The DOI matches its Crossref record; 21 of the 22 references it cites were found in a registry or an index; none of the 2 sources its claims cite is checked for support yet.
Molecular dynamics simulation of deformation behavior in amorphous polymer: nucleation of chain entanglements and network structure under uniaxial tension
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“It is also observed that many chains between clusters are oriented in the tensile direction.”
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“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.”
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“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.”
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- Also stated in: § 3.2 Yield ⇐ hardening behavior · plain
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“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.”
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“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.”
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“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.”
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- Also stated in: § 3.1 Initial equilibrium structure and yield · plain
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“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.”
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“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.”
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“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.”
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“Here, we can see straightened chains notably in the low-density regions, or the void regions between clusters.”
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“The torsion becomes lower than the initial equilibirum at the beginning of the strain hardening, εzz = 1.5.”
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“Most of the entangled chains at the corners and surfaces have disappeared during the yield ⇒ hardening process”
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- Rests on an assumption: Particles with a local density higher than the branched peak ρhigh correspond to entanglements.
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“The strain hardening is due to the directional orientation and stretching of molecular chains between entanglements in the nucleated structure.”
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“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.”
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“(ii) The change at ② is the conformational change of molecular chains to relax the bending angle strained.”
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“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.”
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- 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
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“(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.”
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“(2) the energy exchange occurs between the bond stretch and bending, by changing the bending angle to relax the bond stretch at its limit”
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“(1) the small variation of bond stretch absorbs the deformation primarily”
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“This implies the inner molecular chains become straight from εzz = 0.5.”
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“(3) the stress begins to decrease when the bending change cannot absorb the deformation anymore.”
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“suggests that the dihedral rotation plays an important role in the stress decrease.”
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“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.”
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- Rests on an assumption: The structural change of molecular chains such as chain folding requires more time in real polymeric materials.
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“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.”
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“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”
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“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].”
What the sources say
- Not matchedcites [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) -
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“It shows a linear elastic relationship up to the strain of 0.012”
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“Then the stress increases again and shows the maximum peak of σzz = 0.92 GPa at εzz = 0.027 (Arrow ②).”
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“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.”
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“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”
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“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.”
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“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.”
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“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.”
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In the paper
“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.”
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“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.”
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“Many of the entanglements are observed in the center of the cross section, a few at the surface, and none at the corners.”
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- Rests on an assumption: Particles with a local density higher than the branched peak ρhigh correspond to entanglements.
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In the paper
“that decreases the system energy, are subtly balanced with the probability of the trans ⇒ gauche transition, that increases the energy.”
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“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.”
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“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.”
What the sources say
- Not matchedcites 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) -
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In the paper
“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.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.
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.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ 1 Introduction
“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”
§ References
“[18] Ichiyanagi, J., Research about the Hierarchical Modeling of Amorphous Polymer, Solid Mechanics Research Report, No.0010 (2000). (in Japanese)”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Abstract
“The stress-strain curve shows a linear elastic relationship at the initial stage of εzz ≤ 0.03 at ¿zz = 5.0 × 1011/s.”
§ 3.1 Initial equilibrium structure and yield
“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.”
Citations
Cites
A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
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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
A theory for the low-temperature plastic deformation of glassy polymers
Argon, A. S. (1973) · Philosophical Magazine · doi:10.1080/14786437308220987 · Cited by 801
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
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
A molecular-dynamics study of polyethylene crystallization
Kavassalis, T. A., & Sundararajan, P. R. (1993) · Macromolecules · doi:10.1021/ma00068a012 · Cited by 212
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
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
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
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
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
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
Semino, R., Ramsahye, N. A., Ghoufi, A., & Maurin, G. (2015) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.5b10150 · Cited by 179
Kröger, M., Dietz, J. D., Hoy, R. S., & Luap, C. (2022) · Computer Physics Communications · doi:10.1016/j.cpc.2022.108567 · Cited by 142
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
Metadata
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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