Download Patterning Lines by Capillary Flows - ACS Publications

NANO
LETTERS
Patterning Lines by Capillary Flows
Saurabh Vyawahare, Kate M. Craig, and Axel Scherer*
2006
Vol. 6, No. 2
271-276
Thomas J. Watson, Sr. Laboratories of Applied Physics,
California Institute of Technology, Pasadena, California 91125
Received November 15, 2005; Revised Manuscript Received December 7, 2005
ABSTRACT
We report that capillary flows in an evaporating thin film create line patterns, with widths ranging from a few micrometers to less than 100
nm. Deliberate patterning of such lines requires contact-line pinning and the presence of foaming surfactants. Large-scale photolithography
can guide and control these structures by creating pinning points and steering evaporation. We provide demonstrations of this process by
making self-assembling lines of colloidal quantum dots and microspheres.
Looking at a soap bubble, one can appreciate how capillary
forces cause unexpected patterns and shapes.1 Surface tension
is involved in the coffee-drop effect,2-4 fingering patterns
in Hele-Shaw cells,5,6 microsphere ordering to form two-dimensional crystals,7,8, combing of DNA,9 and skeleton formation in marine creatures called radiolarians.10 Although it is
common, using surface tension as a practical lithographic tool
is beset with problems involving control of the process.11 Here,
we report a new general method for depositing controlled line
patterns, based on capillary flows in thin films of liquids.12,13
When a coffee drop evaporates on a table, ring-shaped
coffee stains remain on drying. In this case, the boundary
between air, solid, and liquid, the contact line,14 is pinned,
that is, immobilized on surface defects. Then, capillary flows
push coffee particles to the boundary.2 In experiments
described in this paper, we find, under certain conditions,
instead of rings, lines are formed. Three main conditions are
necessary: (1) evaporating solutions between partially wetting surfaces, (2) the presence pinning points, and (3) the
presence of foaming surfactants, molecules with a lyophilic
or solvent-liking and lyophobic or solvent-repulsing part.
Surfactant molecules prefer to aggregate at surfaces15 and
tend to lower surface tension.
Our initial experiments used solutions containing foaming
protein surfactant16,17 bovine serum albumin (BSA), which
belongs to a class of sticky proteins found in large quantities
in blood and milk. An aqueous solution of BSA is sandwiched between either two cover glasses or two silicon
wafers. The liquid spreads until it balances the weight on
top of it (Figure 1a). If this solution is left to evaporate for
a few hours, then wire-like patterns stick out of the receding
boundary (Figure 1b), growing perpendicular to the contact
line. Each line starts with a small clump of BSA that
* Corresponding author. E-mail: [email protected]. Tel: 1-626-3954691. Fax: 1-626-577-8442. Correspondence and requests for materials
should be addressed to M/C 200-36, Caltech, Pasadena, CA 91125.
10.1021/nl0522678 CCC: $33.50
Published on Web 01/05/2006
© 2006 American Chemical Society
crystallized or formed a gel at the tip, creating a self-pinning
point.18 The lines can stretch many millimeters and are a
few micrometers wide. They stop growing only by breaking
from the contact line, this is usually due to another clump
of BSA nearby, causing depinning.
This process is not very sensitive to concentration, and
solutions of BSA from 10 nM to 10 mM all formed lines.
Higher concentrations render the solution gellike because of
an increase in viscosity; lower concentrations are too dilute
and waterlike, unable to form stable lines. The two surfaces
may be peeled apart. This leaves a pattern on one surface
that is the mirror of the pattern on the other surface; the
lines seem to break at the center, leaving behind material
on each surface with approximately half the height (Figures
1c and 4a) This allows access to the lines directly.
As mentioned earlier, a thin film of liquid between parallel
plates is necessary; a drop of BSA solution on a surface will
leave ring-shaped patterns. The main difference between the
two geometries is that liquid cannot evaporate in the third
dimension, perpendicular to the plane, when sandwiched.
Also, in the sandwich geometry, pure water will form short
lines that snap and reduce to a series of drops because of
Rayleigh’s instability.19 A random impurity or a designed
pinning point, described later in the paper, does the pinning
in this case. And if the substrate, silicon or glass, is
chemically treated to increase wetting, fewer BSA lines
result, showing that partially wet surfaces are required.
To better visualize this process, we added quantum dots
to the solution. Quantum dots got concentrated in the lines,
which could be seen by the photoluminescence intensity. We
find that the shape of the contact line near the wire can be
fitted to a second-order polynomial (Figure 2a and b). The
shape is a parabola or a catenary (which is a parabola to the
first approximation). This is different from three-dimensional
pinned drops, where the shape of the contact line has been
shown to be exponential.20
bubble appears near the receding contact line. Quantum dots
tend to collect at its edges. Eventually, the bubble pinches
off from the contact line and becomes a pinning point for a
new line.
Solution in the lines is constantly evaporating, and a new
supply of liquid must be maintained to prevent lines from
drying up. This flow brings with it additional solutes that
tend to concentrate in these lines. The pressure gradient
created by the parabolic shape, combined with the flows due
to the receding contact line, creates a flow pattern as shown
in Figure 2d (see Supporting Information video 1).
Why are the lines stable, and what determines their width?
A complete theoretical analysis is still a work in progress
and will not be described in this paper. But, qualitatively,
we believe that the physics of this process is analogous to
that of soap bubbles and foams.22 Soap bubbles have film
thickness between 5 nm and a few micrometers.23 These lines
are similar to the thin film between two coalescing bubbles,
the bubbles in this case being the air that surrounds the line
on either side. Two effects keep soap bubbles from shrinking: one, the repulsion between molecules, also known as
the disjoining pressure.24 We believe that this force prevents
these lines from collapsing to zero width. Second, although
poorly understood, the Gibbs-Marangoni effect plays a
major role in foam formation.1 In these lines, this effect
should provide a restoring force acting against change in
width of the lines, resulting in lines whose widths are
constant throughout, as observed.
Surfactants are essential for this process, they energetically
prefer to be at the air-liquid interface and increase the Gibbs
film elasticity25,26 E
E)
Figure 1. Line formation. (a) Cartoon of the geometry showing
fluid sandwiched between two parallel plates. Surfactant molecules
tend to collect at the interface. (b) BSA line formation self-pinning.
The clump at the tip of the line is the self-pinning point made up
of a BSA clump that precipitated out. The dark area in the upper
right is the evaporating liquid. Note that the lines are remarkably
straight over small distances. (c) SEM image of two BSA lines
that are pulled together to form a junction. In foams, the junction
is called a plateau and the radiating arms are called lamellae.
The growth rate of lines was measured on the scale of a
few minutes, and it varied linearly with time (Figure 2c).
This was true, irrespective of the solution used. We believe
that the rate-determining factor is simply the evaporation rate,
which, if constant, makes the contact line recede at constant
velocity.
Besides lines, other patterns are also present. Two nearby
lines can coalesce if nonuniform contact-line motion forces
them closer, and this leads to pronglike structures (Figures
1c and 3a). The angle between the arms of the prong is found
to be close to 120° every time, which represents an energy
minimum.21 Bubbles in the solution lead to the formation of
structures shaped like “lollipops”. Figure 3b-e shows a
sequence of images showing the formation of lollipops. The
272
dσ
d ln A
(1)
where σ is the surface tension and A is the surface area.
Growth of a line requires an increase in surface area, and
surface tension forces oppose this change. In the presence
of surfactants, an increase in area is also accompanied by
the diffusion of surfactants from the bulk to the surface,
which compensates for the energy loss due to change in area,
making the process more energetically favorable.
There are other similarities between these lines and foams,
junctions between two wires, described earlier, are similar
to structures formed when two bubbles coalesce; the junction
is called the plateau, and the bubble films leading to it are
called lamellae1 (Figure 1c). When two lines combine, they
tend to suck in colloidal particles (see Supporting Information
video 2). This behavior is very similar to that of a foam
bubble plateau; the negative pressure in the plateau tends to
suck in fluids and is one of the main mechanisms for drainage
of bubbles. Also like soap films, the lines are metastable
and increase in viscosity (for instance, by the concentration
of solutes) and stability.
The lines formed by BSA (Figure 4a) are spaced randomly,
depending on self-pinning points at the boundary. Instead,
we would like to be able to exert more control over areas
where lines are created. This is possible by making artificial
Nano Lett., Vol. 6, No. 2, 2006
Figure 2. Flow patterns, shape, and growth rate of lines. (a) A line formed by BSA solution with 200-nm fluorescent microspheres. (b)
Parabolic fit for the shape of the curve joining the line to the bulk fluid. (c) Line growth measured over a period of a few minutes is linear
and depends only on how fast the receding contact line moves. All of these experiments were done at 23 °C and 33% humidity. (d) A
cartoon of the flow patterns that are set up with the contact line receding and the lines growing. Please see the Supporting Information for
a video of the flow patterns with quantum dots.
pinning points using photolithography. Various shapes were
created on a silicon wafer surface using photoresist SU8,
including squares, circles, and triangles of different sizes.
Spinning photoresist at varying speeds varied the height of
these shapes. A cover glass, placed on top of the resist,
provided a viewing window to see the motion of the contact
line. As the contact line recedes, lines are formed as expected
(Figure 5a). The shape of the pinning point does not seem
to matter; circles, squares, and triangles all produce single
lines (Figure 5a-c). Specially designed structures with two
prongs result only in a single line. Our conclusion is that
the shape of the pinning point does not play an important
role in this system, as long as the fluid continues to touch
both surfaces. Moreover, the width of the line does not
depend on the pinning point. Pinning structures can be much
larger that the width of the line. Greater distance between
the two parallel surfaces leads to wider lines. When the
contact line moves across two pinning points, it leaves behind
line deposits that connect the two pinning points (Figure 5c).
This provides a way to make interconnection wires.
The creation of pinning points allows precise control over
the location of deposited lines. Because the pinning points may
be much larger than the line widths, photolithography does
Nano Lett., Vol. 6, No. 2, 2006
not need to have the same resolution as the structures that are
produced by the process. Additionally, photolithography allows
us to steer evaporation in the direction we want. Besides using
evaporation, we also attempted dip-coating27 of substrates
with pinning points; but we were unable to form lines.
With the ability to create pinning points, the next step was
to test other foaming surfactants; we find that sodium dodecyl
sulfate (SDS), sodium oleate, Triton X-100 (octyl phenol
ethoxylate), zonyl fluoro-surfactants FSN and FS300 (DuPont), and tween-20 all cause formation of continuous lines.
The most stable lines had high concentrations of surfactants,
exceeding the critical micelle concentration. Coffee, known
to form ring stains when evaporating from a drop,2 will form
lines in this geometry too. Thus, we believe that any foaming
surfactant can form lines in this geometry.
The lines formed by these surfactants are different from
BSA lines. First, there is no self-pinning and pinning points
have to be artificially created to obtain lines. Second, soap
films are classified as rigid or mobile24 and compared to
BSA, these surfactants form lines that tend to be less rigid
and more fluidlike.28 This also explains the formation of
droplets in place of lines, if it is cut off from the contactline boundary, stopping flow (Figure 4b). The lines formed
273
Figure 3. Quantum dots and other shapes. (a) When the contact line evaporates nonuniformly, two nearby lines can meet. This results in
a prong formation. The angle between the three lines is usually close to 120°. This solution contained quantum dots that emit at a peak
wavelength of 565 nm. (b-e) A bubble at the edge of the contact line results in the formation a “lollipop” shape. The pictures were taken
at t ) 0, 9, 18, and 27 min. Here the solution contains quantum dots that emit at a peak wavelength of 605 nm.
Figure 4. BSA and other surfactants. (a) SEM image of BSA
forming a junction after drying. The line consists of a thin layer of
BSA with a wall at the center. (b) A line of Triton X-100 surfactant
breaking into droplets when flow was stopped. Unlike BSA, this
surfactant forms nonrigid lines.
are initially wide, tens of micrometers and then they tend to
thin down, eventually becoming drops, when flow stops.
With BSA, the rigidity slows down droplet formation by
Rayleigh instability19 once flow stops. Scanning electron
micrographs of the BSA lines after drying show a dark and
274
bright region (Figures 1c and 4a). We believe that the dark
region is a thin film on the surface and the bright region is
the BSA line. The base of the line is wider than the center.
Lines can be made more rigid by simply adding other solutes
or colloids, increasing viscosity, and slowing formation of a
series of drops. Thus, adding solutes allows other surfactants
to form stable lines similar to BSA.
To test whether we can insert other kinds of colloids into
the lines, besides quantum dots, we added microspheres to
the solution. The beads used were made of polystyrene or
silica. The surface was either plain or with an amine/carboxyl
group. The beads were 50 nm to 3 μm in diameter. We find
that beads enter the lines; this is confirmed both by
visualizing using fluorescent beads and by scanning electron
micrographs (Figure 5d and e). Smaller microspheres had a
greater tendency to precipitate out of the receding contact
line. Larger beads tend to form lines of the best quality. In
BSA solution with smaller beads, we observe the phenomena
of bridging, where the line is bridged by a bead. The BSA
line formed in this case can be smaller than the size of the
bead (Figure 5e).
In conclusion, we have demonstrated a new way to create
and control line patterns using capillary flow. This method
is quite general, and may be used for creating a variety of
lines. The fact that different types of surfactants can be used
provides considerable flexibility for applications. Also, the
patterning depends on flows, largely independent of the
solute, and a variety of colloidal particles and protein
molecules may be used, demonstrated by making lines of
BSA, quantum dots, and microspheres. We believe that this
method will find use in many future micro- and nanofabrication procedures. Further work on this subject will involve
testing more surfactants, colloids, and substrates as well as
developing a complete theory for the process.
Nano Lett., Vol. 6, No. 2, 2006
Figure 5. Various types of pinning points, surfactants and microspheres. (a) Circular pinning points with a solution containing BSA. (b)
Triangular pinning points with a solution containing surfactant Triton X-100. (c) A quantum-dot line forming between two pinning points.
This could provide a way of making interconnect wires. (d) SEM image of 2-μm silica beads in a aqueous Zonyl FSN solution that have
assembled into a line. There are two defects in the periodic structure with one bead out of place and another missing. (e) Small-sized beads
can sometimes act as bridge between lines of BSA. Small particles are often antifoaming agents, and this is one of the mechanisms by
which they operate.
Methods. Materials and Instruments. Beads were obtained
from Bangs Laboratories (Fisher, IN) or PolySciences Inc.
(Warrington, PA), borate buffer kit from Pierce Biotechnology (Rockford, IL), and strepavidin-coated quantum dots
from Quantum Dot Corporation (Hayward, CA). All other
chemicals were obtained from Sigma Aldrich (St. Louis, MO)
and used as obtained. Most experiments used no. 1 Cover
glass from VWR (West Chester, PA) or silicon test wafer
from Silicon Quest International (Santa Clara, CA). SU8
Nano Lett., Vol. 6, No. 2, 2006
2010 and 2025 photoresist from Microchem (Newton, MA)
was spun at different speeds to obtain pinning points of
various sizes. Imaging was done with a Nikon TE200
inverted microscope (fluorescence imaging) and a Zeiss
MAX ERB (bright field imaging). SEM imaging was done
using Hitachi S4500 or FEI Sirion.
Experimental Protocols and Imaging. All experiments
were done at room temperature (∼23°). Borate buffer at pH
8 was used with BSA protein. The humidity was kept
275
constant in some experiments by the use of a special humidity
chamber. A typical experiment involved putting a 1-μL drop
on a substrate that was then covered with another surface
and then observed under a microscope. RCA cleaning
procedure 129 was done on cover glass or silicon if we needed
to make it more hydrophilic. We measured the change in
weight of the samples to check if the evaporation rate was
constant and found it to be so for substantial periods of time.
Acknowledgment. We thank Heun Jin Lee for helping
with optics, Koichi Okamoto for SEM training, and Chris
Lacenere, Mike Van Dam, Todd Squires, Sandra Troian,
Michael Cross, and Steve Quake for helpful discussions.
K.M.C. thanks Caltech for a summer undergrad research
fellowship. Funding for this work was provided by the
DARPA Optofluidics Center.
Supporting Information Available: Video 1 shows flow
patterns and line formation. Line-pattern formation in a
solution of quantum dots and BSA. The pinning of contact
lines creates a flow pattern, which pumps quantum dots into
the line. Solutes can also be seen moving parallel to the
contact line as it recedes. This video has been sped up 2x
compared to real time. Video 2 shows two lines forming a
junction. Because of nonuniform evaporation, two lines may
be brought together. They form a “plateau” that sucks in
more solutes. The end result is a pronglike structure. This
material is available free of charge via the Internet at http://
pubs.acs.org.
References
(1) Isenberg, C. The Science of Soap Films and Soap Bubbles; Dover
Publications (originally printed by Tieto, Ltd. Clevedon, Avon,
England): New York, 1992.
276
(2) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.;
Witten, T. A. Nature 1997, 389, 827-829.
(3) Cross, M. C.; Hohenberg, P. C. ReV. Mod. Phys. 1993, 65, 8511112.
(4) Whitesides, G. M.; Grzybowski, B. Science 2002, 295, 2418-2421.
(5) Troian, S. M.; Wu, X. L.; Safran, S. A. Phys. ReV. Lett. 1989, 62,
1496-1499.
(6) Kopfsill, A. R.; Homsy, G. M. Phys. Fluids 1987, 30, 2607-2609.
(7) Fan, F. Q.; Stebe, K. J. Langmuir 2004, 20, 3062-3067.
(8) Vlasov, Y. A.; Bo, X. Z.; Sturm, J. C.; Norris, D. J. Nature 2001,
414, 289-93.
(9) Bensimon, D.; Simon, A. J.; Croquette, V.; Bensimon, A. Phys. ReV.
Lett. 1995, 74, 4754-4757.
(10) Thompson, D. A. W. On Growth and Form, Complete Revised
Edition; Dover Publications: New York, 1992.
(11) Tang, Z. Y.; Kotov, N. A. AdV. Mater. 2005, 17, 951-962.
(12) Myers, T. G. Siam ReV. 1998, 40, 441-462.
(13) Scriven, L. E.; Sternling, C. V. Nature 1960, 187, 186-188.
(14) Dussan, E. B. Annu. ReV. Fluid Mech. 1979, 11, 371-400.
(15) Krotov, V. V.; Rusanov, A. I.. Physicochemical Hydrodynamics of
Capillary Systems; Imperial College Press: London, 1999; p 475.
(16) Binks, B. P. Curr. Opin. Colloid Interface Sci. 2002, 7, 21-41.
(17) Murray, B. S.; Ettelaie, R. Curr. Opin. Colloid Interface Sci. 2004,
9, 314-320.
(18) de Gennes, P. G. ReV. Mod. Phys. 1985, 57.
(19) Rayleigh, Scientific Papers; Cambridge Press: Cambridge, U.K.,
1964; Vol. 1-6.
(20) Raphael, E.; Degennes, P. G. J. Chem. Phys. 1989, 90, 7577-7584.
(21) Almgren, F. J.; Taylor, J. E. Sci. Am. 1976, 235, 82-93.
(22) Pugh, R. J. AdV. Colloid Interface Sci. 1996, 64, 67-142.
(23) Dennis Weaire, S. H. The Physics of Foams; Oxford University
Press: Oxford, U.K., 1999.
(24) Mysels, K. S. K.; Frankel, S. Soap Films, Studies of their Thinning;
Pergamon Press: New York, 1959.
(25) Raphael, E.; Joanny, J. F. Europhys. Lett. 1993, 21, 483-488.
(26) Rusanov, A. I.; Krotov, V. V. Colloid J. 2004, 66, 204-207.
(27) Ruschak, K. J. Annu. ReV. Fluid Mech. 1985, 17, 65-89.
(28) Koehler, S. A.; Hilgenfeldt, S.; Weeks, E. R.; Stone, H. A. Phys.
ReV. E: Stat. Nonlin. Soft Matter Phys. 2002, 66, 040601.
(29) Handbook of Semiconductor Cleaning Technology; Kern, W., Ed.;
Noyes Publishing: Park Ridge, NJ, 1993.
NL0522678
Nano Lett., Vol. 6, No. 2, 2006