Melting and nonmelting of solid surfaces and nanosystems

We present an extensive but concise review of our present understanding, largely based on theory and simulation work from our group, on the equilibrium behavior of solid surfaces and nanosystems close to the bulk melting point. In the first part we define phenomena, in particular surface melting and nonmelting, and review some related theoretical approaches, from heuristic theories to computer simulation. In the second part we describe the surface melting/nonmelting behavior of several different classes of solids, ranging from van der Waals crystals, to valence semiconductors, to ionic crystals and metals. In the third part, we address special cases such as strained solids, the defreezing of glass surfaces, and rotational surface melting. Next, we digress briefly to surface layering of a liquid metal, possibly leading to solid-like or hexatic two-dimensional phases floating on the liquid. In the final part, the relationship of surface melting to the premelting of nanoclusters and nanowires is reviewed.     

Superheating and solid-liquid phase coexistence in nanoparticles with nonmelting surfaces

We present a phenomenological model of melting in nanoparticles with facets that are only partially wet by their liquid phase. We show that in this model, as the solid nanoparticle seeks to avoid coexistence with the liquid, the microcanonical melting temperature can exceed the bulk melting point and that the onset of coexistence is a first-order transition. We show that these results are consistent with molecular dynamics simulations of aluminum nanoparticles which remain solid above the bulk melting temperature.     

Short-time dynamics of partial wetting

When a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid. For example, a millimeter-sized water droplet will wet an area having the same diameter as the drop within a millisecond. For perfectly wetting systems, this spreading is inertially dominated. Here we identify that even in the presence of a contact line, the initial wetting is dominated by inertia rather than viscosity. We find that the spreading radius follows a power-law scaling in time where the exponent depends on the equilibrium contact angle. We propose a model, consistent with the experimental results, in which the surface spreading is regulated by the generation of capillary waves.     

Morphological stability analysis of partial wetting

We develop a macroscopic static theory of the morphological stability of partial wetting. The system we studied consist of a smooth horizontal solid surface and some non-volatile liquid on it. A necessary condition for the stable equilibrium of such systems is known as the Young condition on the contact angle made at the contact line where the free surface of liquid meets the solid surface. But this condition is local and is not sufficient for the stability. We present a formulation for studying the stability of systems which satisfy the Young condition. Then we apply this to several morphologies of wetting. We find that there are at least two fundamental morphologies that we call a hole and a ridge, which are thermodynamically unstable against certain infinitesimal deformations of the contact lines. The hole type instability has also been found recently [D. J. Srolovitz and S. A. Safran, J. Appl. Phyys., 60 (1986), 1]. We also derived a reduced expression for the wetting energy as a functional of the contact line positions under the assumption of almost flat free surface of the liquid. This serves us to understand the characteristic length scale which appears in the ridge type instability. Besides these instabilities there is another category of morphological instability in which the system becomes unstable against an infinitesimal deformation of the free surface of liquid. We show this by an illustrating example in which the instability is described as the so-called tangent bifureation in nonlinear systems.     

Interplay of wetting and phase separation at surfaces

We review our understanding of surface-directed spinodal decomposition (SDSD), i.e., the interplay of wetting and phase separation in an unstable AB mixture placed in contact with a wetting surface. In this context, we present results for two problems, viz., SDSD in a semi-infinite geometry with a completely wet surface; and SDSD in a thin-film geometry with partially wet surfaces.     

The phenomenon of wetting at solid/solid interface

When a V₂O₅ crystallite is placed on an anatase pellet and heated at 823–923 K, vanadium ions migrate over the surface of anatase grains enveloping them in a thin overlayer. XPS, X-ray and EPR studies show that at 823 K a very thin layer is formed, its properties being strongly modified by interaction with the anatase support. At 923 K, on top of this inner layer an outer layer migrates, whose properties are similar to V₂O₅. As in the same conditions no migration is observed on rutile, it is concluded that this phenomenon is a manifestation of wetting of one oxide by another oxide, the difference in the surface free energy being the driving force of the migration.     

Thermodynamics of solid surfaces

In contrast to the thermodynamics of fluid surfaces, the thermodynamics of solid surfaces was not elaborated in detail by Gibbs and other founders of surface thermodynamics. During recent decades, significant progress in this field has been achieved in both the understanding of old notions, like chemical potentials, and in formulating new areas. Applying to solid surfaces, basic relationships of classical theory of capillarity, such as the Laplace equation, the Young equation, the Gibbs adsorption equation, the Gibbs-Curie principle, the Wulff theorem and the Dupré rule, were reformulated and generalized. The thermodynamics of self-dispersion of solids and the thermodynamics of contact line phenomena were developed as well. This review provides a fresh insight into the modern state of the thermodynamics of solid surfaces. Not only a solid surface itself, both in a macroscopic body and in the system of fine particles, but also the interaction of solid surfaces with fluid phases, such as wetting phenomenon, will be analyzed. As the development of surface thermodynamics has given a powerful impetus to the creation of new experimental methods, some of these will be described as examples.     

Suspended penetration wetting state of droplets on microstructured surfaces

When a water droplet on a micropillar-structured hydrophobic surface is submitted to gradually increased pressure, the CassieBaxter wetting state transforms into the Wenzel wetting state once the pressure exceeds a critical value. It has been assumed that the reverse transition(Wenzel-to-Cassie-Baxter wetting state) cannot happen spontaneously after the pressure has been removed.In this paper, we report a new wetting-state transition. When external pressure is exerted on a droplet in the Cassie-Baxter wetting state on textured surfaces with high micropillars to trigger the breakdown of this wetting state, the droplet penetrates the micropillars but does not touch the base of the surface to trigger the occurrence of the Wenzel wetting state. We have named this state the suspended penetration wetting state. Spontaneous recovery from the suspended penetration wetting state to the initial Cassie-Baxter wetting state is achieved when the pressure is removed. Based on the experimental results, we built models to establish the penetration depth that the suspended penetration wetting state could achieve and to understand the energy barrier that influences the equilibrium position of the liquid surface. These results deepen our understanding of wetting states on rough surfaces subjected to external disturbances and shed new light on the design of superhydrophobic materials with a robust wetting stability.     

Riemann surfaces and partial wave models

Within the context of simple partial wave models for elastic scattering the problem of uniformizing the partial wave amplitude and classifying its Riemann surface is studied. Starting with the analytic continuation of the amplitude an analysis of the Riemann surface is made through its group of covering transformations relative to a simpler base surface. A model based on the Yukawa potential is studied in this manner and the Riemann surface of interest is found to be the universal covering surface of the thrice punctured sphere. The uniformization of the amplitude can be done explicitly in this case by use of the elliptic modular function. In terms of the uniformizing variable, the original discontinuity relations for the amplitude then reduce to functional equations involving elements of the modular group.     

Tailoring the wetting response of silicon surfaces via fs laser structuring

Control over the wettability of solids and manufacturing of functional surfaces with special hydrophobic and self-cleaning properties has aroused great interest because of its significance for a vast range of applications in daily life, industry and agriculture. We report here a simple method for preparing stable superhydrophobic surfaces by irradiating silicon (Si) wafers with femtosecond (fs) laser pulses and subsequently coating them with chloroalkylsilane monolayers. It is possible, by varying the laser pulse fluence on the surface, to achieve control of the wetting properties through a systematic and reproducible variation of roughness at micro- and nano-scale which mimics both the topology of the “model” superhydrophobic surface—the natural lotus leaf—, as well as its wetting response. Water droplets can move along these irradiated superhydrophobic surfaces, under the action of small gravitational forces, and experience subsequent immobilization, induced by surface tension gradients. These results demonstrate the potential of manipulating liquid motion through selective laser patterning.     

Measures of wettability of solid surfaces

The surface tension of a solid surface is not amenable to direct experimental measurement. The most common method for assessing this surface tension is by contact angle measurements. The currently optimal way to measure and interpret contact angles is discussed, emphasizing the yet unresolved issues. It is argued that the most meaningful measurements to be done are of the most stable apparent contact angle (from which the surface tension of the solid is eventually assessed) and the contact angle hysteresis range (which indicates the existence and degree of chemical heterogeneities and roughness).     

Theory of decoherence at solid surfaces

Decoherence processes at solid surfaces are observed at all time scales. The most common surface processes are classified according to the presently common view on decoherence theory. Prominent examples of decoherent surface processes are electronic relaxation and deexcitation, vibrational relaxation, diffusion, inelastic scattering, sticking, STM-induced chemical reactions and desorption, localization of adsorbates. Various mechanisms, suggested at the present state of the art of decoherence theory, are investigated for their ability of providing the understanding of decoherence at solid surfaces. In some cases environmental decoherence by coupling to phonons and electron-hole pairs in the surface is a viable mechanism. Some new ideas are introduced, which have not been discussed in the framework of decoherence theory so far.