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Supporting Information: Carbonization with misfusion (Advanced Materials, 2016)

Summary

This PDF is the Supporting Information for Carbonization with misfusion: Fundamental limits of carbon fiber strength revisited (Adv. Mater. 2016). It documents simulation design (periodic D-loop pairs vs single D-loop non-periodic cells), von Mises stress definitions, strain/stress protocols, and length-contraction simulations of N-terminated graphene nanoribbons referenced in the main article, plus an elliptical-hole elasticity discussion relating idealized holes to non-elliptical D-loop stress concentration (SI §4). Read strengths and mechanisms together with 2016gupta-venue-paper.

Methods

  • von Mises stress: Explicit Cauchy stress tensor formula (Eq. (SI.1)) used with simulation stresses.
  • Configuration (i) — periodic D-loop pairs: Strain-controlled loading along x via unit cell deformation; engineering strain from L_x; stress from LAMMPS stress tensor; 16 θ orientations with Table S1 cell dimensions L_x, L_y and chiral indices (n,m); W > w width scaling rule for wider pairs; initial θ grid chosen so initial cell dimension drift is < 2% despite graphene anisotropy (SI text).
  • Configuration (ii) — single D-loop: Non-periodic (free-standing) sheet with edge “handles” constrained in-plane; stress-controlled ramped opposing forces; fracture stress from force–distance slope breaks.
  • Length contraction: N-terminated nanoribbons of length 150 graphene unit cells; widths w–5w; Langevin thermostat heating; segment-resolved end-to-end vectors used in Eq. (SI.2–SI.3) style analysis; Figure S1 reports contraction % vs T up to 1500 K with linear K·T fit for the plotted regime.

Ensemble / controls (SI): Heating and contraction segments use NVT-style Langevin thermostat control as written in the SI text. Time step (fs) and total heated duration in ps/ns for each width series: N/A — not copied from the SI into this wiki page—read papers/ReaxFF_others/Gupta_D_Loops_AdvMat_SupportingInfo.pdf. Barostat / hydrostatic pressure: N/A — not used for these NVT heating sweeps.

Findings

  • SI tables tie crystallographic orientation of D-loop pairs to simulation cell vectors used in strength statistics.
  • Length-contraction curves vs temperature show width-dependent contraction amplitudes, supporting the main text’s link between carbonization heating and misfusion defect formation.
  • Figure S1b indicates differences in contraction between ribbon widths can reach ~3% at the highest temperatures shown, underscoring finite-width effects on thermomechanical response in the SI model.
  • Table S1 lists representative chiral indices (n,m) and L_x, L_y for each θ used in periodic D-loop studies, enabling readers to map simulation boxes to graphene orientations (SI PDF).

Limitations

Corpus holds SI only; interpret scientific claims together with the primary article wiki page 2016gupta-venue-paper.

Relevance to group

Mechanical protocol details for ReaxFF/LAMMPS D-loop models—useful for reproducibility notes when comparing to other graphene fracture studies.

Citations and evidence anchors