Search results for "Persistence length"
showing 10 items of 54 documents
Breakdown of the Kratky-Porod Wormlike Chain Model for Semiflexible Polymers in Two Dimensions
2011
By large-scale Monte Carlo simulations of semiflexible polymers in $d=2$ dimensions the applicability of the Kratky-Porod model is tested. This model is widely used as "standard model" for describing conformations and force versus extension curves of stiff polymers. It is shown that semiflexible polymers in $d=2$ show a crossover from hard rods to self-avoiding walks, the intermediate Gaussian regime (implied by the Kratky-Porod model) is completely absent. Hence the latter can also describe force versus extension curves only if the contour length is only a few times larger than the persistence length. Consequences for experiments on biopolymers at interfaces are briefly discussed.
Universal monomer dynamics of a two dimensional semi-flexible chain
2013
We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs) of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 \nu / (1+ 2\nu)} where \nu is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive moti…
Effect of Chain Stiffness on the Adsorption Transition of Polymers
2013
Polymers grafted with one chain end to an impenetrable flat hard wall which attracts the monomers with a short-range adsorption potential (of strength e) are studied by large scale Monte Carlo simulations, using the pruned–enriched Rosenbluth method (PERM). Chain lengths up to N = 25600 steps are considered, and the intrinsic flexibility of the chain is varied via an energy penalty for nonzero bond angles, eb. Choosing qb = exp(−eb/kBT) in the range from qb = 1 (fully flexible chains) to qb = 0.005 (rather stiff chains with a persistence length of about lp=52 lattice spacings), the adsorption transition is found to vary from about e/kBTc ≈ 0.286 to e/kBTc ≈ 0.011, confirming the theoretical…
Semiflexible polymers under good solvent conditions interacting with repulsive walls.
2016
Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and Molecular Dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion caused by the monomer-wall repulsion. A coarse-grained bead-spring model with bond bending potential is studied, varying both the contour length and the persistence length of the polymers, as well as the monomer concentration in the solution (good solvent conditions are assumed throughout, and solvent molecules are not included explicitly). The profiles of monomer density and pressure tensor components near the wall are studied, and the surface tension of…
Understanding the Multiple Length Scales Describing the Structure of Bottle-brush Polymers by Monte Carlo Simulation Methods
2011
Bottle-brush polymers contain a long flexible macromolecule as a backbone to which flexible side chains are grafted. Through the choice of the grafting density and the length of the side chains the local stiffness of this cylindrical molecular brush can be controlled, but a quantitative understanding of these phenomena is lacking. Monte Carlo simulation results are presented and discussed which address this issue, extractingmesoscopic length scales (such as the cross-sectional radius, persistence length, and contour length of these objects). Large-scale simulations of the bond fluctuation model are combined with simulations of the simple selfavoiding walk (SAW) model with flexibility contro…
Conformations and orientational ordering of semiflexible polymers in spherical confinement.
2017
Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains a…
Monte Carlo Simulations of Semi-Flexible Polymers
2005
We present Monte Carlo simulations on the phase behavior of semiflexible macromolecules. For a single chain this question is of biophysical interest given the fact that long and stiff DNA chains are typically folded up into very tight compartments. So one can ask the question how the state diagram of a semiflexible chain differs from the coilglobule behavior of a flexible macromolecule. Another effect connected with rigidity of the chains is their tendency to aggregate and form nematically ordered structures. As a consequence one has two competing phase transitions: a gas-liquid and an isotropic-nematic transition potentially giving rise to a complicated phase diagram.
Persistence Length of Cylindrical Brush Molecules Measured by Atomic Force Microscopy
2006
Mechanical properties of single cylindrical polymer brushes with polyisopropylacrylamide (PNIPAM) side chains deposited on mica were probed by atomic force microscopy. Visualization and stretching of individual molecules in aqueous solution clearly reveal the semiflexible nature of the cylindrical macromolecules. Imaging of the brushes on mica and inferring lp from a 〈R2〉 vs L plot results in an average persistence length of lp = 29 ± 3 nm, assuming the chains adopt their equilibrium conformation on the surface. Stretching experiments suggest that an exact determination of the persistence length using force extension curves is impeded by the contribution of the side-chain elasticity. Modeli…
Ejection of a Polymer Chain from a Nanopore: Theory and Computer Experiment
2010
We consider the ejection dynamics of a flexible polymer chain out of confined environment. This situation arises in different physical contexts, including a flexible synthetic polymer partially confined in a nanopore and a viral genome partially ejected from its capsid. We describe the chain release from confinement both analytically and by means of dynamic Monte Carlo simulation. We find two distinct regimes of ejection dynamics depending on whether the chain is fully or partially confined. Partially confined chains are ejected from a pore of length L and diameter D after a typical time τ ∝ L2D5/3, regardless of their contour length N. The process is driven by a constant force f ≈ 5kBT/D a…
Understanding the properties of liquid-crystalline polymers by computational modeling
2020
Abstract A topical review of recent theoretical work on the properties of lyotropic solutions and melts containing semiflexible polymers in thermal equilibrium is given, with a focus on the liquid-crystalline and smectic order of these systems in the bulk and under confinement. Starting with a discussion of single chain properties in terms of the Kratky-Porod worm-like chain model and its limitations, extensions along the lines of Onsager’s theory for the isotropic-nematic transition of solutions of hard rods are briefly reviewed. This discussion is followed by a review of recent Molecular Dynamics simulations and classical Density Functional Theory calculations. It is argued that, even in …