Molecular dynamics simulation of deformation behavior in amorphous polymer: nucleation of chain entanglements and network structure under uniaxial tension

• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingMany chains between clusters are oriented in the tensile direction.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingThe distribution of bond length and bending angle in the initial equilibrium state shows a pulse-like sharp peak at r0 and θ0, implying almost every node is at the equilibrium length and angle.From the paper’s own data. Not checkable against an outside source.§ 3.1 Initial equilibrium structure and yield
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingThe material yields by elongating without significant stress increase up to a strain of about 1.5, where strain hardening appears.From the paper’s own data. Not checkable against an outside source.§ Abstract
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingThe initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingMany flexion nodes are straightened during the deformation.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingThe gauche→trans transition takes place during yielding.From the paper’s own data. Not checkable against an outside source.§ Abstract
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingAt the beginning of strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingThe inhomogeneity in density becomes clearer at εzz = 1.0, where splitting clusters of molecular chains with voids can be observed.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingA new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm3 in the density distribution at εzz = 1.5.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.
• Own resultA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.FindingStraightened chains are notably seen in the low-density regions, or the void regions between clusters.From the paper’s own data. Not checkable against an outside source.§ 3.3 Chain entanglements and directional orientation Figure 9 shows the snapshots of molecular chains in the tensile simulation. In the figure, a rectangular region in the center of the specimen, of which initial size is 10 nm × 10 nm × 3 nm, is drawn. The black particles indicate the flexion nodes at the initial equilibrium, as described later. The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear in contrast with the deformation of an amorphous metal [21]. The inhomogeneity in the density becomes clearer in the figure with εzz = 1.0, where splitting clusters of molecular chains with voids can be observed. Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters. At the beginning of the strain hardening at εzz = 1.5, a new network structure is generated where long straightened chains connect the clusters of entangled chains. It is also observed that many chains between clusters are oriented in the tensile direction. After a strain of 1.5, some clusters dissolve but the material deforms mainly by the stretching of the oriented chains between clusters keeping the generated network structure, as recognized from the positions of clusters I and Ⅱ in the figures with εzz = 1.5 ∼ 3.0. It should be concluded from these facts that the stress increase in the present simulation, where no chain connects the top and bottom of the specimen, is caused by the nucleation of the network chain structure with the "entanglements" and the orientation and stretch of the chains bridging them. In order to clarify the characteristics of the entanglements at the initial equilibrium state, the "flexion nodes" in all molecular chains are investigated. As schematically illustrated in Fig. 10, the interior angle between two position vectors from the target particle A to the particles B and C, 10 backward and forward monomers, are evaluated. The particles, at which the angle is less than 90 deg at the initial equilibrium, are drawn in black in Fig. 9 as flexion nodes. Dense flexion nodes can be observed at the entanglements in the figure with εzz = 3.0, thus it is suggested that the flexion nodes tend to make entanglements. It is also pointed out, however, that there are many flexion nodes straightened during the deformation, since many black particles can be seen in the long straightened chains. From these remarks and the figure of εzz = 0.0, we can see that the initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process. The configuration or distance of the entanglements, of great interest from the viewpoint of hierarchical modelling, may not be easily characterized by the initial chain structure but depends on the history of complicated local deformations. The change in the distribution of local density during the yield ⇒ hardening process is shown in Fig. 11. In the figures with εzz = 0.5 and 1.0, the peak translates to the lower side by tension, however, the distribution maintains a broad base at the higher side because of the clusters shown in Fig. 9. It is confirmed quantitatively from the figure with εzz = 1.5 that a new structure nucleates at the beginning of the strain hardening, since another small peak appears near ρ = 0.53 g/cm³ in the density distribution. Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0. Clusters A, B and C are indicated by ellipsoids in the figure as an example to make the relative position of the clusters clear. Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners. Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process, sn ne t na s stte et etie distance between the entanglements could not be decided quantitatively, since they disperse widely as can be seen in the figure. The relationship between the distance and the average molecular weight remains to be invesitigated statistically in the next study.

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