Chain dimension of a guest polymer in the semidilute solution of compatible and incompatible polymers

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Abstract
A small number of « guest » polymeric chains (index of polymerization N) are dissolved in a semidilute solution of a host polymer (index P, concentration Φ) which is itself in a good solvent; the radius of gyration Rg and the second virial coefficient A2 are studied on the basis of the thermal- and concentration-blob models. The renormalized excluded — volume parameter τ has the form τ(ΦP3ν-1, χ) where ν is the index for the N — dependence of Rg in a good solvent ( Rg ∼ Nν) and χ the interaction parameter between the guest and host polymers. Analytical expressions of Rg and A2 are given as functions of N, P, Φ and χ, which have the following scaled forms for Φ > Φ* ≡ P1-3ν (overlap concentration) : Rg ∝ NνfR { ΦN3ν-1, τ(NΦ1/(3ν-1)) 1/2}; A2 ∝ N3ν-2 f A{ΦN3ν-1, τ(NΦ1/(3ν-1) )1/2}. According to these scaled forms, several regions are defined, and the characteristic behaviour of each region is discussed. A concentration-dependent collapse of a N-chain in small P-chains (N >> P) has been found around Φ = Φ*