Conformations of a Long Polymer in a Melt of Shorter Chains: Generalizations of the Flory Theorem

Large-scale simulations of the swelling of a long N-mer in a melt of chemically identical P-mers are used to investigate a discrepancy between theory and experiments. Classical theory predicts an increase of probe chain size R ∼ P^-0.18 with decreasing degree of polymerization P of melt chains in the range of 1 < P < N^1/2. However, both experiment and simulation data are more consistent with an apparently slower swelling R ∼ P^-0.1 over a wider range of melt degrees of polymerization. This anomaly is explained by taking into account the recently discovered long-range bond correlations in polymer melts and corrections to excluded volume. We generalize the Flory theorem and demonstrate that it is in excellent agreement with experiments and simulations.