Figure 1: Geometric structure of nanotubes

The discovery of carbon nanotubes in 1991, by the japanese researcher Sumio Iijima, during the study of fullerenes (C60) synthesis reveals a new cristalline form of carbon. These cylindric structures of carbon consist of a graphitic plane rolled into a tube having a nanometric diameter (10^-9 meter = 1 nanometer) and can be divided in two groups: single wall carbon nanotubes (C-SWNT) and multi-walls carbon nanotubes (C-MWNT).

Figure 2: Schematic of C-SWNT and C-MWNT

The amazing properties of carbon nanotubes have motivated an intense scientific research effort. Indeed, this material presents outstanding mechanical, electrical, thermal and chemical properties: 100 times stronger than steel, best field emission emitter, can maintain current density of more than 10⁹ A/cm², thermal conductivity comparable to that of diamond. Such properties could lead to the development of many applications as field emission device (flat screen displays), composite materials, conductive polymers, sensors,etc.

Figure 3: Carbon nanotubes pictures (left) C-SWNT deposit obtained with plasma torch, bundles diameter of 10-15 nm (right) C-MWNT on carbon paper, diameter of 20-100nm.

Present state of production techniques

The major obstacle to the development of these technological applications to a commercial scale is the poor yield of conventionnal production processes, (electrical arc, CVD, laser vaporization), the high production cost and also the lack of understanding of the nucleation of the C-SWNT and C-MWNT. Keeping in mind this problematic, Olivier Smiljanìc and professor Barry L. Stansfield, of the INRS-EMT (Energy, Materials and Telecommunication), developed a new synthesis process based on an atmospheric plasma torch.^[1,2] This process has the advantage to be continuous and also to be scalable to a commercial production.

Frédéric Larouche contribute to the process improvement by developing a recuperation system of the C-SWNT.

A new growth mechanism: the BMI model

We believe the comprehension of the carbon nanotubes growth mecanism is an unavoidable question for a fair control of the C-SWNT production. Several models have been proposed in the last few years to explain the growth of single-walled carbon nanotubes. They have succeeded in clarifying the role of the catalyst in the growth of nanotubes and the general scenario leading to their growth.

However, the nucleation process of the nanotubes at the surface of the catalyst is still a problem. The last models^[3,4] have suggested that an instability present at the surface of the catalyst (similar to those involved in solidification processes in crystal growth) could be responsible for this phenomenon. Since this hypothesis has been presenting some problems, we recently suggested a new idea, the BMI model.^[5]

In this new model, it is proposed that an hydrodynamical instability, -the Bénard-Marangoni instability- could be generated at the surface of the catalyst, explaining both the nucleation process and the bundle structure of single-walled carbon nanotubes observed in experiments. The segregation process of carbon towards the surface of the catalyst, invoked in the previous models to explain the growth in a general way, would be responsible for the formation of a nanometric liquid layer, supersaturated in carbon, at the surface of the catalyst. Then, the conditions present in the synthesis of the nanotubes could allow the instability to be generated in this layer in order to form a pattern of hexagonal convection cells, which would be responsible for the collective growth of the nanotubes, one nanotube per cell.

Figure 4: Growth of a nanotube bundle within an hexagonal pattern of convection cells generated by a Bénard-Marangoni instability

Our aim is to reinforce this hypothesis by developping the mathematical background behind the model. First, we proceeded to a linear stability analysis of the flow at the surface of the catalyst to determine if the Bénard-Marangoni instability (solutal type) could be generated in the conditions of synthesis, this for a plane and spherical geometry. Then, we have done a nonlinear stability analysis of the flow in order to determine if a pattern of hexagonal convection cells was favored in these conditions (in the same geometries). These analyses have revealed themselves to be clearly positive from a theoritical point of view.^[6] Numerical simulations could be done to investigate further this hypothesis.

Literature

[1] O. Smiljanìc, T. Dellero, A. Serventi, G. Lebrun, B.L. Stansfield, J.-P. Dodelet, M. Trudeau and S. Désilets, Growth of carbon nanotubes on Ohmically heated carbon paper, Chem. Phys. Lett. 342 (2001), 503-509. (pdf)

[2] O. Smiljanìc, B.L. Stansfield, J.-P. Dodelet, A. Serventi and S. Désilets, Gas-phase synthesis of SWNT by an atmospheric pressure plasma jet, Chem. Phys. Lett. 356 (2002), 189-193. (pdf)

[3] J. Gavillet et al., Microscopic mechanisms for the catalyst assisted growth of single-wall carbon nanotubes, Carbon 40 (2002), 1649-1663.

[4] J. Gavillet et al., Nucleation and growth of single-walled nanotubes: the role of metallic catalysts, J. Nanosci. Nanotech. 4 (2004), 346-359.

[5] F. Larouche, O. Smiljanìc, X. Sun and B.L. Stansfield, Solutal Bénard-Marangoni instability as a growth mechanism for single-walled carbon nanotubes, Carbon 43 (2005), 986-993. (abstract) (pdf)

[6] F. Larouche, J. Duquette, L. Cortelezzi, B.L. Stansfield and N. Nigam, Nucleation and growth of bundles of single-wall carbon nanotubes (C-SWNTs): the Bénard-Marangoni Instability (BMI) model, Preprint at LANL. (pdf)

Authors: Frédéric Larouche et Jonathan Duquette