Statistics of randomly branched polymers in a semi-space

Details Statistics of randomly branched polymers in a semi-space Statistics of randomly branched polymers in a semi-space

2004-08-26

arxiv.org/abs/cond-mat/0408575v2

Physics

Condensed Matter

Statistical Mechanics

15 pages 7 figsures; section VII is slightly reorganized, discussion is revised

Scientific paper

10.1140/epje/i2005-10007-9

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 $Z(N,d)=N^{-\theta} e^{\gamma N}$ in 3D, we find the "surface" critical exponent $\theta={5/2}$, 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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