Stretching Homopolymers

TL;DR

This paper combines theory and simulations to analyze how homopolymers stretch under force in different solvents, revealing scaling behaviors, structural transitions, and the conditions needed to observe predicted regimes.

Contribution

It provides new theoretical predictions and simulation results on the force response and structural transitions of homopolymers in good and poor solvents, including the Pincus regime.

Findings

Mean extension scales as f and f^{2/3} in good solvents.

Simulations agree with theory for N=100 and 1600, but Pincus regime not observed at these sizes.

Strongly hydrophobic polymers undergo a first-order transition from globule to rod at a critical force.

Abstract

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {{sufficiently large}} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $<Z>\sim f$ for small $f$, and $<Z>\sim f^{{2/3}}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for $\la Z\ra$ as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {{We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.