We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls. The non-adsorption case of adsorption interaction energy ε = 0 and the weak adsorption case of ε= -1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D. Several special entropy effects on the confined compact polymer chains, such as a damped oscillation in the segment density profile for the large separation distance D, are observed and discussed for different separation distances D in the non-adsorption case. In the weak adsorption case, investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer. Moreover, the scaling laws of the damped oscillation period Td and the depletion layer width Ld are obtained for the confined compact chains. Most of these results are obtained for the first time so far as we know, which are expected to understand the properties of the confined compact polymer chains more completely.
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.
