WETTING PROPERTIES OF THE MULTI-SCALED
NANOSTRUCTURED POLYMER AND METALLIC
SUPERHYDROPHOBIC SURFACES
Edward Bormashenko*, Tamir Stein, Gene Whyman, Yelena Bormashenko,
Roman Pogreb
The College of Judea and Samaria, the Research Institute, 44837, Ariel, Israel
Abstract
A superhydrophobic surface is produced from industrial grade polymer materials. The
surface comprises partly disordered triple-scaled arrays of PVDF globules. An
inherently superhydrophobic metallic surface is produced with polymer template. The
mathematical model based on the Cassie-Baxter hypothesis of air trapping under a
water drop is built, which gives the apparent contact angle on the manifold-scaled
interface. The presence of several scales itself is not a sufficient condition of
hydrophobicity of inherently wettable surfaces. The geometrical features favouring
the increase of the vapour–water interface fraction are necessary for this phenomenon.
Keywords: superhydrophobicity, wetting, twofold relief, PVDF, metallic.
1. Introduction
Wetting of textured surface has been studied intensively in the past decade [1-25]. In
spite of the fact that the main theoretical approaches to the wetting of highly
developed relieves were developed by Cassie and Wenzel 50 years ago the problem
still turns to be attractive to investigators. According to the Cassie model air can
remain trapped below the drop, forming “air pockets”. Thus, hydrophobicity is
strengthened because the drop sits partially on the air. On the other hand, according to
the Wenzel model the roughness increases the surface area of the solid, which also
geometrically modifies hydrophobicity [1]. It is conventional to relate so-called
moderate hydrophobicity to the Wenzel regime, whereas Cassie scenario results in
strong water-repellent surface properties. However, the Cassie regime has been
reported recently for slightly hydrophobic interfaces, moreover coexistence of Cassie
and Wenzel regimes at the same surfaces has been reported [4, 24]. Lack of the
reproducible experimental data in the field has to be emphasized.
The phenomenon of superhydrophobicity when apparent contact angle
becomes close to 180º was reported recently by different groups [2, 3, 8]. Various
sophisticated techniques (UV, soft lithography11, temperature directed capillary
molding [24]) and materials (perfluoroacrylates [4], alkylketene dimmers [10]) were
applied for manufacturing super water-repellent surfaces. Superhydrophobic surfaces
are also found in nature [9, 12]. The biological expedience of the phenomenon, called
the lotus effect, consists in the possibility of self-cleaning of plant leafs due to the
rolling of drops without water spreading on the leaf surface [9, 12]. The underlying
physical problem was how hydrophobicity can develop on materials which are
partially wettable [9]. This phenomenon has been explained by forming the large
water-air interface under a water droplet in consequence of the air trapping in pockets
of a highly textured substrate. Since the surface energy of the water-air interface is
large, the droplet tends to decrease the underlying area increasing the contact angle.
*
Corresponding author. E-mail: Edward@yosh.ac.il
146
In spite of significant experimental and theoretical efforts, reproducible
inexpensive manufacturing of superhydrophobic surfaces remains problematic. We
report triple-scaled superhydrophobic surfaces manufactured with industrial grade
polyvinylidene fluoride (PVDF) particles, dispersed at the polyethylene substrate. It is
important to emphasize that PVDF is inherently hydrophilic material [14]; its
calculated contact angle equals 80– 86º, and a measured value on our nanometrically
flat samples was 75°. Surfaces, prepared according to our process and comprising
nanometrically scaled PVDF beads, demonstrated apparent contact angle as high as
160º (see Figure 1a).
a
b
Fig. 1.a, Droplets deposited on the polymer triple-scaled relief; b, droplets on the gold
coated relief.
Amongst the recent achievements metallic superhydrophobic surfaces attract
significant attention. Metallic surfaces are well-known as “high-energy interfaces”,
for which the chemical binding is of order of 1 eV, and on which nearly every liquid
spreads [1]. Superhydrophobic metallic surfaces are usually obtained with a
monolayer of n-dodecanthiol assembled on textured metallic surfaces [15-17]. We
will demonstrate in our paper that it is possible to form inherently hydrophobic
metallic interface, when the later is micrometrically textured, with a contact angle as
high as 150º, Figure 1b.
2. Experimental
We obtained highly developed polymer surfaces by two different techniques
(Figure 2a-b).
1. Tilted substrates were coated with chlorinated solvents based solutions
comprising polycarbonate and PVDF beads. Polycarbonate is soluble in the
chlorinated solvents, whereas PVDF is not, thus colloidal suspension was formed,
dripped on the quartz glass substrates as depicted in Figure 2a and dried with a room
temperature air current. The structure of the dry film studied by means of scanning
147
electron microscopy shows interconnected colloidal arrays (ICA), such as presented in
Figure 3a-b. These arrays are microscopically scaled aggregates comprised of PVDF
particles embedded in PC that filled the porosity between PVDF beads. The average
dimension of these aggregates was determined as 3-10 μm. The aggregates
incorporate 104-106 PVDF nanoparticles. The relief displayed in Figure 3 is
mentioned further as relief A.
Polyvinylidene fluoride nano-beads were supplied by Aldrich, molecular
weight Mw= 534 000, Tg = 38.0 °C, density ρ = 1.74 g/cm3. The average diameter of
particles was established as 130 nm. Polycarbonate (PC) Lexan 141 was supplied by
GE Plastics. Solvent chloroform CHCl3 (pure for analysis) was supplied by Karlo
Erba Reagenti. At the first stage solutions containing 2-5 % wt. of PC dissolved in
98-95 % wt. of chloroform were prepared. Then particles of PVDF (2 % wt.) were
PVDF particles
t = 85°C
solution
Crimped
stamp
air stream
PVDF
beads
PE
substrate
t = 85°C
α
a
b
added under stirring (PVDF is insoluble in chlorinated solvents). Two types of
Fig. 2. Schemes of the manufacturing of highly-developed surfaces.
substrates (quartz glass and polypropylene (PP)) were coated, such as depicted in
Figure 2a. The slope of the substrate was α = 19–22°.
2. Under the second technique a powder comprising PVDF beads has been
spread uniformly on the low density polyethylene film of the thickness of 100 μm and
covered with a crimpled surface (see Figure 2b). This sandwich has been exposed to
hot pressing; the final thickness of the PVDF layer was established as 70 μm. The
polyethylene substrate had been softened under the pressing and trapped single PVDF
particles (which were still solid under the pressing temperature) and globular
aggregates comprised of PVDF beads. PVDF aggregates composed of nanometrically
scaled beads, frozen in the polyethylene matrix, form highly developed interface
depicted in Figure 4a-b, this random triple-scaled interfaces is mentioned below as
relief B. Pressed stamp indentations form “channels” important for hydrophobicity
strengthening, as it will be explained below. Hot pressing has been carried under
t=85ºC. The characteristic distance between indentations of the riffled stamp was
100 μm, the depth of the indentations was 20 μm.
At the next stage relieves A and B were coated with 360 Å gold films by a
sputtering procedure in argon atmosphere. A SPI sputter coater was used. A thickness
of coating was determined by time of sputtering.
Then bidistilled water droplets were dripped carefully on the coated templates.
The volume of the droplets was 2-5 μl.
148
a
b
Fig. 3. a, SEM picture of the surface relief based on the aggregates comprised of
PDVF nano-beads (relief A); b, single aggregate of PDVF nano-beads.
3. Results and discussion
The strongest hydrophobicity has been achieved with a surface topography
displayed in Figure 4a-b. Three spatial scales are inherent for this topography: 100 μm
which is the distance between “channels”, 10 μm – the characteristic size of the PVDF
beads aggregate and 0.1 μm – the diameter of a single PVDF particle. The apparent
contact angles are summarized in Table 1.
Table 1. Wetting properties of the textured surfaces.
Apparent
contact angle
Measured
Calculated
Relief A
95+5º
94º
Gold coated
relief A
95+5º
97º
Relief B
160+5º
172º
Gold coated
relief B
150+5º
144º
The theory explaining such transition from hydrophility to hydrophobicity occurring
on the fractal-like surfaces was proposed recently by Herminghaus [9], where the
expression for the apparent contact angle θ* has been derived starting from the Young
formula
   SL
cosθE = SV
.
(1)

Here θE is the microscopic contact angle, γSV, γSL and γ are the surface tension
coefficients on the solid-vapor, solid-liquid and liquid-vapor interfaces, respectively.
The expression for cosθ* was obtained9 from Eq.(1) on substitution of γSL by the
properly determined energy per unit area of the textured solid-liquid interface. Below
we follow a more traditional way ascending to Bico et al [5] and based on
thermodynamics. Consider the surface textured on two scales with the air trapped in
"large" and "small" pockets. Let w be the fraction of large pockets liquid-air interface
in the underlying substrate surface; v be the fraction of small pockets cross-section in
the relief surface, and g(θE) be a geometric factor that is the ratio between the relief
surface and its projection onto the substrate. Note that for the relief of Figures 3, 5
g(θE) is a decreasing function of θE. Further, in spirit of Ref. [5], when a drop of liquid
moves in all directions by the distance dx, the apparent surface under the drop
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increases by ldx where l is the length of the intersection line of the three interfaces.
From these, new liquid-vapor interfaces appear over large pockets, wldx, and over
small pockets, gv(1-w)ldx. At last, g2(1-v)(1-w)ldx is a new liquid-solid interface
replacing a solid-vapor one. Therefore the variation of the energy per unit area is
dE=(w+ gv(1 - w))γ + g2(1-v)(1-w)(γSL - γSV) + γ cosθ*
(2)
where the last term accounts for a increase of the upper liquid-vapor interface of the
drop. From the minimum condition dE = 0 we get on account of (1)
cosθ*= g(1 - w)(gcosθE (1 - v) - v) - w
(3)
For the convex profile of Figure 3 and an acute contact angle the equilibrium
of a liquid-air interface is possible if the later descends below the equatorial plane of
spheres. It is seen that indentations in the SEM picture are formed by balls of two
types with the radii R and R' (Figure 5) on different size scales, so the Herminghaus
mechanism [9] can be realized.
a
b
Fig. 4.a, SEM image of the random triple-scaled interface composed of PVDF beads
aggregates deposited on PE substrates (relief B); b, detailed SEM image of the
channel surrounded with PVDF beads aggregates.
For numerical estimation, the double-scaled system of spheres shown in
Figure 5 was chosen. Fractality means, in particular w=v, and from simple
trigonometry w=1–(2πR2sin2θE)/((2R+a)2√3), g=1/sin2(θE /2) where R is the radius
of balls and a is the shortest distance between their surfaces. For θE = 75° and a=R,
modelling the relief B, we have from Eq. (3) θ*=172°. Note that in the case of a single
scale, Eq. (3) is converted into cosθ*= (1 - w)cosθE – w from Ref. [5] that gives the
much smaller value θ*=86°. To model the experimental situation, we also considered
the close packed spheres case on the large scale, w(a=0), and incompact packing on
the small scale, v(a=R), relief A. For gold coated relieves the local contact angle was
changed to experimentally established one 60º (see also [17]). The comparison of the
data in Table 1 shows a satisfactory agreement with the experimental data. It should
be mentioned that close packing of spheres on the both scales leads to the complete
wetting for the considered contact angles. This is explained by small fraction of a
liquid-air interface and large fraction of liquid-solid interface under the droplet. Thus,
the manifold-scaling makeup of the surface is not a sufficient condition of
150
hydrophobicity of inherently wettable surfaces. The geometrical features favouring
the increase of the vapour-water interface fraction are necessary for this phenomenon.
a
a′
θE
R
θE
R′
Fig 5. The model of the double-scaled surface (R'/R=a'/a).
It was instructive to study the kinetics of water droplet evaporation deposited
on the superhydrophobic surface depicted in Fig. 5. This investigation supplied
information concerning advancing θ1 and receding θ2 apparent contact angles (Fig. 6).
The contact angle hysteresis was estimated as 15-18º. The hysteresis is relatively large
for Cassie-Baxter wetting situation. At first glance, our experimental observations
contradict to recent results presented by Gao and McCarthy [2]. They asserted that
texturing on two scales: microscopic and nanometric brings into existence extremely
low contact angle hysteresis.
2
3
1
a
b
Fig 6. Scheme presenting evaporation of water droplet deposited at the
superhydrophobic surface depicted in Fig. 4. a – kinetics of droplet evaporation, b –
151
advancing θ1 and receding θ2 contact angles, acute contact angle θ3 observed at the
final stage of evaporation
However, in the case of PVDF the local contact angle is much lower, θE = 75°,
than 103° on flat silicon [2]. Such low microscopic angle leads the large fracture 1-v
of the water-PVDF interface on the nanometric scale since more than a half of the
nanosphere is in contact with water (see Figure 5). Therefore the movement of the
contact line is hindered and the contact angle hysteresis is substantial. A similar
situation has been observed by Baldacchini et al [25] for hexadecane. Contrary to this,
in Ref [2] the surface of the nanopattern covered with water on tops of posts is very
small. For θE =104° and θ* = 176° from Ref. [2] we obtain putting, e.g., w = v, g = 1
in Eq (3), the water-air interface fracture v = 0.95 that corresponds seemingly to the
microphotographs [2]. Polyethylene and polypropylene possess the close values of a
local contact angles (103° - 107°), so the proposed simple method of the
superhydrophobic surface production may give patterns on these materials with a low
hysteresis and higher apparent angles.
Somewhat surprisingly, the acute apparent angle θ3 has been observed at the
final stage of the evaporation, when initially pinned droplet jumps, as is displayed in
Fig. 6B. This may be ascribed to the extremely small size of a drop at the final
evaporation stage compatible with the distance between channels on Figure 4a. Under
these circumstances the drop can penetrate the channel.
4. Conclusions
The simple and inexpensive technique of producing superhydrophobic surfaces is
proposed which is based on hot pressing of PVDF beads on polyethylene substrate.
The obtained partially ordered pseudo fractal surface shows superhydrophobicity with
the apparent contact angle as high as 160° although with substantial hysteresis ~20°
between advancing and receding angles. After covering the obtained surface with a
gold layer the measured apparent contact angle was 150°. Thus, the both type surfaces
exhibit the superhydrophobicity on inherently wetting materials.
The effect is explained on the basis of the Cassie-Baxter model of air trapping.
The corresponding mathematical model takes into account the existence of two scales
of the surface and may be easily generalized the arbitrary number of scales. The
comparison of the data in Table 1 shows a satisfactory agreement of the model results
with the experimental data.
The manifold scaled interface makeup by itself is not a sufficient condition of
hydrophobicity of inherently wetted surfaces. The geometrical features favouring the
increase of the vapour –water interface fraction are necessary for this phenomenon.
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