A Variational Approach to Trap Macromolecules

TL;DR

This paper introduces a variational method to trap and analyze macromolecules, effectively capturing their conformations, transitions, and interactions across different conditions with quantitative agreement to experiments.

Contribution

A novel variational approach that self-consistently models macromolecule trapping, enabling detailed analysis of conformations and transitions in polymer physics.

Findings

Successfully models single-chain conformations across solvent regimes.

Captures globule-pearl necklace-coil transition behavior.

Quantitative agreement with experimental data on polymer interactions.

Abstract

Trapping macromolecules is impoartant for the study of their conformations, interactions, dynamics and kinetic processes. Here, we develop a variational approach which self-consistently introduces a mean force that controls the center-of-mass position and a self-adjustable harmonic potential that counters the center-of-mass fluctuation. The effectiveness and versatility of our approach is verified in three classical yet not fully understood problems in polymer physics: (1) single-chain conformation in the entire solvent regimes, (2) globule-pearl necklace-coil transition of a polyelectrolyte and (3) inter-chain interaction by simultaneously trapping two polymers. The scaling relationships and $\theta$ behaviors are well captured. Conformations with large shape anisotropy appearing in charged polymers are clearly depicted. Our theoretical predictions are in quantitative agreement with experimental results reported in the literature.