The name is absent

4.2.2 Functional derivatives of free energies

In order to solve eqn. 4.2 for the density profile, the functional derivative of the
free energy is required. The functional derivative of the free energy can be inter-
preted as the inhomogeneous chemical potential. The different contributions to the
inhomogeneous chemical potential of a segment a are given by

^{0(ЗАЕХЛЗ} =                                     (4 14)

δpa⁹(r) J ^OT1 δp^s_a^e9(r) ’                             ^J

XβΛEX,att        Г

L-M = Σ /      ⅛∕⅛'(∣r-rιiK'(n),      (4.15)

ðpɑ W ~_γ √∣r-r₁∣>_σα7

г         _x._w q ™ ,           г χj(_r,)i _sι_nrj(_rι)

s_pr∙(r) - ∑ ^ln^^w - — ⁺ 2 ⁺∑J ^(ri) ∑ ¹ ^ —--

^{H k ,}       4∈Γ(<≈) ^{L                             j} 7=1 ^J            A∈Γ(t^,) ^{L               j} ' ^{V 7}

-                                      (4.16)

where is the set of associating sites on segment a. In eqn. 4.16, the fraction
of segments that are not bonded at an associating site (ʃɪ(r)) and the functional
derivatives            ^arc required. Michelsen and Hendriks [117] showed by alge-

braic manipulation that for homogeneous systems the association chemical potential
could be written in a form that does not involve the derivatives of fractions of non-
bonded segments. A similar simplification is obtained for inhomogeneous systems
by manipulating eqs. 4.9 and 4.16. The inhomogeneous chemical potential due to

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