In surface characterizing, the RMS roughness is undeniably one of the most important parameters. For wetting of volatile liquid, however, surface micro-structure play an important role due to capillary forces and hence adhesion force. Consider two solid surface that are sufficiently close to each other, vapor condenses into liquid following the Kelvin’s equation (Eq. 7). This phenomenon (capillary condensation), is important in describing some adhesion phenomena. 𝑅𝑇 ln𝑃𝑃 0= 𝛾𝑉𝑚( 1 𝑟1+ 1 𝑟2) (2.7)
Where P and P0 is the vapor pressure and saturation pressure, respectively. γ is the surface tension, Vm is the liquid molar volume, and r1 and r2 are principal radii of curvature. It therefore follows that, if surface asperities are very sharp (low radius), then propensity to condense vapor will be very high altering the surface energy of the substrate. Presence of a monolayer, however, may reduce the overall size of these crevices mitigating condensation of surface energy mismatched vapors.
But is a condensate a reason for concern in delineating surface properties? For a simplified case, the capillary force Fcap of a liquid in between two spherical surfaces is described as (Eq.
8);
𝐹𝑐𝑎𝑝 = 4𝜋𝛾𝑐𝑅∗(1 − 𝐷
√𝜋𝑅1𝑉 +𝐷2) (2.8)
Where c is a constant associated with the contact angle of the liquid on the two surfaces. R1
and R* are the radius of one particle and the effective radii (derived from the radii of the two
particles), respectively. V is the constant volume, and D is the distance of two surface. Detailed descriptions and explanations have been summarized by Butt and Kappl. 60 The capillary force contributes to the adhesion force on a textured surface as captured in this relation (Eq. 9).
𝐹𝑎𝑑ℎ = 4𝜋𝛾𝑐𝑅∗ = 𝐹𝑐𝑎𝑝 (1 − 𝐷 √ 𝑉
𝜋𝑅1+𝐷2
)
⁄ (2.9)
From this equation it is clear that the radii of the particles are affecting the adhesion force, suggesting that curvature (as surface morphology in some cases) matters in governing the nature of interaction between a surface and a probe liquid. To extend, beyond spherical surfaces, the geometries of the two surfaces also have significant effect on the adhesion force (Figure 6). Therefore, on surfaces that have micro-structure the effect of those structure on wetting should not be neglected. A challenge in this discourse is the role of nanoscale surface defects on adhesion and, by extension, wetting.
Figure 2.6 Simplified demonstrations of effect of geometries on the corresponding capillary
force.60 Extension of these macroscale phenomena is complicated by capillary effects once below the capillary length of the probe liquid.
In other studies that are based on SAMs such as large area tunneling junctions, it has been shown that the entirety of surface morphology, rather than simple roughness, significantly affect the SAM structure as manifested in corresponding properties.45, 61 Nijhuis and coworkers45, 61 for example, observed that in addition to roughness, the number of grains and the width of corresponding grain boundaries can affect SAM packing, and therefore; i) affects the rectification ratio of molecular diodes, and ii) the yield of working devices. Bearing volume (BV), a parameter associated with grain size and boundary widths, was found to correlate with device performance.45, 61
The micro/nano-structure on the substrate surface, such as grain size and grain boundaries, in some case is independent from the RMS roughness. Figure 7a shows AFM images of two metal surfaces, the AuTS and AgFe-TS, which bear comparable R
RMS (~2.2nm). These two surface, however, have significantly different grain sizes, which can be directly observed from AFM images. The silver surface has larger grains than the gold surface but also deeper defects (at the boundaries). Due to the morphology, proposed formation of SAMs were illustrated in Figure 7a. AuAD, which has smaller grains and is considered defects dominant, does not have
flat regions to form ordered SAMs or at least islands of SAMs. AgFe-TS, however, has considerably larger grains, which turns into flat region for ordered SAMs formation.
Figure 2.7 The effect of grain size on contact angle. a) The morphology of two substrate
surface. Similar RRMS but different grain structure, and the proposed SAMs formation at those two surfaces. b) The water contact angle on AgFe-TS and AuTS, and a comparison with consideration of the packing and tilting effect.32 (Copyright from ACS)
Difference in substrate surface morphology lead to difference in SAMs wetting properties. The water contact angle on SAMs on both substrates (Figure 7b) does not show an odd-even effect, indicating larger grains cannot compensate for the effect of roughness on SAMs structure and hence wetting (or analogous) properties. As previously shown, we can correct for differences in SAM packing densities on the contact angles (Figure 7b, triangles) but this does not account
for the differences between the wetting properties. This variance in hydrophobicity of Ag and Au rough surfaces can either be due to capillary force or differences in SAM structure.12, 29
Figure 2.8. Effect of substrate nature and subtle change on molecular wetting behaviors. a)
AFM images of AgAl-TS and AuTS, whose surface morphology are similar, and AuFe-TS with lower roughness. b) Ideal SAM structure and molecular orientation on Ag and Au surface. c) The difference in contact angle on SAMs formed on Ag and Au surface with similar morphology and roughness. d) The difference in contact angle between Au and Ag substrates disappears at around C3. e) The change of contact angle on SAMs over slight substrate roughness variance. (Copyright from ACS)
As a molecular phenomenon, factors other than surface morphology that affects the molecular structure are important in the observed wetting results. Surfaces with similar morphology (roughness, bearing volume, coverage, etc.32) but different identities, AuTS and AgAl-TS, have been used as substrates for SAMs (Figure 8ai and 8aii). The ideal SAMs structure on these surface are expected to be different (Figure 8b) and, as expected, show differences in the oscillation in their odd-even effect (Figure 8c). Form this work, it was observed that the odd- even effects in hydrophobicity were due to difference in contact angles on SAME, but this difference decreases and vanishes at C3, as in Figure 8d.32 This observation of diminished effect of the substrate identity to the wetting properties of the SAM, may be in part due to decreased order in the SAMs suggesting that degree of SAM order will decrease with molecular length for shorter chain-length SAMs. We qualify this observation since for longer SAMs (>C14), the contact angles seem to be different for both SAME and SAMO.
In addition, small changes in the morphology (mainly decrease in roughness by ~ 0.2 nm) of the surface also leads to slight changes in wetting results (Figure 8e). We have demonstrated that using substrate with reduced roughness, such as AuFe-TS (roughness RMS= 0.2 nm), the contact angle on the SAMs that are fabricated on these surface shows a roughness dependence (Figure 8e).30 Extrapolation of this data followed by empirical evidence over both Au30 and Ag31-32 suggests that there is a limit to the observation of the odd-even effect in hydrophobicity of these SAMs through sessile droplet contact angles.