Abstract
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.
Highlights
Mesoscopic models of polymers are constructed by substituting a large number of microscopic degrees of freedom by a single effective interaction center
The contribution of mesoscopic models to basic theoretical understanding of polymeric materials has been significant, and representative examples are available in various topical reviews.[3−11] mesoscopic simulations are a key element of algorithms developed for hierarchical modeling of polymeric materials, where equilibrated samples described by soft models are used to recover the microscopic description through efficient fine-graining procedures.[5,12−15]
We find that the ability of mesoscopic models to accurately describe knotting properties is crucially affected by the relationship between two length scales: the size of the excluded volume and the length scale characterizing the stiffness of the polymer chain
Summary
Mesoscopic models of polymers are constructed by substituting a large number of microscopic degrees of freedom by a single effective interaction center Such models are indispensable for studying polymeric materials on scales between a few and up to several hundreds of nanometers, benefiting from efficient sampling of configurational space. Even local excluded volume effects or, more generally, microscopic liquid structure can significantly influence the behavior of polymer knots These observations lead to a basic question: Can mesoscopic models describe knots in polymer melts, given the absence of hard excluded volume and simplified local liquid structure?. We qualitatively explain the trends of knotting behavior in mesoscopic and microscopic simulations benefiting from a free energy model of simple knots available in the literature.[36,58]
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