Abstract

We review the current state on the thermodynamic behavior and structural phases of self- and mutually-attractive dilute semiflexible polymers that undergo temperature-driven transitions. In extreme dilution, polymers may be considered isolated, and this single polymer undergoes a collapse or folding transition depending on the internal structure. This may go as far as to stable knot phases. Adding polymers results in aggregation, where structural motifs again depend on the internal structure. We discuss in detail the effect of semiflexibility on the collapse and aggregation transition and provide perspectives for interesting future investigations.

Highlights

  • Understanding the basics of polymer chemistry and physics has been a subject of research for many decades

  • We focus on the statistical mechanics of aggregation in dilute homopolymer models

  • We provided a brief overview about the structural transitions and motifs that occur in a statistical mechanics description of dilute semiflexible polymers with self- and mutual attraction in a solvent

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Summary

Introduction

Understanding the basics of polymer chemistry and physics has been a subject of research for many decades. The understanding of microscopic processes and the involved transitions was facilitated by employing computer simulations, which have been drastically improved over the last few decades This approach is based on a (microscopic) statistical mechanics formulation of phase space with a proper Hamiltonian that incorporates all relevant interactions. This step may involve simplifications, such as implicit solvents or coarse-graining, to focus on the key processes of interest. Direct dynamical information is traded with the possibility to define suitable move sets between microstates and the flexibility to devise generalized ensembles that are especially tailored to the problem at hand This greatly improves the accuracy, often by many orders of magnitudes. This approach connects chemical or synthetic polymers, which can be rather flexible, and biopolymers, which are commonly rather stiff

Off-Lattice Polymer Models with Attractive Interaction
Monte Carlo Simulation and Analysis Methods
Generalized-Ensemble Methods
Reweighting from Generalized Ensembles
Canonical and Microcanonical Analysis
Phase Behavior of Isolated Semiflexible Polymers
Structural Phase Diagram
Order of the Collapse Transition Line
Knots as Stable Phase
Aggregation of Dilute Semiflexible Polymers
End-to-End Order Parameter
Structural Motifs Induced by Semiflexibility
Competition between Single-Chain Collapse and Many-Chain Aggregation
Conclusions
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