A method to shape thin polymer films into periodic array of lenses is presented. A liquid layer placed on top of a much thinner polymer film is exposed to a transverse temperature gradient. The upper liquid layer undergoes the short-wavelength Bénard-Marangoni instability, which leads to periodic shear stresses at the liquid-liquid interface and corresponding interfacial deformations. The structures formed are solidified by curing with ultraviolet light. In comparison to previously reported single-layer patterning techniques, the presented method achieves structures of very high horizontal planform symmetry (highly ordered structures). Furthermore, other shapes of technical interest can be easily fabricated by engineering the temperature distribution at the liquid-gas interface.

1.
K.
Ziemelis
, “
The future of microelectronics
,”
Nature
406
,
6799
(
2000
).
2.
H.
Sirringhaus
,
T.
Kawase
,
R. H.
Friend
,
T.
Shimoda
,
M.
Inbasekaran
,
W.
Wu
, and
E. P.
Woo
, “
High-resolution inkjet printing of all-polymer transistor circuits
,”
Science
290
,
2123
2126
(
2000
).
3.
T. R.
Hebner
,
C. C.
Wu
,
D.
Marcy
,
M. H.
Lu
, and
J. C.
Sturm
, “
Ink-jet printing of doped polymers for organic light emitting devices
,”
Appl. Phys. Lett.
72
,
519
521
(
1998
).
4.
J.
Kim
,
H.
Oh
, and
S. S.
Kim
, “
Electrohydrodynamic drop-on-demand patterning in pulsed cone-jet mode at various frequencies
,”
J. Aerosol Sci.
39
,
819
825
(
2008
).
5.
L.
Peng
,
Y.
Deng
,
P.
Yi
, and
X.
Lai
, “
Micro hot embossing of thermoplastic polymers: A review
,”
J. Micromech. Microeng.
24
,
013001
(
2014
).
6.
S. Y.
Chou
,
L.
Zhuang
, and
L.
Guo
, “
Lithographically induced self-construction of polymer microstructures for resistless patterning
,”
Appl. Phys. Lett.
75
,
1004
(
1999
).
7.
E.
Schäffer
,
S.
Harkema
,
M.
Roerdink
,
R.
Blossey
, and
U.
Steiner
, “
Thermomechanical lithography: Pattern replication using a temperature gradient driven instability
,”
Adv. Mater.
15
,
514
517
(
2003
).
8.
M.
Dietzel
and
S. M.
Troian
, “
Mechanism for spontaneous growth of nanopillar arrays in ultrathin films subject to a thermal gradient
,”
J. Appl. Phys.
108
,
074308
(
2010
).
9.
E.
McLeod
,
Y.
Liu
, and
S. M.
Troian
, “
Experimental verification of the formation mechanism for pillar arrays in nanofilms subject to large thermal gradients
,”
Phys. Rev. Lett.
106
,
175501
(
2011
).
10.
M.
Dietzel
and
S. M.
Troian
, “
Thermocapillary patterning of nanoscale polymer films
,” in
Materials Research Society Symposium Proceedings
,
2009
, Vol.
1179
.
11.
D.
Merkt
,
A.
Pototsky
,
M.
Bestehorn
, and
U.
Thiele
, “
Long-wave theory of bounded two-layer films with a free liquid-liquid interface: Short- and long-time evolution
,”
Phys. Fluids
17
,
064104
(
2005
).
12.
D.
Semwogerere
and
M. F.
Schatz
, “
Evolution of hexagonal patterns from controlled initial conditions in a Bénard-Marangoni convection experiment
,”
Phys. Rev. Lett.
88
,
054501
(
2002
).
13.
Q.
Ouyang
and
H. L.
Swinney
, “
Transition from a uniform state to hexagonal and striped Turing patterns
,”
Nature
352
,
610
612
(
1991
).
14.
P.
Cerisier
,
C.
Jamond
,
J.
Pantaloni
, and
C.
Pérez Garcia
, “
Stability of roll and hexagonal patterns in Bénard-Marangoni convection
,”
Phys. Fluids
30
,
954
(
1987
).
15.
G.
Widawski
,
M.
Rawiso
, and
B.
Francois
, “
Self-organized honeycomb morphology of star-polymer polystyrene films
,”
Nature
369
,
387
389
(
1994
).
16.
L.
Cui
and
Y.
Han
, “
Honeycomb pattern formation via polystyrene/poly(2-vinylpyridine) phase separation
,”
Langmuir
21
,
11085
11091
(
2005
).
17.
Y.
Cai
and
B. Z.
Newby
, “
Marangoni flow-induced self-assembly of hexagonal and stripelike nanoparticle patterns
,”
J. Am. Chem. Soc.
130
,
6076
6077
(
2008
).
18.
H.
Yabu
and
M.
Shimomura
, “
Preparation of self-organized mesoscale polymer patterns on a solid substrate: Continuous pattern formation from a receding meniscus
,”
Adv. Funct. Mater.
15
,
575
581
(
2005
).
19.
Z.
Mitov
and
E.
Kumacheva
, “
Convection-induced patterns in phase-separating polymeric fluids
,”
Phys. Rev. Lett.
81
,
3427
3430
(
1998
).
20.
I.
Nejati
,
M.
Dietzel
, and
S.
Hardt
, “
Conjugated liquid layers driven by the short-wavelength Bénard-Marangoni instability: Experiment and numerical simulation
,”
J. Fluid Mech.
783
,
46
71
(
2015
).
21.
M. F.
Schatz
and
G. P.
Neitzel
, “
Experiments on thermocapillary instabilities
,”
Annu. Rev. Fluid Mech.
33
,
93
127
(
2001
).
22.
S. J.
VanHook
,
M. F.
Schatz
,
J. B.
Swift
,
W. D.
McCormick
, and
H. L.
Swinney
, “
Long-wavelength surface-tension-driven Bénard convection: Experiment and theory
,”
J. Fluid Mech.
345
,
45
78
(
1997
).
23.
K. A.
Smith
, “
On convective instability induced by surface-tension gradients
,”
J. Fluid Mech.
24
,
401
414
(
1966
).
24.
A.
Thess
and
M.
Bestehorn
, “
Planform selection in Bénard-Marangoni convection: l hexagons versus g hexagons
,”
Phys. Rev. E
52
,
6358
6367
(
1995
).
25.
E.
Schäffer
,
S.
Harkema
,
R.
Blossey
, and
U.
Steiner
, “
Temperature-gradient-induced instability in polymer films
,”
Europhys. Lett.
60
,
255
261
(
2002
).
26.
A. A.
Golovin
,
A. A.
Nepomnyashchy
, and
L. M.
Pismen
, “
Interaction between short-scale Marangoni convection and long-scale deformational instability
,”
Phys. Fluids
6
,
34
(
1994
).
27.
A.
Oron
,
S. H.
Davis
, and
S. G.
Bankoff
, “
Long-scale evolution of thin liquid films
,”
Rev. Mod. Phys.
69
,
931
980
(
1997
).
28.
J.
Arai
,
H.
Kawai
, and
F.
Okano
, “
Microlens arrays for integral imaging system
,”
Appl. Opt.
45
,
9066
9078
(
2006
).
29.
M.-H.
Wu
and
G. M.
Whitesides
, “
Fabrication of two-dimensional arrays of microlenses and their applications in photolithography
,”
J. Micromech. Microeng.
12
,
747
(
2002
).
30.
J.
Tseng
,
Y.
Chen
,
C.
Pan
,
T.
Wu
, and
M.
Chung
, “
Application of optical film with micro-lens array on a solar concentrator
,”
Sol. Energy
85
,
2167
2178
(
2011
).
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