Super water-repellent surfaces resulting from fractal structure

Article abstract of DOI:10.1021/jp9616728

Super water-repellent surfaces showing a contact angle of 174° for water droplets have been made of alkylketene dimer (AKD). Water droplets roll around without attachment on the super water-repellent surfaces when tilted slightly. The AKD is a kind of wax and forms spontaneously a fractal structure in its surfaces by solidification from the melt. The fractal surfaces of AKD repel a water droplet completely and show a contact angle larger than 170° without any fluorination treatments. Theoretical prediction of the wettability of the fractal surfaces has been given in the previous paper.³ The relationship between the contact angle of the flat surface θ and that of the fractal surface θ_f is expressed by the equation cos θ_f = (L/l)^D-2 cos θ where (L/l)^D-2 is the surface area magnification factor. The fractal dimension of the solid AKD surface was determined to be D ≈ 2.3 applying the box-counting method to the SEM images of the AKD cross section. L and l, which are the largest and the smallest size limits of the fractal behavior of the surface, are also estimated from the box-counting method. The contact angles of some water/1,4-dioxane mixtures on the fractal and the flat AKD surfaces were determined, and the values of cos θ_f were plotted against cos θ. The plot of cos θ_f against cos θ agrees well with the theoretical prediction. It has been demonstrated by this work that the fractal concept is a powerful tool to develop some novel functional materials.

Full text of DOI:10.1021/jp9616728

19512
J. Phys. Chem. 1996, 100, 19512-19517
Super Water-Repellent Surfaces Resulting from Fractal Structure
Satoshi Shibuichi,† Tomohiro Onda,‡ Naoki Satoh,† and Kaoru Tsujii*,†
Tokyo Research Center, Kao Corporation, 2-1-3 Bunka, Sumida-ku, Tokyo 131, Japan, and
Recording and Imaging Science Laboratories, Kao Corporation, 2606, Akabane, Ichikai-machi,
Haga-gun, Tochigi 321-34, Japan
ReceiVed: June 6, 1996; In Final Form: September 3, 1996X
Super water-repellent surfaces showing a contact angle of 174° for water droplets have been made of alkylketene
dimer (AKD). Water droplets roll around without attachment on the super water-repellent surfaces when
tilted slightly. The AKD is a kind of wax and forms spontaneously a fractal structure in its surfaces by
solidification from the melt. The fractal surfaces of AKD repel a water droplet completely and show a contact
angle larger than 170° without any fluorination treatments. Theoretical prediction of the wettability of the
fractal surfaces has been given in the previous paper.3 The relationship between the contact angle of the flat
surface θ and that of the fractal surface θf is expressed by the equation cos θf ) (L/l)D-2 cos θ where (L/l)D-2
is the surface area magnification factor. The fractal dimension of the solid AKD surface was determined to
be D ≈ 2.3 applying the box-counting method to the SEM images of the AKD cross section. L and l, which
are the largest and the smallest size limits of the fractal behavior of the surface, are also estimated from the
box-counting method. The contact angles of some water/1,4-dioxane mixtures on the fractal and the flat
AKD surfaces were determined, and the values of cos θf were plotted against cos θ. The plot of cos θf
against cos θ agrees well with the theoretical prediction. It has been demonstrated by this work that the
fractal concept is a powerful tool to develop some novel functional materials.
1. Introduction
actual surface area of a rough surface to the geometric projected
area. Then, the relationship between θ′ and θ is given by eq 3.
Wettability of solid surfaces with a liquid (water in particular)
is a very important phenomenon in our daily life as well as in
many industrial processes. The wettability is governed by two
factors. One is the chemical factor, and the other is the
geometrical (surface structural) factor of the solid surfaces.1,2
Water-repellent surfaces are usually designed by the former
factor utilizing the low surface free energy of fluorinated
compounds. We have paid special attention to the geometrical
structure of solid surfaces and found the excellent effectiveness
of fractal structure on the wettability.3 In our previous paper,
we have provided the theoretical results on the wettability of
fractal surfaces and the experimental verification of the theoreti-
cal prediction.3 The present paper is an extension of the
previous work, and deals with the experimental realization of
super water-repellent surfaces that repel completely the water
droplet.
cos θ′ ) r cos θ
(3)
Equation 3 indicates that the rough surface will be more water-
repellent (more wattable) to a liquid when θ is greater (less)
than 90°. In this work, fractal structure is adopted as an
extremely rough surface to achieve the super water-repellent
surfaces.
2. Experimental Section
2.1. Materials. Alkylketene dimer (AKD) was synthesized
by the procedures shown in Figure 1.4 Precautions were taken
to dry glassware and organic solvents to avoid hydrolysis of
AKD to dialkylketone (DAK). Stearoyl chloride (60.6 g)
(Tokyo Chemical Industry Co., Ltd.) dissolved in 100 mL of
toluene was added dropwise to a solution of triethylamine (22.3
g) (Tokyo Chemical Industry Co., Ltd.) in 300 mL of toluene
at 323 K with stirring in a glass flask. After the reaction
finished, the by-product of triethylamine hydrochloride was
filtered off at 323 K. Crude AKD sample was obtained with a
weak brown color by evaporating the solvent in vacuo. The
crude AKD was purified by using a silica-gel column under
the following conditions: 35 g of the crude AKD in 200 mL of
a chloroform/n-hexane mixture (6/4 in volume) was put on a
silica-gel (C200; WAKO) column gently and eluted with the
chloroform/n-hexane mixtures having gradients of 0/100 to 50/
1. Pure AKD (mp ) 66-67 °C) was obtained as the early
fractions of the elute. The brown-colored impurities in the crude
AKD were readily adsorbed on the top of the silica-gel column.
The impurities of fatty acid, DAK, and oligomers in the crude
AKD are also separated out by this purification procedure using
a silica-gel column. Special care is necessary not to exceed 5
min in the column chromatography, otherwise the decomposition
of AKD will start to occur probably because of the catalytic
action of the silica-gel. The final sample of the AKD was
The contact angle θ between a flat solid surface and a liquid
droplet is given by Young’s equation (1).
γS - γSL
cos θ )
(1)
γL
where γSL, γS, and γL denote the interfacial tensions of the
solid-liquid, the solid-gas, and the liquid-gas interfaces,
respectively. Wenzel suggested that the contact angle θ′ of a
liquid droplet placed on the rough solid surface was written as
eq 2.
r(γS - γSL)
cos θ′ )
(2)
γL
where r is a roughness factor, which is defined as the ratio of
† Tokyo Research Center.
‡ Recording and Imaging Science Laboratories.
X Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01672-3 CCC: $12.00 © 1996 American Chemical Society

Super Water-Repellent Surfaces
J. Phys. Chem., Vol. 100, No. 50, 1996 19513
Figure 2. Contact angles of water droplets of ∼1 mm diameter on a
solid AKD surface plotted against curing time of the AKD crystal after
solidification of the melted AKD. Equilibrated contact angle was
obtained after about 3 days. Solid AKD was left standing for curing in
a dry N2 gas atmosphere. Each datum point is an averaged value of
3-5 water droplets placed on different positions of one AKD surface.
The AKD sample surfaces prepared independently and taken out of
the drybox at appropriate intervals were used for one run of the contact
angle measurement.
Figure 1. Synthetic procedures of alkylketene dimer (AKD) and dialkyl
ketone (DAK).
checked to be more than 98% pure by gas chromatography (GC),
GPC, and titration technique of the â-lactone ring. A main
impurity still remaining was the DAK. GPC analysis was done
with a column of TSK gel-2000H (Tosoh Co., Ltd.) and a RI
detector, using THF as an eluting solvent. The monomethy-
lamine (MMA) titration method was utilized to determine the
concentration of â-lactone ring of the AKD molecule.
Repeated recrystallization of the crude AKD from n-hexane
was not effective enough to remove the DAK. The AKD
sample purified by the recrystallization method, however,
showed super water-repellency, even if it contained 5-10 wt
% DAK. This result suggests that the DAK does not impede
formation of a super water-repellent surface with AKD. The
DAK was sometimes used as an additive to control the fractal
dimension of AKD surfaces. The DAK (mp ) 84 °C) was
obtained as a third fraction in the silica-gel chromatography
mentioned previously. 1,4-Dioxane was purchased from Kanto
Chemical Co. and used without further purification. Water
used in the contact angle measurements was deionized and once
distilled.
×6000, and ×30000) to estimate the scale of self-similarity of
the AKD surface.
2.4. Contact Angle Measurements. Wettability of the AKD
surfaces was evaluated by the contact angle measurements with
an optical contact angle meter (Kyowa Interface Science Co.
Ltd., type CA-A). Aqueous solutions of 1,4-dioxane were used
as the sample liquids. The surface tension of the liquid changes
from 36 mN/m for pure 1,4-dioxane to 72 mN/m for pure water,
depending upon the concentration of 1,4-dioxane. A liquid
droplet of about 1mm diameter was dropped carefully onto an
AKD solid surface from a height of 5 cm and then given gentle
vibration by tapping the sample stand with a finger to obtain
the equilibrium contact angle.
3. Results
2.2. Preparation of Super Water-Repellent AKD Sur-
faces. Super water-repellent surfaces were prepared by solidi-
fication from the melted mixtures of AKD and DAK. The
mixing ratio of AKD/DAK was changed from 10/0 to 8/2 to
obtain the different fractal dimensions of the surfaces. A AKD
(precontaining ∼2 wt % DAK)/DAK mixture was put on a glass
plate (76 mm × 26 mm × 1 mm) and heated at 363 K on an
electric hot plate. After the mixture melted, the glass plate was
cooled down to room temperature in a dry nitrogen gas
atmosphere, and the AKD sample was allowed to solidify. The
microscopic observations under a crossed polarizer of this
solidification process show that the DAK with a higher melting
point forms first some crystalline nuclei and the AKD crystals
grow from these nuclei. The higher mixing ratio of DAK results
in the formation of a greater number of nuclei. This may be
the reason why the fractal dimension of the AKD surface can
be controlled by the DAK content. The water-repellency of
the AKD surface progressively improves for about 3 days and
finally shows the super water-repellency having a contact angle
larger than 170°.
2.3. SEM Observations of the AKD Cross Section. To
estimate the fractal dimension of the AKD cross section, a AKD
film peeled off from a glass plate was cleaved with the aid of
a razor blade, and the AKD film so obtained was set to the
aluminum sample stage using an electroconductive paste
(Fujikura-kasei Co., Ltd., Type D-550). After Pt-Ag evapora-
tion onto the sample surface, the field emission scanning electron
microscope (FE-SEM; Hitachi, S-4000) images of its cross
section were taken at several magnifications (×150, ×1500,
3.1. Super Water-Repellency of AKD Surfaces. The
contact angles of water on an AKD surface are plotted against
time elapsed after AKD solidification in Figure 2. The contact
angle of a water droplet placed on the AKD surface increases
with time after solidification and finally becomes greater than
170° after 3 days (Figure 3a). SEM observations indicate that
the AKD surface just after solidification has no special structure
in the surface. After 3 days, however, the solid surface exhibits
extreme roughness with some stratified structures, as shown in
Figure 4. One can see from the figure that there are two kinds
of structures of roughness. One has a spherical shape having a
scale of roughness of about 30 µm, and the other is a flakelike
structure, the scale of which is about 1 µm. This stratified
structure suggests that the AKD surface is fractal as actually
substantiated later. The water-repellency and the surface
structure of roughness can be controlled by the ratio of AKD
and DAK mixed. The size of the spherical structure mentioned
above becomes smaller, and the number of structures increases
with increasing concentration of DAK.
The AKD sample with a flat surface is also prepared as a
reference by mechanical cutting with a knife. The surface is
confirmed to be flat by SEM observations. The flat surface is,
of course, not very water-repellent, showing a contact angle
not larger than 109° (Figure 3b). One can understand conse-
quently that the super water-repellency of the surface can be
realized by the surface roughness of the AKD.
3.2. Determination of the Fractal Dimension of Super
Water-Repellent AKD Surfaces. The box-counting method

19514 J. Phys. Chem., Vol. 100, No. 50, 1996
Shibuichi et al.
Figure 3. Photographs of water droplets placed on the AKD surfaces: (a) rough surface (the contact angle ) 174°); (b) flat surface (the contact
angle ) 109°).
Figure 4. Surface SEM images of a super water-repellent AKD surface at different magnification. The AKD was solidified in a dry N2 gas
atmosphere at room temperature and left standing for curing under the same conditions for 3 days.
is widely used to find a fractal dimension. Self-similarity and
the fractal dimension D can be evaluated by the following
relationship.5,6
Figure 5 shows the SEM images of the cross section of an
AKD surface with a magnification of ×150 and ×1500. The
SEM magnifications of the photographs were adjusted to each
other with a grating replica for a scale standard, because the
size of box used in the box-counting measurements depends
on the magnification of the SEM images. Trace curves of the
solid surface were drawn from the cross sectional SEM images
and are shown in Figure 6. The box size r was changed from
0.05 to 320 µm. Figure 7 shows the log N(r) against log r plot
for four AKD surfaces with different water-repellency. The
slopes of the straight lines give us the fractal dimensions of the
surface structures. In the case of AKD/DAK ) 10/0, one can
see clearly that the straight line has two break points at r ) 0.2
µm and r ) 34 µm and two different slopes. One slope is -1.29
between the two critical sizes, and the other is -1 in their outside
range. So, the cross section of the surface is fractal with the
N(r) r-D
(4)
where r is the size of boxes, N(r) the number of boxes to cover
the object, and D the fractal dimension of the object. The fractal
dimension D can be obtained from the slope of the log N(r) vs
log r plot.
The box-counting method was applied to three kinds of
samples with different mixing ratios of AKD and DAK. The
fractal dimension of cross section Dcross (1 e Dcross < 2) has
been measured by the box-counting method, since the direct
measurement of the fractal dimension D(2 e D < 3) of the
solid AKD surface is difficult. The fractal dimension D(2 e
D < 3) of the surface has been evaluated as D = Dcross + 1.7

Super Water-Repellent Surfaces
J. Phys. Chem., Vol. 100, No. 50, 1996 19515
Figure 5. SEM images of the cross section of a super water-repellent AKD surface. Magnifications are ×150 (a) and ×1500 (b).
Figure 6. Trace curves of the cross section of a super water-repellent
AKD surface. Tracing was made for the SEM photographs shown in
Figure 5.
dimension of Dcross ) 1.29, and the self-similarity is found to
hold between L ) 34 µm and l ) 0.2 µm. The fractal dimension
of the surface was, then, evaluated to be 2.29.
Figure 7. Plots of log N(r) vs log r for the cross sectional trace curves
of the flat and the three rough surfaces of AKD. Each plot for rough
surfaces shows that the surface is fractal in the range between some
limited lengths. The values of L and l could not be detected in the
figure of the AKD/DAK ) 8/2 since no clear break point was observed.
A kink at log r ) 0 in the figure of the flat surface may appear probably
because of the imperfect adjustment of the magnification of the SEM
photographs.
The fractal analysis was applied to three kinds of samples
with different mixing ratios of AKD and DAK. The values of
L and l for the sample of AKD/DAK ) 8/2 could not be detected
unfortunately from Figure 7. The fractal parameters (L, l, D)
so obtained for each surface are listed in Table 1. We have
found that these surfaces have different fractal parameters. The
fractal dimension of the surfaces and also the surface area
magnification factor increase with AKD concentration. This
behavior corresponds well with the change of contact angle of
the water droplet.
3.3. Contact Angles of Liquid on the Flat and Fractal
AKD Surfaces. Figure 8 shows the contact angles of water/
1,4-dioxane mixtures on the flat and the fractal surfaces of AKD
plotted against volume fraction of water. In the case of a flat
surface, the contact angle θ of a liquid droplet increases

19516 J. Phys. Chem., Vol. 100, No. 50, 1996
Shibuichi et al.
TABLE 1: Fractal Parameters (L,l,D) and Surface Area
Magnification Factor (L/l)D-2 for AKD Surfaces Showing
Different Water-Repellency
AKD/DAK
La/µm
lb/µm
Dsurface
(L/l)D-2 c
θwater
10/0
9/1
8/2
34
157
d
0.2
1.9
d
2.29
2.22
2.10
2.03
4.43
2.64
d
164-174
156-163
126-131
110
(flat)
1.00
a L, upper limit scale of fractal. b l, lower limit scale of fractal. c (L/
l)D-2, surface area magnification factor. d Data couldn’t be determined
from Figure 7.
Figure 9. Schematic illustration of the relationship between cos θf
and cos θ predicted theoretically.3 The contact angles of θ and θf denote
those of some liquid put on the flat and the fractal surfaces.
Figure 8. Contact angles of the liquid droplet of water/1,4-dioxane
mixtures placed on the AKD solid surfaces plotted against the volume
fraction of water in the liquid.
gradually with increasing surface tension γL of the liquid. The
contact angles θf of the fractal surfaces, however, change more
abruptly with water concentration, having the same crossing
point at ∼90°. Wettability of the surface is enhanced by the
surface roughness with a boundary of contact angle θ ) 90°.
4. Discussion
The contact angle θf of a liquid droplet placed on a fractal
solid surface is given by eq 5.2,3
cos θf ) (L/l)D-2 cos θ
(5)
where L and l are the upper and the lower limit lengths of fractal
behavior, respectively; D(2 e D < 3) is the fractal dimension
of the solid surface. It is assumed that (1) l is much larger
than the diameter of molecules composing a liquid, (2) L is
much smaller than the diameter of a liquid droplet, and (3) the
interfacial tension of a solid is isotropic, being independent of
crystal orientation. The contact angle of a liquid droplet placed
on the fractal surface can be changed dramatically when
compared with nonfractal surfaces. The surface area magnifica-
tion factor (L/l)D-2 can be estimated experimentally from the
cos θf vs cos θ plot, as mentioned in the previous section. The
broken line drawn in Figure 9 shows the theoretical expression
of eq 5. Applicability of eq 5 is, however, limited. In fact, eq
5 cannot give any contact angle when the absolute value of its
right-hand side exceeds unity. A universal expression for θf
can be obtained by taking account of the adsorption of a gas
on the solid-liquid interface and that of a liquid on the solid-
gas fractal interface. The behavior of extended theory is also
shown in Figure 9 by the thick line. According to the extended
theory, the surface area magnification factor should be expressed
by the slope at the origin in the cos θf vs cos θ plot.3
Figure 10. Plots of cos θf against cos θ determined experimentally
for the AKD surfaces. The theoretical curves passing through the origin
are also drawn by the thin solid straight lines.
the surfaces, changing the surface tension of the sample liquid.
The data of contact angles shown in Figure 8 are replotted in
the form of cos θf against cos θ (Figure 10). The straight lines
of cos θf against cos θ having the surface area magnification
To verify the theoretical prediction, the relationship between
cos θf and cos θ was observed by measuring the wettability of
factor (L/l)D-2 ) (34/0.2)2.29-2 = 4.43 and ) (157/1.9)2.22-2
=

Super Water-Repellent Surfaces
J. Phys. Chem., Vol. 100, No. 50, 1996 19517
2.64 calculated from fractal parameters listed in Table 1 are
also drawn by the thin solid lines in Figure 10. The surface
area magnification factor evaluated from the fractal parameters
agrees well with the slope of the experimental data of the
wettability.
The fractal theory for the wetting phenomena of a solid
surface was verified experimentally by the contact angle
measurements of a liquid droplet and the fractal analysis of the
surfaces being done independently. However, each plot does
not pass through the original point (0,0), presumably because
the exact equilibrium of contact angle of the liquid droplets is
not established on the rough surfaces.
fractal surface was verified experimentally by the cos θf vs cos
θ plot.
Acknowledgment. The authors would like to express their
sincere thanks to Prof. Toyoichi Tanaka of MIT for his helpful
discussions and comments. They also thank Mr. Sodebayashi
(Kao Corp.) for taking photos of the liquid droplets. They
finally would like to thank Dr. J. Mino (Head of R&D division
of Kao Corp.) for his permission to publish this paper.
References and Notes
(1) Wenzel, R. W. Ind. Eng. Chem. 1936, 28, 988-994.
(2) Hazlett, R. D. J. Colloid Interface Sci. 1990, 137, 527-533.
(3) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12,
2125-2127.
(4) Imai, I.; Wakabayashi, T.; Machihata, I.; Yoshino, M. Yukagaku
1951, 10, 49-56.
(5) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: New
York, 1982.
(6) Takayasu, H. Fractal (in Japanese); Asakura Shoten: Tokyo, 1986;
Chapter 1.
(7) Vicsek, T. Fractal Growth Phenomena; World Scientific Publish-
ing: Singapore, 1989; Chapter 2.
5. Conclusion
The AKD forms spontaneously an extremely rough surface
by solidification from the melted state. The surface structure
of the AKD solid was confirmed to be a fractal by box-counting
measurements. A super water-repellent surface ( θf ) 174°)
was obtained utilizing this fractal surface without any fluorina-
tion treatments. The theory of the wetting phenomena of a
JP9616728