Compressive response and helix formation of a semiflexible polymer confined in a nanochannel

Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length $l_p$ is much longer than the channel diameter $D:l_p/D\gg 1$. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression: random deflection along the channel, a helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.

Figure 1

Typical snapshots of a (un)compressed polymer chain in the cylinder of the length $X\left(t\right)=510\sigma$ (a), $414\sigma$ (b), $362.32\sigma$ (c), $238\sigma$ (d), and $190\sigma$ (e). In each case, the three-dimensional configuration (top), and its projection onto the $x-y$ plane (bottom) and the $y-z$ plane (right) are shown. Because the aspect ration of the system is too large, the scale of the $x$ coordinate is different from those of the $y$ and $z$ coordinates.

Figure 2

(a) Kymographic representation of the chain configuration characterized by the sequence of the $y$ coordinate of beads. Horizontal and vertical axes specify the channel length $X$ and the bead index $i$, respectively, The $y$ coordinate is shown in the gray scale. (b) Average bending energy per bending angle as a function of $X$. The dashed line represents the analytic expression for noise-free structure given in Eq. (7).

Figure 3

Kymographic representation of the spatio-temporal configurations of the chain at $X=498\sigma$ (a), $483\sigma$ (b), $475\sigma$ (c), and $467\sigma$ (d). The $y$ coordinate is shown in the gray scale.

Figure 4

(a) The bond correlation function $C_b$ is plotted in the vicinity of $X_c$ for $X=500\sigma (\circ )$, $485\sigma \left(▴\right)$, $477\sigma \left(\blacksquare \right)$, and $469\sigma (•)$ with $l_p=500$. (b) Characteristic decay lengths $x_b(\circ )$ and inverse wave number $1/k_b\left(▴\right)$ of the bond correlation function as a function of $X$. (c) Phase sift $\theta$ in the bond correlation function as a function of $X$. (d) Helical order parameter $\eta$ as a function of $X$: the numerical results (+) and the analytical expression (14) without thermal noise (broken line). The probability distribution $P$ of the projected chain length $L_x$ without compression is overlaid with the common $x$ axis (blue line).