Multiple radial corrugations in multiwalled carbon nanotubes under pressure

Abstract

Abstract. Radial elastic corrugation of multi-walled carbon nanotubes under hydrostatic pressure is demonstrated by using the continuum elastic theory. Various corrugation patterns are observed under several GPa, wherein the stable cross-sectional shape depends on the innermost tube diameter D and the total number N of concentric walls. A phase diagram is established to obtain the requisite values of D and N for a desired corrugation pattern among choices. In all corrugation patterns, the cylindrical symmetry of the innermost tube is maintained even under high external pressures.

Diverse corrugation pattern in radially shrinking carbon nanotubes

“…͑1͒ is the negative of the work done by p during cross-sectional deformation. It can be proved that 21 all the three terms are functions of u i ͑p , ͒ and the circumferential displacement v i ͑p , ͒ of the ith wall under p.…”

“…20 This scenario, however, fails in the case of multiwalled nanotubes ͑MWNTs͒. It has been shown that MWNTs consisting of several tens of concentric walls undergo a novel crosssectional deformation, called radial corrugation, 21 in which the outer walls exhibit wavy structures along the circumferential direction. The radial corrugation originates from the multilayered nature, i.e., the competing effects between the mechanical instability of outer walls with large radii and the radial rigidity of inner walls with small radii.…”

Thin-shell theory based analysis of radially pressurized multiwall carbon nanotubes

“…The solution (7) represents a wavy structure of a MWNT's cross-section, called the radial corrugation with a mode index n. The integer n indicates the wave number of the corrugated walls, being uniquely determined by the one-to-one relation between n and p c [34]. We will find below that n depends systematically on N and the innermost tube diameter D ≡ r 1 as presented in Fig.…”

“…The stable cross-sections of MWNTs under p minimize the mechanical energy U of the whole system that is described by [34] …”

“…The contrast in the radial rigidity between the outermost walls and the innermost ones triggers a non-trivial cross-sectional deformation observed in radially pressurized MWNTs. In fact, the linearized buckling analysis leads to the conclusion that immediately above a critical pressure p c , the circular cross section of MWNTs becomes radially deformed as described by [34] …”