The name is absent

4.3.1 Ideal chains

In terms of multipoint molecular density (p_M(R)), the exact equilibrium density

profile of a random flight ideal chain in an external field is given by [111]

m— 1                   m

_pm(R) = exp(⅛M - β £ ⅛‰¹ (∣r_i+, - r,∣) -     V≈^,(r,)).       (4.35)

z=l                          i~l

The density profile of segment j is given by

p_j∙(r) = ʃ dR<5(r - γ_j∙)p_m(R),                     (4.36)

or

p_j(r_j) = exp(/^_M) .. dr₁..dr_j^₁dr_j+l..dr_mexp[-β'^2 ½^ea‰)] exp[-/?Cnd(l^ri+ι~^ri∣)]∙

JJ                       i=l             i=ι

(4.37)

One of the strengths of modified iSAFT is that it automatically accounts for
the direct bond connectivity between the segments in the chain, a constraint that is
normally forced through the ideal chain functional in the existing theories. Instead
we can readily write down the free energy functional for an ideal chain from modified
iSAFT in terms of segment densities. From this functional, the density profile of a

96

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