Interfacial energy solid-vapor

Molecular dynamics and density functional theory studies (see Section IX-2) of the Lennard-Jones 6-12 system determine the interfacial tension for the solid-liquid and solid-vapor interfaces [47-49]. The dimensionless interfacial tension ya /kT, where a is the Lennard-Jones molecular size, increases from about 0.83 for the solid-liquid interface to 2.38 for the solid-vapor at the triple point [49], reflecting the large energy associated with a solid-vapor interface. 

Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

T Solid-vapor interfacial energy dyn/cm dyn/cm z Pow der shear stress kg/cm psf... 

Interfacial energies between the solid-liquid, solid-vapor, and vapor-liquid are represented by ysL, ysv, and ylv, respectively. From K. M. Ralls, T. H. Courtney, and J. Wulff, Introduction to Materials Science and Engineering. Copyright 1976 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc. 

The three interfacial surface energies, as shown at the three-phase junction in Figure 2.29, can be used to perform a simple force balance. The liquid-solid interfacial energy plus the component of the liquid-vapor interfacial energy that lies in the same direction must exactly balance the solid-vapor interfacial energy at equilibrium ... 

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]...

FIO. 20-66 Contact angle on a powder surface, where y , y, y " are the solid-vapor, solid-liquid, and liquid-vapor interfacial energies, and 0 is the contact angle measured through the liquid. 

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-... 

IGC can be used to determine various properties of the stationary phase, such as the transition temperatures, polymer—polymer interaction parameters, acid-base characteristics, solubility parameters, crystallinity, surface tension, and surface area. IGC can also be used to determine properties of the vapor-solid system, such as adsorption properties, heat of adsorption, interaction parameters, interfacial energy, and diffusion coefficients. The advantages of IGC are simplicity and speed of data collection, accuracy and precision of the data, relatively low capital investment, and dependability and low operating cost of the equipment. 

We simply have to take into account that three interfacial tensions compete / snvt for the solid-vapor interface, f t for the liquid-vapor interface, and /j 1, for the solid-liquid interface. We have surface melting if /im - (/ini + /,ni) = A/ > 0. The effective free energy replacing eq. (263) is, for short range forces, being the melting temperature... 

Viscous sintering is a process of densification driven by interfacial energy (81). Material moves by viscous flow in such a way as to eliminate porosity and thereby reduce the solid-vapor interfacial area. The rate of viscous sintering is proportional to the surface area and inversely propor-... 

In thermodynamic theory of heterogeneous nucleation of solid from vapor,P a nucleus on a substrate is considered to be cap-shaped with a contact angle to the substrate. Young s equation dictates the relationship among the surface and interfacial energies as ... 

The values of the evaporation and sublimation heats are usually quite close to each other, as well as the densities of solid substances and their melts, measured at the melting point. Consequently, the values of the surface energy at the liquid-vapor, aLV, and at the solid-vapor, osv, interfaces are nearly identical. Oppositely, the interfacial energy oSL at the interface between the solid phase and its melt is usually low oSL values normally do not exceed 1/10 of surface tension values of melt (note that the heats of melting are also on the order of -10% of those of evaporation). 

The laws governing the interfacial phenomena between condensed phases and their vapor (or air) in single- and two-component systems, described in previous chapters, are largely applicable to the interfaces between two condensed phases, i.e., between two liquids, two solids, or between a solid and a liquid. At the same time, these interfaces have some important peculiarities, primarily related to the partial compensation of the intermolecular interactions. The degree of saturation of the surface forces is determined by the similarity in the molecular nature of the phases in contact. When adsorption of surfactants takes place at such interfaces, it may substantially enhance the decrease in the interfacial energy. The latter is of great importance, since surfactants play a major role in the formation and degradation of disperse systems (see Chapters IV, VI-VIII). 

In addition to overcoming experimental difficulties, the Naval Research Laboratory group has contributed many important generalizations and new concepts-for example, the concepts of low energy solid [33,69], critical surface tension [33,61], and autophobic liquid [32,41]. These developments have also stimulated the search for an interpretative scheme capable of yielding values of solid-vapor and solid-liquid interfacial tensions. 

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