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A modified Wenzel model for hydrophobic behavior of nanostructured surfaces
Thin Solid Films 515 (2007) 4666 – 4669 www.elsevier.com/locate/tsf
A modified Wenzel model for hydrophobic behavior of nanostructured surfaces Tao-Yun Han a,⁎, Jin-Fang Shr b , Chu-Fu Wu b , Chien-Te Hsieh c a
c
Department of Civil Engineering and Engineering Informatics, Chung-Hua University, Hsinchu 300, Taiwan b Graduate Institute of Construction Management, Chung-Hua University, Hsinchu 300, Taiwan Department of Chemical Engineering and Materials Science/Fuel Cell Center, Yuan Ze University, Taoyuan 320, Taiwan Received 1 March 2006; received in revised form 3 October 2006; accepted 3 November 2006 Available online 22 January 2007
Abstract A modified Wenzel model was proposed to explore the influence of pore size distributions (PSDs) on water repellency of nanostructured surfaces. Rough surfaces with different porous structures, including surface areas and PSDs, were fabricated by stacking different solid ratios of TiO2 nanoparticles. These fluorinated surfaces exhibited an excellent hydrophobic performance with the highest value of contact angle ∼ 165°. The PSDs of these surfaces, determined from Dubinin–Stoeckli equation, were found to vary with the solid ratios. The modified Wenzel model incorporated with the PSDs gave a fairly good prediction in describing the variation of contact angle with surface roughness, which is very close to the experimental data. These results demonstrated that the heterogeneity of surfaces caused by different PSDs would induce the hydrophobic behavior. © 2006 Elsevier B.V. All rights reserved. Keyword: Nanostructures; Water repellency; Wenzel model; Pore size distribution; Contact angle
1. Introduction Water repellency of solid surfaces with a liquid in air is a promising phenomenon that can be applied in a variety of applications such as microfluidic devices, antisoiling or antifouling surfaces, efficient heat-transfer areas, or nonbinding biopassive surfaces [1]. Such hydrophobic surfaces usually reach a high value of contact angle N 150° or higher. For a daily application, a functional coating on automobile windscreen enables safe driving since raindrops can be bead up and wash off dust in a rainy day [2–6]. In fact, nature has achieved this fascinating effect through the use of a surface topography that presents at least two different length scales to the out environment, i.e., “self-cleaning” or “lotus effect”. Probing this character, the hydrophobicity of surfaces is mainly affected by two factors: the first one is the chemical factor of the solid surface and the liquid with a low surface energy; the other is the geometrical factor of the rough surfaces [5–8]. ⁎ Corresponding author. Tel.: +886 3 4638800x2577; fax: +886 3 4559373. E-mail address: [email protected] (C.-T. Hsieh). 0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.11.008
Apart from chemical nature, Wenzel [9] and Cassie [10] models have initially published a relationship between physical structure and contact angle for a hydrophobic surface. Both the two models have put emphasis on the geometrical structure of solid surfaces that acts as a crucial factor in determining the hydrophobicity. Typically, the Wenzel equation is a simple model to characterize the influence of the surface roughness on the wettability of solid. This model is valid only when the droplet completely contacts the surface over their mutual interface [9,11]. However, a few studies demonstrate that theoretical models are suitable for describing the hydrophobicity of rough surfaces in nanoscale. This study aims to modify the Wenzel model for the description of hydrophobic behavior of nanostructured surfaces. In general, a very rough surface is heterogeneous due to contributions from chemical composition, porosity, pore size distribution, and so on [12–14]. These above factors probably influence the interfacial behavior between vapor, liquid and solid. This suggests that the Wenzel model has to be modified for a porous or very rough surface, especially in nanoscale. In the present work, a series of nanostructured surfaces with
T.-Y. Han et al. / Thin Solid Films 515 (2007) 4666–4669 Table 1 Surface characteristics of rough surfaces with different extents of solid ratios TiO2 loading (wt.%)
BET surface area (m2/g)
Total pore vol. (cm3/g)
Pore size distribution Micro. (%)
Meso. (%)
0 2 4 6 8 10
2.51 6.26 10.2 13.3 16.2 18.7
0.0008 0.0033 0.0052 0.0073 0.0081 0.0089
ND 23 30 36 49 51
ND 77 70 64 51 49
different roughnesses were prepared to study their hydrophobicities. The present work intends to correlate the hydrophobicity of surfaces with their pore size distributions (PSDs) through a modified Wenzel model. The approach presented in this study would probably shed some light on how pore size variation would induce the hydrophobicity of the nanostructured surfaces. 2. Experimental section Titanium dioxide nanoparticles (P25, Degussa Co.) with an average diameter of 20–50 nm were stacked to create different roughened surfaces. At first, different solid ratios of TiO2 slurry, ranging from 2 to 10 wt.%, were mixed and well dispersed with distilled water. A fluoro-containing mixture of perfluoroalkyl methacrylic copolymer (Zonyl 8740, Dupont Co.) and distilled water (7/3 in v/v) was prepared and then mixed with the titania slurry solution. Here the fluorinated copolymer not only acts as a hydrophobic agent to lower surface tension, but also as a binder that provides two bonds: the interface between each particle, and the interface between particle and substrate. According to our previous report [15], the concentration of ∼ 4.8 vol.% of the fluorinated mixture in the total slurry is optimum exhibiting the best hydrophobic performance. We employed a Si (100) wafer as a substrate to avoid surface roughness interference that may come from the substrate. Each piece of the Si wafer was carefully cut into an area of 1 × 1 cm2. After significant dispersion under an ultrasonic bath, the slurries with different TiO2 loadings were spread onto Si wafers, using a spin coater that was operated in a two-stage coating process. The spinning speed of the initial coating was set at 200 rpm for 5 s, and then the second-step speed was raised to 3000 rpm and stayed at this speed for 10 s. Then all the prepared samples were dried at 85 °C in a vacuum oven for 12 h. An automated adsorption apparatus (Micromeritics, ASAP 2010) was employed to measure surface porosity, using adsorption of N2 as a probe species at − 196 °C. The amount of N2 adsorbed at relative pressures near unity was employed to determine the total pore volume, which corresponds to the sum of the micropore and mesopore volumes. All the adsorbed amounts are obtained under equilibrium relative pressure. Surface areas and micropore volumes of the samples were determined from the application of the Brunauer–Emmett– Teller (BET) and Dubinin–Radushkevich (D–R) equations, respectively [16,17]. Contact angles of liquid droplets on the
4667
nanostructured surfaces were determined by an optical contact angle meter (Kyowa Interface Science Co., Ltd., model CA-A). The liquid droplet was dropped to the sample surface from a distance of 5 cm by vibrating the syringe. The diameter of the droplet was around 1 mm. The sample plate was vibrated slightly by tapping the sample stand before each measurement to obtain the equilibrium contact angle. 3. Results and discussion Surface characteristics of the prepared surfaces determined from N2-physisorption measurements are presented in Table 1. It is observed from Table 1 that since the porosity was contributed from surface roughness, both the BET surface area and pore volume have an increasing trend with the solid ratio. This reflects from the fact that the architecture of a nanostructured surface is strongly dominated by the concentration of TiO2 particles in the coating solution. Higher concentration leads to a rougher surface. The relationship between contact angle and BET surface area is drawn in Fig. 1. It can be observed that the contact angle of a water droplet significantly increases with the surface roughness. Comparing the water repellency between samples with and without TiO2 nanoparticles, the contact angles of water droplets show an increase of up to 70%, i.e. from 97° to 165°. A simple model to characterize the influence of surface roughness on wettability of a solid was proposed in the Wenzel equation, which can be represented as follows [9] cos H⁎ ¼ Rw
gSV −gSL ¼ Rw cos H gLV
ð1Þ
where Rw is solid roughness that is defined as the ratio between the actual surface area of a rough surface to the projected one. Eq. (1) clearly indicates the relationship between the contact angle of the flat surface Θ and that of the rough surface Θ⁎. In
Fig. 1. Variation of contact angles with BET surface areas of the surfaces.
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general, the value of Rw is greater than unity, reflecting Θ⁎ N Θ for a hydrophobic situation. Strictly speaking, the applicability of Eq. (1) is limited. This is due to that Wenzel model which is valid only when the droplet completely contacts with the surface over their mutual interface. This means that only well-ordered array or uniform porous media with homogeneous character properly suits to this model. Unfortunately, the above situation is not typical because surface heterogeneity from different PSDs usually exists in real applications. In this sense, a PSD is a fundamental description of heterogeneity of a hydrophobic solid surface. Eq. (1) is only applicable to wettability simulation by liquid droplet on a homogeneous rough surface. However, the distribution of pore size is characteristic of the surface itself; that is, each pore size has its own behavior. How Eq. (1) can be incorporated with the PSDs will be discussed later. According to the above argument, a modified Wenzel model in describing the heterogeneous surfaces is proposed. There are some assumptions for the modified model as depicted as follows: (i) all regions of the rough surface have uniform chemical properties; (ii) surface heterogeneity of the surface is composed of numerous homogeneous areas; (iii) hydrophobic behavior of each small area can be well described by Wenzel model. Accordingly, a Wenzel model based on a modified Rw is rewritten as n P
Si
R Xmax
F ð X ÞdX d cos H ¼ Xmin d cos H S S Z Xmax cos H ¼ d F ð X ÞdX S Xmin
cos H⁎ ¼
i¼1
ð2Þ
where S and Si are the projected area per unit gram flat surface and each rough surface varied with different pore sizes X, respectively. Thus the summation of Si represents a total surface area of rough surfaces. Here, F(X )dX is the actual surface area per gram rough surface in PSD having pore sizes within X and
Fig. 2. Pore size distributions of the prepared surfaces with different solid ratios determined by D–S equation, using Eq. (3).
Table 2 Most suitable parameters of the Dubinin–Stoeckli equation for different rough surfaces TiO2 loading (wt.%)
W0 (cm3/g)
X0 (nm)
δ (nm)
2 4 6 8 10
0.0037 0.0045 0.0069 0.0080 0.0083
1.21 1.01 0.92 0.86 0.82
0.66 0.55 0.53 0.38 0.34
X + d X. Since both cosΘ and S are constants, the two values can thus be brought out of the integral, as showed in the final form of Eq. (2). The lower limit Xmin is the minimum pore size accessible to a nitrogen molecule. Nitrogen has a molecular radius of 0.35 nm, and this value was chosen as the lower limit for the integration. The upper limit Xmax is the maximum size of pores that can be measured by gas adsorption. The value of Θ depends on the contact angle for a fluorinated flat surface ∼ 97°. To resolve PSD of rough surfaces requires further investigation that is described in the following section. Here we assume that the rough surface is heterogeneous, and the surface consists of many small homogeneous regions. To resolve Eq. (2), let F(X ) be the function of PSD initially. The Dubinin–Stoeckli (D–S) equation has been widely employed to determine the distribution of micropore sizes in porous media [18,19]. The D–S model assumes that micropore volume has a normal Gaussian distribution with respect to the size. Assuming the micropores having parallel sided slits, the differential increase in the surface area, dS, is related to the differential increase in the pore volume as follows: " # dW W0 1 ðX0 −X Þ2 dS ¼ ¼ pffiffiffiffiffiffi exp − dX ¼ F ð X ÞdX ð3Þ X 2d2 d 2p X where W is the cumulative micropore volume, W0 is the total micropore volume determined from the D–R equation, X0 is the micropore half width at the distribution curve maximum, and δ is the dispersion parameter. This distribution function can be obtained from the N2 adsorption isotherm by correlating X and the relative pressure, using the Kelvin equation [18,19]. Taking Eq. (3) into Eq. (2), the modified Wenzel model can be completely expressed as " # Z cos H Xmax W0 1 ðX0 −X Þ2 ⁎ pffiffiffiffiffiffi − cos H ¼ dX S 2d2 Xmin d 2p X Based on the N2 isotherms, the pore size distributions of the surfaces investigated were determined from the D–S equation shown as Eq. (4). Since the value of X can be related to P / P0 by employing the Kelvin equation, two independent parameters, X0 and δ, have to be estimated in the fitting to construct a D–S type of distribution. The PSDs of the surfaces were thus determined, and the results are presented in Fig. 2, and the D–S parameters are shown in Table 2. The distribution results show that the sample
T.-Y. Han et al. / Thin Solid Films 515 (2007) 4666–4669
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on hydrophobic behavior. After surface fluorination treatments, contact angles of the rough surfaces had an increase with their specific surface areas. The contact angle of the roughest surface had the highest value of 165°, i.e., an increase of 70%. D–S analysis showed that the PSDs of the surfaces were obviously affected by the solid ratio; that is, the major peak height gradually shifted to a larger pore size as the solid ratio increased. By incorporating the distribution determined by the D–S equation, the modified Wenzel model provides an excellent prediction for the hydrophobicity of water droplets of the nanostructured surfaces. The satisfactory results in the present work demonstrate that the various wettabilities of rough surfaces can be attributed to a surface heterogeneity from different PSDs. Acknowledgments Fig. 3. Variation of contact angles with surface roughness (Rw). The solid line was predicted by the modified Wenzel model, using Eq. (4).
with a lower solid ratio (2 wt.%) has a flatter distribution as well as a larger mean pore size, whereas the sample with 10 wt.% TiO2 particles exhibits the greatest peak-height pore distribution among all samples. As expected, the 10 wt.% surface shows the greatest cumulative surface area when integrating the D–S function for all samples. These results of D–S analysis are consistent with that of Table 1. The parameters employed in Table 2 are used to predict the hydrophobic behavior of surfaces with different solid ratios, and the calculated curve is presented in Fig. 3 to compare with the experimental data. The preceding argument can be supported by that apparent control of the contact angle by PSD's if the hydrophobicity of rough surfaces with different PSDs is well predicted by Eq. (4). Fig. 3 clearly shows that Eq. (4) provides equally good fits for all prepared surfaces over the entire experimental range. The results demonstrate that the porosity in nanoscale would significantly affect the hydrophobicity of the surfaces. As the particle stack grows, the peak pore size would shift toward a narrower pore size, leading to a vast surface area. This enhancement of surface roughness leads to an increase of contact angle, as shown in Fig. 3. According the above finding, we can infer that the PSD in nanosized roughness is characteristic of the rough surface itself; that is, each pore size has its own behavior. Since the PSDs have been considered in the prediction of contact angle, the satisfactory results of the present work suggest that the hydrophobicity would be dominated by the PSDs of the nanoporous surfaces. 4. Conclusions The present work proposed a modified Wenzel model to examine the influence of pore size distribution of rough surfaces
The authors gratefully acknowledge the financial support from the National Science Council (NSC) and the Ministry of Education (MOE) of Taiwan, Republic of China (R.O.C). References [1] K.K.S. Lau, J. Bico, K.B.K. Teo, M. Chhowalla, G.A.J. Amaratunga, W.I. Milne, G.H. McKinley, K.K. Gleason, Nano Lett. 3 (2003) 1701. [2] H.J. Jeong, D.K. Kim, S.B. Lee, S.H. Kwon, K.J. Kadono, J. Colloid Interface Sci. 235 (2001) 130. [3] S. Shibuchi, T. Yamamoto, T. Onda, K.J. Tsujii, J. Colloid Interface Sci. 208 (1998) 287. [4] E. Kokkoli, C.F.J. Zukoski, J. Colloid Interface Sci. 230 (2000) 176. [5] W. Chen, A.Y. Fadeev, M.C. Hsieh, D. Öner, J. Youngblood, T.J. McCarthy, Langmuir 15 (1999) 3395. [6] D. Quéré, Nat. Maters 1 (2002) 14. [7] R. Blossey, Nat. Maters 2 (2003) 301. [8] B.S. Hong, J.H. Han, S.T. Kim, Y.J. Cho, M.S. Park, T. Dolukhhanyan, C. Sung, Thin Solid Films 351 (1999) 274. [9] R.N. Wenzel, Ind. Eng. Chem. 28 (1936) 988. [10] A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 40 (1944) 546. [11] T. Onda, S. Shibuichi, N. Satoh, K. Tsujii, Langmuir 12 (1996) 2125. [12] C.T. Hsieh, J.M. Chen, J. Colloid Interface Sci. 255 (2002) 248. [13] C.T. Hsieh, H. Teng, J. Colloid Interface Sci. 230 (2000) 171. [14] K. Kinoshita, Carbon: Electrochemical and Physicochemical Properties, John & Wiley, New York, 1987. [15] C.T. Hsieh, J.M. Chen, R.R. Kuo, T.S. Lin, C.F. Wu, Appl. Surf. Sci. 240 (2005) 318. [16] D.M. Ruthven, Principles of Adsorption and Adsorption Process, John Wiley & Sons, New York, 1984. [17] D.D. Do, Adsorption Analysis: Equilibria and Kinetics, Imperial College Press, London, 1998. [18] M.M. Dubinin, Carbon 27 (1989) 457. [19] M.M. Dubinin, Carbon 23 (1985) 373.
A modified Wenzel model for hydrophobic behavior of nanostructured surfaces Tao-Yun Han a,⁎, Jin-Fang Shr b , Chu-Fu Wu b , Chien-Te Hsieh c a
c
Department of Civil Engineering and Engineering Informatics, Chung-Hua University, Hsinchu 300, Taiwan b Graduate Institute of Construction Management, Chung-Hua University, Hsinchu 300, Taiwan Department of Chemical Engineering and Materials Science/Fuel Cell Center, Yuan Ze University, Taoyuan 320, Taiwan Received 1 March 2006; received in revised form 3 October 2006; accepted 3 November 2006 Available online 22 January 2007
Abstract A modified Wenzel model was proposed to explore the influence of pore size distributions (PSDs) on water repellency of nanostructured surfaces. Rough surfaces with different porous structures, including surface areas and PSDs, were fabricated by stacking different solid ratios of TiO2 nanoparticles. These fluorinated surfaces exhibited an excellent hydrophobic performance with the highest value of contact angle ∼ 165°. The PSDs of these surfaces, determined from Dubinin–Stoeckli equation, were found to vary with the solid ratios. The modified Wenzel model incorporated with the PSDs gave a fairly good prediction in describing the variation of contact angle with surface roughness, which is very close to the experimental data. These results demonstrated that the heterogeneity of surfaces caused by different PSDs would induce the hydrophobic behavior. © 2006 Elsevier B.V. All rights reserved. Keyword: Nanostructures; Water repellency; Wenzel model; Pore size distribution; Contact angle
1. Introduction Water repellency of solid surfaces with a liquid in air is a promising phenomenon that can be applied in a variety of applications such as microfluidic devices, antisoiling or antifouling surfaces, efficient heat-transfer areas, or nonbinding biopassive surfaces [1]. Such hydrophobic surfaces usually reach a high value of contact angle N 150° or higher. For a daily application, a functional coating on automobile windscreen enables safe driving since raindrops can be bead up and wash off dust in a rainy day [2–6]. In fact, nature has achieved this fascinating effect through the use of a surface topography that presents at least two different length scales to the out environment, i.e., “self-cleaning” or “lotus effect”. Probing this character, the hydrophobicity of surfaces is mainly affected by two factors: the first one is the chemical factor of the solid surface and the liquid with a low surface energy; the other is the geometrical factor of the rough surfaces [5–8]. ⁎ Corresponding author. Tel.: +886 3 4638800x2577; fax: +886 3 4559373. E-mail address: [email protected] (C.-T. Hsieh). 0040-6090/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2006.11.008
Apart from chemical nature, Wenzel [9] and Cassie [10] models have initially published a relationship between physical structure and contact angle for a hydrophobic surface. Both the two models have put emphasis on the geometrical structure of solid surfaces that acts as a crucial factor in determining the hydrophobicity. Typically, the Wenzel equation is a simple model to characterize the influence of the surface roughness on the wettability of solid. This model is valid only when the droplet completely contacts the surface over their mutual interface [9,11]. However, a few studies demonstrate that theoretical models are suitable for describing the hydrophobicity of rough surfaces in nanoscale. This study aims to modify the Wenzel model for the description of hydrophobic behavior of nanostructured surfaces. In general, a very rough surface is heterogeneous due to contributions from chemical composition, porosity, pore size distribution, and so on [12–14]. These above factors probably influence the interfacial behavior between vapor, liquid and solid. This suggests that the Wenzel model has to be modified for a porous or very rough surface, especially in nanoscale. In the present work, a series of nanostructured surfaces with
T.-Y. Han et al. / Thin Solid Films 515 (2007) 4666–4669 Table 1 Surface characteristics of rough surfaces with different extents of solid ratios TiO2 loading (wt.%)
BET surface area (m2/g)
Total pore vol. (cm3/g)
Pore size distribution Micro. (%)
Meso. (%)
0 2 4 6 8 10
2.51 6.26 10.2 13.3 16.2 18.7
0.0008 0.0033 0.0052 0.0073 0.0081 0.0089
ND 23 30 36 49 51
ND 77 70 64 51 49
different roughnesses were prepared to study their hydrophobicities. The present work intends to correlate the hydrophobicity of surfaces with their pore size distributions (PSDs) through a modified Wenzel model. The approach presented in this study would probably shed some light on how pore size variation would induce the hydrophobicity of the nanostructured surfaces. 2. Experimental section Titanium dioxide nanoparticles (P25, Degussa Co.) with an average diameter of 20–50 nm were stacked to create different roughened surfaces. At first, different solid ratios of TiO2 slurry, ranging from 2 to 10 wt.%, were mixed and well dispersed with distilled water. A fluoro-containing mixture of perfluoroalkyl methacrylic copolymer (Zonyl 8740, Dupont Co.) and distilled water (7/3 in v/v) was prepared and then mixed with the titania slurry solution. Here the fluorinated copolymer not only acts as a hydrophobic agent to lower surface tension, but also as a binder that provides two bonds: the interface between each particle, and the interface between particle and substrate. According to our previous report [15], the concentration of ∼ 4.8 vol.% of the fluorinated mixture in the total slurry is optimum exhibiting the best hydrophobic performance. We employed a Si (100) wafer as a substrate to avoid surface roughness interference that may come from the substrate. Each piece of the Si wafer was carefully cut into an area of 1 × 1 cm2. After significant dispersion under an ultrasonic bath, the slurries with different TiO2 loadings were spread onto Si wafers, using a spin coater that was operated in a two-stage coating process. The spinning speed of the initial coating was set at 200 rpm for 5 s, and then the second-step speed was raised to 3000 rpm and stayed at this speed for 10 s. Then all the prepared samples were dried at 85 °C in a vacuum oven for 12 h. An automated adsorption apparatus (Micromeritics, ASAP 2010) was employed to measure surface porosity, using adsorption of N2 as a probe species at − 196 °C. The amount of N2 adsorbed at relative pressures near unity was employed to determine the total pore volume, which corresponds to the sum of the micropore and mesopore volumes. All the adsorbed amounts are obtained under equilibrium relative pressure. Surface areas and micropore volumes of the samples were determined from the application of the Brunauer–Emmett– Teller (BET) and Dubinin–Radushkevich (D–R) equations, respectively [16,17]. Contact angles of liquid droplets on the
4667
nanostructured surfaces were determined by an optical contact angle meter (Kyowa Interface Science Co., Ltd., model CA-A). The liquid droplet was dropped to the sample surface from a distance of 5 cm by vibrating the syringe. The diameter of the droplet was around 1 mm. The sample plate was vibrated slightly by tapping the sample stand before each measurement to obtain the equilibrium contact angle. 3. Results and discussion Surface characteristics of the prepared surfaces determined from N2-physisorption measurements are presented in Table 1. It is observed from Table 1 that since the porosity was contributed from surface roughness, both the BET surface area and pore volume have an increasing trend with the solid ratio. This reflects from the fact that the architecture of a nanostructured surface is strongly dominated by the concentration of TiO2 particles in the coating solution. Higher concentration leads to a rougher surface. The relationship between contact angle and BET surface area is drawn in Fig. 1. It can be observed that the contact angle of a water droplet significantly increases with the surface roughness. Comparing the water repellency between samples with and without TiO2 nanoparticles, the contact angles of water droplets show an increase of up to 70%, i.e. from 97° to 165°. A simple model to characterize the influence of surface roughness on wettability of a solid was proposed in the Wenzel equation, which can be represented as follows [9] cos H⁎ ¼ Rw
gSV −gSL ¼ Rw cos H gLV
ð1Þ
where Rw is solid roughness that is defined as the ratio between the actual surface area of a rough surface to the projected one. Eq. (1) clearly indicates the relationship between the contact angle of the flat surface Θ and that of the rough surface Θ⁎. In
Fig. 1. Variation of contact angles with BET surface areas of the surfaces.
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T.-Y. Han et al. / Thin Solid Films 515 (2007) 4666–4669
general, the value of Rw is greater than unity, reflecting Θ⁎ N Θ for a hydrophobic situation. Strictly speaking, the applicability of Eq. (1) is limited. This is due to that Wenzel model which is valid only when the droplet completely contacts with the surface over their mutual interface. This means that only well-ordered array or uniform porous media with homogeneous character properly suits to this model. Unfortunately, the above situation is not typical because surface heterogeneity from different PSDs usually exists in real applications. In this sense, a PSD is a fundamental description of heterogeneity of a hydrophobic solid surface. Eq. (1) is only applicable to wettability simulation by liquid droplet on a homogeneous rough surface. However, the distribution of pore size is characteristic of the surface itself; that is, each pore size has its own behavior. How Eq. (1) can be incorporated with the PSDs will be discussed later. According to the above argument, a modified Wenzel model in describing the heterogeneous surfaces is proposed. There are some assumptions for the modified model as depicted as follows: (i) all regions of the rough surface have uniform chemical properties; (ii) surface heterogeneity of the surface is composed of numerous homogeneous areas; (iii) hydrophobic behavior of each small area can be well described by Wenzel model. Accordingly, a Wenzel model based on a modified Rw is rewritten as n P
Si
R Xmax
F ð X ÞdX d cos H ¼ Xmin d cos H S S Z Xmax cos H ¼ d F ð X ÞdX S Xmin
cos H⁎ ¼
i¼1
ð2Þ
where S and Si are the projected area per unit gram flat surface and each rough surface varied with different pore sizes X, respectively. Thus the summation of Si represents a total surface area of rough surfaces. Here, F(X )dX is the actual surface area per gram rough surface in PSD having pore sizes within X and
Fig. 2. Pore size distributions of the prepared surfaces with different solid ratios determined by D–S equation, using Eq. (3).
Table 2 Most suitable parameters of the Dubinin–Stoeckli equation for different rough surfaces TiO2 loading (wt.%)
W0 (cm3/g)
X0 (nm)
δ (nm)
2 4 6 8 10
0.0037 0.0045 0.0069 0.0080 0.0083
1.21 1.01 0.92 0.86 0.82
0.66 0.55 0.53 0.38 0.34
X + d X. Since both cosΘ and S are constants, the two values can thus be brought out of the integral, as showed in the final form of Eq. (2). The lower limit Xmin is the minimum pore size accessible to a nitrogen molecule. Nitrogen has a molecular radius of 0.35 nm, and this value was chosen as the lower limit for the integration. The upper limit Xmax is the maximum size of pores that can be measured by gas adsorption. The value of Θ depends on the contact angle for a fluorinated flat surface ∼ 97°. To resolve PSD of rough surfaces requires further investigation that is described in the following section. Here we assume that the rough surface is heterogeneous, and the surface consists of many small homogeneous regions. To resolve Eq. (2), let F(X ) be the function of PSD initially. The Dubinin–Stoeckli (D–S) equation has been widely employed to determine the distribution of micropore sizes in porous media [18,19]. The D–S model assumes that micropore volume has a normal Gaussian distribution with respect to the size. Assuming the micropores having parallel sided slits, the differential increase in the surface area, dS, is related to the differential increase in the pore volume as follows: " # dW W0 1 ðX0 −X Þ2 dS ¼ ¼ pffiffiffiffiffiffi exp − dX ¼ F ð X ÞdX ð3Þ X 2d2 d 2p X where W is the cumulative micropore volume, W0 is the total micropore volume determined from the D–R equation, X0 is the micropore half width at the distribution curve maximum, and δ is the dispersion parameter. This distribution function can be obtained from the N2 adsorption isotherm by correlating X and the relative pressure, using the Kelvin equation [18,19]. Taking Eq. (3) into Eq. (2), the modified Wenzel model can be completely expressed as " # Z cos H Xmax W0 1 ðX0 −X Þ2 ⁎ pffiffiffiffiffiffi − cos H ¼ dX S 2d2 Xmin d 2p X Based on the N2 isotherms, the pore size distributions of the surfaces investigated were determined from the D–S equation shown as Eq. (4). Since the value of X can be related to P / P0 by employing the Kelvin equation, two independent parameters, X0 and δ, have to be estimated in the fitting to construct a D–S type of distribution. The PSDs of the surfaces were thus determined, and the results are presented in Fig. 2, and the D–S parameters are shown in Table 2. The distribution results show that the sample
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on hydrophobic behavior. After surface fluorination treatments, contact angles of the rough surfaces had an increase with their specific surface areas. The contact angle of the roughest surface had the highest value of 165°, i.e., an increase of 70%. D–S analysis showed that the PSDs of the surfaces were obviously affected by the solid ratio; that is, the major peak height gradually shifted to a larger pore size as the solid ratio increased. By incorporating the distribution determined by the D–S equation, the modified Wenzel model provides an excellent prediction for the hydrophobicity of water droplets of the nanostructured surfaces. The satisfactory results in the present work demonstrate that the various wettabilities of rough surfaces can be attributed to a surface heterogeneity from different PSDs. Acknowledgments Fig. 3. Variation of contact angles with surface roughness (Rw). The solid line was predicted by the modified Wenzel model, using Eq. (4).
with a lower solid ratio (2 wt.%) has a flatter distribution as well as a larger mean pore size, whereas the sample with 10 wt.% TiO2 particles exhibits the greatest peak-height pore distribution among all samples. As expected, the 10 wt.% surface shows the greatest cumulative surface area when integrating the D–S function for all samples. These results of D–S analysis are consistent with that of Table 1. The parameters employed in Table 2 are used to predict the hydrophobic behavior of surfaces with different solid ratios, and the calculated curve is presented in Fig. 3 to compare with the experimental data. The preceding argument can be supported by that apparent control of the contact angle by PSD's if the hydrophobicity of rough surfaces with different PSDs is well predicted by Eq. (4). Fig. 3 clearly shows that Eq. (4) provides equally good fits for all prepared surfaces over the entire experimental range. The results demonstrate that the porosity in nanoscale would significantly affect the hydrophobicity of the surfaces. As the particle stack grows, the peak pore size would shift toward a narrower pore size, leading to a vast surface area. This enhancement of surface roughness leads to an increase of contact angle, as shown in Fig. 3. According the above finding, we can infer that the PSD in nanosized roughness is characteristic of the rough surface itself; that is, each pore size has its own behavior. Since the PSDs have been considered in the prediction of contact angle, the satisfactory results of the present work suggest that the hydrophobicity would be dominated by the PSDs of the nanoporous surfaces. 4. Conclusions The present work proposed a modified Wenzel model to examine the influence of pore size distribution of rough surfaces
The authors gratefully acknowledge the financial support from the National Science Council (NSC) and the Ministry of Education (MOE) of Taiwan, Republic of China (R.O.C). References [1] K.K.S. Lau, J. Bico, K.B.K. Teo, M. Chhowalla, G.A.J. Amaratunga, W.I. Milne, G.H. McKinley, K.K. Gleason, Nano Lett. 3 (2003) 1701. [2] H.J. Jeong, D.K. Kim, S.B. Lee, S.H. Kwon, K.J. Kadono, J. Colloid Interface Sci. 235 (2001) 130. [3] S. Shibuchi, T. Yamamoto, T. Onda, K.J. Tsujii, J. Colloid Interface Sci. 208 (1998) 287. [4] E. Kokkoli, C.F.J. Zukoski, J. Colloid Interface Sci. 230 (2000) 176. [5] W. Chen, A.Y. Fadeev, M.C. Hsieh, D. Öner, J. Youngblood, T.J. McCarthy, Langmuir 15 (1999) 3395. [6] D. Quéré, Nat. Maters 1 (2002) 14. [7] R. Blossey, Nat. Maters 2 (2003) 301. [8] B.S. Hong, J.H. Han, S.T. Kim, Y.J. Cho, M.S. Park, T. Dolukhhanyan, C. Sung, Thin Solid Films 351 (1999) 274. [9] R.N. Wenzel, Ind. Eng. Chem. 28 (1936) 988. [10] A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 40 (1944) 546. [11] T. Onda, S. Shibuichi, N. Satoh, K. Tsujii, Langmuir 12 (1996) 2125. [12] C.T. Hsieh, J.M. Chen, J. Colloid Interface Sci. 255 (2002) 248. [13] C.T. Hsieh, H. Teng, J. Colloid Interface Sci. 230 (2000) 171. [14] K. Kinoshita, Carbon: Electrochemical and Physicochemical Properties, John & Wiley, New York, 1987. [15] C.T. Hsieh, J.M. Chen, R.R. Kuo, T.S. Lin, C.F. Wu, Appl. Surf. Sci. 240 (2005) 318. [16] D.M. Ruthven, Principles of Adsorption and Adsorption Process, John Wiley & Sons, New York, 1984. [17] D.D. Do, Adsorption Analysis: Equilibria and Kinetics, Imperial College Press, London, 1998. [18] M.M. Dubinin, Carbon 27 (1989) 457. [19] M.M. Dubinin, Carbon 23 (1985) 373.