we derive a hydrodynamic scaling relation for the
deposited film thickness which agrees very well with interferometric measurements of dip-coated
liquid lines. Due to the lateral confinement of the liquid, our scaling relation differs considerably
from the classic Landau–Levich formula for chemically homogeneous surfaces. Dip coating is a
simple method for creating large area arrays of liquid microstructures for applications involving
chemical analysis and synthesis, biochemical assays, or wet printing of liquid polymer or ink
patterns. © 2000 American Institute of Physics. 关S0021-8979共00兲07122-X兴

I. INTRODUCTION chemically patterned surfaces for use as chemical microreac-

tors. Biebuyck and Whitesides have used an immersion coat-
Thin liquid films are commonly deposited on planar or ing technique to fabricate microlens arrays on a chemically
cylindrical surfaces by a dip-coating process. This technique patterned surface.19 Qin et al.20 applied a similar technique
is widely used in industrial applications because of its sim- to fabricate CuSO4 and KNO3 microcrystals from aqueous
plicity and high throughput. A flat or curved substrate, which solutions. Braun and Meyer21 have produced a structured
is normally smooth and wettable by the liquid coating, is thin polymer film by dip coating an array of water droplets
withdrawn at constant velocity from a liquid reservoir. De- on a hydrophilized gold surface. These approaches provide a
pending on liquid composition, layered coatings can be de- simple yet elegant method for selective material deposition.
posited in this way in a controlled manner. The challenge to In this article, we investigate the dip coating of chemi-
this technique, especially at higher withdrawal speed, is to cally micropatterned surfaces. Besides the liquid material
form a smooth coating without defects like blisters, holes, properties like the viscosity, surface tension, and density, the
cracks, or local material accumulation.1–3 thickness of the liquid coating which adheres to the hydro-
With the aid of photolithography or microcontact philic portions depends critically on the pattern size, geom-
printing,4,5 the wetting properties of surfaces can be tailored etry and orientation. Since our application of interest is the
with submicron resolution. Molecules like alkylsilanes or al- ‘‘printing’’ of liquid micropatterns onto a secondary target
kylthiols form so-called self-assembled monolayers which surface, we require pattern fidelity between the designed
render a hydrophilic surface like silicon dioxide or gold hy- chemical pattern and the liquid microstructures formed, as
drophobic. This is reflected, for example, in the large in- well as a uniform coating thickness across structures of vary-
crease of the contact angle of water from 0° to about 110°. ing size or shapes. In addition to these experimental investi-
By patterning such a hydrophobic monolayer, ultrasmall vol- gations, we derive a hydrodynamic model for the maximum
umes of liquid in the nanoliter to femtoliter range can be film height deposited on vertically oriented hydrophilic strips
precisely distributed at desired locations by dip coating the on a hydrophobic plane. The predictions of this model,
substrate into a liquid bath or slot. Such small volume distri- which differs in two key ways from the traditional dip-
butions are difficult or even impossible to attain with con- coating analysis on homogeneous surfaces, agree remarkably
ventional dispensing techniques like ink jetting or microsy- well with experimental results.
ringe delivery.
The dip coating of plates, cylinders, and fibers has been
II. EXPERIMENTAL SETUP
investigated for over six decades. The majority of experi-
mental and theoretical studies6–18 have focused exclusively The samples were prepared from 关001兴-oriented p-type
on chemically homogeneous surfaces. As the number of doped silicon wafers using optical lithography. The wafers
techniques available for microfabrication and micropattern- were first cleaned by immersion in a solution of concentrated
ing grows, there is interest in selectively coating or ‘‘inking’’ sulfuric acid and hydrogen peroxide 共volume ratio of 7–3兲 at
90 °C for 15 min, then thoroughly rinsed in ultrapure, de-
a兲
Author to whom correspondence should be addressed; electronic mail: ionized water 共18 M⍀). Subsequently, thin layers of Cr 共5
stroian@princeton.edu nm兲 and Au 共40 nm兲 were deposited with an electron beam

0021-8979/2000/88(9)/5119/8/$17.00 5119 © 2000 American Institute of Physics

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 5120 J. Appl. Phys., Vol. 88, No. 9, 1 November 2000 Darhuber et al.

evaporator. A layer of photoresist was spin coated onto the As discussed by Wilson,14 this result is only valid for low
metal layers, which were then patterned by optical lithogra- capillary numbers, Ca⫽ ␮ U/ ␴ Ⰶ1, since the viscous contri-
phy and wet chemical etching using TFA 共Transene bution to the normal pressure is neglected in the derivation.
Comp., Inc.兲 and CR-7 共Cyantek Corp.兲. After stripping Here, U is the plate withdrawal speed from liquid reservoir
off the photoresist, the samples were immersed in a 1 mM and ␮ , ␴ , and ␳ denote the liquid viscosity, surface tension,
solution of hexadecanethiol 共HDT兲 in pure ethanol at a tem- and density, respectively. The key point in obtaining this
perature of 30 °C for 45 min. The thiol end groups of the expression relies on matching the flat film profile above the
HDT molecules bond to the gold forming a hydrophobic reservoir to the profile of a static meniscus.7 The character-
self-assembled monolayer since the alkane chains orient istic length, l c ⫽ 冑␴ /2␳ g, which determines the thickness of
away from the gold surface. The contact angle of water on the entrained film, represents the radius of curvature of a
HDT was measured to be 108°⫾3°. static capillary meniscus on a completely wetting wall or
Regions where the gold and chromium layers are re- likewise the height of capillary rise. For different geometries
moved and the silicon-dioxide exposed are hydrophilic with like the dip coating of a very fine fiber, for which the menis-
a contact angle below 5°. If the samples are exposed to cus radius of curvature is much larger than the fiber radius,
ambient air, the contact angle on the hydrophilic parts in- the relevant length scale becomes the fiber radius since its
creases over several days. This is likely due to organic con- associated capillary pressure dominates the flow.18 The cor-
tamination of silicon-dioxide, which is known to have a high responding prefactor in Eq. 共1兲 also changes slightly but re-
surface energy. mains of order one.
The masks used for the optical lithography of the Modifications by White and Tallmadge10 and Spiers
samples were printed on a transparent polymer foil by a et al.13 extended the applicability of this model toward larger
high-resolution image setter. The minimum feature size was values of Ca. Wilson14 later corrected these two analyses and
approximately 25 ␮ m. Smaller spacings between individual derived an expression valid to second order in Ca by using
elements could not be resolved by the image setter. the method of matched expansions
The liquid used in this study was glycerol 共1,2,3 trihy-
droxy propane, C3H8O3 ). It has a very low vapor pressure
such that evaporation could be held to a minimum, an im-
h ⬁⫽ 冑 ␴ 1
␳ g 冑1⫺sin ␣

冋 册
portant consideration given the small scale structures
formed. Glycerol is hygroscopic, however, and the absorp- 0.10685 cos ␣
⫻ 0.94581Ca2/3 ⫺ Ca , 共2兲
tion of water reduces the viscosity significantly. The viscos- 1⫺sin ␣
ity was measured with a capillary viscometer as 0.975 where ␣ is the angle of inclination as illustrated in Fig. 1共a兲.
⫾0.060 Pa s at 22 °C, the surface tension of glycerol is The film thickness predicted by Eq. 共2兲 as a function of the
0.0634 N/m at 20 °C.22 speed of withdrawal U and the angle of inclination ␣ for
The apparatus used for dip coating the patterned silicon pure glycerol ( ␮ ⫽1.760 Pa s兲 is plotted in Figs. 1共b兲 and
wafers consisted of a computer controlled sample stage, 1共c兲. More recent numerical studies of the dip-coating pro-
which allows for precise control of the speed of withdrawal. cess have been presented by Tanguy et al.15 and Reglat
The direction of withdrawal with respect to the liquid reser- et al.16 Schunk et al.17 have extended the model to include
voir and the in-plane orientation of the sample were con- mass loss due to solvent evaporation within the framework
trolled with a precision of approximately ⫾2°. Film thick- of a one- and two-phase flow model relevant to sol-gel pro-
ness profiles of the deposited liquid microstructures were cessing.
measured by optical microscopy 共Olympus BX60兲 using a
green bandpass filter whose transmission band was centered
about 550 nm. B. Capillary rise on a heterogeneous surface
As outlined in the previous section, the curvature of the
共vertical兲 static meniscus has a decisive influence on the en-
III. THEORETICAL DESCRIPTION trained film thickness. When dip-coating patterned surfaces,
like vertically oriented hydrophilic strips, however, there is a
A. Dip-coating of homogeneous surfaces
second curvature in the direction transverse to the liquid rib-
Landau and Levich6,7 and Deryagin8 were the first to bon adhering to the hydrophilic strip. As we will show, the
calculate the maximum thickness of a film, h ⬁ , entrained on transverse curvature depresses the radius of curvature in the
an infinite flat plate withdrawn vertically from a reservoir of vertical direction and thus the entrained film thickness. This
a Newtonian liquid. In their derivation, they assumed that allows for the deposition of much thinner liquid films.
gravitational drainage was negligible and that the coating We conducted energy minimization calculations24 of the
thickness was established by a balance between viscous and shape of the static meniscus on an isolated vertical hydro-
capillary forces. Their expression, obtained in the lubrication philic strip as shown in Fig. 2共a兲. As the input parameters for
approximation, which essentially requires laminar and small the computations, we used the material constants of glycerol
aspect ratio flow,23 is given by and equilibrium contact angles of 5° and 95° on the hydro-
philic and the hydrophobic regions, respectively. The com-
h ⬁ ⫽0.946 冑 ␴
␳g
Ca2/3. 共1兲
putational domain had dimensions of 12⫻12 mm2 , which is
much larger than the capillary length 冑␴ / ␳ g⫽2.26 mm.
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 J. Appl. Phys., Vol. 88, No. 9, 1 November 2000 Darhuber et al. 5121

FIG. 1. 共a兲 Sketch of the dip-coating geometry for homogeneous substrates.

Entrained film thickness of glycerol as a function of 共b兲 the speed of with-
drawal U and 共c兲 the inclination angle ␣ on a homogeneous plate.

Figure 2共a兲 shows a front view of the static meniscus FIG. 2. 共a兲 Liquid surface profile of a vertical 312 ␮ m wide hydrophilic line
on a hydrophobic surface. 共b兲 Linear meniscus profiles in the vertical sym-
profile on a 312 ␮ m wide isolated hydrophilic line. In Fig. metry plane of isolated lines for various linewidths ranging from 78.1 to
2共b兲, we compare various cross sections of the calculated 2500 ␮ m. The linewidth increases by a factor of 2 from one curve to the
surface profiles through a vertical plane at the center of the next. 共c兲 Linear meniscus profiles in the vertical symmetry plane of 312 ␮ m
hydrophilic line for a series of six linewidths ranging from wide lines in a periodic array with line separations ranging from 0.78 to 12
mm.
78.1 to 2500 ␮ m. For linewidths large compared to l c , the
meniscus profile is indistinguishable from that formed on an
infinite, uniformly hydrophilic plane surface. For linewidths
much smaller than l c , the meniscus shape away from the strip. Meniscus shapes for linewidths smaller than about 78
wall is depressed downward, similar to the behavior of a ␮ m require excessive computational time since very fine sur-
hydrophilic liquid against an infinite, uniformly hydrophobic face triangulation is required to capture the detailed profile
plane. In the immediate neighborhood of the wall, the liquid shape at the plane surface. However, the observed trend of a
senses the chemical heterogeneity and wets the hydrophilic linear decrease in both the height of capillary rise and the
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 5122 J. Appl. Phys., Vol. 88, No. 9, 1 November 2000 Darhuber et al.

vertical radius of curvature, remains valid down to much plate, we restrict attention to low capillary number flow
smaller linewidths provided the film coating is not so thin (CaⰆ1), small aspect ratios and negligible Bond number
that disjoining forces become important. (Bo⫽ ␳ gh ⬁2 / ␴ Ⰶ1).
Figure 2共a兲 shows an interesting detail involving the The flow profile exhibits three distinct regions. Far
shape of the contact line as the liquid is forced to accommo- above the reservoir, the thickness of the entrained liquid film,
date the presence two chemically different regions. The con- h ⬁ , is uniform and independent of x. In this region only
tact line precisely follows the vertical junction between the viscous forces determine the upward flux of liquid since cap-
hydrophilic and hydrophobic portions over a fairly long dis- illary pressure gradients vanish in the streamwise direction.
tance. This point has been addressed by Boruvka and At the reservoir the liquid surface assumes the shape of a
Neumann,25 who derived a semi-analytical solution of the static meniscus whose profile is strictly determined by the
Laplace–Young equation for the case of zero gravity. The balance of capillary and hydrostatic pressures. The transition
contact angle is found to change from its hydrophobic to the zone between these two regions, often called the dynamic
hydrophilic value along this vertical segment. Schwartz and meniscus regime, is governed by a balance between viscous
Garoff26,27 performed similar studies of the shape of the and capillary forces. The film curvature in this region
liquid–solid contact lines on surfaces of mixed wettability. smoothly matches the value of the static meniscus curvature
For a dense array of vertical lines, the meniscus shape at the lower end and the film thickness approaches h ⬁ as x
depends not only on the linewidth but also on the line sepa- →⫹⬁.
ration. Plotted in Fig. 2共c兲 are the meniscus profiles along the Within the lubrication approximation,23 the Navier-
vertical symmetry plane of a 312 ␮ m wide hydrophilic line Stokes equation governing the steady-state flow field in the
for line separations ranging from 781 ␮ m to 12 mm. The transition zone reduces to
meniscus shape for 6 and 12 mm is practically identical.
However, as the line separation decreases below the capillary ⳵p ⳵ 2u
length 共2.26 mm兲, interference effects with neighboring lines ⫺ ⫹ ␮ 2 ⫽0, 共3兲
⳵x ⳵y
increase the meniscus radius of curvature. This ‘‘cross-talk’’
leads to thicker film deposition on dense arrays than isolated which represents a balance between the capillary pressure
lines. The increased liquid pickup can promote coalescence gradient and the gradient in shear for nearly one-dimensional
with neighboring lines to produce a film coating which cov- flow, based on the geometric requirement (h ⬁ /W) 2 Ⰶ1. The
ers not only the hydrophilic but the intervening hydrophobic pressure, viscosity, and streamwise velocity are given by p,
portions as well. ␮ , and u, respectively. This equation is solved subject to the
The surface profile of an infinite line after dip coating no-slip condition at the solid-liquid interface
corresponds to a section of a circular cylinder. The contact
angle depends both on the natural contact angle on the hy- u⫽U at y⫽0, 共4兲
drophilic strip and on the deposited liquid volume. If the and vanishing shear stress at the air-liquid interface
natural contact angle is larger than the contact angle corre-
sponding to the liquid pickup, the liquid will recede from ⳵u
part of the line and capillary breakup of the continuous line ␮ ⫽0 at y⫽h 共 x,z 兲 . 共5兲
⳵y
into two or more segments is very likely to occur.28 If the
hydrophilic strips are not completely wetting and if the speed The pressure appearing in Eq. 共3兲 is governed by the
of withdrawal is smaller than the maximum contact line Laplace pressure
velocity,29 very little or no liquid may be entrained on the
hydrophilic parts. This is observed primarily for contami- ⫺ ␦ p⫽ ␴ ⵜ s n̂

冋 册
nated samples, where the contact angle is notably larger than
0°. h xx 共 1⫹h z2 兲 ⫹h zz 共 1⫹h 2x 兲 ⫺2h x h z h xz
⫽␴ , 共6兲
共 1⫹h 2x ⫹h z2 兲 3/2

where ⵜ s is the surface gradient operator and n̂ the outward

C. Dip coating of a vertical hydrophilic strip: Scaling
unit normal of the air-liquid interface. The subscripts refer to
analysis for h ⴥ
partial differentiation, i.e., h xx ⫽ ⳵ 2 h/ ⳵ x 2 .
In what follows, we develop a model for the maximum Within the lubrication approximation, since h 2x Ⰶ1 and
film thickness of a hydrophilic liquid entrained on a hydro- h z Ⰶ1, the earlier expression reduces to
2

philic strip surrounded by a hydrophobic coating. Consider

the dip coating of a narrow, hydrophilic, vertical strip of ⫺ ␦ p⬇ ␴ 共 h xx ⫹h zz 兲 . 共7兲
half-width W surrounded by a planar, hydrophobic surface as
Substituting this expression for the pressure into Eq. 共3兲,
sketched in Fig. 2共a兲. A Cartesian coordinate system is de-
integrating twice with respect to y, and using the boundary
fined with x̂ the direction of plate withdrawal 共i.e., the conditions in Eqs. 共4兲 and 共5兲 yields the parabolic velocity
streamwise direction兲, ŷ the direction normal to the plate, profile

冉 冊
and ẑ in the plane of the plate and normal to the direction of
withdrawal. In deriving a relation for the maximum film ␴ y2
u⫽U⫺ ⫺hy 共 h xxx ⫹h xzz 兲 . 共8兲
thickness and liquid flux dragged upwards by the moving ␮ 2
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The volumetric flow rate per unit width, which is con- In the general case where both the streamwise and trans-
trolled by the competition between the upward drag of fluid verse curvature contribute to the flow, there are two condi-
and the downward capillary drainage, is given by tions which determine the scaling behavior of X s , namely

Q⫽
1
2W
冕 冕 ⫹W

⫺W
h

0
udydz 共9兲 X s ⬃W and X s ⬃
h ⬁3
W2
共 Ca兲 ⫺1 . 共17兲

␴h3 The linear relation between X s and W was also obtained from
⫽AhU⫹B 共 h ⫹h xzz 兲 , 共10兲 our simulations of the static meniscus discussed in Sec. III B.
3 ␮ xxx
Equating these two expressions leads to the final result
where A and B are constants of order one resulting from the
h ⬁ ⬃W 共 Ca兲 1/3. 共18兲
nonuniformity of the film profile in the ẑ direction. Equation
共10兲 assumes that the streamwise gradient of the capillary In contrast to the Landau–Levich result in Eq. 共1兲, the expo-
pressure is only weakly dependent on z. Far above the dy- nent associated with the capillary number is decreased from
namic meniscus region, the entrained film thickness is uni- 2/3 to 1/3. In addition, the length scale controlling the de-
formly flat in the direction of withdrawal. Under steady-state posited film thickness is not the capillary length but the
conditions, the flow rate emanating from the dynamic menis- channel half-width W. These two differences allow for depo-
cus regime must therefore equal the flow rate as x→⫹⬁, sition of much thinner coatings for comparable material con-
namely Q⫽Ch ⬁ U. The film thickness h ⬁ represents the stants and withdrawal speeds.
steady-state height at the center of the strip 共i.e., at z⫽0).
The constant C is a number of order one which results from IV. EXPERIMENTAL RESULTS
averaging the film profile in the z direction. 共For example, The key variables which control the film thickness de-
C⫽2/3 for a liquid ribbon whose cross section is the arc of a posited on a homogeneous surface by dip coating include the
circle.兲 Equating the two expressions for the flow rate yields speed of withdrawal, liquid viscosity, surface tension, and
a third order equation for the interface shape, h(x,z) density. For micropatterned surfaces, additional variables

冉 冊
3␮U
␴
Ah⫹Bh 3 共 h xxx ⫹h xzz 兲 ⫽
3␮U
␴
Ch ⬁ . 冉 冊 共11兲
like the angular orientation of the hydrophilic shapes with
respect to the withdrawal direction, and the width and geom-
etry of the dipped patterns affect the shape and thickness of
Since the capillary pressure terms vanish and h→h ⬁ as x the coating film. We investigate the influence of these vari-
→⬁, A⫽C and Eq. 共11兲 becomes ables next.
h 3 共 h xxx ⫹h xzz 兲 ⫽K 共 3Ca兲共 h ⬁ ⫺h 兲 , 共12兲
A. Velocity
where K⫽A/B denotes a constant of order one.
This equation may be written in dimensionless form by Using optical interferometry, we measured the maxi-
introducing the set of reduced variables mum film thickness of glycerol entrained on an isolated 49
␮ m wide and 4 mm long hydrophilic strip on a 1⫻1 cm2
h z x hydrophobic sample. The cross section of the entrained liq-
␩⫽ , ␨⫽ , ␰⫽ , 共13兲 uid ribbon forms a sector of a circle. The sample was
h⬁ W Xs
clamped at one of the upper corners and the line completely
where X s is a characteristic length scale in the streamwise immersed in the liquid bath prior to withdrawal. The experi-
direction to be determined later from the matching of the mental data for the maximum film height h ⬁ of glycerol
curvature to the static meniscus. entrained on a hydrophilic line versus the speed of with-
Introducing these scaled variables into Eq. 共11兲 gives drawal U is shown in Fig. 3. The solid line indicates power

冋冉 冊 册
2 law behavior of the form h ⬁ ⬃U 0.33⫾0.005 in excellent agree-
W X sW 2
␩3 ␩ ␰␰␰ ⫹ ␩ ␰␨␨ ⫽K 共 3Ca兲 关 1⫺ ␩ 兴 . 共14兲 ment with the theoretical prediction of Eq. 共18兲. Lines cor-
Xs h ⬁3 responding to exponents of 0.32 and 0.34 are drawn for com-
parison.
For the limiting case of a homogeneous flat plate, K⫽1 and
(W/X s ) 2 →⬁, and Eq. 共14兲 reduces to
B. Angular orientation
X s3 We have measured the entrained coating film as a func-
␩ 3 ␩ ␰␰␰ ⫽ 共 3Ca兲关 1⫺ ␩ 兴 , 共15兲
h ⬁3 tion of the azimuthal sample orientation, where the substrate
is held vertical but rotated about an axis normal to the
which determines the dependence of the streamwise length sample. The sample was withdrawn at a speed of 40 ␮ m/s.
scale on the capillary number The experimental data for the entrained film thickness are
plotted in Fig. 4. The solid line serves as a guide to the eye.
X s ⫽h ⬁ 共 3Ca兲 ⫺1/3. 共16兲
As can be seen, h ⬁ increases monotonically from about 1.5
Using this relation in matching the film curvature at the ␮ m for vertically oriented lines to approximately twice this
lower end to the static meniscus yields the classical result value for horizontal lines. The azimuthal dependence is
given in Eq. 共1兲. rather weak for the range of angles 0⭐ ␸ ⭐45°. This plateau
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 5124 J. Appl. Phys., Vol. 88, No. 9, 1 November 2000 Darhuber et al.

FIG. 3. Dependence of the height of entrained liquid lines on the speed of FIG. 5. Dependence of the height of the liquid lines on the width of the
withdrawal U. The solid line represents a power law relation h ⬁ ⬃U ␤ with hydrophilic channels. Several different samples were investigated as indi-
␤ ⫽0.33. The dashed and dotted lines represent equivalent power law rela- cated by the circles, squares, and triangles.
tions with exponents 0.32 and 0.34, respectively.

locity U/cos ␣ parallel to the sample surface, if the sample is

region is highly advantageous for printing purposes since the tilted and withdrawn at the same vertical velocity U. The
entrained film thickness is rather uniform across a broad much smaller increase of h ⬁ on the lower side as compared
range of angles. to the upper side is qualitatively consistent with the reduced
We also investigated the influence of tilting the sample meniscus curvature on the upper side of the sample.
during withdrawal, i.e., the sample was rotated around an
axis parallel to both the reservoir and the sample surface. C. Width and geometry
Figure 1 suggests that the liquid volume pick-up increases on
the upper side ( ␣ ⬎0) and decreases on the lower side ( ␣ To determine the dependence of the entrained volume on
⬍0) of the sample. Eberle and Reich have used this effect the linewidth of the hydrophilic strip, we investigated the
for the fabrication of optical filters.30 In our case, however, dip-coating process for linewidths ranging from 40 to 110
the vector of the sample velocity during withdrawal was not ␮ m withdrawn at a speed of 30␮ m/s. The experimental re-
parallel to the sample surface as shown Fig. 1共a兲, but perpen- sults for three different samples are shown in Fig. 5. Within
dicular to the surface of the liquid bath. Thus, the flow pro- experimental error, the maximum film thickness entrained on
file is different from the one which leads to the derivation of a vertical strip scales linearly with the linewidth.
Eq. 共2兲 and the results are not fully comparable. The experi- Given the dependence of the maximum film thickness on
mental result for a tilt angle of ␣ ⫽30° is an increase of h ⬁ the linewidth perpendicular to the direction of withdrawal, a
by about 7% on the upper side for linewidths ranging from sample withdrawn at an azimuthal angle ␸ ⫽0 will present
46 to 65 ␮ m and a very small increase on the lower side. We an effective linewidth W/cos ␸. This larger width should en-
attribute the increased pickup to the higher contact line ve- train more liquid, which implies that hydrophilic lines ori-
ented toward the horizontal will entrain a thicker coating
than lines oriented closer to the vertical.
This is an undesirable consequence for printing applica-
tions where a uniform film height prior to printing is re-
quired. For patterns containing lines of arbitrary orientation,
however, one could chemically micropattern a surface such
as to segment lines into smaller rectangles to maintain a uni-
form film height throughout all hydrophilic regions. These
hydrophilic patches would be separated by very narrow hy-
drophobic regions. Upon contact printing, these elements
would coalesce and establish a continuous line as desired.
We are exploring this tessellation procedure as a workaround
to the orientation dependence of film height produced by dip
coating as discussed above.
An additional problem involving nonuniform liquid
pickup exists for the case of closed loops consisting of hy-
drophilic lines on a hydrophobic substrate. In Fig. 6共a兲 is
shown a square loop consisting of four straight line segments
FIG. 4. Dependence of the height of the entrained liquid lines on the azi-
muthal sample orientation. The continuous line serves only as a guide to the 100 ␮ m in width and 1 mm in length. When such a loop is
eye. withdrawn at speeds ranging from 10 to 1000 ␮ m/s, the en-
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 J. Appl. Phys., Vol. 88, No. 9, 1 November 2000 Darhuber et al. 5125

FIG. 7. The liquid volume entrained on a half-loop structure depends on its

azimuthal orientation with respect to the direction of withdrawal. 共a兲 De-
signed pattern in an upright position, 共b兲–共e兲 experimental hydrophilic half
loops dipped in various orientations with the same speed of withdrawal, 共f兲
disconnected half loop. Whereas the half loop structure picks up much more
liquid in the orientations shown in 共d兲 and 共e兲, a disconnection of the upper
part of the half loop avoids the undesired entrapment of liquid in the hydro-
phobic interior region.

which would otherwise be trapped in the hydrophobic inte-

rior of the hydrophilic loop, as the liquid meniscus recedes
FIG. 6. 共a兲 The designed pattern is a closed square loop, which 共b兲 is filled from the loop region. Therefore, the topological solution to
completely with liquid during the dip-coating process. 共c兲 This undesired interior entrapment of liquid is to disconnect closed line seg-
effect can be avoided by breaking the loop in at least one position in the ments.
upper portion.
The position of the broken or disconnected point in an
otherwise closed loop is critical for the deposition process
since the volume entrained depends strongly on the pattern
tire interior 共hydrophobic兲 region becomes coated with a liq- orientation. In Fig. 7共a兲 is shown a sketch of a U-shaped
uid film whose height exceeds the height entrained on an open loop. If during the vertical withdrawal process, the loop
isolated hydrophilic strip of the same width and length. assumes orientations as shown in 共a兲–共c兲 共in which 0⭐ ␸
As the square loop just exits the reservoir during the ⭐90°), the level of liquid pickup is approximately invariant.
withdrawal process, a meniscus forms between the lower However, once rotated beyond this angle such that the con-
horizontal segment and the liquid bath. When this meniscus tinuous part of the half loop appears at the top as in Figs.
snaps off, the contact line recedes to the exterior edges of the 7共d兲 and 7共e兲, liquid once again becomes entrapped in the
loop thereby entrapping liquid throughout the hydrophobic interior hydrophobic region as discussed earlier for a closed
interior as shown in Fig. 6共b兲. This behavior induces a com- loop. The excess volume does not distribute evenly on the
plete loss of pattern fidelity which is detrimental for printing hydrophobic interior but recedes to the inner corners of the
applications. Liquid entrapment of this sort occurs for loops structure in order to minimize the overall surface curvature
of arbitrary azimuthal orientation withdrawn at speeds rang- and contact energy. These liquid bulges would again induce
ing over two orders of magnitude whose feature sizes span a loss of pattern fidelity upon printing.
length scales ranging from microns to millimeters. The solution to this problem rests with inducing multiple
Figure 6共c兲 illustrates a solution to this problem. The disconnection points. When the half loop is separated into
loop shown consists of lines measuring 60 ␮ m in width and three straight line segments as shown in Fig. 7共f兲, no liquid
600 ␮ m in length and is disconnected in the leftmost corner. entrapment occurred. Furthermore, the liquid pickup on each
This single interruption allows for a dewetting of the liquid, separated line segment is not vastly different. The spacing
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 5126 J. Appl. Phys., Vol. 88, No. 9, 1 November 2000 Darhuber et al.

between the lines can be made even smaller than that shown 1
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2
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V. SUMMARY 5
L. Libioulle, A. Bietsch, H. Schmid, B. Michel, and E. Delamarche, Lang-
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We have investigated theoretically and experimentally 6
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8
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uid coatings with thicknesses in the micron range. We have 9
C. Gutfinger and J. A. Tallmadge, AIChE J. 11, 403 共1965兲.
studied the entrained film height as a function of the speed of 10
D. A. White and J. A. Tallmadge, Chem. Eng. Sci. 20, 33 共1965兲.
withdrawal. Sample orientation and pattern geometry also 11
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strongly influence the level of liquid pickup. For the case of
12
C. Y. Lee and J. A. Tallmadge, AIChE J. 19, 403 共1973兲.
13
R. P. Spiers, C. V. Subbaraman, and W. L. Wilkinson, Chem. Eng. Sci.
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S. D. R. Wilson, J. Eng. Math. 16, 209 共1982兲.
15
the experimental results. This model extends the classical P. Tanguy, M. Fortin, and L. Choplin, Int. J. Numer. Methods Fluids 4,
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16
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cropatterned substrates. High fidelity between the chemical 17
P. R. Schunk, A. J. Hurd, and C. J. Brinker, in Liquid Film Coating, edited
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quire design changes including pattern segmentation or the 18
D. Quéré, Annu. Rev. Fluid Mech. 10, 2790 共1994兲.
introduction of disconnection points. This solution resolves
19
H. A. Biebuyck and G. M. Whitesides, Langmuir 31, 347 共1999兲.
20
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involving high-resolution wet printing. 21
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22
Handbook of Chemistry and Physics, edited by R. C. Weast and M. J.
ACKNOWLEDGMENTS Astle 共Chemical Rubber Corp., Boca Raton, FL, 1982兲.
23
R. F. Probstein, Physicochemical Hydrodynamics: An Introduction
This project is funded by the Electronic Technology Of- 共Wiley, New York, 1994兲.
24
fice of the Defense Advanced Research Projects Agency as We used the software package Surface Evolver for our simulations,
which was developed by Kenneth Brakke of Susquehanna University,
part of the Molecular Level Printing Program. The authors Selinsgrove, PA. For a review see K. Brakke, Exp. Math. 1, 141 共1992兲.
also gratefully acknowledge the Austrian Fonds zur Förde- 25
A. L. Boruvka and W. Neumann, J. Colloid Interface Sci. 65, 315 共1978兲.
rung der wissenschaftlichen Forschung for a postdoctoral fel- 26
L. W. Schwartz and S. Garoff, Langmuir 1, 219 共1985兲.
lowship 共AAD兲 and the Eastman Kodak Corporation for a
27
L. W. Schwartz and S. Garoff, J. Colloid Interface Sci. 106, 422 共1985兲.
28
A. A. Darhuber, S. M. Troian, S. M. Miller, and S. Wagner, J. Appl. Phys.
graduate fellowship 共SMM兲. Dr. N. Pittet and Dr. C. Mon- 87, 7768 共2000兲.
nereau assisted with the assembly of the dip-coating appara- 29
J. G. Petrov and R. V. Sedev, Colloids Surface 13, 313 共1985兲.
tus. 30
A. Eberle and A. Reich, J. Non-Cryst. Solids 218, 156 共1997兲.

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