- Email: [email protected]
Characterization of irregularly micro-structured surfaces related to their wetting properties
Accepted Manuscript Title: Characterization of irregularly micro-structured surfaces related to their wetting properties Author: Ping Li Jin Xie Zhenjie Deng PII: DOI: Reference:
S0169-4332(15)00262-7 http://dx.doi.org/doi:10.1016/j.apsusc.2015.01.220 APSUSC 29657
To appear in:
APSUSC
Received date: Revised date: Accepted date:
3-12-2014 28-1-2015 28-1-2015
Please cite this article as: P. Li, J. Xie, Z. Deng, Characterization of irregularly microstructured surfaces related to their wetting properties, Applied Surface Science (2015), http://dx.doi.org/10.1016/j.apsusc.2015.01.220 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights
Irregular micro-structure is characterized by volume ratio through 3D
ip t
measurement
cr
The volume ratio illustrates 3D the contact information of liquid-solid interfaces
us
The irregular Si surface produces hydrophobicity with decreasing volume ratio
Ac ce p
te
d
M
an
The volume ratio may be used to predict the wettability of irregular surfaces
Page 1 of 25
Characterization of irregularly micro-structured surfaces related to their wetting properties
ip t
Ping Li, Jin Xie* and Zhenjie Deng
Guangzhou 510640, China Tel: +86-20-87114634
Fax: +86-20-87111038
an
us
*Corresponding author: [email protected]
cr
School of Mechanical and Automotive Engineering, South China University of Technology
M
*Corresponding author: Dr. Prof. J Xie
Mailing Address: School of Mechanical and Automotive Engineering, South China
Ac ce p
Fax: +86-20-87111038
te
Tel: +86-20-87114634
d
University of Technology, Guangzhou 510640, China
E-mail: [email protected]
Page 2 of 25
Abstract: It is difficult to control a surface wetting due to the random surface texture, but its fabrication is easy. Hence, the volume ratio is proposed through the 3D characterization of micro-structured surface in contrast to traditional roughness factor, fractal dimension and
ip t
aspect ratio through 2D characterization. The objective is to investigate the wetting properties related to the characterization of irregularly micro-structured surface. First, the irregularly micro-structured Si surfaces with 0.22-3.58 μm in depth were machined by the rubbing, the
cr
polishing and the grinding with different diamond abrasive grain size and random abrasive
us
grain shape, respectively; secondly, the surface wetting properties were investigated with regard to the characterized parameters of measured micro-topographic surfaces; finally, the
an
irregular wetting model was constructed by using volume ratio on the base of non-composite wetting. It is shown that the contact angle increases with increasing roughness factor and aspect ratio and decreasing fractal dimension on the irregularly micro-structured surfaces, but
M
it is different from the prediction of non-composite wetting model. Moreover, the irregularly micro-structured surfaces without anisotropic properties produce smaller contact angles than
d
regularly micro-structured surfaces with anisotropic properties. The experimental results show
te
that an increase in volume ratio leads to a decrease in contact angle. It is identical to the predictions of the proposed model. This is because the volume ratio precisely illustrates 3D
Ac ce p
contact information between the liquid and solid interfaces. It is confirmed that the volume ratio may be utilized to predict and control the wetting of irregularly micro-structured surface.
Keywords: irregularly micro-structured surface; micro-topographical characters; wettability;
diamond micro-grinding
Page 3 of 25
1.
Introduction It has been well-known that the wetting properties of the solid surface are influenced by
surface energy and surface roughness. Various patterning and surface modifying strategies for hydrophobic surfaces, especially superhydrophobic surfaces, have been achieved by
ip t
combining the use of low surface energy materials and the modification of surface roughness
[1]. For example, Liu et al. made a lotus-leaf-like superhydrophobic surface on carbon steel
cr
substrate by electro-brush plating surface modification [2], Steele et al. provided a titanium superhydrophobic surface by the ultrafast laser irradiation with a fluoropolymer coating [3].
us
However, these approaches were complicated and expensive for engineering application. As for fabrication of micro-structured surfaces, Salvadori et al. fabricated
an
microcavity-arrays by combining nanocasting with electroplating to study the surface dynamic wettability [4]. Sommers and Jacobi studied the anisotropy wetting on the grooved
M
surface fabricated by etching [5]. Moreover, Kong et al. produced the frustum ridge structured surface by raster milling to study the surface self-cleaning and optical functions [6]. However,
d
most of them were only focused on the regularly patterned surface. Moreover, the characterizations of regularly micro-structured surfaces with their
te
functional properties have massively been reported to date [7-9]. However, little research
Ac ce p
concerned the design and characterization of irregularly micro-structured surfaces with reference to their surface properties. Medina et. al derived an analytical solution to the stress concentration factor for irregularly roughened surface [10], but the effect of irregular structures on surface was not investigated. Although our previous study has investigated the characterization of the regularly micro-grooved surface relating to its anisotropic wetting properties [11], its fabrication was costly and time-consuming. Because of the easy fabrication of irregular structures, the irregularly micro-structured surfaces with wetting properties allow for new opportunities in controlling the microflows of fluid in micro-devices [12]. It has been known that the irregular surface roughness was effective in improving the light extraction in light–emitting diodes [13-14]. Moreover, it influenced the scattering light [15-16]. Recently, the wetting on irregularly micro-structured surface has been focused on interfacial phenomena. For example, David and Neumann [17] calculated the energy barriers
Page 4 of 25
between the Cassie state [18] and Wenzel state [19] on self-affine roughness surface using analytical methods. Furuta et al. investigated the wetting mode transition on irregularly micro-structured surface [20]. Moreover, the dynamic wetting such as transition energy barriers was studied through droplet interactions [21]. Even though the wetting properties on
ip t
the irregularly micro-structured surface were theoretically simulated with regard to the
relationship between surface fractal feather and heterogeneous nucleation [22], the simulated
cr
results were not further verified by corresponding experiments or actual applications.
In this paper, a grinding method is employed to fabricate irregularly micro-structured
us
surface with the random micro cutting edges of diamond grains distributed on wheel working surface. It produces low energy consumption compared with laser machining and high
an
machining efficiency with chemical etching, respectively. In contrast to roughness factor, aspect ratio and fractal dimension, the volume ratio is proposed as a micro-scale
M
micro-topographic parameter of irregularly micro-structured surfaces. The objective is to improve wetting properties. First, the irregularly micro-structured Si surfaces with 3.58-0.22
d
μm in depth were respectively machined by the polishing, the rubbing and the grinding with different diamond abrasive grain size and random abrasive grain shape; secondly, the surface
te
wetting properties were investigated with regard to micro-topographic parameters; finally, the
Ac ce p
irregular wetting model was constructed by using the volume ratio as an alternative parameter on the base of non-composite wetting mode.
2. Fabrication of irregularly micro-structured surface Fig. 1 shows the fabrication scheme of irregularly micro-structured surfaces using a
diamond micro-grinding. In grinding, many micro diamond grains are dispersedly distributed on grinding wheel surface. The irregularly micro-structured Si surfaces were fabricated by the traditional plane grinding along a same feed direction (Fig. 1a) with #60, #320, #600, #1200, #3000 diamond grinding wheels, respectively. The micro diamond grains gradually cut in and cut out the Si surface with a given wheel speed vw and feed speed vf along the cycloid grain
trace (Fig. 1b). If ductile-mode cutting is performed, the irregular micro-grooves are gradually produced by continuously replicating grain profiles on the Si surface. The micro-groove angle is dominated by top grain angle. In general, the top grain angle of the diamond grinding wheel
Page 5 of 25
cr
ip t
ranges 90-170 degrees.
us
Fig. 1. The fabrication of irregularly micro-structured surface using the diamond grinding with regular abrasive grain shape.
an
Moreover, the rubbing was performed by using a mechanical machining with dissociative SiC abrasives with the grain size of 8.5-17 µm under the processing condition.
M
The compression force was 15-27.5 kPa and the turn table rotation speed was 40-60 rpm. The dissociating SiC grains were used to produce the irregularly micro-structure on Si surface
te
3. Measurement
d
through micro cutting.
3.1 Measurement of contact angle
Ac ce p
Before the measurement, the micro-structured Si surfaces were rinsed thoroughly in running distilled water and were placed in absolute alcohol for ultrasonic washing (50 W in power) for 8 minutes. Then, the Si surfaces were rinsed in running distilled water thoroughly again. Finally, they were dried naturally. In measurement, an optical contact-angle measuring device (Dataphysics OCA40 Micro,
Filderstadt, Germany) was employed to measure the contact-angle using the sessile drop method. The distilled water droplets of 2 µl volume were placed on each sample with a microsyringe. Five points were measured for each sample. The determination error of contact-angle is estimated to be ±0.1°. In order to ensure the droplet in a steady state, the static water contact angle was recorded in constant temperature room of 25 Celsius. The static water droplet contact angles on micro-structured surfaces were recorded in a clean room with relative humidity of 58%.
Page 6 of 25
3.2 Measurement of topography Fig. 2 shows the 3D topographies and scanning electron microscope (SEM) photos of the ground irregularly micro-structured Si surfaces. The micro-structured 3D surfaces were measured by a white light interferometer (WLI: BMT SMS Expert 3D). Interferometry is a
ip t
non-destructive and non-contact measurement with extremely high sensitivity in Z-direction.
An ACM 600 confocal microscopy was used here with its objective lens of 50 times lateral
cr
magnification, the vertical resolution of 30 nm and the lateral resolution of 3 μm. It is shown that the plane grinding produced rough and irregular micro-grooves on Si surfaces with micro
us
cutting edges of diamond grains (Fig. 2a and b). The irregularly micro-structured Si surfaces were also machined by rubbing and polishing which produced the micro-structures showing
Ac ce p
te
d
M
an
various directions (Fig. 2c and d).
Page 7 of 25
Fig. 2. The 3D topographies and SEM photos of irregularly micro-structured surfaces. (a) The surface ground by #60 diamond grinding wheel, (b) the surface ground by #3000 diamond grinding wheel, (c) the surface machined by rubbing and (d) by polishing. For comparison, the regularly micro-structured surfaces were also fabricated by
ip t
micro-grinding of the trued #3000 diamond V-tip wheel with micron-scale depth of cut. The
wheel V-tip angle was designed as 60 degrees (deg). This micro-grinding can precisely
cr
fabricate micro-structured Si surface [8, 23]. The micro-fabricated regularly micro-structured surfaces were shown in Fig. 3. It is seen that the micro-grooves were identical and regularly
Ac ce p
te
d
M
an
us
patterned on the surfaces different cutting depths d and pitches p.
Fig. 3. 3D topographies and SEM photos of regularly structured surfaces with different cutting depth d and pitches p. (a) d = 43 µm, p=50 µm, (b) d = 60 µm, p=70 µm and (c) d =
Page 8 of 25
86 µm, p=100 µm. Fig. 4 shows the droplet topographies on irregularly and regularly micro-structured surfaces. In the case of irregularly micro-structured surface, the topographic shapes of droplets were near circle (Fig. 4a). It is shown that the contact angles on the rough and
ip t
irregularly micro-structured Si surfaces were larger than the one on the polishing surface. A consideration then arises is that the droplet may invade into the irregular structures, and be
cr
trapped by the irregular structure edges, thus leading to confined spreading and compromising the Si surface towards to water-repellent character.
us
In the case of regularly micro-structured surfaces, the droplet circumference, however, was formed from a near circle to an ellipse by changing micro-groove pitch p (Fig. 4b).
an
Because of this particular drop shape, strongly differences of contact angles measured from different directions on regularly micro-structured surface were observed. Here, the contact
M
angles measured from the direction was perpendicular to micro-groove longitudinal fins. However, the wetting behavior on irregularly micro-structured surface did not show such
d
anisotropic property even though the micro-grooves existed. It is seen that the contact angles on these micro-structured surfaces increased with the increase of surface roughness. The
te
regularly micro-structured surfaces even approximated superhydrophobicity, which is similar
Ac ce p
to our previous research in Ref. [11].
Fig. 4. The droplet topographies. (a) Irregularly micro-structured surfaces and (b) regularly micro-structured surfaces.
Page 9 of 25
4. Characterization of irregularly micro-structured surfaces Fig. 5 shows a schematic illustration of roughness in distance Rd and roughness in height Rh. The surface profile was measured on the irregularly micro-structured surface ground by #60 diamond grinding wheel. The X-axis is determined by the average of y values. The Rd-n
ip t
corresponds to the cross distance of X-axis between the (2n-1)th plot and the (2n+1)th plot (Fig. 5a). The average roughness distance Rd is calculated as follows: 1 m Rd n m n 1
cr
Rd
(1)
us
And the difference in Y-axis between maximum and minimum values is measured for each Rd area. Then the average roughness height Rh is calculated as follows: 1 m Rhn m n 1
an
Rh
(2)
Combined Eq. (1) with Eq. (2), the aspect ratio is defined as follows: Rh Rd
(3)
M
In fact, the aspect ratio on irregularly micro-structured surface is dominated by top grain
d
angle since the aspect ratio is a function of micro-groove angle. Generally, the angle patterned
te
on the irregularly micro-structured surface by diamond grains is correspondingly larger than the one on regularly micro-structured surface patterned by diamond wheel V-tip. As a result,
Ac ce p
the aspect ratio on irregularly micro-structured surface is less than the one on regularly micro-structured surface.
Fig. 5b and Fig. 5c shows the profiles of irregularly micro-structured surface
perpendicular to and parallel to the grinding traces, respectively. The average roughness in height Rh// (Rh⊥) and the average roughness in distance Rd// (Rd⊥) were calculated for each
direction along and perpendicular to the surface texture from the obtained coordinate data. It is seen that the profile perpendicular to grinding traces is much more rough than the one that parallel to grinding traces, which suggests a greater value of Rh⊥than Rh//. After calculations, the values of Rh ⊥ were greatly different for all the irregularly
micro-structured surfaces, as well as the values of Rd⊥. In contrast, the Rd// and the Rh// were very close to, mainly ranged 6.3-9.7μm and 0.78-0.92 μm, respectively. Thus, the Rh⊥and Rd⊥ were used to characterize the roughness of irregularly micro-structured surface.
Page 10 of 25
ip t cr
us
Fig. 5. The illustration of surface roughness. (a) Schematic illustration of roughness in distance Rd and roughness in height Rh, (b) the profiles of irregularly micro-structured
an
surface perpendicular to and (c) parallel to the grinding traces.
Fig. 6 shows the WLI measured topography of irregularly micro-structured surface. It is
M
characterized with Wenzel roughness factor γw (Fig. 6a) and volume ratio χ (Fig. 6b), respectively. The Wenzel roughness factor γw is defined as the ratio of the real area St to its
d
projected area Sp of the rough surface (Wenzel 1936). It is described as follows: m n
2 2 2 i , j ( n n n j 1 i 1
te
S w t Sp
x
y
z
n 2 n 2 )i, j x
y
m n
(4)
i, j j 1 i 1
Ac ce p
where，ni,j=(nx,ny,nz)i,j is the normal of the gridding surface si,j, σi,j is an area of the projected area that is dispersed to small grids, and. The Wenzel roughness factor γw considered the actual area of the interface, but it is hard
to characterize the surface 3D topography. For example, Bartell and Shepard once showed in his experiment that the contact angles of droplets on roughness surfaces within contact line were identical to those of smooth surfaces [24]. In fact, the roughness factor only presents a composite measure of surface topography. As for the irregularly structured surface, the surface roughness was characterized by three-dimensinal irregular geometry [12]. To understand the influence of surface 3D morphology on the wetting behavior, the volume ratio χ was introduced to characterize the
topography of irregularly micro-structured surface (Fig. 6b). It is defined as the true occupied volume VR to its corresponding ideal volume V of the rough surface as follows:
Page 11 of 25
n
VR V
m
f ( xi , yi ) i , j i 1 j 1 n
(5)
m
Rh i , j i 1 j 1
us
cr
ip t
where, f(xi, yi) is vertex of σi,j, and Rh is the surface section height roughness.
an
Fig. 6. 3D topography of irregularly micro-structured surface with micro-characterized variables. (a) Roughness factor γw and (b) volume ratio χ.
M
The complicity of the surface morphology has been described by fractal dimensions. The fractal theory has been used to study the influence on wetting behavior by Hazlett [25]. Because of the existing irregular structures and the different roughness in the direction
d
perpendicular and parallel to surface textures, the fractal dimensions of these surfaces range
te
from 2 to 3 [26]. The fractal dimensions could be calculated according to the box-counting method. Self-similarity and the fractal dimension β can be evaluated by the following
Ac ce p
relationship reported by Pfeifer and Avnir [26]
N (l ) 1Sl
(6)
Where, l is the size of boxes, N(l) the number of boxes to cover the object, S the area of
underlying surface, and β the fractal dimension of the object. From the slope of the log N(l) vs. logl plot, the fractal dimension β is obtained. The contact angle and the
micro-topographical characters are given in table 1. Where, Ra is the arithmetic mean
deviation of the surface.
Page 12 of 25
Table 1. The micro-topographical characters of the ground irregularly micro-structured surfaces Fabrication #60
β
α (×10-2)
γ
χ
Ra (μm)
Rh (μm)
Rd (μm)
90. 5
2.04
10.29
1.93
0.135
7.24
3.58
34.8
#320
86.3
2.17
8.44
1.82
0.207
4.55
2.42
27.6
#600
81.9
2.30
7.31
1.76
0.220
2.85
1.52
20.8
#1200
80.5
2.24
6.80
1.70
0.268
1.14
1.15
16.9
2.40
6.13
1.67
0.474
0.60
0.95
15.5
74.3
2.16
5.92
1.46
0.561
1.48
3.04
51.3
Polishing
60.5
2.0
1.54
1.15
0.933
0.21
0.22
14.25
5. Theory of wetting on the micro-structured surface 5.1 Wenzel and Cassie model
cr
75.6
Rubbing
us
#3000
ip t
Grinding
θ (deg)
an
Two wetting models are generally employed to correlate the surface roughness theoretically with the apparent contact angles, which were developed independently by Cassie
M
and Wenzel [19, 20]. The contact angle in noncomposite state is used to be described by the non-composite wetting model (Wenzel model) as follows: (7)
d
cos w cos e
where, γw is roughness factor as mentioned before, θe is an intrinsic angle.
te
As for the contact angle in composite state, however, is used to be described by the
Ac ce p
composite wetting model (Cassie model) as follows: cos c f cos e c 1
(8)
where, γc is the fraction of the droplet's base area contacting with solid, called Cassie roughness factor. f is the ratio of the actual area to the projected area of droplet solid contact.
It is equal to 1.0 generally.
As pointed out by Sommers and Jacobi, the absence of discernable roughness features on
the baseline surface prevented a composite surface [5]. It is further verified by our experiments that the droplet sank down to the irregularly-structured surface bottoms, as is illustrated in the vibration impact experiment shown in Fig.7 as well as the visual inspection shown in Fig.7s of supplementary material. The outcomes of vibration impact on the micro-structured surfaces determined by taking snapshots with a high speed camera. The purpose is to identify the surface robustness of disturbance and to figure out the wetting state
Page 13 of 25
of droplet on the micro-structured surfaces. The droplet disturbance experiment was performed by exerting a vertical vibration. The order number 1, order numbers 2-7 and order number 8 in snapshots show the droplet wetting state before vibration, in vibration and after vibration, respectively.
ip t
First, the droplet was pinned on the micro-groove longitudinal fins (Fig. 7a-1). After adding vibration, the droplet progressively invaded into the gaps among the micro-grooves
cr
due to the gradual disappearance of the air pockets shown in Fig. 7a-3 to Fig. 7a-6. Then, the
droplet completely penetrated into the micro-groove bottoms (Fig. 7a-7). As a result, the
us
contact angle was dropped down to 102.5 deg from 152.4 deg. Nevertheless, as for the irregularly micro-structured surface, the droplet generally maintained its shape after suffering
an
the vibration, and the contact angle slightly decreased (Fig. 7b). This is because the droplet has sunk down to the micro-structure bottoms since the beginning. It was also proved by the
M
digital microscopic vision of droplet contact (Fig. 7 Supplementary). Thus, in this study, the composite state of droplet wetting on irregularly structured surfaces was out of the scope of
Ac ce p
te
d
discussion.
Fig. 7. The vibration impact on the (a) regularly micro-structured surface and (b) irregularly
micro-structured surface.
5.2 Fractal wetting model
When considering the effects of fractal dimension on the contact angle, it is easily
deduced the fractal wetting model from Wenzel formula as follows cos 2 R sin / l
2
cos e
(9)
where, β is the fractal dimension, l is the measurement scale which can be assumed as 1 nm as this value is generally larger than the lattice constant of any solid structure and less than the scale of an embryo [22]. R is the radius of the droplet. It can be calculated as
Page 14 of 25
R(
1 / 3 3V 2 / 3 ) 2 3 cos cos 3
(10)
V is the volume of the droplet. 5.3 Irregular wetting model
ip t
The Wenzel model shows that the effect of surface roughness is to increase the hydrophobia of hydrophobic surfaces and to increase the hydrophile of hydrophilic surfaces.
That is: if θe>90°, θ>θe, but if θe<90° then θ<θe. But, about the wettability of hydrophilic
cr
surface is transferred toward hydrophobia by roughing its surface, the Wenzel model is hardly
cos cos e
(11)
an
where, χ is the volume ratio.
us
suitable for use. Thus, the irregular wetting model was proposed as follows:
Because wetting is a thermodynamic process, the magnitude of the internal force change
M
determines the wetting process [19]. Consider the volume force [27, 28], the unit volume force of the solid (α) is different with the one of the liquid (β) as well as the air (δ). For a droplet resting on an ideally smooth surface, take a fixed volume Vs into account, it is fully
te
d
composed of the solid (Fig. 8a). Thus, the volume force will be
F1 Vs
(12)
Ac ce p
As for rough surface, the fix volume Vs is composed of liquid Vl2, solid V's and air Va (Fig. 8b). So the solid volume force will be
F2 Vs '
(13)
In general, a volume force problem can be considered as the superposition of a properly
chosen stress-known problem and another boundary-loaded problem. For volume force F, the
part of boundary loads is F'. In the interface, to strike the balance of adhesive tension and
boundary load F' in ideally smooth surface (Fig. 8a), there will be
F ' cos e
(14)
where, τ is surface tension. As for the irregularly structured interface, the boundary load F' is derived from F2 that is also equal to α (χVs). The force equation in such surface (Fig. 8b) is then given by
F ' cos
(15)
Page 15 of 25
Combine Eq. (14) with Eq. (15), the Eq. (11) is obtained. As a result, the total volume force is decreased. As the volume force on roughened surface decreased, the energy of the system would decrease correspondingly. Then, the droplet on such surface will then spontaneously assume a
ip t
more spherical form (Fig. 8). Therefore, the rough surface is more water-repellent. This is
identical to the fact that coating a hydrophilic surface with a low energy material to decrease
cr
the surface energy in order to gain a hydrophobic surface [20]. If apply external force to this system, such as mechanical vibration [29] and acoustic vibration [30], the droplet on the
d
M
an
us
roughened surface will spread more widely.
te
Fig. 8. The scheme of a droplet wetting. (a) On ideal smooth surface and (b) rough surface.
Ac ce p
6 Micro-topographical characters of irregularly micro-structured surface Fig. 9 shows contact angle θ versus roughness factor and fractal dimension with
reference to Wenzel, Cassie and fractal wetting models. As for irregularly micro-structured surface, the contact angle decreased with increasing roughness factor (Fig. 9a) according to Wenzel model. However, the changes of the measured contact angles were not identical to it. It is seen that the contact angles decreased with the increase of fractal dimension on the ground irregularly micro-structured surfaces (Fig. 9b), which is similar to the trend of fractal wetting model. However, the measured values of the contact angle were much larger than the
predicted ones. This occurs may because that both Wenzel model and fractal wetting model considered from the changes of liquid-solid contact area and three-phase contact line [28], but ignored the effect of the droplet change in 3D shape. As for the regularly structured surface, the droplet was in the composite state [11] so that
Page 16 of 25
the wetting can be characterized by Cassie model (Fig. 9c). Besides, the contact angle on regularly structured surfaces was much easier to reach to superhydrophobic state when
us
cr
ip t
increased the surface roughness (Fig. 4b).
an
Fig. 9. The contact angle θ versus roughness factor γ (γw and γc) and fractal dimension β with reference to (a) Wenzel model, (b) fractal wetting model and (c) Cassie model.
M
Fig. 10 shows the contact angle θ versus aspect ratio α and volume ratio χ. The contact angles on both irregularly and regularly micro-structured surfaces were increasing along with the increase of aspect ratio (Fig. 10a). It is identical to the results in microcavity-array
d
patterned surface reported by Salvadori et al. [4] and the Si nanopatterns combined with
te
diamond-like carbon and perfluoropolyether films reported by Pham et al. [1]. In the case of irregularly micro-structured surface, a decrease in volume ratio χ led to an increase in contact
Ac ce p
angle (Fig. 9b). The change of the contact angle was quite consistent with the proposed model concerning volume ratio χ. It can be explained as the volume ratio illustrates real 3D contact
information between the liquid and solid interfaces. As a result, the proposed volume ratio χ
may be able to predict the contact angle of irregularly micro-structured surface. In the case of regularly micro-structured surface, the change of contact angle did not
agree with the proposed model (Fig. 10b). It also means that the irregular wetting model, which is used the volume ratio as a characteristic parameter, is not able to predict the contact angle on the composite state of regularly micro-structured surface. It is due to the fact that the irregular wetting model is valid in the case of a droplet being noncomposite state rather than being composite state. It is also seen that the irregularly micro-structured surfaces resulted much smaller contact angle than the regularly micro-structured surfaces even if their volume ratios are identical.
Page 17 of 25
The reason is that the wetting on the regularly micro-structured surface is in composite state rather than non-composite state. Although the micro-grooves existed on irregularly micro-structured Si surfaces (Fig. 2), the wetting property differed from the regularly micro-structured surface. It is because the shapes and the depths of these micro-grooves were
ip t
irregular, which was unable to be specifically recognized and identified by the surface
M
an
us
cr
geometrical parameters.
d
Fig. 10. The contact angle θ versus characterized variables on irregularly and regularly
7 Conclusions
te
micro-structured surfaces. (a) Aspect ratio α and (b) volume ratio χ.
Ac ce p
The irregularly micro-structured surfaces were fabricated by rubbing, polishing and
grinding with different abrasive grain size and random grain shape. The roughness factor, aspect ratio, fractal dimension and volume ratio were constructed as micro-topographical parameters to characterize the WLI-measured micro-structured surface. The irregular wetting model introduced by considering the volume ratio as characterized parameter, which was identified by the experimental results. It may be used to predict the wetting on irregularly micro-structured surface. 1.
Although regularly micro-grooved surface produces anisotropic wetting properties, the irregularly micro-grooved Si surface has no anisotropic properties. Besides, it results in larger contact angle than the irregularly micro-grooved surface.
2.
On the hydrophilic Si surface, the contact angle increases with the increase of roughness factor and aspect ratio and the decrease of fractal dimension when the irregular
Page 18 of 25
micro-structures are patterned. It is different from the prediction of non-composite wetting model. 3.
On the irregularly micro-structured surfaces, the contact angles increases with decreasing volume ratio, their correlation agrees well with the proposed irregular wetting model.
ip t
This is because the volume ratio indicates real 3D contact information between the liquid
cr
and solid interfaces.
Acknowledgements
us
This project was supported by the National Natural Science Foundation of China (Grant
an
No. 61475046).
Reference
M
[1] D.C. Pham, K. Na, S. Piao, Wetting behavior and nanotribological properties of silicon nanopatterns combined with diamond-like carbon and perfluoropolyether films. Nanotechnol. 22 (2011) 395303.
d
[2] H.T. Liu, X.M. Wang, H.M. Ji, Fabrication of lotus-leaf-like superhydrophobic surfaces
te
via Ni-based nano-composite electro-brush plating. Appl. Surf. Sci. 288 (2014) 341-348. [3] A. Steele, B.K. Nayak, A. Davis, M.C. Gupta, E. Loth, Linear abrasion of a titanium
Ac ce p
superhydrophobic surface prepared by ultrafast laser microtexturing. J. Micromech. Microeng. 23 (2013) 115012.
[4] M.C. Salvadori, M.R.S. Oliveira, R. Spirin, F.S. Teixeira, M. Cattani, I.G. Brown, Microcavity-array superhydrophobic surfaces: Limits of the model. J. Appl. Phys. 114 (2013) 174911.
[5] A.D. Sommers, A.M. Jacobi, Creating micro-scale surface topology to achieve anisotropic wettability on an aluminum surface. J. Micromech. Microeng. 16 (2006) 1571-8. [6] L.B. Kong, C.F. Cheung, S. To, C.T. Cheng, Modeling and characterization of generation of 3D micro-structured surfaces with self-cleaning and optical functions. Optik 124 (2012) 2848-2853. [7] C. O'Mahony, M. Hill, M. Brunet, R. Duane, A. Mathewson, Characterization of micromechanical structures using white-light interferometry. Meas. Sci. Technol. 14 (2003)
Page 19 of 25
1807-1814. [8] J. Xie, X.R. Liu, K.K. Wu, Y.J. Lu, P. Li, Evaluation on 3D micro-ground profile accuracy of micro-pyramid-structured Si surface using an adaptive-orientation WLI measurement. Precis. Eng. 37 (2013) 918-923.
ip t
[9] D.P. Yu, X. Zhong, Y.S. Wong, G.S. Hong, W.F. Lu, H.L. Cheng, An automatic form error
evaluation method for characterizing micro-structured surfaces. Meas. Sci. Technol. 22 (2011)
cr
015105.
[10] H. Medina, B. Hinderliter, The stress concentration factor for slightly roughened random
us
surfaces: Analytical solution. Int. J. Solids Struct. 51 (2014) 2012-2018.
[11] P. Li, J. Xie, J. Cheng and K.K. Wu, Anisotropic wetting properties on a
Micromech. Microeng. 24 (2014) 075004.
an
precision-ground micro-V-grooved Si surface related to their micro-characterized variables. J.
M
[12] M. De Marchis, E. Napoli, Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows. Int. J. Heat Fluid Fl. 36 (2012) 7-17
d
[13] D.Y. Zhou, X.B. Shi; C.H. Gao, S.D. Cai, Y. Jin, L.S. Liao, Light extraction enhancement
314 (2014) 858-63.
te
from organic light-emitting diodes with randomly scattered surface fixture. Appl. Surf. Sci.
Ac ce p
[14] J.W. Shin, D.H. Cho, J. Moon, C.W. Joo, S.K. Park, J. Lee, J.H. Han, N.S. Cho, J. Hwang, J.W. Huh, H.Y. Chu, J.I. Lee, Random nano-structures as light extraction functionals for organic light-emitting diode applications. Org. Electron. 15 (2014) 196-202. [15] C. Liu, R. L. Panetta, P. Yang, The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes. J. Quant. Spectrosc. Ra. 129 (2013) 169-185. [16] O. Kemppinen, T. Nousiainen, H. Lindqvist, The impact of surface roughness on scattering by realistically shaped wavelength-scale dust particles. J. Quant. Spectrosc. Ra. 150 (2015) 55-67. [17] R. David, A.W. Neumann, Energy barriers between the Cassie and Wenzel states on random, surperhydroplethobic surfaces. Colloid Surface A. 425 (2013) 51-58. [18] A.B.D. Cassie, Contact angles. Discuss. Faraday Soc. 3 (1948) 11-16. [19] R.N. Wenzel, Resistance of Solid Surfaces to Wetting by Water. J. Phys. Chem. 28 (1936)
Page 20 of 25
988–994. [20] T. Furuta, T. Isobe, M. Sakai, S. Matsushita, A. Nakajima, Wetting mode transition of nanoliter scale water droplets during evaporation on superhydrophobic surfaces with random roughness structure. Appl. Surf. Sci. 258 (2012) 2378-2383.
ip t
[21] P.M.M. Pereira, A.S. Moita, G.A. Monteiro, D.M.F. Prazeres, Characterization of the
topography and wettability of English weed leaves and biomimetic replicas. J. Bionic Eng. 11
cr
(2014) 346-359.
[22] M. Wang, Y. Zhang, H.Y. Zheng, X. Lin, W.D. Huang, Investigation of the
us
Heterogeneous Nucleation on Fractal Surfaces. J. Mater Sci. Technol. 28 (2012) 1169-1174. [23] J. Xie, Y.J. Liu, Y. Tang, A. Kubo, J. Tamaki, Ground surface integrity of granite by using
an
dry electro-contact discharge dressing of #600 diamond grinding wheel. J. Mater. Process. Tech. 209 (2009) 6004–6009.
M
[24] F.E. Bartell, J.W. Shepard, Surface Roughness as Related to Hysteresis of Contact Angles. II. The Systems Paraffin–3 Molar Calcium Chloride Solution–Air and
d
Paraffin–Glycerol–Air. J. Phys. Chem. 57 (1953) 455-458.
137 (1990) 527–533.
te
[25] R.D. Hazlett, Fractal applications: Wettability and contact angle. J Colloid Interf. Sci.
Ac ce p
[26] P. Pfeifer, D. Avnir, Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. J. Chem. Phys. 79 (1983) 3558-65. [27] E.G.W. Chow, Analogy between body force and inelastic strain gradient in all crystal systems Int. J. Eng. Sci. 10 (1972) 841-849. [28] H.H. Sherief, N.M. El-Maghraby, Effect of body forces on a 2D generalized thermoelastic long cylinder. Comput. Math. Appl. 66 (2013) 1181-1191. [29] A. Shastry, M.J. K.F. Bohringer, Directing droplets using microstructured surfaces. Langmuir. 22 (2006) 6161-6167. [30] V. Palan, W.S. Shepard, K.A. Williams, Removal of excess product water in a PEM fuel cell stack by vibrational and acoustical methods. J. Power Sources. 161 (2006) 1116-1125.
Page 21 of 25
Figure captions
ip t
Fig. 1. The fabrication of irregularly micro-structured surface using the diamond grinding
cr
with regular abrasive grain shape.
us
Fig. 2. The 3D topographies and SEM photos of irregularly micro-structured surfaces. (a) The surface ground by #60 diamond grinding wheel, (b) the surface ground by #3000 diamond
an
grinding wheel, (c) the surface machined by rubbing and (d) by polishing.
Fig. 3. 3D topographies and SEM photos of regularly structured surfaces with different
M
cutting depth d and pitches p. (a) d = 43 µm, p=50 µm, (b) d = 60 µm, p=70 µm and (c) d =
d
86 µm, p=100 µm.
te
Fig. 4. The droplet topographies. (a) Irregularly micro-structured surfaces and (b) regularly
Ac ce p
micro-structured surfaces.
Fig. 5. The illustration of surface roughness. (a) Schematic illustration of roughness in distance Rd and roughness in height Rh, (b) the profiles of irregularly micro-structured surface perpendicular to and (c) parallel to the grinding traces. Fig. 6. 3D topography of irregularly micro-structured surface with micro-characterized variables. (a) Roughness factor γw and (b) volume ratio χ. Fig. 7. The vibration impact on the (a) regularly micro-structured surface and (b) irregularly
micro-structured surface.
Page 22 of 25
Fig. 8. The scheme of a droplet wetting. (a) On ideal smooth surface and (b) rough surface. Fig. 9. The contact angle θ versus roughness factor γ (γw and γc) and fractal dimension β with
ip t
reference to (a) Wenzel model, (b) fractal wetting model and (c) Cassie model.
Ac ce p
te
d
M
an
us
micro-structured surfaces. (a) Aspect ratio α and (b) volume ratio χ.
cr
Fig. 10. The contact angle θ versus characterized variables on irregularly and regularly
Page 23 of 25
Tables
Table 1.
ip t
The micro-topographical characters of the ground irregularly micro-structured surfaces β
α (×10-2)
γ
χ
Sa (μm)
Sh (μm)
Sd (μm)
#60
90. 5
2.04
10.29
1.93
0.135
7.24
3.58
34.8
#320
86.3
2.17
8.44
1.82
0.207
4.55
2.42
27.6
#600
81.9
2.30
7.31
1.76
0.220
2.85
1.52
20.8
#1200
80.5
2.24
6.80
1.70
0.268
1.14
1.15
16.9
#3000
75.6
2.40
6.13
1.67
0.474
0.60
0.95
15.5
Rubbing
74.3
2.16
5.92
Polishing
60.5
2.0
1.54
us
an 1.46
0.561
1.48
3.04
51.3
1.15
0.933
0.21
0.22
14.25
Ac ce p
te
d
M
Grinding
cr
θ (deg)
Fabrication
Page 24 of 25
Ac
ce
pt
ed
M
an
us
cr
i
Graphical Abstract (for review)
Page 25 of 25
S0169-4332(15)00262-7 http://dx.doi.org/doi:10.1016/j.apsusc.2015.01.220 APSUSC 29657
To appear in:
APSUSC
Received date: Revised date: Accepted date:
3-12-2014 28-1-2015 28-1-2015
Please cite this article as: P. Li, J. Xie, Z. Deng, Characterization of irregularly microstructured surfaces related to their wetting properties, Applied Surface Science (2015), http://dx.doi.org/10.1016/j.apsusc.2015.01.220 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Highlights
Irregular micro-structure is characterized by volume ratio through 3D
ip t
measurement
cr
The volume ratio illustrates 3D the contact information of liquid-solid interfaces
us
The irregular Si surface produces hydrophobicity with decreasing volume ratio
Ac ce p
te
d
M
an
The volume ratio may be used to predict the wettability of irregular surfaces
Page 1 of 25
Characterization of irregularly micro-structured surfaces related to their wetting properties
ip t
Ping Li, Jin Xie* and Zhenjie Deng
Guangzhou 510640, China Tel: +86-20-87114634
Fax: +86-20-87111038
an
us
*Corresponding author: [email protected]
cr
School of Mechanical and Automotive Engineering, South China University of Technology
M
*Corresponding author: Dr. Prof. J Xie
Mailing Address: School of Mechanical and Automotive Engineering, South China
Ac ce p
Fax: +86-20-87111038
te
Tel: +86-20-87114634
d
University of Technology, Guangzhou 510640, China
E-mail: [email protected]
Page 2 of 25
Abstract: It is difficult to control a surface wetting due to the random surface texture, but its fabrication is easy. Hence, the volume ratio is proposed through the 3D characterization of micro-structured surface in contrast to traditional roughness factor, fractal dimension and
ip t
aspect ratio through 2D characterization. The objective is to investigate the wetting properties related to the characterization of irregularly micro-structured surface. First, the irregularly micro-structured Si surfaces with 0.22-3.58 μm in depth were machined by the rubbing, the
cr
polishing and the grinding with different diamond abrasive grain size and random abrasive
us
grain shape, respectively; secondly, the surface wetting properties were investigated with regard to the characterized parameters of measured micro-topographic surfaces; finally, the
an
irregular wetting model was constructed by using volume ratio on the base of non-composite wetting. It is shown that the contact angle increases with increasing roughness factor and aspect ratio and decreasing fractal dimension on the irregularly micro-structured surfaces, but
M
it is different from the prediction of non-composite wetting model. Moreover, the irregularly micro-structured surfaces without anisotropic properties produce smaller contact angles than
d
regularly micro-structured surfaces with anisotropic properties. The experimental results show
te
that an increase in volume ratio leads to a decrease in contact angle. It is identical to the predictions of the proposed model. This is because the volume ratio precisely illustrates 3D
Ac ce p
contact information between the liquid and solid interfaces. It is confirmed that the volume ratio may be utilized to predict and control the wetting of irregularly micro-structured surface.
Keywords: irregularly micro-structured surface; micro-topographical characters; wettability;
diamond micro-grinding
Page 3 of 25
1.
Introduction It has been well-known that the wetting properties of the solid surface are influenced by
surface energy and surface roughness. Various patterning and surface modifying strategies for hydrophobic surfaces, especially superhydrophobic surfaces, have been achieved by
ip t
combining the use of low surface energy materials and the modification of surface roughness
[1]. For example, Liu et al. made a lotus-leaf-like superhydrophobic surface on carbon steel
cr
substrate by electro-brush plating surface modification [2], Steele et al. provided a titanium superhydrophobic surface by the ultrafast laser irradiation with a fluoropolymer coating [3].
us
However, these approaches were complicated and expensive for engineering application. As for fabrication of micro-structured surfaces, Salvadori et al. fabricated
an
microcavity-arrays by combining nanocasting with electroplating to study the surface dynamic wettability [4]. Sommers and Jacobi studied the anisotropy wetting on the grooved
M
surface fabricated by etching [5]. Moreover, Kong et al. produced the frustum ridge structured surface by raster milling to study the surface self-cleaning and optical functions [6]. However,
d
most of them were only focused on the regularly patterned surface. Moreover, the characterizations of regularly micro-structured surfaces with their
te
functional properties have massively been reported to date [7-9]. However, little research
Ac ce p
concerned the design and characterization of irregularly micro-structured surfaces with reference to their surface properties. Medina et. al derived an analytical solution to the stress concentration factor for irregularly roughened surface [10], but the effect of irregular structures on surface was not investigated. Although our previous study has investigated the characterization of the regularly micro-grooved surface relating to its anisotropic wetting properties [11], its fabrication was costly and time-consuming. Because of the easy fabrication of irregular structures, the irregularly micro-structured surfaces with wetting properties allow for new opportunities in controlling the microflows of fluid in micro-devices [12]. It has been known that the irregular surface roughness was effective in improving the light extraction in light–emitting diodes [13-14]. Moreover, it influenced the scattering light [15-16]. Recently, the wetting on irregularly micro-structured surface has been focused on interfacial phenomena. For example, David and Neumann [17] calculated the energy barriers
Page 4 of 25
between the Cassie state [18] and Wenzel state [19] on self-affine roughness surface using analytical methods. Furuta et al. investigated the wetting mode transition on irregularly micro-structured surface [20]. Moreover, the dynamic wetting such as transition energy barriers was studied through droplet interactions [21]. Even though the wetting properties on
ip t
the irregularly micro-structured surface were theoretically simulated with regard to the
relationship between surface fractal feather and heterogeneous nucleation [22], the simulated
cr
results were not further verified by corresponding experiments or actual applications.
In this paper, a grinding method is employed to fabricate irregularly micro-structured
us
surface with the random micro cutting edges of diamond grains distributed on wheel working surface. It produces low energy consumption compared with laser machining and high
an
machining efficiency with chemical etching, respectively. In contrast to roughness factor, aspect ratio and fractal dimension, the volume ratio is proposed as a micro-scale
M
micro-topographic parameter of irregularly micro-structured surfaces. The objective is to improve wetting properties. First, the irregularly micro-structured Si surfaces with 3.58-0.22
d
μm in depth were respectively machined by the polishing, the rubbing and the grinding with different diamond abrasive grain size and random abrasive grain shape; secondly, the surface
te
wetting properties were investigated with regard to micro-topographic parameters; finally, the
Ac ce p
irregular wetting model was constructed by using the volume ratio as an alternative parameter on the base of non-composite wetting mode.
2. Fabrication of irregularly micro-structured surface Fig. 1 shows the fabrication scheme of irregularly micro-structured surfaces using a
diamond micro-grinding. In grinding, many micro diamond grains are dispersedly distributed on grinding wheel surface. The irregularly micro-structured Si surfaces were fabricated by the traditional plane grinding along a same feed direction (Fig. 1a) with #60, #320, #600, #1200, #3000 diamond grinding wheels, respectively. The micro diamond grains gradually cut in and cut out the Si surface with a given wheel speed vw and feed speed vf along the cycloid grain
trace (Fig. 1b). If ductile-mode cutting is performed, the irregular micro-grooves are gradually produced by continuously replicating grain profiles on the Si surface. The micro-groove angle is dominated by top grain angle. In general, the top grain angle of the diamond grinding wheel
Page 5 of 25
cr
ip t
ranges 90-170 degrees.
us
Fig. 1. The fabrication of irregularly micro-structured surface using the diamond grinding with regular abrasive grain shape.
an
Moreover, the rubbing was performed by using a mechanical machining with dissociative SiC abrasives with the grain size of 8.5-17 µm under the processing condition.
M
The compression force was 15-27.5 kPa and the turn table rotation speed was 40-60 rpm. The dissociating SiC grains were used to produce the irregularly micro-structure on Si surface
te
3. Measurement
d
through micro cutting.
3.1 Measurement of contact angle
Ac ce p
Before the measurement, the micro-structured Si surfaces were rinsed thoroughly in running distilled water and were placed in absolute alcohol for ultrasonic washing (50 W in power) for 8 minutes. Then, the Si surfaces were rinsed in running distilled water thoroughly again. Finally, they were dried naturally. In measurement, an optical contact-angle measuring device (Dataphysics OCA40 Micro,
Filderstadt, Germany) was employed to measure the contact-angle using the sessile drop method. The distilled water droplets of 2 µl volume were placed on each sample with a microsyringe. Five points were measured for each sample. The determination error of contact-angle is estimated to be ±0.1°. In order to ensure the droplet in a steady state, the static water contact angle was recorded in constant temperature room of 25 Celsius. The static water droplet contact angles on micro-structured surfaces were recorded in a clean room with relative humidity of 58%.
Page 6 of 25
3.2 Measurement of topography Fig. 2 shows the 3D topographies and scanning electron microscope (SEM) photos of the ground irregularly micro-structured Si surfaces. The micro-structured 3D surfaces were measured by a white light interferometer (WLI: BMT SMS Expert 3D). Interferometry is a
ip t
non-destructive and non-contact measurement with extremely high sensitivity in Z-direction.
An ACM 600 confocal microscopy was used here with its objective lens of 50 times lateral
cr
magnification, the vertical resolution of 30 nm and the lateral resolution of 3 μm. It is shown that the plane grinding produced rough and irregular micro-grooves on Si surfaces with micro
us
cutting edges of diamond grains (Fig. 2a and b). The irregularly micro-structured Si surfaces were also machined by rubbing and polishing which produced the micro-structures showing
Ac ce p
te
d
M
an
various directions (Fig. 2c and d).
Page 7 of 25
Fig. 2. The 3D topographies and SEM photos of irregularly micro-structured surfaces. (a) The surface ground by #60 diamond grinding wheel, (b) the surface ground by #3000 diamond grinding wheel, (c) the surface machined by rubbing and (d) by polishing. For comparison, the regularly micro-structured surfaces were also fabricated by
ip t
micro-grinding of the trued #3000 diamond V-tip wheel with micron-scale depth of cut. The
wheel V-tip angle was designed as 60 degrees (deg). This micro-grinding can precisely
cr
fabricate micro-structured Si surface [8, 23]. The micro-fabricated regularly micro-structured surfaces were shown in Fig. 3. It is seen that the micro-grooves were identical and regularly
Ac ce p
te
d
M
an
us
patterned on the surfaces different cutting depths d and pitches p.
Fig. 3. 3D topographies and SEM photos of regularly structured surfaces with different cutting depth d and pitches p. (a) d = 43 µm, p=50 µm, (b) d = 60 µm, p=70 µm and (c) d =
Page 8 of 25
86 µm, p=100 µm. Fig. 4 shows the droplet topographies on irregularly and regularly micro-structured surfaces. In the case of irregularly micro-structured surface, the topographic shapes of droplets were near circle (Fig. 4a). It is shown that the contact angles on the rough and
ip t
irregularly micro-structured Si surfaces were larger than the one on the polishing surface. A consideration then arises is that the droplet may invade into the irregular structures, and be
cr
trapped by the irregular structure edges, thus leading to confined spreading and compromising the Si surface towards to water-repellent character.
us
In the case of regularly micro-structured surfaces, the droplet circumference, however, was formed from a near circle to an ellipse by changing micro-groove pitch p (Fig. 4b).
an
Because of this particular drop shape, strongly differences of contact angles measured from different directions on regularly micro-structured surface were observed. Here, the contact
M
angles measured from the direction was perpendicular to micro-groove longitudinal fins. However, the wetting behavior on irregularly micro-structured surface did not show such
d
anisotropic property even though the micro-grooves existed. It is seen that the contact angles on these micro-structured surfaces increased with the increase of surface roughness. The
te
regularly micro-structured surfaces even approximated superhydrophobicity, which is similar
Ac ce p
to our previous research in Ref. [11].
Fig. 4. The droplet topographies. (a) Irregularly micro-structured surfaces and (b) regularly micro-structured surfaces.
Page 9 of 25
4. Characterization of irregularly micro-structured surfaces Fig. 5 shows a schematic illustration of roughness in distance Rd and roughness in height Rh. The surface profile was measured on the irregularly micro-structured surface ground by #60 diamond grinding wheel. The X-axis is determined by the average of y values. The Rd-n
ip t
corresponds to the cross distance of X-axis between the (2n-1)th plot and the (2n+1)th plot (Fig. 5a). The average roughness distance Rd is calculated as follows: 1 m Rd n m n 1
cr
Rd
(1)
us
And the difference in Y-axis between maximum and minimum values is measured for each Rd area. Then the average roughness height Rh is calculated as follows: 1 m Rhn m n 1
an
Rh
(2)
Combined Eq. (1) with Eq. (2), the aspect ratio is defined as follows: Rh Rd
(3)
M
In fact, the aspect ratio on irregularly micro-structured surface is dominated by top grain
d
angle since the aspect ratio is a function of micro-groove angle. Generally, the angle patterned
te
on the irregularly micro-structured surface by diamond grains is correspondingly larger than the one on regularly micro-structured surface patterned by diamond wheel V-tip. As a result,
Ac ce p
the aspect ratio on irregularly micro-structured surface is less than the one on regularly micro-structured surface.
Fig. 5b and Fig. 5c shows the profiles of irregularly micro-structured surface
perpendicular to and parallel to the grinding traces, respectively. The average roughness in height Rh// (Rh⊥) and the average roughness in distance Rd// (Rd⊥) were calculated for each
direction along and perpendicular to the surface texture from the obtained coordinate data. It is seen that the profile perpendicular to grinding traces is much more rough than the one that parallel to grinding traces, which suggests a greater value of Rh⊥than Rh//. After calculations, the values of Rh ⊥ were greatly different for all the irregularly
micro-structured surfaces, as well as the values of Rd⊥. In contrast, the Rd// and the Rh// were very close to, mainly ranged 6.3-9.7μm and 0.78-0.92 μm, respectively. Thus, the Rh⊥and Rd⊥ were used to characterize the roughness of irregularly micro-structured surface.
Page 10 of 25
ip t cr
us
Fig. 5. The illustration of surface roughness. (a) Schematic illustration of roughness in distance Rd and roughness in height Rh, (b) the profiles of irregularly micro-structured
an
surface perpendicular to and (c) parallel to the grinding traces.
Fig. 6 shows the WLI measured topography of irregularly micro-structured surface. It is
M
characterized with Wenzel roughness factor γw (Fig. 6a) and volume ratio χ (Fig. 6b), respectively. The Wenzel roughness factor γw is defined as the ratio of the real area St to its
d
projected area Sp of the rough surface (Wenzel 1936). It is described as follows: m n
2 2 2 i , j ( n n n j 1 i 1
te
S w t Sp
x
y
z
n 2 n 2 )i, j x
y
m n
(4)
i, j j 1 i 1
Ac ce p
where，ni,j=(nx,ny,nz)i,j is the normal of the gridding surface si,j, σi,j is an area of the projected area that is dispersed to small grids, and. The Wenzel roughness factor γw considered the actual area of the interface, but it is hard
to characterize the surface 3D topography. For example, Bartell and Shepard once showed in his experiment that the contact angles of droplets on roughness surfaces within contact line were identical to those of smooth surfaces [24]. In fact, the roughness factor only presents a composite measure of surface topography. As for the irregularly structured surface, the surface roughness was characterized by three-dimensinal irregular geometry [12]. To understand the influence of surface 3D morphology on the wetting behavior, the volume ratio χ was introduced to characterize the
topography of irregularly micro-structured surface (Fig. 6b). It is defined as the true occupied volume VR to its corresponding ideal volume V of the rough surface as follows:
Page 11 of 25
n
VR V
m
f ( xi , yi ) i , j i 1 j 1 n
(5)
m
Rh i , j i 1 j 1
us
cr
ip t
where, f(xi, yi) is vertex of σi,j, and Rh is the surface section height roughness.
an
Fig. 6. 3D topography of irregularly micro-structured surface with micro-characterized variables. (a) Roughness factor γw and (b) volume ratio χ.
M
The complicity of the surface morphology has been described by fractal dimensions. The fractal theory has been used to study the influence on wetting behavior by Hazlett [25]. Because of the existing irregular structures and the different roughness in the direction
d
perpendicular and parallel to surface textures, the fractal dimensions of these surfaces range
te
from 2 to 3 [26]. The fractal dimensions could be calculated according to the box-counting method. Self-similarity and the fractal dimension β can be evaluated by the following
Ac ce p
relationship reported by Pfeifer and Avnir [26]
N (l ) 1Sl
(6)
Where, l is the size of boxes, N(l) the number of boxes to cover the object, S the area of
underlying surface, and β the fractal dimension of the object. From the slope of the log N(l) vs. logl plot, the fractal dimension β is obtained. The contact angle and the
micro-topographical characters are given in table 1. Where, Ra is the arithmetic mean
deviation of the surface.
Page 12 of 25
Table 1. The micro-topographical characters of the ground irregularly micro-structured surfaces Fabrication #60
β
α (×10-2)
γ
χ
Ra (μm)
Rh (μm)
Rd (μm)
90. 5
2.04
10.29
1.93
0.135
7.24
3.58
34.8
#320
86.3
2.17
8.44
1.82
0.207
4.55
2.42
27.6
#600
81.9
2.30
7.31
1.76
0.220
2.85
1.52
20.8
#1200
80.5
2.24
6.80
1.70
0.268
1.14
1.15
16.9
2.40
6.13
1.67
0.474
0.60
0.95
15.5
74.3
2.16
5.92
1.46
0.561
1.48
3.04
51.3
Polishing
60.5
2.0
1.54
1.15
0.933
0.21
0.22
14.25
5. Theory of wetting on the micro-structured surface 5.1 Wenzel and Cassie model
cr
75.6
Rubbing
us
#3000
ip t
Grinding
θ (deg)
an
Two wetting models are generally employed to correlate the surface roughness theoretically with the apparent contact angles, which were developed independently by Cassie
M
and Wenzel [19, 20]. The contact angle in noncomposite state is used to be described by the non-composite wetting model (Wenzel model) as follows: (7)
d
cos w cos e
where, γw is roughness factor as mentioned before, θe is an intrinsic angle.
te
As for the contact angle in composite state, however, is used to be described by the
Ac ce p
composite wetting model (Cassie model) as follows: cos c f cos e c 1
(8)
where, γc is the fraction of the droplet's base area contacting with solid, called Cassie roughness factor. f is the ratio of the actual area to the projected area of droplet solid contact.
It is equal to 1.0 generally.
As pointed out by Sommers and Jacobi, the absence of discernable roughness features on
the baseline surface prevented a composite surface [5]. It is further verified by our experiments that the droplet sank down to the irregularly-structured surface bottoms, as is illustrated in the vibration impact experiment shown in Fig.7 as well as the visual inspection shown in Fig.7s of supplementary material. The outcomes of vibration impact on the micro-structured surfaces determined by taking snapshots with a high speed camera. The purpose is to identify the surface robustness of disturbance and to figure out the wetting state
Page 13 of 25
of droplet on the micro-structured surfaces. The droplet disturbance experiment was performed by exerting a vertical vibration. The order number 1, order numbers 2-7 and order number 8 in snapshots show the droplet wetting state before vibration, in vibration and after vibration, respectively.
ip t
First, the droplet was pinned on the micro-groove longitudinal fins (Fig. 7a-1). After adding vibration, the droplet progressively invaded into the gaps among the micro-grooves
cr
due to the gradual disappearance of the air pockets shown in Fig. 7a-3 to Fig. 7a-6. Then, the
droplet completely penetrated into the micro-groove bottoms (Fig. 7a-7). As a result, the
us
contact angle was dropped down to 102.5 deg from 152.4 deg. Nevertheless, as for the irregularly micro-structured surface, the droplet generally maintained its shape after suffering
an
the vibration, and the contact angle slightly decreased (Fig. 7b). This is because the droplet has sunk down to the micro-structure bottoms since the beginning. It was also proved by the
M
digital microscopic vision of droplet contact (Fig. 7 Supplementary). Thus, in this study, the composite state of droplet wetting on irregularly structured surfaces was out of the scope of
Ac ce p
te
d
discussion.
Fig. 7. The vibration impact on the (a) regularly micro-structured surface and (b) irregularly
micro-structured surface.
5.2 Fractal wetting model
When considering the effects of fractal dimension on the contact angle, it is easily
deduced the fractal wetting model from Wenzel formula as follows cos 2 R sin / l
2
cos e
(9)
where, β is the fractal dimension, l is the measurement scale which can be assumed as 1 nm as this value is generally larger than the lattice constant of any solid structure and less than the scale of an embryo [22]. R is the radius of the droplet. It can be calculated as
Page 14 of 25
R(
1 / 3 3V 2 / 3 ) 2 3 cos cos 3
(10)
V is the volume of the droplet. 5.3 Irregular wetting model
ip t
The Wenzel model shows that the effect of surface roughness is to increase the hydrophobia of hydrophobic surfaces and to increase the hydrophile of hydrophilic surfaces.
That is: if θe>90°, θ>θe, but if θe<90° then θ<θe. But, about the wettability of hydrophilic
cr
surface is transferred toward hydrophobia by roughing its surface, the Wenzel model is hardly
cos cos e
(11)
an
where, χ is the volume ratio.
us
suitable for use. Thus, the irregular wetting model was proposed as follows:
Because wetting is a thermodynamic process, the magnitude of the internal force change
M
determines the wetting process [19]. Consider the volume force [27, 28], the unit volume force of the solid (α) is different with the one of the liquid (β) as well as the air (δ). For a droplet resting on an ideally smooth surface, take a fixed volume Vs into account, it is fully
te
d
composed of the solid (Fig. 8a). Thus, the volume force will be
F1 Vs
(12)
Ac ce p
As for rough surface, the fix volume Vs is composed of liquid Vl2, solid V's and air Va (Fig. 8b). So the solid volume force will be
F2 Vs '
(13)
In general, a volume force problem can be considered as the superposition of a properly
chosen stress-known problem and another boundary-loaded problem. For volume force F, the
part of boundary loads is F'. In the interface, to strike the balance of adhesive tension and
boundary load F' in ideally smooth surface (Fig. 8a), there will be
F ' cos e
(14)
where, τ is surface tension. As for the irregularly structured interface, the boundary load F' is derived from F2 that is also equal to α (χVs). The force equation in such surface (Fig. 8b) is then given by
F ' cos
(15)
Page 15 of 25
Combine Eq. (14) with Eq. (15), the Eq. (11) is obtained. As a result, the total volume force is decreased. As the volume force on roughened surface decreased, the energy of the system would decrease correspondingly. Then, the droplet on such surface will then spontaneously assume a
ip t
more spherical form (Fig. 8). Therefore, the rough surface is more water-repellent. This is
identical to the fact that coating a hydrophilic surface with a low energy material to decrease
cr
the surface energy in order to gain a hydrophobic surface [20]. If apply external force to this system, such as mechanical vibration [29] and acoustic vibration [30], the droplet on the
d
M
an
us
roughened surface will spread more widely.
te
Fig. 8. The scheme of a droplet wetting. (a) On ideal smooth surface and (b) rough surface.
Ac ce p
6 Micro-topographical characters of irregularly micro-structured surface Fig. 9 shows contact angle θ versus roughness factor and fractal dimension with
reference to Wenzel, Cassie and fractal wetting models. As for irregularly micro-structured surface, the contact angle decreased with increasing roughness factor (Fig. 9a) according to Wenzel model. However, the changes of the measured contact angles were not identical to it. It is seen that the contact angles decreased with the increase of fractal dimension on the ground irregularly micro-structured surfaces (Fig. 9b), which is similar to the trend of fractal wetting model. However, the measured values of the contact angle were much larger than the
predicted ones. This occurs may because that both Wenzel model and fractal wetting model considered from the changes of liquid-solid contact area and three-phase contact line [28], but ignored the effect of the droplet change in 3D shape. As for the regularly structured surface, the droplet was in the composite state [11] so that
Page 16 of 25
the wetting can be characterized by Cassie model (Fig. 9c). Besides, the contact angle on regularly structured surfaces was much easier to reach to superhydrophobic state when
us
cr
ip t
increased the surface roughness (Fig. 4b).
an
Fig. 9. The contact angle θ versus roughness factor γ (γw and γc) and fractal dimension β with reference to (a) Wenzel model, (b) fractal wetting model and (c) Cassie model.
M
Fig. 10 shows the contact angle θ versus aspect ratio α and volume ratio χ. The contact angles on both irregularly and regularly micro-structured surfaces were increasing along with the increase of aspect ratio (Fig. 10a). It is identical to the results in microcavity-array
d
patterned surface reported by Salvadori et al. [4] and the Si nanopatterns combined with
te
diamond-like carbon and perfluoropolyether films reported by Pham et al. [1]. In the case of irregularly micro-structured surface, a decrease in volume ratio χ led to an increase in contact
Ac ce p
angle (Fig. 9b). The change of the contact angle was quite consistent with the proposed model concerning volume ratio χ. It can be explained as the volume ratio illustrates real 3D contact
information between the liquid and solid interfaces. As a result, the proposed volume ratio χ
may be able to predict the contact angle of irregularly micro-structured surface. In the case of regularly micro-structured surface, the change of contact angle did not
agree with the proposed model (Fig. 10b). It also means that the irregular wetting model, which is used the volume ratio as a characteristic parameter, is not able to predict the contact angle on the composite state of regularly micro-structured surface. It is due to the fact that the irregular wetting model is valid in the case of a droplet being noncomposite state rather than being composite state. It is also seen that the irregularly micro-structured surfaces resulted much smaller contact angle than the regularly micro-structured surfaces even if their volume ratios are identical.
Page 17 of 25
The reason is that the wetting on the regularly micro-structured surface is in composite state rather than non-composite state. Although the micro-grooves existed on irregularly micro-structured Si surfaces (Fig. 2), the wetting property differed from the regularly micro-structured surface. It is because the shapes and the depths of these micro-grooves were
ip t
irregular, which was unable to be specifically recognized and identified by the surface
M
an
us
cr
geometrical parameters.
d
Fig. 10. The contact angle θ versus characterized variables on irregularly and regularly
7 Conclusions
te
micro-structured surfaces. (a) Aspect ratio α and (b) volume ratio χ.
Ac ce p
The irregularly micro-structured surfaces were fabricated by rubbing, polishing and
grinding with different abrasive grain size and random grain shape. The roughness factor, aspect ratio, fractal dimension and volume ratio were constructed as micro-topographical parameters to characterize the WLI-measured micro-structured surface. The irregular wetting model introduced by considering the volume ratio as characterized parameter, which was identified by the experimental results. It may be used to predict the wetting on irregularly micro-structured surface. 1.
Although regularly micro-grooved surface produces anisotropic wetting properties, the irregularly micro-grooved Si surface has no anisotropic properties. Besides, it results in larger contact angle than the irregularly micro-grooved surface.
2.
On the hydrophilic Si surface, the contact angle increases with the increase of roughness factor and aspect ratio and the decrease of fractal dimension when the irregular
Page 18 of 25
micro-structures are patterned. It is different from the prediction of non-composite wetting model. 3.
On the irregularly micro-structured surfaces, the contact angles increases with decreasing volume ratio, their correlation agrees well with the proposed irregular wetting model.
ip t
This is because the volume ratio indicates real 3D contact information between the liquid
cr
and solid interfaces.
Acknowledgements
us
This project was supported by the National Natural Science Foundation of China (Grant
an
No. 61475046).
Reference
M
[1] D.C. Pham, K. Na, S. Piao, Wetting behavior and nanotribological properties of silicon nanopatterns combined with diamond-like carbon and perfluoropolyether films. Nanotechnol. 22 (2011) 395303.
d
[2] H.T. Liu, X.M. Wang, H.M. Ji, Fabrication of lotus-leaf-like superhydrophobic surfaces
te
via Ni-based nano-composite electro-brush plating. Appl. Surf. Sci. 288 (2014) 341-348. [3] A. Steele, B.K. Nayak, A. Davis, M.C. Gupta, E. Loth, Linear abrasion of a titanium
Ac ce p
superhydrophobic surface prepared by ultrafast laser microtexturing. J. Micromech. Microeng. 23 (2013) 115012.
[4] M.C. Salvadori, M.R.S. Oliveira, R. Spirin, F.S. Teixeira, M. Cattani, I.G. Brown, Microcavity-array superhydrophobic surfaces: Limits of the model. J. Appl. Phys. 114 (2013) 174911.
[5] A.D. Sommers, A.M. Jacobi, Creating micro-scale surface topology to achieve anisotropic wettability on an aluminum surface. J. Micromech. Microeng. 16 (2006) 1571-8. [6] L.B. Kong, C.F. Cheung, S. To, C.T. Cheng, Modeling and characterization of generation of 3D micro-structured surfaces with self-cleaning and optical functions. Optik 124 (2012) 2848-2853. [7] C. O'Mahony, M. Hill, M. Brunet, R. Duane, A. Mathewson, Characterization of micromechanical structures using white-light interferometry. Meas. Sci. Technol. 14 (2003)
Page 19 of 25
1807-1814. [8] J. Xie, X.R. Liu, K.K. Wu, Y.J. Lu, P. Li, Evaluation on 3D micro-ground profile accuracy of micro-pyramid-structured Si surface using an adaptive-orientation WLI measurement. Precis. Eng. 37 (2013) 918-923.
ip t
[9] D.P. Yu, X. Zhong, Y.S. Wong, G.S. Hong, W.F. Lu, H.L. Cheng, An automatic form error
evaluation method for characterizing micro-structured surfaces. Meas. Sci. Technol. 22 (2011)
cr
015105.
[10] H. Medina, B. Hinderliter, The stress concentration factor for slightly roughened random
us
surfaces: Analytical solution. Int. J. Solids Struct. 51 (2014) 2012-2018.
[11] P. Li, J. Xie, J. Cheng and K.K. Wu, Anisotropic wetting properties on a
Micromech. Microeng. 24 (2014) 075004.
an
precision-ground micro-V-grooved Si surface related to their micro-characterized variables. J.
M
[12] M. De Marchis, E. Napoli, Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows. Int. J. Heat Fluid Fl. 36 (2012) 7-17
d
[13] D.Y. Zhou, X.B. Shi; C.H. Gao, S.D. Cai, Y. Jin, L.S. Liao, Light extraction enhancement
314 (2014) 858-63.
te
from organic light-emitting diodes with randomly scattered surface fixture. Appl. Surf. Sci.
Ac ce p
[14] J.W. Shin, D.H. Cho, J. Moon, C.W. Joo, S.K. Park, J. Lee, J.H. Han, N.S. Cho, J. Hwang, J.W. Huh, H.Y. Chu, J.I. Lee, Random nano-structures as light extraction functionals for organic light-emitting diode applications. Org. Electron. 15 (2014) 196-202. [15] C. Liu, R. L. Panetta, P. Yang, The effects of surface roughness on the scattering properties of hexagonal columns with sizes from the Rayleigh to the geometric optics regimes. J. Quant. Spectrosc. Ra. 129 (2013) 169-185. [16] O. Kemppinen, T. Nousiainen, H. Lindqvist, The impact of surface roughness on scattering by realistically shaped wavelength-scale dust particles. J. Quant. Spectrosc. Ra. 150 (2015) 55-67. [17] R. David, A.W. Neumann, Energy barriers between the Cassie and Wenzel states on random, surperhydroplethobic surfaces. Colloid Surface A. 425 (2013) 51-58. [18] A.B.D. Cassie, Contact angles. Discuss. Faraday Soc. 3 (1948) 11-16. [19] R.N. Wenzel, Resistance of Solid Surfaces to Wetting by Water. J. Phys. Chem. 28 (1936)
Page 20 of 25
988–994. [20] T. Furuta, T. Isobe, M. Sakai, S. Matsushita, A. Nakajima, Wetting mode transition of nanoliter scale water droplets during evaporation on superhydrophobic surfaces with random roughness structure. Appl. Surf. Sci. 258 (2012) 2378-2383.
ip t
[21] P.M.M. Pereira, A.S. Moita, G.A. Monteiro, D.M.F. Prazeres, Characterization of the
topography and wettability of English weed leaves and biomimetic replicas. J. Bionic Eng. 11
cr
(2014) 346-359.
[22] M. Wang, Y. Zhang, H.Y. Zheng, X. Lin, W.D. Huang, Investigation of the
us
Heterogeneous Nucleation on Fractal Surfaces. J. Mater Sci. Technol. 28 (2012) 1169-1174. [23] J. Xie, Y.J. Liu, Y. Tang, A. Kubo, J. Tamaki, Ground surface integrity of granite by using
an
dry electro-contact discharge dressing of #600 diamond grinding wheel. J. Mater. Process. Tech. 209 (2009) 6004–6009.
M
[24] F.E. Bartell, J.W. Shepard, Surface Roughness as Related to Hysteresis of Contact Angles. II. The Systems Paraffin–3 Molar Calcium Chloride Solution–Air and
d
Paraffin–Glycerol–Air. J. Phys. Chem. 57 (1953) 455-458.
137 (1990) 527–533.
te
[25] R.D. Hazlett, Fractal applications: Wettability and contact angle. J Colloid Interf. Sci.
Ac ce p
[26] P. Pfeifer, D. Avnir, Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces. J. Chem. Phys. 79 (1983) 3558-65. [27] E.G.W. Chow, Analogy between body force and inelastic strain gradient in all crystal systems Int. J. Eng. Sci. 10 (1972) 841-849. [28] H.H. Sherief, N.M. El-Maghraby, Effect of body forces on a 2D generalized thermoelastic long cylinder. Comput. Math. Appl. 66 (2013) 1181-1191. [29] A. Shastry, M.J. K.F. Bohringer, Directing droplets using microstructured surfaces. Langmuir. 22 (2006) 6161-6167. [30] V. Palan, W.S. Shepard, K.A. Williams, Removal of excess product water in a PEM fuel cell stack by vibrational and acoustical methods. J. Power Sources. 161 (2006) 1116-1125.
Page 21 of 25
Figure captions
ip t
Fig. 1. The fabrication of irregularly micro-structured surface using the diamond grinding
cr
with regular abrasive grain shape.
us
Fig. 2. The 3D topographies and SEM photos of irregularly micro-structured surfaces. (a) The surface ground by #60 diamond grinding wheel, (b) the surface ground by #3000 diamond
an
grinding wheel, (c) the surface machined by rubbing and (d) by polishing.
Fig. 3. 3D topographies and SEM photos of regularly structured surfaces with different
M
cutting depth d and pitches p. (a) d = 43 µm, p=50 µm, (b) d = 60 µm, p=70 µm and (c) d =
d
86 µm, p=100 µm.
te
Fig. 4. The droplet topographies. (a) Irregularly micro-structured surfaces and (b) regularly
Ac ce p
micro-structured surfaces.
Fig. 5. The illustration of surface roughness. (a) Schematic illustration of roughness in distance Rd and roughness in height Rh, (b) the profiles of irregularly micro-structured surface perpendicular to and (c) parallel to the grinding traces. Fig. 6. 3D topography of irregularly micro-structured surface with micro-characterized variables. (a) Roughness factor γw and (b) volume ratio χ. Fig. 7. The vibration impact on the (a) regularly micro-structured surface and (b) irregularly
micro-structured surface.
Page 22 of 25
Fig. 8. The scheme of a droplet wetting. (a) On ideal smooth surface and (b) rough surface. Fig. 9. The contact angle θ versus roughness factor γ (γw and γc) and fractal dimension β with
ip t
reference to (a) Wenzel model, (b) fractal wetting model and (c) Cassie model.
Ac ce p
te
d
M
an
us
micro-structured surfaces. (a) Aspect ratio α and (b) volume ratio χ.
cr
Fig. 10. The contact angle θ versus characterized variables on irregularly and regularly
Page 23 of 25
Tables
Table 1.
ip t
The micro-topographical characters of the ground irregularly micro-structured surfaces β
α (×10-2)
γ
χ
Sa (μm)
Sh (μm)
Sd (μm)
#60
90. 5
2.04
10.29
1.93
0.135
7.24
3.58
34.8
#320
86.3
2.17
8.44
1.82
0.207
4.55
2.42
27.6
#600
81.9
2.30
7.31
1.76
0.220
2.85
1.52
20.8
#1200
80.5
2.24
6.80
1.70
0.268
1.14
1.15
16.9
#3000
75.6
2.40
6.13
1.67
0.474
0.60
0.95
15.5
Rubbing
74.3
2.16
5.92
Polishing
60.5
2.0
1.54
us
an 1.46
0.561
1.48
3.04
51.3
1.15
0.933
0.21
0.22
14.25
Ac ce p
te
d
M
Grinding
cr
θ (deg)
Fabrication
Page 24 of 25
Ac
ce
pt
ed
M
an
us
cr
i
Graphical Abstract (for review)
Page 25 of 25