Phase equilibria, free energy surface

Tie lines are in fact common tangents to the Gibbs free energy surfaces of the phases that coexist in equilibrium. Let s assume that a and p phases, both of which form solid solutions, coexist. The following figure shows two arbitraiy surfaces, a and p ... 

Interfacial Energy of Adhesion. When the polyelectrolyte-grafted nylon surface, in equilibrium with 50% relative humidity, is brought into contact with water or a salt solution, various interactions will occur together they comprise the reversible work of adhesion or free energy of adhesion at the interface of these two phases. This free energy of adhesion should be composed of the following contributions ... 

This study is consistent with the idea that crystal surfaces at temperatures close to melting have some kind of disordered layer or layers, often called liquid-like . Due to the different equilibrium volumes of the liquid and solid phases, this region makes the surface either contract (as in the case of the ice surface) or expand (as it is for Lennard-Jones systems). The positive interfacial excess stress of the ice/water interface therefore makes it similar to liq-uid/vapor interfaces, and the water/vapor interface in particular, for which the excess stress is equal to the interfacial free energy (surface tension). 

Equilibrium, stability, and criticality arc important concepts that are closely related. In this chapter, after the formulation of simple methods for phase-equilibria calculations, the concepts of stability and criticality are introduced, and the application of the Gibbs free energy surface analysis to phase-equilibrium calculations is demonstrated. Then the stability and criticality concepts are presented in detail. These concepts are useful for a broad range of problems in engineering and physics. 

The quantitative application of free energy data requires rigorous definitions of the system. Since the equilibrium constant for the distribution between the bulk and surface phases (i.e., Kd) is not well defined due to the uncertainty in the thickness (i. e., volume) of the adsorption layer, the values of AG are only approximate [186]. 

The most important property of a liquid-gas interface is its surface energy. Surface tension arises at the boundary because of the grossly unequal attractive forces of the liquid subphase for molecules at its surface relative to their attraction by the molecules of the gas phase. These forces tend to pull the surface molecules into the interior of the liquid phase and, as a consequence, cause liquids to minimize their surface area. If equilibrium thermodynamics apply, the surface tension 7 is the partial derivative of the Helmholtz free energy of the system with respect to the area of the interface—when all other conditions are held constant. For a phase surface, the corresponding relation of 7 to Gibbs free energy G and surface area A is shown in eq. [ 1 ]. 

Most discussions, such as those cited above, of monolayer films are presented within the context of equilibrium thermodynamics. The applications of the two-dimensional gas law, ttA = kT, the phase rule, and relations between surface tension and surface pressure to free energy all assume reversibility. Perhaps it seems odd to... 

Retaining the approximations of an incompressible liquid phase, a discontinuous density profile and curvature independent surface tension the conditions are those studied by Rao, Berne and Kalos (2). The essential physics was unchanged from the usual treatment in an open system, except that a minimum in the free energy of formation is found which corresponds to the unique equilibrium phase separated state whose symmetry, in the absence of an external field, is spherical. 

Stripping of chlorine from hydroxides such as Cl2Sn(OH)2 could eventually lead to gas-phase SnO or Sn02. However, at the relatively low temperatures typical of tin oxide CVD ( 873-973 K), we do not expect these oxides to form, based on the equilibrium calculations described above. Thus, the formation of tin hydroxides is not only thermodynamically favored (i.e., based on minimization of the Gibbs free energy), but there are also exothermic reaction pathways that we expect to be kinetically favorable. The primary tin carrier in the CVD process could therefore be a tin hydroxide. Complete conversion to Sn02 would most likely occur via reactions on the surface. 

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