Marginally compact hyperbranched polymer trees

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.

arXiv comment14 pages, 11 figures

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• Marginally compact fractal trees with semiflexibility
• Fractional Brownian motion meets topology: statistical and topological properties of globular macromolecules with volume interactions
• Effective Hamiltonian of topologically stabilized polymer states