Solid-Liquid Interfacial Free Energy

One remarkably simple yet seemingly robust outcome of Turnbull s experiments was his empirical finding that the solid-liquid interfacial free energy was... 

The present discussion is restricted to an introductory demonstration of how, in principle, adsorption data may be employed to determine changes in the solid-gas interfacial free energy. A typical adsorption isotherm (of the physical adsorption type) is shown in Fig. X-1. In this figure, the amount adsorbed per gram of powdered quartz is plotted against P/F, where P is the pressure of the adsorbate vapor and P is the vapor pressure of the pure liquid adsorbate. 

Fig. 9. Schematic of contact angle of a liquid on a solid. By balancing components of interfacial free energies in the horizontal direction, we can obtain the Young s equation.

Considering a solid-liquid system, this relationship may be combined with the well-known Young s equation to eliminate the interfacial free energy. Hence,... 

IVa represents a physical bond resulting from highly localized intermolecular dispersion forces. It is equal to the sum of the surface free energies of the liquid, 7, and the solid, 72. loss the interfacial free energy, 7,2. It follows that Eq. (2.1) can be related to a model of a liquid drop on a solid shown in Fig. 2.2. Resolution of forces in the horizontal direction at the point A where the three phases are in contact yields Young s equation... 

Fig. 14. Schematic illustration of a drop ofliquid spreading in contact with a solid surface, showing the relations between the relevant parameters the contact angle, 0 the solid/vapor interfacial free energy, Ysv the liquid/vapor interfacial free energy, yLV and the solid/liquid interfacial free energy, ySL. Young s equation describes the relationship between these parameters for a stationary drop at thermodynamic equilibrium [175]...

Surface and Interfacial Tension. Some properties of liquid surfaces are suggestive of a skin that exercises a contracting force or tension parallel to the surface. Mathematical models based on this effect have been used in explanation of surface phenomena, such as capillary rise. The terms surface tension (gas—liquid or gas—solid interface) and interfacial tension (liquid—liquid or liquid—solid) relate to these models which do not reflect the actual behavior of molecules and ions at interfaces. Surface tension is the force per unit length required to create a new unit area of gas—liquid surface (mN/m (= dyn/cm)). It is numerically equal to the free-surface energy. Similady, interfacial tension is the force per unit length required to create a new unit area of liquid—liquid interface and is numerically equal to the interfacial free energy. 

J J. Hoyt et al., Method for computing the anisotropy of the solid-liquid interfacial free energy. Phys. Rev. Lett. 86, 5530-5533 (2001)... 

By definition, Wad is the sum of surface free energies of a liquid (Fiv) and a solid in vacuum (F8) minus the interfacial free energy (Fsl) according to Dupre s equation ... 

Consider a system consisting of a solid with a cross-section of unit area and a liquid of a different species, immiscible with the solid, held at constant temperature. Both the solid and liquid surfaces are assumed free of any adsorbed species. When the solid surface is lowered towards the liquid until contact is established (Figure 1.34.a), the change of interfacial free energy of the system, or the work gained, is given by ... 

When the condition < a is fulfilled, the liquid wets not only the groove but it also expands on the free solid surface on both sides of the groove to a distance 1 as shown on Figure H.2.b. The equilibrium value of 1 can be calculated by minimising the interfacial free energy of the system for a small lateral displacement <51 of the liquid perpendicularly to the groove (Lorrain 1996) ... 

An alternative method for determining the interfacial free energy applies to substances in which the liquid does not wet the crystal at the melting point. In such cases the contact angles, which the liquid drops form with the crystal surface, can be measured and deduced. Zell and Mutaftschiev applied this method first to the (0001) surface of cadmium and more recently to the alkali halides NaCP° and KCP and to mixed alkali halide systems. The number of substances in which the liquid does not wet the solid appears limited, however, so this method cannot be applied in all cases. 

One of the first and most extensively applied models for the liquid-solid interfacial free energy is that due to Skapski. His approach begins with the assumption that a liquid will wet its crystal, so the contact angle 6 in the three-phase equilibrium between crystal, liquid, and vapor is 0. (This corresponds in Fig. 1 to the replacement of the substrate with the solid, the solid with the liquid, and the liquid with the vapor.) The analog of Eq. (2.15) then has 0 = 0 and cos 0 = 1, so that the result is... 

Over the last two decades the exploration of microscopic processes at interfaces has advanced at a rapid pace. With the active use of computer simulations and density functional theory the theory of liquid/vapor, liquid/liquid and vacuum/crystal interfaces has progressed from a simple phenomenological treatment to sophisticated ah initio calculations of their electronic, structural and dynamic properties [1], However, for the case of liquid/crystal interfaces progress has been achieved only in understanding the simplest density profiles, while the mechanism of formation of solid/liquid interfaces, emergence of interfacial excess stress and the anisotropy of interfacial free energy are not yet completely established [2],... 

This study is consistent with the idea that crystal surfaces at temperatures close to melting have some kind of disordered layer or layers, often called liquid-like . Due to the different equilibrium volumes of the liquid and solid phases, this region makes the surface either contract (as in the case of the ice surface) or expand (as it is for Lennard-Jones systems). The positive interfacial excess stress of the ice/water interface therefore makes it similar to liq-uid/vapor interfaces, and the water/vapor interface in particular, for which the excess stress is equal to the interfacial free energy (surface tension). 

This process involves extraction of fine particles from an aqueous phase into an oil phase. The effectiveness of this technique, as shown in Figure 2, is based on the stability of emulsion droplets with solid particles. If a particle is partially wetted by two immiscible liquids the particle will concentrate at the liquid-liquid interface. The thermodynamic criteria for distribution of solids at the interface of two immiscible liquids is the lowering in the interfacial free energy of the system when particles come in contact with two immiscible liquids. (12) If ygw, yWQ and ygp are the interfacial tensions of solid-water, water-oil and solid-oil interfaces respectively, and if ygQ > y + ygw then the solid particles are preferentially dispersed within the water phase. However, if ygw > ywq + ygQ, the solid is dispersed within the oil phase. On the other hand, if yWQ > ygQ + ysw, or if none of the three interfacial tensions is greater than the sum of the other two, the solids in such case will be distributed at the oil-water interface. 

Equation 6.3 is generally called Young s equation and the quantity yM cos 0 the adhesion tension (Bartell, 1934). Note that ySA, the interfacial tension in equilibrium with the gas and liquid phases in the system, is not ys, the free energy per unit area of the solid in a vacuum, but ys — n, where n is the reduction in interfacial free energy per unit area of S resulting from adsorption of vapor of L that is, n = ys-isA-... 

---