User:FlamingBuffalo/sandbox/Graphene Helix

Graphene Helix is the helical arrangement of a 2-dimensional hexagonal lattice, or "honeycomb" shape, of sp2 hybridizedcarbon atoms that form single-walled carbon nanotubes (SWNTs).

The helical structure of SWNTs is a result of the spiral growth of a graphene nanoribbon which was observed under High-Resolution Transmission Electron Microscopy (HRTEM) and atomic force microscopy (AFM). The structure is generalized using the plane indices, or Miller Indices, of hexagonal space groups instead of using chiral vectors.

Graphene nanoribbons have two types of edge structures that also affect the electronic state of the nanoribbons, the "armchair" and "zigzag" structures, which follow different angles in relation to the tubule axis for helical growth.. Armchair structured nanoribbons follow a 30° angle away from the tubule axis, while the zigzag structured nanoribbon follows a 60° angle away from the tubule axis.

Observation of Helical Structure
The helical structure was identified by Park et al. to have defects in the sp2 hybridized carbon molecules of the graphene, featuring abnormal appearances of D mode frequencies observed by Raman Spectroscopy.

D Mode Association with Graphene
D modes, also called D bands or D peaks, are vibrational frequencies observed at around 1350 cm-1 using Raman spectroscopy that are associated with disorders or defects present in the sp2 hybridized carbon graphene structures. These D modes are used to measure the quality of the nanotubes by comparing the relatively low intensity of it to that of the G band, or graphite band, which is observed to be around 1582 cm-1.

As for the single-walled carbon nanotubes, the D modes were observed to appear at the edges of the graphene as opposed to the center of the graphene. This suggests that the D modes of graphene are associated with edge defects of graphene where well-crystalized single-walled carbon nanotubes should not have D mode appearances due to their relatively negligible edge areas compared to their atomic thickness.

Park et al. were also able to identify that the helical structures were noticeable when SWNT samples were irradiated by High-Resolution Transmission Electron Microscopy (HRTEM) at 200kV and also when SWNTs were exposed to electron beams at 137 pA/cm2 for 6 minutes. This in turn showed that the edges of the graphene helixes are unstable defects which allow the helical SWNTs to be prone to energy.

Helical Structure Properties
The helical structure of the SWNTs was observed to have differing strain energies and electronic band gaps from the conventional cylindrical structure.

Electronic Structure Properties
The previously conceived structure of SWNTs was based on the turbostratic graphene sheet stacking of multi-wall carbon nanotubes (MWNTs), in which there are random relative positions and rotations on the X, Y, and Z-axes.

It has been discovered by Lee, et al., that MWNTs are made up of graphene helices with widths of approximately 5 nm. This helical structure of MWNTs was due to how the AA-stacked graphene ribbons grew helically, in contrast to the previously proposed circular growth at the nanotube edges.

It's also noted that the armchair and zigzag helical graphene ribbons have strain energies only about a quarter that of their seamless cylindrical counterparts, thus it is suggested that the growth of the seamless cylindrical SWNTs are "energetically prohibitive and uncompetitive" compared to the helical structures which was calculated based on the respective electronic band structures. The strain energies for all of the compared helical and cylindrical armchair and zigzag structures, however, were based on how small their tubular radii were, with larger radii having lower strain energies.

Electronic and Carrier Properties of N=6, 7, & 8 Prototype Armchair Graphene Nanoribbons (AGNRs)
Thakur et al. reported that helical twists of graphene nanoribbons have profound effects on the effective mass and carrier mobilities compared to that of stretched planar nanoribbons. Prototype N=6 Hydrogen-terminated armchair graphene nanoribbons (HAGNRs) and Fluorine-terminated armchair graphene nanoribbons (FAGNRs) were reported to have the highest electronic band-gaps of 1.14eV and 1.41eV out of the tested prototypes which allows it to act as a semiconductor. Upon increased torsional strain in the N=6 HAGNR, the electronic band gap showed drastically increased results, but the N=6 FAGNR, the band gap did not change as much.

Much like previous findings as more torsional strain was applied, the N=8 H and F AGNRs electronic band-gap increased. While this allows the N=6 & N=8 to be categorized together, the N=6 AGNRs still have larger band-gap values due to the quantum size of it compared to the N=8 AGNRs.

On the other hand, the N=7 H and F AGNRs showed decrease in electronic band gaps as more torsional strain was applied, thus having a negative slope relation between the band-gap to the intensity of the helical twist. This result` categorizes the N=7 AGNRs separately from the N=6 and N=8 AGNRs.

Tensile Properties of Helical Structure
Helical SWNTs have a consistently observed tensile strength of 30-45 GPa, and yield strains of 5.3-5.8%, which is approximately 3-4 times more of a deviation than that of the seamless cylindrical SWNT structures.

Jhon et al. proposed that this change in deviation is either caused by SWNTs having weak anchoring to tensile devices or the mechanical deterioration in SWNTs caused by the Stone-Thrower-Wales (STW) defects created in the synthesis of SWNTs.

It was ruled out that SWNTs are able to be broken repeatedly and that Jhon et al. "only consider the cases of robust end-point connections in evaluating the tensile strength." This is also supported due to how different end-point adhesions of SWNTs share similar maximum tensile strains within 5% deviation of each other. It was also ruled out that the tensile strength deterioration that is caused by any defect is less severe than what is observed. It is to be noted that areas of vacancy must exist in SWNTs in order to obtain the same experimental data found by Zhang et al.

Based on the results from Lee et al., it is known that there are traces of spiral growth associated with the helical defects on SWNTs from their results with HRTEM and AFM, which they hypothesized as the reason as to how various SWNTs have consistently similar tensile properties.

Jhon et al. reported that the atomic details of the helical defects based on the screw-dislocation-like (SDL) growth model and the effects of helical defects on SWNTs are associated with the consistently similar tensile strength and yield strains of 3 different SWNTs: a pristine SWNT synthesized by restoring tear damages (denoted SWNT-PR), a topologically-staggered nodelike based helical defect SWNT (denoted SWNT-HL1), and a topologically-coherent nodelike based helical defect SWNT (denoted SWNT-HL2). It was concluded that the tensile strengths and yield strains of SWNT-PR, SWNT-HL1, and SWNT-HL2, are ~117.1 GPa and ~17.6%, ~35.9 GPa and ~4.7%, and ~35.9 GPa and ~4.9% respectively. Even though the results for SWNT-PR are significantly larger than that of SWNT-HL1 and SWNT-HL2, all of the results support the values obtained by Yu et al. (30 GPa and 5.3%) and Walters et al. (45 GPa and 5.8%).

The varying tensile strengths of the observed SWNTs were reported to be determined only by type of the defects and not the density of the defect.