A steered molecular dynamics study on the elastic behaviour of knotted polymer chains

In this paper the influence of a knot on the structure of a polymethylene （PM） strand in the tensile process is investigated by using the steered molecular dynamics （SMD） method. The gradual increasing of end-to-end distance, R, results in a tighter knot and a more stretched contour. That the break in a knotted rope almost invariably occurs at a point just outside the ＇entrance＇ to the knot, which has been shown in a good many experiments, is further theoretically verified in this paper through the calculation of some structural and thermodynamic parameters. Moreover, it is found that the analyses on bond length, torsion angle and strain energy can facilitate to the study of the localization and the size of a knot in the tensile process. The symmetries of torsion angles, bond lengths and bond angles in the knot result in the whole symmetry of the knot in microstructure, thereby adapting itself to the strain applied. Additionally, the statistical property of the force-dependent average knot size illuminates in detail the change in size of a knot with force f, and therefore the minimum size of the knot in the restriction of the potentials considered in this work for a PM chain is deduced. At the same time, the difference in response to uniaxial strain, between a knotted PM strand and an unknotted one is also investigated. The force-extension profile is easily obtained from the simulation. As expected, for a given f, the knotted chain has an R significantly smaller than that of an unknotted polymer. However, the scaled difference becomes less pronounced for larger values of N, and the results for longer chains approach those of the unknotted chains.

A STEERED MOLECULAR DYNAMICS SIMULATION ON THE ELASTIC BEHAVIOR OF ADSORBED STAR POLYMER CHAINS

Elastic behavior of 4-branched star polymer chain with different chain length N adsorbed on attractive surface is investigated using steered molecular dynamics （SMD） simulation method based on the united-atom （UA） model for branched alkanes. The simulation is realized by pulling up the chain via a linear spring with a constant velocity v = 0.005 nm/ps. At the beginning, the chain lies extensionally on adsorbed surface and suffers continuous deformations during the tensile process. Statistical parameters as mean-square radii of gyration 〈S2〉xy, 〈S2〉z, shape factor 〈δ〉, describing the conformational changes, sectional density 〈den〉 which gives the states of the chain, and average surface attractive energy 〈Ua〉, average total energy 〈U〉, average force 〈f〉 probed by the spring, which characterize the thermodynamic properties, are calculated in the stimulant process. Remarkably, distinguishing from the case in linear chains that there only exists one long plateau in the curve of 〈f 〉, the force plateau in our study for star chains is multiple, denoting different steps of desorption, and this agrees well with the experimental results in essence. We find during the tensile process, there are three characteristic distances Zc, Zt and Z0 from the attractive surface, and these values vary with N. When Z = Zc, the chain is stripped from the surface, but due to the form of wall-monomer interaction, the surface retains weak influence on the chain till Z = Zc. From Z = Zt, parameters 〈Ua〉, 〈U〉 and 〈f〉 respectively reach a stable value, while the shape and the size of the chain still need adjustments after Zt till Zo to reach their equilibrium states. Specifically, for short chain of N = 41, Zt and Z0 are incorporated. These results may help us to deepen the knowledge about the elastic behavior of adsorbed star polymer chains.