where drM = drι<7r2 ■ ■ ■ Лгм represents a set of differential volume, ⅛(γm) is the
bonding potential which represents the chain connectivity.
ехр[-Ж(гм)] = ∏ *itlri+1, ⅛ σ'∖ (3.16)
ɪɪ 47Γ(Tι
i=l ɪ
where M is the number of segments in the chain. On the contrary, the excess free
energy was derived as a functional of the segment densities. It is decomposed as
PAEX[pM\ = у dr (Φ⅛√r)}] + Φc'ιαi"[K(r)}]) , (3.17)
where Φλ's[{πq(γ)}] and Φchαm[{nct(r)}] are the reduced free energy densities due to
hard sphere repulsion and chain connectivity, respectively, and {nα(r)} is the set of
the weighted densities. Both {nα(r)} and Φhs[{nct(r)}] are computed from FMT. The
chain connectivity term is based on SAFT for a bulk fluid. For a bulk fluid it is given
by,
φcftoi"ιb = lzJHpιfcιnyW(σι) (3.18)
where p1b is the bulk segment density and y∏,6(σ1) is the contact value of the cavity
correlation function between segments in the bulk. To extend eq. 3.18 to inhomo-
geneous systems using FMT (following the same methodology as used by Segura et.
al. [62]), pib is replaced by n0ιζι and ‰,b(σχ) is replaced by,
yιι(σι,na) =
ɪ ⅞σιζ ⅞σιC
l-n3 4(l-n3)2 72(1 -n3)3’
(3.19)
72