At thermodynamic equilibrium, the contact angle θ of a minute droplet of a liquid deposited onto the (supposedly perfectly flat and horizontal) surface of a solid reflects the balance between so-called surface tensions exerted by its own surface (in the presence of its vapour), the surface tension of the solid (also in the presence of the vapour of the liquid), and the interfacial tension between solid and liquid. The equilibrium shape of the droplet is schematized in Fig. 1 (where symbols are defined) and is summarized by the famous Young’s equation:
$$\cos \vartheta = (\gamma_{SV} - \gamma_{SL} )/\gamma_{L}$$
(1)
An abundant literature is available about this topic [1–5], which is relevant for lots of phenomena at work in nature (e.g. a dewdrop trapped in a spider net), in industry (e.g. oil extraction, textile tint), and of course in every days life (e.g. grilling a steak in a frying pan is very much a matter of adhesion between the hot surface and a piece of matter that contains around 80 % of water). In this article, we study the equilibrium shape of droplets of various liquids put in contact with the surface of intermetallic alloys formed by alloying aluminium with transition metals such as Cu, Cr or Fe. Such compounds encompass a broad variety of crystal structures, including quasicrystals first discovered by Shechtman et al. in 1982 in melt spun Al–Mn alloys [6], but also forming stable compounds as was shown few years later by Tsai and his co-workers at Tohoku University, Japan [7, 8]. In strong contrast to normal metallic alloys and even more so, pure metals like aluminium, the contact angle that we found is large, and is equal to or larger than 90° although the metallic samples are covered by a thin layer of their native oxide when handled in ambient atmosphere.
The origin of adhesion is usually assigned to extreme surface interactions and is split into two components: one arising from the constant movement of electrostatic charges within the interfacial region (few atomic distances thick) between liquid and solid, or so-called Lifshitz-van der Waals forces on the one hand, and Lewis acid–base interactions on the other hand, which reflect the exchange of charges through the interfacial region [9]. They will be labelled with LW and AB subscripts, respectively, in the following. In fact, we will assign the AB subscript to index every kind of interaction (dangling bonds for instance) that is not of LW type. Having this in mind, we can define the reversible adhesion energy W
L of liquid L on solid S at thermodynamic equilibrium by the following equation [9]:
$$W_{L} = \gamma_{S} + \gamma_{L} - \gamma_{SL}$$
(2)
where γ
i, i = S or L, is the surface energy of material S or L, γ
SL is the interfacial energy between S and L, and all γ‘s are taken identical, respectively, to their surface tension counterparts defined in Fig. 1. Combining Eqs. (1) and (2) leads then to:
$$W_{L} = \gamma_{L} \left( {1 + cos\,\vartheta } \right) + \varPi$$
(3)
where Π = γ
S − γ
SL is called the film pressure. This term becomes negligible whenever the contact angle is large enough, which also means that it is well defined, or in other words, the liquid does not spread out on the solid surface to form a film. We checked that the film pressure is negligible on most of our samples, except pure metals and oxides. Assuming then that Π → 0, Eq. (3) can be re-written as:
$$W_{L} = \gamma_{L} \left( {1 + cos\,\theta } \right) = 2(\gamma_{L}^{LW} \gamma_{S}^{LW} )^{1/2} + I_{SL}^{AB}$$
(4)
in which we introduced the Lifshitz-van der Waals components of the surface energy of the liquid and solid, respectively, and gathered all other interactions between solid and liquid into the \(I_{SL}^{AB} = 0\) term [9]. The LW and AB interactions may be tuned by varying the nature of the liquid, which can be apolar like diodomethane or strongly polar like water. As a consequence, a plot of cosθ as a function of the ratio \(x = \sqrt {\gamma_{L}^{LW} } /\gamma_{L}\) will be linear if, and only if, \(I_{SL}^{AB} = 0\), which will be observed if the liquids are apolar, or the solid is apolar, or both. Furthermore, the slope of this plot will supply a measure of \(2\sqrt {\gamma_{S}^{LW} }\) whereas this plot goes to cos θ = −1 when x → 0 if, and only if, \(I_{SL}^{AB} = 0\).
A typical example of this plot is shown in Fig. 2. The five liquids that were used to produce the data are introduced in the next section. The samples for contact angle measurements (also described in the next section) were PTFE, a famous apolar solid with very reduced surface energy, a single crystal of pure alumina designed for optical windows, which is in contrast a very polar solid, and a single grain of an Al-Pd-Mn icosahedral quasicrystal grown by Czochralsky pulling from the liquid alloy [10]. This material is covered by a thin layer of alumina oxide in ambient air. Surprisingly, the plot of cosθ versus x is linear and resembles that of PTFE, which is apolar, yet with a larger slope. It is not comparable to that of the pure oxide, which departs from a linear plot and does not tend to cos θ = −1 for x = 0. This clearly signs the polar nature of the Al2O3 surface. As a consequence, the surface energy of the quasicrystalline material must show a vanishingly small AB component, which is in strong contrast to the behaviour of the covering oxide and to what is known for the pure metal equipped with the same native oxide.
The motivation of our study was thus to better understand the origin of such a strange behaviour and to see if it can be traced to a specific property of the metallic substrate itself, thus taking our interpretation away from classical literature. To this end, we have studied a large number of Al-based compounds, crystalline as well as quasicrystalline, that can be grown out of Al-TM (TM: transition metal) alloy systems upon conventional metallurgical techniques since they are all stable. Using the very same samples, we have gained insight into their electronic structure, using soft X-ray spectroscopy. We have characterized their surface oxide layers by direct microscopy observations and XPS experiments. We have measured their roughness and assessed their wettability, using contact angle determinations, most often against water, but also against other types of liquids. Finally, we came to the conclusion that the reversible adhesion energy of water on those surfaces is essentially of Lifshitz-van der Waals type whenever the oxide layer is thin enough and the complexity of the metallic substrate large (or the unit cell of the compound contains at least few hundreds atoms). This result is in line with the selection of certain quasicrystalline alloys for the industrial production of low-stick cookware that was secured in patents by one of us long ago [11, 12].
Thus, the article is organised in four sections. The next one deals with experimental details, the third one with experimental results (effect of roughness and of the oxide layer, influence of the electron density of states underneath the oxide), the forth section is dedicated to a model that interprets the data, and the fifth raises few conclusions.