Surface force free energy isotherms

When a fresh solid surface is formed, say by cleavage, the molecules in the freshly generated surface may take a long time to reach their equilibrium positions, so that the new surface is a non-equilibrium structure. This is in contrast to the situation with liquids, where the mobility of the molecules enables the surface to reach an equilibrium configuration almost as soon as it is formed. For a solid surface a free energy can be defined in terms of the reversible, isothermal work needed to produqe the new surface, while it is convenient to define surface tension in terms of the forces needed to bring the freshly exposed surface to an equilibrium state. 

Forces of surface tension act on the surface of the particles in the liquid phase. It can be expressed as the work for the formation of a unit of interphase surface under constant thermodynamic parameters of the state (temperature, pressure, chemical potentials of the components). This process is reversible and isothermal. The surface tension forces can be regarded also as free energy per unit area, i.e. specific free energy (Gs). Then, the free energy per unit weight of particles would be... 

At the liquid-liquid interface between a hydrocarbon oil and water under mixing, the molecules encounter unbalanced attraction forces, pull inwardly, and contract as other molecules leave the interface for the interior of the bulk liquid. As a result, spherical droplets are formed. Customarily, the boundaries between a liquid and gas and between two liquids are the surface and the interface, respectively. The interfacial tension (or interfacial free energy) is defined as the work required to increase the interfacial area of one liquid phase over the other liquid phase isothermally and reversibly. Moving molecules away from the bulk to the surface or interfacial surface requires work (i.e., an increase in free energy). Water molecules and hydrocarbon oil molecules at the interface are attracted to the bulk water phase as a result of water-water interaction forces (i.e., van der Waals dispersion y and hydrogen bonding y ), to the bulk oil phase due to the oil-oil dispersion forces, y 1, and to the oil-water phase by oil-water interactions, y )W (i.e., dispersion forces). As mentioned in Chapter 3, the oil-water dispersion interactions are related to the geometric mean of the water-water and oil-oil dispersion interactions. The interfacial tension is written as ... 

The presence of walls causes a change of the free energy of the system. In general, this change depends on the separation between the walls which, thus, results in an attractive or repulsive force between them. Here, by system we refer to the liquid crystal in which the confining walls are immersed, so that the volume and the surface of the liquid crystal are preserved by changing the separation between walls. In an isothermal process the force is related to the free energy of a system as... 

The situation is still more complex in the presence of surfactants. Recently, a self-consistent electrostatic theory has been presented to predict disjoining pressure isotherms of aqueous thin-liquid films, surface tension, and potentials of air bubbles immersed in electrolyte solutions with nonionic surfactants [53], The proposed model combines specific adsorption of hydroxide ions at the interface with image charge and dispersion forces on ions in the diffuse double layer. These two additional ion interaction free energies are incorporated into the Boltzmann equation, and a simple model for the specific adsorption of the hydroxide ions is used for achieving the description of the ion distribution. Then, by combining this distribution with the Poisson equation for the electrostatic potential, an MPB nonlinear differential equation appears. 

Let the arm XX of the frame in Fig. 7.1(a) move without friction and let the liquid film (shown shaded) be in equilibrium under the external force F. When the arm XX is moved through a distance dx in the direction of F the surface area is increased by 2(XX)dJC, the factor 2 arising because the liquid film has two surfaces (see Fig. 7.1(b)). If the increase in surface area is carried out reversibly and isothermally, the surface free energy of the liquid film is increased by an amount 2(XX)djC7. The applied force F does work on the liquid film equal to F dx. Therefore ... 

In the geological and soil science literature, ion exchange and precipitation are frequently considered as adsorption and thermodynamically described by adsorption equations, or isotherms. This is not correct because, as shown previously, the processes are principally different adsorption is directed by the decrease of surface energy, and it takes place on the free surface sites ion exchange is just a competitive process on an already covered surface, determined by the ionic composition of the liquid phase. Precipitation, including colloid formation, is governed by the composition of the liquid phase, the crystal structure (coprecipitation), or primary chemical forces. 

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