Fabrication of Superhydrophobic Textiles
199
solid-liquid are could be higher than the apparent surface contact area and as a result
the wettability/repellency of the surface could increase. He proposed that the rough
surface can be filled by the water droplet on the solid roughened surface (Fig. 3c)
and the surface free energy of droplet could be given by Eq. (2)
δ E = r
γ
sl
−γ
sa
dx + γ
la cosθ w · dx
(2)
In Eq. (2) the δE represents the change in surface energy of the wetting system
and dx represents the small moving distance of the water droplet. In a balanced
system, the relationship between the intrinsic water contact angle θ z and apparent
water contact angle θ w is shown by Eq. (3) because of the smallest the surface free
energy (δE = 0)
Cosθ w = r
γ
sa
−γ
sl
γ
sl
(3)
Here in Eq. (3), θ w is the angle on solid surface known as Wenzel’s apparent
water contact angle and r is the roughness factor of the surface i.e. the ratio of actual
surface area to the apparent surface area. It was obvious from the Wenzel’s model
that functions and the effects of soil–air interfacial surface tension and solid–liquid
interfacial surface tension on surface free energy were now different and changed by
surface roughness directly, leading to the different contact angle on the roughened
solid surface than on infinitely flat and smooth solid surface. If there is a possibility
of filling the grooves by water droplet, then a non-composite state could be formed
between water droplet and the surface grove showing that the actual contact area
of solid to liquid is higher than the apparent geometric area. The roughness factor
“r” is always greater than 1 (r > 1), if the contact angle is greater than 90° i.e. θ z
> 90° then surface roughness is responsible for the hydrophobicity of material but
in case of contact angle lesser that 90° i.e. θ z < 90
◦ , then the surface roughness
will be responsible for wettability of the surface. From Eq. (3) it is obvious that the
cosθ w of a rough surface could be greater than 1 i.e. cosθ w > 1, or the chemical
composition of the surface could be different. In such cases the Wenzel’s model is
not applicable because in some cases the intrinsic contact angle is even more than
180° i.e. θ w > 180
◦ thus the Wenzel’s model does not obey the real phenomenon
under such conditions.
Thus to address these issues and the limitations of Wenzel’s model instead of
non-composite contact, composite contact model was proposed in 1944 by Cassieand Baxter [20] in which it was suggested that the water droplet could not fully
fill the surface grooves because the surface roughness is nano-scaled and the water
droplet is larger than these grooves. The liquid-solid contact is basically composed
of solid-air and solid-liquid contact surface due to presence of air in the grooves
under the water drop as shown in Fig. 3d.
The variation in surface free energy of the system is shown by Eq. (4) when three
phase contact line of water droplet moves a small distance
199
solid-liquid are could be higher than the apparent surface contact area and as a result
the wettability/repellency of the surface could increase. He proposed that the rough
surface can be filled by the water droplet on the solid roughened surface (Fig. 3c)
and the surface free energy of droplet could be given by Eq. (2)
δ E = r
γ
sl
−γ
sa
dx + γ
la cosθ w · dx
(2)
In Eq. (2) the δE represents the change in surface energy of the wetting system
and dx represents the small moving distance of the water droplet. In a balanced
system, the relationship between the intrinsic water contact angle θ z and apparent
water contact angle θ w is shown by Eq. (3) because of the smallest the surface free
energy (δE = 0)
Cosθ w = r
γ
sa
−γ
sl
γ
sl
(3)
Here in Eq. (3), θ w is the angle on solid surface known as Wenzel’s apparent
water contact angle and r is the roughness factor of the surface i.e. the ratio of actual
surface area to the apparent surface area. It was obvious from the Wenzel’s model
that functions and the effects of soil–air interfacial surface tension and solid–liquid
interfacial surface tension on surface free energy were now different and changed by
surface roughness directly, leading to the different contact angle on the roughened
solid surface than on infinitely flat and smooth solid surface. If there is a possibility
of filling the grooves by water droplet, then a non-composite state could be formed
between water droplet and the surface grove showing that the actual contact area
of solid to liquid is higher than the apparent geometric area. The roughness factor
“r” is always greater than 1 (r > 1), if the contact angle is greater than 90° i.e. θ z
> 90° then surface roughness is responsible for the hydrophobicity of material but
in case of contact angle lesser that 90° i.e. θ z < 90
◦ , then the surface roughness
will be responsible for wettability of the surface. From Eq. (3) it is obvious that the
cosθ w of a rough surface could be greater than 1 i.e. cosθ w > 1, or the chemical
composition of the surface could be different. In such cases the Wenzel’s model is
not applicable because in some cases the intrinsic contact angle is even more than
180° i.e. θ w > 180
◦ thus the Wenzel’s model does not obey the real phenomenon
under such conditions.
Thus to address these issues and the limitations of Wenzel’s model instead of
non-composite contact, composite contact model was proposed in 1944 by Cassieand Baxter [20] in which it was suggested that the water droplet could not fully
fill the surface grooves because the surface roughness is nano-scaled and the water
droplet is larger than these grooves. The liquid-solid contact is basically composed
of solid-air and solid-liquid contact surface due to presence of air in the grooves
under the water drop as shown in Fig. 3d.
The variation in surface free energy of the system is shown by Eq. (4) when three
phase contact line of water droplet moves a small distance