National Hispanic Heritage Month ran from September 15 to October 15 recently.1 To help celebrate the occasion, students in the Bradley University Chem/Biochem Learning Community put up colorful tissue paper banners. Papel picado or “chopped paper” banners have origins in Mexico that can be traced back to Aztec culture, and have been used for a number of festive events in Mexico.2 In some areas of Mexico, stacks of tissue paper are cut with chisels to produce many banners, but individual banners can be produced by cutting folded tissue paper with a pair of scissors.2 One of the patterns on one of the banners on campus was reminiscent of pairs of chromosomes, which got this author wondering if there were chemistry-related patterns that could be used on the rectangular flags. As shown in previous write-ups, paper can be folded, cut, and then unfolded to produce a variety of flat symmetrical patterns that can be used as models of molecule-scale structures.3-5
After a little trial and error, pieces of tissue paper were folded and cut to produce patterns resembling square arrays of cations and anions in ionic compounds. Square sheets of paper were folded into smaller squares, which were then cut with scissors to resemble the template pattern shown in Figure 1. The pattern shows a quarter of a small circle with part of a “+” sign in the middle and a quarter of a large circle with part of a “-“ sign in the middle. It is important to note that the large quarter circle does not need to be oriented to any particular corner of the folded paper square before cutting.
Figure 1. Template showing a way to cut square folded tissue paper to produce banner model of two-dimensional array of cations and anions.
When the cut paper was unfolded, the pattern produced was a square array of larger anionic circles and smaller cationic circles that resembled a layer within a sodium chloride structure. The final unfolded patterns had some variation as to which ions were in the corners, but they had the same overall alternating pattern. Since many ionic compounds have structures similar to the sodium chloride (rock salt) structure, this square pattern can model many ionic compounds. Figure 2 shows three tissue paper banners, all based on the template pattern in Figure 1. The banners are different sizes, so folding each banner with the same number of folds before cutting produces the same type of pattern but with different sized ions. In Figure 2, the larger banner with the largest ion circles is red, the intermediate banner is green, and the smallest banner with the smallest ion circles is blue.
Figure 2. Folded tissue paper banners modeling two-dimensional arrays of cations and anions. The banners and their ions get smaller moving from left to right..
The banners shown in Figure 2 are accompanied by a sign quoting a website describing a History of Papel Picado.2 The banners are also accompanied by a sign that says
As ion size decreases:
unit cell size decreases
lattice energy increases
melting point increases
band gap energy increases
As noted by the sign, the banners with varying ion sizes can be used to illustrate real structures with varying ion sizes. Lattice energy, the energy required to separate one mole of an ionic solid into its gas phase ions, increases in magnitude as ion size decreases.6 So, the blue banner in Figure 2 represents the structure with the greatest lattice energy.
Ionic and covalent compounds with smaller atom sizes often have larger band gap energy.7 Band gap energy can be described as the energy difference between the highest energy level in the valence band (when valence electrons are localized at specific bonds or atoms in the solid) and the lowest energy level in the conduction band (when the electrons are able to move throughout the solid). The colors of light produced by light-emitting diodes can be related to the bandgap energies of the semiconductors in the diodes. Materials with larger atoms and smaller band gaps can emit light at longer, redder wavelengths, and materials with smaller atoms and larger band gaps can emit light at shorter, bluer wavelengths. Band gap energy is why the red, green, and blue color was selected for the banners. The blue banner in Figure 2, with the smallest atoms, represents the structure with the greatest band gap energy.
An ionic structure tissue paper banner can also be cut between neighboring rows of ions to demonstrate how ionic crystals fracture or cleave. When an ionic crystal is mechanically stressed, ions of like charge can be pushed closer to each other and their electrostatic repulsion pushes the crystal apart.7 When one portion of the banner is slid with respect to the other portion of the banner, similar ions can be shown as getting closer to one another. Then the banner portion is pulled away from the other portion to represent crystal fracture, as shown in Figure 3 and Video 1.
Figure 3. Cut tissue paper banners modeling fracture of ionic crystals.
Video 1. Cut tissue paper banners modeling fracture of ionic crystals. ChemDemos YouTube Channel (accessed 11/3/2023)
The tissue paper banners depicted in Figure 2 were shown in General Chemistry and Materials Chemistry courses in the context of atom size influence on band gap and lattice energy, and to illustrate ionic crystal fracture. No doubt, many other chemistry-related patterns can be developed and connected to classroom learning. Whatever the patterns, the banners provide a colorful way to celebrate National Hispanic Heritage Month.
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.
- Wikipedia. National Hispanic Heritage Month (United States). https://en.wikipedia.org/wiki/National_Hispanic_Heritage_Month_(United_States) (accessed November, 2023).
- Amols' Specialty Inc. History of Papel Picado. https://www.amols.com/blog/history-of-papel-picado (accessed November, 2023).
- Robinson, K. F.; Nguyen, P. N.; Applegren, N.; Campbell, D. J. “Illustrating Close-Packed and Graphite Structures with Paper Snowflake Cutouts.” The Chemical Educator, 2007, 12,163-166.
- Campbell, D. Dr. Campbell’s Favorite Demos: Folded paper "snowflakes" with different symmetries. http://campbelldemo.blogspot.com/2016/02/folded-paper-snowflakes-with-di... (accessed November, 2023).
- Campbell, D. J.; Walls, K.; Steres, C. ChemEd Exchange. “Paper Snowflakes to Model Flat Symmetrical Molecules.” https://www.chemedx.org/blog/paper-snowflakes-model-flat-symmetrical-mol... (accessed November, 2023).
- Flowers, P.; Theopold, K.; Langley, R.; Robinson, W. R. Chemistry 2e; OpenStax: Houston, Texas, 2019.
- Ellis, A. B.; Geselbracht, M. J.; Johnson, B. J.; Lisensky, G. C.; Robinson, W. R. Teaching General Chemistry: A Materials Science Companion; American Chemical Society: Washington, DC, 1993.
For Laboratory Work: Please refer to the ACS Guidelines for Chemical Laboratory Safety in Secondary Schools (2016).
For Demonstrations: Please refer to the ACS Division of Chemical Education Safety Guidelines for Chemical Demonstrations.
Other Safety resources
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