Gel-like modes. of polymer solutions in « θ » solvents

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Abstract
A polymer solution forms a transient network of lifetime Tr. In good solvents, the mesh size l is identical to the correlation length ξ for the fluctuations of the monomer concentration c. But in « θ » solvents (where the pair interaction vanishes), / is much smaller than ξ. The dynamics involve then two quantitatively very different elastic moduli E : :1) at low frequencies, E = E0 = kT/ξ3 N c3 is small; 2) at higher frequencies, E = E gel kTc2 and Egel > E0. This leads to two modes in photon-beat experiments at wave vectors q larger than a certain value qg, the high frequency mode being the gel mode. Although this gives only a small fraction of the total scattered light, it still dominates the slope of the dynamical structure factor S(q, t) at small times. We investigate the corresponding diffusion coefficient D g in the three regimes : a) « many chain » regime (qg < q < 1/ξ), Dg ≃ kT/6 πη s a is very high (a is a monomer size and ηs the solvent viscosity) ; b) entangled « single chain » regime (ξ-1 < q < l-1 ), Dg(q) ∼ 1/q; c) disentangled « single chain » regime (ql > 1), Dg ∼q. The regimes b) and c) could be observed only in neutron experiments. But the cross-over from a) to b) could explain certain photon-beat results on PS in cyclohexane