Knot Theory Perspective to the Globular States of Linear Polymers

Investigations into the globular states of linear polymers have traditionally utilized the density fluctuation model, distinguishing core-interface regions. However, under poor solvent conditions and near θ-temperature, computational results revealed a plateau region in the scaling of chain dimensions, with a Flory scaling exponent far below 1/3. Under these conditions, the density-based approach does not delineate the boundaries between distinct globular states due to the self-knotting phenomenon of chain, transcending the capabilities of mean-field methods as indicated by the Ginzburg criterion. By incorporating Molecular Dynamics simulations with knot analysis and comparing the results of linear chains to ring polymers (which lack chain ends and cannot form knots), we discovered that knot theory analysis can quantitatively distinguish between globular states. This offers a complementary perspective to traditional mean-field theories.

This work was supported by NSF DMR 2114640