Surface Roughness as Related to Hysteresis of Contact Angles. III. The Systems Paraffin–Ethylene Glycol–Air, Paraffin–Methyl Cellosolve–Air and Paraffin–Methanol–Air

Remodeling of Super-hydrophobic Surfaces

“…20,28,42 The Cassie−Baxter equation, frequently used to estimate apparent contact angles, does not reflect the underlying physical process 43,44 nor does it produce accurate estimates. 2,[17][18][19]28,43,44 ■ CONCLUSIONS Videos captured with confocal microscopy by Butt and coworkers confirm earlier claims that water advances across pillared super-hydrophobic surfaces with an apparent contact angle of 180°. By adapting an existing model that assumes linear averaging along the contact line, it was possible to accurately estimate apparent contact angles and sliding angles for their surfaces.…”

“…Confocal microscopy confirmed that drops were suspended atop the pillars. At the advancing edge, the water interface descended downward and flattened across the pillars, effectively producing an apparent advancing contact angle (θ apa ) of 180°, as previously anticipated. ,− Locally the advancing contact angle sometimes exceeded 180° due to curvature of the air–water interface at the pillars, reaching values as high as 188° . (As an aside, Butt and co-workers’ measurements with a goniometer equipped with a camera and drop shape analysis software gave a “low” value of θ apa = 165 ± 3°.…”

“…Butt and co-workers echoed concerns raised previously. Goniometers tend to underestimate large θ apa . ,, Surfaces that are super-hydrophobic generally produce θ apa = 180°. − , Both advancing and receding angles are required to understand repellency. ,, The Cassie–Baxter equation, frequently used to estimate apparent contact angles, does not reflect the underlying physical process , nor does it produce accurate estimates. ,− ,,, …”

Molecular Desorption by a Moving Contact Line

“…If we name θ d the contact angle of the liquid on the chemical defect, a Cassie-Baxter approach [34] leads to ϵ max ¼ Φ max ½ðcos θ 0 − cos θ d Þ= cos θ 0 . Using advancing contact angles measured from the experimental force curves in the stationary state for θ 0 and values of advancing contact angles on paraffin wax (to mimic hydrocarbons) from the literature for θ d [35][36][37][38], we show in Table I that the experimental and calculated values of ϵ max agree reasonably for Φ max ¼ 0.07. Assuming dominant contaminant molecules as short hydrocarbon chains [30] with size d ∼ 0.25 nm, we estimate the maximum coverage to about one molecule per nm 2 of the surface.…”

Coupled-cluster method for an incomplete model space

“…This equality only holds for the specific form of the S ( K ) operator: (9) With these assumptions the effective Hamiltonian operator of Eq.…”