The name is absent

m has one association site labeled ^tB^,. Site ‘A’ on component ^ζi^, can associate only with
site ‘B’ on component ‘i+Г. The chain is formed in the limit of complete association.
To extend the model to branched chains, the segments at which the branches attach
to the backbone will have additional sites to bond with the segments in the branch.
The Helmholtz free energy of such a mixture of associating spheres can be written as

A[{p_a }] = A^id[{ρ_a }] + A^EX’^hs[{p_a}] + A^εx>^ass°^c [U }] ₊ A^EX^[{_Pa}],     (4.3)

where various contributions to the free energy functional are: A^td is the ideal gas
free energy contribution, A^EX,hs due to volume exclusion∕short range hard sphere
repulsion, A^EX,assoc due to association, and A^εx'^att due to long range attraction.

4.2.1 Free energies

The ideal gas functional is defined by

/m

*ι∑∕>Γ(rι)(ln∕⅛'⁹(rι)-l).            (4.4)

α=l

where β = ∖∕kT, к is the Boltzmann’s constant, T is the temperature. Here, the
de Broglie wavelength and other temperature dependent terms that do not affect
the fluid structure have been ignored. A^εx'^hs is calculated from a density functional
theory for a mixture of hard spheres. Rosenfeld’s fundamental measure theory [110]

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