The phase behaviour of a single polyethylene chain is studied by using molecular dynamics simulations. A free chain and a chain with fixing one end are considered here, since the atomic force microscope (AFM) tip can play a significant role in polymer crystallization in experiment. For a free chain, it is confirmed in our calculation that the polymer chain exhibits an extended coil state at high temperatures, collapses into a condensed state at low temperatures, i.e. the coil-to-globule transition that is determined by a high temperature shoulder of the heat capacity curve, and an additional liquid-to-solid transition that is described by a low temperature peak of the same heat curve. These results accord with previous studies of square-well chains and Lennard-Jones homopolymers. However, when one of the end monomers of the same chain is fixed the results become very different, and the chain cannot reach an extended coil-like state as a free chain does at high temperatures, i.e. there exists no coil-to-globule-like transition. These results may provide some insights into the influence of AFM tip when it is used to study the phase behaviour of polymer chains. If the interaction force between AFM tip and polymer monomers is strong, some monomers or one of them can be seen as being fixed by the tip, which is similar to our simulation model, and it is also found that AFM tip could induce polymer crystallization.
The composition and residue-residue interactions of knotted proteins, compared with those of other proteins, can provide considerable insight into the driver of the knots in proteins. In this paper, we calculate the probabilities of 20 amino acids in 273 knotted entries from the Protein Data Bank (PDB). The collection of 273 entries contains all knotted structures in the PDB, and it is not a subset. With an appropriate value of Rc, the numbers of all residue-residue contacts are counted in all 273 knotted structures. To make an accurate comparison, we count up to 9000 other entries from the PDB as well, and these entries spread over all sorts. In knotted structures, Leu occupies a maximal proportion of 9.62% among all 20 amino acids, and Leu, Phe, Trp, Gly, His, Gln, Asp, Lys and Pro may all play a more important role. Also, we analyse the effects of amino acid residues on the long-range contacts. We observe a larger average number of long-range contacts in the knotted structures than that in other ones, implying their important role in achieving the knots. Accordingly, the average number of short-range contacts becomes small when the structure becomes knotted because it depends mainly on the short-haul sequence of amino acids to form the short-range contact. In addition, the shape distribution of knotted proteins and the contrast with the other proteins are also presented. A comparison shows that the knots may make structures more globular because the average shape factor is 0.059 for the knotted proteins, which is only about 1/3 of the average shape factor for the other proteins.
The phase behaviours of diblock copolymers under cylindrical confinement are studied in two-dimensional space by using the self-consistent field theory. Several phase parameters are adjusted to investigate the cylindrical-confinement-induced phase behaviours of diblock copolymers. A series of lamella-cylinder mixture phases, such as the mixture of broken-lamellae and cylinders and the mixture of square-lamellae and cylinders, are observed by varying the phase parameters, in which the behaviours of these mixture phases are discussed in the corresponding phase diagrams. Fur-thermore, the free energies of these mixture phases are investigated to illustrate their evolution processes. Our results are compared with the available observations from the experiments and simulations respectively, and they are in good agreement and provide an insight into the phase behaviours under cylindrical confinement.
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.
The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations. In this paper,we focus on the collapse of the polyethylene knotted ring chain,and also present the results of linear and ring chains for comparison. At high temperatures,a fully extensive knot structure is observed. The mean-square radius of gyration per bond S 2/(Nb2) and the shape factor δ depend on not only the chain length but also the knot type. With temperature decreasing,chain collapse is observed,and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity C v ,and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse,which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.
The phase behaviors of symmetric diblock copolymer thin films confined between two hard, parallel and diversified patterned surfaces are investigated by three-dimensional dissipative particle dynamics (DPD) simulations. The induction of diversified patterned surfaces on phase separation of symmetric diblock copolymer films in snapshots, density profiles and concentration diagrams of the simulated systems are presented. The phase separations can be controlled by the patterned surfaces. In the meantime, the mean-square end-to-end distance of the confined polymer chains (R2) is also discussed. Surface-induced phase separation for diblock copolymers can help us to create novel and controlled nanostructured materials.
