Solid-liquid interface surface free energy

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

Equation (42) provides a thermodynamically valid way to determine y for an interface involving a solid. The thermodynamic approach makes it clear that curvature has an effect on activity for any curved surface. The surface free energy interpretation of y is more plausible for solids than the surface tension interpretation, which is so useful for liquid surfaces. Either interpretation is valid in both cases, and there are situations in which both are useful. From solubility studies on a particle of known size, y5 can be determined by the method of Example 6.2. 

Because of the high surface free energy at the liquid-solid interface, it is suggested that the stages of nucleation, transport of species by surface diffusion, and crystallization occur at the interface in the boundary layer. Culfaz and Sand in this volume (48) propose a mechanism with nucleation at the solid-liquid interface. This mechanism should be most evident in more concentrated gel systems where interparticle contact is maximized for aggregation, coalescence, or ripening processes. The epitaxy observed by Kerr et al. (84) in cocrystallization of zeolites L, offretite, and erionite further supports a surface nucleation mechanism. 

The cosine cannot exceed one. Then we might ask What happens, if 7s — 7sl — 7l > 0 or 7S - 7Si is higher than 7// Does this not violate Young s equation No, it does not because in thermodynamic equilibrium 7s — Ysl — 1l can never become positive. This is easy to see. If we could create a situation with 7s > 7SL + 7l, then the Gibbs free energy of the system could decrease by forming a continuous liquid film on the solid surface. Vapor would condense onto the solid until such a film is formed and the free solid surface would be replaced to a solid-liquid interface plus a liquid surface. 

The lower the surface free energy of the shell chemistry, the smaller is the contact angle hysteresis on the closely packed surface arrays. Further the contact angles varied with increasing height roughness. A possible explanation for this behaviour is that the vertical roughness influences the curvature radius of the liquid in trapped air pockets at the solid-liquid interface as was already assumed in the literature for nanostructured metal surfaces and paraffin-coated steel balls. 

Capillary Rise. In the absence of external forces, a body of liquid tends to assume a shape of minimum area. It is normally prevented from assuming spherical shape by the force of gravity, as well as by contact with other objects. When a liquid is in contact with a solid surface, there exists a specific surface free energy for the interface, or interfacial tension yi2- A solid surface itself has a surface tension 72. vvhich is often large in comparison with the surface tensions of liquids. Let a liquid with surface tension 7i be in contact with a solid with surface tension yj, with which it has an interfacial tension 7i2- Under what circumstances will a liquid film spread freely over the solid surface and wet it This will happen if, in creating a liquid-solid interface and an equal area of liquid surface at the expense of an equal area of solid surface, the free energy of the entire system decreases ... 

Contact angle measurements provide information on the wettability of the sample, the surface energetics of the solid, and the interfacial properties of the solid-liquid interface. The samples were immersed in water and captive air and octane bubbles were determined by measuring the bubble dimensions. By measurement of both air and octane contact angles the surface free energy (.y) of the solid-vapor ( > ) interface may be calculated by use of Young s equation and the narmonic mean hypothesis for separation of the dispersive and polar components of the work of adhesion. This method for determination of surface and interfacial proper-... 

Here the first term is the surface free energy, proportional to the surface area of the crystallite, while the second is the bulk free energy, proportional to its volume. The first term is always positive because of the work that must be done to create an interface, while the second is negative in the supercooled liquid, because the solid has the lower free energy under these circumstances. It is clear from the form of this equation that the free energy of the crystallites increases up to a size i, which is called the critical nucleus and represents a barrier that must be surmounted on the path from pure liquid to pure crystal. 

The most extensive simulation of surface excess properties, and the first study to determine a directly, was that of Broughton and Gilmer, who looked at the fee (100), (110), and (111) surfaces of a Lennard-Jones crystal-melt system. They determined the surface free energy by calculating the reversible work necessary to cleave the solid and liquid phases and to join the two systems to form a liquid-solid interface. They found the results... 

Given the difficulties outlined above in measuring or simulating the surface free energy of the liquid-solid interface, the natural question is whether theoretical methods can predict its magnitude and the physical processes that affect it. In this section we outline a number of theoretical approaches developed between 1950 and 1980, and in the next section we give a more extensive discussion of a recent density functional approach. 

Harrowell and Oxtoby have shown how the density functional theory for the solid-liquid interface outlined in Section III D can be generalized to study the nucleation of a crystal. If the critical nucleus is assumed spherical (a reasonable approximation for the alkali metals considered, given the near isotropy of the calculated surface free energy) then the inhomogeneous density of Eq. (3.13) can reasonably be generalized to... 

The processes on solid/vapor interfaces (or solid surfaces) and solid/liquid interfaces differ sufficiently from the liquid/vapor systems. Due to huge relaxation times in the solid phase, the atoms or molecules in the interior are not capable of moving to the surface to accommodate the new area created, as in the case of liquid surfaces. It was noted in [1,48] that the excess stress at solid surfaces and solid/liquid interfaces can have opposite sign. However, there was no clear explanation of that fact. The relation between the surface stress a, and solid surface free energy 7sv, was first pointed out by Shuttleworth [49],... 

---