Molecular dynamics simulation of deformation behavior in amorphous polymer: nucleation of chain entanglements and network structure under uniaxial tension
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- Findingown data§ 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.
Many chains between clusters are oriented in the tensile direction.
“It is also observed that many chains between clusters are oriented in the tensile direction.”
Quote in the paperSubstantial claim - Findingown data§ 3.1 Initial equilibrium structure and yield
The 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.
“The distribution of bond length and angle shows a pulse-like sharp peak at the position of ro and θ0, implying almost every node is at the equilibrium length and angle.”
Quote in the paperNot a substantial claim - Findingown data§ Abstract
The material yields by elongating without significant stress increase up to a strain of about 1.5, where strain hardening appears.
“Then the material “yields” by elongating without stress increase up to the strain of 1.5, where strain hardening appears.”
- Also stated in: § 3.2 Yield ⇐ hardening behavior · plain
“After the initial yield described in the previous section, the material elongates without significant stress increase until the strain of about 1.5, showing stress fluctuation. On the other hand, stress prominently increases after εzz = 1.5 just like the strain hardening observed in the macroscopic tension test.”
Quote in the paperSubstantial claim - Also stated in: § 3.2 Yield ⇐ hardening behavior · plain
- Findingown data§ 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.
The initial arrangement of the dense flexion nodes does not correlate well with the entanglements nucleated during the yield ⇒ hardening process.
“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.”
Quote in the paperSubstantial claim - Findingown data§ 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.
Many flexion nodes are straightened during the deformation.
“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.”
Quote in the paperNot a substantial claim
- Findingown data§ Abstract
The gauche→trans transition takes place during yielding.
“the gauche→trans transition takes place during yielding”
- Also stated in: § 3.1 Initial equilibrium structure and yield · plain
“resulting in the gauche ⇔ trans transition.”
Quote in the paperSubstantial claim - Also stated in: § 3.1 Initial equilibrium structure and yield · plain
- Findingown data§ 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.
At 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.
“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.”
Quote in the paperSubstantial claim - Findingown data§ 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.
The inhomogeneity in density becomes clearer at εzz = 1.0, where splitting clusters of molecular chains with voids can be observed.
“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.”
Quote in the paperSubstantial claim - Findingown data§ 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.
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 at εzz = 1.5.
“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.”
Quote in the paperSubstantial claim - Findingown data§ 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.
Straightened chains are notably seen in the low-density regions, or the void regions between clusters.
“Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters.”
Quote in the paperSubstantial claim - Findingown data§ 3.2 Yield ⇐ hardening behavior
The torsion becomes lower than the initial equilibrium at the beginning of the strain hardening, εzz = 1.5.
“The torsion becomes lower than the initial equilibirum at the beginning of the strain hardening, εzz = 1.5.”
Quote in the paperSubstantial claim - Findingown data§ 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.
Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process.
“Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process”
Quote in the paperNot a substantial claim- Rests on an assumption: Particles with a local density higher than the branched peak ρhigh correspond to entanglements.
- Interpretationreasoning§ Abstract
The strain hardening is due to the directional orientation and stretching of molecular chains between entanglements in the nucleated structure.
“The strain hardening is due to the directional orientation and stretching of molecular chains between entanglements in the nucleated structure.”
Quote in the paperSubstantial claim - Interpretationown data§ 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.
Dense flexion nodes can be observed at the entanglements at εzz = 3.0, suggesting that flexion nodes tend to make entanglements.
“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.”
Quote in the paperNot a substantial claim - Interpretationreasoning§ 3.1 Initial equilibrium structure and yield
The change at 2 is the conformational change of molecular chains to relax the bending angle strained.
“(ii) The change at ② is the conformational change of molecular chains to relax the bending angle strained.”
Quote in the paperSubstantial claim - Interpretationown data§ Abstract
The gauche→trans transition generates a new network-like structure composed of entangled molecular clusters and oriented chains bridging them.
“generating a new network-like structure composed of entangled molecular clusters and oriented chains bridging them.”
- Also stated in: § 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. · plain
“a new network structure is generated where long straightened chains connect the clusters of entangled chains.”
Quote in the paperSubstantial claim - Also stated in: § 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. · plain
- Interpretationreasoning§ 3.1 Initial equilibrium structure and yield
The change at 1 is the relaxation of the dihedral angles, which have higher energy in the initial equilibrium structure, by the driving force of the applied strain.
“(i) The change at ① is the relaxation of the dihedral angles, which have higher energy in the initial equilibrium structure, by the driving force of the applied strain.”
Quote in the paperSubstantial claim - Interpretationown data§ 3.1 Initial equilibrium structure and yield
Energy exchange occurs between the bond stretch and bending, by changing the bending angle to relax the bond stretch at its limit.
“(2) the energy exchange occurs between the bond stretch and bending, by changing the bending angle to relax the bond stretch at its limit”
Quote in the paperSubstantial claim - Interpretationown data§ 3.1 Initial equilibrium structure and yield
The small variation of bond stretch absorbs the deformation primarily.
“(1) the small variation of bond stretch absorbs the deformation primarily”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.2 Yield ⇐ hardening behavior
The inner molecular chains become straight from εzz = 0.5.
“This implies the inner molecular chains become straight from εzz = 0.5.”
Quote in the paperSubstantial claim - Interpretationreasoning§ 3.1 Initial equilibrium structure and yield
The stress begins to decrease when the bending change cannot absorb the deformation anymore.
“(3) the stress begins to decrease when the bending change cannot absorb the deformation anymore.”
Quote in the paperSubstantial claim - Interpretationown data§ 3.1 Initial equilibrium structure and yield
The dihedral rotation plays an important role in the stress decrease.
“suggests that the dihedral rotation plays an important role in the stress decrease.”
Quote in the paperSubstantial claim - Interpretationreasoning§ Conclusive Remarks 4
There is still a large difference particularly in the time scale, between the mechanism presented and the phenomena in real materials.
“Thus it is true that there is still a large difference particularly in the time scale, between the mechanism presented and the phenomena in real materials.”
Quote in the paperNot a substantial claim- Rests on an assumption: The structural change of molecular chains such as chain folding requires more time in real polymeric materials.
- May combine two claims. 15
- The quote only partly states this claim. 1
- Classified as probably not a substantial claim. 2
May combine two claims.
Findingown data§ 3.1 Initial equilibrium structure and yieldThe nominal stress-nominal strain curve at the initial stage shows a linear elastic relationship up to the strain of 0.012, where the stress decreases slightly and makes a small peak (Arrow 1).
“It shows a linear elastic relationship up to the strain of 0.012, where the stress decreases slightly and makes a small peak as indicated by Arrow ①.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ 3.1 Initial equilibrium structure and yieldThe strain of both Lines 1 and 2 coincides with the local maximum of bending potential and almost the local minimum of the bond stretch potential.
“The strain of both Lines ① and ② coincides with the (local) maximum of bending potential and almost the local minimum of the bond stree”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ 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.The material deforms homogeneously and maintains the initial chain structure until εzz = 0.5, however, a few voids appear.
“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].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [21] [21] Matsumoto, R., Kitagawa, H., Nakatani, K., Nakatani, A., Molecular dynamics simulation on a crack propagating in amorhous metal, Transaction of the Japan Society of Mechanical Engineers, Series A 76–653 (2001), 23–29. (in Japanese) -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
The quote only partly states this claim.
Findingown data§ 3.1 Initial equilibrium structure and yieldThe simulated stress-strain curve shows a linear elastic relationship at the initial stage of straining up to a strain of 0.012 at a strain rate of 5.0×10^11/s.
“It shows a linear elastic relationship up to the strain of 0.012”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ 3.1 Initial equilibrium structure and yieldAfter the small peak, the stress increases again and shows the maximum peak of σzz = 0.92 GPa at εzz = 0.027 (Arrow 2).
“Then the stress increases again and shows the maximum peak of σzz = 0.92 GPa at εzz = 0.027 (Arrow ②).”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ 3.1 Initial equilibrium structure and yieldThe torsion angle distribution has peaks at the stable and metastable points of trans and gauche, but many nodes are deviated from the stable or metastable angle so that the peaks have broader bases.
“The torsion angle also has its peaks at the stable and metastable points of trans and gauche, however, there are many nodes deviated from the stable or metastable angle so that the peaks have broader bases.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ 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.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.
“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”
Quote in the paperSubstantial claimMay combine two claims.
Findingreasoning§ 3.2 Yield ⇐ hardening behaviorThe number of gauche nodes decreases and that of trans increases after εzz = 0.5, because both transitions decrease monotonically and the gauche ⇒ trans transition is twice as much as the other.
“Then, the number of gauche nodes decreases and that of trans increases after εzz = 0.5, from the fact that both transitions decrease monotonically and the gauche ⇒ trans transition is twice as much as the other.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ 3.2 Yield ⇐ hardening behaviorIn the yield region, only the torsion shows remarkable change at εzz = 0.5, where it turns to decrease, while the bond stretch and bending increase monotonically.
“In the yield region, only the torsion shows remarkable change at εzz = 0.5, where it turns to decrease, while the bond stretch and bending increase monotonically.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ 3.1 Initial equilibrium structure and yieldThe atomic density has its peak at the controlled density of 0.87 g/cm3 and a wide distribution in the lower side due to the surfaces.
“The atomic density has its peak at the controlled density of 0.87g/cm³ and a wide distribution in the lower side due to the surfaces.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ 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.In the local density distribution during yield ⇒ hardening, the peak translates to the lower side by tension, but the distribution maintains a broad base at the higher side because of the clusters.
“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.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown data§ 3.1 Initial equilibrium structure and yieldThe rotation of the dihedral angle observed during 1 and 2 is within ±30 deg while that after 2 exceeds ±60 deg, resulting in the gauche ⇔ trans transition.
“the rotation of the dihedral angle observed during ① and ② is within ±30 deg while that after ② exceeds ±60 deg, resulting in the gauche ⇔ trans transition.”
Quote in the paperSubstantial claimMay combine two claims.
Findingown data§ 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.Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners.
“Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners.”
Quote in the paperNot a substantial claim- Rests on an assumption: Particles with a local density higher than the branched peak ρhigh correspond to entanglements.
May combine two claims.
Interpretationown data§ 3.2 Yield ⇐ hardening behaviorThe gauche ⇒ trans transition decreases the system energy, and is subtly balanced with the probability of the trans ⇒ gauche transition, which increases the energy.
“that decreases the system energy, are subtly balanced with the probability of the trans ⇒ gauche transition, that increases the energy.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown data§ 3.1 Initial equilibrium structure and yieldThe potential energy of the whole system is minimum by the initial relaxation but some torsion angles remain at the high energy state in the intricated amorphous chain structure.
“This implies the potential energy of the whole system is minimum by the initial relaxation but some torsion angles remain at the high energy state in the intricated amorphous chain structure.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Premisecitation§ Simulation Procedure 2The potential functions and parameters adopted are proposed by Kuwajima et al. [20] for amorphous polyethylene.
“The potential functions and parameters adopted are proposed by Kuwajima et al. [20] for amorphous polyethelene as shown in the equations below with the parameters listed in Table 1.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Kuwajima et al. [20] [20] Kuwajima, S., Noma, H., Ohsaka, T., Proceedings of the 4th symposium of the society of computer chemistry, Japan (1994), 53–56. (in Japanese) -
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Probably not a substantial claim: may not pass S4 (based). May combine two claims.
Study design and conductnone given§ 1 IntroductionThe simulation eliminates any periodicity and the chain connecting the top and bottom of the specimen, which would undesirably determine the mechanical properties with its characteristic length.
“By eliminating any periodicity and the chain connecting the top and bottom of the specimen, which undesirably determines the mechanical properties with its “characteristic length”, the fundamental mechanism of chain entanglements is investigated in detail.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
The structural change of molecular chains such as chain folding requires more time in real polymeric materials.
“The structural change of molecular chains such as chain folding requires more time in real polymetric materials.”
The paper relies on this without support.
Particles with a local density higher than the branched peak ρhigh correspond to entanglements.
“Figure 12 illustrates particles with a higher local density than the branched peak, ρhigh, at each strain of 1.5~3.0.”
The paper relies on this without support.
The nanoscopic specimen with about 2 million methylene groups is large enough to capture the fundamental mechanism of chain entanglements in amorphous polymers.
“For fundamental understanding of the deformation behavior of large, irregular and massive molecular chains in an amorphous polymer, it may still be indispensable to directly trace the motion of all chains with a huge number of molecules.”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Reference 18 is attributed to the wrong authors
MinorThe discussion attributes reference 18 to Shibutani and colleagues, whereas the reference list identifies Ichiyanagi as its author.
“In fact, Shibutani et al. [18] have faced the problem that the mechanical properties in the atomic simulations are strongly affected by the size of the periodic cell”
“[18] Ichiyanagi, J., Research about the Hierarchical Modeling of Amorphous Polymer, Solid Mechanics Research Report, No.0010 (2000). (in Japanese)”
Elastic-range limit differs between abstract and results
MinorThe abstract describes the response as linear elastic through a strain of 0.03, but the results say linear elasticity ends at 0.012 and describe a stress decrease before 0.03.
“The stress-strain curve shows a linear elastic relationship at the initial stage of εzz ≤ 0.03 at ¿zz = 5.0 × 1011/s.”
“It shows a linear elastic relationship up to the strain of 0.012, where the stress decreases slightly and makes a small peak as indicated by Arrow ①.”
Cites
A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
Arruda, E. M., & Boyce, M. C. (1993) · Journal of the Mechanics and Physics of Solids · doi:10.1016/0022-5096(93)90013-6 · Cited by 3,239 · see citing works
Large inelastic deformation of glassy polymers. part I: rate dependent constitutive model
Boyce, M. C., Parks, D. M., & Argon, A. S. (1988) · Mechanics of Materials · doi:10.1016/0167-6636(88)90003-8 · Cited by 1,110 · see citing works
A theory for the low-temperature plastic deformation of glassy polymers
Argon, A. S. (1973) · Philosophical Magazine · doi:10.1080/14786437308220987 · Cited by 801 · see citing works
A method for accelerating the molecular dynamics simulation of infrequent events
Voter, A. F. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473503 · Cited by 608 · see citing works
Wu, P. D., & Van Der Giessen, E. (1993) · Journal of the Mechanics and Physics of Solids · doi:10.1016/0022-5096(93)90043-f · Cited by 591 · see citing works
A molecular-dynamics study of polyethylene crystallization
Kavassalis, T. A., & Sundararajan, P. R. (1993) · Macromolecules · doi:10.1021/ma00068a012 · Cited by 212 · see citing works
From many monomers to many polymers: Soft ellipsoid model for polymer melts and mixtures
Murat, M., & Kremer, K. (1998) · The Journal of Chemical Physics · doi:10.1063/1.475835 · Cited by 138 · see citing works
A general-purpose coarse-grained molecular dynamics program
Aoyagi, T., Sawa, F., Shoji, T., Fukunaga, H., Takimoto, J.-I., & Doi, M. (2002) · Computer Physics Communications · doi:10.1016/s0010-4655(02)00271-0 · Cited by 138 · see citing works
Atomistic modelling of plastic deformation of glassy polymers
Mott, P. H., Argon, A. S., & Suter, U. W. (1993) · Philosophical Magazine A · doi:10.1080/01418619308213969 · Cited by 130 · see citing works
Molecular dynamics simulation of structural formation of short polymer chains
Fujiwara, S., & Sato, T. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.991 · Cited by 87 · see citing works
Molecular dynamics simulation of structure formation of short chain molecules
Fujiwara, S., & Sato, T. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478941 · Cited by 86 · see citing works
Molecular dynamics simulation of polymer ordering. II. Crystallization from the melt
Yamamoto, T. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1410377 · Cited by 80 · see citing works
Prediction of deformation behavior of glassy polymers based on molecular chain network model
Tomita, Y., & Tanaka, S. (1995) · International Journal of Solids and Structures · doi:10.1016/0020-7683(94)00315-n · Cited by 77 · see citing works
Self-citationYashiro, K., Naito, M., & Tomita, Y. (2002) · International Journal of Mechanical Sciences · doi:10.1016/s0020-7403(02)00138-8 · Cited by 72 · see citing works
Self-citationMolecular dynamics simulation of polymer ordering. I. Crystallization from vapor phase
Yamamoto, T. (1998) · The Journal of Chemical Physics · doi:10.1063/1.477068 · Cited by 49 · see citing works
Hierarchical simulation approach to structure and dynamics of polymers
Uhlherr, A., & Theodorou, D. N. (1998) · Current Opinion in Solid State and Materials Science · doi:10.1016/s1359-0286(98)80023-5 · Cited by 43 · see citing works
Molecular dynamics simulation of large deformation in an amorphous polymer
Ogura, I., & Yamamoto, T. (1995) · Polymer · doi:10.1016/0032-3861(95)95914-m · Cited by 36 · see citing works
TOMITA, Y., & TANAKA, S. (1995) · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A · doi:10.1299/kikaia.61.120 · Cited by 3
Self-citationTOMITA, Y., & ADACHI, T. (1996) · Advances in Engineering Plasticity and its Applications (aepa 1996) · doi:10.1016/b978-0-08-042824-6.50093-3
Self-citationTschöp (1998) · doi:10.1002/(sici)1521-4044(199802)49:2/3
Molecular Dynamics Simulation of Dislocation in γ/γ' Microstructure in Ni-based Superalloy
YASHIRO, K., NAITO, M., & TOMITA, Y. (2002) · The Proceedings of Conference of Kansai Branch · doi:10.1299/jsmekansai.2002.77._1-43_
Self-citation
Flagged first, then by citations
1 of the 22 references couldn’t be matched to a known paper.
Research works printed but not linked: 3
- Furukawa, 2001, System for three-dimensional reconstruction of TEM images based on computerized tomography method, JEOL News, 36, 50
- Tschöp, 1998, Simulation of polymer melts. II. From coarse-grained models back to atomistic description, Acta Polymer, 49, 75, 10.1002/(SICI)1521-4044(199802)49:2/3<75::AID-APOL75>3.0.CO;2-5 · DOI
- Kuwajima S, Noma H, Ohsaka T. Proceedings of the Fourth Symposium of the Society of Computer Chemistry, Japan, 1994, pp. 53–6 [in Japanese].
Cited by
Sorted by citations
Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene
Hossain, D., Tschopp, M. A., Ward, D. K., Bouvard, J. L., Wang, P., & Horstemeyer, M. F. (2010) · Polymer · doi:10.1016/j.polymer.2010.10.009 · Cited by 462 · see citing works
Strain hardening of polymer glasses: Effect of entanglement density, temperature, and rate
Hoy, R. S., & Robbins, M. O. (2006) · Journal of Polymer Science Part B: Polymer Physics · doi:10.1002/polb.21012 · Cited by 219 · see citing works
Semino, R., Ramsahye, N. A., Ghoufi, A., & Maurin, G. (2015) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.5b10150 · Cited by 179 · see citing works
Kröger, M., Dietz, J. D., Hoy, R. S., & Luap, C. (2022) · Computer Physics Communications · doi:10.1016/j.cpc.2022.108567 · Cited by 140 · see citing works
Zhao, K., Zhang, T., Chang, H., Yang, Y., Xiao, P., Zhang, H., Li, C., Tiwary, C. S., Ajayan, P. M., & Chen, Y. (2019) · Science Advances · doi:10.1126/sciadv.aav2589 · Cited by 118 · see citing works
Nonlinear Mechanooptical Behavior of Uniaxially Stretched Poly(lactic acid): Dynamic Phase Behavior
Mulligan, J. H., & Çakmak, M. (2005) · Macromolecules · doi:10.1021/ma048794f · Cited by 97 · see citing works
Review of Hierarchical Multiscale Modeling to Describe the Mechanical Behavior of Amorphous Polymers
Bouvard, J., Ward, D. K., Hossain, D., Nouranian, S., Marin, E. B., & Horstemeyer, M. F. (2009) · Journal of Engineering Materials and Technology · doi:10.1115/1.3183779 · Cited by 82 · see citing works
Atomistic molecular dynamics study of cross-linked phenolic resins
(2012) · doi:10.1039/c2sm25067e · Cited by 79 · see citing works
Fujimoto, K., Tang, Z., Shinoda, W., & Okazaki, S. (2019) · Polymer · doi:10.1016/j.polymer.2019.121570 · Cited by 71 · see citing works
Ma, C., Ji, T., Robertson, C. G., Rajeshbabu, R., Zhu, J., & Dong, Y. (2017) · Physical Chemistry Chemical Physics · doi:10.1039/c7cp01142c · Cited by 66 · see citing works
Bowman, A. L., Mun, S., Nouranian, S., Huddleston, B. D., Gwaltney, S. R., Baskes, M. I., & Horstemeyer, M. F. (2019) · Polymer · doi:10.1016/j.polymer.2019.02.060 · Cited by 66 · see citing works
Sundararaghavan, V., & Kumar, A. (2013) · International Journal of Plasticity · doi:10.1016/j.ijplas.2013.01.004 · Cited by 64 · see citing works
Patel, M., Dubey, D. K., & Singh, S. P. (2019) · Materials Science and Engineering C · doi:10.1016/j.msec.2019.110414 · Cited by 59 · see citing works
Void nucleation and disentanglement in glassy amorphous polymers
Mahajan, D. K., Singh, B., & Basu, S. (2010) · Physical Review E · doi:10.1103/physreve.82.011803 · Cited by 55 · see citing works
A multiscale multisurface constitutive model for the thermo-plastic behavior of polyethylene
Vu‐Bac, N., Areias, P. M. D. A., & Rabczuk, T. (2016) · Polymer · doi:10.1016/j.polymer.2016.10.039 · Cited by 52 · see citing works
Xu, K., Liu, L., Zhao, Z., Luo, G., & Chen, W. (2023) · International Journal of Mechanical Sciences · doi:10.1016/j.ijmecsci.2023.108697 · Cited by 40 · see citing works
Wan, C., Chen, X., Lv, F., et al. (2019) · Polymer · doi:10.1016/j.polymer.2019.01.021 · Cited by 40 · see citing works
Shang, Y., Zhang, X., Xu, H., Li, J., & Jiang, S. (2015) · Polymer · doi:10.1016/j.polymer.2015.09.017 · Cited by 32 · see citing works
Qiang, Y., Wu, W., Lu, J., Jiang, B., & Ziegmann, G. (2020) · Langmuir · doi:10.1021/acs.langmuir.0c01949 · Cited by 32 · see citing works
Ebrahimi, S., Ghafoori-Tabrizi, K., & Rafii‐Tabar, H. (2011) · Computational Materials Science · doi:10.1016/j.commatsci.2011.08.034 · Cited by 29 · see citing works
Nikkhah, S. J., Moghbeli, M. R., & Hashemianzadeh, S. M. (2016) · Macromolecular Theory and Simulations · doi:10.1002/mats.201600069 · Cited by 28 · see citing works
Prasad, A., Grover, T., & Basu, S. (2010) · International Journal of Engineering Science and Technology · doi:10.4314/ijest.v2i4.59196 · Cited by 28 · see citing works
A molecular dynamics study on the strength and ductility of high T g polymers
Negi, A., & Basu, S. (2006) · Modelling and Simulation in Materials Science and Engineering · doi:10.1088/0965-0393/14/4/002 · Cited by 24 · see citing works
Ding, G., Tam, L., & Wu, C. (2024) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2024.08.487 · Cited by 24 · see citing works
(2009) · doi:10.1016/j.ijmecsci.2009.08.005 · Cited by 23 · see citing works
Self-citationNanoindentation on crystal/amorphous polyethylene: Molecular dynamics study
(2006) · doi:10.1016/j.commatsci.2006.02.001 · Cited by 22 · see citing works
Self-citationLi, C., Shang, Y., Li, J., & Jiang, S. (2022) · Colloid & Polymer Science · doi:10.1007/s00396-022-04975-1 · Cited by 16 · see citing works
Kumar, S., & Pattanayek, S. K. (2019) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.9b00139 · Cited by 18 · see citing works
Rate-dependent failure mechanism of elastomers
(2017) · doi:10.1016/j.ijmecsci.2017.05.033 · Cited by 16 · see citing works
Investigations into the applicability of rubber elastic analogy to hardening in glassy polymers
Mahajan, D. K., & Basu, S. (2010) · Modelling and Simulation in Materials Science and Engineering · doi:10.1088/0965-0393/18/2/025001 · Cited by 14 · see citing works
Li, J., Liang, Z., Liu, J., Yu, C., Zhang, X., & Kan, Q. (2023) · Smart Materials and Structures · doi:10.1088/1361-665x/acb676 · Cited by 16 · see citing works
Fracture mechanism of amorphous polymers at strain fields
Huang, L., Yang, X., Jia, X., & Cao, D. (2014) · Physical Chemistry Chemical Physics · doi:10.1039/c4cp03120b · Cited by 15 · see citing works
Fujimoto, K., Payal, R. S., Hattori, T., Shinoda, W., Nakagaki, M., Sakaki, S., & Okazaki, S. (2019) · Journal of Computational Chemistry · doi:10.1002/jcc.26034 · Cited by 11 · see citing works
Majumder, M. K., Ramkumar, S., Mahajan, D. K., & Basu, S. (2010) · Physical Review E · doi:10.1103/physreve.81.011803 · Cited by 12 · see citing works
Tschopp, M. A., Bouvard, J., Ward, D. K., Bammann, D. J., & Horstemeyer, M. F. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1310.0728 · Cited by 9 · see citing works
Three-dimensional numerical modeling of the damage mechanism of amorphous polymer network
Jin, Y., & Wang, T. J. (2009) · Computational Materials Science · doi:10.1016/j.commatsci.2009.06.019 · Cited by 8 · see citing works
Robust Artificial Spider Silk via Synergistic Cross-Linking of Slide-Ring and Covalent Bonds
Mei, G., Su, Z., Liu, N., Qu, J., Liu, X., Qian, D., Zhou, X. Y., & Liu, Z. (2025) · Macromolecules · doi:10.1021/acs.macromol.5c02101 · Cited by 9 · see citing works
Xu, S., Stoclet, G., Tahon, J., de Waele, I., & Gaucher, V. (2025) · Macromolecules · doi:10.1021/acs.macromol.5c00607 · Cited by 8 · see citing works
Modeling of Interface Behavior in Carbon Nanotube Composites
(2006) · doi:10.2514/6.2006-1677 · Cited by 8 · see citing works
Wu, W., Duan, F., Zhao, B., Qiang, Y., Zhou, M., & Jiang, B. (2022) · Polymers · doi:10.3390/polym14153218 · Cited by 7 · see citing works
Fujimoto, K., Ishikawa, H., Tang, Z., & Okazaki, S. (2023) · Polymer · doi:10.1016/j.polymer.2023.126276 · Cited by 6 · see citing works
Fracture and Toughening Mechanisms of Glassy Polymer at the Molecular Level
Fujimoto, K. (2022) · Nihon Reoroji Gakkaishi · doi:10.1678/rheology.50.37 · Cited by 5 · see citing works
Takazawa, A., Yamanobe, T., Uehara, H., Ohnishi, T., Wakabayashi, Y., Aoyama, K., Sekiguchi, H., & Kakiage, M. (2024) · Polymer · doi:10.1016/j.polymer.2024.127683 · Cited by 6 · see citing works
Grommes, D., & Reith, D. (2020) · Soft Materials · doi:10.1080/1539445x.2020.1722692 · Cited by 6 · see citing works
(2007) · doi:10.4028/www.scientific.net/kem.340-341.1017 · Cited by 6 · see citing works
Self-citationZeng, S., Li, Z.-K., Zhang, K.-Q., Hu, C., & Wang, Z. (2024) · Polymer · doi:10.1016/j.polymer.2024.127503 · Cited by 5 · see citing works
Leelaprachakul, T., Kubo, A., & Umeno, Y. (2024) · Computational Materials Science · doi:10.1016/j.commatsci.2024.113028 · Cited by 5 · see citing works
Patel, M., Dubey, D. K., & Singh, S. P. (2021) · Macromolecular Research · doi:10.1007/s13233-021-9084-6 · Cited by 6 · see citing works
Feng, J., Liao, Q., Zhu, X., Wu, R. Z., Wang, H., Ding, Y., & YASHIRO, K. (2011) · Chinese Science Bulletin · doi:10.1007/s11434-010-4317-7 · Cited by 5 · see citing works
Self-citationZeng, F., Hu, E., Sun, Y., & Qu, J. (2015) · Journal of Polymer Science Part B Polymer Physics · doi:10.1002/polb.23727 · Cited by 4 · see citing works
Gaikwad, A., & Kolluru, P. V. (2023) · Macromolecular Materials and Engineering · doi:10.1002/mame.202300313 · Cited by 4 · see citing works
Morimura, A., Nishino, H., Kajihara, M., Nakao, Y., & Yonezu, A. (2023) · Journal of Polymer Research · doi:10.1007/s10965-023-03616-7 · Cited by 4 · see citing works
Mu, G., Li, H., Sun, W., Wu, H., Luo, Y., Gao, Y., Zhao, X., & Zhang, L. (2020) · Engineering Fracture Mechanics · doi:10.1016/j.engfracmech.2020.107229 · Cited by 4 · see citing works
Molecular dynamic simulations of deformation behaviour of blended polyethylene
Shi, J., Zhou, J. C., Liu, L., Liu, W., & Miao, C. (2023) · Molecular Simulation · doi:10.1080/08927022.2023.2260496 · Cited by 4 · see citing works
(2009) · doi:10.1299/kikaia.75.881 · Cited by 3 · see citing works
Self-citationModeling and Simulation of Deformation Behavior of Polymer Based on Molecular Chain Network Theory
TOMITA, Y. (2013) · Journal of the Society of Materials Science Japan · doi:10.2472/jsms.62.465 · Cited by 3 · see citing works
Self-citationShi, J., Zhou, J. C., Liu, L., & Miao, C. (2024) · Journal of Macromolecular Science Part B · doi:10.1080/00222348.2024.2397923 · Cited by 3 · see citing works
Le, T.-T. (2020) · Computer Methods in Materials Science. · doi:10.7494/cmms.2020.2.0653 · Cited by 3 · see citing works
Effect of Cooling Rate and Molecular Weight on the Nonisothermal Crystallization of Polyethylene
Hao, T., Li, X., Wales, D. J., Ming, Y., Nie, Y., Zhou, Z., & Yan, D. (2025) · Journal of Applied Polymer Science · doi:10.1002/app.56936 · Cited by 3 · see citing works
Simulation of Deformation Behavior of Polymeric Materials by Chain Network Model
Shinozaki, A., KISHIMOTO, K., & INOUE, H. (2006) · Key engineering materials · doi:10.4028/www.scientific.net/kem.306-308.983 · Cited by 2 · see citing works
Wu, W., Shan, S., Zhao, H., Lin, Y., & Zhang, A. (2022) · Journal of Macromolecular Science Part B · doi:10.1080/00222348.2022.2116914 · Cited by 2 · see citing works
- Authors
- Yashiro, K., Ito, T., & Tomita, Y.
- Affiliations
- Kobe University (JP)
- Corresponding author
- Yashiro, Kisaragi
- Venue
- International Journal of Mechanical Sciences
- Publisher
- Elsevier BV
- Published
- 2003-11
- Volume
- 45
- Issue
- 11
- Pages
- 1863-1876
- ISSN
- 0020-7403 (ISSN-L)
- OpenAlex
- W2144689690
- Semantic Scholar
- d307b6838de9534cb03e6a2d50fcfac5fe44fb9e
- Cited by
- 128
- References
- 22
- Citations by year
- 2026: 5 · 2025: 9 · 2024: 13 · 2023: 10 · 2022: 10 · 2021: 3 · 2020: 9 · 2019: 9 · 2018: 1 · 2017: 4 · 2016: 5 · 2015: 5 · 2014: 1 · 2013: 3 · 2012: 3
- FWCI
- 3.59
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Locations
- International Journal of Mechanical Sciences (publishedVersion)
- Institutional Repositories DataBase (IRDB) (submittedVersion)
- Kobe University Repository Kernel (Kobe University) (submittedVersion, other-oa)
- Funders
- Ministry of Education, Culture, Sports, Science and Technology
- Topics
- Physical Sciences › Materials Science › Polymers and Plastics › Polymer crystallization and properties
- Physical Sciences › Chemical Engineering › Fluid Flow and Transfer Processes › Rheology and Fluid Dynamics Studies
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- amorphous polymers, amorphous polyethylene, uniaxial tension, chain entanglement, entanglement network, strain hardening, yielding, chain orientation, stress-strain behavior, dihedral angle
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