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Statistics of ideal randomly branched polymers in a semi-space

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Abstract.

We investigate the statistical properties of a randomly branched 3-functional N-link polymer chain without excluded volume, whose one point is fixed at the distance d from the impenetrable surface in a 3-dimensional space. Exactly solving the Dyson-type equation for the partition function Z(N, d )= N-θeγN in 3D, we find the “surface” critical exponent θ = \( {\frac{{5}}{{2}}}\), as well as the density profiles of 3-functional units and of dead ends. Our approach enables to compute also the pairwise correlation function of a randomly branched polymer in a 3D semi-space.

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Authors and Affiliations

  1. Physics Department, Moscow State University, 119992, Moscow, Russia

    M. V. Tamm & I. Ya. Erukhimovich

  2. LPTMS, Université Paris Sud, 91405, Orsay Cedex, France

    M. V. Tamm & S. K. Nechaev

  3. Landau Institute for Theoretical Physics, 117334, Moscow, Russia

    S. K. Nechaev

  4. A.N. Nesmeyanov Institute of Organoelement Compounds RAS, Vavilova str. 28, 119991, Moscow, Russia

    I. Ya. Erukhimovich

Authors
  1. M. V. Tamm
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  2. S. K. Nechaev
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  3. I. Ya. Erukhimovich
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Correspondence to M. V. Tamm.

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Tamm, M.V., Nechaev, S.K. & Erukhimovich, I.Y. Statistics of ideal randomly branched polymers in a semi-space. Eur. Phys. J. E 17, 209–219 (2005). https://doi.org/10.1140/epje/i2005-10007-9

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  • DOI: https://doi.org/10.1140/epje/i2005-10007-9

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