Surface Science 540 (2003) 355–362
www.elsevier.com/locate/susc
Contact angle hysteresis on nano-structured surfaces
S.M.M. Ramos a,*, E. Charlaix a, A. Benyagoub b
a Laboratoire de Physique de la Mati�eere Condens�eee et Nanostructures (UMR CNRS 5586) Universit�ee Claude Bernard LYON I,
43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, Franceb CIRIL, B.P. 5133, F-14040 Caen Cedex 5, France
Received 7 March 2003; accepted for publication 3 June 2003
Abstract
We present results from an experimental study on the phenomenon of contact angle hysteresis on solid surfaces
decorated by a random array of nanometric hollows. For weak values of the areal density of defects /d, the hysteresis Hincreases linearly with /d. This evolution is described by a pinning–depinning process of the contact line by individual
defects. At higher values of /d, a collective pinning effect appears and H decreases with increasing /d. In the linear
regime, our experimental results are compared to theoretical predictions for contact angle hysteresis induced by a single
isolated defect on the solid surface. We suggest that the crossover from the individual to the collective pinning effects
could be interpreted in terms of an overlapping of wetting cross sections. Finally, we analyse the influence of both the
size and the morphology (hollows/hillocks) of defects on the anchorage of the contact line.
� 2003 Elsevier B.V. All rights reserved.
Keywords: Contact; Wetting; Surface defects; Ion bombardment
1. Introduction
It is now well established that the wettingproperties of the real solid surfaces are strongly
affected by their roughness and chemical hetero-
geneities. In many practical situations these het-
erogeneities pin the contact line inducing a contact
angle hysteresis. In this case, the static angle be-
tween the solid surface and the fluid interface takes
two different values depending on the contact line
motion; it advances with a contact angle hA and
* Corresponding author. Tel.: +33-0-472-431-218; fax: +33-0-
472-431-592.
E-mail address: [email protected] (S.M.M. Ra-
mos).
0039-6028/$ - see front matter � 2003 Elsevier B.V. All rights reserv
doi:10.1016/S0039-6028(03)00852-5
recedes with hR (hA > hR). In the last 20 years
much theoretical and experimental work has been
devoted to investigation of the motion of a fluidinterface on an heterogeneous surface and of the
contact angle hysteresis [1–10]. From an experi-
mental point of view, it has been shown that
chemical heterogeneities and geometrical defects
(roughness) do not have a similar effects on the
hysteresis. Although the contact angle hysteresis
has been under investigations for many years, the
experimental studies performed up to now dealtessentially with surfaces structured at the micro-
scopic scale, with patterns of a few 10s of mi-
crometers in size. To date, in spite of the many
fundamental and potential applications, the ex-
perimental investigations taking into account the
roughness effects at a nanometer range still remain
ed.
356 S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362
limited, probably due to the difficulties usually
encountered for the preparation of well charac-
terized surfaces with controlled defect distribu-
tions.
Recently, we have attacked the problem of
wetting on nano-rough surfaces by investigatingthe phenomenon of contact angle hysteresis on
surfaces structured by a random distribution of
nanometric hillocks [11].
The aim of the present work is to study the
effects of nanometric hollows on the contact angle
hysteresis. In these experiments, we analyse the
influence of both the size and the morphology
(hollows or hillocks) of defects on the contact linemotion. For this purpose, we have processed our
surfaces by using swift heavy ion (SHI) irradia-
tions. As we reported in the recent past, the pro-
jectile impacts at the glass slices surface induce the
formation of nanometric hollows [12]. The hollow
dimensions depend on both the ion mass and the
irradiation energy, whereas the concentration of
such structures and consequently the surfaceroughness is governed by the irradiation fluence.
The role played by topographical defects in the
contact angle hysteresis phenomenon is investi-
gated here via two complementary techniques:
atomic force microscopy AFM observations and
contact angle measurements.
Table 1
Irradiation fluence /d (hollow concentration), average distance betw
(advancing and receding) contact angles hA and hR collected for the s
/d (·109ions cm�2)
k (nm) aPb (%) aKr (%) P
h
Reference
surface
– 0 0 1
0.5 447 1.8 – 1
1.0 316 3.5 – 1
3.0 182 10.0 – 1
5.0 141 – 1.6 –
6.0 129 19.0 – 1
7.0 119 – 2.3 –
10.0 100 29.7 3.3 1
15.0 82 41.0 – 1
20.0 71 50.5 6.4 1
40.0 50 75.5 –
60.0 41 87.9 17.8
80.0 35 – 23.2 –
The contact angle measurements were done optically with an accurac
2. Experimental section
2.1. Surface processing
The starting material is constituted of glass sli-ces with a low roughness value purchased from
Prolabo. The surfaces of these slices were pro-
cessed twice: first, hollows of nanometric size were
created by using swift heavy ions irradiations at
Grand Acc�eel�eerateur National d�Ions Lourds
(GANIL). In order to modify the hollow dimen-
sions, two different kinds of ions were used: 208Pb
ions of 250 MeV energy and 78Kr of 240 MeVenergy. All the irradiations were performed at
room temperature with fluences extending from
5 · 108 to 8 · 1010 cm�2. For the different irradia-
tion conditions we have listed in Table 1, the
corresponding average distance (k) between two
neighbouring defects and the fraction of the sur-
face covered by the defects (a). The a values were
determined by using the following relation, whichis based on a direct impact model [13]
a ¼ 1� expð�/dAÞ ð1Þ
where A is the defect cross-section and /d is the
irradiation fluence.
Second, in order to obtain contact angles large
enough to be accurately measured and to have a
een hollows k, coverage rate of the surface by defects a, andamples irradiated with Kr or Pb ions
b Kr
A (�) hR (�) hA (�) hR (�)
00.0 89.0 100.0 89.0
00.0 86.0 – –
01.0 84.0 – –
02.0 83.0 – –
– 101.0 89.0
05.0 83.0 – –
– 104.0 91.0
03.0 83.0 103.0 86.0
02.0 83.0 – –
01.0 84.0 106.0 87.0
99.0 86.0 – –
96.0 86.0 101.0 88.0
– 99.0 90.0
y of 3�.
Fig. 1. 3D view of a virgin (a) and an irradiated (/d ¼ 1010
Pb cm�2) sample (b).
S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362 357
wide range of variation of the contact angle hys-
teresis, octadecyltrichlorosilane (OTS) molecules
were grafted on the tailored surfaces. The prepa-
ration method of these surfaces is explained below
briefly. Prior to the OTS deposition, the samples
were cleaned according to the following procedure:rinsing thoroughly in hot water with Micro90 de-
tergent in an ultrasonic bath for �30 min, and
rinsing again in deionised water. The cleaned
substrates were immersed in a reaction bath con-
sisting of a freshly prepared millimolar solution of
OTS in toluene (Prolabo, 99%) for 1 h. To remove
all excess reactants, the samples were rinsed in two
successive chloroform ultrasound baths. Finallythe samples were rinsed in deionised water, and
excess water droplets were blown away with dry
N2 gas. In order to provide a reference surface the
OTS molecules were also grafted on a virgin
sample.
2.2. Surface characterization
An Explorer Nanoscope atomic force micro-
scope (AFM) operating in a tapping mode was
used. The surfaces were probed under ambient
conditions with silicon tips having a nominal ra-
dius curvature of �15 nm. Each sample was pro-
bed at least three different locations, the images
were flattened (to eliminate the experimentally
obtained bowing effects) and no other filtering wasdone. Prior to characterize the topographic mod-
ifications induced at the irradiated surfaces, both
the pristine sample and the as-grafted monolayer
onto glass slices were examined by AFM. The rms
roughness values, measured on a scanned zone of 1
lm2, are of 0.07 and 0.13 nm, respectively. These
low roughness values evidence the high quality of
both the starting sample and the monolayergrafting, which constitute our reference surfaces.
The sessile drop method was used to charac-
terize the wettability properties of processed sur-
faces. The samples were introduced in a glass
chamber and the water drop was put onto the
substrate through a microsyringe. Steady-state
advancing contact angles, hA, and receding contact
angles hR, were measured using �1 ll drops ofdeionized water (with a surface tension c ¼ 72:0mNm�1). All measurements were made at room
temperature in a saturated atmosphere in order to
minimize the evaporation problems. At least five
different measurements were performed on differ-
ent areas of each sample. This procedure allows
one to take into account a possible non-uniformity
of the surface probed by the contact angle.
3. Results and discussion
3.1. Surface topography
Fig. 1 shows two 3D views of AFM micro-
graphs recorded, respectively, on a pristine and anirradiated surface. The circular hollows visible in
Fig. 1b result from the individual interaction of
each energetic ion at the solid surface. As we re-
ported in the recent past [12], this specific effect
(i.e., crater formation in the amorphous silica)
supports the previous observation of the isotropic
compaction measured by a decrease of the width
of the irradiated sample [14]. For all samples
Fig. 2. Top view and surface profiles recorded on glass slices: (a) irradiated with 5· 109 Kr cm�2 of 450 MeV energy; (b) irradiated with
1010 Pb cm�2 of 250 MeV energy and (c) irradiated sample (/d ¼ 6� 109 Pb cm�2) after OTS grafting.
358 S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362
investigated a good agreement between the hol-
lows density and the irradiation fluence was found.
Profile line scans performed over exposed areasare given in Fig. 2, where the marks indicate the
border between the damaged zone and the sur-
rounding region. For the study of the hollow di-
mensions more than 40 impacts were analyzed and
both a mean basal diameter D and a mean depth hwere extracted from these measurements. The
following values were obtained: DPb ¼ 72� 6 nm;
hPb ¼ 3� 1 nm; DKr ¼ 22� 3 nm; hKr ¼ 0:6� 0:2nm for Pb ions and Kr ions, respectively. It is
worth noticing that the confidence in the depthmeasurements decreases at low hollow diameters.
For small diameters, close to the tip probe di-
mensions, the measured values are probably un-
derestimated.
Finally, the surface characterization was com-
pleted by AFM observations after OTS grafting on
the irradiated samples. A typical result is displayed
(a)
(b)
0
5
10
15
20
25
30
0 5 10 15 20 25 30
φd (defects.cm-2)
H(m
N.m
-1)
0
5
10
15
20
25
30
0
5
10
15
20
25
30
0 20 40 60 80 100
φd (defects.cm-2)
H(m
N.m
-1)
∆S
(mN
.m-1)
PbKr
Fig. 3. (a) Contact angle hysteresis H and wettability contrast
DS versus the areal defect concentration /d and (b) zoom of the
H curve in the low /d regime.
S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362 359
Fig. 2c. No significant patterns formation at the
surface is observed and the film seems to follow
very well the surface topography. Meanwhile, the
OTS grafting induces a small (�7%) decrease in
the hollow dimensions. The following values for
the average diameter d� and for the mean depth h�
were found: d�Pb ¼ 68� 7 nm; h�Pb ¼ 2:7� 0:8 nm;
d�Kr ¼ 20:5� 2:5 nm; h�Kr ¼ 0:4� 0:2 nm, for Pb
ions and Kr ions, respectively. From the ensemble
of our observations we have no evidence about the
OTS deposition inside the hollows.
3.2. Wetting properties
3.2.1. Data processing
From the experimental measurements of both
advancing (hA) and receding (hR) contact angles
(given in Table 1) we have determined, for each
processed surface, two fundamental parameters
for the wetting investigations. The first one is the
wettability contrast, i.e., the difference of spread-
ing coefficient on a solid surface with chemicaldefects Sd and a pristine one, S0. This parameter is
defined as DS ¼ Sd � S0;¼ cðcos hd � cos h0Þ wherecos hi (i ¼ d or 0) is the average contact angle de-
fined as cos hi ¼ ðcos hA þ cos hRÞ=2. The second
parameter is the contact angle hysteresis, defined
as H ¼ cðcos hR � cos hAÞ. The values obtained for
these two parameters in our reference (unirradi-
ated) surface are DS ¼ 0 mNm�1, H ¼ 13:2mNm�1, respectively.
The evolution of both the wettability contrast
DS and the contact angle hysteresis H versus the
defect concentration is displayed in Fig. 3. The
figure shows that DS varies very slightly with the
defect density. Although not shown here, a similar
evolution is observed on surfaces irradiated with
Kr ions. In both cases, one can estimate from dataof Table 1 and Fig. 3 that the chemical heteroge-
neity does not exceed DðcSV � cSlÞ ¼ 4 mNm�1,
indicating that a chemical heterogeneity of the
defects, due to an eventual small variation in the
coverage of the surface by OTS molecules, can be
reasonably neglected.
From Fig. 3 it is clearly evidenced that the
contact angle hysteresis is not a monotonic func-tion of the defect concentration. Two different re-
gimes are identified:
• At low defect concentration, /d < /c (where /c �6� 109 defects cm�2 for Pb and /c � 20� 109
defects cm�2 for Kr), H grows linearly with /d.
This variation suggests that each defect pins
the contact line individually. The slope of the
straight line fitting the experimental points cor-responds to the total energy W dissipated by
one defect on the hysteresis cycle. From our ex-
periments we found the following energy values:
WPb ¼ 2:2� 10�16 Nm and WKr ¼ 5:7� 10�17
Nm.
• At higher defect concentration (/d > /c), H de-
creases with increasing /d. This behaviour indi-
cates that, despite the rather large mean distancewhich remains between two individual impacts
(e.g., for /d ¼ 2� 1010 Kr cm�2 the average
360 S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362
distance between two defects is still of 71 nm
and the defect surface coverage is 6%) an over-
lap in the deformation of the contact line occurs.
It appears from these curves a converse corre-lation between the value of the critical defect
concentration /c and the hollow diameters.
However, additional data are required to confirm
this trend.
Note that we do not discuss here the evolution
of the contact angles versus the defect concentra-
tion. This evolutions is similar than observed for
surfaces decorated by a random distribution of thenanometric hillocks. We have largely discussed
such an evolution in a previous study devoted to
the wetting properties of nanorough surfaces [11].
Fig. 4. Schematic representation of both the distortion of the
contact line induced by one isolated defect (a) and the inter-
action of two wetting cross-sections. This interaction occurs
when k < 2gmax (b).
3.2.2. Data analysis
To quantify the defect force exerted on the
contact line in the linear regime of the hysteresis,
we compare our experimental results with theavailable predictions [3] concerning the behaviour
of a contact line in the presence of a single, lo-
calized defect. In this approach, the equilibrium
position of the triple line on a solid surface results
from the action of two opposed forces: the force
due to the defect which pins the contact line and
the elastic restoring force which tends to bring
the line back to the undisturbed original posi-tion. The latter force is proportional to the
amplitude of the line deformation. The deforma-
tion of the contact line induced by the presence of
a defect is schematised in Fig. 4a. This deforma-
tion is assumed to result from a topographical
defect on a planar surface. Considering the case
where the balance between these forces leads to an
hysteresis and taking into account the fact thatthese defects should anchor the contact line in
both advancing and receding motions, the total
energy dissipated by one defect around an hys-
teresis cycle is given by dimensional analysis as:
W ¼ f 2
Kð2Þ
where f is the defect force and K is the spring
constant characteristic of the restoring force,
written as K ¼ ð2pcð1� cos h0ÞÞ= lnðL=d�Þ, whered� is the size of the defect while L is the range of
deformation of the contact line. In this approach,the maximum amplitude of the contact line de-
formation gmax can be determined by the following
relation: gmax ¼ f =K.From our experimental results we determine the
value of three parameters: the spring constant K,the interacting force between the surface and the
triple line f and the maximum amplitude of the
contact line distortion gmax. In our calculations weassume that the range of deformation of the con-
tact line L corresponds to the capillary length j�1
of the liquid and we use the following experimental
data: j�1 ¼ 2:7 mm, c ¼ 72 mNm�1 and h0 ¼ 95.
The values obtained for f and gmax are presented
in Table 2. These results lead to the following re-
marks: (i) the defect force f is directly correlated to
the defect size, in agreement with what is expectedfrom the wetting of a heterogeneous surface with
purely geometrical defects; (ii) the maximum de-
formation amplitude gmax of the contact line by a
Table 2
Defect force f , maximum deformation amplitude of the contact
line gmax, wetting cross-section r and fraction of surface ac in-fluenced by gmax values determined from our experimental re-
sults
Ion f (nN) gmax : (nm) r (nm2) ac (%)
Kr 1.5 37.0 4300 57.6
Pb 3.2 69.0 14957 59.2
S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362 361
single isolated defect is correlated to the average
distance between two defects k. As can be seen
from Table 1, k > 2gmax at low defect concentra-
tions (/d < /c), whereas k < 2gmax at /d P/c re-
gime (e.g., for /c ¼ 6� 109 Pb cm�2, k ¼ 129 nm
< 2gmax ¼ 138 nm). These results suggest the fol-
lowing criterion for the transition between the two
anchorage (individual or collective) regimes at thecontact line k � 2gmax. As a consequence the crit-
ical defect concentration /c should be given by
/c � 1=4g2max.
On the other hand, notice that the defect force
values given in Table 2, are in good accordance
with those about the influence of the nanometric
hillock structures on the wetting properties [11]. In
that study the contact line is pinned by hillocks of19 nm diameter. In the linear regime of the hys-
teresis a defect force f ¼ 3:5� 10�9 N was found.
This value is very close to the values presented in
Table 2 indicating that, at a nanometric scale, the
anchorage force exerted by an isolated defect on
the contact line does not seem to depend on the
defect morphology (hollows/hillocks).
The hysteresis behaviour observed in the regimeof higher defect concentration is more intricate.
The slope inversion in the H curve occurs at quite
low fluence values. In the greater part of the flu-
ence range the distance between two defects is
large enough so that their individual characteris-
tics remain unchanged because the probability of
ion impact overlapping remains low. Therefore the
occurrence of this different regime of variation ofthe hysteresis has necessary relationship with the
onset of collective effects in pinning. In order to
clarify this particular hysteresis regime, we suggest
that two different mechanisms could be responsible
of this behaviour. The first one is related to the
range of action of one individual defect on the
contact line. By identifying gmax with the range of
action of the defect on the contact line we define a
wetting cross-section, r ¼ pg2max, whose values are
reported in Table 2. In addition, inserting both the
r and /c values in relation (1), we also determined
the fraction of surface ac influenced by gmax. As
typified in Fig. 4b, and in agreement with ac valuesgiven in Table 2, the individual wetting cross-sec-
tions interact at a fluence much lower than re-
quired for overlapping two neighbouring defects.
The presence of such a destructive interaction at
the contact line could correspond to the crossover
between the individual to the collective pinning
effects, which occurs at a low critical value /c.
The second mechanism that should explain theslope inversion in the experimental hysteresis curve
is linked to a possible formation of nano-bubbles
at the water-OTS interface as shown in AFM in-
vestigation by Tyrell and Attard [15]. As these
nano-bubbles appear at the non-wetting OTS
surface we can suppose that their formation
should be favored by the presence of roughness
defects at sufficiently high concentration, and thatin return they screen those defects, which would
result in a decrease of the contact angle hysteresis.
4. Conclusion
In this work we have investigated the phenom-
enon of the contact angle hysteresis on surfacesdecorated by a random distribution of nanometric
hollows. Our experimental results confirm the ex-
istence of two different regimes on the hysteresis
evolution that depend on the defect concentration.
At low /d values, each defect individually pins the
contact line inducing a linear increase of H with
/d. The decrease of hysteresis with increasing /d,
observed at higher /d values indicates that a col-lective pinning effect on the contact line occurs.
Such a behaviour seems to be the signature of
topographical nanometric defects on the hysteresis
phenomenon.
In addition, our results also exhibit two other
features: first, the trap efficiency of the contact line
by the topographical defects seems to be insensitive
to the defect morphology (hollow/hillock). In fact,the pinning effect of the line by hollow or by hillock
structures is quantitatively quite similar. Second,
362 S.M.M. Ramos et al. / Surface Science 540 (2003) 355–362
the break up in the linearity of H curve occurs at a
critical defect concentration /c, which is directly
correlated to the defect size. The low values of /c
seem reasonably described by a destructive inter-
action of wetting cross-sections at the contact line.
Finally, this work is pursued at present by per-forming complementary experiments using wider
defect concentrations and liquids of different sur-
face tensions and also by carrying out numerical
simulations in order to better understand the in-
fluence of the defect characteristics (e.g., size and
density) on the motion of the contact line on a
topographically nano-structured surface.
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