Paper Snowflakes to Model Flat Symmetrical Molecules

Co-Authored by Dean J. Campbell*, Kaitlyn Walls*, and Carley Steres*

*Bradley University, Peoria, Illinois

Paper can be folded and cut, and then unfolded to produce a variety of flat symmetrical patterns. Many people have used this technique to make decorations like paper snowflakes, but this approach has also been used to make models of molecule-scale structures.¹ Here, instructions are provided to build models of chemical structures with varying degrees of complexity and symmetry.

The paper models might be used for a variety of situations. A high school teacher colleague has noted that these sorts of activities could be useful for filling in small gaps in class, for example, as a semester is wrapping up. The templates contain a bit of information about the species being modeled, such as name and chemical formula. The various chemistry topics that could be associated with the models are scalable in the sense that not all of the structures need to be made, and symmetry concepts associated with the models can be covered with variable depth. Students could be assigned one of the chemical species to explore further with respect to reactivity, uses, and toxicity. The Supporting Information contains the PowerPoint drawn templates that can be printed onto paper, which can then be folded, cut, and opened to produce several molecular models. There is a QR code on each template linked to a video that shows how to build the paper model.

All of these paper models contain symmetry elements such as reflection planes and axes of rotation. For a reflection plane, the paper structure on one side of the plane is the mirror image or reflection of the paper structure on the other side of the plane. A rotation axis is denoted C_n, where rotating the paper structure about the axis by 360°/n produces the same structure.² Structures with a C₂ axis will have the identical structure after rotation about the axis by 360°/2 = 180°. Structures with a C₆ axis will have the identical structure after rotation about the axis by a 360°/6 = 60°. Figure 1, from Reference 3, shows folded paper structures, where the number of reflection planes in the structure is given by the number symbolically represented in the structure itself. For example, the number “5” can be seen in the paper structure with the five mirror planes in the top right corner of the figure. That particular structure also has a C₅ axis perpendicular to the sheet of paper. The structures in Figure 1 also show C₂ through C₁₂ axes.³

Figure 1. Folded paper structures featuring (TOP) one through ten mirror planes, (BOTTOM LEFT) eleven mirror planes, and (BOTTOM RIGHT) twelve mirror planes. Photographs from Reference 3.

 

The structures in Figure 1 all have what is referred to as D_nh symmetry, where there is a main vertical C_n axis perpendicular to a horizontal reflection plane. There are also n vertical reflection planes that contain the vertical C_n axis AND C₂ axes that are in the horizontal reflection plane (). There are also n vertical reflection planes () that contain the vertical C_n axis AND C₂ axes that are in the horizontal reflection plane. An example of a macroscopic structure with D_6h symmetry is a typical water ice snowflake, with six “sides”.⁴ (Sadly, many people represent snowflakes incorrectly with four sides and D_4h symmetry.) In the folded paper structures, the sheet of paper is in the horizontal reflection plane, and the creases in the paper from folding and unfolding the structure can correspond to the C₂ axes of rotation and vertical reflection planes. Figure 2 shows a paper structure which has D_6h symmetry and is a model of a portion of the sheet-like carbon structure graphene. Symmetry elements are represented by LEGO bricks. The blue bricks represent the vertical reflection planes, the baseplate represents a horizontal reflection plane, the yellow bricks represent the C₆ axis, and the red bricks represent C₂ axes. Video 1 shows how the paper model is constructed by folding and cutting the paper template in the Supporting Information. The template itself contains a QR code linked to this folding video.

Figure 2. Symmetry elements represented by LEGO brick associated with a paper model of a portion of the structure of graphene. The blue bricks and baseplate represent reflection planes, the yellow bricks represent the C₆ axis, and the red bricks represent C₂ axes.

 

Video 1. Folding and cutting the paper model of graphene.  ChemDemos YouTube Channel (accessed 2/20/2022)

 

The graphene paper model shown in Figure 2 potentially represents only a small portion of a much larger sheet of carbon atoms. Regardless of sheet size, all of the carbon atoms in graphene are arranged in adjacent six-carbon rings and are each connected to three other carbon atoms. Carbon atoms tend to form four bonds in neutral structures, but this model shows a delocalized structure that does not distinguish between single bonds, double bonds, or other bond orders. The model merely shows connections between the sp² hybridized carbon atoms. Because these carbon sheets are only one atom thick, graphene has great potential to be a high tech material. It is electrically and thermally conductive. It is nearly transparent, impervious to even small atoms, and very strong.⁵ The specific 24-carbon graphene structure modeled by the paper structure is thought to have been observed in space.⁶ At a down-to-earth level, graphite is comprised of stacked sheets of graphene. These sheets can slide past each other, enabling graphite to be used as a lubricant and to be used in pencils. This can be readily demonstrated with the models by placing one paper sheet over the other and sliding it back and forth.¹

Other chemical structures contain adjacent six-carbon rings. These include polycyclic aromatic hydrocarbons (PAHs), which contain other atoms such as hydrogen attached to the carbon rings. PAHs are commonly found as a product of burned fossil fuels. Their emissions can be found naturally, such as a forest fire, or by human activity, such as industrial use of crude oil and grilling meat.⁷ Many humans are exposed to PAHs through tobacco smoke. Long term exposure to PAHs can produce effects that range from skin inflammation to eye, kidney, and liver damage to cancer. PAHs can be found in aquatic, terrestrial, and atmospheric environments.⁸ Scientists have experimented with PAHs, which are naturally found in space, mixed with very cold water ice to try to mimic conditions that comets experience when moving towards the sun. As the mixture warmed, crystalline ice formed at its surface, expelling some of the PAHs and creating a sort of icy crust with the PAHs on top. The findings suggest that some comets resemble deep-fried ice cream, as both have a crunchy outside with a cold, porous interior.⁹ PAHs have also been found in meteorites.¹⁰

Although the paper model of graphene only represents rings of carbon atoms, the carbon skeleton of PAHs can look very similar to this. If the particular structure represented by the graphene paper model had a hydrogen atom on each edge carbon atom that was connected to only two other carbon atoms, the structure would represent the PAH called coronene. The graphene paper model can be cut down with a scissors to represent the carbon skeleton of other PAHs. This model can be used to produce ring structures to represent the carbon skeletons of the following carbon and hydrogen structures.¹¹

- 1 ring: benzene

- 2 rings: naphthalene

- 3 rings: anthracene, phenanthrene

- 4 rings: pyrene, benzo(e) pyrene, triphenylene, benzo(c) phenanthrene, benzophenalene

- 5 rings: perylene, pentahelicene, 2H-benzo(cd) pyrene

- 6 rings: benzo(ghi) perylene

 - 7 rings: coronene

Figure 3 shows the variety of PAH skeletons that can be produced from the graphene paper snowflake. Some of these structures have D_6h symmetry, some have other symmetry classifications.

Figure 3. PAH skeletons that can be produced from the graphene paper model.

 

A template in the Supporting Information can be used to produce a paper molecular model of copper(II) phthalocyanine, CuC₃₂H₁₆N₈. With a C₄ axis of rotation perpendicular to the flat plane of the molecule, this model has D_4h symmetry. Copper (II) phthalocyanine is commonly found as a bright blue pigment, used in a variety of artistic applications: paint, printing ink, emulsion paints, and more.¹² Another template in the Supporting Information can be used to produce a paper molecular model of copper (II) tetraphenylporphyrin, CuC₄₄H₂₈N₄. This paper model with a C₄ axis of rotation and D_4h symmetry appears flat when unfolded, but in reality the phenyl rings of this molecule can twist out of the molecular plane. This can also be shown in the model by adding twists to the paper structure. Porphyrin structures are sometimes found in biomolecules such as hemoglobin and chlorophyll.¹³ Figure 4 shows paper models of copper (II) phthalocyanine and copper (II) tetraphenylporphyrin. Templates for models with this level of complexity were produced by finding ball and stick images of the molecular structures in Google image searches and moving them to PowerPoint in order to guide placement of PowerPoint circles representing the atoms. Videos 2 and 3 show how the paper models are constructed by folding and cutting the paper templates in the Supporting Information. The templates themselves contain QR codes linked to these folding videos.

Figure 4. Paper models of copper(II) phthalocyanine and copper(II) tetraphenylporphyrin.

 

Video 2. Folding and cutting the paper model of copper(II) phthalocyanine.  ChemDemos YouTube Channel (accessed 2/20/2022)

 

Video 3. Folding and cutting the paper model of copper(II) tetraphenylporphyrin.  ChemDemos YouTube Channel (accessed 2/20/2022)

 

Other molecular symmetries can be shown with the paper snowflakes. A template in the Supporting Information can be used to produce a paper molecular model of 2,4,6-tris(4-pyridyl)-1,3,5-triazine, C₁₈H₁₂N₆. With a C₃ axis of rotation perpendicular to the flat plane of the molecule, this model has D_3h symmetry. This compound is used in some rather specialized applications, including metal-organic framework structures.¹⁴ Yet another template in the Supporting Information can be used to produce a paper molecular model of pentacyanocyclopentadienide ion, C₁₀N₅^-, with a C₅ axis of rotation perpendicular to the flat plane of the molecule. This model has D_5h symmetry. The ion has also been explored for use in metal-organic framework structures.¹⁵

The chemical species modeled by these paper structures vary in their hazards to humans and the environment. Safety Data sheets can provide some insights into the hazards that these species present, but finding clear, consistent safety information can be a challenge. An interesting chemical species from a green chemistry standpoint is the rhodizonate ion, C₆O₆^2-. This is a rather simple ion with D_6h symmetry, having a C₆ axis of rotation perpendicular to the flat plane of the molecule. Its template for this structure, which also resembles a simple benzene ring, is in the Supporting Information. The rhodizonate ion is formed by removing two hydrogen ions from rhodizonic acid, and the rhodizonic acid itself can be synthesized from inositol, a biologically available sugar.¹⁶ This is in alignment with principle 7 of the Twelve Principles of Green Chemistry: Use of Renewable Feedstocks.¹⁷ The rhodizonate ion can react with metals to form colorful compounds. The most common use for rhodizonate ions are in chemical tests for lead, but barium and other metal ions can be detected as well.¹⁸ Figure 5 shows paper models of 2,4,6-tris(4-pyridyl)-1,3,5-triazine, the pentacyanocyclopentadienide ion, and the rhodizonate ion. Videos 4, 5, and 6 show how the paper models are constructed by folding and cutting the paper templates in the Supporting Information. The templates themselves contain QR codes linked to these folding videos.

Figure 5. Paper models of 2,4,6-tris(4-pyridyl)-1,3,5-triazine, the pentacyanocyclopentadienide ion, and the rhodizonate ion.

 

Video 4. Folding and cutting the paper model of 2,4,6-tris(4-pyridyl)-1,3,5-triazine.  ChemDemos YouTube Channel (accessed 2/20/2022)

 

Video 5. Folding and cutting the paper model of the pentacyanocyclopentadienide ion.  ChemDemos YouTube Channel (accessed 2/20/2022)

 

Video 6. Folding and cutting the paper model of the rhodizonate ion.  ChemDemos YouTube Channel (accessed 2/20/2022)

 

As noted above, the paper models might be used for a variety of educational situations. At the very least, the paper structures resemble paper snowflakes and can be used as winter decorations with a chemical theme.

 

Safety Sharper scissors cut more easily through multiple layers of paper, but they also cut skin more easily. Consider the hand-eye coordination of individuals being asked to cut the paper.

Acknowledgements This work was supported by Bradley University and the Mund-Lagowski Department of Chemistry and Biochemistry with additional support from the Illinois Heartland Section of the American Chemical Society. The material contained in this document is based upon work supported by a National Aeronautics and Space Administration (NASA) grant or cooperative agreement. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of NASA. This work was supported through a NASA grant awarded to the Illinois/NASA Space Grant Consortium. We also thank Kyle Grice for letting us know about the rhodizonate ion.

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