When the liquid droplet enters the valleys of rough

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When the liquid droplet enters the valleys of rough surface and completely wets the surface, the Wenzel equation is valid: cos h a ¼ c cos h Table 4 Water contact angle and surface roughness [ 97 ] Phosphating conditions Surface Surface roughness Water contact angle ( ° ) Ra Rz Ry Low temperature phosphating Phosphating film 2.10 13.12 17.34 25–30 Super-hydrophobic film 1.78 8.00 11.42 168 Middle temperature phosphating Phosphating film 1.40 7.10 10.46 15–20 Super-hydrophobic film 1.14 5.86 7.17 154 High temperature phosphating Phosphating film 1.52 7.33 11.00 20–25 Super-hydrophobic film 1.28 6.38 8.94 165 J Sol-Gel Sci Technol (2010) 54:174–187 183 123
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where h a is the apparent contact angle, c is the roughness parameter defined by the ratio of the real surface area to the projected surface area. Because c C 1, roughness on a hydrophobic surface ( h [ 90 ° ) renders it more hydropho- bic, whereas on a hydrophilic surface ( h \ 90 ° ) roughness has the opposite effect, decreasing h toward 0 ° . When the liquid cannot wet the rough surface and there is a liquid–vapor interface below the droplet, Cassie and Baxter postulated that the cosine of the contact angle on a heterogeneous solid/air surface is the sum of the cosine of the contact angles of the respective homogeneous surfaces weighted by the surface fraction of the solid: cos h a ¼ ² 1 þ U S ð 1 þ cos h Þ where U S is the surface fraction of solid. As the ratio of the pillar width to interpillar distance of a regular lithograph- ically defined surface decreases or the roughness of a random, porous (e.g., fractal) surface increases, U S approaches zero, and h approaches 180 ° . In conclusion, whether liquid water droplet wets the surface or not, surface roughness can increase the contact angle of hydrophobic surface remarkably and make the surface more hydrophobic. With the help of surface roughness, expensive perflu- orosegments in polymers are not necessary to obtain super- hydrophobic surface. Although the following coatings are not necessary to deposition on metal substrates, super- hydrophobic films are attained by with the help of surface roughness. Super-hydrophobic films by adding polyethylene glycol in the silica sol precursor have been prepared. The solu- tions are cast on the glass and add poor solvent ( n -hexane) on it. Surface roughness of the films is obtained by removing polymer from the films at high temperature. The hydrophobic group on the surfaces is obtained by reaction with hexamethyldisilazane (HMDS). The contact angle of the film prepared by spraying n -hexane onto each coating layer for four times after casting process is greater than 150 ° [ 98 ]. Surface roughness of the films is obtained by removing polymer from the films at 700 ° C [ 99 ]. Polycarbonate (PC) was used for creating white or col- orful super-hydrophobic coatings on the surfaces of various material substrates simply by using its solvent and non- solvents suitably selected. The cleaned substrates were first dipped into the PC solution and then further treated with the PC non-solvent, forming a super-hydrophobic coating at ambient room temperature within 21 min. The super-
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