Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

Abstract

We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

Chromatographic separation of active polymer–like worm mixtures by contour length and activity

“…Last, the conformations sampled by the active worms play an important role in the transport through the pillar array (and for the hydrodynamic properties in general). We hope that our experimental results will stimulate theoretical work and simulations to obtain quantitative models for these conformations and their dynamics, beyond the current models and works already performed on conventional polymers (56,(59)(60)(61)(62).…”

Marginal Distributions at the Tip of a Grafted Stiff Polymer: Analytical and Monte Carlo Investigations

“…[23] If a WLC is subjected to a force, the force-extension relation in the long-chain limit can be derived by numerically solving the Fokker-Planck equation. [24][25][26] The mechanical behavior of short chains has been studied with a focus on the buckling instability problem. [23,27,28] In the case of the pure WLC bending problem, Monte Carlo simulations [20] have shown that the reduced distribution in the transverse direction exhibits a double-peaked structure at intermediate stiffness instead of a Gaussian distribution.…”

“…When an external potential is present, we use a propagator P(r, u; s) to represent the probability of finding a polymer segment of length s with its terminal end located at a specific point in space represented by the vector r and pointing in a particular direction specified by the unit vector u. This function satisfies the Fokker-Planck equation [26,32] 𝜕 𝜕s P(r, u; s) =…”

“…When an external potential is present, we use a propagator P ( r , u ; s ) to represent the probability of finding a polymer segment of length s with its terminal end located at a specific point in space represented by the vector r and pointing in a particular direction specified by the unit vector u . This function satisfies the Fokker–Planck equation [ 26,32 ] $$$$\begin{equation} \frac{\partial }{\partial s} P(\mathbf {r}, \mathbf {u} ; s)={\left[-\mathbf {u} \cdot \nabla _{\mathbf {r}}+\frac{1}{p} \nabla _{\mathbf {u}}{ }^2\right]} P(\mathbf {r}, \mathbf {u} ; s) \end{equation}$$$$Remarkably, this equation establishes an exact mapping between the trajectories of an ABP and a persistent random walker.…”

Stretching a Semiflexible Polymer of Finite Length

“…The forced stretching problem adds to the original free-space model a potential energy term characterized by a prefactor f . For the finite-chain problem, previous theoretical studies featured Monte Carlo computer simulations (mostly based on the discrete version) or analytical solutions to the partition function of the WLC Hamiltonian, for specific parameter regimes. ,,, Figure b shows the parameter space, described by L /2λ and a reduced force. Considering the even simpler problem of a finite WLC without excluded volume, most studies have not provided a comprehensive view of the behavior spanning from the known extension–force relations of rodlike filaments, through to the long polymer results originally presented by Marko and Siggia.…”