Statistics of randomly branched polymers in a semi-space

TL;DR

This paper analyzes the statistical properties of a specific model of randomly branched polymers near a surface, providing exact solutions for partition functions, density profiles, and correlation functions in three-dimensional semi-space.

Contribution

It presents an exact analytical solution for the partition function and related properties of a 3-functional branched polymer near a surface, including critical exponents and density profiles.

Findings

Surface critical exponent θ=5/2

Density profiles of units and dead ends computed

Pairwise correlation function derived

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.