associating segments enumerated as 1, 2, ..., m, bj∙l, bj∙2, ..., bj∙mj∙, b⅛l, b⅛2, ..., bfe∏⅛.
These associating segments have hard cores and highly directional associating sites.
In the limit of complete association, these association sites bond to form chains. To
obtain our branched chain model, an associating segment can only associate with
its neighboring segments in the chain, as shown in fig. 7. lb. The Helmholtz free
energy functional of such a mixture of associating segments can be written using a
perturbation expansion as
A[{pα}] = Aid [U }] + Λ≡λs[{∕U] + Aεx'cham [U }] + Aεx∙att [{pα }], (7.3)
where Azd is the ideal gas free energy contribution, and rest are the excess con-
tributions: Aεx,hs due to volume exclusion∕repuslive interactions, Aεx'cham due to
association between the segments to form chains, and Aεx'att due to long range at-
tractions.
The free energies and their functional derivatives were derived in detail in chapter
4. In brevity, the functional derivatives of the free energies or the different contribu-
tions to inhomogeneous chemical potentials of the segment iot' are given by
⅜⅛⅜}∣ _ ln „ m
(7.4)
C /'∙.∙'∖ ɪɪɪpɑ(ɪjl
<)Pα(r)
wEXΛs[{pq}] ɪ r 5φ[{n√n)}]
δpa(r) J rι δpa(τ)
186