Surface energy thermodynamic treatment

A thermodynamic treatment is first suggested on the basis of which one can explain the inclined phase transition that occurs in monolayers of insoluble surfactants. By minimizing the Helmholtz free energy of the monolayer, the equilibrium radius and the equilibrium area fraction of the LC islands are obtained as functions of the average molecular surface area A. The mixing entropy provides a negligible effect on... 

The correct thermodynamic treatment of adsorption processes is possible only on liquid-gas and liquid-liquid interfaces, where the surface energy or the surface tension of the liquid can precisely be determined. For these systems, the Gibbs adsorption isotherm can be applied. For example on a liquid-liquid interface,... 

For situations of overlapping chains, where lateral fluctuations in the segment concentration become rather small, mean-field descriptions become appropriate. The most successful of this type of theoiy is the lattice model of Scheutjens and Fleer (SF-theoiy). In chapter II.5 some aspects of this model were discussed. This theory predicts how the adsorbed amount and the concentration profile 0(z) depend on the interaction parameters and x and on the chain length N. From the statistical-thermodynamic treatment the Helmholtz energy and, hence, the surface pressure ti can also be obtcdned. When n is expressed as a function of the profile 0(z), the result may be written as ... 

The thermodynamic treatment discussed so far employed the harmonic approximation. Its use for weak intermolecular interactions is, however, not entirely justified. With strong vdW molecules (of course, except strong hydrogen-bonded complexes, vide supra) we can hope that the anharmonicity (in connection with thermodynamic treatment) does not play a crucial role. There exists another complication concerning complexes possessing a double-minimum on energy hyper-surface. If the minima are separated by low energy barrier the harmonic approximation is not adequate . The role of anharmonicity is essential with true vdW molecules. Unfortunately, except for the H O... HF and (HjO), complexes no complete experimental thermodynamic characteristics are available for the for-... 

All liquid droplets spontaneously assume the form of a sphere in order to minimize their surface free energy by minimizing their surface area to volume ratio, as we will see in the thermodynamic treatment in Chapter 3. The surface area to volume ratio can easily be calculated for materials having exact geometric shapes by using well-known geometric formulas. For example, for a sphere and a cube this ratio is... 

The XPS results indicated that there were about 3-5 at. % sulfur and 27-47 at. % oxygen incorporated onto the sulfur dioxide plasma treated LDPE substrate surfaces (Table 1). The sulfur atomic concentration reached a maximum at about 50 A from the sample surface (0 = 30°) right after the plasma treatment (Figure 3). (The uncertainty of the XPS multiplex scan for atomic concentration analysis is believed to be 0.5-1.0 at. %.) The sulfur-containing species diffused into the bulk of the polymer (> 100 A) as shown from the XPS data collected eleven days after the plasma reaction. This phenomenon is due to the mobility of the polymer surface. s After the sulfur dioxide plasma modification, the hydrophilic sulfonyl groups on the LDPE backbone diffuse away from the polymer surface toward the bulk of the material so that a lower surface energy can be attained. Because the air/LDPE interface has a low surface tension, thermodynamic equilibrium favors a hydrophobic surface. As a result, the sulfur atomic concentrations in the top 100 A of the substrates decreased with time as the sulfonyl groups diffused away from this surface layer. 

We now can develop a similar thermodynamic treatment for the surface phase a, which is the interface between the phases a and (, and is in equilibrium with these two phases. When the adsorbed phase is treated as a two dimensional surface, fundamental equations in classical thermodynamics can still be applied. Applying the same procedure to surface free energy, we will obtain the Gibbs adsorption equation. This is done as follows. The total differentiation of the surface free energy takes the form similar to eq. (2.3-1) with P dV being replaced by 7idA ... 

The thermodynamic treatment of phase transitions is usually based upon the equilibrium properties of the bulk phases involved. A description of the formation of a new phase requires consideration of at least two additional factors, the contribution of changes in the surface states to the total energy, and the influence of these changes on the rate of formation of the new phase. 

As early as 1901, Wulff described a thermodynamic treatment of the crystal shape changes based on an energy minimized total surface area [39]. It is nowadays well known that this purely thermodynamic treatment cannot always predict the crystal shape, because crystalhzation and crystal shape often also rely on kinetic effects and defect structures Hke screw dislocations or kinks etc. The specific adsorption of ions or organic additives to particu-... 

Sorption measurements are a useful method in the characterization of solid materials. From these data, it is possible to obtain information about the capacity of adsorption, but also thermodynamic properties—enthalpies of adsorption, surface energy—as well as kinetic information, such as diffusion rates. Sorption measurements can be obtained either by static or dynamic methods. Static methods carried out the adsorption measurements under vacuum, after a pre-treatment at high temperature in order to clean the material surface. Dynamic methods use a flowing gas device. Inverse gas chromatography (IGC) is a dynamic method. In comparison to static adsorption systems, dynamic sorption techniques show shorter measurement time, and a wider range of experimental possibilities. 

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