Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields
Abstract
A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.
- Authors:
-
[3];
- Univ. of Chicago, IL (United States)
- Univ. Autónoma Metropolitana, Iztapalapa (Mexico)
- Univ. Nacional de Colombia, Medellín (Colombia); Univ. of Chicago, IL (United States)
- Univ. of Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
- Publication Date:
- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of Wisconsin, Madison, WI (United States); Univ. of Chicago, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Univ. Nacional de Colombia Ph.D. grant; COLCIENCIAS; USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1237493
- Alternate Identifier(s):
- OSTI ID: 1228705; OSTI ID: 1603429
- Grant/Contract Number:
- AC02-06CH11357; SC0004025; 110-165-843-748
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Chemical Physics
- Additional Journal Information:
- Journal Volume: 143; Journal Issue: 4; Journal ID: ISSN 0021-9606
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Armas-Pérez, Julio C., Londono-Hurtado, Alejandro, Guzmán, Orlando, Hernández-Ortiz, Juan P., and de Pablo, Juan J. Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields. United States: N. p., 2015.
Web. doi:10.1063/1.4926790.
Armas-Pérez, Julio C., Londono-Hurtado, Alejandro, Guzmán, Orlando, Hernández-Ortiz, Juan P., & de Pablo, Juan J. Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields. United States. https://doi.org/10.1063/1.4926790
Armas-Pérez, Julio C., Londono-Hurtado, Alejandro, Guzmán, Orlando, Hernández-Ortiz, Juan P., and de Pablo, Juan J. Mon .
"Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields". United States. https://doi.org/10.1063/1.4926790. https://www.osti.gov/servlets/purl/1237493.
@article{osti_1237493,
title = {Theoretically informed Monte Carlo simulation of liquid crystals by sampling of alignment-tensor fields},
author = {Armas-Pérez, Julio C. and Londono-Hurtado, Alejandro and Guzmán, Orlando and Hernández-Ortiz, Juan P. and de Pablo, Juan J.},
abstractNote = {A theoretically informed coarse-grained Monte Carlo method is proposed for studying liquid crystals. The free energy functional of the system is described in the framework of the Landau-de Gennes formalism. The alignment field and its gradients are approximated by finite differences, and the free energy is minimized through a stochastic sampling technique. The validity of the proposed method is established by comparing the results of the proposed approach to those of traditional free energy minimization techniques. Its usefulness is illustrated in the context of three systems, namely, a nematic liquid crystal confined in a slit channel, a nematic liquid crystal droplet, and a chiral liquid crystal in the bulk. It is found that for systems that exhibit multiple metastable morphologies, the proposed Monte Carlo method is generally able to identify lower free energy states that are often missed by traditional approaches. Importantly, the Monte Carlo method identifies such states from random initial configurations, thereby obviating the need for educated initial guesses that can be difficult to formulate.},
doi = {10.1063/1.4926790},
journal = {Journal of Chemical Physics},
number = 4,
volume = 143,
place = {United States},
year = {Mon Jul 27 00:00:00 EDT 2015},
month = {Mon Jul 27 00:00:00 EDT 2015}
}
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Works referenced in this record:
Landau–de Gennes modelling of nematic liquid crystal colloids
journal, August 2009
- Ravnik, Miha; Žumer, Slobodan
- Liquid Crystals, Vol. 36, Issue 10-11
Orientational multiplicity and transitions in liquid crystalline droplets
journal, February 2007
- Goyal, Rajesh K.; Denn, Morton M.
- Physical Review E, Vol. 75, Issue 2
A numerical technique for predicting microstructure in liquid crystalline polymers
journal, August 1997
- Hobdell, John; Windle, Alan
- Liquid Crystals, Vol. 23, Issue 2
Monodisperse Emulsions through Templating Polyelectrolyte Multilayer Capsules
journal, March 2008
- Sivakumar, Sri; Gupta, Jugal K.; Abbott, Nicholas L.
- Chemistry of Materials, Vol. 20, Issue 6
Mesoscopic modelling of colloids in chiral nematics
journal, January 2010
- Ravnik, Miha; Alexander, Gareth P.; Yeomans, Julia M.
- Faraday Discuss., Vol. 144
Quadrupolar particles in a nematic liquid crystal: Effects of particle size and shape
journal, February 2009
- Hung, Francisco R.
- Physical Review E, Vol. 79, Issue 2
Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals
journal, January 2005
- Dupuis, A.; Marenduzzo, D.; Yeomans, J. M.
- Physical Review E, Vol. 71, Issue 1
Monte Carlo simulations of biaxial structure in thin hybrid nematic film based upon spatially anisotropic pair potential
journal, March 2009
- Zhi-Dong, Zhang; Chun-Rui, Chang; Dong-Lai, Ma
- Chinese Physics B, Vol. 18, Issue 4
Two-dimensional dipolar nematic colloidal crystals
journal, November 2007
- Škarabot, M.; Ravnik, M.; Žumer, S.
- Physical Review E, Vol. 76, Issue 5
Nematic Ordering, Conjugation, and Density of States of Soluble Polymeric Semiconductors
journal, July 2013
- Gemünden, Patrick; Poelking, Carl; Kremer, Kurt
- Macromolecules, Vol. 46, Issue 14
Elastic and flow properties of biaxial nematics
journal, November 1981
- Saupe, A.
- The Journal of Chemical Physics, Vol. 75, Issue 10
An extension of the Landau-Ginzburg-de Gennes theory for liquid crystals
journal, November 1987
- Longa, L.; Monselesan, D.; Trebin, H. -R.
- Liquid Crystals, Vol. 2, Issue 6
Equilibrium structures and pretransitional fluctuations in a very thin hybrid nematic film
journal, August 1999
- Šarlah, A.; Žumer, S.
- Physical Review E, Vol. 60, Issue 2
A new configurational transition in inhomogeneous nematics
journal, April 1994
- Palffy-muhoray, P.; Gartland, E. C.; Kelly, J. R.
- Liquid Crystals, Vol. 16, Issue 4
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
Monte Carlo simulation of topological defects in the nematic liquid crystal matrix around a spherical colloid particle
journal, November 1997
- Ruhwandl, R. W.; Terentjev, E. M.
- Physical Review E, Vol. 56, Issue 5
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
Simulations of theoretically informed coarse grain models of polymeric systems
journal, January 2010
- Detcheverry, François A.; Pike, Darin Q.; Nealey, Paul F.
- Faraday Discuss., Vol. 144
Structures and transitions in thin hybrid nematic films: A Monte Carlo study
journal, May 2003
- Chiccoli, C.; Pasini, P.; Šarlah, A.
- Physical Review E, Vol. 67, Issue 5
Numerical method of lines for the relaxational dynamics of nematic liquid crystals
journal, August 2008
- Bhattacharjee, A. K.; Menon, Gautam I.; Adhikari, R.
- Physical Review E, Vol. 78, Issue 2
Inequalities in Liquid Crystal Theory
journal, January 1966
- Ericksen, J. L.
- Physics of Fluids, Vol. 9, Issue 6
Fluctuating dynamics of nematic liquid crystals using the stochastic method of lines
journal, July 2010
- Bhattacharjee, A. K.; Menon, Gautam I.; Adhikari, R.
- The Journal of Chemical Physics, Vol. 133, Issue 4
Slow dynamics of thin nematic films in the presence of adsorbed nanoparticles
journal, January 2005
- Grollau, S.; Guzmán, O.; Abbott, N. L.
- The Journal of Chemical Physics, Vol. 122, Issue 2
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
Endotoxin-Induced Structural Transformations in Liquid Crystalline Droplets
journal, May 2011
- Lin, I. -H.; Miller, D. S.; Bertics, P. J.
- Science, Vol. 332, Issue 6035
Monte Carlo Simulation of the Director Field of a Nematic Liquid Crystal with Three Elastic Coefficients
journal, January 1996
- Gruhn, T.; Hess, S.
- Zeitschrift für Naturforschung A, Vol. 51, Issue 1-2
Size-Dependent Ordering of Liquid Crystals Observed in Polymeric Capsules with Micrometer and Smaller Diameters
journal, January 2009
- Gupta, Jugal K.; Sivakumar, Sri; Caruso, Frank
- Angewandte Chemie International Edition, Vol. 48, Issue 9
Morphological transitions in liquid crystal nanodroplets
journal, January 2012
- Tomar, V.; Hernández, S. I.; Abbott, N. L.
- Soft Matter, Vol. 8, Issue 33
Thermotropic Liquid Crystals as Substrates for Imaging the Reorganization of Matrigel by Human Embryonic Stem Cells
journal, March 2006
- Lockwood, N. A.; Mohr, J. C.; Ji, L.
- Advanced Functional Materials, Vol. 16, Issue 5
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
Nonequilibrium Simulations of Lamellae Forming Block Copolymers under Steady Shear: A Comparison of Dissipative Particle Dynamics and Brownian Dynamics
journal, September 2012
- Peters, Brandon L.; Ramírez-Hernández, Abelardo; Pike, Darin Q.
- Macromolecules, Vol. 45, Issue 19
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
Configuration transition in a nematic liquid crystal confined to a small spherical cavity
journal, April 1990
- Erdmann, John H.; Žumer, Slobodan; Doane, J. William
- Physical Review Letters, Vol. 64, Issue 16
Homeotropic nano-particle assembly on degenerate planar nematic interfaces: films and droplets
journal, January 2015
- Londoño-Hurtado, Alejandro; Armas-Pérez, Julio C.; Hernández-Ortiz, Juan P.
- Soft Matter, Vol. 11, Issue 25
Stability and Instability of an Uniaxial Alignment Against Biaxial Distortions in the Isotropic and Nematic Phases of Liquid Crystals
journal, January 1992
- Kaiser, P.; Wiese, W.; Hess, S.
- Journal of Non-Equilibrium Thermodynamics, Vol. 17, Issue 2
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
Multidimensional Director Modeling Using the Q Tensor Representation in a Liquid Crystal Cell and Its Application to the π Cell with Patterned Electrodes
journal, January 1999
- Mori, Hiroyuki; Gartland, Eugene C.; Kelly, Jack R.
- Japanese Journal of Applied Physics, Vol. 38, Issue Part 1, No. 1A
Critical thickness of a hybrid aligned nematic liquid crystal cell
journal, January 1983
- Barbero, G.; Barberi, R.
- Journal de Physique, Vol. 44, Issue 5
A Pairwise Additive Potential for the Elastic Interaction Energy of a Chiral Nematic
journal, January 2003
- Luckhurst, Geoffrey R.; Saielli, Giacomo
- Molecular Crystals and Liquid Crystals, Vol. 395, Issue 1
Liquid crystals and anisotropic melts. A general discussion
journal, January 1933
- Bernal, Bernal; Lawrence, Lawrence; Oseen, Oseen
- Trans. Faraday Soc., Vol. 29, Issue 140
I. Liquid crystals. On the theory of liquid crystals
journal, January 1958
- Frank, F. C.
- Discussions of the Faraday Society, Vol. 25
Fréedericksz transitions in supra-μm nematic droplets
journal, February 1992
- Kralj, S.; Žumer, S.
- Physical Review A, Vol. 45, Issue 4
A molecular level simulation of a twisted nematic cell
journal, January 2010
- Ricci, Matteo; Mazzeo, Marco; Berardi, Roberto
- Faraday Discuss., Vol. 144
Self-Assembled Colloidal Superparticles from Nanorods
journal, October 2012
- Wang, T.; Zhuang, J.; Lynch, J.
- Science, Vol. 338, Issue 6105
Liquid Crystal Chemical Sensors That Cells Can Wear
journal, November 2013
- Manna, Uttam; Zayas-Gonzalez, Yashira M.; Carlton, Rebecca J.
- Angewandte Chemie International Edition, Vol. 52, Issue 52
The theory of liquid crystals
journal, January 1933
- Oseen, C. W.
- Transactions of the Faraday Society, Vol. 29, Issue 140
Geometrical frustration of chiral ordering in cholesteric droplets
journal, January 2012
- Seč, David; Porenta, Tine; Ravnik, Miha
- Soft Matter, Vol. 8, Issue 48
Monte Carlo lattice simulations of the elastic behaviour of nematic liquid crystals
journal, May 2001
- Masurier, P. J. Le; Luckhurst, G. R.; Saielli, G.
- Liquid Crystals, Vol. 28, Issue 5
Modeling planar degenerate wetting and anchoring in nematic liquid crystals
journal, November 2005
- Fournier, J. -B; Galatola, P.
- Europhysics Letters (EPL), Vol. 72, Issue 3
Stable configurations in hybrid nematic cells in relation to thickness and surface order
journal, December 1997
- Galabova, H. G.; Kothekar, N.; Allender, D. W.
- Liquid Crystals, Vol. 23, Issue 6
Surface waves in nematic liquid crystals
journal, November 1969
- Papoular, M.; Rapini, A.
- Solid State Communications, Vol. 7, Issue 22
Molecular Description of Nematic Liquid Crystals
journal, December 1970
- Lubensky, T. C.
- Physical Review A, Vol. 2, Issue 6
Disorientation-induced disordering at a nematic-liquid-crystal–solid interface
journal, November 1992
- Nobili, M.; Durand, G.
- Physical Review A, Vol. 46, Issue 10
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
Instability of radial hedgehog configurations in nematic liquid crystals under Landau–de Gennes free-energy models
journal, January 1999
- Gartland, E. C.; Mkaddem, S.
- Physical Review E, Vol. 59, Issue 1
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
Defect structures and three-body potential of the mean force for nanoparticles in a nematic host: Nanoparticles in a Nematic Host
journal, March 2005
- Guzmán, O.; Abbott, N. L.; de Pablo, J. J.
- Journal of Polymer Science Part B: Polymer Physics, Vol. 43, Issue 8
The Physics of Liquid Crystals
journal, May 1995
- de Gennes, P. G.; Prost, J.; Pelcovits, Robert
- Physics Today, Vol. 48, Issue 5
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
Works referencing / citing this record:
Fluctuations and phase transitions of uniaxial and biaxial liquid crystals using a theoretically informed Monte Carlo and a Landau free energy density
journal, March 2019
- Villada-Gil, Stiven; Palacio-Betancur, Viviana; Armas-Pérez, Julio C.
- Journal of Physics: Condensed Matter, Vol. 31, Issue 17
Topological defects in an unconfined nematic fluid induced by single and double spherical colloidal particles
journal, October 2017
- Wang, Yiwei; Zhang, Pingwen; Chen, Jeff Z. Y.
- Physical Review E, Vol. 96, Issue 4