vent molecules are parameterized with a Flory cχ, parameter. The solution is assumed
to be locally incompressible.
In the canonical ensemble, the solution consists of a mixture of ng solvent molecules
and np polymer molecules in a system of fixed volume V and temperature T. Each
polymer chain occupies a volume ι⅛N, where ⅝ is the volume of a statistical seg-
ment and its conformational properties are described by the continuous Gaussian
chain model. The solvent molecules also occupy the same volume, t⅛. Thus the total
number density of the solution, p0 = 1∕∙vq. While, the microscopic densities of the
polymer segments and solvent are defined, respectively, by
Pp(γ) = ∑ / ds δ(r ~ (8∙25)
j=ι Jo
ns
⅞(r) = ∑<*(r~rj)∙ (8∙26)
J=I
By analogy with the Flory-Huggins lattice theory, the interaction energy between the
solvent molecules and the polymer segments is described by
∕3t∕ι[rns+n^] = Vθχps [ ⅛(r)⅛(r) (8.27)
This Flory parameter χps describes the energetic strength of local contacts between
solvent molecules and polymer segments, relative to solvent-solvent and polymer-
216
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