Nanostructures

Using the more advanced features of Solidworks we can design models for known fascinating structures such as Buckminsterfullerene C60, Graphene, Carbon Nanotube, COVID, RNA and DNA.

What are these nanostructures ?

Nano-structures are structures at the molecular scale of generally carbon atoms, but can be of other types of atoms as well. For example, graphene, the compound of carbon found in pencils, is actually a sheet of carbon atoms in a hexagonal matrix with atoms at each vertex. Such structures are often used in building materials, such as those for airplanes, due to their tensile strength. Other nano-structures include DNA, RNA, and other biological macromolecules, such as viruses and proteins.

Bucky Ball (Buckminsterfullerene C60)

This nano-structure resembles a soccer ball in terms of its layout of vertices, being a mix of 12 pentagons and 20 hexagons, corresponding to the vertices and faces of an icosahedron. To see that, we can think of cutting each of the icosahedron’s vertices with a plane — this gives the pentagons. The hexagons come from the faces — three sides from the existing ones of the triangles, and three new sides, from the freshly-cut pentagons. This structure is commonly found in soot. The compound is very stable, withstanding high pressure and temperature. It also forms a purple solution when dissolved in hydrocarbon solutions.

The Bucky Ball itself is a complex but fairly regular lattice of hexagons and pentagons, so one way we can build it is by first constructing a regular icosahedron and then framing the pentagons on the vertices and hexagons on the faces. The main operations used are revolves and circular patterns, because a regular icosahedron has many rotational symmetries.

To create our regular icosahedron, we look at its geometry. We notice that every vertex has a pentagonal pyramid centered at that vertex, with equilateral triangles as its lateral faces. Moreover, these pyramids are all identical but rotated copies.

For instance, consider the pyramid with blue, magenta, yellow, red and black faces, and the axis perpendicular to the black face, in its center.

A 120-degree rotation of it around this axis leaves the black triangle unchanged, and sends the blue to the red, the red to the light green, the light green to the blue. Moreover, it sends the magenta to the orange, and the yellow to the dark green. Therefore, the initial pyramid is sent to the black, red, orange, dark and light green one.

Thus in SolidWorks we can create only one pyramid body, and then use appropriate circular patterns to copy-rotate it 120 degrees around axes perpendicular to faces and passing through their centers, to complete the icosahedron.

Creating one pyramid

To create a pyramid body, we can use the loft operation, from the base sketch, through a 3D sketch containing the sides and the summit vertex. To do this, we need to create these two sketches. For the base, we pick a plane, e.g. the top one, and sketch a regular pentagon centered on the origin.

For the sides and summit, we create a 3D sketch, where we first draw a line of arbitrary length along the vertical axis, perpendicular to the base plane. Then we draw the sides, connecting the vertices of the pentagon base to the summit. Once that is finished, we add relations between the segments from vertex to peak to make them equal to each other and to one of the sides of the pentagon. We can pick any side, since it is a regular pentagon. Finally, now that we have our two sketches — the base one and the 3D one — we can do the loft, by selecting them, to create a regular pentagonal pyramid.

Replicating the pyramid for all the icosahedron vertices

Next, we want use circular patterns to copy this pyramid around, for the rest of the icosahedron. We select the loft, and we click on one face to give the rotation axis perpendicular to it: SolidWorks understands the rotation direction. Then we select “Instance spacing” and put 120 degrees, and three instances. The yellow wireframe lines indicate the result of the operation, and the light-blue highlighted face is the one around which the rotation is taking place. A total of three instances comprises the initial one and two copies. Once we validate, a whole section of the icosahedron appears. Then we can continue the same kind of operation, around other faces, until the icosahedron is complete.

We can also obtain the same icosahedron with other successions of circular patterns, such as those around diametral axes, and using also a mirror-copy operation about a central plane.

This is so because we can notice that an icosahedron has “two pyramidal caps” (which are mirrored), and a “band” of ten “alternating” triangles, which can be obtained from the rotation of one of the side-pyramids, by angles of 72 degrees. The value of 72 comes from 360/5, being the smallest rotation sending a regular pentagon onto itself (and the pentagons are the bases of the pyramids).

To do that in SolidWorks, we need to create axes which are perpendicular to the pentagonal bases of at least two pyramids, and intersect them, using reference geometry, to obtain the center C of the icosahedron we are building. This can be done right after the first rotation. Then we build a plane P perpendicular to one of these axes, e.g. axis A, and passing through C. We select a pyramid with base parallel to P, and mirror-copy it with respect to P. This gives the other “cap” of the icosahedron. Finally, we rotate-copy with circular patterns, the side pyramids about the axis A.

Building the pentagons and hexagons around the icosahedron

Since the regular icosahedron can be inscribed in a sphere, so are going to be the pentagons and hexagons around it, from the Bucky Ball. This means the vertices of these pentagons and hexagons (that is, the sites of the 60 carbon atoms) are all on a sphere with center C, the same as the one of the icosahedron. Thus they belong to some arcs with center C and passing also through vertices of the icosahedron. We can therefore take advantage of these properties and build them in SolidWorks, from arcs to polygons, gradually imposing the appropriate geometrical constraints.

So, in SolidWorks, we start by 3D sketching construction arcs from adjacent vertices, and constraining their centers to be the center C of the icosahedron.

This is achieved for instance by sketching the three-point arc from a vertex to another and through some random point and validating. Then we select together the now-highlighted center of the arc and the center C, and request them to coincide, by clicking on the ‘Merge’ button. Once we validate, the ‘Coincident’ relationship appears, and the arc is now on the sphere.

We use this method after we fix a vertex V and its five adjacent vertices V1, V2, V3, V4, V5, to 3D sketch the five corresponding arcs, from V to each of the five adjacent. We also 3D sketch one more arc, from V1 to V2, the same way. Now we are ready for the pentagon and hexagon. We 3D sketch a pentagon with its vertices somewhere on the arcs, and constrain its sides to be equal. Finally, after building one more arc from two vertices adjacent to each other and to e.g. V1 and V2, we can also build the hexagon the same way, and also constrain its sides to be equal. All this is also going to ensure that the hexagon and the pentagon have the same side. Since these polygons cover the buckyball, before replicate them all around the sphere we only need to create the atom and bonds representations, as spheres connected with cylinders

Atom sites and bonds as spheres and cylinders

The atom sites are the pentagon and hexagon vertices and their bonds the sides of these polygons. Therefore this is where we center the spheres and cylinders. We can achieve this by sketching an arc and rectangle in the plane containing the side common to the pentagon and hexagon and the center of the icosahedron (and circumscribed sphere), and then making a revolved boss around them.

Finally, before replicating everything around the sphere in a similar way to the icosahedron build process, we add one more cylinder, adjacent to the sphere.

This can be done with a simple extrusion, of a circle sketched in plane (7) perpendicular to plane (6) which is defined to contain the adjacent hexagon side and the center of the icosahedron.

Building the whole buckyball using circular patterns

Now we are ready to use circular patterns around various axes of the icosahedron, to replicate the spheres and cylinders for the whole structure. First we do it around the axis through the icosahedron vertex centered underneath the sketched pentagon.

Then we replicate this newly built structure around another axis, through a pair of opposite icosahedron vertices. Finally, we repeat this two more times, to obtain the complete buckyball.

We can see how the pentagons correspond to the icosahedron vertices and are centered on them, while the hexagons correspond to the icosahedron faces, also centered on them. We can of course also look at the whole structure by itself, without the internal icosahedron.

Graphene

This nano-structure is probably the most well known of the three structures modeled here. It is a planar tessellation of hexagons with carbon atoms at vertices. It has very weak connections between planes, causing it to slide off easily, the phenomenon used in pencils. However, within a plane, the bonds are strong, resulting in a very high tensile strength of ~130 GPa and Young’s modulus of ~1TPa.

Since the graphene sheet is made of similarly bonded atoms in hexagonal structures, we can reuse the basic graphic building blocks — the sphere for the atom site and the cylinder for the bond. We need to build one such hexagon, and then we can replicate it for instance with circular patterns around an axis perpendicular to its plane.

We start by sketching a hexagon in the top plane and then we sketch the circle and rectangle to revolve, in order to create the sphere and cylinder for the atom site and its bond.

Then, using a circular pattern, we replicate this around the axis perpendicular to the hexagonal plane and passing through its center, and then we replicate the whole construction around with more circular patterns.

Carbon Nanotube

This nano-structure is akin to a sheet of graphene coiled into a cylinder. They are semiconductors, meaning that they conduct electricity under specific conditions but not otherwise. Similar to graphene, they have a high tensile strength and thermal conductivity. Applications include acting as scaffolding for bone growth as well as commercial uses in bicycle parts.

Here the challenge is to create the hexagonal tiling on a large cylindrical wall. We can do that in a different way, to facilitate the actual 3D printing process. We first build a solid cylinder, and then we use extrusion cuts with a hexagonal pattern, which we then rotate with a circular pattern to create a first ring. Afterwards, we can simply use a linear pattern to replicate the ring cut along the whole cylinder.

SARS-CoV causing COVID-19

The coronavirus, which negatively impacted our life on the whole planet on an unprecedented scale, has a structure composed of a spherical shell containing its genetic code, from which protein spikes project outwards. These spikes allow the virus to bind to organisms cells to enter them and inject its code for replication. It can be modeled as a sphere with its so-called spikes. The spikes can be modeled as truncated cones with a small sphere at their tip. Along similar lines to the sphere and cylinder model for carbon atom sites and their bonds, after building the main viral spherical body, I sketched a section of the cone, completed with arcs, and then I revolved them around an axis passing through the center of the sphere, finishing with a base fillet.

Then, several circular patterns can be used to replicate the spike around, ending the construction with a final mirror.

RNA and DNA

These are the fundamental genetic code structures, which contain the information necessary for living organisms to build themselves and to function properly. The encoding is done through specific chemical compounds called nitrogenous bases, acting as letters (Adenine, Guanine, Cytosine and Thymine for DNA, and Adenine, Guanine, Cytosine and Uracil for RNA), arranged on a specific helicoidal backbone made of sugar-phosphates. The main feature of these important molecules are the helicoidal backbone and the stair-ladder-like nucleotides. The DNA comprises two helicoidal backbones starting 180 degrees apart, while RNA has only one. When constructing the bodies in SolidWorks, if we keep them as two separate entities, the RNA can be obtained by simply masking the other half of the DNA. Thus, only the DNA construction needs to be described in detail.

Each helicoidal backbone can be built from the SolidWorks helix construction, along which we use the SolidWorks sweep operation. To build the helix, we first sketch a circle in the top plane, and then we simply request a helix, for instance of 150mm pitch, with two revolutions, one of them starting precisely from 360 degrees.

This way we ensure that t the height equal to its pitch, an axis parallel to the top plane and thus perpendicular to the front plane, and passing through the central (vertical) axis of the helix (contained in the front plane) would intersect the helix.

Therefore, a cylinder extruded from a small circle sketched on the front plane, along this horizontal axis, would end up being perpendicular to the helicoidal backbone in that point, exactly like the nucleotides. The other helix, of the same pitch and starting from 180 degrees from the same base circle, would have the same property at the pitch height.

This is important, because the horizontal cylinders need to line up and connect the two helicoidal backbones, since nucleotides also pair up in a specific way. Thus, also to allow for the RNA to be separated out from the DNA, the horizontal cylinders are to be extruded in pairs, from the front plane towards each helix, but without merging the two bodies.

Finally, the curve-driven pattern replicating the horizontal cylinders while keeping them intersecting the backbones at 90 degrees can be built on the helicoidal curve. For the orientation, we first construct a helicoidal surface sweep, from a simple horizontal segment from the start of the vertical helix, following the helix. Then the pattern is made tangent to the helix, following the edge of the surface sweep and normal to it, to have the cylinders twist around the helicoidal backbone, finalizing the whole structure.

Printing the models

Like most models without a clear base, much support is needed for the Bucky Ball. In such cases, the printing time is exponential with respect to size, so we diminish the size to 40% yielding an 8.5 hour printing time. The height of the ball is approximately 10 cm, so it would be something to hold in the average hand.

The Carbon Nanotube is significantly easier to print since it can simply stand on the cylinder base like so. However, the model’s dimensions are too small so they need to be resized at ~300%. The cylinder’s radius is ~40 mm and it is 152 cm tall.

The DNA and RNA are best printed vertically, but they require a lot of support. They are each ~18cm tall. Their scaling is about 60% for both. Printing time is 7 hours.

The Graphene sheet is likely the simplest nanostructure, though it requires using the 3mf file. Select all the pieces with ^A or ⌘A, rotate it to be horizontal, and then scale it to be 15%. The printing time is ~5 hours, and the size is 17×15 cm with a height of ~0.5cm.

The Coronavirus can be printed very simply in one color, however in 2 colors, alternating, it looks very interesting. There are two ways to do this: one is to export the Solidworks part as a 3mf and color each part by hand in the slicer. Another is to hide the bodies that do not have the target color and export as stl. Then do the opposite and again export as stl. In the slicer then we can bring the models together and choose the move option, selecting everyone and clicking “Align Together”.