Graphene, rolling

Carbon nanotubes (CNTs) are sheets of graphene rolled into cylindrical tubes and exhibit high degree of hydrophobicity, curvature, and surface-area-to-volume ratios, making them as stationary phases for reversed-phase and affinity... 

There are two main types of CNTs, i.e., single-waUed carbon nanotubes (SWCNT) consisting of a single sheet of graphene rolled seamlessly to form a cylinder and multiwalled carbon nanotubes (MWCNT) consisting of an array of such cylinders formed concentrically and separated by 0.35 nm. 

Carbon nanotube research was greatly stimulated by the initial report of observation of carbon tubules of nanometer dimensions[l] and the subsequent report on the observation of conditions for the synthesis of large quantities of nanotubes[2,3]. Since these early reports, much work has been done, and the results show basically that carbon nanotubes behave like rolled-up cylinders of graphene sheets of bonded carbon atoms, except that the tubule diameters in some cases are small enough to exhibit the effects of one-dimensional (ID) periodicity. In this article, we review simple aspects of the symmetry of carbon nanotubules (both monolayer and multilayer) and comment on the significance of symmetry for the unique properties predicted for carbon nanotubes because of their ID periodicity. 

Fig. 2. By rolling up a graphene sheet (a single layer of ear-bon atoms from a 3D graphite erystal) as a cylinder and capping each end of the eyiinder with half of a fullerene molecule, a fullerene-derived tubule, one layer in thickness, is formed. Shown here is a schematic theoretical model for a single-wall carbon tubule with the tubule axis OB (see Fig. 1) normal to (a) the 6 = 30° direction (an armchair tubule), (b) the 6 = 0° direction (a zigzag tubule), and (c) a general direction B with 0 < 6 < 30° (a chiral tubule). The actual tubules shown in the figure correspond to (n,m) values of (a) (5,5), (b) (9,0), and (c) (10,5).

Following a standard notation[ 12,13], a cylindrical tubule can be described by the (L,M) couple of integers, as represented in Fig. 1. When the plane graphene sheet (Fig. 1) is rolled into a cylinder so that the equivalent points 0 and M of the graphene sheet are superimposed, a tubule labeled (L,M) is formed. L and M are the numbers of six membered rings separating 0 from L and L from M, respectively. Without loss of generality, it can be assumed that L>M. 

The detailed analysis of the way in which the overall and internal structure of PCNTs apparently arise is discussed elsewhere[20j. Here, we draw attention to some particularly interesting and unusual structures which occur in the body of the nanotubes. An expansion of the section of the central core which lies ca. 5 below the tip of the nanotube in Fig. 1 is shown in Fig. 2. Loop structures occur at points a-d and a -d in the walls in directly opposing pairs. This parallel behaviour must, on the basis of statistical arguments, be related and we interpret the patterns as evidence for a hemi-toroidal connection between the inner and outer adjacent concentric graphene tubes (i.e., turnovers similar to a rolled-over sock). That the loops, seen in the HRTEM, are evidence for very narrow single-walled closed-ended tubes trapped within the walls can be discounted, also on statistical grounds. 

An important question relating to the structure of nanotubes is Are nanotubes made of embedded closed tubes, like "Russian dolls," or are they composed of a single graphene layer which is spirally wound, like a roll of paper Ijima et al. [2] espouse the "Russian doll" model based on TEM work which shows that the same number of sheets appear on each side of the central channel. Dravid et al. [4], however, support a "paper roll" structural model for nanotubes. 

Carbon nanotubes (CNTs) were discovered in 1991 by Iijima [182] and since then they have attracted much attention in many research fields. CNTs can be described as tubular structures rolled up from a graphene sheet. Depending on the number of tubular walls CNTs can be classified as single-walled carbon nanotubes (S WCNTs)... 

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