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Anisotropic wetting properties on various shape of parallel grooved microstructure
Journal of Colloid and Interface Science 453 (2015) 142–150
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Anisotropic wetting properties on various shape of parallel grooved microstructure Lu Tie a, Zhiguang Guo a,b,⇑, Weimin Liu a a
State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China Hubei Collaborative Innovation Centre for Advanced Organic Chemical Materials, Ministry of Education Key Laboratory for the Green Preparation and Application of Functional Materials, Hubei University, Wuhan 430062, China b
g r a p h i c a l a b s t r a c t
a r t i c l e
i n f o
Article history: Received 18 March 2015 Accepted 29 April 2015 Available online 8 May 2015 Keywords: Superhydrophobic Anisotropy Free energy Equilibrium contact angle
a b s t r a c t It has been revealed experimentally that some superhydrophobic surfaces in nature, such as rice leaf, show strong anisotropic wetting behavior. In this work, based on a thermodynamic approach, the effects of profile shape of parallel grooved microstructure on free energy (FE) with its barrier (FEB) and equilibrium contact angle (ECA) with its hysteresis (CAH) for various orientations of different parallel micro texture surface have been systematically investigated in detail. The results indicated that the anisotropy of wetting properties strongly depended on the specific topographical features and wetting state. In particular, a paraboloidal profile of parallel micro-texture surface is used as an important example to theoretically establish the relationship between surface geometry and anisotropic wetting behavior for optimal design, showing that the wetting behavior of the composite state is similar to that of the non-composite state and the anisotropy will possibly be appeared with the decrease of height or intrinsic contact angle of paraboloidal profile of micro texture. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction
⇑ Corresponding author at: State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China. E-mail address: [email protected] (Z. Guo). http://dx.doi.org/10.1016/j.jcis.2015.04.066 0021-9797/Ó 2015 Elsevier Inc. All rights reserved.
Anisotropic wettability on patterned surfaces has recently attracted significant attention in both academic research and designs of controllable wetting applications [1–5]. In nature, anisotropic wetting is observed on biological surfaces [6–12]. The
L. Tie et al. / Journal of Colloid and Interface Science 453 (2015) 142–150
combination of fabricating surface topographic structure [13–15] and chemical modification [16–18] would provide chances for well-designed anisotropic surfaces. As a result, numerous methods to fabricate the anisotropic superhydrophobic surfaces have been reported [18,19]. In the aspect of experiments, a better water-shedding property in the parallel direction of the grooved surface than the pillar structure has been reported [20]. Additionally, the wetting anisotropy on hierarchical structures is investigated [21]. Besides, Mizukoshi et al. [22] discussed the effect of various orderly groove structures on the slide anisotropic behavior, but there are no further investigations of the relationship between geometric parameters and contact angle. In the aspect of theory, Chen et al. showed the 3-D shape profile of a drop does not wet into the grooves of the rough surface on a 1-D grooved surface and obtained similar results as Brandon did [13,23]. Besides, some known models to explain their experimental results on anisotropic wetting have been reported [3,9,18,24–27]. However, these studies are agreement with specific experiment; even there are some contradictions each other [14,15]. It is well known that different micro texture shape with the same roughness value can exhibit completely different superhydrophobic behavior [20]. Meanwhile, for a fixed micro texture, the wetting behavior is closely related to the concerned orientation [28]. Thus, how the topographical features and surface geometries or micro texture affect anisotropic wettability behavior have still remained, especially, in theoretical aspect. In addition, a more general models aimed at fitting experiment is needed. This is helpful to design or control the anisotropy of wetting by tailoring topographic structure and the surface chemistry. In this paper, based on the thermodynamic approach, four different shapes of parallel grooved microstructures were employed to compare with the anisotropic wetting behavior: pillar, trapeziod, paraboloid and triangle (see Fig. 1). Here, it is stressed that the different cross-sectional shapes with the same roughness factor along the direction of cutting angle a = 90° have been considered. The assumption does not mean that the system has the same roughness factor in any cutting direction. The pillar represents a frequently used surface which has been proposed by Li and Amirfazli [29,30], unfortunately, this micro texture is ideal and different from the practical surfaces. While, the paraboloidal profile represent a micro texture of the Lotus leaf [31], and the paraboloidal profile micro texture hardly involves shape edges or corners, Thus it can be fabricated by the practical micro or nano-techniques. Additionally, the trapezoidal profile micro texture can be fabricated by a micro-grinding technique [32]. The theoretical investigations of the paper are well agreement with the experimental specific activities [33–35]. Meanwhile, the conclusions of this study may yield some standards for the design of the controllable microfluidic channels.
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A main aim is to analyze free energy (FE) and free energy barrier (FEB) completely for any direction of a surface microstructure. Numerous experiments show that the equilibrium contact angle (ECA) for a micro texture along different cutting angle is different [20–27]. Based on minimizing free energy (FE) of a system, a 3-D trapezoidal and paraboloidal profile of parallel grooved micro texture surface as shown in Fig. 1(a) and (f) is also simplified into a 2-D model as illustrated in Fig. 1(e) and (j) by cutting the 3-dimensional structure along a given orientation. This 2-D model can show a different surface geometry, depending on the cutting orientation. Based on such simplification, the thermodynamic status related to surface geometrical configurations of the system and subsequent numerical calculation of FEB can be readily conducted by the corresponding 2-D model. The FEB is the free energy difference between a local minimum and an adjacent maximum in the direction of three-phase line movement. A point to note is that the drop size is much larger than surface micro texture feature size. In our previous work [36], we used a set of geometrical parameters of trapezoidal and paraboloidal base radius (R), space (b), and height (h) to describe a 2-D model resulting from a 3-D surface structure. In the present study, for a given cutting angle (a) in the 3-D groove structure, the corresponding trapezoidal and paraboloidal width (Ra) and space (ba) in the resultant 2-D model can be expressed as:
Ra ¼
R b ; ba ¼ sin a sin a
ð2Þ
where R and b are base radius and space of micro texture (Fig. 1(a) and (f)), respectively, and the cutting angle (a) is given in the x–y reference frame indicated in Fig. 1. It is stressed that the height (h) may be different on various shape of parallel grooved microstructure to ensure that the different cross-sectional shapes with the same roughness factor along the direction of cutting angle a = 90°. For a given orientation with cutting angle (a), Fig. 1(h)–(j) shows a paraboloidal profile micro texture surface and the two states. Along a given orientation with cutting angle (a), the shape of a paraboloid of revolution is described as
z ¼ aa x2
ð3Þ
where x and z are the radial and vertical coordinate measured downward from the apex (see Fig. 1(j)). aa = h sin2a/R2 is the steepness which stands for the shape of paraboloidal profile along a given orientation (a), h stands for the paraboloidal base height and R is the paraboloidal base radius (see Fig. 1(f)). The apparent contact angle (hW) of non-composite state is expressed by Wenzel’s Equation [37]:
cos hW ¼ r cos hY
ð4Þ
From Fig. 1(d) and (i), the roughness factors of trapezoidal r1 and paraboloidal r2 profile in the direction with the cutting angle a are 2. Thermodynamic analysis 2.1. General theoretical considerations
r1 ¼
The contact angle (CA) of a water droplet on an ideal smooth solid surface can be obtained by the Young’s Equation
r2 ¼
cla cos hY ¼ csa cls
ð1Þ
where hY is intrinsic CA. cla, csa, and cls are the surface tension at liquid–air, solid–air, and liquid–solid interfaces, respectively. For a rough surface, there are two wetting states: the non-composite state (complete liquid wet into the troughs of a roughness surface) and composite state (the entrapment of air in the troughs of a roughness surface).
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð2R 2h= tan UÞ þ 2h ðsin aÞ þ ðcot UÞ2 þ b 2R þ b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 sin a=RÞ R2 þ 4h sin a þ R arcsinhð2h þb 2h sin a 2R þ b
ð5Þ
ð6Þ
where U is the base angle of trapezoidal micro texture (Fig. 1(a)). For the composite wetting state, droplets are located on a composite surface composed of solid and air. The apparent contact angle (hCB) can be expressed by Cassie–Baxter Equation [38]:
cos hCB ¼ r f f cos hY þ f 1
ð7Þ
The angle b can be defined as shown in Fig. 1(h). Roughness ratio of the wet area and the solid fraction for the trapezoidal (rf1, f1) and
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Fig. 1. An enlarged view of a 3-D parallel trapezoidal (a) micro texture surface with vertical view (b) and paraboloidal micro texture surface (f) with vertical view (g); a typical 2-D trapezoidal micro textured surface with composite (c) and non-composite (d) along the direction of a; a typical 2-D paraboloidal micro texture surface with composite (h) and non-composite (i) along the direction of a; illustration of variation of a composite droplet on trapezoidal (e) and paraboloidal (j) micro texture surface from state A to B (or to C) along the direction of a.
paraboloidal profile (rf2, f2) along the cutting angle a may be represented as (see Fig. 1(c) and (h)):
2.2. Thermodynamic analysis
rf 1 ¼ 1
In this article, on the basis of thermodynamic analysis, four different cross-sectional shapes of grooved micro texture were used to compare with the anisotropic wetting behavior of the various surface topographies: pillar, trapeziod, paraboloid and triangle (see Fig. 2). Some assumptions have been made as before [29]; meanwhile, the 2-D droplet profile can be considered as a spherical cap and have a constant area for different orientations (analogue of constant volume in 3-D model). FE and FEB associated with CA and CAH for any of cutting orientation both non-composite and composite states can be numerically calculated. In a cutting two-dimensional direction, the expression of FE can be written in the following dimensionless form [36]:
f1 ¼
rf 2
ð2R 2h= tan UÞ 2R þ b
tan b ¼ Arc sinhð2cotbÞ þ 4
f2 ¼
ð8Þ
2R2 ð2R þ bÞðh sin a tan bÞ
ð9Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4cot2 b 2
ð10Þ
ð11Þ
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Fig. 2. Four different profile of 3-D solid surface topographies. (a) a pillar; (b) a trapezoid; (c) a paraboloid; (d) a triangle.
F ¼
F 2cla S1=2
¼ ðh sin h cos hÞ
1=2
Fig. 3. (a) Illustration of variation of a non-composite droplet on paraboloidal micro texture surface from point A to B (or to C) along the direction of a; (b) illustration of FE analysis for the transition between non-composite and composite states (note drop volume is considered constant for both states).
½h ðr f f cos hY þ f 1Þ sin h ð12Þ
where S is area of the droplet. For a non-composite state (see Fig. 1(e)), if the droplet recedes from position A (CA of hA and droplet size of LA) to B (CA of hB and droplet size of LB) along the cutting angle, the geometrical relationship parameters (h, R, b) and the relative FEB for transition from A to B with trapezoidal profile of micro texture surface along the cutting angle a can be written as:
hA
L2A 2
sin hA
DF A!B
cla
L2A cot hA ¼ hB
¼ hB
L2B sin h2B
L2B cot hB
LB LA ð2R 2h= tan UÞ hA þ cos hY sin a sin hB sin hA
ð13Þ
2h 2b 2 h hA 2 L2A cothA ¼ hC L coth þ þ C C tan U sin a sin a sinh2C sin hA L2C
cla
LC LA hA sin hC sin hA qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b 2 þ 2h 1 þ 1=ðtan U sin aÞ cos hY sin a
2
sin hA
¼ hC
¼ hB
DF A!B
cla
L2B sin h2B
Meanwhile, the geometrical relationship parameters (h, R, b) and the relative FEB for transition from A to B along the cutting angle with paraboloidal profile of micro texture surface can be expressed as (see Fig. 3(a)):
L2B
Z
R sin a
2
hðsin aÞ x2
0
2LB sin a cot hB 2 b þ 2R
! dx
R2 Z R
hðsin aÞ x2
0
R2
sin a
!
2
dx
ð17Þ
LB LA hA sin hB sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R 2 4 sin a b 4h ðsin aÞ x2 A @ þ þ 1þ dx cos hY sin a R4 0
¼ hB
ð18Þ
Similarly, if the droplet advances from A to C along the cutting angle (see Fig. 3(a)), the geometrical relationship and the relative FEB for the transition can be obtained, respectively.
L2A 2
sin hA þ
DF A!C
cla
L2A cot hA
2LA sin a ðb þ 2RÞh 2 sin a b þ 2R
¼ hC ð16Þ
L2A cot hA
2LA sin a ðb þ 2RÞh þ 2 sin a b þ 2R
hA ð15Þ
DF A!C
L2A
ð14Þ
Similarly, one can obtain the geometrical relationship and the relative FEB for the transition with trapezoidal profile of micro texture surface when the droplet advances from A to C along the cutting angle (see Fig. 1(e)), respectively.
L2A
hA
L2C sin h2C
L2C
Z
R sin a
2
hðsin aÞ x2
0
2LC sin a cot hC 2 b þ 2R
R2 Z
R sin a
! dx 2
hðsin aÞ x2
0
LC LA hA sin hC sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R 2 4 sin a 4h ðsin aÞ x2 A @ 1þ dx cos hY 4 R 0
R2
! dx
ð19Þ
¼ hC
ð20Þ
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For a composite state (see Fig. 1(e)), the geometrical relationship and the FEB for transition of trapezoidal profile micro texture anisotropic surface, respectively, can be derived as:
hA
L2A 2
sin hA
DF A!C
cla
L2A cot hA ¼ hC
¼ hC
L2C sin h2C
L2C cot hC
LC LA b 2h hA þ þ sin a tan U sin a sin hC sin hA
ð21Þ
ð22Þ
The position of local minima FE should be analyzed to obtain CAH or to calculate advancing and receding CAs [39,40]. It is demonstrated that not all values of b are possible (see Fig. 1(j)). Under the boundary conditions of constant volume and constant hY, the value b = arc cot [(tanhY)/2] [36]. The geometrical relationship and the FEB for transition with paraboloidal profile of anisotropic surface along the cutting angle (a), respectively, can be expressed as (see Fig. 1(j)):
hA
L2A 2
sin hA
cla
hA
LB LA hA sin hB sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R2 2 4 4h ðsin aÞ x2 A hðsin aÞ2 tan b þ@ 1þ dx cos hY 4 R 0 ! b þ 2R 2R2 2 sin a hðsin aÞ tan b
DF A!C
cla
Similarly, the FE change of trapezoidal profile micro texture for the transition from non-composite state to composite state can be written as:
ð23Þ
¼ hB
ð24Þ
L2A cothA þ
LC LA hA sin hC sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R2 2 4 4h ðsin aÞ x2 A hðsin aÞ2 tan b @ 1þ dx cos hY R4 0
ð27Þ
h sin a tan b
! Z R2 2 2 2LA sin a ðb þ 2RÞR2 hðsin aÞ2 tanb hðsin aÞ x 2 dx 2 b þ 2R hðsin aÞ3 ðtanbÞ2 R2 sin hA 0 ! 2 Z R 2 2 L2 2LC sin a hðsin aÞ2 tanb hðsin aÞ x ð25Þ ¼ hC C 2 L2C cothC 2 dx b þ 2R sinhC R2 0 L2A
Lcom Lnon hnon sin hcom sin hnon ( Lcom sin a b þ 2R 2R2 2 sin a 2R þ b h sin a tan b sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 9 2 Z R 2 4 = sin a b 4x2 h sin a 5 4 þ2 þ 1þ dx cos hY ; R2 sin a R 2
DE1 ¼ hcom
L2A cothA
! Z R2 2 2 2LA sin a ðb þ 2RÞR2 hðsin aÞ2 tanb hðsin aÞ x þ 2 dx b þ 2R hðsin aÞ3 ðtanbÞ2 R2 0 ! Z R2 2 2 L2 2LB sin a hðsin aÞ2 tanb hðsin aÞ x ¼ hB B 2 L2B cothB 2 dx b þ 2R sinhB R2 0
DF A!B
receding CA (hr) as well as CAH defined as (ha hr) can be obtained by the intersecting values of advancing and receding curves with the x-axis, respectively. Here it should be pointed out that the out vibrational energy [41] is assumed to have a value of zero. Further, we consider non-composite state associated with a droplet width (Lnon) and a CA (hnon) (see Fig. 3(b)). If such a system shows a composite state associated with an equivalent droplet width (Lnon = Lcom) and a CA (hcom), the FE change of paraboloidal profile of micro texture for the transition from non-composite state to composite state can be expressed as:
¼ hC
ð26Þ
Combine Eqs. (13)–(26), the FE and FEB curve can be obtained. Fig. 4(a) illustrates two FE curves both the non-composite and composite wetting state. One can see that there is only one value of the lowest FE for each curve which is associated with the ECA. However, if CA varies slightly on the order of 103 degree (drop advances from a position A to B and recedes from A to C, as illustrated in Fig. 1), the local curve can shows a fluctuation in FE (see the inset of Fig. 4(a)). It is indicated that the FE curve contains numerous local minimum and maximum FE, corresponding to the metastable and unstable equilibrium states. The FEB is defined as the difference between local minimum and maximum along three-phase line motion. It should be stressed that the variation of advancing or receding contact angle is different from the experimental results. If the contact line recedes from point A to C (Fig. 4(a)), the droplet will not remain adhesive. If the value of FEB equals to zero, the droplet will be pinned. In this case, the maximum advancing and minimum receding CAs are calculated by the zero FEB equations (see Fig. 4(b)). The advancing CA (ha) and
Lcom Lnon hnon sin hcom sin hnon Lcom sin a b 2h þ 2R þ b sin a sin a tan U " ) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# b 1 cos h þ 2h 1 þ þ Y 2 sin a ðsin a tan UÞ
DE2 ¼ hcom
ð28Þ
3. Effect of different profile shape of parallel grooved micro texture 3.1. Effect of different profile shape of parallel grooved micro texture on FE and FEB Dependence of normalized free energy (FE) against apparent CA for different profile shape of micro texture is shown in Fig. 5(a) and (b). Compared Fig. 5(a) and (b), it is important to note that if the cutting angle a is lower than the critical value ac, the FE is lower than that of composite state. It is indicated that the non-composite state is more stable than the composite state. Thus, the system will prefer the non-composite state. However, if the cutting angle a exceeds the critical values, the system will prefer the composite state. Further comparison the four different profile shape of micro texture shows that the thermodynamic stable ability in non-composite state is sequenced as following, triangle > paraboloid > trapezoid > pillar. However, the thermodynamic stable ability in composite state is paraboloid < triangle < trapezoid < pillar. Furthermore, Fig. 5(c) and (d) shows the effect of different profile shape of micro texture on FEB both non-composite and composite states. It is interesting to note that the advancing and receding CA of trapezoidal and pillar micro texture keeps unchanged as free energy barrier equal zero. However, the receding FEB and CA (hr) of paraboloidal micro texture is lower in non-composite or higher in composite state than the corresponding value of trapezoidal and pillar micro texture; the advancing FEB and CA (ha) of paraboloidal micro texture is higher in non-composite or lower in composite state than the corresponding value of trapezoidal and pillar profile of micro texture. It is also found that the receding FEB of trapezoidal profile of micro texture is lower than the corresponding value with pillar shape, but the advancing FEB of trapezoidal profile of micro texture is lower in
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Fig. 4. (a) Variation of normalized FE with CA for a non-composite (non) and composite (com) states. The inset shows an enlarge view of a segment of FE curve illustrating the FEB; positions A, B, and C correspond to those in Fig. 1(j). DAB and DAC represent the FEB for receding and advancing contact line, respectively; (b) determining receding and advancing CAs as well as CAH from the typical curves of advancing and receding FEBs for a non-composite wetting state (L = 0.01 m, b = 2 lm, R = 1.0 lm, h = 2.6 lm; cutting angle a = 30°;intrinsic CA, hY = 120°). The CAH shown is the maximum value associated with zero FEB on the advancing and receding branches of the FE curve.
Fig. 5. Dependence of normalized FE against apparent CA for different micro texture shape with non-composite and composite wetting states ((a) a = 20° and (b) a = 80°); (c) variations of normalized free energy barrier (FEB) with respect to apparent CA for different micro texture shape with non-composite (non) and composite (com) wetting states ((c) a = 20° and (d) a = 80°). (L0 = 0.01 m; hY = 120°; b = 2 lm; R = 1 lm; pillar U = 90°, h = 1.87 lm; trapezoid U = 78°, h = 2.3 lm; paraboloid h = 2.6 lm; triangle U = 69.6°, h = 2.7 lm.)
non-composite or higher in composite state than the corresponding value of pillar shape. 3.2. Effect of different profile shape of parallel grooved micro texture on ECA, CAH and the wetting transition The criterion for the transition from non-composite to composite wetting states can be obtained by Eqs. (27) and (28) when we ignore the outer vibrational energy, i. e., DE1 = 0 and DE2 = 0. At the transition point, i. e., hcom = hnc, the critical cutting angle ac with trapezoidal and paraboloidal profile of micro texture for the
transition between the non-composite and composite states can be obtained. It is demonstrated that critical height or base angle are necessary to promote the transition from non-composite to composite states [20,42,43]. Here, it is important to note from Fig. 6(a) and (b) that there is a critical cutting angle ac. If the cutting angle a exceeds the critical value ac, the transition from non-composite to composite state may be occurred. Meanwhile, for the flatted top micro texture shape, it is significantly pointed out that the critical cutting angle ac decreases with increasing the base angle (U); however, for the non-flatted top, such as paraboloidal profile micro texture, the critical cutting angle is larger
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than the corresponding value of flatted top pillar and trapezoidal profile micro texture. Further investigation shows that for the triangle micro texture, the system always stays in non-composite wetting state. This indicates that, if base angle U of flatted top shape micro texture decreases largely or the micro texture shape changes from flatted top pillar or trapezoid to non-flatted top paraboloid, the wetting behavior of the composite state is similar to that of the non-composite state and the anisotropy will possibly be appear. To further quantify the contact angle and hysteresis anisotropy, the anisotropic index of contact angle and hysteresis for each system, dCA and dCAH, can be defined as:
R ac
hW da hCB da; R hW da þ þpac=2 0 R ac h da 0 HW ¼ R ac R p=2 hHW da þ ac hHCB da 0
dCA ¼ R ac dCAH
0
ð29Þ
where hW and hCB stands for the equilibrium contact angle in non-composite and composite wetting state; hHW and hHCB stands for the contact angle hysteresis in non-composite and composite wetting state. ac is the critical cutting angle for the transition from the non-composite to composite wetting state. The results suggest that the anisotropic index of contact angle and hysteresis for different micro texture shape are different as illustrated in Fig. 6(c). Further, it is indicated that the anisotropic wetting behavior of non-flatted top paraboloidal profile micro texture is much stronger than that of flatted top pillar and trapezoidal profile micro texture; however, the anisotropic wetting behavior of paraboloidal profile micro texture is lower than that of triangle profile micro texture. Further, the results imply that the anisotropic wetting behavior of trapezoidal profile micro texture is stronger than that of pillar profile of micro texture. The above results imply that the anisotropy of
ECA and CAH strongly depend on the specific topographical features. Besides, variations of ECA in both non-composite and composite states for various micro texture shapes are shown in Fig. 6(a). It is of interest to see that the effect of micro texture shape on ECA for the non-composite state is entirely opposite to that for the composite state. One can also find that for the non-composite state, the calculated ECA increases sharply with the increase of cutting angle a and shows obvious wetting anisotropy. However, the calculated ECA almost keep unchanged with the increase of cutting angle and shows wetting isotropic in the composite state. Further investigation shows that effect of the specific topographical features on ECA in non-composite almost keep unchanged. However, it is obvious in composite state and for fixed the cutting angle (a) that the ECA is sequenced as following, paraboloid > trapezoid > pillar. The above analysis provides another possible theoretical interpretation for the Sommers et al.’s experimental phenomenon that a droplet on a certain microstructure surface can exhibit both non-composite and composite states at the same time, depending on the orientation [44]. Further, from Fig. 6(b), it is obviously noted that for the non-composite state, the CAH increases sharply with the increase of cutting angle a and shows obvious wetting anisotropy, meanwhile, for fixed the cutting angle a, the CAH is sequenced as following, triangle < trapezoid < pillar < paraboloid. However, for the composite state, the calculated CAH almost keep unchanged with the increase of cutting angle, more significantly, for non-flatted top paraboloidal profile micro texture, there is a shift from a bigger to smaller value of CAH. Thus, the CAH of paraboloidal profile micro texture is much lower than the corresponding of pillar and trapeziod. This comes from the flatted top edges of pillar and trapezoid which possesses the pinning of the droplet. It is understood that the re-entrant structures exists obvious advantages for fabricating superhydrophobic and omniphobic
Fig. 6. (a) Variation of ECA for different micro texture shape against cutting angle with non-composite and composite wetting states; (b) thermodynamically plausible variations of CAH for different micro texture shape versus cutting angle; (c) anisotropic index of contact angle and contact angle hysteresis versus different micro texture shape; (pillar U = 90°, h = 1.87 lm; trapezoid U = 78°, h = 2.3 lm; paraboloid h = 2.6 lm; triangle U = 69.6°, h = 2.7 lm) (d) critical contact angle for different micro texture shape versus cutting angle a. (L0 = 0.01 m; hY = 120°; R = 1 lm; b = 2 lm.)
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Fig. 7. Dependence of normalized FE (a) and FEB (b) against CA for paraboloidal profile of groove micro texture surface with different cutting angle in non-composite and composite wetting states. (L0 = 0.01 m; hY = 120°; b = 2 lm; R = 1 lm; h = 2.6 lm); thermodynamically plausible variations of ECA (c) and CAH (d) against height of paraboloidal profile of groove micro texture surface, intrinsic angle (hY) and cutting angle in non-composite and composite wetting states. (L0 = 0.01 m; hY = 120°; b = 2 lm; R = 1 lm.)
surfaces [45]. Recently, Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference [14]. The paraboloidal profile of parallel micro-structure surface is prepared by the femtosecond laser irradiation method [46,47]. It is known that the ECA does not increases much with increasing the roughness beyond the transition value and may become susceptible to mechanical breakage [48]. Therefore, this paper mainly pays attention to the wetting criteria, that is the transition value of ECA and CAH between the non-composite and composite wetting state. Fig. 6(d) shows that the critical ECA against the cutting angle a for the various surface topographies. It is indicated the ECA and CAH are closely related to the specific topographical features and wetting state. The paraboloidal profile of parallel micro-texture surface is used as more advantageous in superhydrophobicity among these topographies due to the critical ECA is relatively higher and the CAH is lower; while this micro-texture exists stronger anisotropic wetting behavior.
4. Anisotropic wetting behavior on gradient of paraboloidal profile of parallel micro texture surface It is illustrated that the FE and the receding FEB with corresponding CA (hr) or advancing FEB with corresponding CA (ha) of paraboloidal profile of micro texture increased with increasing the cutting angle as shown in Fig. 7(a) and (b). Consider a droplet on depth or chemical gradient of paraboloidal profile of parallel
micro texture surface, the contact angles had axial asymmetry, leading to different contact angles along the gradient micro-groove. Such an asymmetric droplet shape implies a Laplace pressure gradient, [49] thus leading to the droplet’s favorable movement along the gradient direction. However, this phenomenon did not exist in a level micro-paraboloid grooved surface; owing to all micro-groove height is same. From Fig. 7(c), for paraboloidal profile micro texture, it is noted that the anisotropy of ECA in non-composite state has been amplified with the increase of micro-paraboloid-groove height (h) or chemical intrinsic CA (hY). The conclusion is consistent with the experimental result [50] meanwhile, the ECA increases with increasing the micro-paraboloidal grooved height (h) or chemical intrinsic CA (hY). Moreover, from Fig. 7(d), it leads to much or less of CAH with increasing the height or intrinsic CA in non-composite state; however, the CAH keep a constant value with variation of the height or intrinsic CA of the paraboloidal profile grooved micro texture in the composite state. This means that the gradient micro-paraboloidal grooved surface with large micro-groove gradient height or small chemical intrinsic CA produced a large difference in advancing contact angles ha and receding contact angle hr. This will lead to strong droplet self-movement trend to shallow or large chemistry intrinsic CA of paraboloidal micro-grooved. Additionally, one can obviously see that the critical cutting angle for the transition from non-composite to composite wetting state increases with decreasing the height or intrinsic CA of paraboloidal profile micro texture. This indicates that the wetting behavior of the composite state is same to that for the non-composite state and the anisotropy will
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possibly be appear with decreasing the steepness or intrinsic CA of paraboloidal profile micro texture. Such an anisotropic behavior in the transition of thermodynamic states may find potential applications in the liquid delivery or transfer; therefore, it is a practical strategy to promote a thermodynamic transition from non-composite to composite in order to achieve this desired controllable wetting behavior. 5. Conclusions Compared to the previous paper [29,30,36], how the topographical features and surface geometries or micro texture affect anisotropic wettability behavior have been theoretically investigated. Various parallel micro texture surfaces have been systematically investigated in detail. It is demonstrated that the anisotropic wetting behavior is closely related to the specific topographical features and wetting state. Meanwhile, it is of interest to see that the effect of micro texture shape on ECA and CAH for the non-composite state is entirely opposite to that for the composite state. The paraboloidal profile of parallel micro texture surfaces is considered more advantageous in superhydrophobicity. While this micro-texture exists stronger anisotropic wetting behavior. Particularly, it is indicated that the wetting behavior of the composite state is similar to that of the non-composite state and the anisotropy wetting property may be appeared with decreasing the height or intrinsic CA of paraboloidal profile micro texture. These conclusions are likely to be used both academic research and design of controllable wetting applications [1–5]. Acknowledgments The National Natural Science Foundation of China under Grant Nos. 11172301, and 21203217, and the Western Light Talent Culture project and the Top Hundred Talents project of Chinese Academy of Sciences. The National 973 project of China under Grant No. 2013CB632300. References [1] Y.M. Zheng, X.F. Gao, L. Jiang, Soft Matter 3 (2007) 178–182. [2] T. Kim, K.Y. Suh, Soft Matter 5 (2009) 4131–4135. [3] N.A. Malvadkar, M.J. Hancock, K. Sekeroglu, W.J. Dressick, M.C. Demirel, Nat. Mater. 9 (2010) 1023–1028. [4] C. Rascon, A.O. Parry, Nature 407 (2000) 986–989. [5] H. Gau, S. Herminghaus, P. Lenz, R. Lipowsky, Science 283 (1999) 46–49. [6] Z. Guo, F. Zhou, J. Hao, Y. Liang, W. Liu, W. Huck, Appl. Phys. Lett. 89 (2006) 081911–81913. [7] Y. Liu, X. Chen, J.H. Xin, Bioinspired Biomimet. 3 (2008) 046007.
[8] H.M. Whitney, M. Kolle, P. Andrew, L. Chittka, U. Steiner, B.J. Glover, Science 323 (2009) 130–133. [9] Z.G. Guo, W.M. Liu, Plant Sci. 172 (2007) 1103–1112. [10] L. Feng, Y.A. Zhang, J.M. Xi, Y. Zhu, N. Wang, F. Xia, L. Jiang, Langmuir 24 (2008) 4114–4119. [11] K. Liu, X. Yao, L. Jiang, Chem. Soc. Rev. 39 (2010) 3240–3255. [12] L. Feng, S.H. Li, Y.S. Li, H.J. Li, L.J. Zhang, J. Zhai, Y.L. Song, B.Q. Liu, L. Jiang, D.B. Zhu, Adv. Mater. 14 (2002) 1857–1860. [13] (a) X. Zhang, F. Shi, J. Niu, Y.G. Jiang, Z.Q. Wang, J. Mater. Chem. 18 (2008) 621– 633; (b) Y. Chen, B. He, J. Lee, N.A. Patankar, J. Colloid Interface Sci. 281 (2005) 458– 464. [14] Y. Zhao, Q. Lu, M. Li, X. Li, Langmuir 23 (2007) 6212–6217. [15] J.Y. Chung, J.P. Youngblood, C.M. Stafford, Soft Matter 3 (2007) 1163–1169. [16] B. Zhao, J.S. Moore, D.J. Beebe, Science 291 (2001) 1023–1026 (N.Y.). [17] B. Zhao, J.S. Moore, D.J. Beebe, J. Anal. Chem. 74 (2002) 4259–4268. [18] M. Morita, T. Koga, H. Otsuka, A. Takahara, Langmuir 21 (2005) 911–918. [19] D. Zhang, F. Chen, G. Fang, Q. Yang, D. Xie, G. Qiao, W. Li, J. Shi, X. Hou, J. Micromech. Microeng. 20 (2010) 075029. [20] Z. Yoshimitsu, A. Nakajima, T. Watanabe, K. Hashimoto, Langmuir 18 (2002) 5818–5822. [21] F. Zhang, H.Y. Low, Langmuir 23 (2007) 7793–7798. [22] T. Mizukoshi, H. Matsumoto, M. Minagawa, J. Appl. Polym. Sci. 103 (6) (2007) 3811–3817. [23] S. Brandon, N. Haimovich, E. Yeger, A. Marmur, J. Colloid Interface Sci. 263 (2003) 237–243. [24] X. Yong, L.T. Zhang, Langmuir 25 (2009) 5045–5053. [25] H. Kusumaatmaja, J.M. Yeomans, Soft Matter 5 (2009) 2704–2707. [26] K.-H. Chu, R. Xiao, E.N. Wang, Nat. Mater. 9 (2010) 413–417. [27] H. Kusumaatmaja, J. Leopoldes, A. Dupuis, J.M. Yeomans, Euro-phys. Lett. 73 (2006) 740. [28] M. Gleiche, L.F. Chi, H. Fuchs, Nature (London) 403 (6766) (2000) 173–175. [29] W. Li, A. Amirfazli, J. Colloid Interface Sci. 292 (2005) 195. [30] W. Li, A. Amirfazli, Adv. Colloid Interface Sci. 132 (2007) 51. [31] A. Marmur, Langmuir 20 (2004) 3517–3519. [32] P. Li, J. Xie, J. Cheng, K.K. Wu, J. Micromech. Microeng. 24 (2014) 075004. [33] M. Santini, M. Guilizzoni, S. Fest-Santini, J. Colloid Interface Sci. 409 (2013) 204–210. [34] M. Santini, M. Guilizzoni, S. Fest-Santini, M. Lorenzi, Rev. Sci. Instrum. 86 (2015) 023708. [35] M. Santini, M. Guilizzoni, Communications 1 (2014) 14–17. [36] L. Tie, Z.G. Guo, W. Li, J. Colloid Interface Sci. 436 (2014) 19–28. [37] R.N. Wenzel, Ind. Eng. Chem. 28 (1936) 988–994. [38] A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 50 (1944) 546–551. [39] A. Marmur, B. Krasovitski, Langmuir 18 (2002) 8919–8923. [40] N.A. Patankar, Langmuir 20 (2004) 7097–7102. [41] T.S. Meiron, A. Marmur, I.S. Saguy, J. Colloid Interface Sci. 274 (2004) 637–644. [42] C.W. Extrand, Langmuir 18 (2002) 7991–7999. [43] W. Li, X.S. Cui, G.P. Fang, Langmuir 26 (2010) 3194–3202. [44] A.D. Sommers, A.M. Jacobi, J. Micromech. Microeng. 16 (2006) 1571–1578. [45] A. Tuteja, W. Choi, M. Ma, et al., Science 318 (2007) 1618–1622. [46] A.M. Kietzig, S.G. Hatzikiriakos, P. Englezos, Langmuir 25 (8) (2009) 4821– 4827. [47] S. Moradi, S. Kamal, P. Englezos, S.G. Hatzikiriakos, Nanotechnology 24 (2013) 415302. [48] R.E. Johnson, R.H. Dettre, Adv. Chem. Ser. 43 (1964) 112–135. [49] M.K. Chaudhury, G.M. Whitesides, Science 256 (1992). 1539–14.. [50] D. Wu, Q.D. Chen, J. Yao, Y.C. Guan, J.N. Wang, L.G. Niu, H.H. Fang, H.B. Sun, Appl. Phys. Lett. 96 (2010). 053704-3.
Contents lists available at ScienceDirect
Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Anisotropic wetting properties on various shape of parallel grooved microstructure Lu Tie a, Zhiguang Guo a,b,⇑, Weimin Liu a a
State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China Hubei Collaborative Innovation Centre for Advanced Organic Chemical Materials, Ministry of Education Key Laboratory for the Green Preparation and Application of Functional Materials, Hubei University, Wuhan 430062, China b
g r a p h i c a l a b s t r a c t
a r t i c l e
i n f o
Article history: Received 18 March 2015 Accepted 29 April 2015 Available online 8 May 2015 Keywords: Superhydrophobic Anisotropy Free energy Equilibrium contact angle
a b s t r a c t It has been revealed experimentally that some superhydrophobic surfaces in nature, such as rice leaf, show strong anisotropic wetting behavior. In this work, based on a thermodynamic approach, the effects of profile shape of parallel grooved microstructure on free energy (FE) with its barrier (FEB) and equilibrium contact angle (ECA) with its hysteresis (CAH) for various orientations of different parallel micro texture surface have been systematically investigated in detail. The results indicated that the anisotropy of wetting properties strongly depended on the specific topographical features and wetting state. In particular, a paraboloidal profile of parallel micro-texture surface is used as an important example to theoretically establish the relationship between surface geometry and anisotropic wetting behavior for optimal design, showing that the wetting behavior of the composite state is similar to that of the non-composite state and the anisotropy will possibly be appeared with the decrease of height or intrinsic contact angle of paraboloidal profile of micro texture. Ó 2015 Elsevier Inc. All rights reserved.
1. Introduction
⇑ Corresponding author at: State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China. E-mail address: [email protected] (Z. Guo). http://dx.doi.org/10.1016/j.jcis.2015.04.066 0021-9797/Ó 2015 Elsevier Inc. All rights reserved.
Anisotropic wettability on patterned surfaces has recently attracted significant attention in both academic research and designs of controllable wetting applications [1–5]. In nature, anisotropic wetting is observed on biological surfaces [6–12]. The
L. Tie et al. / Journal of Colloid and Interface Science 453 (2015) 142–150
combination of fabricating surface topographic structure [13–15] and chemical modification [16–18] would provide chances for well-designed anisotropic surfaces. As a result, numerous methods to fabricate the anisotropic superhydrophobic surfaces have been reported [18,19]. In the aspect of experiments, a better water-shedding property in the parallel direction of the grooved surface than the pillar structure has been reported [20]. Additionally, the wetting anisotropy on hierarchical structures is investigated [21]. Besides, Mizukoshi et al. [22] discussed the effect of various orderly groove structures on the slide anisotropic behavior, but there are no further investigations of the relationship between geometric parameters and contact angle. In the aspect of theory, Chen et al. showed the 3-D shape profile of a drop does not wet into the grooves of the rough surface on a 1-D grooved surface and obtained similar results as Brandon did [13,23]. Besides, some known models to explain their experimental results on anisotropic wetting have been reported [3,9,18,24–27]. However, these studies are agreement with specific experiment; even there are some contradictions each other [14,15]. It is well known that different micro texture shape with the same roughness value can exhibit completely different superhydrophobic behavior [20]. Meanwhile, for a fixed micro texture, the wetting behavior is closely related to the concerned orientation [28]. Thus, how the topographical features and surface geometries or micro texture affect anisotropic wettability behavior have still remained, especially, in theoretical aspect. In addition, a more general models aimed at fitting experiment is needed. This is helpful to design or control the anisotropy of wetting by tailoring topographic structure and the surface chemistry. In this paper, based on the thermodynamic approach, four different shapes of parallel grooved microstructures were employed to compare with the anisotropic wetting behavior: pillar, trapeziod, paraboloid and triangle (see Fig. 1). Here, it is stressed that the different cross-sectional shapes with the same roughness factor along the direction of cutting angle a = 90° have been considered. The assumption does not mean that the system has the same roughness factor in any cutting direction. The pillar represents a frequently used surface which has been proposed by Li and Amirfazli [29,30], unfortunately, this micro texture is ideal and different from the practical surfaces. While, the paraboloidal profile represent a micro texture of the Lotus leaf [31], and the paraboloidal profile micro texture hardly involves shape edges or corners, Thus it can be fabricated by the practical micro or nano-techniques. Additionally, the trapezoidal profile micro texture can be fabricated by a micro-grinding technique [32]. The theoretical investigations of the paper are well agreement with the experimental specific activities [33–35]. Meanwhile, the conclusions of this study may yield some standards for the design of the controllable microfluidic channels.
143
A main aim is to analyze free energy (FE) and free energy barrier (FEB) completely for any direction of a surface microstructure. Numerous experiments show that the equilibrium contact angle (ECA) for a micro texture along different cutting angle is different [20–27]. Based on minimizing free energy (FE) of a system, a 3-D trapezoidal and paraboloidal profile of parallel grooved micro texture surface as shown in Fig. 1(a) and (f) is also simplified into a 2-D model as illustrated in Fig. 1(e) and (j) by cutting the 3-dimensional structure along a given orientation. This 2-D model can show a different surface geometry, depending on the cutting orientation. Based on such simplification, the thermodynamic status related to surface geometrical configurations of the system and subsequent numerical calculation of FEB can be readily conducted by the corresponding 2-D model. The FEB is the free energy difference between a local minimum and an adjacent maximum in the direction of three-phase line movement. A point to note is that the drop size is much larger than surface micro texture feature size. In our previous work [36], we used a set of geometrical parameters of trapezoidal and paraboloidal base radius (R), space (b), and height (h) to describe a 2-D model resulting from a 3-D surface structure. In the present study, for a given cutting angle (a) in the 3-D groove structure, the corresponding trapezoidal and paraboloidal width (Ra) and space (ba) in the resultant 2-D model can be expressed as:
Ra ¼
R b ; ba ¼ sin a sin a
ð2Þ
where R and b are base radius and space of micro texture (Fig. 1(a) and (f)), respectively, and the cutting angle (a) is given in the x–y reference frame indicated in Fig. 1. It is stressed that the height (h) may be different on various shape of parallel grooved microstructure to ensure that the different cross-sectional shapes with the same roughness factor along the direction of cutting angle a = 90°. For a given orientation with cutting angle (a), Fig. 1(h)–(j) shows a paraboloidal profile micro texture surface and the two states. Along a given orientation with cutting angle (a), the shape of a paraboloid of revolution is described as
z ¼ aa x2
ð3Þ
where x and z are the radial and vertical coordinate measured downward from the apex (see Fig. 1(j)). aa = h sin2a/R2 is the steepness which stands for the shape of paraboloidal profile along a given orientation (a), h stands for the paraboloidal base height and R is the paraboloidal base radius (see Fig. 1(f)). The apparent contact angle (hW) of non-composite state is expressed by Wenzel’s Equation [37]:
cos hW ¼ r cos hY
ð4Þ
From Fig. 1(d) and (i), the roughness factors of trapezoidal r1 and paraboloidal r2 profile in the direction with the cutting angle a are 2. Thermodynamic analysis 2.1. General theoretical considerations
r1 ¼
The contact angle (CA) of a water droplet on an ideal smooth solid surface can be obtained by the Young’s Equation
r2 ¼
cla cos hY ¼ csa cls
ð1Þ
where hY is intrinsic CA. cla, csa, and cls are the surface tension at liquid–air, solid–air, and liquid–solid interfaces, respectively. For a rough surface, there are two wetting states: the non-composite state (complete liquid wet into the troughs of a roughness surface) and composite state (the entrapment of air in the troughs of a roughness surface).
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð2R 2h= tan UÞ þ 2h ðsin aÞ þ ðcot UÞ2 þ b 2R þ b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 sin a=RÞ R2 þ 4h sin a þ R arcsinhð2h þb 2h sin a 2R þ b
ð5Þ
ð6Þ
where U is the base angle of trapezoidal micro texture (Fig. 1(a)). For the composite wetting state, droplets are located on a composite surface composed of solid and air. The apparent contact angle (hCB) can be expressed by Cassie–Baxter Equation [38]:
cos hCB ¼ r f f cos hY þ f 1
ð7Þ
The angle b can be defined as shown in Fig. 1(h). Roughness ratio of the wet area and the solid fraction for the trapezoidal (rf1, f1) and
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Fig. 1. An enlarged view of a 3-D parallel trapezoidal (a) micro texture surface with vertical view (b) and paraboloidal micro texture surface (f) with vertical view (g); a typical 2-D trapezoidal micro textured surface with composite (c) and non-composite (d) along the direction of a; a typical 2-D paraboloidal micro texture surface with composite (h) and non-composite (i) along the direction of a; illustration of variation of a composite droplet on trapezoidal (e) and paraboloidal (j) micro texture surface from state A to B (or to C) along the direction of a.
paraboloidal profile (rf2, f2) along the cutting angle a may be represented as (see Fig. 1(c) and (h)):
2.2. Thermodynamic analysis
rf 1 ¼ 1
In this article, on the basis of thermodynamic analysis, four different cross-sectional shapes of grooved micro texture were used to compare with the anisotropic wetting behavior of the various surface topographies: pillar, trapeziod, paraboloid and triangle (see Fig. 2). Some assumptions have been made as before [29]; meanwhile, the 2-D droplet profile can be considered as a spherical cap and have a constant area for different orientations (analogue of constant volume in 3-D model). FE and FEB associated with CA and CAH for any of cutting orientation both non-composite and composite states can be numerically calculated. In a cutting two-dimensional direction, the expression of FE can be written in the following dimensionless form [36]:
f1 ¼
rf 2
ð2R 2h= tan UÞ 2R þ b
tan b ¼ Arc sinhð2cotbÞ þ 4
f2 ¼
ð8Þ
2R2 ð2R þ bÞðh sin a tan bÞ
ð9Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 4cot2 b 2
ð10Þ
ð11Þ
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Fig. 2. Four different profile of 3-D solid surface topographies. (a) a pillar; (b) a trapezoid; (c) a paraboloid; (d) a triangle.
F ¼
F 2cla S1=2
¼ ðh sin h cos hÞ
1=2
Fig. 3. (a) Illustration of variation of a non-composite droplet on paraboloidal micro texture surface from point A to B (or to C) along the direction of a; (b) illustration of FE analysis for the transition between non-composite and composite states (note drop volume is considered constant for both states).
½h ðr f f cos hY þ f 1Þ sin h ð12Þ
where S is area of the droplet. For a non-composite state (see Fig. 1(e)), if the droplet recedes from position A (CA of hA and droplet size of LA) to B (CA of hB and droplet size of LB) along the cutting angle, the geometrical relationship parameters (h, R, b) and the relative FEB for transition from A to B with trapezoidal profile of micro texture surface along the cutting angle a can be written as:
hA
L2A 2
sin hA
DF A!B
cla
L2A cot hA ¼ hB
¼ hB
L2B sin h2B
L2B cot hB
LB LA ð2R 2h= tan UÞ hA þ cos hY sin a sin hB sin hA
ð13Þ
2h 2b 2 h hA 2 L2A cothA ¼ hC L coth þ þ C C tan U sin a sin a sinh2C sin hA L2C
cla
LC LA hA sin hC sin hA qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b 2 þ 2h 1 þ 1=ðtan U sin aÞ cos hY sin a
2
sin hA
¼ hC
¼ hB
DF A!B
cla
L2B sin h2B
Meanwhile, the geometrical relationship parameters (h, R, b) and the relative FEB for transition from A to B along the cutting angle with paraboloidal profile of micro texture surface can be expressed as (see Fig. 3(a)):
L2B
Z
R sin a
2
hðsin aÞ x2
0
2LB sin a cot hB 2 b þ 2R
! dx
R2 Z R
hðsin aÞ x2
0
R2
sin a
!
2
dx
ð17Þ
LB LA hA sin hB sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R 2 4 sin a b 4h ðsin aÞ x2 A @ þ þ 1þ dx cos hY sin a R4 0
¼ hB
ð18Þ
Similarly, if the droplet advances from A to C along the cutting angle (see Fig. 3(a)), the geometrical relationship and the relative FEB for the transition can be obtained, respectively.
L2A 2
sin hA þ
DF A!C
cla
L2A cot hA
2LA sin a ðb þ 2RÞh 2 sin a b þ 2R
¼ hC ð16Þ
L2A cot hA
2LA sin a ðb þ 2RÞh þ 2 sin a b þ 2R
hA ð15Þ
DF A!C
L2A
ð14Þ
Similarly, one can obtain the geometrical relationship and the relative FEB for the transition with trapezoidal profile of micro texture surface when the droplet advances from A to C along the cutting angle (see Fig. 1(e)), respectively.
L2A
hA
L2C sin h2C
L2C
Z
R sin a
2
hðsin aÞ x2
0
2LC sin a cot hC 2 b þ 2R
R2 Z
R sin a
! dx 2
hðsin aÞ x2
0
LC LA hA sin hC sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R 2 4 sin a 4h ðsin aÞ x2 A @ 1þ dx cos hY 4 R 0
R2
! dx
ð19Þ
¼ hC
ð20Þ
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For a composite state (see Fig. 1(e)), the geometrical relationship and the FEB for transition of trapezoidal profile micro texture anisotropic surface, respectively, can be derived as:
hA
L2A 2
sin hA
DF A!C
cla
L2A cot hA ¼ hC
¼ hC
L2C sin h2C
L2C cot hC
LC LA b 2h hA þ þ sin a tan U sin a sin hC sin hA
ð21Þ
ð22Þ
The position of local minima FE should be analyzed to obtain CAH or to calculate advancing and receding CAs [39,40]. It is demonstrated that not all values of b are possible (see Fig. 1(j)). Under the boundary conditions of constant volume and constant hY, the value b = arc cot [(tanhY)/2] [36]. The geometrical relationship and the FEB for transition with paraboloidal profile of anisotropic surface along the cutting angle (a), respectively, can be expressed as (see Fig. 1(j)):
hA
L2A 2
sin hA
cla
hA
LB LA hA sin hB sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R2 2 4 4h ðsin aÞ x2 A hðsin aÞ2 tan b þ@ 1þ dx cos hY 4 R 0 ! b þ 2R 2R2 2 sin a hðsin aÞ tan b
DF A!C
cla
Similarly, the FE change of trapezoidal profile micro texture for the transition from non-composite state to composite state can be written as:
ð23Þ
¼ hB
ð24Þ
L2A cothA þ
LC LA hA sin hC sin hA 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Z R2 2 4 4h ðsin aÞ x2 A hðsin aÞ2 tan b @ 1þ dx cos hY R4 0
ð27Þ
h sin a tan b
! Z R2 2 2 2LA sin a ðb þ 2RÞR2 hðsin aÞ2 tanb hðsin aÞ x 2 dx 2 b þ 2R hðsin aÞ3 ðtanbÞ2 R2 sin hA 0 ! 2 Z R 2 2 L2 2LC sin a hðsin aÞ2 tanb hðsin aÞ x ð25Þ ¼ hC C 2 L2C cothC 2 dx b þ 2R sinhC R2 0 L2A
Lcom Lnon hnon sin hcom sin hnon ( Lcom sin a b þ 2R 2R2 2 sin a 2R þ b h sin a tan b sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 9 2 Z R 2 4 = sin a b 4x2 h sin a 5 4 þ2 þ 1þ dx cos hY ; R2 sin a R 2
DE1 ¼ hcom
L2A cothA
! Z R2 2 2 2LA sin a ðb þ 2RÞR2 hðsin aÞ2 tanb hðsin aÞ x þ 2 dx b þ 2R hðsin aÞ3 ðtanbÞ2 R2 0 ! Z R2 2 2 L2 2LB sin a hðsin aÞ2 tanb hðsin aÞ x ¼ hB B 2 L2B cothB 2 dx b þ 2R sinhB R2 0
DF A!B
receding CA (hr) as well as CAH defined as (ha hr) can be obtained by the intersecting values of advancing and receding curves with the x-axis, respectively. Here it should be pointed out that the out vibrational energy [41] is assumed to have a value of zero. Further, we consider non-composite state associated with a droplet width (Lnon) and a CA (hnon) (see Fig. 3(b)). If such a system shows a composite state associated with an equivalent droplet width (Lnon = Lcom) and a CA (hcom), the FE change of paraboloidal profile of micro texture for the transition from non-composite state to composite state can be expressed as:
¼ hC
ð26Þ
Combine Eqs. (13)–(26), the FE and FEB curve can be obtained. Fig. 4(a) illustrates two FE curves both the non-composite and composite wetting state. One can see that there is only one value of the lowest FE for each curve which is associated with the ECA. However, if CA varies slightly on the order of 103 degree (drop advances from a position A to B and recedes from A to C, as illustrated in Fig. 1), the local curve can shows a fluctuation in FE (see the inset of Fig. 4(a)). It is indicated that the FE curve contains numerous local minimum and maximum FE, corresponding to the metastable and unstable equilibrium states. The FEB is defined as the difference between local minimum and maximum along three-phase line motion. It should be stressed that the variation of advancing or receding contact angle is different from the experimental results. If the contact line recedes from point A to C (Fig. 4(a)), the droplet will not remain adhesive. If the value of FEB equals to zero, the droplet will be pinned. In this case, the maximum advancing and minimum receding CAs are calculated by the zero FEB equations (see Fig. 4(b)). The advancing CA (ha) and
Lcom Lnon hnon sin hcom sin hnon Lcom sin a b 2h þ 2R þ b sin a sin a tan U " ) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi# b 1 cos h þ 2h 1 þ þ Y 2 sin a ðsin a tan UÞ
DE2 ¼ hcom
ð28Þ
3. Effect of different profile shape of parallel grooved micro texture 3.1. Effect of different profile shape of parallel grooved micro texture on FE and FEB Dependence of normalized free energy (FE) against apparent CA for different profile shape of micro texture is shown in Fig. 5(a) and (b). Compared Fig. 5(a) and (b), it is important to note that if the cutting angle a is lower than the critical value ac, the FE is lower than that of composite state. It is indicated that the non-composite state is more stable than the composite state. Thus, the system will prefer the non-composite state. However, if the cutting angle a exceeds the critical values, the system will prefer the composite state. Further comparison the four different profile shape of micro texture shows that the thermodynamic stable ability in non-composite state is sequenced as following, triangle > paraboloid > trapezoid > pillar. However, the thermodynamic stable ability in composite state is paraboloid < triangle < trapezoid < pillar. Furthermore, Fig. 5(c) and (d) shows the effect of different profile shape of micro texture on FEB both non-composite and composite states. It is interesting to note that the advancing and receding CA of trapezoidal and pillar micro texture keeps unchanged as free energy barrier equal zero. However, the receding FEB and CA (hr) of paraboloidal micro texture is lower in non-composite or higher in composite state than the corresponding value of trapezoidal and pillar micro texture; the advancing FEB and CA (ha) of paraboloidal micro texture is higher in non-composite or lower in composite state than the corresponding value of trapezoidal and pillar profile of micro texture. It is also found that the receding FEB of trapezoidal profile of micro texture is lower than the corresponding value with pillar shape, but the advancing FEB of trapezoidal profile of micro texture is lower in
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Fig. 4. (a) Variation of normalized FE with CA for a non-composite (non) and composite (com) states. The inset shows an enlarge view of a segment of FE curve illustrating the FEB; positions A, B, and C correspond to those in Fig. 1(j). DAB and DAC represent the FEB for receding and advancing contact line, respectively; (b) determining receding and advancing CAs as well as CAH from the typical curves of advancing and receding FEBs for a non-composite wetting state (L = 0.01 m, b = 2 lm, R = 1.0 lm, h = 2.6 lm; cutting angle a = 30°;intrinsic CA, hY = 120°). The CAH shown is the maximum value associated with zero FEB on the advancing and receding branches of the FE curve.
Fig. 5. Dependence of normalized FE against apparent CA for different micro texture shape with non-composite and composite wetting states ((a) a = 20° and (b) a = 80°); (c) variations of normalized free energy barrier (FEB) with respect to apparent CA for different micro texture shape with non-composite (non) and composite (com) wetting states ((c) a = 20° and (d) a = 80°). (L0 = 0.01 m; hY = 120°; b = 2 lm; R = 1 lm; pillar U = 90°, h = 1.87 lm; trapezoid U = 78°, h = 2.3 lm; paraboloid h = 2.6 lm; triangle U = 69.6°, h = 2.7 lm.)
non-composite or higher in composite state than the corresponding value of pillar shape. 3.2. Effect of different profile shape of parallel grooved micro texture on ECA, CAH and the wetting transition The criterion for the transition from non-composite to composite wetting states can be obtained by Eqs. (27) and (28) when we ignore the outer vibrational energy, i. e., DE1 = 0 and DE2 = 0. At the transition point, i. e., hcom = hnc, the critical cutting angle ac with trapezoidal and paraboloidal profile of micro texture for the
transition between the non-composite and composite states can be obtained. It is demonstrated that critical height or base angle are necessary to promote the transition from non-composite to composite states [20,42,43]. Here, it is important to note from Fig. 6(a) and (b) that there is a critical cutting angle ac. If the cutting angle a exceeds the critical value ac, the transition from non-composite to composite state may be occurred. Meanwhile, for the flatted top micro texture shape, it is significantly pointed out that the critical cutting angle ac decreases with increasing the base angle (U); however, for the non-flatted top, such as paraboloidal profile micro texture, the critical cutting angle is larger
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than the corresponding value of flatted top pillar and trapezoidal profile micro texture. Further investigation shows that for the triangle micro texture, the system always stays in non-composite wetting state. This indicates that, if base angle U of flatted top shape micro texture decreases largely or the micro texture shape changes from flatted top pillar or trapezoid to non-flatted top paraboloid, the wetting behavior of the composite state is similar to that of the non-composite state and the anisotropy will possibly be appear. To further quantify the contact angle and hysteresis anisotropy, the anisotropic index of contact angle and hysteresis for each system, dCA and dCAH, can be defined as:
R ac
hW da hCB da; R hW da þ þpac=2 0 R ac h da 0 HW ¼ R ac R p=2 hHW da þ ac hHCB da 0
dCA ¼ R ac dCAH
0
ð29Þ
where hW and hCB stands for the equilibrium contact angle in non-composite and composite wetting state; hHW and hHCB stands for the contact angle hysteresis in non-composite and composite wetting state. ac is the critical cutting angle for the transition from the non-composite to composite wetting state. The results suggest that the anisotropic index of contact angle and hysteresis for different micro texture shape are different as illustrated in Fig. 6(c). Further, it is indicated that the anisotropic wetting behavior of non-flatted top paraboloidal profile micro texture is much stronger than that of flatted top pillar and trapezoidal profile micro texture; however, the anisotropic wetting behavior of paraboloidal profile micro texture is lower than that of triangle profile micro texture. Further, the results imply that the anisotropic wetting behavior of trapezoidal profile micro texture is stronger than that of pillar profile of micro texture. The above results imply that the anisotropy of
ECA and CAH strongly depend on the specific topographical features. Besides, variations of ECA in both non-composite and composite states for various micro texture shapes are shown in Fig. 6(a). It is of interest to see that the effect of micro texture shape on ECA for the non-composite state is entirely opposite to that for the composite state. One can also find that for the non-composite state, the calculated ECA increases sharply with the increase of cutting angle a and shows obvious wetting anisotropy. However, the calculated ECA almost keep unchanged with the increase of cutting angle and shows wetting isotropic in the composite state. Further investigation shows that effect of the specific topographical features on ECA in non-composite almost keep unchanged. However, it is obvious in composite state and for fixed the cutting angle (a) that the ECA is sequenced as following, paraboloid > trapezoid > pillar. The above analysis provides another possible theoretical interpretation for the Sommers et al.’s experimental phenomenon that a droplet on a certain microstructure surface can exhibit both non-composite and composite states at the same time, depending on the orientation [44]. Further, from Fig. 6(b), it is obviously noted that for the non-composite state, the CAH increases sharply with the increase of cutting angle a and shows obvious wetting anisotropy, meanwhile, for fixed the cutting angle a, the CAH is sequenced as following, triangle < trapezoid < pillar < paraboloid. However, for the composite state, the calculated CAH almost keep unchanged with the increase of cutting angle, more significantly, for non-flatted top paraboloidal profile micro texture, there is a shift from a bigger to smaller value of CAH. Thus, the CAH of paraboloidal profile micro texture is much lower than the corresponding of pillar and trapeziod. This comes from the flatted top edges of pillar and trapezoid which possesses the pinning of the droplet. It is understood that the re-entrant structures exists obvious advantages for fabricating superhydrophobic and omniphobic
Fig. 6. (a) Variation of ECA for different micro texture shape against cutting angle with non-composite and composite wetting states; (b) thermodynamically plausible variations of CAH for different micro texture shape versus cutting angle; (c) anisotropic index of contact angle and contact angle hysteresis versus different micro texture shape; (pillar U = 90°, h = 1.87 lm; trapezoid U = 78°, h = 2.3 lm; paraboloid h = 2.6 lm; triangle U = 69.6°, h = 2.7 lm) (d) critical contact angle for different micro texture shape versus cutting angle a. (L0 = 0.01 m; hY = 120°; R = 1 lm; b = 2 lm.)
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Fig. 7. Dependence of normalized FE (a) and FEB (b) against CA for paraboloidal profile of groove micro texture surface with different cutting angle in non-composite and composite wetting states. (L0 = 0.01 m; hY = 120°; b = 2 lm; R = 1 lm; h = 2.6 lm); thermodynamically plausible variations of ECA (c) and CAH (d) against height of paraboloidal profile of groove micro texture surface, intrinsic angle (hY) and cutting angle in non-composite and composite wetting states. (L0 = 0.01 m; hY = 120°; b = 2 lm; R = 1 lm.)
surfaces [45]. Recently, Submicrometer-scale periodic structures consisting of parallel grooves were prepared on azobenzene-containing multiarm star polymer films by laser interference [14]. The paraboloidal profile of parallel micro-structure surface is prepared by the femtosecond laser irradiation method [46,47]. It is known that the ECA does not increases much with increasing the roughness beyond the transition value and may become susceptible to mechanical breakage [48]. Therefore, this paper mainly pays attention to the wetting criteria, that is the transition value of ECA and CAH between the non-composite and composite wetting state. Fig. 6(d) shows that the critical ECA against the cutting angle a for the various surface topographies. It is indicated the ECA and CAH are closely related to the specific topographical features and wetting state. The paraboloidal profile of parallel micro-texture surface is used as more advantageous in superhydrophobicity among these topographies due to the critical ECA is relatively higher and the CAH is lower; while this micro-texture exists stronger anisotropic wetting behavior.
4. Anisotropic wetting behavior on gradient of paraboloidal profile of parallel micro texture surface It is illustrated that the FE and the receding FEB with corresponding CA (hr) or advancing FEB with corresponding CA (ha) of paraboloidal profile of micro texture increased with increasing the cutting angle as shown in Fig. 7(a) and (b). Consider a droplet on depth or chemical gradient of paraboloidal profile of parallel
micro texture surface, the contact angles had axial asymmetry, leading to different contact angles along the gradient micro-groove. Such an asymmetric droplet shape implies a Laplace pressure gradient, [49] thus leading to the droplet’s favorable movement along the gradient direction. However, this phenomenon did not exist in a level micro-paraboloid grooved surface; owing to all micro-groove height is same. From Fig. 7(c), for paraboloidal profile micro texture, it is noted that the anisotropy of ECA in non-composite state has been amplified with the increase of micro-paraboloid-groove height (h) or chemical intrinsic CA (hY). The conclusion is consistent with the experimental result [50] meanwhile, the ECA increases with increasing the micro-paraboloidal grooved height (h) or chemical intrinsic CA (hY). Moreover, from Fig. 7(d), it leads to much or less of CAH with increasing the height or intrinsic CA in non-composite state; however, the CAH keep a constant value with variation of the height or intrinsic CA of the paraboloidal profile grooved micro texture in the composite state. This means that the gradient micro-paraboloidal grooved surface with large micro-groove gradient height or small chemical intrinsic CA produced a large difference in advancing contact angles ha and receding contact angle hr. This will lead to strong droplet self-movement trend to shallow or large chemistry intrinsic CA of paraboloidal micro-grooved. Additionally, one can obviously see that the critical cutting angle for the transition from non-composite to composite wetting state increases with decreasing the height or intrinsic CA of paraboloidal profile micro texture. This indicates that the wetting behavior of the composite state is same to that for the non-composite state and the anisotropy will
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possibly be appear with decreasing the steepness or intrinsic CA of paraboloidal profile micro texture. Such an anisotropic behavior in the transition of thermodynamic states may find potential applications in the liquid delivery or transfer; therefore, it is a practical strategy to promote a thermodynamic transition from non-composite to composite in order to achieve this desired controllable wetting behavior. 5. Conclusions Compared to the previous paper [29,30,36], how the topographical features and surface geometries or micro texture affect anisotropic wettability behavior have been theoretically investigated. Various parallel micro texture surfaces have been systematically investigated in detail. It is demonstrated that the anisotropic wetting behavior is closely related to the specific topographical features and wetting state. Meanwhile, it is of interest to see that the effect of micro texture shape on ECA and CAH for the non-composite state is entirely opposite to that for the composite state. The paraboloidal profile of parallel micro texture surfaces is considered more advantageous in superhydrophobicity. While this micro-texture exists stronger anisotropic wetting behavior. Particularly, it is indicated that the wetting behavior of the composite state is similar to that of the non-composite state and the anisotropy wetting property may be appeared with decreasing the height or intrinsic CA of paraboloidal profile micro texture. These conclusions are likely to be used both academic research and design of controllable wetting applications [1–5]. Acknowledgments The National Natural Science Foundation of China under Grant Nos. 11172301, and 21203217, and the Western Light Talent Culture project and the Top Hundred Talents project of Chinese Academy of Sciences. The National 973 project of China under Grant No. 2013CB632300. References [1] Y.M. Zheng, X.F. Gao, L. Jiang, Soft Matter 3 (2007) 178–182. [2] T. Kim, K.Y. Suh, Soft Matter 5 (2009) 4131–4135. [3] N.A. Malvadkar, M.J. Hancock, K. Sekeroglu, W.J. Dressick, M.C. Demirel, Nat. Mater. 9 (2010) 1023–1028. [4] C. Rascon, A.O. Parry, Nature 407 (2000) 986–989. [5] H. Gau, S. Herminghaus, P. Lenz, R. Lipowsky, Science 283 (1999) 46–49. [6] Z. Guo, F. Zhou, J. Hao, Y. Liang, W. Liu, W. Huck, Appl. Phys. Lett. 89 (2006) 081911–81913. [7] Y. Liu, X. Chen, J.H. Xin, Bioinspired Biomimet. 3 (2008) 046007.
[8] H.M. Whitney, M. Kolle, P. Andrew, L. Chittka, U. Steiner, B.J. Glover, Science 323 (2009) 130–133. [9] Z.G. Guo, W.M. Liu, Plant Sci. 172 (2007) 1103–1112. [10] L. Feng, Y.A. Zhang, J.M. Xi, Y. Zhu, N. Wang, F. Xia, L. Jiang, Langmuir 24 (2008) 4114–4119. [11] K. Liu, X. Yao, L. Jiang, Chem. Soc. Rev. 39 (2010) 3240–3255. [12] L. Feng, S.H. Li, Y.S. Li, H.J. Li, L.J. Zhang, J. Zhai, Y.L. Song, B.Q. Liu, L. Jiang, D.B. Zhu, Adv. Mater. 14 (2002) 1857–1860. [13] (a) X. Zhang, F. Shi, J. Niu, Y.G. Jiang, Z.Q. Wang, J. Mater. Chem. 18 (2008) 621– 633; (b) Y. Chen, B. He, J. Lee, N.A. Patankar, J. Colloid Interface Sci. 281 (2005) 458– 464. [14] Y. Zhao, Q. Lu, M. Li, X. Li, Langmuir 23 (2007) 6212–6217. [15] J.Y. Chung, J.P. Youngblood, C.M. Stafford, Soft Matter 3 (2007) 1163–1169. [16] B. Zhao, J.S. Moore, D.J. Beebe, Science 291 (2001) 1023–1026 (N.Y.). [17] B. Zhao, J.S. Moore, D.J. Beebe, J. Anal. Chem. 74 (2002) 4259–4268. [18] M. Morita, T. Koga, H. Otsuka, A. Takahara, Langmuir 21 (2005) 911–918. [19] D. Zhang, F. Chen, G. Fang, Q. Yang, D. Xie, G. Qiao, W. Li, J. Shi, X. Hou, J. Micromech. Microeng. 20 (2010) 075029. [20] Z. Yoshimitsu, A. Nakajima, T. Watanabe, K. Hashimoto, Langmuir 18 (2002) 5818–5822. [21] F. Zhang, H.Y. Low, Langmuir 23 (2007) 7793–7798. [22] T. Mizukoshi, H. Matsumoto, M. Minagawa, J. Appl. Polym. Sci. 103 (6) (2007) 3811–3817. [23] S. Brandon, N. Haimovich, E. Yeger, A. Marmur, J. Colloid Interface Sci. 263 (2003) 237–243. [24] X. Yong, L.T. Zhang, Langmuir 25 (2009) 5045–5053. [25] H. Kusumaatmaja, J.M. Yeomans, Soft Matter 5 (2009) 2704–2707. [26] K.-H. Chu, R. Xiao, E.N. Wang, Nat. Mater. 9 (2010) 413–417. [27] H. Kusumaatmaja, J. Leopoldes, A. Dupuis, J.M. Yeomans, Euro-phys. Lett. 73 (2006) 740. [28] M. Gleiche, L.F. Chi, H. Fuchs, Nature (London) 403 (6766) (2000) 173–175. [29] W. Li, A. Amirfazli, J. Colloid Interface Sci. 292 (2005) 195. [30] W. Li, A. Amirfazli, Adv. Colloid Interface Sci. 132 (2007) 51. [31] A. Marmur, Langmuir 20 (2004) 3517–3519. [32] P. Li, J. Xie, J. Cheng, K.K. Wu, J. Micromech. Microeng. 24 (2014) 075004. [33] M. Santini, M. Guilizzoni, S. Fest-Santini, J. Colloid Interface Sci. 409 (2013) 204–210. [34] M. Santini, M. Guilizzoni, S. Fest-Santini, M. Lorenzi, Rev. Sci. Instrum. 86 (2015) 023708. [35] M. Santini, M. Guilizzoni, Communications 1 (2014) 14–17. [36] L. Tie, Z.G. Guo, W. Li, J. Colloid Interface Sci. 436 (2014) 19–28. [37] R.N. Wenzel, Ind. Eng. Chem. 28 (1936) 988–994. [38] A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 50 (1944) 546–551. [39] A. Marmur, B. Krasovitski, Langmuir 18 (2002) 8919–8923. [40] N.A. Patankar, Langmuir 20 (2004) 7097–7102. [41] T.S. Meiron, A. Marmur, I.S. Saguy, J. Colloid Interface Sci. 274 (2004) 637–644. [42] C.W. Extrand, Langmuir 18 (2002) 7991–7999. [43] W. Li, X.S. Cui, G.P. Fang, Langmuir 26 (2010) 3194–3202. [44] A.D. Sommers, A.M. Jacobi, J. Micromech. Microeng. 16 (2006) 1571–1578. [45] A. Tuteja, W. Choi, M. Ma, et al., Science 318 (2007) 1618–1622. [46] A.M. Kietzig, S.G. Hatzikiriakos, P. Englezos, Langmuir 25 (8) (2009) 4821– 4827. [47] S. Moradi, S. Kamal, P. Englezos, S.G. Hatzikiriakos, Nanotechnology 24 (2013) 415302. [48] R.E. Johnson, R.H. Dettre, Adv. Chem. Ser. 43 (1964) 112–135. [49] M.K. Chaudhury, G.M. Whitesides, Science 256 (1992). 1539–14.. [50] D. Wu, Q.D. Chen, J. Yao, Y.C. Guan, J.N. Wang, L.G. Niu, H.H. Fang, H.B. Sun, Appl. Phys. Lett. 96 (2010). 053704-3.