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Title: Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach

Abstract

A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. Finally, the validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.

Authors:
 [1]; ORCiD logo [2];  [3]
  1. Univ. of Chicago, IL (United States)
  2. Univ. of Chicago, IL (United States); Univ. Nacional de Columbia, Medellin (Columbia)
  3. Univ. of Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
Publication Date:
Research Org.:
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); National Science Foundation (NSF); Consejo Nacional de Ciencia y Tecnología in Mexico (CONACyT); Universidad Nacional de Columbia
OSTI Identifier:
1603430
Alternate Identifier(s):
OSTI ID: 1234048
Grant/Contract Number:  
SC0004025; DMR-1410674; 110-165-843-748; 186166; 203840
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 24; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Armas-Pérez, Julio C., Hernández-Ortiz, Juan P., and de Pablo, Juan J. Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach. United States: N. p., 2015. Web. doi:10.1063/1.4937628.
Armas-Pérez, Julio C., Hernández-Ortiz, Juan P., & de Pablo, Juan J. Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach. United States. doi:10.1063/1.4937628.
Armas-Pérez, Julio C., Hernández-Ortiz, Juan P., and de Pablo, Juan J. Tue . "Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach". United States. doi:10.1063/1.4937628. https://www.osti.gov/servlets/purl/1603430.
@article{osti_1603430,
title = {Liquid crystal free energy relaxation by a theoretically informed Monte Carlo method using a finite element quadrature approach},
author = {Armas-Pérez, Julio C. and Hernández-Ortiz, Juan P. and de Pablo, Juan J.},
abstractNote = {A theoretically informed Monte Carlo method is proposed for Monte Carlo simulation of liquid crystals on the basis of theoretical representations in terms of coarse-grained free energy functionals. The free energy functional is described in the framework of the Landau-de Gennes formalism. A piecewise finite element discretization is used to approximate the alignment field, thereby providing an excellent geometrical representation of curved interfaces and accurate integration of the free energy. The method is suitable for situations where the free energy functional includes highly non-linear terms, including chirality or high-order deformation modes. Finally, the validity of the method is established by comparing the results of Monte Carlo simulations to traditional Ginzburg-Landau minimizations of the free energy using a finite difference scheme, and its usefulness is demonstrated in the context of simulations of chiral liquid crystal droplets with and without nanoparticle inclusions.},
doi = {10.1063/1.4937628},
journal = {Journal of Chemical Physics},
number = 24,
volume = 143,
place = {United States},
year = {2015},
month = {12}
}

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Works referenced in this record:

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
  • DOI: 10.1002/adfm.200500768

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


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
  • DOI: 10.1021/cm703237a

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
  • DOI: 10.1002/anie.200804500

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
  • DOI: 10.1002/anie.201306630

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

Atomistic simulations of liquid crystal mixtures of alkoxy substituted phenylpyrimidines 2PhP and PhP14
journal, March 2012

  • Yan, Fangyong; Earl, David J.
  • The Journal of Chemical Physics, Vol. 136, Issue 12
  • DOI: 10.1063/1.3692731

Comparative study of local structure of two cyanobiphenyl liquid crystals by molecular dynamics method
journal, August 2014

  • Gerts, Egor D.; Komolkin, Andrei V.; Burmistrov, Vladimir A.
  • The Journal of Chemical Physics, Vol. 141, Issue 7
  • DOI: 10.1063/1.4892877

Effect of counter-ion on the thermotropic liquid crystal behaviour of bis(alkyl)-tris(imidazolium salt) compounds
journal, August 2014


A multiscale approach to triglycerides simulations: from atomistic to coarse-grained models and back
journal, January 2012

  • Brasiello, Antonio; Crescitelli, Silvestro; Milano, Giuseppe
  • Faraday Discussions, Vol. 158
  • DOI: 10.1039/c2fd20037f

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

Fractionation in Gay-Berne liquid crystal mixtures
journal, October 2007

  • Moreno-Razo, J. Antonio; Díaz-Herrera, Enrique; Klapp, Sabine H. L.
  • Physical Review E, Vol. 76, Issue 4
  • DOI: 10.1103/PhysRevE.76.041703

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

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

Nematic-Field-Driven Positioning of Particles in Liquid Crystal Droplets
journal, November 2013


Structure and dynamics of a Gay–Berne liquid crystal confined in cylindrical nanopores
journal, June 2009

  • Ji, Qing; Lefort, Ronan; Busselez, Rémi
  • The Journal of Chemical Physics, Vol. 130, Issue 23
  • DOI: 10.1063/1.3148889

Pore dimensionality effects on the dynamics of a nanoconfined liquid-crystal
journal, November 2009


Influence of pore shape on the structure of a nanoconfined Gay–Berne liquid crystal
journal, August 2009


The shear flow behavior of LCPs based on a generalized Doi model with distortional elasticity
journal, February 2002


The effects of surfactants on drop deformation and breakup
journal, November 1990


Poisson-bracket approach to the dynamics of nematic liquid crystals
journal, June 2003


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

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

Quench sensitivity to defects and shear banding in nematic polymer film flows
journal, June 2009

  • Yang, Xiaofeng; Forest, M. Gregory; Mullins, William
  • Journal of Non-Newtonian Fluid Mechanics, Vol. 159, Issue 1-3
  • DOI: 10.1016/j.jnnfm.2009.02.005

Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions
journal, May 2009

  • Yang, Xiaofeng; Forest, M. Gregory; Mullins, William
  • Journal of Rheology, Vol. 53, Issue 3
  • DOI: 10.1122/1.3089622

The Physics of Liquid Crystals
journal, May 1995

  • de Gennes, P. G.; Prost, J.; Pelcovits, Robert
  • Physics Today, Vol. 48, Issue 5
  • DOI: 10.1063/1.2808028

Calculation of the Elastic Constants of Nematic Liquid Crystals
journal, June 1972

  • Nehring, Jürgen; Saupe, Alfred
  • The Journal of Chemical Physics, Vol. 56, Issue 11
  • DOI: 10.1063/1.1677071

On the Elastic Theory of Uniaxial Liquid Crystals
journal, January 1971

  • Nehring, Jürgen; Saupe, Alfred
  • The Journal of Chemical Physics, Vol. 54, Issue 1
  • DOI: 10.1063/1.1674612

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
  • DOI: 10.1063/1.1831253

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


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

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

Stability and rewiring of nematic braids in chiral nematic colloids
journal, January 2012

  • Čopar, Simon; Porenta, Tine; Jampani, V. S. R.
  • Soft Matter, Vol. 8, Issue 33
  • DOI: 10.1039/c2sm25952d

Configuration transition in a nematic liquid crystal confined to a small spherical cavity
journal, April 1990


Three-dimensional colloidal crystals in liquid crystalline blue phases
journal, February 2011

  • Ravnik, M.; Alexander, G. P.; Yeomans, J. M.
  • Proceedings of the National Academy of Sciences, Vol. 108, Issue 13
  • DOI: 10.1073/pnas.1015831108

Mesoscopic modelling of colloids in chiral nematics
journal, January 2010

  • Ravnik, Miha; Alexander, Gareth P.; Yeomans, Julia M.
  • Faraday Discuss., Vol. 144
  • DOI: 10.1039/B908676E

Confining blue phase colloids to thin layers
journal, January 2011

  • Ravnik, Miha; Fukuda, Jun-ichi; Yeomans, Julia M.
  • Soft Matter, Vol. 7, Issue 21
  • DOI: 10.1039/c1sm05707c

Geometrical frustration of chiral ordering in cholesteric droplets
journal, January 2012

  • Seč, David; Porenta, Tine; Ravnik, Miha
  • Soft Matter, Vol. 8, Issue 48
  • DOI: 10.1039/C2SM27048J

Interactions of quadrupolar nematic colloids
journal, March 2008


Monte Carlo Simulation of the Director Field of a Nematic Liquid Crystal with Three Elastic Coefficients
journal, January 1996


Monte Carlo simulation of topological defects in the nematic liquid crystal matrix around a spherical colloid particle
journal, November 1997


Monte Carlo lattice simulations of the elastic behaviour of nematic liquid crystals
journal, May 2001


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
  • DOI: 10.1080/15421400390193765

Monte Carlo simulations of biaxial structure in thin hybrid nematic film based upon spatially anisotropic pair potential
journal, March 2009


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


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

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
  • DOI: 10.1039/C5SM00940E

Nanoparticle self-assembly at the interface of liquid crystal droplets
journal, April 2015

  • Rahimi, Mohammad; Roberts, Tyler F.; Armas-Pérez, Julio C.
  • Proceedings of the National Academy of Sciences, Vol. 112, Issue 17
  • DOI: 10.1073/pnas.1422785112

Lattice Boltzmann simulations of liquid crystalline fluids: active gels and blue phases
journal, January 2009

  • Cates, M. E.; Henrich, O.; Marenduzzo, D.
  • Soft Matter, Vol. 5, Issue 20
  • DOI: 10.1039/b908659p

Confined cubic blue phases under shear
journal, June 2012


Colloids in liquid crystals: a lattice Boltzmann study
journal, January 2010

  • Lintuvuori, J. S.; Marenduzzo, D.; Stratford, K.
  • Journal of Materials Chemistry, Vol. 20, Issue 46
  • DOI: 10.1039/c0jm01824d

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

Molecular Description of Nematic Liquid Crystals
journal, December 1970


Elastic and flow properties of biaxial nematics
journal, November 1981

  • Saupe, A.
  • The Journal of Chemical Physics, Vol. 75, Issue 10
  • DOI: 10.1063/1.441903

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


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
  • DOI: 10.1063/1.3455206

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
  • DOI: 10.1002/polb.20393

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

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
  • DOI: 10.1143/JJAP.38.135

The theory of liquid crystals
journal, January 1933


Liquid crystals and anisotropic melts. A general discussion
journal, January 1933

  • Bernal, Bernal; Lawrence, Lawrence; Oseen, Oseen
  • Trans. Faraday Soc., Vol. 29, Issue 140
  • DOI: 10.1039/tf9332901060

I. Liquid crystals. On the theory of liquid crystals
journal, January 1958


Surface waves in nematic liquid crystals
journal, November 1969


Disorientation-induced disordering at a nematic-liquid-crystal–solid interface
journal, November 1992


Two-dimensional dipolar nematic colloidal crystals
journal, November 2007


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


Modeling planar degenerate wetting and anchoring in nematic liquid crystals
journal, November 2005


libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations
journal, November 2006

  • Kirk, Benjamin S.; Peterson, John W.; Stogner, Roy H.
  • Engineering with Computers, Vol. 22, Issue 3-4
  • DOI: 10.1007/s00366-006-0049-3

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

SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
journal, June 2003

  • Li, Xiaoye S.; Demmel, James W.
  • ACM Transactions on Mathematical Software, Vol. 29, Issue 2
  • DOI: 10.1145/779359.779361

A Supernodal Approach to Sparse Partial Pivoting
journal, January 1999

  • Demmel, James W.; Eisenstat, Stanley C.; Gilbert, John R.
  • SIAM Journal on Matrix Analysis and Applications, Vol. 20, Issue 3
  • DOI: 10.1137/S0895479895291765