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Nanosleeves: Morphology transitions of infilled carbon nanotubes

Fan Xu's picture

Morphology instability of substrate-supported carbon atomic layers can be harnessed to modulate physical properties and functions, which has drawn interesting attention. Curvature would be a critical factor affecting surface morphology and its stability characteristics. Infilled carbon nanotubes, that is to say carbon monolayers with curved geometry and infilled substrates, namely nanosleeves, widely exist in the literature and have many potential applications. Here, we reveal an unprecedented rich post-buckling phenomenon of nanosleeves, which involves multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The nanosleeve initially buckles into periodic axisymmetric wrinkles at the threshold and then evolves into a localized mode with one single ridge growing upon further axial compression. Finally, the amplitude of the ridge reaches a limit and the symmetry is broken with the ridge sagging into a recumbent fold that can be axisymmetric or non-axisymmetric. Such rich morphology transition is first revealed by molecular dynamics simulation, and then theoretically predicted by a finite strain core-shell continuum model. An analytical solution of the critical threshold of primary smooth-wrinkle transition is further provided, which explicitly indicates the crucial role played by curvature and van der Waals interaction between the carbon monolayers and infilled metals. Such multiple-bifurcation scenario and curvature-determined mechanism are found to be inherently universal.

J. Mech. Phys. Solids,


Zhaohe Dai's picture

Hi Fan,

Beautiful work! Thanks for sharing. Just a quick question that I was curious about but didn't think of carefully yet: Does the substrate curvature play a role in modifying the vdW-type Winkler foundation in your work? The length scale should be important in the sense that the sheet cannot effectively 'feel' the curvature if its radius is too large. But don't know how this length scale explicitly appears in the foundation model and how it is compared to those in the system you studied. 


Fan Xu's picture

Hi Zhaohe,

Good point! We tried to calculate the integration of atom-atom interaction between a cylinderical monolayer and a cylindrical core, but it is in fact the so-called elliptic integral. This kind of integral cannot be written in an explicit expression in terms of elementary functions (Conrad, Impossibility theorems for elementary integration, Academy Colloquium Series, 2005; Rosenlicht, Integration in Finite Terms, Am. Math. Mon. 79, 963-972, 1972). Hence, we consider the interaction between an atomic layer and a semi-infinite substrate instead. Similar strategy works well in macroscopic models of both cylindrical and spherical film/substrate systems. For modest curvature, such Winkler-type foundation (only in function of w) describes the interaction between the surface layer and an infinite thick substrate, while Zhao et al., J. Mech. Phys. Solids 73, 212, 2014; Xu and Potier-Ferry, J. Mech. Phys. Solids 94, 68, 2016 theoretically and numerically showed that this assumption works well for shallow curved substrates, as well as doubly curved spherical substrate (Xu et al., J. Mech. Phys. Solids 137, 103892, 2020; Zhao et al., J. Mech. Phys. Solids 135, 103798, 2020). In the present work, results obtained from our continuum model agree with MD simulations, and the radius effect of the substrate considered in our cases appears insignificant.



L. Roy Xu's picture


This is an important topic.


Fan Xu's picture

Hi Roy,

Many thanks for your interest!



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