The name is absent

of species 'i', and the singlet densities are replaced by the fraction of non-associated
segments (¾) as prescribed by Chapman [58]. To be precise, X∖ is the fraction of
molecules of species T that are not associated at their site ‘A’. This fraction is given
by the law of mass action [58, 62].

^a '    ₁ , V^m V ∕dr'd^'pj(r^,)Xh(r',ω')g^ref(∣r-Г'|)Г_Ав(|Г—r'∣,ω,cv') ' ^V ’ ^,

^{i +} Tj=I ΔB∈Γj!                ∫dω'

where g^ref is the radial distribution function of the reference hard sphere fluid, and î^b
is the Mayer f-function for the association potential given as f^β = exp(-∕3u^^oc) — 1.
It has to be noted that these equations are written for a potentially inhomogeneous
associating atomic fluid - the densities are position dependent. The expressions for
the free energy of a homogeneous fluid can be obtained by ignoring the dependence of
densities on position. Thus a common basis can be used to develop theories for both
homogeneous and inhomogeneous associating atomic fluids or its extension to chain-
like molecules by imposing the limit of complete association between the different
species in the mixture of associating atomic fluids. The extension in case of homo-
geneous polymeric fluids is popularly known as statistical associating fluid theory
(SAFT) while the inhomogeneous version leads to the new density functional theory
(DFT) called modified Interfacial-SAFT (or iSAFT) developed in this research work.

Few assumptions are made while extending TPTl to the limit of complete as-
sociation∕bonding, when the associating atomic molecules become the segments of
the chain. The chain molecules that are formed are freely-jointed chains where the

26

<<   35   36   37   38   39   40   41   >>

More intriguing information