Marginally compact hyperbranched polymer trees

TL;DR

This paper studies hyperbranched polymer trees that are marginally compact, analyzing their static and dynamic properties through theory and simulations, revealing unique scaling behaviors and the diminishing effect of self-contact density with spacer length.

Contribution

It introduces a model for hyperbranched polymer trees with marginal compactness and explores their static and dynamic properties, including deviations from Rouse behavior.

Findings

Self-contact density diverges logarithmically with mass but becomes negligible with longer spacers.

Relaxation times scale as (N/p)^{5/3} for compact trees, differing from linear chains.

Standard Rouse analysis is inadequate for these compact polymer structures.

Abstract

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution or the shear-stress relaxation modulus, are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass $N$, this effect becomes rapidly irrelevant with increasing spacer length $S$. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time $\tau_p$ of mode $p$ must scale as $\tau_p \sim (N/p)^{5/3}$ rather than the usual square power law for linear chains.