Self-Similar Polymer Ring Conformations Based on Elementary Loops: A Direct Observation by SANS

We report small angle neutron scattering (SANS) results on very large polyethylene-oxide (PEO) rings in the melt. Major findings are (i) the observation of a cross over in the SANS pattern from a strong Q-dependence at intermediate Q to a Q^–2 dependence at higher Q that is independent of the ring size. Summing up scattering amplitudes in a minimal model that contains the ring closure and a cross over from Gaussian statistics at short distances to more compact structures at larger distances, we identify the cross over to occur at a distance along the ring of N_e,0 = 45 ± 2.5. We consider this finding as a clear signature of the theoretically predicted elementary loops that build up the ring conformation. Their size is in the range of an entanglement strand for linear PEO melts and they are characterized by Gaussian statistics. (ii) The chain length dependence of the radius of gyration R_g follows rather closely the prediction of Obukhov’s decorated ring model. (iii) Other than extracted from numerous simulations that are interpreted in terms of a cross over to mass fractal behavior around N ≅ 10N_e,0 with a fractal dimension d_f = 3 and exponent ν = 1/3, we do not observe such a cross over, but R_g(N) ∼ N^ν=0.39 holds over the entire size range.