Comparison of the effect of geometric shape and Cross-section of rod particles in biaxial and homeotropic phase formation

Mizani, Sakine; Aliabadi, Roohollah; Salehi, ,Hamdollah

doi:10.22055/jrmbs.2021.16783

Comparison of the effect of geometric shape and Cross-section of rod particles in biaxial and homeotropic phase formation

Document Type : Full length research Paper

Authors

Sakine Mizani ¹

Roohollah Aliabadi ²

,Hamdollah Salehi ³

¹ 1Department of Physics, Faculty of Science, ShahidChamran University of Ahvaz, Ahvaz, Iran

² 2Department of Physics, Faculty of Science,Fasa University, Fasa, Iran

³ Department of Physics, Faculty of Science, ShahidChamran University of Ahvaz, Ahvaz, Iran

10.22055/jrmbs.2021.16783

Abstract

In this article we investigate the effects of particles’ geometry on the uniaxial-biaxial and planar nematic-homeotropic phase transition of hard cylinders and hard rectangular rods between two structureless walls. The calculations are doneusing the Parsons-Lee theory into the Zwanzig approximation. These particles show a first order phase transition from planar to homeotropic that disappears at a critical point for both particles which this critical point is and for hard rectangular and cylinder rods, respectively. In addition, there is a second order phase transition called uniaxial planar nematic to biaxial planar nematicwhere there is three different optical axes for both shapes. This transition occurs at higher densities for the particles with smaller shape anisiorpies due to decreasing of excluded area inplanar order. Our calculations depict that both types of phase transitions take place at lower densities

Keywords

uniaxial

biaxial

planar

homeotropic

Parsons-Lee

Subjects

Condensed matter

[1] L. Mederos, E. Velasco, Y. Martínez-Ratón, Hard-body models of bulk liquid crystals, Journal of Physics: Condensed Matter 26 (2014) 463101-463151. 10.1088/0953-8984/26/46/463101

[2] S. Chandrasekhar, Liquid crystals (Second Edition), Cambridge University Press, (1992). https://www.tandfonline.com/doi/pdf/10.1080/13583149308628627

[3] F.C. Bawden, N.W. Pirie, J.D. Bernal, I. Fankuchen. Liquid crystalline substances from virus-infected plants, Nature 138 (1936) 3503-3520. 10.1038/1381051a0

[4] L. Onsager, The effects of shape on the interaction of colloidal particles, Annals of the New York Academy of Science 51 (1949) 627-660. 10.1111/j.1749-6632.1949.tb27296.x

[5] H.H. Wensink, H. Löwen, M. Marechal et al., Differently shaped hard body colloids in confinement: From passive to active particles, The European Physical Journal: Special Topics 222 (2013) 3023-3038. 10.1140/epjst/e2013-02073-0

[6] A.B.G.M. Leferink op Reininka, E. van den Pol et al., Phase behaviour of lyotropic liquid crystals in external fields and confinement, The European Physical Journal: Special Topics 222 (2013) 3053-3070. 10.1140/epjst/e2013-02075-x

[7] R. Aliabadi, M. Moradi, S. Varga, Orientational ordering of confined hard rods: the effect of shape anisotropy on surface ordering and capillary nematization, Physical Review E 92 (2015) 032503-032525. https://doi.org/10.1103/PhysRevE.92.032503

[8] G.J. Vroege, H.N.W. Lekkerkerker, Phase transition in lyotropic colloidal and polymer liquid crystals, Reports on Progress in Physics 55 (1992) 1241-1257. https://doi.org/10.1088/0034-4885/55/8/003

[9] R. Aliabadi, P. Gurin, E. Velasco, S. Varga, Ordering transitions of weakly anisotroic hard rods in narrow slit-like pores, Physical Review E 97 (2017) 01273-01293. 10.1103/PhysRevE.97.012703

[10] R. Aliabadi, M. Moradi, S. Varga, Tracking three-phase coexistences in binary mixtures of hard plates and spheres, The Journal of Chemical Physics 144 (2016) 074902-074923. https://doi.org/10.1063/1.4941981

[11] P.G. Bolhuis, A. Stroobants, D. Frenkel et al., Numerical study of the phase behavior of rod-like colloids with attractive interaction, The Journal of Chemical Physics 107 (1997) 1551-1563. https://doi.org/10.1063/1.474508

[12] M. Moradi, G. Rickayzen, The structure of a hard sphere fluid mixture confined to a slit, Molecular Physics 66 (1989) 143-162. https://doi.org/10.1080/00268978900100081

[13] M. Moradi, R.J. Wheatley, A. Avazpour, Density functional theory of liquid crystals and surface anchoring, Physical Review E 72 (2005) 061706-061720. https://doi.org/10.1103/PhysRevE.72.061706

[14] A. Malijevsky, S. Varga, Phase behaviour of parallel hard rods in confinement: an Onsager theory study, Journal of Physics: Condensed Matter 22 (2010) 175002-175015. 10.1088/0953-8984/22/17/175002

[15] P. Sheng, Phase transition in surface-aligned nematic films, Physical Review Letters 37 (1976) 1059-1063. https://doi.org/10.1103/PhysRevLett.37.1059

[16] D. de las Heras, E. Velasco, L Mederos, Capillary effects in a confined smectic phase of hard spherocylinders: Influence of particle elongation, Physical Review E 74 (2006) 011709-011721. https://doi.org/10.1103/PhysRevE.74.011709

[17] P.I.C. Teixeira, T.J. Sluckin, Microscopic theory of anchoring transitions at the surfaces of pure liquid crystals and their mixtures. I. The Fowler approximation, The Journal of Chemical Physics 97 (1992) 1498-1510. https://doi.org/10.1063/1.463226

[18] M.A. Semiromi, A. Avazpour, Computer simulation of confined prolate hard spherocylinder liquids between hard walls, Liquid Crystal 45 (2018) 262-269. https://doi.org/10.1080/02678292.2017.1318185

[19] P. Poier, S.A. Egorov, C.N. Likos, R Blaak, Concentration-induced planar-to-homeotropic anchoring transition of stiff ring polymers on hard walls, Soft Matter 12 (2016) 7983-8000. 10.1039/c6sm01453d

[20] R.J. Bushby, O.R. Lozman, Discotic liquid crystals on 25 years, Current opinion in colloids and interface science 7 (2002) 343-357. https://doi.org/10.1080/02678292.2011.603262

[21] D. Heras, E. Velasco, L. Mederos, Capillary smectization and layering in a confined liquid crystal, Physical Review Letters 94 (2005) 017801-017805. https://doi.org/10.1103/PhysRevLett.94.017801

[22] H. Salehi, S. Mizani, R. Aliabadi, S. Varga, Biaxial layering transition of hard rod-like particles in narrow slit-like pores, Physical Review E 98 (2018) 032703-032718. https://doi.org/10.1103/PhysRevE.98.032703

[23] Y. Galerne, L. Liebert, Anti ferroelectric chiral smectic-O* liquid crystal, Physical Review Letters 66 (1991) 2891-2909. https://doi.org/10.1103/PhysRevLett.66.2891

[24] J.D. Parsons, Nematic ordering in a system of rods, Physical Review A 19 (1979) 1225-1240. https://doi.org/10.1103/PhysRevA.19.1225

[25] S. Lee, A numerical investigation of nematic ordering based on a simple hard‐rod model, The Journal of Chemical Physics 87 (1987) 4972-4985. https://aip.scitation.org/doi/10.1063/1.452811

[26] Y. Martinez-Raton, S. Varga, E. Velasco, Biaxial nematic phases in fluids of hard board-like particles, Physical Chemistry Chemical Physics 13 (2011) 13247-13265. http://dx.doi.org/10.1039/C1CP20698B

[27] M. Gonzalez-Pinto, Y. Martínez-Ratón, E. Velasco, Liquid-crystal patterns of rectangular particles in a square nanocavity, Physical Review E 88 (2013) 032506-032537. https://doi.org/10.1103/PhysRevE.88.032506

[28] G. Bautista-Carbajal, P. Gurin, S. Varga, and G. Odriozola, Phase diagram of hard squares in slit confinement, Scientific Reports 8 (2018) 8886-8899. 10.1038/s41598-018-26922-3

[29] X. Zhou, H. Chen, M. Iwamoto, Orientational orders of small anisotropic molecules confined in slit pores, The Journal of Chemical Physics 120 (2004) 5322-5327. 10.1063/1.1647517

[30] F. Barmes, D.J. Cleaver, Computer simulation of a liquid-crystal anchoring transition, Physical Review E 69 (2004) 061705-061717. https://doi.org/10.1103/PhysRevE.69.061705

[31] P. Poier, S.A. Egorov, C.N. Likos, R. Blaak, Concentration-induced planar-to-homeotropic anchoring transition of stiff ring polymers on hard walls, Soft Matter 12 (2016) 7983-7994. http://dx.doi.org/10.1039/C6SM01453D