Specific component of surface free energy

Table 8 Specific Components of Surface Free Energy of Adsorption of MSX, SX-I, and SX-I... 

Polar probes have both dispersive and specific components of surface free energy of adsorption. The specific component of surface free energy of adsorption (AGa is determined by subtracting the dispersive contribution from the total free energy of adsorption, and can be obtained from the vertical distance between the alkane reference line [Eq. (30) Figure 21] and the polar probes of interest according to the following equation (60) ... 

Authors of Ref. [49] proved that the variation of the term RT In Vn as a function of the molar deformation polarization of n-alkanes Pdp is a straight line which slope equal to C Pds is proportional to the surface ability for dispersive interactions. AG = 0 is defined in the same way as in the case of Saint Flour-Papirer s method. However, in this procedure AG = 0 values are always positive while in approach [48] the negative values of the specific component of the free energy of adsorption were observed. Later, Donnet et al. [29] observed that their earlier proposal (i.e. that from Ref.[49]) based on the fundamental London equation gives only a first approximation of the ionization energy of a molecule. They proposed to use Eq.(15) in the form ... 

If RTlnV is plotted versus a(yL ) for a series of alkanes a straight line results and the dispersive contribution of the surface energy can be calculated from the slope. If polar probe molecules are injected, specific interactions can be determined. In the above-mentioned plot, points representing a polar probe are located above the straight line. The distance is equal to the specific component of the free energy JG /. (equation 5). 

In the early 1960s, Fowkes [88,89] introduced the concept of the surface free energy of a solid. The surface free energy is expressed by the sum two components a dispersive component, attributable to London attraction, and a specific (or polar) component, y p, owing to all other types of interactions (Debye, Keesom, hydrogen bonding, and other polar effects, as similarly described before in Sec. II. C... 

In such cases a local-equilibrium structure may be obtained theoretically by minimization of the free energy of the system under the constraint of a fixed alloy composition in the surface region [8,17-24]. Although this approach is very similar to the one used for bulk systems, it should be modified due to the specific features introduced by the surface. First of all, since the structure of the underlying bulk system is fixed, it acts as the source of an external field for the surface alloy, creating, for instance, epitaxial strain. Secondly, since the surface is an open system, it allows the formation of a great variety of different structures, which may not have any connection at all to the crystal structure of the substrate. Finally, the surface is a spatially inhomogeneous system, and thus different alloy components have their own... 

Bearing in mind that spontaneous formation of chemical and crystalline formations is accompanied by a decrease of the free energy of the system, which can be much smaller than its initial value (v i), especially when the newly produced compound is more stable than the mixture of initial components. The inverse case of p i is seldom encountered (nitrogen oxide or N2 + O2 mixture) or when (,i>2 = V l (HI or H2 + I2 mixture). As a rule, for porous materials phase transformations are accompanied by reduction of their specific surface area. 

Inverse gas chromatographic measurements may be carried out both at infinite dilution and at finite solute concentrations [1]. In the first case vapours of testing solutes are injected onto the colurtm and their concentrations in the adsorbed layer proceed to zero. Testing substances interact with strong active sites on the examined surface. The retention data are then converted into, e.g. dispersive component of the surface free energy and specific component of free energy of adsorption. In the second case, i.e. at finite solute concentrations, the appropriate adsorption isotherms are used to describe the surface properties of polymer or filler. The differential isosteric heat of adsorption is also calculated under the assumption that the isotherms were obtained at small temperature intervals. 

Finally, there are several approaches to determine the specific component of the surface free energy of carbon materials [71-73]. Among these, that proposed by Donnet et al [73] uses the standard adsorption free energy which is plotted against (hr L) o-10 , where h is the Planck constant, is the characteristic vibration frequency of the electron and a is the deformation polarizability. The method seems to provide reasonable results, although it does not take into account the effect of the surface irregularities. 

The surface free energy of a solid (7s) can be expressed as a sum of two components 7sd (the dispersive component), describing London-type interactions, and 7ssp (the specific component), including all other interactions (H-bonding, polar, and so forth). 

Specific Component of the Surface Free Energy of Heat-Treated Silicas. Specific interaction capacities of heat-treated silicas, that is, their ability to interact with polar molecules, were examined with chloroform (Lewis acid probe) and toluene and benzene (amphoteric molecules). Figure 2 provides examples of the evolution of the specific interaction parameter Zsp of the different silicas with chloroform as a probe. 

Specific Component of the Surface Free Energy of Heat-Treated Silicas... 

In a one-component system the specific surface free energy, G, is frequently called the surface tension or surface pressure and is denoted by y. Here y may be viewed as a pressure along the surface opposing the creation of new surface. It has dimensions of force per unit length (dynes per centimeter, ergs per square centimeter, or newtons per meter). The surface tension y for an unstrained phase is also equal to the increase of the total free energy of the system per unit increase of the surface area as follows ... 

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