Stretching of a semiflexible chain composed of elastic bonds (original) (raw)
Related papers
Stretching of semiflexible polymers with elastic bonds
European Physical Journal E 14, 17-34 (2004), 2004
A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible polymer in a unified manner. The interplay between bond extension and external force can be described by an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length.We discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear response for weak stretching depends on the relative size of the contour length and the persistence length which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension relations are corroborated by transfer matrix and variational calculations.
The Journal of Chemical Physics, 2012
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: uniform stretching by external forces and non-uniform stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g. fluid in uniform motion, or uniform electric field) by a universal physical framework which leads to general conclusions on different types of polymers. We derive analytical results both for the freely-jointed chain and the worm-like chain models based on classical statistical mechanics. Moreover, we provide a Monte Carlo numerical analysis of the mechanical properties of flexible and semi-flexible polymers anchored at one end. The simulations confirm the analytical achievements, and moreover allow to study the situations where the theory can not provide explicit and useful results. In all cases we evaluate the average conformation of the polymer and its fluctuation statistics as a function of the chain length, bending rigidity and field strength.
Viscoelasticity of stretched polymer chains: Analytical theory and computer-aided simulation
Polymer Science Series A, 2008
The viscoelasticity of stretched polymer chains has been studied by the method of collisional dynamics. To this end, time correlation functions of the fluctuations of the microscopic stress tensor are modeled and relaxation moduli are expressed. Before, for stretched polymer networks, correlation functions used to be calculated in terms of an approximate theory that allowed one to estimate the strain dependences of loss modulus. The calculated dependences are shown to agree qualitatively with the results of measurements performed over a wide interval of strains, including prefracture strains. This theory is verified by comparing the time correlation functions of stress tensor fluctuations for a single stretched chain; these functions are found by computer-aided simulation and calculated on the basis of the existing analytical theory. In this case, a simple theory is adopted according to which a polymer molecule represents a chain composed of N atoms connected by freely jointed elastic bonds. The first and N th atoms of this chain are attached by harmonic springs to immobile points located at a fixed distance. The decay of time correlation functions under study can be resolved into three stages. After a short initial interval provided by local motions, one can observe a region of power-law decay, which is followed by monoexponential decay at long times. The results of computer-aided simulation generally agree with the predictions of analytical theory. Certain discrepancies primarily concern the dependences of the exponent of power-law relaxation on the degree of chain stretching.
Dynamics of stretched polymer chains. 2
Macromolecules, 1985
We study the internal modes of an ideal polymer chain that is being stretched by an external force. The effects of the force on the hydrodynamic interaction are investigated by using a preaveraged Oseen tensor approach, for both Gaussian and freely jointed polymer chains.
Dynamics of a stretched nonlinear polymer chain
The Journal of Chemical Physics, 2008
We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modelled as a string of beads, connected by anharmonic springs, subject to a tensile force applied at the end monomer of the chain while the other end is fixed at the origin of coordinates. The impact of bond non-linearity on the relaxation dynamics of the polymer at different degrees of stretching is treated analytically within the Gaussian self-consistent approach (GSC) and then compared to simulation results derived from two different methods: Monte-Carlo (MC) and Molecular Dynamics (MD).
Stretching dynamics of semiflexible polymers
The European Physical Journal E, 2007
We analyze the nonequilibrium dynamics of single inextensible semiflexible biopolymers as stretching forces are applied at the ends. Based on different (contradicting) heuristic arguments, various scaling laws have been proposed for the propagation speed of the backbone tension which is induced in response to stretching. Here, we employ a newly developed unified theory to systematically substantiate, restrict, and extend these approaches. Introducing the practically relevant scenario of a chain equilibrated under some prestretching force fpre that is suddenly exposed to a different external force fext at the ends, we give a concise physical explanation of the underlying relaxation processes by means of an intuitive blob picture. We discuss the corresponding intermediate asymptotics, derive results for experimentally relevant observables, and support our conclusions by numerical solutions of the coarse-grained equations of motion for the tension.
Extension of chains composed of freely joined elastic segments
Russian Journal of Physical Chemistry B, 2009
A relatively simple formula for the mean distance between the ends of a model chain composed of elastic freely joined segments as a function of an extending force applied to its ends was derived. It was assumed that the stiffness coefficient, which characterizes the ability of the segment to extend and contract, is rather high. In the limit of infinite stiffness the relationship obtained transforms into the Langevin function. The formula predicts the existence of two Hook regions in the force-relative extension dependence. The first of them is characterized by small extensions, whereas the second one, by extensions exceeding the equilibrium contour length. The existence of the latter is confirmed by recent experiments. The magnitude of fluctuations of the relative extension was estimated. The obtained relationships for the relative extension and its scatter are in close agreement with the results of computer simulations performed using collisional molecular dynamics for chains composed of 25, 50, 100, and 200 segments.
A model for the dynamics of extensible semiflexible polymers
Journal of Statistical Mechanics: Theory and Experiment, 2012
We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match the experimental forceextension curve for double-stranded DNA. Near the ground state of the Hamiltonian, the eigenvalues for the longitudinal (stretching) and the transversal (bending) modes of a chain with N springs, indexed by p, scale as λ l p ∼ (p/N) 2 and λ t p ∼ p 2 (p − 1) 2 /N 4 respectively for small p. We also show that the associated decay times τ p ∼ (N/p) 4 will not be observed if they exceed the orientational time scale τ r ∼ N 3 for an equally-long rigid rod, as the driven decay is then washed out by diffusive motion.
Molecular stress and strain in an oriented extended-chain polymer of finite molecular length
Macromolecules, 1995
ABSTRACT: We have developed constitutive and molecular mechanics models to investigate the influence of chain-end defects on the macroscopic tensile properties of extended-chain polymers of finite molecular weight. Molecular mechanics simulations have been performed on the rigid-rod polymer PBZO, poly@-phenylene benzobisoxazole), using the Dreiding I1 force field. The distance between chain ends (i, e., the chain length) can be varied systematically by increasing the size of the simulation unit cell in the chain direction ...
The molecular dynamics of polymer chains with rigid bonds. Local relaxation times
1980
Local movements of small elements (one or a pair of chain units) of the chain composed of parts joined by rigid bonds have been examined by molecular dynamics. "]7he chain was immersed in a solvent of low molecular weight. The interactions between the particles or between them and similar solvent particles are described by the Lennard-Jones potential. Chains possessing various numbers of units were examined at various temperatures and concentrations. The results of numerous experiments have been compared with the analytical results for the elastic Hearst-Harris model. The relaxation of the average eonsine of angles of rotation of the rigid chain elements is ldentmal in practme with that of the equivalent pseudo-elastic elements of the Hearst~-Harris model. Each elastic element in the model is equivalent to one rigid chain unit and the average angle between the elements in the elastxc model is similar to that between rigid chain units. The relaxation of the mean square cosine of angles of rotation is more rapid than in the elastic model. The ratio of t, the average and the mean square cosine of angles of rotation is similar to that for a separate, lagid, anisotropie particle in a viscous solvent. Pronounced anisotropy of the local relaxation properties is shown to exist; the values of the various times which can elapse in dielectrm relaxation and the depolalazation of luminescence have been established.