Model and Experimental Study of Surfactant Solutions and Pure Liquids Contact Angles on Complex Surfaces - Drops and Bubbles in Contact with Solid Surfaces - page 187

Similarly to the Wenzel mode predictions, in Fig. 2b and d (showing Cassie mode
wetting) surfactants are seen to decrease contact angle for any given f . In the Cassie
mode however, it is seen, e.g., for f 0 . 5and θ y = 120 ◦

=

the decrease in Cassie

13 ◦ over the entire range of C S (Fig. 2a). This can be

mode contact angles is only ∼

21 ◦ compared to a decrease of 1). In this way, the f

parameter can be seen as attenuating the effect of surfactant adsorption.
The effect of intrinsic contact angle is seen to be less complicated for Cassie
mode wetting (Fig. 2b and d) compared to the case of Wenzel mode wetting (Fig. 2a
and c). For the Cassie mode, intrinsic contact angle determines the starting contact
angle for high values of f , and surfactant adsorption leads to a relatively gradual
decrease in contact angle. However, at lower values of f the Cassie contact angle
becomes largely independent of intrinsic contact angle and/or concentration, again
explained by the attenuating effects of f .
In addition to this attenuation, decreasing f is seen to increase contact angle,
due to the (1

∼ for a smooth surface ( f =

f ) term in the modified Cassie equation (Eq. (10e)), indicating that
the drop is 'sitting' on more air. In this way, the f parameter can also be thought
of as acting in opposition to the effects of surfactant adsorption. Both the attenu-
ation and opposition are expected intuitively, since there is less solid-liquid area
under the drop for surfactants to adsorb to. This means that for low (but not zero) f
planes (i.e., a superhydrophobic surface) surfactant concentration has little total ef-
fect; although adsorption still decreases the Cassie mode contact angle. This is not
a full explanation for previous works [26, 73-78], that have found surfactant solu-
tions often fail to wet SHS. A full explanation requires an explanation of how the
Cassie mode (or perhaps a mode of partial penetration) is maintained, because the
unpentrated Cassie mode is thermodynamically unlikely as surfactant concentration
increases [32, 33]. This will be discussed in the Section E.
Considering Fig. 2a-d, one should note that the wetting mode (Wenzel or Cassie)
of a drop, and thus which set of predictions to use (Fig. 2a and c or b and d), depends
upon the topography and intrinsic contact angle of a surface. Predicting the wetting
mode requires a thermodynamic analysis of the free energy. However, it is generally
seen [32, 33] higher contact angles are less thermodynamically favorable. As such
the predicted 180 ◦ contact angles in Fig. 2a and c for the Wenzel mode are likely
thermodynamically unfavorable. Since determination of the favored mode requires
[32, 33] apriori knowledge of both r and f , and since there is no one-to-one
pairing of these parameters until a specific surface texture is chosen, the favored
wetting mode could not be determined in Fig. 2a-d. In a recent paper these issues
were investigated in a more theoretical way [27]. In this chapter, the developed
model will be used to investigate and understand the experimental data presented in
Section E.
Before considering the experimental data, the model for surfactant adsorption on
heterogeneous surfaces will be briefly explored. A two material smooth ( f 1 +

−

f 2 =

1) heterogeneous surface is considered in Fig. 2e. As stated, θ y | 1 = 70 ◦ (with ma-

0 ◦

terial 1 not experiencing the autophobic effect), while θ y | 2 =

(with material 2