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Polymers with self-avoiding interaction in random media: a localization-delocalization transition

Yadin Y. Goldschmidt·Yohannes Shiferaw
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Abstract

In this paper we investigate the problem of a long self-avoiding polymer chain immersed in a random medium. We find that in the limit of a very long chain and when the self-avoiding interaction is weak, the conformation of the chain consists of many ``blobs'' with connecting segments. The blobs are sections of the molecule curled up in regions of low potential in the case of a Gaussian distributed random potential or in regions of relatively low density of obstacles in the case of randomly distributed hard obstacles. We find that as the strength of the self-avoiding interaction is increased the chain undergoes a delocalization transition in the sense that the appropriate free energy per monomer is no longer negative. The chain is then no longer bound to a particular location in the medium but can easily wander around under the influence of a small perturbation. For a localized chain we estimate quantitatively the expected number of monomers in the ``blobs'' and in the connecting segments.

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Yadin Y. Goldschmidt, Yohannes Shiferaw. 2002-07-21. Polymers with self-avoiding interaction in random media: a localization-delocalization transition. https://doi.org/10.1140/epjb%2Fe2003-00077-7

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