Teaching first order phase transition using a zipper model
Abstract
In 1968, Kittel published the zipper model for demonstrating the first order phase transition which is applicable to DNA like structures. This paper utilize this model to explain the behavior of many thermodynamic properties before, at and after phase transition to get a clear picture about what the changes are happening to the system during phase transition. Many textbooks say that entropy and volume show discontinuity at phase transition whereas Gibbs free energy is continuous. The zipper model shows that energy is also discontinuous as shown in the paper. Understanding the phase transition is still a difficult topic for the undergraduate students and hopefully this paper can help them to overcome this difficulty.
References
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Xiong, S., Qi, W., Huang, B., Wang, M., & Wei, L. (2011). Gibbs free energy and size–temperature phase diagram of hafnium nanoparticles. The Journal of Physical Chemistry C, 115(21), 10365–10369. https://doi.org/10.1021/jp200093a
Zeng, F.-L., Zhou, X.-Y., Li, N., Wang, A.-B., Wang, W.-K., Jin, Z.-Q., Ren, Y.-R., Fang, B.-J., Yuan, N.-Y., & Ding, J.-N. (2021). A multifunctional zipper-like sulfur electrode enables the stable operation of lithium-sulfur battery through self-healing chemistry. Energy Storage Materials, 34, 755–767. https://doi.org/10.1016/j.ensm.2020.10.025
Zhu, M., Ren, K., Liu, L., Lv, S., Miao, X., Xu, M., & Song, Z. (2019). Direct observation of partial disorder and zipperlike transition in crystalline phase change materials. Physical Review Materials, 3(3), 033603. https://doi.org/10.1103/PhysRevMaterials.3.033603
Badasyan, A. (2021). System size dependence in the Zimm–Bragg model: partition function limits, transition temperature and interval. Polymers, 13(12), 1985. https://doi.org/10.3390/polym13121985
Bagchi, B. (2018). Statistical mechanics for chemistry and materials science. CRC Press. https://doi.org/10.1201/9781315113951
Banuti, D., Raju, M., Ma, P. C., Ihme, M., & Hickey, J.-P. (2017). Seven questions about supercritical fluids - towards a new fluid state diagram. 55th AIAA Aerospace Sciences Meeting, 1106. https://doi.org/10.2514/6.2017-1106
Bellantuono, L., Janik, R. A., Jankowski, J., & Soltanpanahi, H. (2019). Dynamics near a first order phase transition. Journal of High Energy Physics, 2019(10), 146. https://doi.org/10.1007/JHEP10(2019)146
Brahmachari, S., & Marko, J. F. (2018). DNA mechanics and topology. In Biomechanics in Oncology (pp. 11–39). Springer. https://doi.org/10.1007/978-3-319-95294-9_2
Carvalho-Silva, V. H., Coutinho, N. D., & Aquilanti, V. (2020). From the kinetic theory of gases to the kinetics of rate processes: On the verge of the thermodynamic and kinetic limits. Molecules, 25(9), 2098. https://doi.org/10.3390/molecules25092098
Deger, A., Brandner, K., & Flindt, C. (2018). Lee-Yang zeros and large-deviation statistics of a molecular zipper. Physical Review E, 97(1), 012115. https://doi.org/10.1103/PhysRevE.97.012115
Deger, A., & Flindt, C. (2019). Determination of universal critical exponents using Lee-Yang theory. Physical Review Research, 1(2), 023004. https://doi.org/10.1103/PhysRevResearch.1.023004
Dos Anjos, P. H. R. (2019). Phase transitions and zeros of the partition function: An introduction. Orbital: The Electronic Journal of Chemistry, 11(2). https://doi.org/10.17807/orbital.v11i2.1362
Finkelstein, A. V, & Ptitsyn, O. (2016). Protein physics: A course of lectures. Elsevier.
Fultz, B. (2020). Phase transitions in materials. Cambridge University Press.
Gridnev, S. A., & Popov, I. I. (2020). Kinetics of phase transformation at the Curie point of ferroelectric ceramic Ba 0.8 Sr 0.2 TiO 3. Ferroelectrics, 561(1), 127–134. https://doi.org/10.1080/00150193.2020.1736925
Inaba, H. (2015). The development of ensemble theory. The European Physical Journal H, 40(4–5), 489–526. https://doi.org/10.1140/epjh/e2015-60034-2
Janke, W., Schierz, P., & Zierenberg, J. (2017). Transition barrier at a first-order phase transition in the canonical and microcanonical ensemble. Journal of Physics: Conference Series, 921(1), 012018. https://doi.org/10.1088/1742-6596/921/1/012018
Kojima, C., Sk, U. H., Fukushima, D., Irie, K., Akazawa, N., Umeda, M., & Niidome, T. (2015). Effect of main chain conformation on thermosensitivity in elastin-like peptide-grafted polylysine. RSC Advances, 5(127), 104900–104906. https://doi.org/10.1039/C5RA23865J
Koksharov, Y. A. (2020). Analytic solutions of the Weiss mean field equation. Journal of Magnetism and Magnetic Materials, 516, 167179. https://doi.org/10.1016/j.jmmm.2020.167179
Mogliacci, S., Kolbé, I., & Horowitz, W. A. (2019). Phase transitions in finite size systems. Journal of Physics: Conference Series, 1271(1), 012022. https://doi.org/10.1088/1742-6596/1271/1/012022
Naiser, T., Kayser, J., Mai, T., Michel, W., & Ott, A. (2008). Position dependent mismatch discrimination on DNA microarrays – experiments and model. BMC Bioinformatics, 9(1), 509. https://doi.org/10.1186/1471-2105-9-509
Oono, Y. (2017). Perspectives on statistical thermodynamics. Cambridge University Press.
Park, W. M. (2020). Coiled-coils: The molecular zippers that self-assemble protein nanostructures. International Journal of Molecular Sciences, 21(10), 3584. https://doi.org/10.3390/ijms21103584
Sauer, T. (2017). A look back at the Ehrenfest classification. The European Physical Journal Special Topics, 226(4), 539–549. https://doi.org/10.1140/epjst/e2016-60344-y
Shamis, M., & Zeitouni, O. (2018). The Curie–Weiss model with complex temperature: Phase transitions. Journal of Statistical Physics, 172(2), 569–591. https://doi.org/10.1007/s10955-017-1812-0
Thiele, U., Frohoff-Hülsmann, T., Engelnkemper, S., Knobloch, E., & Archer, A. J. (2019). First order phase transitions and the thermodynamic limit. New Journal of Physics, 21(12), 123021. https://doi.org/10.1088/1367-2630/ab5caf
Xiong, S., Qi, W., Huang, B., Wang, M., & Wei, L. (2011). Gibbs free energy and size–temperature phase diagram of hafnium nanoparticles. The Journal of Physical Chemistry C, 115(21), 10365–10369. https://doi.org/10.1021/jp200093a
Zeng, F.-L., Zhou, X.-Y., Li, N., Wang, A.-B., Wang, W.-K., Jin, Z.-Q., Ren, Y.-R., Fang, B.-J., Yuan, N.-Y., & Ding, J.-N. (2021). A multifunctional zipper-like sulfur electrode enables the stable operation of lithium-sulfur battery through self-healing chemistry. Energy Storage Materials, 34, 755–767. https://doi.org/10.1016/j.ensm.2020.10.025
Zhu, M., Ren, K., Liu, L., Lv, S., Miao, X., Xu, M., & Song, Z. (2019). Direct observation of partial disorder and zipperlike transition in crystalline phase change materials. Physical Review Materials, 3(3), 033603. https://doi.org/10.1103/PhysRevMaterials.3.033603
Authors
Perayil, R., Murkoth, U. K., & Pulinchery, P. (2022). Teaching first order phase transition using a zipper model. Momentum: Physics Education Journal, 6(1), 1–9. https://doi.org/10.21067/mpej.v6i1.5850
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