Statistics of randomly branched polymers in a semi-space

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 $Z(N,d)=N^{-\theta }{e}^{\gamma N}$ 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.

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

References in corpus (2)

• Theory of Sol-Gel Transition in Thermoreversible Gels with due Regard for Fundamental Role of Mesoscopic Cyclization Effects. I. Thermodynamic and Structural Characteristics of Gel Phase
• Dimensional Reduction and Crossover to Mean-Field Behavior for Branched Polymers

Cited by in corpus (1)

• The confinement free energies of non-ideal branched polymers and ideal unbranched polymers are the same