In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals

Sidky, Hythem; de Pablo, Juan J.; Whitmer, Jonathan K.

doi:10.1103/PhysRevLett.120.107801

In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals

Journal Article · Fri Mar 09 00:00:00 EST 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.120.107801· OSTI ID:1459901

Sidky, Hythem ^[1]; de Pablo, Juan J. ^[2]; Whitmer, Jonathan K. ^[1]

Univ. of Notre Dame, IN (United States). Dept. of Chemical and Biomolecular Engineering
Univ. of Chicago, IL (United States). Inst. for Molecular Engineering; Argonne National Lab. (ANL), Argonne, IL (United States)

Experiments on confined droplets of the nematic liquid crystal 5CB have questioned long-established bounds imposed on the elastic free energy of nematic systems. This elasticity, which derives from molecular alignment within nematic systems, is quantified through a set of moduli which can be difficult to measure experimentally and, in some cases, can only be probed indirectly. This is particularly true of the surfacelike saddle-splay elastic term, for which the available experimental data indicate values on the cusp of stability, often with large uncertainties. Here, we demonstrate that all nematic elastic moduli, including the saddle-splay elastic constant k₂₄, may be calculated directly from atomistic molecular simulations. Importantly, results obtained through in silico measurements of the 5CB elastic properties demonstrate unambiguously that saddle-splay elasticity alone is unable to describe the observed confined morphologies.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); U.S. Department of Defense (DOD) - Department of the Army; USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division - Midwest Integrated Center for Computational Materials (MICCoM)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1459901

Alternate ID(s):: OSTI ID: 1425231

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 120; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (47)

Size-Dependent Ordering of Liquid Crystals Observed in Polymeric Capsules with Micrometer and Smaller Diameters Gupta, Jugal K.; Sivakumar, Sri; Caruso, Frank Angewandte Chemie International Edition, Vol. 48, Issue 9 https://doi.org/10.1002/anie.200804500	journal	January 2009
Towards in Silico Liquid Crystals. Realistic Transition Temperatures and Physical Properties for n -Cyanobiphenyls via Molecular Dynamics Simulations Tiberio, Giustiniano; Muccioli, Luca; Berardi, Roberto ChemPhysChem, Vol. 10, Issue 1 https://doi.org/10.1002/cphc.200800231	journal	January 2009
Order and Conformation of Biphenyl in Cyanobiphenyl Liquid Crystals: A Combined Atomistic Molecular Dynamics and ¹ H NMR Study Pizzirusso, Antonio; Di Pietro, Maria Enrica; De Luca, Giuseppina ChemPhysChem, Vol. 15, Issue 7 https://doi.org/10.1002/cphc.201400082	journal	April 2014
PACKMOL: A package for building initial configurations for molecular dynamics simulations Martínez, L.; Andrade, R.; Birgin, E. G. Journal of Computational Chemistry, Vol. 30, Issue 13 https://doi.org/10.1002/jcc.21224	journal	October 2009
Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation Zakharov, A. V.; Maliniak, A. The European Physical Journal E, Vol. 4, Issue 1 https://doi.org/10.1007/s101890170146	journal	January 2001
Curvature elasticity in liquid crystals Shri, Singh Physics Reports, Vol. 277, Issue 5-6 https://doi.org/10.1016/S0370-1573(96)00016-6	journal	December 1996
GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers Abraham, Mark James; Murtola, Teemu; Schulz, Roland SoftwareX, Vol. 1-2 https://doi.org/10.1016/j.softx.2015.06.001	journal	September 2015
Understanding Atomic-Scale Behavior of Liquid Crystals at Aqueous Interfaces Ramezani-Dakhel, Hadi; Sadati, Monirosadat; Rahimi, Mohammad Journal of Chemical Theory and Computation, Vol. 13, Issue 1 https://doi.org/10.1021/acs.jctc.6b00844	journal	December 2016
Directed Self-Assembly of Colloidal Particles onto Nematic Liquid Crystalline Defects Engineered by Chemically Patterned Surfaces Li, Xiao; Armas-Pérez, Julio C.; Hernández-Ortiz, Juan P. ACS Nano, Vol. 11, Issue 6 https://doi.org/10.1021/acsnano.7b03641	journal	May 2017
The missing term in effective pair potentials Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. The Journal of Physical Chemistry, Vol. 91, Issue 24 https://doi.org/10.1021/j100308a038	journal	November 1987
Molecular Structure of Canonical Liquid Crystal Interfaces Sadati, Monirosadat; Ramezani-Dakhel, Hadi; Bu, Wei Journal of the American Chemical Society, Vol. 139, Issue 10 https://doi.org/10.1021/jacs.7b00167	journal	March 2017
Segregation of liquid crystal mixtures in topological defects Rahimi, Mohammad; Ramezani-Dakhel, Hadi; Zhang, Rui Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15064	journal	April 2017
Influence of droplet size, pH and ionic strength on endotoxin-triggered ordering transitions in liquid crystalline droplets Miller, Daniel S.; Abbott, Nicholas L. Soft Matter, Vol. 9, Issue 2 https://doi.org/10.1039/C2SM26811F	journal	January 2013
Measuring liquid crystal elastic constants with free energy perturbations Joshi, Abhijeet A.; Whitmer, Jonathan K.; Guzmán, Orlando Soft Matter, Vol. 10, Issue 6 https://doi.org/10.1039/C3SM51919H	journal	January 2014
Saddle-splay screening and chiral symmetry breaking in toroidal nematics Koning, Vinzenz; van Zuiden, Benjamin C.; Kamien, Randall D. Soft Matter, Vol. 10, Issue 23 https://doi.org/10.1039/C4SM00076E	journal	January 2014
Optimization of the GAFF force field to describe liquid crystal molecules: the path to a dramatic improvement in transition temperature predictions Boyd, Nicola Jane; Wilson, Mark R. Physical Chemistry Chemical Physics, Vol. 17, Issue 38 https://doi.org/10.1039/C5CP03702F	journal	January 2015
Relevance of saddle-splay elasticity in complex nematic geometries Kos, Žiga; Ravnik, Miha Soft Matter, Vol. 12, Issue 4 https://doi.org/10.1039/C5SM02417J	journal	January 2016
Elastic response and phase behavior in binary liquid crystal mixtures Sidky, Hythem; Whitmer, Jonathan K. Soft Matter, Vol. 12, Issue 19 https://doi.org/10.1039/C5SM03107A	journal	January 2016
Liquid crystals for twisted nematic display devices Gray, George W.; Kelly, Stephen M. Journal of Materials Chemistry, Vol. 9, Issue 9 https://doi.org/10.1039/a902682g	journal	January 1999
Curvature elasticity of nematic liquid crystals: simply a matter of molecular shape? Insights from atomistic modeling Cestari, Mirko; Ferrarini, Alberta Soft Matter, Vol. 5, Issue 20 https://doi.org/10.1039/b904606b	journal	January 2009
Morphological transitions in liquid crystal nanodroplets Tomar, V.; Hernández, S. I.; Abbott, N. L. Soft Matter, Vol. 8, Issue 33 https://doi.org/10.1039/c2sm25383f	journal	January 2012
Electrically switchable volume gratings in polymer‐dispersed liquid crystals Sutherland, R. L.; Tondiglia, V. P.; Natarajan, L. V. Applied Physics Letters, Vol. 64, Issue 9, p. 1074-1076 https://doi.org/10.1063/1.110936	journal	February 1994
Inequalities in Liquid Crystal Theory Ericksen, J. L. Physics of Fluids, Vol. 9, Issue 6 https://doi.org/10.1063/1.1761821	journal	January 1966
Lyotropic chromonic liquid crystal semiconductors for water-solution processable organic electronics Nazarenko, V. G.; Boiko, O. P.; Anisimov, M. I. Applied Physics Letters, Vol. 97, Issue 26 https://doi.org/10.1063/1.3533814	journal	December 2010
Modification of the overlap potential to mimic a linear site–site potential Gay, J. G.; Berne, B. J. The Journal of Chemical Physics, Vol. 74, Issue 6 https://doi.org/10.1063/1.441483	journal	March 1981
Molecular dynamics simulations of a Gay–Berne nematic liquid crystal: Elastic properties from direct correlation functions Stelzer, Joachim; Longa, Lech; Trebin, Hans‐Rainer The Journal of Chemical Physics, Vol. 103, Issue 8 https://doi.org/10.1063/1.470268	journal	August 1995
Molecular dynamics calculation of elastic constants in Gay–Berne nematic liquid crystals Allen, Michael P.; Warren, Mark A.; Wilson, Mark R. The Journal of Chemical Physics, Vol. 105, Issue 7 https://doi.org/10.1063/1.472147	journal	August 1996
SSAGES: Software Suite for Advanced General Ensemble Simulations Sidky, Hythem; Colón, Yamil J.; Helfferich, Julian The Journal of Chemical Physics, Vol. 148, Issue 4 https://doi.org/10.1063/1.5008853	journal	January 2018
Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications Li, G.; Mathine, D. L.; Valley, P. Proceedings of the National Academy of Sciences, Vol. 103, Issue 16 https://doi.org/10.1073/pnas.0600850103	journal	April 2006
Stable nematic droplets with handles Pairam, Ekapop; Vallamkondu, Jayalakshmi; Koning, Vinzenz Proceedings of the National Academy of Sciences, Vol. 110, Issue 23 https://doi.org/10.1073/pnas.1221380110	journal	May 2013
Lassoing saddle splay and the geometrical control of topological defects Tran, Lisa; Lavrentovich, Maxim O.; Beller, Daniel A. Proceedings of the National Academy of Sciences, Vol. 113, Issue 26 https://doi.org/10.1073/pnas.1602703113	journal	May 2016
Elasticity and Orientational Order in Some Cyanobiphenyls: Part IV. Reanalysis of the Data Madhusudana, N. V.; Pratibha, R. Molecular Crystals and Liquid Crystals, Vol. 89, Issue 1-4 https://doi.org/10.1080/00268948208074481	journal	October 1982
Elastic constants and dynamics in nematic liquid crystals Humpert, Anja; Allen, Michael P. Molecular Physics, Vol. 113, Issue 17-18 https://doi.org/10.1080/00268976.2015.1067730	journal	July 2015
Elastic properties of common Gay–Berne nematogens from density of states (DOS) simulations Sidky, Hythem; Whitmer, Jonathan K. Liquid Crystals, Vol. 43, Issue 13-15 https://doi.org/10.1080/02678292.2016.1201869	journal	July 2016
Determination of Ki (i = 1–3) and μj (j = 2–6) in 5CB by observing the angular dependence of Rayleigh line spectral widths Chen, Guo-Ping; Takezoe, Hideo; Fukuda, Atsuo Liquid Crystals, Vol. 5, Issue 1 https://doi.org/10.1080/02678298908026375	journal	July 1989
Lyotropic Chromonic Liquid Crystals for Biological Sensing Applications Shiyanovskii, S. V.; Lavrentovich, O. D.; Schneider, T. Molecular Crystals and Liquid Crystals, Vol. 434, Issue 1 https://doi.org/10.1080/15421400590957288	journal	June 2005
Chemical and biological sensing using liquid crystals Carlton, Rebecca J.; Hunter, Jacob T.; Miller, Daniel S. Liquid Crystals Reviews, Vol. 1, Issue 1 https://doi.org/10.1080/21680396.2013.769310	journal	June 2013
Computer simulations of the elastic properties of liquid crystals Cleaver, Douglas J.; Allen, Michael P. Physical Review A, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevA.43.1918	journal	February 1991
Nematic-Liquid-Crystal Order—A Monte Carlo Calculation Lebwohl, P. A.; Lasher, G. Physical Review A, Vol. 6, Issue 1 https://doi.org/10.1103/PhysRevA.6.426	journal	July 1972
Periodic stripe domains and hybrid-alignment regime in nematic liquid crystals: Threshold analysis Sparavigna, A.; Lavrentovich, O. D.; Strigazzi, A. Physical Review E, Vol. 49, Issue 2 https://doi.org/10.1103/PhysRevE.49.1344	journal	February 1994
Optical determination of the saddle-splay elastic constant K 24 in nematic liquid crystals Polak, R. D.; Crawford, G. P.; Kostival, B. C. Physical Review E, Vol. 49, Issue 2 https://doi.org/10.1103/PhysRevE.49.R978	journal	February 1994
Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity Davidson, Zoey S.; Kang, Louis; Jeong, Joonwoo Physical Review E, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevE.91.050501	journal	May 2015
Basis Function Sampling: A New Paradigm for Material Property Computation Whitmer, Jonathan K.; Chiu, Chi-cheng; Joshi, Abhijeet A. Physical Review Letters, Vol. 113, Issue 19 https://doi.org/10.1103/PhysRevLett.113.190602	journal	November 2014
Normal-distortion-mode approach to liquid crystal elastic energy Schmidt, V. Hugo Physical Review Letters, Vol. 64, Issue 5 https://doi.org/10.1103/PhysRevLett.64.535	journal	January 1990
Determination of the liquid-crystal surface elastic constant K 24 Allender, D. W.; Crawford, G. P.; Doane, J. W. Physical Review Letters, Vol. 67, Issue 11 https://doi.org/10.1103/PhysRevLett.67.1442	journal	September 1991
Endotoxin-Induced Structural Transformations in Liquid Crystalline Droplets Lin, I. -H.; Miller, D. S.; Bertics, P. J. Science, Vol. 332, Issue 6035 https://doi.org/10.1126/science.1195639	journal	May 2011
Multidimensional Director Modeling Using the Q Tensor Representation in a Liquid Crystal Cell and Its Application to the π Cell with Patterned Electrodes Mori, Hiroyuki; Gartland, Eugene C.; Kelly, Jack R. Japanese Journal of Applied Physics, Vol. 38, Issue Part 1, No. 1A https://doi.org/10.1143/JJAP.38.135	journal	January 1999

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