Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: towards the physics of crumpling
Abstract
A Flory theory is constructed for a long polymer ring in a melt of unknotted and non-concatenated rings. The theory assumes that the ring forms an effective annealed branched object and computes its primitive path. It is shown that the primitive path follows self-avoiding statistics and is characterized by the corresponding Flory exponent of a polymer with excluded volume. Based on that, it is shown that rings in the melt are compact objects with overall size proportional to their length raised to the 1/3 power. Furthermore, the contact probability exponent γcontact is estimated, albeit by a poorly controlled approximation, with the result close to 1.1 consistent with both numerical and experimental data.
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Evidence Hub reads this as a theoretical / analytical, done in animal, not in people. Its evidence level is 5 of 5 (Very low · case / narrative / animal / in vitro / in silico). Case reports, narrative reviews, and animal, cell or computer-model studies give the weakest evidence for human health.
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