## 2 Results and Discussion
### Formation and Finishing of the Nanotube  
The way in which rolling up takes place, is represented graphically in Figure 5, wherein coordinates defined in the plane become coordinates of a cylinder (the NT). Coordinates of point B in the flat sheet are transformed to coordinates on the cylinder by means of the arc length equation. The NT notation used in this work is formed by the number of atoms along C side on Figure 5, and also the number of parallel layers (in relation to C side) which defines the NT length, numbered along A or D sides. In Figure 5 red lines define a graphene sheet giving a zigzag (C8)6 NT according to the explained notation.  
Figure 4: Schematic representation of parameters defining NT diameter and configuration.  
To accomplish the rolling up process the algorithm makes use of the following main classes:  
**Rectangular_Area:** This is a class that contains mainly 8 variables, 4 of them are points and the other 4 are straight lines. This class was created with the purpose of generating the information needed for cutting the selection area on the graphene sheet and then rolling up the selected area. Some methods included in this class are:  
* Rectangular_Area: Creates the rectangular area, on the base of two points for the height, and two points for the width, or on the base of four points of a rectangle.
* Contains: This method returns _true_ value if the point in consideration belongs to the selected area, or _false_ if it does not.
* Distances: Over each point (or atom) of the graphene sheet, it creates a perpendicular pair of straight lines (a cross) which are, in turn, perpendicular to the rectangle sides, and returns the distance of both traced lines to the respective sides; one of these values corresponds to the height of the atom in the cylinder, and the other distance corresponds to the rotation of the point during the rolling up.
* ToCircle: It changes Cartesian coordinates to circumference coordinates.  
**Straight:** This class simulates a straight line having the same value as a geometrical straight line, between the starting and the finishing points. Two of the most important methods are, \"create a parallel straight line\" and \"create a perpendicular straight line\".  
Figure 5: Schematic view representing the rolling up process.  
So, the width of the selected area represents the perimeter of the cylinder, and the length of the selected area is the height of the cylinder.  
Generation of a zipper, is represented in Figure 6, where a graphene sheet corresponding to a (3,3) armchair NT is modified by adding atoms such that pentagons are formed at both edges of the sheet previous to rolling it up.  
In Figure 7 is represented a (C13)10 zipper NT; this notation is used to represent 13 carbon atoms in a layer giving the NT width and 10 layers length, generated with MCAD and optimized at the level of MM+ forcefield using HyperChem software package [14]. A pattern of two condensed pentagons alternating with octagons is repeated along NT longitudinal axis.  
When two modified graphene sheets are matched together, and then rolled up as shown for zipper NT generation, a multiple zipper NT is obtained.  
In Figure 8 processes used to get the correct NT structures (including zipper NTs) after the graphene sheet rolling up step is carried out, are shown. In process 1, coordinates of atoms that are very near or that overlap to each other, are fused into single coordinates. In process 2, non-bonded  
Figure 6: Modification of the graphene sheet to generate a zipper NT.  
Figure 7: A zipper NT representation generated by MCAD.  
atoms that are located at a distance similar to a bond length become linked. In process 3 non-bonded atoms located at a distance highly different from a bond length, are deleted.