Free energy functionals simple liquids

In general, use of the ideal gas functional in terms of the molecular density requires computation. Despite the computational intensive nature of the resulting theory, this is probably the most widely used functional for polymers and is described greater detail below. As mentioned earlier, the approximations for the excess free energy functional are similar to those used for simple liquids. The exact expression for the ideal gas functional in this case is... 

A simple and successful approximation for the excess free energy functional is to first assume that the excess free energy functional is only a functional of the average site density profile, denoted p(r), and then invoke standard approximations, similar to those used for simple liquids, for FEX- With a judicious choice of Fkx[Pm], the free energy functional can be exactly decomposed as... 

Over the last two decades the exploration of microscopic processes at interfaces has advanced at a rapid pace. With the active use of computer simulations and density functional theory the theory of liquid/vapor, liquid/liquid and vacuum/crystal interfaces has progressed from a simple phenomenological treatment to sophisticated ah initio calculations of their electronic, structural and dynamic properties [1], However, for the case of liquid/crystal interfaces progress has been achieved only in understanding the simplest density profiles, while the mechanism of formation of solid/liquid interfaces, emergence of interfacial excess stress and the anisotropy of interfacial free energy are not yet completely established [2],... 

Silica exists in a broad variety of forms, in spite of its simple chemical formula. This diversity is particularly true for divided silicas, each form of which is characterized by a particular structure (crystalline or amorphous) and specific physicochemical surface properties. The variety results in a broad set of applications, such as chromatography, dehydration, polymer reinforcement, gelification of liquids, thermal isolation, liquid-crystal posting, fluidification of powders, and catalysts. The properties of these materials can of course be expected to be related to their surface chemistry and hence to their surface free energy and energetic homogeneity as well. This chapter examines the evolution of these different characteristics as a function not only of the nature of the silica (i.e., amorphous or crystalline), but also as a function of its mode of synthesis their evolution upon modification of the surface chemistry of the solids by chemical or heat treatment is also followed. 

---