Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density
Abstract
In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi 's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.
- Authors:
-
- Univ. Nacional de Colombia, Medellín (United States); Politécnico Colombiano Jaime Isaza Cadavid, Medellín (Colombia)
- Univ. Nacional de Colombia, Medellín (United States); Univ. of Chicago, IL (United States)
- Univ. de Guanajuato, Guanajuato (Mexico)
- Univ. of Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
- Univ. Nacional de Colombia, Medellín (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- Universidad Nacional de Colombia - Bogata; National Science Foundation (NSF)
- OSTI Identifier:
- 1558006
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. Condensed Matter
- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 17; Journal ID: ISSN 0953-8984
- Publisher:
- IOP Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Landau free energy; biaxial phase; liquid crystals; uniaxial phase
Citation Formats
Villada-Gil, Stiven, Palacio-Betancur, Viviana, Armas-Pérez, Julio C., de Pablo, Juan J., and Hernández-Ortiz, Juan P. Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density. United States: N. p., 2019.
Web. doi:10.1088/1361-648X/ab0394.
Villada-Gil, Stiven, Palacio-Betancur, Viviana, Armas-Pérez, Julio C., de Pablo, Juan J., & Hernández-Ortiz, Juan P. Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density. United States. https://doi.org/10.1088/1361-648X/ab0394
Villada-Gil, Stiven, Palacio-Betancur, Viviana, Armas-Pérez, Julio C., de Pablo, Juan J., and Hernández-Ortiz, Juan P. Fri .
"Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density". United States. https://doi.org/10.1088/1361-648X/ab0394. https://www.osti.gov/servlets/purl/1558006.
@article{osti_1558006,
title = {Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density},
author = {Villada-Gil, Stiven and Palacio-Betancur, Viviana and Armas-Pérez, Julio C. and de Pablo, Juan J. and Hernández-Ortiz, Juan P.},
abstractNote = {In this work, we explore fluctuations during phase transitions of uniaxial and biaxial liquid crystals using a phenomenological free energy functional. We rely on a continuum-level description of the liquid crystal ordering with a tensorial parameter and a temperature dependent Landau polynomial expansion of the tensor's invariants. The free energy functional, over a three-dimensional periodic domain, is integrated with a Gaussian quadrature and minimized with a theoretically informed Monte Carlo method. We reconstruct analytical phase diagrams, following Landau and Doi 's notations, to verify that the free energy relaxation reaches the global minimum. Importantly, our relaxation method is able to follow the thermodynamic behavior provided by other non-phenomenological approaches; we predict the first order character of the isotropic-nematic transition, and we identify the uniaxial-biaxial transition as second order. Finally, we use a finite-size scaling method, using the nematic susceptibility, to calculate the transition temperatures for 4-Cyano-4'-pentylbiphenyl (5CB) and N-(4-methoxybenzylidene)-4-butylaniline (MBBA). Our results show good agreement with experimental values, thereby validating our minimization method. Our approach is an alternative towards the relaxation of temperature dependent continuum-level free energy functionals, in any geometry, and can incorporate complicated elastic and surface energy densities.},
doi = {10.1088/1361-648X/ab0394},
journal = {Journal of Physics. Condensed Matter},
number = 17,
volume = 31,
place = {United States},
year = {Fri Mar 01 00:00:00 EST 2019},
month = {Fri Mar 01 00:00:00 EST 2019}
}
Web of Science
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