Longitudinal response of confined semiflexible polymers

The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, for example, in nanofluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tubelike geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-known linear response, the influence of confinement on the nonlinear dynamics can largely be described as that of an effective prestress. We also study the free relaxation of an initially confined chain, finding a surprising superlinear $~t^{9/8}$ growth law for the change in end-to-end distance at short times.

Figure 1

Illustration of the three scenarios investigated in this work. Top (pulling): Both ends of an initially tension-free backbone, which is equilibrated in a channel of constant diameter, are pulled apart by an externally applied force $\mathfrak{f}$. Middle (release): The confined polymer is equilibrated under an externally applied prestretching force $\mathfrak{f}$, which is suddenly released. Bottom (free relaxation from confinement): The contour is equilibrated in confinement and relaxes in free space. In all cases, the sudden change in external conditions propagates along the contour within growing boundary layers of size ${\ell }_{\parallel }(t)$.