Similar
to macroscopic ropes and cables, long polymers create knots.
We address the fundamental question whether and under which conditions
it is possible to describe these intriguing objects with crude models
that capture only mesoscale polymer properties. We focus on melts
of long polymers which we describe by a model typical for mesoscopic
simulations. A worm-like chain model defines the polymer architecture.
To describe nonbonded interactions, we deliberately choose a generic
“soft” repulsive potential that leads to strongly overlapping
monomers and coarse local liquid structure. The soft model is parametrized
to accurately reproduce mesoscopic structure and conformations of
reference polymer melts described by a microscopic model. The microscopically
resolved samples retain all generic features affecting polymer topology
and provide, therefore, reliable reference data on knots. We compare
characteristic knotting properties in mesoscopic and microscopically
resolved melts for different cases of chain stiffness. We conclude
that mesoscopic models can reliably describe knots in those melts,
where the length scale characterizing polymer stiffness is substantially
larger than the size of monomer–monomer excluded volume. In
this case, simplified local liquid structure influences knotting properties
only marginally. In contrast, mesoscopic models perform poorly in
melts with flexible chains. We qualitatively explain our findings
through a free energy model of simple knots available in the literature.