# Unexpected behaviour in numerical simulation of polymer

I noticed some strange behaviour when simulating the behaviour of a polymer subjected to an external pulling force at both ends, and would like to better understand its origin.

I used LAMMPS to simulate a 101-atom polymer, with spring potential energy given by

$V_{bond} = \frac{3 k_B T}{2} \sum\limits_{i=1}^N d_i^2$

where $d_i$ is the distance between atom #i and atom #i+1, undergoing Langevin time integration.

I meant to apply equal and opposing external forces (through a range of magnitudes) to the atoms at the two ends. Plotting the mean square extension $<r^2>$ of the polymer as a function of the tension should then give something like:

But what I got, at first, was:

I later discovered the nature of my error - I made an error in my LAMMPS script, and was accidentally applying the opposing forces to atom #1 and atom #3, rather than atom #1 and atom #101. I fixed this and obtained the expected result. The data collection to find $<r^2>$ was consistently performed correctly: on atoms #1 and #101.

I kept wondering about my initial wrong answer, however. The much smaller range of $<r^2>$ values was easy to explain since the tension was applied only to a small segment and the bulk of the polymer would not be directly affected. But what I can't wrap my head around is the origin of that peculiar little 'dip' around $F = 1.4$.

My question is: how is it, qualitatively, that applying tension to a subsection of a polymer can actually decrease the mean squared extension of the total polymer?

• Very strange. I think that the reason must be somehow that for $F\approx 1.4$ you are locally increasing the rigidity without actually stretching the polymer so much. – valerio Jan 22 '18 at 19:55
• Might 1.4 actually be $\sqrt{2}$? – probably_someone Jan 22 '18 at 20:01
• Could be. I can redo the fit with a more closely spaced search space for that parameter. – Drubbels Jan 22 '18 at 21:19