Solid-vapor interface

Systems involving an interface are often metastable, that is, essentially in equilibrium in some aspects although in principle evolving slowly to a final state of global equilibrium. The solid-vapor interface is a good example of this. We can have adsorption equilibrium and calculate various thermodynamic quantities for the adsorption process yet the particles of a solid are unstable toward a drift to the final equilibrium condition of a single, perfect crystal. Much of Chapters IX and XVII are thus thermodynamic in content. 

Molecular dynamics calculations have been made on atomic crystals using a Lennard-Jones potential. These have to be done near the melting point in order for the iterations not to be too lengthy and have yielded density functioi). as one passes through the solid-vapor interface (see Ref. 45). The calculations showed considerable mobility in the surface region, amounting to the presence of a... 

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. 

There is a number of very pleasing and instructive relationships between adsorption from a binary solution at the solid-solution interface and that at the solution-vapor and the solid-vapor interfaces. The subject is sufficiently specialized, however, that the reader is referred to the general references and, in particular, to Ref. 153. Finally, some studies on the effect of high pressure (up to several thousand atmospheres) on binary adsorption isotherms have been reported [154]. Quite appreciable effects were found, indicating that significant partial molal volume changes may occur on adsorption. 

Eleat transfer occurs not only within the solid surface, droplet and vapor phases, but also at the liquid-solid and solid-vapor interface. Thus, the energy-balance equations for all phases and interfaces are solved to determine the heat-transfer rate and evaporation rate. 

Equation (10.18) was derived for capillary rise or depression assuming complete wetting, that is, 6 = 180°. In the case of contact angles greater than 0° and less than 180°, equation (10.18) must be modified. As liquid moves up the capillary during capillary rise the solid-vapor interface disappears and the solid-liquid interface appears. The work required for this process is... 

Solid/vapor interface motion can be produced by evaporation—the atoms that compose the solid phase are removed from the surface via the vapor phase reverse motion can be produced by condensation where a vapor-phase flux is directed onto the solid phase. Figure 14.2 illustrates how simultaneous evaporation and condensation can result in surface smoothing. 

Values of surface energy measured by this technique were found to be 1.140 J/m2 for Ag at 903 °C, 1400J/m2 for Au at 1204 °C, and 1.650 J/m2 for Cu at 1000 °C. The solid-vapor surface energy is relatively independent of the temperature, but the surface energy of a solid-vapor interface depends on its crystallographic orientation, so these measured values must reflect an average value for many orientations. 

The work of dispersion, Wd, involved in wetting a unit area of the solid substrate is given by the difference between the interfacial tension of the solid/liquid interface, ysL, and that of the solid/vapor interface, ySv,... 

Wadsworth and coworkers (13, 14) have found considerable evidence for surface polarization in double-beam infrared spectroscopy. Not only do new differential peaks due to adsorption appear in the spectrograms but also the bands due entirely to the adsorbent are frequently appreciably shifted by adsorption. This occurred, for example, in calcium fluorite treated with oleic acid, in samples of bentonites taken from aqueous solutions of different pH, and in various minerals treated by flotation collectors. In fact, it is more the rule than the exception that the spectrograms of finely divided solids dispersed in the KI or KBr window exhibit distortion due to adsorption, whether adsorption occurs at the solid-aqueous solution or at the solid-vapor interface. For example, Eyring and Wadsworth (13) found that two (differential) peaks were produced by adsorption on willemite either from the vapor or aqueous solution of hexanethiol. These peaks were due to the influence of adsorption of the hexanethiol on the Si-O bands of the willemite and occurred at about 9.2 and 12.3 microns. 

Contact angle — The contact angle is the angle of contact between a droplet of liquid and a flat rigid solid, measured within the liquid and perpendicular to the contact line where three phases (liquid, solid, vapor) meet. The simplest theoretical model of contact angle assumes thermodynamic equilibrium between three pure phases at constant temperature and pressure [i, ii]. Also, the droplet is assumed to be so small that the force of gravity does not distort its shape. If we denote the - interfacial tension of the solid-vapor interface as ysv. the interfacial tension of the solid-liquid interface as ySL and the interfacial tension of the liquid-vapor interface as yLV, then by a horizontal balance of mechanical forces (9 < 90°)... 

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-... 

As in the two phase liquid reactions there are fewer mass transport steps in vapor phase reactions than in three phase processes. These steps are shown in Fig. 5.13. The gaseous reactants must pass through the gas/solid interface to reach the catalyst particle. They then migrate through the particle to become adsorbed on the active sites. After reaction the product desorbs, migrates back through the particle to the solid/vapor interface which it passes through to enter the vapor phase in the reactor. 

As a simple model we consider Fa P 47rRefrysv FaP 4reFp7s, where Rt = radius of curvature of the tip and Rp = radius of curvature of the particle and Feff = (1/Ft + 1/Rp). = surface energy at the solid/vapor interface. In order... 

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],... 

Immersional wetting corresponds to a process where a solid—vacuum or solid-vapor interface is replaced by a soHd—liquid one. When starting from a solid-vacuum interface, the free energy variation during the process is (per unit area)... 

Now, when starting from a solid-vapor interface (i.e., a solid surface in equifib-rium with a vapor at pressure P), the free energy variation is... 

Spreading wetting corresponds to a process where a solid-vapor interface is progressively replaced by a solid-Hquid interface. The corresponding free energy variation per unit area is... 

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... 

When a solid powder is used as the stationary phase in the inverse gas chromatography method, the interaction of a well-known gas or organic vapor is measured, and the adsorption results for gaseous molecules on the solid powder are used to calculate the difference in surface free energy of bare stationary solid surface and that of the solid-vapor interface (ys - ysv). 

A captive air (or other gas) bubble is formed in the liquid contacting with the solid by means of an inverted micrometer syringe beneath the substrate which is kept in the test liquid. The contact angle is measured by means of a goniometer microscope or video camera. In this method, the solid-vapor interface is in equilibrium with the saturated vapor... 

Although Zlsman has appeared never to attribute a specific fundamental meaning to his Yc> others have considered Y o be the surface tension that the solid would have were Its cohesive forces the same as those acting across the solid-liquid Interface. Thus for a hydrocarbon solid, which has been supposed to Interact only through dispersion forces both cohesively and across the solid-liquid Interface, Yq should be the actual surface tension of the solid-vapor interface. This Is essentially what Is observed Yc for PE Is approximately that measured for a high molecular weight liquid hydrocarbon. On the other hand, if water Is considered to Interact with a hydrocarbon only through dispersion... 

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