TY - JOUR

T1 - Mechanical buckling of single-walled carbon nanotubes

T2 - Atomistic simulations

AU - Chang, I. Ling

AU - Chiang, Bing Chen

N1 - Funding Information:
This research work was supported by the National Science Council of Taiwan under Grant Nos. NSC97-2221-E-194-015 and NSC98-2221-E-194-012-MY2. The support of AFOSR under Contract No. FA2386-09-1-4152 AOARD 094152 is also acknowledged. Table I. The radii and lengths of the modeled armchair CNTs. ( m , n ) (5,5) (8,8) (10,10) Radius (Å) 3.39 5.424 6.78 Length (Å)/SR 7.38 ∕ 2.18 12.3 ∕ 2.27 14.76 ∕ 2.18 12.30 ∕ 3.63 19.68 ∕ 3.63 24.595 ∕ 3.63 36.89 ∕ 10.88 59.03 ∕ 10.88 73.79 ∕ 10.88 61.49 ∕ 18.14 98.38 ∕ 18.14 122.98 ∕ 18.14 86.08 ∕ 25.39 137.73 ∕ 25.39 172.165 ∕ 25.39 147.57 ∕ 43.53 236.11 ∕ 43.53 295.14 ∕ 43.53 Table II. The radii and lengths of the modeled zigzag CNTs. ( m , n ) (9,0) (14,0) (17,0) Radius (Å) 3.523 5.48 6.655 Length (Å)/SR 8.52 ∕ 2.42 12.78 ∕ 2.33 17.04 ∕ 2.56 12.78 ∕ 3.63 21.3 ∕ 3.89 25.56 ∕ 3.84 38.34 ∕ 10.88 59.64 ∕ 10.88 72.42 ∕ 10.88 63.9 ∕ 18.14 97.98 ∕ 17.88 119.28 ∕ 17.92 89.46 ∕ 25.39 140.58 ∕ 25.65 170.4 ∕ 25.60 153.36 ∕ 43.53 238.56 ∕ 43.53 289.68 ∕ 43.53 Table III. The radii and lengths of the modeled zigzag CNTs. ( m , n ) (6,4) (9,6) (12,8) Radius (Å) 3.413 5.119 6.825 Length (Å)/SR 18.569 ∕ 5.44 18.569 ∕ 3.62 18.569 ∕ 2.72 37.138 ∕ 10.88 55.707 ∕ 10.88 74.276 ∕ 10.88 55.707 ∕ 16.32 92.845 ∕ 18.14 129.982 ∕ 18.92 92.845 ∕ 27.20 129.982 ∕ 25.39 167.712 ∕ 24.57 148.55 ∕ 43.52 222.83 ∕ 43.53 297.10 ∕ 43.53 FIG. 1. The relation between the system energies and compressive strains for (5,5) CNT with length of 7.38 Å . FIG. 2. The buckled shapes of CNTs. (a) shell wall, (b) column, and (c) bump on the wall. FIG. 3. The relationship between the buckling strain and slenderness ratio for CNTs with different chiralities. (a) armchair, (b) zigzag, and (c) chiral. (The solid symbols indicate column buckling and the hollow ones indicate shell wall buckling.) FIG. 4. The comparisons between the continuum predictions and molecular simulation results for CNTs with similar radii. (a) 3.44 Å , (b) 5.34 Å , and (c) 6.75 Å . (Dashed lines: continuum prediction of shell-like buckling; solid lines: prediction based on the Euler–Bernoulli beam theory.)

PY - 2009

Y1 - 2009

N2 - Various geometric sizes and helical types (i.e., armchair, zigzag, and chiral) of single-walled carbon nanotubes (CNTs) are considered in molecular dynamics simulations in order to systematically examine the length-to-radius ratio and chirality effects on the buckling mechanism. The buckling strain is getting smaller as the CNT becomes slender for most nanotubes, which implies that the slender nanotubes have lower buckling resistance regardless of the radius of the CNTs. The applicability of the continuum buckling theory, which has been well developed for thin tubes, on predicting the buckling strain of the CNT is also examined. In general, the corresponding buckling strain and buckling type predicted by the continuum buckling theory could agree reasonably well with simulation results except at the transition region due to the competition of two buckling mechanisms.

AB - Various geometric sizes and helical types (i.e., armchair, zigzag, and chiral) of single-walled carbon nanotubes (CNTs) are considered in molecular dynamics simulations in order to systematically examine the length-to-radius ratio and chirality effects on the buckling mechanism. The buckling strain is getting smaller as the CNT becomes slender for most nanotubes, which implies that the slender nanotubes have lower buckling resistance regardless of the radius of the CNTs. The applicability of the continuum buckling theory, which has been well developed for thin tubes, on predicting the buckling strain of the CNT is also examined. In general, the corresponding buckling strain and buckling type predicted by the continuum buckling theory could agree reasonably well with simulation results except at the transition region due to the competition of two buckling mechanisms.

UR - http://www.scopus.com/inward/record.url?scp=72449208520&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72449208520&partnerID=8YFLogxK

U2 - 10.1063/1.3260239

DO - 10.1063/1.3260239

M3 - Article

AN - SCOPUS:72449208520

VL - 106

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 11

M1 - 114313

ER -