محاسبه ضرایب فلکسوالکتریسیته سهم دوقطبی در بلور مایع با مولکولهای گلابی شکل سخت

نوع مقاله: مقاله پژوهشی کامل

نویسندگان

1 گروه فیزیک- دانشگاه یاسوج

2 دانشیار فیزیک/دانشگاه یاسوج

10.22055/jrmbs.2019.14593

چکیده

در بلورهای مایع، مولکول‌های گلابی و موزی شکل به دلیل عدم تقارن، به ترتیب آرایش گسترده( ) یا خمیده( ) پیدا می‌کنند. در این بلورها انحراف بردار راستار از حالت تعادلی، تولید قطبش خالص می‌نماید. این خاصیت فلکسوالکتریسیته نامیده می‌شود. ضرایب فلکسوالکتریسیته در مایعات بلوری از روش‌های شبیه‌سازی و تجربی محاسبه گردیده‌اند. در نظریه تابعی چگالی این ضرایب به تابع همبسته مستقیم بین مولکول‌ها و تابع توزیع زاویه‌ای مولکول‌ها بستگی دارند. در کار حاضر با استفاده از روش پارامتری گائوسی سخت، تابع کمترین تماس بین مولکول های گلابی شکل محاسبه می شود. با استفاده از این تابع تماس عبارت تقریبی برای تابع همبسته مستقیم مولکول‌های گلابی شکل سخت به دست می‌آید. با استفاده از این تابع همبسته و تابع توزیع جهتی مناسب محاسبه شده، ضرایب فلکسوالکتریسیته سهم دوقطبی، برای بلور مایع با مولکول‌های گلابی شکل سخت با طول به پهنای 3 و 5 محاسبه شده‌اند. نتایج کار حاضر با نتایج شبیه‌سازی سازگاری کیفی دارند.

کلیدواژه‌ها


عنوان مقاله [English]

Calculation of Dipolar Flexoelectric Coefficients in Liquid Crystal with Hard Pear Shape Molecules

نویسندگان [English]

  • Sadrallah Fathi 1
  • Maryam Abdipour 1
  • Abolghasem Avazpour 2
1 Dep. of Physics, Yasouj University
2 Associated Professor/ Yasouj University
چکیده [English]

In liquid crystals, pear-shaped and banana molecules find a splay and bend arrangements, due to their asymmetry. In these crystals, the director deviation from equilibrium produces pure polarization. This effect is called Flexoelectricity. Flexoelectric coefficients in liquid crystals were derived from simulation and experimental methods. In density functional theory, these coefficients depend on the direct correlation and the angular distribution functions of molecules. In this work, by using parameterized hard Gaussian overlap method the closest distance of hard pear shape molecules is calculated. By using this closest distance, the approximate direct correlation function of pear-shaped molecules is obtained. Using this correlation function and deduced proper distribution function, the dipolar Flexoelectric coefficients for liquid crystals with elongations 3 and 5 pear-shaped molecules are calculated. The results are consistent with the simulation results qualitatively.

کلیدواژه‌ها [English]

  • Flexoelectric coefficients
  • Nematic crystal
  • Direct correlation function
  • orientation distribution function
  • Pear shape molecule

[1] F.C. Frank, On the theory of liquid crystals, Discuss. Faraday Soc. 25 (1958) 19-28.

[2] J. Stelzer, R. Berardi, C. Zannoni, Flexoelectric Coefficients for Model Pear Shaped Molecules from Monte Carlo Simulations, Molecular Crystals and Liquid Crystals 352 (2000) 187- 194.

[3] R.B. Meyer, Piezoelectric Effects In Liquid Crystals, Physical Review Letters 22 18 (1969) 918-921.

[4] M.A. Osipov, The order parameter dependence of the flexoelectric coefficients in nematic liquid crystals, Journal de Physique Letters 45 16 (1984) 823-826.

[5] J. Prost, J.P. Marcerou, On the microscopic interpretation of flexoelectricity, Le. J. De. Physique, 38 (1977) 315-324.

[6] J.P. Straley, Theory of piezoelectricity in nematic liquid crystals, and of the cholesteric ordering, Physical Review A 14 5 (1976) 1835–1841.

[7] M.A. Osipov, Molecular theory of flexoelectric effect in nematic liquid crystals, Soviet Physics JETP 58 6 (1983) 1167–1171.

[8] A. Ferrarini, Shape model for the molecular interpretation of the flexoelectric effect, Physical Review E 64 2 (2001) 021710/1–11.

[9] A. Ferrarini, C. Greco, G.R. Luckhurst, On the flexoelectric coefficients of liquid crystal monomers and dimers: a computational methodology bridging length-scales, Journal of Material Chemistry 17 11 (2007) 1039–1042.

[10] Y. Singh, U.P. Singh, density functional theory of the flexoelectric effects in nematic liquids, Physical Review A 39 8 (1989) 4254-4262.

[11] A.M. Somoza, P. Tarazona, Density functional theory of the elastic constants of a nematic liquid crystal, Molecular Physics 72 4 (1991) 911-926.

[12] J. Stelzer, R. Berardi, C. Zannoni, Flexoelectric effects in liquid crystals formed by pear-shaped molecules. A computer simulation study, Chemical Phyics Leters 299 (1999) 9–16.

[13] D.L. Cheung, S.J. Clark, M.R. Wilson, Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation, Journal of Chemical Physics 121 18 (2004) 9131–9139.

[14] A.V. Emelyanenko, M.A. Osipov, Theoretical model for the discrete flexoelectric effect and a description for the sequence of intermediate smectic phases with increasing periodicity, Physical Review E 68 5 (2003) 051703/1–16.

[15] N.V. Madhusudana, Chapter 2. Flexoelectro-optics and measurements of flexo-coecients. In eds. A. Buka and N. Eber, Flexoelectricity in Liquid Crystals. Theory, Experiments and applications, Imperial College Press, London, )2012( 33–60.

[16] P.S. Salter, C. Tschierske, S.J. Elston, E.P. Raynes, Flexoelectric measurements of a bent-core nematic liquid crystal, Physical Review E 84 3 (2011) 031708/1–5.

[17] B. Kundu, A. Roy, R. Pratibha, N.V. Madhusudana, Flexoelectric studies o made of rod like and bent-core molecules, Applied Physics Letters 95 8 (2009) 081902/1–3.

[18] C.C. Tartan, S.J. Elston. Hybrid aligned nematic based measurement of the sum (e1+e3) of the flexoelectric coefficients, Journal of Applied Physics 117 (2015) 064107/1-7

[19] L. Jianfei, Y. Huairui, Y. Zhang, D. Shizhuo and L. Xuan Flexoelectric effect in cylindrical hybrid aligned nematic liquid crystals cell, Liquid Crystals, Published online: 28 Sep 2018.

[20] A. Poniewierski, J. Stecki, Statistical theory of the elastic constants of nematic liquid crystals, Molecular Physics 38 (1979) 1931-1940.

[21] A. Avazpour, M. Moradi, The direct correlation functions of hard Gaussian overlap and hard ellipsoidal fluids, Physica B 392 (2007) 242-250.

[22] F. Barmes, M. Ricci, C. Zannoni, D.J. Cleaver, Computer simulations of hard pear-shaped particles, Physical Review E 68 (2003) 021708/1-11.

[23] L. Onsager, The Effects of Shape on the Interaction of Colloidal Particles. Annals of the New York Academy of Sciences 51 (1949 627-659.

[24] G.P. Lepage, A new algorithm for adaptive multidimensional integration, Journal of Computational Physics 27 (1978) 192-203.

[25] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran 77, (Cambridge University Press, second edition, Cambridge )1997).

[26] L.J. Ellison, Computer simulations of tapered particles. Ph.D. thesis, Sheffield Hallam University, (2008).

[1] F.C. Frank, On the theory of liquid crystals, Discuss. Faraday Soc. 25 (1958) 19-28.

[2] J. Stelzer, R. Berardi, C. Zannoni, Flexoelectric Coefficients for Model Pear Shaped Molecules from Monte Carlo Simulations, Molecular Crystals and Liquid Crystals 352 (2000) 187- 194.

[3] R.B. Meyer, Piezoelectric Effects In Liquid Crystals, Physical Review Letters 22 18 (1969) 918-921.

[4] M.A. Osipov, The order parameter dependence of the flexoelectric coefficients in nematic liquid crystals, Journal de Physique Letters 45 16 (1984) 823-826.

[5] J. Prost, J.P. Marcerou, On the microscopic interpretation of flexoelectricity, Le. J. De. Physique, 38 (1977) 315-324.

[6] J.P. Straley, Theory of piezoelectricity in nematic liquid crystals, and of the cholesteric ordering, Physical Review A 14 5 (1976) 1835–1841.

[7] M.A. Osipov, Molecular theory of flexoelectric effect in nematic liquid crystals, Soviet Physics JETP 58 6 (1983) 1167–1171.

[8] A. Ferrarini, Shape model for the molecular interpretation of the flexoelectric effect, Physical Review E 64 2 (2001) 021710/1–11.

[9] A. Ferrarini, C. Greco, G.R. Luckhurst, On the flexoelectric coefficients of liquid crystal monomers and dimers: a computational methodology bridging length-scales, Journal of Material Chemistry 17 11 (2007) 1039–1042.

[10] Y. Singh, U.P. Singh, density functional theory of the flexoelectric effects in nematic liquids, Physical Review A 39 8 (1989) 4254-4262.

[11] A.M. Somoza, P. Tarazona, Density functional theory of the elastic constants of a nematic liquid crystal, Molecular Physics 72 4 (1991) 911-926.

[12] J. Stelzer, R. Berardi, C. Zannoni, Flexoelectric effects in liquid crystals formed by pear-shaped molecules. A computer simulation study, Chemical Phyics Leters 299 (1999) 9–16.

[13] D.L. Cheung, S.J. Clark, M.R. Wilson, Calculation of flexoelectric coefficients for a nematic liquid crystal by atomistic simulation, Journal of Chemical Physics 121 18 (2004) 9131–9139.

[14] A.V. Emelyanenko, M.A. Osipov, Theoretical model for the discrete flexoelectric effect and a description for the sequence of intermediate smectic phases with increasing periodicity, Physical Review E 68 5 (2003) 051703/1–16.

[15] N.V. Madhusudana, Chapter 2. Flexoelectro-optics and measurements of flexo-coecients. In eds. A. Buka and N. Eber, Flexoelectricity in Liquid Crystals. Theory, Experiments and applications, Imperial College Press, London, )2012( 33–60.

[16] P.S. Salter, C. Tschierske, S.J. Elston, E.P. Raynes, Flexoelectric measurements of a bent-core nematic liquid crystal, Physical Review E 84 3 (2011) 031708/1–5.

[17] B. Kundu, A. Roy, R. Pratibha, N.V. Madhusudana, Flexoelectric studies o made of rod like and bent-core molecules, Applied Physics Letters 95 8 (2009) 081902/1–3.

[18] C.C. Tartan, S.J. Elston. Hybrid aligned nematic based measurement of the sum (e1+e3) of the flexoelectric coefficients, Journal of Applied Physics 117 (2015) 064107/1-7

[19] L. Jianfei, Y. Huairui, Y. Zhang, D. Shizhuo and L. Xuan Flexoelectric effect in cylindrical hybrid aligned nematic liquid crystals cell, Liquid Crystals, Published online: 28 Sep 2018.

[20] A. Poniewierski, J. Stecki, Statistical theory of the elastic constants of nematic liquid crystals, Molecular Physics 38 (1979) 1931-1940.

[21] A. Avazpour, M. Moradi, The direct correlation functions of hard Gaussian overlap and hard ellipsoidal fluids, Physica B 392 (2007) 242-250.

[22] F. Barmes, M. Ricci, C. Zannoni, D.J. Cleaver, Computer simulations of hard pear-shaped particles, Physical Review E 68 (2003) 021708/1-11.

[23] L. Onsager, The Effects of Shape on the Interaction of Colloidal Particles. Annals of the New York Academy of Sciences 51 (1949 627-659.

[24] G.P. Lepage, A new algorithm for adaptive multidimensional integration, Journal of Computational Physics 27 (1978) 192-203.

[25] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran 77, (Cambridge University Press, second edition, Cambridge )1997).

[26] L.J. Ellison, Computer simulations of tapered particles. Ph.D. thesis, Sheffield Hallam University, (2008).