Definition of Surface

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

A third definition of surface mobility is essentially a rheological one it represents the extension to films of the criteria we use for bulk phases and, of course, it is the basis for distinguishing states of films on liquid substrates. Thus as discussed in Chapter IV, solid films should be ordered and should show elastic and yield point behavior liquid films should be coherent and show viscous flow gaseous films should be in rapid equilibrium with all parts of the surface. 

Because of the influence of potential gradients, the work function depends on the position of the point to which the electron is transferred. As in the definition of surface potential, a point a) situated in the vacuum just outside the metal is regarded as the terminal point of transfer. It is assumed, moreover, that when the transfer has been completed, the velocity of the electron is close to zero (i.e., no kinetic energy is imparted on it). 

Gibbs surface model and definition of surface tension... 

The surface area of fibres increases during refining. However, the definition of surface area for cellulose is not straightforward and it is necessary to define it a little more precisely. It can be measured when the pulp is in either the wet or the dry state and very different... 

The surface basicity of a solid catalyst can be defined in a way analogous to that applied to conventional bases. Thus, a surface Lewis base site is one that is able to donate an electron pair to an adsorbed molecule. If we take the definition of surface basicity in a more general way, it could be said that the active surface corresponds to sites with relatively high local electron densities. This general definition will include not only Lewis basicity but also single electron donor sites. We emphasize that the literature of heterogeneous catalysis often reports that both single-electron and electron-pair donor sites exist on basic catalysts. 

The separation process shown in Fignre 2.35a consists of the formation of two new interfaces, each of nnit cross-sectional area, at a location where no interface previously existed. The free energy change associated with the separation process comes directly from the definition of surface energy [Eq. (2.61)] where two snrfaces of unit surface area are formed. With appropriate assumptions regarding constant temperature, pressure, and incompressible fluids, we can equate this free energy change with the... 

At first sight it would look as if the definition of surface potential (x) described in Section 6.4.8 would overlap with the definition of the workfunction. Does this mean that both quantities are the same but with opposite signs To answer this question, let us look closer to the trajectory of the electron as defined in the work function (Fig. 6.45). The electron starts in a point deep inside the metal, where all different types of chemical bondings and interactions exist. After breaking all these forces, the electron moves itself free from inside the metal to a point close to the surface. Then, from here it has to cross the barrier of dipoles (see Section 6.3.8) to reach a point just outside the metal. 

The definition of surface excess, on the other hand, starts with the concentration profile, but involves an integration between limits Kq. (6.65)]. Once the integration is done and limits are inserted, one obtains a number (so many moles per square centimeter) and loses all knowledge of the function c((x). In other words, after the integration is carried out and the surface excess evaluated, the concentration profile... 

Thus, surface tension changes have been related to changes in the absolute potential differences across an electrode/electrolyte interface and to changes in the chemical potential of all the species, i.e., to changes in solution composition. Only one other quantity is missing, the surface excess. This can be easily introduced by recalling the definition of surface excess [Eq. (6.66)], i.e.,... 

This supplies a second definition of surface tension It equals the work per unit area required to produce a new surface. In terms of this definition, the units of 7 are energy per area — J m 2 in SI or erg cm"2 in the cgs system. 

When air is exhaled the small alveoli of the lungs could collapse if it were not for the surface active material (surfactant) present in the fluid that coats the lungs. e In fact, the lack of adequate surfactant is the cause of respiratory distress syndrome, a major cause of death among premature infants and a disease that may develop in acute form in adults. The surfactant material forms a thin film of high fluidity at the air-liquid interface and lowers the surface tension from the 72 mN/m of pure water to <10 mN/mfs (Pay attention to the definition of surface tension.11)... 

The extent of the surface-containing region is not specified by the definition of the surface excess. This region must contain all of the solution whose concentration differs from that of the bulk liquid and may contain any amount of bulk solution. The bulk solution makes no contribution to the value of the surface excess. No assumption is involved in the definition of surface excess as to whether either component forms a monolayer on the surface. 

There are two definitions of protein hydrophobicity average hydrophobicity and surface hydrophobicity. The average hydrophobicity was defined by Bigelow (1967) as the total hydrophobicity of all amino acid residues comprising a protein divided by the number of amino acids in the protein. There is no standard definition of surface (or effective) hydrophobicity except the concept that there must be hydrophobic regions on the molecular surface that play an effective role in protein function. Readers who are interested in a more detailed discussion are referred to Nakai and Li-Chan (1988). 

We call this Pt(100) surface reconstructed. Surface reconstruction is defined as the state of the clean surface when its LEED pattern indicates the presence of a surface unit mesh different from the bulklike (1 x 1) unit mesh that is expected from the projection of the bulk X-ray unit cell. Conversely, an unreconstructed surface has a surface structure and a so-called (1 x 1) diffraction pattern that is expected from the projection of the X-ray unit cell for that particular surface. Such a definition of surface reconstruction does not tell us anything about possible changes in the interlayer distances between the first and the second layers of atoms at the surface. Contraction or expansion in the direction perpendicular to the surface can take place without changing the (1 x 1) two-dimensional surface unit cell size or orientation. Indeed, several low Miller index surfaces of clean monatomic and diatomic solids exhibit unreconstructed surfaces, but the surface structure also exhibits contraction or expansion perpendicular to the surface plane in the first layer of atoms (9b). 

When describing liquid surfaces, the surface tension was of fundamental importance. If we try to extend the definition of surface tension to solids, a major problem arises [324], If the surface of a liquid increases, then the number of surface atoms increases in proportion. For a solid surface this plastic increase of the surface area is not the only possible process. Usually more important is an elastic increase of the surface area. If the solid surface is increased by mechanically stretching, the distance between neighboring surface atoms changes, while the number of surface atoms remains constant. The change in surface area is commonly described in terms of the surface strain. The total surface strain etot is given by the change in surface area divided by the whole surface area detot = dA/A. The surface strain may be divided into a plastic strain dep and an elastic strain dse so that dstot = dep + dee. 

The last method which will be considered here is the GEPOL, which was first elaborated in Pisa by Tomasi and Pascual-Ahuir [15]. GEPOL will be presented in two steps in this section we will treat the excluded volume filling, whereas the definition of surface elements will be given in the next section. 

Mata, A.M., Matthews, I., Tunwell, R.E.A., Sharma, R.P., Lee, A.G., East, J.M. (1992). Definition of surface-exposed and trans-membranous regions of the (Ca2+-Mg2+)-ATPase of sarcoplasmic reticulum using anti-peptide antibodies. Biochem. J. 286, 567-580. 

Sherman and Eyring (54, 55), it is only recently that quantum mechanical techniques have become available for the treatment of chemisorption. In addition, lack of precise experimental definition of surfaces has made it difficult to construct proper surface models. It is expected that theoretical models of surfaces will become increasingly useful in the future owing to the active work being performed on these problems. 

These values are not accurate and cannot be reproduced in a reliable manner. It is due to the fact that apart from the easily definable factors (such as current density, material of electrodes, temperature, pressure etc.) the overvoltage also depends to a great degree on factors that cannot be controlled so easily i. e. on the state of the electrode surface, way of the mechanical treatment of the same, its past (i. e. whether it had been polarized beforehand or not) even traces of impurities prove important. The difficulties connected with the definition of surface properties of electrodes are aggravated by the variability of the overvoltage in the very course of electrolysis. 

SURFACE [number] [description] Implicit definition of surface composition -equilibrate number... 

It is well known that the effect of surface tension is to minimize the area of a lie surface. From a thermodynamic standpoint, the notion of surface tension can als< applied to a solid surface, although its physical significance is more difficul explain. For our present purpose, we may adopt an analogous definition of surface tension of a clean solid adsorbent to that for a clean liquid surface. Thus,... 

The modeling approaches used to describe the surface reactions of metal ions differ in their definition of surface structure and the charge/potential relationships within the compact layer of the EDL ( 2, 5,. In our previous calculations ( 2) we... 

To link this definition of surface energy to calculations on relaxed slabs we now make the assumption that the entropy in the slab and bulk oxide free energy terms can be neglected. Then the surface energy based on calculated quantities... 

FIGURE 1 Definition of surface and volume integral and Gauss-Green divergence theorem. 

In Eq. (3), is the relevant molecular transition frequency, y is a dam >ing rate, is a polarizability, and (/) is the z-component of the total electric field in the vicinity of the molecule. If (t) were simply of the form i)Cos(fijr), then Eq. (3) is the well-known phenomenological Lorentzian oscillator model of absorption which leads to an approximate Lorentzian form for the absorption cross section [1]. Similar remarks hold for the SP dipole, fi/f), if E t) = ocos(mr), where E t) is the z-component of the total electric field near the SP dipole. The parameters 04,74 and a, in this case are chosen such that the resulting Lorentzian cross section proximates the known exact sur ce plasmon absorption cross section or its appropriate form in the quasistatic (a A=2 tic/cs) limit. Note that I am using a simplified notation compared to the various notations of Refs. [13-15]. (Relative to Ref. [13], for example, my definitions of surface plasmon dipole... 

A problem arises here in the definition of surface coverage since C" is not a single molecular weight, It cannot be equated with the fraction of occupied sites. Furthermore, It is assumed that two surface species are in equilibrium, which is not likely. 

Since the definition of surface area can sometimes be ambiguous, it is important to recognize that the macroscopic determination of surface area generally involves the measurement of a certain property of the solid (e.g., equilibrium adsorption capacity) which can be a qualitative measure of the development of the surface. This property can then be related to the actual surface area through an appropriate theory (e.g., BET isotherm). Therefore, one should not be surprised that the results from different models may give different values of the surface area. 

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