Semiflexible Polymers Interacting With Planar Surfaces: Weak versus Strong Adsorption.

Andrey Milchev,Kurt Binder

doi:10.3390/polym12020255

Abstract

Semiflexible polymers bound to planar substrates by a short-range surface potential are studied by Molecular Dynamics simulations to clarify the extent to which these chain molecules can be considered as strictly two-dimensional. Applying a coarse-grained bead-spring model, the chain length N and stiffness as well as the strength of the adsorption potential are varied over a wide range. The excluded-volume (EV) interactions inherent in this model can also be “switched off” to provide a discretized version of the Kratky–Porod wormlike chain model. We study both local order parameters (fraction f of monomers within the range of the potential, bond-orientational order parameter ) and the mean square gyration radius parallel, , and perpendicular, , to the wall. While for strongly adsorbed chains EV has negligible effect on f and , we find that is strongly affected when the chain contour length exceeds the persistence length. Monomer coordinates in perpendicular (⊥) direction are correlated over the scale of the deflection length which is estimated. It is found that , and converge to their asymptotic values with corrections. For both weakly and strongly adsorbed chains, the distribution functions of “loops”, “trains”, and “tails” are analyzed. Some consequences pertaining to the analysis of experiments on adsorbed semiflexible polymers are pointed out.

Highlights

Many macromolecules with linear chemical architecture are neither perfectly flexible nor entirely rigid-rod-like chain molecules, but exhibit instead only local stiffness and are called semiflexible.Within a coarse-grained description, such a polymer chain is modeled as a curve in continuous space~r (s), with s a coordinate along the backbone of the macromolecule
While our previous work focused on estimating the critical strength ewall the potential of the adsorbing wall where adsorption occurs, and the crossover of the decay length ef fp fromp to 2` p upon chain adsorption, we focus on the properties of the adsorbed polymers cr cr − 1)
When the polymer chain is in the non-adsorbed mushroom state, all components h R2gγ i with γ = x, y, z are of the same order whereas in the adsorbed state h R2gz i should converge to a finite value as N → ∞

Summary

Introduction

Many macromolecules with linear chemical architecture are neither perfectly flexible nor entirely rigid-rod-like chain molecules, but exhibit instead only local stiffness and are called semiflexible. The stiffness is due to a nonzero bending modulus κ, which is proportional to the persistence lengthp , describing the length along the contour over which the orientations of subsequent bonds (or tangent vectors along ~r (s), respectively) are correlated [1,2,3] This Kratky–Porod model [3] (-called Wormlike Chain (WLC) model) is widely accepted as a proper phenomenological description of semiflexible polymers, in particular, of biopolymers such as the double-stranded (ds) DNA [4], filamentous (F)-actin [5], etc. The fraction of monomers f within the potential range ∆ is, predicted [15] to be close to unity already when τ exceeds τ ∗ ∝ (∆/` p )4/3 τ ∗∗ These predictions imply that an adsorbed semiflexible polymer is not identical to a strictly two-dimensional chain confined in a plane parallel to the adsorbing surface.

Simulated Model

Distributions of Trains and Loops

Conclusions