DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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:
 [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [5]
  1. Univ. Nacional de Colombia, Medellín (United States); Politécnico Colombiano Jaime Isaza Cadavid, Medellín (Colombia)
  2. Univ. Nacional de Colombia, Medellín (United States); Univ. of Chicago, IL (United States)
  3. Univ. de Guanajuato, Guanajuato (Mexico)
  4. Univ. of Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
  5. 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Discotic liquid crystals: a new generation of organic semiconductors
journal, January 2007

  • Sergeyev, Sergey; Pisula, Wojciech; Geerts, Yves Henri
  • Chemical Society Reviews, Vol. 36, Issue 12
  • DOI: 10.1039/b417320c

Landau–de Gennes theory of biaxial nematics reexamined
journal, July 2008


Hard Competition: Stabilizing the Elusive Biaxial Nematic Phase in Suspensions of Colloidal Particles with Extreme Lengths
journal, April 2018


Landau–de Gennes modelling of nematic liquid crystal colloids
journal, August 2009


DNA Hybridization-Induced Reorientation of Liquid Crystal Anchoring at the Nematic Liquid Crystal/Aqueous Interface
journal, July 2008

  • Price, Andrew D.; Schwartz, Daniel K.
  • Journal of the American Chemical Society, Vol. 130, Issue 26
  • DOI: 10.1021/ja0774055

Interfacial, Boundary, and Size Effects at Critical Points
journal, July 1967


Tricritical behavior of the nematic to smectic-A phase transition in the binary mixture of liquid crystal
journal, March 2013

  • Mukherjee, Prabir K.; Tamarit, Josep Ll.
  • The Journal of Chemical Physics, Vol. 138, Issue 10
  • DOI: 10.1063/1.4794312

Liquid Crystalline Ordering and Charge Transport in Semiconducting Materials
journal, July 2009

  • Pisula, Wojciech; Zorn, Matthias; Chang, Ji Young
  • Macromolecular Rapid Communications, Vol. 30, Issue 14
  • DOI: 10.1002/marc.200900251

Electric-field-induced isotropic-nematic phase transition
journal, November 1993


Cholesteric liquid-crystal laser as an optic fiber-based temperature sensor
journal, October 2004

  • Moreira, M. F.; Carvalho, I. C. S.; Cao, W.
  • Applied Physics Letters, Vol. 85, Issue 14
  • DOI: 10.1063/1.1781363

Inverted and multiple nematic emulsions
journal, January 1998


Measurements of the Bend and Splay Elastic Constants of Octyl-Cyanobiphenyl
journal, September 1986

  • Morris, Stephen W.; Palffy-muhoray, P.; Balzarini, D. A.
  • Molecular Crystals and Liquid Crystals, Vol. 139, Issue 3-4
  • DOI: 10.1080/00268948608080132

Optical Monitoring of Gases with Cholesteric Liquid Crystals
journal, March 2010

  • Han, Yang; Pacheco, Katherine; Bastiaansen, Cees W. M.
  • Journal of the American Chemical Society, Vol. 132, Issue 9
  • DOI: 10.1021/ja907826z

Temperature dependence of the anchoring strength at a nematic liquid crystal‐evaporated SiO interface
journal, May 1987

  • Yokoyama, H.; Kobayashi, S.; Kamei, H.
  • Journal of Applied Physics, Vol. 61, Issue 9
  • DOI: 10.1063/1.338411

Investigations of phase transitions in liquid crystals by means of adiabatic scanning calorimetry
journal, August 2009


Colloidal Structures from Bulk Demixing in Liquid Crystals
journal, December 2004

  • Loudet, J. C.; Barois, P.; Auroy, P.
  • Langmuir, Vol. 20, Issue 26
  • DOI: 10.1021/la048737f

Physicochemical characterization of colloidal drug delivery systems such as reverse micelles, vesicles, liquid crystals and nanoparticles for topical administration
journal, September 2004


Quenched disorder in a liquid-crystal biosensor: Adsorbed nanoparticles at confining walls
journal, May 2005

  • Guzmán, O.; Abbott, N. L.; de Pablo, J. J.
  • The Journal of Chemical Physics, Vol. 122, Issue 18
  • DOI: 10.1063/1.1896354

Landau-deGennes Theory of Biaxial Nematics Re-examined
text, January 2007


Endotoxin-Induced Structural Transformations in Liquid Crystalline Droplets
journal, May 2011


Dynamics of electro-optical switching processes in surface stabilized biaxial nematic phase found in bent-core liquid crystal
journal, February 2007

  • Lee, Ji-Hoon; Lim, Tong-Kun; Kim, Won-Taeck
  • Journal of Applied Physics, Vol. 101, Issue 3
  • DOI: 10.1063/1.2433126

Polydispersity Stabilizes Biaxial Nematic Liquid Crystals
journal, September 2011


Morphological transitions in liquid crystal nanodroplets
journal, January 2012

  • Tomar, V.; Hernández, S. I.; Abbott, N. L.
  • Soft Matter, Vol. 8, Issue 33
  • DOI: 10.1039/c2sm25383f

2-D lid-driven cavity flow of nematic polymers: an unsteady sea of defects
journal, January 2010

  • Yang, Xiaofeng; Forest, M. Gregory; Mullins, William
  • Soft Matter, Vol. 6, Issue 6
  • DOI: 10.1039/b908502e

Light-induced liquid crystallinity
journal, May 2012

  • Kosa, Tamas; Sukhomlinova, Ludmila; Su, Linli
  • Nature, Vol. 485, Issue 7398
  • DOI: 10.1038/nature11122

Liquid Crystal Mediated Interactions Between Nanoparticles in a Nematic Phase
journal, March 2012

  • Tomar, V.; Roberts, T. F.; Abbott, N. L.
  • Langmuir, Vol. 28, Issue 14
  • DOI: 10.1021/la204119p

Molecular dynamics and rheological properties of concentrated solutions of rodlike polymers in isotropic and liquid crystalline phases
journal, February 1981


Effects of flow on topological defects in a nematic liquid crystal near a colloid
journal, February 2014

  • Stieger, Tillmann; Schoen, Martin; Mazza, Marco G.
  • The Journal of Chemical Physics, Vol. 140, Issue 5
  • DOI: 10.1063/1.4862953

Phase behaviour of hard board-like particles
journal, January 2017

  • Cuetos, Alejandro; Dennison, Matthew; Masters, Andrew
  • Soft Matter, Vol. 13, Issue 27
  • DOI: 10.1039/C7SM00726D

Cholesteric liquid crystals for detection of organic vapours
journal, April 2003

  • Winterbottom, Daniel A.; Narayanaswamy, Ramaier; Raimundo, Ivo M.
  • Sensors and Actuators B: Chemical, Vol. 90, Issue 1-3
  • DOI: 10.1016/S0925-4005(03)00021-2

Phase diagram of hard board like colloids from computer simulations
text, January 2013


An Euler–Lagrange approach for studying blood flow in an aneurysmal geometry
journal, March 2017

  • Xenos, M. A.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2199
  • DOI: 10.1098/rspa.2016.0774

A new era for liquid crystal research: Applications of liquid crystals in soft matter nano-, bio- and microtechnology
journal, November 2012


Dynamics of a nematic liquid crystal around a spherical particle
journal, April 2004

  • Fukuda, Jun-ichi; Stark, Holger; Yoneya, Makoto
  • Journal of Physics: Condensed Matter, Vol. 16, Issue 19
  • DOI: 10.1088/0953-8984/16/19/008

Physics of liquid crystals
journal, October 1974


Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model
journal, March 2017

  • Invernizzi, Michele; Valsson, Omar; Parrinello, Michele
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 13
  • DOI: 10.1073/pnas.1618455114

Phase Transitions in a Fluid of Biaxial Particles
journal, April 1973


Role of domain in pattern formation
journal, June 2017

  • Seirin-Lee, Sungrim
  • Development, Growth & Differentiation, Vol. 59, Issue 5
  • DOI: 10.1111/dgd.12377

Hydrogen-bonding and Phase Biaxiality in Nematic Rod-Plate Mixtures
journal, December 1998

  • Vanakaras, A. G.; Mcgrother, S. C.; Jackson, G.
  • Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, Vol. 323, Issue 1
  • DOI: 10.1080/10587259808048442

Phase diagram of hard board-like colloids from computer simulations
journal, January 2013

  • Peroukidis, Stavros D.; Vanakaras, Alexandros G.
  • Soft Matter, Vol. 9, Issue 31
  • DOI: 10.1039/c3sm51165k

Defect Structure around Two Colloids in a Liquid Crystal
journal, December 2003


Synthesis and assembly of colloidal cuboids with tunable shape biaxiality
journal, October 2018


On Molecular Structure and Physical Properties of Thermotropic Liquid Crystals
journal, June 1969


The Frank constants of some nematic liquid crystals
journal, January 1985


Hybrid molecular-colloidal liquid crystals
journal, May 2018


Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach
journal, December 2015

  • Armas-Pérez, Julio C.; Hernández-Ortiz, Juan P.; de Pablo, Juan J.
  • The Journal of Chemical Physics, Vol. 143, Issue 24
  • DOI: 10.1063/1.4937628

Liquid Crystal Emulsions as the Basis of Biological Sensors for the Optical Detection of Bacteria and Viruses
journal, July 2009

  • Sivakumar, Sri; Wark, Kim L.; Gupta, Jugal K.
  • Advanced Functional Materials, Vol. 19, Issue 14
  • DOI: 10.1002/adfm.200900399

Characterization of Adsorbate-Induced Ordering Transitions of Liquid Crystals within Monodisperse Droplets
journal, August 2009

  • Gupta, Jugal K.; Zimmerman, Jacob S.; de Pablo, Juan J.
  • Langmuir, Vol. 25, Issue 16
  • DOI: 10.1021/la900786b

Temperature dependence of the effective anchoring energy for a nematic-ferroelectric interface
journal, August 2006

  • Gunyakov, V. A.; Parshin, A. M.; Shabanov, V. F.
  • The European Physical Journal E, Vol. 20, Issue 4
  • DOI: 10.1140/epje/i2006-10037-9

Splay-bend elasticity and rotational viscosity of liquid crystal mixtures of rod-like and bent-core molecules
journal, January 2011

  • Sathyanarayana, P.; Sadashiva, B. K.; Dhara, Surajit
  • Soft Matter, Vol. 7, Issue 18
  • DOI: 10.1039/c1sm05751k

Bracket formulation of nonequilibrium thermodynamics for systems interacting with the environment
journal, June 2008

  • Beris, Antony N.; Öttinger, Hans Christian
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 152, Issue 1-3
  • DOI: 10.1016/j.jnnfm.2007.10.017

Detection and Quantification of DNA Adsorbed on Solid Surfaces by Using Liquid Crystals
journal, February 2010


Monte Carlo simulation of binary mixtures of hard colloidal cuboids
journal, November 2017


Liquid crystals for twisted nematic display devices
journal, January 1999

  • Gray, George W.; Kelly, Stephen M.
  • Journal of Materials Chemistry, Vol. 9, Issue 9
  • DOI: 10.1039/a902682g

Alignment tensor versus director: Description of defects in nematic liquid crystals
journal, July 1995


Precision and reproducibility of temperature response of a thermo-responsive membrane embedded by binary liquid crystals for drug delivery
journal, June 2001


Euler-Lagrange Elasticity with Dynamics
journal, January 2014


Orientational multiplicity and transitions in liquid crystalline droplets
journal, February 2007


Nematic-Liquid-Crystal Order—A Monte Carlo Calculation
journal, July 1972


Quadrupolar particles in a nematic liquid crystal: Effects of particle size and shape
journal, February 2009


Dynamics and Thermodynamics of Artificial Muscles Based on Nematic Gels
journal, July 1997

  • Hébert, M.; Kant, R.; de Gennes, P. -G.
  • Journal de Physique I, Vol. 7, Issue 7
  • DOI: 10.1051/jp1:1997209

Smectic polymer vesicles
journal, January 2009

  • Jia, Lin; Cao, Amin; Lévy, Daniel
  • Soft Matter, Vol. 5, Issue 18
  • DOI: 10.1039/b907485f

Ordered phases of a liquid of biaxial particles
journal, November 1974


Thermotropic Biaxial Nematic Liquid Crystals
journal, April 2004


Flow induced deformation of defects around nanoparticles and nanodroplets suspended in liquid crystals
journal, January 2010

  • Gettelfinger, Brian T.; Moreno-Razo, José Antonio; Koenig Jr, Gary M.
  • Soft Matter, Vol. 6, Issue 5
  • DOI: 10.1039/b912551e

Biomolecular Interactions at Phospholipid-Decorated Surfaces of Liquid Crystals
journal, December 2003


Isotropic-symmetry-breaking bifurcations in a class of liquid-crystal models
journal, January 1989


Pretransitional Phenomena in the Isotropic Phase of a Nematic Liquid Crystal
journal, August 1970


Phase-field theories for mathematical modeling of biological membranes
journal, January 2015


Liquid-crystal-based microlasers
journal, January 2010

  • Nevskaya, G. E.; Palto, S. P.; Tomilin, M. G.
  • Journal of Optical Technology, Vol. 77, Issue 8
  • DOI: 10.1364/JOT.77.000473

Liquid-crystal-mediated self-assembly at nanodroplet interfaces
journal, May 2012

  • Moreno-Razo, J. A.; Sambriski, E. J.; Abbott, N. L.
  • Nature, Vol. 485, Issue 7396
  • DOI: 10.1038/nature11084

Numerical method of lines for the relaxational dynamics of nematic liquid crystals
journal, August 2008


Specific heat dependence on orientational order at cylindrically confined liquid crystal phase transitions
journal, December 1994


Field response and switching times in biaxial nematics
journal, January 2008

  • Berardi, Roberto; Muccioli, Luca; Zannoni, Claudio
  • The Journal of Chemical Physics, Vol. 128, Issue 2
  • DOI: 10.1063/1.2815804

Uniaxial and biaxial liquid crystal phases in colloidal dispersions of board-like particles
journal, July 2010

  • van den Pol, E.; Thies–Weesie, D. M. E.; Petukhov, A. V.
  • Liquid Crystals, Vol. 37, Issue 6-7
  • DOI: 10.1080/02678291003798164

Landau theory of the nematic-isotropic phase transition
journal, April 1986


Ordered States of a Nematic Liquid
journal, May 1970


Laser and Electric Field Induced Birefringence Studies on the Cyanobiphenyl Homologues
journal, October 1978


Monte Carlo investigation of critical properties of the Landau point of a biaxial liquid-crystal system
journal, May 2016


Memory and topological frustration in nematic liquid crystals confined in porous materials
journal, March 2011

  • Araki, Takeaki; Buscaglia, Marco; Bellini, Tommaso
  • Nature Materials, Vol. 10, Issue 4
  • DOI: 10.1038/nmat2982

On the Molecular Requirements for the Stabilisation of Thermotropic Biaxial Ordering in Rod-Plate Nematics
journal, June 2001

  • Vanakaras, A. G.; Terzis, A. F.; Photinos, D. J.
  • Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, Vol. 362, Issue 1
  • DOI: 10.1080/10587250108025760

Two-Dimensional Nematic Colloidal Crystals Self-Assembled by Topological Defects
journal, August 2006


Elastic, dielectric and optical constants of 4'-pentyl-4-cyanobiphenyl
journal, May 2001


Temperature dependence of the polar anchoring strength of weakly rubbed polyimide films for the nematic liquid crystal (5CB)
journal, July 1992

  • Seo, Dai‐Shik; Iimura, Yasufumi; Kobayashi, Shunsuke
  • Applied Physics Letters, Vol. 61, Issue 2
  • DOI: 10.1063/1.108194

An Eulerian-Lagrangian Approach¶to the Navier-Stokes Equations
journal, February 2001


Liquid crystal nanodroplets, and the balance between bulk and interfacial interactions
journal, January 2012

  • Hernández, S. I.; Moreno-Razo, J. A.; Ramírez-Hernández, A.
  • Soft Matter, Vol. 8, Issue 5
  • DOI: 10.1039/C1SM06425H

Stability and Instability of an Uniaxial Alignment Against Biaxial Distortions in the Isotropic and Nematic Phases of Liquid Crystals
journal, January 1992


Effects of anchoring strength on the diffusivity of nanoparticles in model liquid-crystalline fluids
journal, January 2011

  • Moreno-Razo, J. A.; Sambriski, E. J.; Koenig, G. M.
  • Soft Matter, Vol. 7, Issue 15
  • DOI: 10.1039/c0sm01506g

Pretransition and critical phenomena in the nematic phase of MBBA
journal, March 1974


Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields
journal, July 2015

  • Armas-Pérez, Julio C.; Londono-Hurtado, Alejandro; Guzmán, Orlando
  • The Journal of Chemical Physics, Vol. 143, Issue 4
  • DOI: 10.1063/1.4926790

Weakly first-order character of the nematic-isotropic phase transition in liquid crystals
journal, October 2005


Phase Behavior of Colloidal Hard Tetragonal Parallelepipeds (Cuboids):  A Monte Carlo Simulation Study
journal, December 2005

  • John, Bettina S.; Escobedo, Fernando A.
  • The Journal of Physical Chemistry B, Vol. 109, Issue 48
  • DOI: 10.1021/jp0551521

Liquid Crystal Enabled Early Stage Detection of Beta Amyloid Formation on Lipid Monolayers
journal, September 2015

  • Sadati, Monirosadat; Apik, Aslin Izmitli; Armas-Perez, Julio C.
  • Advanced Functional Materials, Vol. 25, Issue 38
  • DOI: 10.1002/adfm.201502830

Nematic and smectic order in a fluid of biaxial hard particles
journal, September 1991


Elastic properties of liquid crystals
journal, September 2002

  • Zakharov, A. V.; Tsvetkova, M. N.; Korsakov, V. G.
  • Physics of the Solid State, Vol. 44, Issue 9
  • DOI: 10.1134/1.1507268

Measuring liquid crystal elastic constants with free energy perturbations
journal, January 2014

  • Joshi, Abhijeet A.; Whitmer, Jonathan K.; Guzmán, Orlando
  • Soft Matter, Vol. 10, Issue 6
  • DOI: 10.1039/C3SM51919H

Optical patterning
journal, August 1996


Modeling flows of confined nematic liquid crystals
journal, April 2011

  • Hernández-Ortiz, Juan P.; Gettelfinger, Brian T.; Moreno-Razo, Jose
  • The Journal of Chemical Physics, Vol. 134, Issue 13
  • DOI: 10.1063/1.3567098

Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders
journal, February 2012