Statistical Mechanics of Semiflexible Bundles of Wormlike Polymer Chains

We demonstrate that a semiflexible bundle of wormlike chains exhibits a state-dependent bending stiffness that alters fundamentally its scaling behavior with respect to the standard wormlike chain. We explore the equilibrium conformational and mechanical behavior of wormlike bundles in isolation, in cross-linked networks, and in solution.

Figure 1

Illustration of the geometry of a single bundle layer (the full bundle consists of $2M$ layers that are stacked in parallel). The bundle is deflected through the angle $\theta =r_{\perp }^{\prime }$. If filament $i$ stretches the amount $u_i=u_{i+1}+b\theta$, the cross-link (dashed line) remains undeformed with zero shear energy.

Figure 2

End-to-end distance $R(F)/L$ as a function of stretching force $F{L}^2/{\kappa }_f$ for a bundle of $N=4$ filaments and $L=l_p$. The black curves correspond to $\lambda /L=0.01,0.1,\dots ,0.7$. The thick (red) curves relate to (bottom) decoupled and (top) fully coupled bending, respectively. The dashed lines correspond to the respective linear response regimes.

Figure 3

Tube diameter $d^2/(l_c^3/N{l}_p)$ as a function of contour length $L/l_c$ for various $\lambda /l_c$ and $M=20$. Thick (red) curves correspond to (top) decoupled and (bottom) fully coupled bending, respectively. For short filaments, the intermediate regime is visible through the linear slope $d^2\sim L$ [see Eq. (10)]. For long filaments, the fluctuations saturate. By increasing $\lambda$, the tube is becoming wider [Eq. (11)].