Jamming of Semiflexible Polymers

We study jamming in model freely rotating polymers as a function of chain length $N$ and bond angle ${\theta }_0$. The volume fraction at jamming ${\varphi }_J({\theta }_0)$ is minimal for rigid-rodlike chains (${\theta }_0=0$), and increases monotonically with increasing ${\theta }_0\le \pi /2$. In contrast to flexible polymers, marginally jammed states of freely rotating polymers are highly hypostatic, even when bond and angle constraints are accounted for. Large-aspect-ratio (small ${\theta }_0$) chains behave comparably to stiff fibers: resistance to large-scale bending plays a major role in their jamming phenomenology. Low-aspect-ratio (large ${\theta }_0$) chains behave more like flexible polymers, but still jam at much lower densities due to the presence of frozen-in three-body correlations corresponding to the fixed bond angles. Long-chain systems jam at lower $\varphi$ and are more hypostatic at jamming than short-chain systems. Implications of these findings for polymer solidification are discussed.

Figure 1

The freely rotating polymer model employed herein, illustrated for ${\theta }_0=23°$ (with $N=3$). Blue lines represent the covalent bonds.

Figure 2

Jamming for freely rotating polymers: $N$ and ${\theta }_0$ dependence. (a) ${\varphi }_J({\theta }_0)$ for chains of length $N=10$ (purple), $N=25$ (green), $N=50$ (red), and $N=100$ (blue). The inset shows the same results plotted versus $C_{\infty }$. The dotted black line is a fit of the $N=50$ data to ${\varphi }_J(C_{\infty })=a-b\ln (C_{\infty })$. (b) $Z_{\mathrm{nc}}[\varphi ={\varphi }_J({\theta }_0)]$ for the same systems.

Figure 3

Interchain and intrachain structure of marginally jammed states. Solid curves show results for $N=50$ FR chains with ${\theta }_0=5°$ (cyan), ${\theta }_0=23°$ (red), ${\theta }_0=45°$ (purple), ${\theta }_0=71°$ (green), and ${\theta }_0=90°$ (blue) at their respective ${\varphi }_J({\theta }_0)$. Dashed black curves show results for fully flexible $N=50$ chains at ${\varphi }_J^{\text{flex}}$. (a) Pair correlation function $g(r)$, (b) its interchain component $g_{\text{inter}}(r)$, and (c) the dihedral angle distribution $P(|\mathrm{\Psi }|)$.

Figure 4

Dynamics of FR-polymer jamming: pressure $P(\varphi )$ (a), average number of noncovalent contacts per monomer $Z_{\mathrm{nc}}(\varphi )$ (b), and flipper fraction $F_{\text{flip}}(\varphi )$ (c), for the same systems considered in Fig. 3. Vertical dashed lines indicate ${\varphi }_J$ for the corresponding systems, while the horizontal dashed lines indicate $P=0.01\epsilon /{\sigma }^3$ (a) and $Z_{\mathrm{nc}}=2$ and 4 (b).