Dresden 2014 – scientific programme

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BP: Fachverband Biologische Physik

BP 39: The Collapsed State of Polymers: From Physical Concepts to Applications and Biological Systems (accompanying session, joint CPP/BP/DY)

BP 39.2: Talk

Thursday, April 3, 2014, 15:15–15:30, ZEU 250

Melts of unconcatenated and unknotted polymer rings revisited — •Joachim Wittmer, Hendrik Meyer, and Albert Johner — Institut Charles Sadron & CNRS, 23 Rue du Loess, 67034 Strasbourg CEDEX 2, France

A paradigmatic example for soft matter systems ruled by topological interactions is provided by melts of unconcatenated polymer rings. Recent computational studies suggest that sufficiently long rings become compact which begs the question of whether the irregular surfaces of these compact objects may be characterized by a finite fractal surface dimension d_s < 3. We revisit the scaling analysis of the intramolecular structure factor by Halverson et al. [J. Chem. Phys. 134, 204904 (2011)] claiming d_s ≈ 2.8. Our analysis suggests that this conclusion might be due to an inappropriate application of the Generalized Porod Law. We present then in the second part of our talk a “decorated Gaussian loop model" which does not require a finite fractal surface dimension d_s < 3. In this approach the topological interactions between different rings are taken into account by a self-similar and space-filling random tree of polydisperse Gaussian loops ranging from the entanglement length to a skeleton ring of length N^2/3. Individual rings are predicted to be marginally compact with an average chain size R² ∼ N^2/3 (1− 1/N^1/3) where all prefactors have been omitted for clarity. Sluggish 1/N^1/3-corrections to the leading power-law behavior are also shown to arise for other experimentally relevant properties.