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Electric-field-induced patterns in a hockey-stick nematic. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120239] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Jerusalem A, Al-Rekabi Z, Chen H, Ercole A, Malboubi M, Tamayo-Elizalde M, Verhagen L, Contera S. Electrophysiological-mechanical coupling in the neuronal membrane and its role in ultrasound neuromodulation and general anaesthesia. Acta Biomater 2019; 97:116-140. [PMID: 31357005 DOI: 10.1016/j.actbio.2019.07.041] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Revised: 07/20/2019] [Accepted: 07/23/2019] [Indexed: 01/23/2023]
Abstract
The current understanding of the role of the cell membrane is in a state of flux. Recent experiments show that conventional models, considering only electrophysiological properties of a passive membrane, are incomplete. The neuronal membrane is an active structure with mechanical properties that modulate electrophysiology. Protein transport, lipid bilayer phase, membrane pressure and stiffness can all influence membrane capacitance and action potential propagation. A mounting body of evidence indicates that neuronal mechanics and electrophysiology are coupled, and together shape the membrane potential in tight coordination with other physical properties. In this review, we summarise recent updates concerning electrophysiological-mechanical coupling in neuronal function. In particular, we aim at making the link with two relevant yet often disconnected fields with strong clinical potential: the use of mechanical vibrations-ultrasound-to alter the electrophysiogical state of neurons, e.g., in neuromodulation, and the theories attempting to explain the action of general anaesthetics. STATEMENT OF SIGNIFICANCE: General anaesthetics revolutionised medical practice; now an apparently unrelated technique, ultrasound neuromodulation-aimed at controlling neuronal activity by means of ultrasound-is poised to achieve a similar level of impact. While both technologies are known to alter the electrophysiology of neurons, the way they achieve it is still largely unknown. In this review, we argue that in order to explain their mechanisms/effects, the neuronal membrane must be considered as a coupled mechano-electrophysiological system that consists of multiple physical processes occurring concurrently and collaboratively, as opposed to sequentially and independently. In this framework the behaviour of the cell membrane is not the result of stereotypical mechanisms in isolation but instead emerges from the integrative behaviour of a complexly coupled multiphysics system.
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Affiliation(s)
- Antoine Jerusalem
- Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK.
| | - Zeinab Al-Rekabi
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Haoyu Chen
- Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - Ari Ercole
- Division of Anaesthesia, University of Cambridge, Addenbrooke's Hospital, Hills Road, Cambridge CB2 0QQ, UK
| | - Majid Malboubi
- Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - Miren Tamayo-Elizalde
- Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
| | - Lennart Verhagen
- Wellcome Centre for Integrative Neuroimaging (WIN), Department of Experimental Psychology, University of Oxford, Oxford OX1 3TA, UK; WIN, Centre for Functional MRI of the Brain, Nuffield Department of Clinical Neurosciences, John Radcliffe Hospital, University of Oxford, Oxford OX3 9DU, UK
| | - Sonia Contera
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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Chen H, Garcia-Gonzalez D, Jérusalem A. Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation. Phys Rev E 2019; 99:032406. [PMID: 30999419 DOI: 10.1103/physreve.99.032406] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2018] [Indexed: 02/06/2023]
Abstract
For more than half a century, the action potential (AP) has been considered a purely electrical phenomenon. However, experimental observations of membrane deformations occurring during APs have revealed that this process also involves mechanical features. This discovery has recently fuelled a controversy on the real nature of APs: whether they are mechanical or electrical. In order to examine some of the modern hypotheses regarding APs, we propose here a coupled mechanoelectrophysiological membrane finite-element model for neuronal axons. The axon is modeled as an axisymmetric thin-wall cylindrical tube. The electrophysiology of the membrane is modeled using the classic Hodgkin-Huxley (H-H) equations for the Nodes of Ranvier or unmyelinated axons and the cable theory for the internodal regions, whereas the axonal mechanics is modeled by means of viscoelasticity theory. Membrane potential changes induce a strain gradient field via reverse flexoelectricity, whereas mechanical pulses result in an electrical self-polarization field following the direct flexoelectric effect, in turn influencing the membrane potential. Moreover, membrane deformation also alters the values of membrane capacitance and resistance in the H-H equation. These three effects serve as the fundamental coupling mechanisms between the APs and mechanical pulses in the model. A series of numerical studies was systematically conducted to investigate the consequences of interaction between the APs and mechanical waves on both myelinated and unmyelinated axons. Simulation results illustrate that the AP is always accompanied by an in-phase propagating membrane displacement of ≈1nm, whereas mechanical pulses with enough magnitude can also trigger APs. The model demonstrates that mechanical vibrations, such as the ones arising from ultrasound stimulations, can either annihilate or enhance axonal electrophysiology depending on their respective directionality and frequency. It also shows that frequency of pulse repetition can also enhance signal propagation independently of the amplitude of the signal. This result not only reconciles the mechanical and electrical natures of the APs but also provides an explanation for the experimentally observed mechanoelectrophysiological phenomena in axons, especially in the context of ultrasound neuromodulation.
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Affiliation(s)
- Haoyu Chen
- Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
| | | | - Antoine Jérusalem
- Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom
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Chae I, Jeong CK, Ounaies Z, Kim SH. Review on Electromechanical Coupling Properties of Biomaterials. ACS APPLIED BIO MATERIALS 2018; 1:936-953. [DOI: 10.1021/acsabm.8b00309] [Citation(s) in RCA: 56] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Inseok Chae
- Department of Chemical Engineering and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Chang Kyu Jeong
- Division of Advanced Materials Engineering, Chonbuk National University, Jeonju, Jeonbuk 54896, Republic of Korea
| | - Zoubeida Ounaies
- Department of Mechanical and Nuclear Engineering and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Seong H. Kim
- Department of Chemical Engineering and Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States
- Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States
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Vitoriano C, Sátiro C. Consequences of director-density coupling theory for flexoelectricity in nematic liquid crystals. Phys Rev E 2016; 93:022702. [PMID: 26986383 DOI: 10.1103/physreve.93.022702] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2015] [Indexed: 11/07/2022]
Abstract
We theoretically study how the measurements of the flexoelectric coefficients in nematic liquid crystals are affected by the inclusion of the director-density coupling energy. It is shown that this investigation is quite relevant for interpreting the data of experiments.
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Affiliation(s)
- Carlindo Vitoriano
- Unidade Acadêmica do Cabo de Santo Agostinho, Universidade Federal Rural de Pernambuco BR 101 Sul, 5225, Ponte dos Carvalhos, Cabo de Santo Agostinho, Pernambuco, Brazil
| | - Caio Sátiro
- Unidade Acadêmica de Garanhuns, Universidade Federal Rural de Pernambuco Avenue Bom Pastor S/N, 55296-901, Garanhuns, Pernambuco, Brazil
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Sreenilayam SP, Panarin YP, Vij JK, Torgova SI, Lehmann A, Tschierske C. Flexoelectric polarization studies in bent-core nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022502. [PMID: 26382418 DOI: 10.1103/physreve.92.022502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2015] [Indexed: 06/05/2023]
Abstract
The flexoelectric polarization (Pf) of four bent-core nematic liquid crystals (LCs) has been measured using the pyroelectric effect. Hybrid aligned nematic cells are fabricated for measuring the pyroelectric response over the entire range of the nematic phase. It is found that the magnitude of flexoelectric polarization Pf and the sum of the flexoelectric coefficients |e1+e3| for the bent-core LCs studied here are three to six times higher than for the calamitics. Pf is found to depend on the transverse dipole moment of LC molecules. However, |e1+e3| values are by no means giant as |e3| alone had been reported for a bent-core nematic system previously. The dependence of the sum of "splay and bend flexoelectric coefficients" is discussed in terms of the shape of the molecule and of the dipole moment directed normal to the molecular axis.
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Affiliation(s)
- S P Sreenilayam
- Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Ireland
| | - Yu P Panarin
- Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Ireland
- School of Electrical and Electronic Engineering, Dublin Institute of Technology, Dublin 8, Ireland
| | - J K Vij
- Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Ireland
| | - S I Torgova
- P. N. Lebedev Physical Institute of Russian Academy of Sciences, Moscow, Russia
| | - A Lehmann
- Institute of Chemistry, Martin-Luther-University, Halle-Wittenberg, 06120 Halle, Germany
| | - C Tschierske
- Institute of Chemistry, Martin-Luther-University, Halle-Wittenberg, 06120 Halle, Germany
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Gleeson HF, Kaur S, Görtz V, Belaissaoui A, Cowling S, Goodby JW. The nematic phases of bent-core liquid crystals. Chemphyschem 2014; 15:1251-60. [PMID: 24700653 PMCID: PMC4257080 DOI: 10.1002/cphc.201400014] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2014] [Indexed: 11/07/2022]
Abstract
Over the last ten years, the nematic phases of liquid crystals formed from bent-core structures have provoked considerable research because of their remarkable properties. This Minireview summarises some recent measurements of the physical properties of these systems, as well as describing some new data. We concentrate on oxadiazole-based materials as exemplars of this class of nematogens, but also describe some other bent-core systems. The influence of molecular structure on the stability of the nematic phase is described, together with progress in reducing the nematic transition temperatures by modifications to the molecular structure. The physical properties of bent-core nematic materials have proven difficult to study, but patterns are emerging regarding their optical and dielectric properties. Recent breakthroughs in understanding the elastic and flexoelectric behaviour are summarised. Finally, some exemplars of unusual electric field behaviour are described.
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Affiliation(s)
- Helen F Gleeson
- [a] Prof. H. F. Gleeson, Dr. S. Kaur School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL (UK) E-mail:
| | - Sarabjot Kaur
- [a] Prof. H. F. Gleeson, Dr. S. Kaur School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL (UK) E-mail:
| | - Verena Görtz
- Department of ChemistryUniversity of York, Heslington, York YO10 5DD (UK)
- Department of ChemistryLancaster University, Lancaster LA1 4YB (UK)
| | - Abdel Belaissaoui
- Department of ChemistryUniversity of York, Heslington, York YO10 5DD (UK)
| | - Stephen Cowling
- Department of ChemistryUniversity of York, Heslington, York YO10 5DD (UK)
| | - John W Goodby
- Department of ChemistryUniversity of York, Heslington, York YO10 5DD (UK)
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Balachandran R, Panov VP, Vij JK, Lehmann A, Tschierske C. Effect of cybotactic clusters on the elastic and flexoelectric properties of bent-core liquid crystals belonging to the same homologous series. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032503. [PMID: 24125281 DOI: 10.1103/physreve.88.032503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Revised: 07/29/2013] [Indexed: 06/02/2023]
Abstract
We report results of the splay (K_{11}) and bend (K_{33}) elastic constants and the effective flexoelectric coefficient of three bent-core liquid crystals belonging to a homologous series of 4-cyanoresorcinol bisbenzoates with varying chain lengths. Based on the results of x-ray scattering studies, one of the three compounds with a shorter chain length (C4) has few, if any, clusters present in its nematic phase and behaves quite normally, whereas the others two with longer chain lengths (C6 and C7) show the presence of cybotactic nematic phase with smectic C type clusters. These grow in size with a reduction in temperature. K_{33} is found to be the least for C7, whereas it is weakly dependent on temperature. K_{33} is somewhat higher for C4 and C6 and is almost independent of temperature. K_{11} for C6 and C7 is higher by 20% to 50% than C4 depending on the temperature. K_{11} increases linearly with a reduction in temperature for the three compounds. For C6 K_{11}>K_{33} by a factor up to ∼2 depending on the temperature, for C4 it is greater by a factor up to 1.3, and for C7 it is greater by a factor of ∼2.5. These results suggest that the clusters do not have any effect on K_{11}. The magnitude of the effective flexoelectric coefficient e=(|e_{1}-e_{3}|) is measured by creating a uniform lying helix (ULH) configuration in a planar cell. By doping the bent-core system with a small wt% of a chiral dopant, the ULH is obtained by cooling planar cells to the cholesteric phase under weak electric field. The effective flexoelectric coefficient is greater for the bent-core systems than for calamatics but it is much lower than would otherwise have been expected for such systems. |e_{1}-e_{3}| for C4 > C6 ≈ C7 is greater by 20% to 25% than C6 and C7 at the same reduced temperature. These differences in the effective flexoelectric coefficient can easily arise from a difference in the chain lengths among the members of the series but if the presence of clusters were to have an influence on |e_{1}-e_{3}|, then these would reduce it, contrary to the expectations for the bent-core systems.
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Affiliation(s)
- R Balachandran
- Department of Electronic and Electrical Engineering, Trinity College, University of Dublin, Dublin 2, Ireland
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Sathyanarayana P, Dhara S. Antagonistic flexoelectric response in liquid crystal mixtures of bent-core and rodlike molecules. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012506. [PMID: 23410348 DOI: 10.1103/physreve.87.012506] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2012] [Indexed: 06/01/2023]
Abstract
We report the measurements of the temperature variations of the flexoelastic coefficient (e(*)/K) of a host calamitic liquid crystal (RO) and its mixture with two guest bent-core (BC-120 and BC-60) liquid crystals. The bent-core (BC) molecules have different core structures and bend angles; namely, θ=/~120° and =/~60°, respectively. We find that e(*)/K is independent of temperature and decreases rapidly with increasing concentration of BC-120 molecules and changes sign from positive to negative. In mixtures with BC-60, e(*)/K is always positive and its concentration-dependent variation is not unique. At 7M% it is significantly large (three times) near the nematic-isotropic transition and decreases strongly with reducing temperature. Dielectric measurement suggests antagonistic orientation of the dipole axes (arrow axes) of the two BC molecules in the host liquid crystal, and based on this, the opposite sign of e(*)/K is explained.
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Affiliation(s)
- P Sathyanarayana
- School of Physics, University of Hyderabad, Hyderabad-500046, India
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Tadapatri P, Krishnamurthy KS. Competing Instability Modes in an Electrically Driven Bent-Core Nematic Liquid Crystal. J Phys Chem B 2012; 116:782-93. [DOI: 10.1021/jp210383p] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pramod Tadapatri
- Centre for Soft Matter Research, P.O. Box 1329, Jalahalli, Bangalore 560013, India
| | - K. S. Krishnamurthy
- Centre for Soft Matter Research, P.O. Box 1329, Jalahalli, Bangalore 560013, India
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Wang Y, Yoon HG, Bisoyi HK, Kumar S, Li Q. Hybrid rod-like and bent-core liquid crystal dimers exhibiting biaxial smectic A and nematic phases. ACTA ACUST UNITED AC 2012. [DOI: 10.1039/c2jm34315k] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Tadapatri P, Krishnamurthy KS, Weissflog W. Multiple electroconvection scenarios in a bent-core nematic liquid crystal. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:031706. [PMID: 21230090 DOI: 10.1103/physreve.82.031706] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2010] [Indexed: 05/30/2023]
Abstract
We report on the anisotropic electrohydrodynamic states formed over a wide temperature range (∼45 °C) in a planarly aligned bent-core nematic liquid crystal driven by fields of frequency in the range 0.1 Hz-1 MHz. Three different primary bifurcation scenarios are generated in the voltage-frequency (V-f) plane, depending on the temperature T. These, under increasing T, are characterized by the pattern sequences (i) in-plane longitudinal rolls (ILR)→in-plane normal rolls 1 (INR1), (ii) Williams rolls (WR)→ILR→INR1, and (iii) WR→INR2→INR1. Temperature-induced ILR→INR2 transition, the first example of its kind, points to elastic anisotropy as possibly the determining factor in wave vector selection. In the ILR and INR states, at threshold, the director modulations are predominantly azimuthal, and the streamlines, mainly normal to the wave vector, lie in the sample plane. Well above threshold, growing director deviations lead to narrow disclination loops that evolve in regular arrays, with their area density being exponential in voltage. The defects drift in a coordinated manner along the flow lines with a speed that scales nonlinearly with voltage; they mediate in the eventual occurrence of turbulence. The current theories of anisotropic convection based on static electrical parameters fail to account for the observed high-frequency instabilities. The study includes (i) a quantitative characterization of the critical parameter functions V(c)(f), V(c)(T), q(c)(f), and q(c)(T), with q(c) denoting the critical pattern wave number, and (ii) measurement of electrical and elastic parameters of relevance to electroconvection; the latter show anomalous features supporting the cluster hypothesis.
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Affiliation(s)
- Pramod Tadapatri
- Centre for Soft Matter Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India
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Marinov YG, Hinov HP. On the threshold characteristics of the flexoelectric domains arising in a homogeneous electric field: The case of anisotropic elasticity. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 31:179-189. [PMID: 20195685 DOI: 10.1140/epje/i2010-10560-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2009] [Revised: 09/29/2009] [Indexed: 05/28/2023]
Abstract
Precise solutions for the threshold voltage U(c) and wave number q(c) that feature the appearance of longitudinal flexoelectric domains of Vistin'-Pikin-Bobylev at strong anchoring have been derived. Based on the formulated expressions, we present and analyze computer calculations for a planar nematic layer with anisotropic elasticity and both negative and positive dielectric anisotropy under the action of a homogeneous flexoelectrically deforming d.c. electric field. The obtained relations allow a selection of particular values of physical parameters, in order to improve the performance of devices exploiting flexoelectrcity in nematics.
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Affiliation(s)
- Y G Marinov
- Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tzarigradsko Chaussee Blvd., BG-1784, Sofia, Bulgaria.
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Tadapatri P, Hiremath US, Yelamaggad CV, Krishnamurthy KS. Permittivity, Conductivity, Elasticity, and Viscosity Measurements in the Nematic Phase of a Bent-Core Liquid Crystal. J Phys Chem B 2010; 114:1745-50. [DOI: 10.1021/jp905879n] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pramod Tadapatri
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India
| | - Uma S. Hiremath
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India
| | - C. V. Yelamaggad
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India
| | - K. S. Krishnamurthy
- Centre for Liquid Crystal Research, P.O. Box 1329, Jalahalli, Bangalore 560 013, India
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Wang LY, Chiang IH, Yang PJ, Li WS, Chao IT, Lin HC. Configuration Effects of H-Bonded Sites and Rigid Core Lengths on H-Bonded Banana-Shaped Liquid Crystalline Supramolecules Consisting of Symmetric Trimers and Asymmetric Heterodimers. J Phys Chem B 2009; 113:14648-60. [DOI: 10.1021/jp907360c] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Ling-Yung Wang
- Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan (ROC), Institute of Chemistry, Academia Sinica, Taipei, Taiwan (ROC)
| | - I-Hung Chiang
- Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan (ROC), Institute of Chemistry, Academia Sinica, Taipei, Taiwan (ROC)
| | - Po-Jen Yang
- Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan (ROC), Institute of Chemistry, Academia Sinica, Taipei, Taiwan (ROC)
| | - Wan-Sheung Li
- Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan (ROC), Institute of Chemistry, Academia Sinica, Taipei, Taiwan (ROC)
| | - I-To Chao
- Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan (ROC), Institute of Chemistry, Academia Sinica, Taipei, Taiwan (ROC)
| | - Hong-Cheu Lin
- Department of Materials Science and Engineering, National Chiao Tung University, Hsinchu, Taiwan (ROC), Institute of Chemistry, Academia Sinica, Taipei, Taiwan (ROC)
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