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Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface

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Abstract

A Monte Carlo technique is proposed for the simulation of statistical properties of many-arm star polymers on lattices. In this vectorizing algorithm, the length of each arml is increased by one, step by step, from a starting configuration withl=1 orl=2 which is generated directly. This procedure is carried out for a large sample (e.g., 100,000 configurations). As an application, we have studied self-avoiding stars on the square lattice with arm lengths up tol max=125 and up tof=20 arms, both in the bulk and in the geometry where the center of the star is adsorbed on a repulsive surface. The total number of configurations, which behaves asN∼l γG–1μfl, whereμ=2.6386 is the usual effective coordination number for self-avoiding walks on the square lattice, is analyzed, and the resulting exponentsγ G=γ(f) andγ s (f) for the bulk and surface geometries are found to be compatible with predictions of Duplantier and Saleur based on conformai invariance methods. We also obtain distribution functions for the monomer density and the distance of the end of an arm from its center. The results are consistent with a scaling theory developed by us.

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Authors and Affiliations

  1. Institute for Materials Research, Tohoku University, Katahira, Aoba-ku, 980, Sendai, Japan

    Kaoru Ohno

  2. Institut für Physik, Universität Mainz, Staudinger Weg 7, W-6500, Mainz, Germany

    Kaoru Ohno & Kurt Binder

Authors
  1. Kaoru Ohno
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  2. Kurt Binder
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Ohno, K., Binder, K. Monte Carlo simulation of many-arm star polymers in two-dimensional good solvents in the bulk and at a surface. J Stat Phys 64, 781–806 (1991). https://doi.org/10.1007/BF01048315

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  • DOI: https://doi.org/10.1007/BF01048315

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