We
experimentally and theoretically
examine the influence of a double-chain cationic surfactant, didodecyldimethylammonium
bromide (DDAB), on the wetting states and contact angles on superhydrophobic
(SH) surfaces made of hydrophobic microcylinders. We use two types
of micropatterns of different surface roughness, r, and packing fraction, ϕ, and vary nine dimensionless surfactant
concentrations (C
S), normalized by the
critical micelle concentration (CMC), in the experiments. At low C
S, some of the surfactant-laden droplets are
in a gas-trapping, Cassie–Baxter (CB) state on the high-roughness
microstructures. In contrast, some droplets are in a complete-wetting
Wenzel (W) state on the low-roughness microtextures. We found that
the contact angle of CB drops can be well predicted using a thermodynamic
model considering surfactant adsorption at the liquid–vapor
(LV) and solid–liquid (SL) interfaces. At high C
S, however, all of the DDAB drops wet in a Wenzel mode.
Based on a Gibbsian thermodynamic analysis, we find that for the two
types of superhydrophobic surfaces used, the Wenzel state has the
lowest thermodynamic energy and thus is more favorable theoretically.
The CB state, however, is metastable at low C
S due to a thermodynamic energy barrier. The metastable CB
wetting state becomes more stable on the SH microtextures with greater
ϕ and r, in agreement with our experimental
observations. Finally, we generalize this surface-energy analysis
to provide useful designs of surface parameters for a DDAB-laden surfactant
droplet on the SH surface with a stable and robust CB state.