hal-00158338, version 1 - 28 Jun 2007
Slippery or sticky ! Control of wrinkling patterns by selective adhesion
Hugues Vandeparre
1
, Julien L´eopold`es
1
, Christophe Poulard
1
, Sylvain
Desprez
1
, Gwennaelle Derue
1
, Cyprien Gay
2
, and Pascal Damman
1∗
1
Laboratoire de Physicochimie des Polym`eres, Centre d’Innovation et de Recherche en Mat´eriaux Polym`eres (CIRMAP),
Universit´e de Mons Hainaut, 20, Place du Parc, B-7000 Mons, Belgium
2
Centre de recherche Paul-Pascal – CNRS UPR 8641,
Universit´e de Bordeaux 1, 115 avenue Schweitzer, F-33600 Pessac, France
(Dated: June 28, 2007)
Wrinkling patterns at the metallized surface of thin polymer films are shown to be sensitive to the
sticky or slippery character of the polymer/substrate interface (titanium coating, polystyrene film
and coated silicon substrate). Selective prefered wrinkle orient ation and amplitude are achieved.
Existing theoretical models are expand ed to specific boundary conditions (adhesive vs slippery) and
rationalize these observations.
PACS numbers: 47.54.-r, 46.32.+x, 68.55.-a
The formation of wrinkles is an ubiquitous phe-
nomenon in Na tur e [1]. In most cases, wrinkles appea r
when a rigid inextensible thin layer, forming the top-
coat of an elastic foundation, is subjected to compres-
sive forces. This rather simple concept was adapted
to synthetic systems only recently [2, 3, 4, 5, 6, 7,
8, 9, 1 0, 11, 12]. Although a delicate control of the
wrinkling morphogenesis could be extremely useful for
many applications in various contrasting domains such
as optics[2, 13], microfluidics[14], cellular adhesion[15],
. . . Thermal compressive stress is one of the easiest way
to implement wrinkling but yields disor dered patterns
(labyrinthal morphology) due to the high symmetry o f
the stress field. Three strategies were proposed in the
literature to self-or ganize the wrinkles: i) engraving the
foundation or the substrate with a bas-r e lief [2, 4, 6, 11];
ii) tailoring the flexural rigidity of the topmost part of the
foundation [5, 12], iii) guiding the w rinkle orientation by
pressing a non-planar template against the upp e r skin
during the wrinkle formation [8].
In the present Letter, we will describe an original and
easy method to control the spatial layout of wrinkles and
thus obtain objects with patterned roughnesses , which
could be useful in a number of applications (especially
in biophysics areas). To do this, we tune the boundary
conditions at the polymer/substrate interface. This is
achieved by using chemically patterned substrates with
highly contrasted surface free energies (γ), easily pro-
duced by microcontact printing of alkanethiols on gold
substrates [16]. Considering the relation between the
γ’s and adhesion, these surfaces are e xpected to show
well-defined slippery and sticky domains. At first sight,
however, it could se em unrealistic to imagine that the
chemical nature of the substrate could affect the ela stic
instability of the skin through a micron-thick polymer
film. This may be the reason why this possibility has not
been mentioned in the literature so far. In addition, to
explain our original variant of the experiments we will,
in this Letter, also expand the existing mechanisms and
models described in the litterature to take into account
the adhesion at the poly mer/substrate interface.
The samples under study consist of a thin layer of high
molecular weight polystyrene (PS, M
n
≈ 10
6
Da) de-
posited on bare silicon (Si) substrates or chemically pat-
terned gold substrates and further c apped with a thin
titanium layer (Ti). The PS films were obtained by spin-
coating toluene solutions directly onto the different sub-
strates to a thickness ranging from 50 to 10 00 nm, as mea-
sured by ellipsometry. The Ti layer was dep osited onto
the p olymer surface by thermal evaporation at 0.1 nm/s
to a thickness ra nging from 10 to 20nm. The bare Si sub-
strates (1 00) are first cleaned by snowjet and then by ul-
trasonic treatment in chloroform and methanol for 5 min
each. The golden (Au) substrates are prepared by evap-
oration of a 95 nm thick layer of gold on a Silicon (10 0)
wafer that has been precoated with 5 nm of chromium.
These substrates ar e then cleaned by snowjet and by
UV/ozone for 30 min. Finally, heterogeneous samples
were created by microcontact printing of octadecanethiol
chemical lines. For both systems, wrinkling is induced by
heating the bilayer samples at 130
◦
C, i.e., 30
◦
C higher
than the gla ss transition temperature, T
g
, o f the poly-
mer layer for a short period of time, ca. 1 min. This
temper ature is reached at a very high rate (120
◦
C/min).
The resulting metal surface structures were examined by
optical microscopy (OM) and Atomic Fo rce Microscopy
(AFM).
Metal/polymer/substrate trilayers have been re-
ported [9, 10, 11] to exhibit wrinkling when heated above
the T
g
of the polymer (e.g., polystyrene). Conce rning the
origin of wrinkling, despite the general agreement on the
impo rtance of compressive stresses arising from the mis-
match in expansion coefficients for the different layers,
there is some debate [9, 10, 11] on the exact mechanism.
In the following, we pres e nt an original variant of the
exp eriment and show in detail that the mechanism de-
scribed by Okayasu et al. [11] and some aspects of the
model by Cerda and Mahadevan [17] can be expanded to
2
FIG. 1: Op tical Micrographs of wrinkled surfaces obtained
with a 20 nm thick metal layer and a 60 nm polymer layer
on chemically patterned gold substrates, after annealing at
130
◦
C . Alternating stripe widths are (a) 5µm/5µm, (b)
10µm/10µm.
account for the observed effect of boundary conditions a t
the polymer/ substrate interface.
In contrast to pre vious studies made on bare silicon,
we focus on substrates with alternating areas of high
and low adhesion with PS. Thos e areas are stripes (of
width Λ) of either bare gold (adhesive regions ) or oc-
tadecanethiol treated gold (ODT, slippery regions). Sur-
prisingly, the kinetics of wrinkle growth differs on both
stripes. Even though the temperature ramp imposed to
the sample is rather fast (120
◦
C/min), the wrinkles de-
velop first above slippery regions (around 125
◦
C), and
somewhat later above adhesive regions (around 130
◦
C).
As shown in Figure 1, the wrinkle morphology and ori-
entation are a lso markedly different between sticky and
slippery regions: i) observed patterns combine the sub-
strate periodicity (Λ) and wrinkles ”natural” wavelength
(λ), ii) the wrinkles are pre ferentially aligned parallel to
the chemical stripes on slippery regions (ODT) and per-
pendicular to the stripes on adhesive regions (Au), and
iii) the wrinkle amplitude A is smaller above adhes ive
(Au) regions (ca. 15 nm) than above slippery (ODT)
regions (ca. 25 nm).
Note that such una mbiguous experimental results can-
not b e explained by the mechanisms and models pro-
posed recently [9, 11, 17] and highlight the need fo r a
more thorough understanding of wrinkling. Before dis-
cussing the formation of wrinkles on heterogeneous sur-
faces, we will first discuss what could be the influence
of adhesion (i.e., sticky vs. slippery substrates) on the
growth of wrinkles for homogeneous substrates.
For such trilayer systems, the origin o f the wrinkles is
usually related to the mismatch in thermal expansion co-
efficients between the polymer foundation and the thin
metal layer. But this, by itself, does not constitute an ex-
planation for the wrinkling phenomeno n, as pointed out
by Yoo and Lee [9]. Indeed, the (linear ) expansion coeffi-
cient of PS (α
P S
∼ 5 10
−4
K
−1
above T
g
) is much large r
than that of Ti (α
T i
∼ 8 10
−6
K
−1
). Hence, we could
na
¨
ively consider that upon heating the system above the
PS glass transition temperature T
g
, the Ti membrane
should be set under tension rather than under c ompres-
sion.
In fa c t, a s suggested by Okayasu et al.[11], there is also
a thermal expansion mismatch between the Ti membrane
and the Si substrate (α
Si
∼ 3 10
−6
K
−1
), and this mis-
match, by contrast with the Ti/PS mismatch, favours
the compression of the Ti membrane. Paradoxically,
although the Ti/Si mismatch is much weaker than the
Ti/PS mismatch, we will show that it is dominant and
causes the Ti membrane to buckle.
Without any surrounding material, each layer, de-
picted on Figure 2a, would expand isotropically by a fa c -
tor ∆
i
(T ) =
R
T
T
0
α
i
dT (Figure 2b, left), where T
0
is the
reference temperature, at which the system is stress-free,
namely room temperature (if we neg lec t internal stre sses
due to solvent evaporation), i representing the metal, the
polymer and the s ubstrate. The elastic mo duli of the Ti
membrane and of the Si substr ate are obviously much
larger than that of the PS layer, especially above T
g
:
E
s
∼ E
m
≫ E
p
. The thicknesses also differ substan-
tially: H
s
≫ H
p
> h
m
. As a result, the Si substrate is
by far the mo st prominent layer in the thermal expan-
sion process: not only will the overall linear (in-plane)
expansion of the trilayer system almost exactly match
the spontaneous va lue for the substra te (∆
s
), but the
high flexural substrate rigidity (proportio nal to E
s
H
3
s
)
will hinder any attempt to relieve stresses through bend-
ing of the trilaye r as a whole. As a result, the metal
membrane is co mpressed (expansion 1 − ∆
m
+ ∆
s
< 1)
with in-plane compressive stress 2 E
m
(∆
m
− ∆
s
) = 2E
m
δ
(while there is no stress in the out-of-plane direction) and
elastic energ y U
c
∼ 2E
m
h
m
δ
2
.
The random wrinkling pattern observed upon heating
our sa mples has a well-defined characteristic wavelength
(see inset in Figur e 3) which is much larger than the
PS film thickness (λ ≫ H
p
). To determine the criterion
for the se lec tion of the wr inkles wavelength, we expand
the scaling energetic approach proposed by Cerda and
Mahadevan [17]. In the presence of wrinkling, thanks
to the corresponding increase in curvilinear length, the
membrane compression is partly relieved. It is reduced
by π
2
A
2
/λ
2
for a sinusoidal membrane deformation with
amplitude 2A. This obviously lowers the co mpression
3
FIG. 2: Schematic representation of wrinkle formation on a
bare substrate. a) Layered system prior to heating. b) Upon
heating, (left) expansion that would be obtained for each layer
independently in the absence of any surrounding material and
(right) distribution of the compressive stresses in the trilayer
prior to wrinkling. c) Deformation profile in the polymer layer
induced by wrinkling in adhesive (left) and slippery regions
(right).
elastic energ y :
U
c
∼ 2E
m
h
m
(δ − π
2
A
2
/λ
2
)
2
< 2E
m
h
m
δ
2
(1)
Additionally, the energy of the system also includes
the membrane bending ener gy U
b
and the polymer elas-
tic energy U
p
(the foundation must follow the sinusoidal
deformation of the membrane).
The bending energy of the Ti layer, expressed per unit
surface, is determined [17] by the membrane curvature
(typically A/λ
2
):
U
b
∼ E
m
h
3
m
A
λ
2
2
(2)
where E
m
h
3
m
is the order of mag nitude of the membrane
bending rig idity.
As we shall now see, the elastic energy stored in the
polymer foundation due to the s inusoidal membrane de-
formation depends on boundary conditions. Let us con-
sider two limiting cases: no-slippage (sticky) and full-
slippage (slippery), assuming that the true mechanical
behavior at the polymer/substrate interface will be some-
where in between (more sticky on bare Au and more slip-
pery on ODT). Be c ause the polymer is incompressible,
10
3
10
4
1
2
3
4
h
m
= 15 nm
h
m
= 20 nm
m)
h
m
.H
p
(nm
2
)
10 m
0,5
FIG. 3: Evolution of the wavelength versus the product of the
metal and polymer thickness for t rilayers Ti/PS/Si heated at
130
◦
C. The inset shows OM image of a wrinkled surface
obtained with a 15 nm thick metal layer and a 350 nm thick
polymer layer (the FFT of a broad sample area, 10 times
larger than the OM image is also shown).
the membrane vertical displace ment induces horizontal
displacements in the polymer layer. Although the maxi-
mum horizontal displacement in the polymer layer is in-
dependent of boundary conditions for a given amplitude
and wavelength (u ∼ Aλ/H
p
), the displacement profiles
differ, as sketched on Fig. 2c: the maximum displacement
is located at mid-height in the case of a sticky interface,
while it is loc ated at the polymer/substrate interface if
it is slippery. As a result, the shear defor mations ∂u/∂z
(which are on the order of u/H
p
∼ Aλ/H
2
p
) are on aver-
age twice as large in the sticky case than in the slippery
case. Correspondingly, the elastic energy per unit surface
area U
p
∼ E
p
R
(∂u/∂z)
2
dz is larger by a factor 4 in the
sticky case. In the following expression for the polymer
elastic energy, we therefore include a numerical factor K,
where it is understood that K
stick
/K
slip
= 4:
U
p
= KE
p
H
p
Aλ
H
2
p
2
(3)
Note that in the opposite case of a thick polymer film
(λ ≪ H
p
), H
p
must be replaced by λ in the above ex-
pression [17] and the b oundary condition at the lower
interface has no impact.
Minimization of the total e nergy U
c
+ U
b
+ U
p
yields
the wavelength, and the critical deformation, δ
c
:
λ ∼
1
K
1/6
(h
m
H
p
)
1/2
E
m
E
p
1/6
(4)
δ
c
∼ K
1/3
h
m
H
p
E
p
E
m
1/3
(5)
As shown in Figure 3, the observed dependence of the
wrinkle wavelength on the metal and polymer thicknesses
is adequately described by the allometric relation λ ∝
(h
m
H
p
)
1/2
given by (Eq. 4).
4
Let us now r eturn to heterogeneous substrates with
slippery and sticky stripes. The most striking result of
the model is probably the influence of the boundary con-
ditions on the critical stress. Indeed, as δ
c
is pro portional
to K
1/3
(see Eq. 5), the threshold compression for wrin-
kling is expected to be lower for slippery substrates (such
as ODT) than for adhesive ones (such as bare Au).
The fact that wrinkles appear first in the slippery re-
gions will now help us to understand: i) the prefered
wrinkle orientation and ii) the differe nce in wrinkle am-
plitudes in both regions. Before wrinkles appear (say,
at 120
◦
C), the in-plane compressive stress in the mem-
brane is isotropic. Once wrinkles appear in the slip-
pery regions (at ca. 125
◦
C), the compressive stress is
partly relaxed there. The (yet undeformed) membrane
in the sticky regions now tends to expand laterally at the
exp ense of the wrinkled membrane in the slippery re-
gions. Hence, at the border between slippery and sticky
stripes, the membrane is s lightly displaced towards the
slippery regions (see Fig. 4). In the case of rather narrow
stripes, this displacement is expected to be on the order
of [∆
m
(T ) − ∆
s
(T )]Λ = δ(T )Λ. This slight displacement
favours wrinkles oriented parallel to the stripes above the
slippery regions, while the membr ane diplacement in the
direction of the stripes remains unnoticable. By contrast,
when wrinkles later appear in the sticky regions (at ca.
130
◦
C), the membrane displacement at the stripe bor -
der causes the compress ive stress to be weaker in the di-
rection perpendicular to the stripes than in the parallel
direction. The new wrinkles thus tend to develop per-
pendicular to the stripe direction. In addition, the slight
membrane displacement at the stripe border induces a
stronger compression in the slippery regions, resulting in
a larger wrinkle amplitude [17], as indeed observed, se e
Fig. 1.
We have expla ined in detail what could be the origin
of the in-plane compressive stress that induces wrinkling
in thin metal/po ly mer bilayers deposited on a thick sub-
strate. We also showed a new and simple approach to
i) orient wrinkling patterns in thin polymer/metal bilay-
ers by chemically patterning the substrate with regions of
high and low adhesion and ii) elaborating patterns with
contrasted roughnesses. In this way, a mere change in
the surface tension of b oth slippery and sticky regions
makes it possible to obtain a well-contr oled roughnes s
ratio between both areas . Such controled roughness pat-
terns would be useful in a number of areas, including
biophysics. Existing models were expanded to rational-
ize the observed impact of boundary conditions at the
polymer/substrate interface on surface wrinkling.
P.D. and H.V. thank Dr. A. Boudaoud, B. Audoly
and R. Laz z aroni for stimulating discussions. The a u-
thors thank J. Piotte for his contribution. The Bel-
gian National Fund For Scientific Resear ch (FNRS), the
FRIA and the Walloon region (research project COR-
RONET) are acknowledged for financial support. P.D.
FIG. 4: Schematic representation of the slight membrane dis-
placement (and corresponding deformation of the polymer
layer) when wrinkles app ear above slippery regions. This dis-
placement induces t he observed prefered wrinkle orientation
above slippery stripes (and later the observed opposite pre f-
ered orientation above sticky stripes). It is also at the origin
of the contrasted wrinkle amplitude between both types of
regions.
is a Research Associate of the FNRS. C.G. gratefully ac-
knowledges support from the FNRS and hospitality from
LPCP.
∗
Electronic address: pascal.damman@umh.ac.be
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