Investigation of Phase Transitions in Nematic Liquid Crystals by Fractional Calculation

Yıl 2018, Cilt: 14 Sayı: 4, 373 - 377, 28.12.2018

Müjde Durukan Gültepe Zekai Tek

https://doi.org/10.18466/cbayarfbe.393700

Öz

In
this study, we investigate nematic-isotropic phase transitions in liquid
crystals using fractionally generalized form of the Maier-Saupe Theory (MST).
MST is one of the mean-field theories commonly used in the nematic liquid
crystals which proved to be extremely useful in explaining nematic-isotropic
phase transitions. Fractionally obtained results compared with those of the
experimental data for p-azoxyanisole (PAA) in the literature. In this context,
the dependence of fourth rank order parameters on second rank order parameters
is handled by being a measure of fractality of space. It is observed that the
variation of second-rank and fourth rank order parameters versus temperature
are in accordance with some values of fractal dimensions. As a result, we can
conclude that there is a close relationship between temperature and fractional derivative
order parameters.

Anahtar Kelimeler

Fractional Calculus, Nematic Liquid Crystals, Phase Transition, PAA, Maier-Saupe Theory

Kaynakça

• 1. Andrade, R,F, S, Remarks on the behavior of the ising chain in the generalized statistics, Physica A: Statistical Mechanics and its Applications, 1994, 203, 486-494.
• 2. Ramshaw, J, D, Irreversibility and generalized entropies, Physics Letters A, 1993, 175 (3-4), 171.
• 3. Ertik, H, Demirhan, D, Şirin, H, Büyükkılıc, F, A fractional mathematical approach to the distribution functions of quantum gases: Cosmic microwave background radiation problem is revisited, Physica A: Statistical Mechanics and its Applications, 2009, 388 (21), 4573-4585.
• 4. Ertik, H, Demirhan, D, Şirin, H, Büyükkılıc, F, Time fractional development of quantum systems, Journal of Mathematical Physics, 2010, 51 (8), 082102.
• 5. Ubriano, M, R, Entropies based on fractional calculus, Physics Letters A, 2009, 373, 2516-2519.
• 6. Hamley, I, W, Garnett, S, Luckhurst, G, R, Roskilly, S, J, Sedon, J, M, Pedersen, S, Richardson, R, M, Orientational ordering in the nematic phase of a thermotropic liquid crystal: A small angle neutron scattering study, The Journal of Chemical Physics, 1996, 104, 10046.
• 7. Tarasov, V, E, Fractional hydrodynamic equations for fractal media, Annals of Physics, 2005, 318:286-307.
• 8. Tsallis, C, Mendes, R, S, Plastino, A, R, The role of contraints within generalized non extensive statistics, Physica A: Statistical Mechanics and its Applications, 1998, 261, 534-554.
• 9. Metzler, R, Kalfter, J, The random walk’s guide to anomalous diffusion: a fractional approach, Physics Reports, 2000, 339:1-77.
• 10. Biyajima, M, Mizoguchi, T, Suzuki, N, New blackbody radiation low based on fractional calculus and its application to nasa cobe data, Physica A, 2015, 440, 129-138.
• 11. Gabano, J, D, Poinot, T, Kanoun, H, LPV Continuous fractional modeling applied to ultracapacitor impedance identification, Control Engineering Practice, 2015, 45, 86-97.
• 12. Sun, H, Zhang, Y, Baleanu, D, Chen, W, Chen, Y, A new collection of real world applications of fractional calculus işn science and engineering, Commun Nonliear Sci Numer Simulat, 2018, 213-231.
• 13. Hilfer, R, Applications of fractional calculus in physics, World Scientific, 2000, 463p.
• 14. Oldham, K, B, Spainer, J, The fractional calculus, Academic Press, San Diego, 1974, pp 234. 15. Podlubny, I, Fractional differential equations, Academic Press: San Diego, 1999, pp 340.
• 16. Saupe, A, Recent results in the field of liquid crystals, Angew. Chem. International Edittion, England, 1968, vol. 7, pp 97-112.
• 17. Maier, W, Saupe, A, Naturforsch, Z, A simple molecular statistical theory of the nematic crystalline-liquid phase II, 1960, 15a, pp 287.