The name is absent

∞. In this complete bonding limit, Xл and Xβ would vanish throughout the system.
Also, X л = Xв (= X) for all the segments of chain T since each site on the segments
reaches its complete bonding limit at the same rate. This leads to the simplification

• 2 I-Xⁱ
m = ——,                 (2.ιi)

and the excess free energy due to formation of the bonds is
д chain ι ^mi

⅛='2∑Σⁱ<Σ (⅛ + ∣n⅛)-l),     (2.12)

i α=l A∈Γ(^a)

where the constant term containing the energy of association and the bonding volume
has been dropped. The second and third sum over all the segments of chain T and
their bonding sites yield 2(гщ - 1). Therefore,

д chain       __ __

= - ∑Xi(m_i - 1) (In A - 1) - ∑x_i(m_i - 1) (ln⅛(⅛)) .     (2.13)

i                                                     i

The first term in this equation accounts for the decrease in the ideal free energy or the
loss in the translation degrees of freedom due to decrease in the number of molecules
(from N_s spheres to N chains), while the second term accounts for the decrease in
the excluded volume as the chains are formed. Substituting eqs. 2.3, 2.6, and 2.13 in

41

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