The name is absent

associating segments enumerated as 1, 2, ..., m, b_j∙l, b_j∙2, ..., b_j∙m_j∙, 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[{p_α}] = A^id [U }] ₊ Λ≡^λs[{∕U] + A^εx'^cham [U }] + A^εx∙^att [{p_α }],    (7.3)
where A^zd is the ideal gas free energy contribution, and rest are the excess con-
tributions: A^εx,hs due to volume exclusion∕repuslive interactions, A^εx'^cham due to
association between the segments to form chains, and A^εx'^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

C /'∙.∙'∖ ɪɪɪpɑ(ɪjl

<)Pα(r)

_wEXΛs[{_pq}] ɪ r 5φ[{_n√n)}]
δp_a(r) J ^rι δp_a(τ)

186

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