Isotropic liquid interface, surface tension

The surface tension /of an isotropic liquid interface can be thought of as a free energy per unit area of surface (/= dWIdA), or as a force per unit length (Y=dF/dx). It results from an imbalance in intermolecular forces at the surface (liquid-vapor interaction). Since there are fewer molecules at the vapor side than on the liquid side near the surface, molecules at the surface feel a net attractive force (see Figure 2.1a), which leads to the surface tension. The concept of surface tension is simply illustrated considering a liquid film, stretched on a wire frame as shown in Figure 2.1b. The work, TV needed to increase an area by dA is equal the force multiplied by dx, where dA = l dx (1 is the width of the frame). Accordingly,... 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

An interesting phenomenon in water-oil-amphiphile systems is the presence of self-assembled arrays of amphiphiles (surfactants) called micelles. From 1948 to 1950, Philip Alan Winsor reported that upon simple mixing (i.e., without the need for high shear conditions), oil, water, and amphiphiles yielded clear, macro-scopically homogeneous single phases which he termed type IV systems (Winsor, 1948, 1950). The term microemulsion was introduced later by Jack H. Shulman, a Columbia University chemistry professor, to denote these thermodynamically stable optically isotropic, transparent oil-water-amphiphile dispersions (Shulman et al., 1959). Type IV systems contain small droplets of one liquid dispersed within the other, with a self-assembled layer of surfactant molecules (micelles) along the interface between the two phases. The spontaneous self-assembly of the micelle is driven by the thermodynamic tendency to minimize the surface tension between the water and the oil in the presence of the amphiphile (Hoar and Shulman, 1943). 

Defects, particularly screw dislocations, play an important role in the growth of true crystals [9]. Liquid crystal germs present the defects that were described in detail by Frie-del and Grandjean [21] for smectic A phases. The germs elongate perpendicular to the mean direction of the layers, the surface tension being anisotropic, and the focal domains present in the batonnet are arranged such that the layers lie normal to the isotropic interface. A focal line is often present... 

To reduce the free energy contributed by the surface tension term, the molecules at the liquid crystal/vapor interface favor a layer structure. In the smectic phase, the outermost layers favor a better molecular packing than exists in the interior. The enhanced surface order has been reported for various liquid crystal phases, for example the surface SmA order on the bulk isotropic or nematic sample [50] the surface SmI order on a SmA film [47] the surface SmB gx order on a SmA film [45,48] the surface SmI on a SmC film [17,93] the surface B on a SmA film [49] the surface crystal E order on a SmBhex film [100]. Realizing the importance of the surface tension in characterizing the liquid crystal free-standing films, we... 

FIGURE 3.2 Surface tension results from anisotropic cohesive forces at a fluid interface. In this diagram, two molecules in a liquid are highlighted, and the cohesive forces are indicated by the arrows. The molecule in the bulk is subject to an average net force of zero due to isotropic cohesive forces from the surrounding molecules, whereas a molecule at the surface is subject to a net force into the liquid. 

From a mechanical standpoint, the interface between a pure liquid and its own equilibrium vapour (or air, as adsorption is to be neglected here) behaves as a membrane of infinitesimal thickness stretched uniformly and isotropically by a force exerted tangential to it. Rapid relaxation towards equilibrium is the hallmark of liquid surfaces when the viscosity of the liquid is not too high, the freshly formed area has enough time to relax completely and the equilibrium interfacial tension will attain the same value in all surface parts. It is important to realise that, owing... 

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