The shape of a flexible polymer in a cylindrical pore

TL;DR

This paper investigates how the end-to-end distance of a self-avoiding polymer changes within a cylindrical pore, revealing non-monotonic behavior and a minimum at a specific pore size using perturbation theory.

Contribution

It provides a theoretical analysis of polymer conformation in cylindrical confinement, including scaling behavior and crossover phenomena for both hard and soft wall conditions.

Findings

R obeys predicted scaling in large and small D limits

Non-monotonic crossover from 3D to 1D behavior

Minimum R at D ≈ 0.46 R_F

Abstract

We calculate the mean end-to-end distance ($R$) of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius $D$. A self-consistent perturbation theory is used to calculate $R$ as a function of $D$ for impenetrable hard walls and soft walls. In both cases, $R$ obeys the predicted scaling behavior in the limit of large and small $D$. The crossover from the three dimensional behavior ($D\to\infty$) to the fully stretched one dimensional case ($D\to 0$) is non-monotonic. The minimum value of $R$ is found at $D\sim 0.46 R_F$, where $R_F$ is the Flory radius of $R$ at $D \to \infty$. The results for soft walls map onto the hard wall case with a larger cylinder radius.