One-component system surfaces

Thermodynamically, a solid surface is sufficiently characterized by two parameters surface energy (a scalar), with units of energy per area, and surface stress (a second-rank tensor), also with units of energy per area. For a liquid, these two are the same, but they can be very different for solids. We do not discuss the latter in this book, nor shall we distinguish between surface energy and surface tension, which is defined as the reversible work done in creating unit area of new surface. In one-component systems, surface energy and surface tension are numerically equal. 

Work Needed to Create a Surface of a One-Component System Surface Tension... 

WORK NEEDED TO CREATE A SURFACE OF A ONE-COMPONENT SYSTEM SURFACE TENSION... 

To define the thennodynamic state of a system one must specify fhe values of a minimum number of variables, enough to reproduce the system with all its macroscopic properties. If special forces (surface effecls, external fields—electric, magnetic, gravitational, etc) are absent, or if the bulk properties are insensitive to these forces, e.g. the weak terrestrial magnetic field, it ordinarily suffices—for a one-component system—to specify fliree variables, e.g. fhe femperature T, the pressure p and the number of moles n, or an equivalent set. For example, if the volume of a surface layer is negligible in comparison with the total volume, surface effects usually contribute negligibly to bulk thennodynamic properties. 

Figure A2.3.2 (a) P-V-T surface for a one-component system that contracts on freezing, (b) P-Visothenns in the region of the critical point.

This section describes the phase change process for a single component on a molecular level, with both vaporization and condensation occurring simultaneously. Molecules escape from the liquid surface and enter the bulk vapor phase, whereas other molecules leave the bulk vapor phase by becoming attached to the liquid surface. Analytical expressions are developed for the absolute rates of condensation and vaporization in one-component systems. The net rate of phase change, which is defined as the difference between the absolute rates of vaporization and condensation, represents the rate of mass... 

To create a new surface we have to break bonds and remove the superfluous atoms. At equilibrium at constant pressure and temperature the work demanded to increase the surface area of a one-component system by an amount dAs is given as... 

Figure 13.3. A P- V-T surface for a one-component system in which the substance contracts on freezing, such as water. Here Tj represents an isotherm below the triple-point temperature, 72 represents an isotherm between the triple-point temperature and the critical temperature, is the critical temperature, and represents an isotherm above the triple-point temperature. Points g, h, and i represent the molar volumes of sohd, hquid, and vapor, respectively, in equilibrium at the triple-point temperature. Points e and d represent the molar volumes of solid and liquid, respectively, in equihbrium at temperature T2 and the corresponding equilibrium pressure. Points c and b represent the molar volumes of hquid and vapor, respectively, in equilibrium at temperature and the corresponding equihbrium pressure. From F. W. Sears and G. L. Sahnger, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. 3rd ed., Addison-Wesley, Reading, MA, 1975, p. 31.

By the use of other assumptions, the thermodynamic treatment can be simplified and more progress can be made. In particular. Hill has shown that a system of considerable utility can be obtained by considering the adsorption process as a pseudo one-component system. Only the adsorbate is considered as taking an active part. The adsorbent is assumed inert and the only effect of its presence is that its surface provides an attractive force field for the adsorbate molecules. 

The projection of the three-dimensional surface on the pressure-temperature plane gives the familiar pressure-temperature diagram of a one component system. The projection for only the solid, liquid, and vapor phases... 

Figure 13.2. Definition of a defined surface in a one-component system.

We have developed the basic equations for the thermodynamic functions of the defined surface in the preceding paragraphs, but have not discussed the determination of the position of the boundary. Actually, the position is somewhat arbitrary, and as a result we must also discuss the dependence of the properties of the surface on the position. The position can be fixed by assigning the value of zero to one of Equations (13.25)—(13.27) that is, by making one of the nf equal to zero. For a one-component system there is only one such equation. For multicomponent systems we have to choose one of the components for which nf is made zero. The value of nf for the other components then would not be zero in general. The most appropriate choice for dilute solutions would be the solvent. The position of the surface for a one-component system is illustrated in Figure 13.2, where the line c is determined by making the areas of the two shaded portions equal. 

The adsorption of a protein on a surface, in general, is a relatively simple interaction of the surface with a biological component when it is investigated in a simple one-component system. The protein adsorption is considered as the first important step of more complicated interaction of the surface with a biological system, and numerous efforts were made to reduce the protein adsorption in the avenue of creating biocompatible surfaces. 

The application of the Maxwell-Stefan theory for diffusion in microporous media to permeation through zeolitic membranes implies that transport is assumed to occur only via the adsorbed phase (surface diffusion). Upon combination of surface diffusion according to the Maxwell-Stefan model (Eq. 20) with activated-gas translational diffusion (Eq. 12) for a one-component system, the temperature dependence of the flux shows a maximum and a minimum for a given set of parameters (Fig. 15). At low temperatures, surface diffusion is the most important diffusion mechanism. This type of diffusion is highly dependent on the concentration of adsorbed species in the membrane, which is calculated from the adsorption isotherm. At high temperatures, activated-gas translational diffusion takes over, causing an increase in the flux until it levels off at still-higher temperatures. 

Beneficial properties Excellent adhesion without the use of primers minimum surface preparation one-component system self-heahng excellent resistance to ultraviolet radiation good chemical resistance non-staining... 

In all experiments, a constant silver layer thickness of three monolayers was initially deposited. In the multicomponent system, Cd diffuses towards S under thin layer conditions" established by a 2D CdxAgy surface alloy. In the one-component systems, Cd diffuses towards S under semi-infinite conditions. A phase transition... 

It is, of course, obvious that in a one-component system the flnid is uniform from the bulk phase to the surface, but the orientation of the snrface molecnles will be different from the molecnles in the bulk phase. The question we may ask, then, is how sharply the density changes from that of being fluid to that of gas. Is this transition region a monolayer deep or many layers deep ... 

Oxides of a variety of metals on finely divided inert support materials initiate polymerization of ethylene and other vinyl monomers by a mechanism that is assumed to be similar to that of heterogeneous Ziegler-Natta polymerization that is, initiation probably occurs at active sites on the catalyst surface [2j. Unlike the traditional Ziegler-Natta two-component catalyst systems, the supported metal-oxide catalysts are essentially one-component systems. Among the metals that have been investigated for these catalyst... 

In order to treat thermal conduction in one-component systems, we may let Q = U, = U, the total energy of the molecule defined in equation (D-23). Then F becomes the energy per second transported across a surface of unit area that is, F is the heat-flux vector q [see equations (D-28) and (D-29) with neglected]. Hence equation (31) becomes... 

I. SURFACE PHENOMENA AND THE STRUCTURE OF INTERFACES IN ONE-COMPONENT SYSTEMS... 

The derivative of the surface tension with respect to temperature at the interface between condensed phases in binary systems can be either positive, or negative, or even change its sign when the temperature changes, which makes it different from the vapor-liquid interface in a one-component system. Within a certain approximation one may assume that in binary systems, as in single-component ones, the value r = -do/dT is the excess of entropy within the discontinuity surface. Consequently, for the interface between condensed phases, the excess of entropy can not only be positive (as it was with singlecomponent systems), but also negative. This situation is especially typical for the interface between two mutually saturated liquid solutions. 

P25.24 A general change in the Gibbs function of a one-component system with a surface is... 

Equations (52) and (53) hold regardless of any perturbations of the sorbent, etc., as discussed above. However, there is really no advantage in using H, and S., as formally defined above, over H and S [Eqs. (46) and (47)] except in the important special case of an inert adsorbent, by which we mean a hypothetical adsorbent whose own thermodynamic properties are unaffected by the presence of adsorbed molecules and whose surface area is independent of temperature and pressure. We can then replace nx by ft in Eqs. (52) and (53) and SB and Hs become just the entropy and heat content of the one-component system of ni moles of adsorbed gas. In effect, the adsorbent merely plays the role here of an external potential field. At the present early stage of our understanding of physical adsorption, this approximation certainly seems justified in most cases and indeed is made implicitly by almost all workers in the field. We shall make this simplification below except where otherwise noted. 

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