Schematic illustrations of subchains connected to (a) an entanglement node and (b) an end node. The entanglement node has four subchains, , and the end node has a single subchain, . Closed circle indicates the entanglement node, and open circle the end node. Solid segments indicate subchains connected to each node.
Schematic illustration of how to determine the diffusing time in the WB model. Arrows indicate the trajectory of the node (closed sphere). The node is reflected by the WB (solid line).
Schematic illustration of a simulation box confined in the slit channel. , , and are defined as displayed. A simulation box with a size of is confined by two parallel WBs, where is the slit width along the axis. Periodic boundaries are applied to the other boundaries.
Snapshots of (a) all and (b) single liner chains confined in a slit channel with and . Red spheres indicate end nodes, yellow spheres entanglement nodes, and blue lines subchains.
Variation of mean-square radius of gyration as a function of slit width, . Mean-square radius of gyration is projected in the direction (a) normal, , and (b) parallel, , to the wall. Gradually decreases and increases.
Plots of relaxation time of the end-to-end vector as a function of . gradually increases as decreases.
Plots of in-plain diffusivity of the center of mass as a function of . gradually decreases as decreases.
Plots of the mean number of entanglement per single chain as a function of . gradually increases as decreases.
Schematic illustration of the process of creating entanglements near the wall. The hooking partner to create a new entanglement is sought in a sphere of radius (circle in the figure). The center of the figure is located at the end node of a chain (open yellow circle). Possible partners are all subchains in the sphere (solid segments). Other subchains are indicated as dashed segments. Apparently, the position of the newly created entanglement is closer to the bulk side than the wall side.
Scaling laws of the number of entanglement for the relaxation time and in-plain diffusivity. (a) Plots of the relaxation time scaled by , and (b) plots of the in-plain diffusivity scaled by as a function of . is normalized by the average number of entanglement, , calculated by the simulation with periodic boundaries in every direction.
Schematic illustration of the increase in the number of monomers condensed in an end subchain, focusing on a chain with entanglement nodes (closed circles) and subchains (solid segments). Open circle indicates the end node of a chain located near the wall. All other nodes and subchains are indicated as dashed circles and lines, respectively. The osmotic pressure gradient is directed normal to the wall (open arrow). The number of monomers in the end subchain is increased by monomers in the near-wall chain sliding to the wall (closed arrow).
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