Colloidal liquid crystals in rectangular confinement: theory and experiment
We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the '...
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| Published in | Soft matter Vol. 1; no. 39; pp. 7865 - 7873 |
|---|---|
| Main Authors | , , , , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
England
21.10.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1744-683X 1744-6848 1744-6848 |
| DOI | 10.1039/c4sm01123f |
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| Abstract | We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type
fd
-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the
fd
-virus.
We theoretically and experimentally study equilibrium states of nematic liquid crystals within shallow rectangular wells. |
|---|---|
| AbstractList | We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen–Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the ‘diagonal’ and ‘rotated’ solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen–Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type
fd
-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the
fd
-virus. We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus. We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd -virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd -virus. We theoretically and experimentally study equilibrium states of nematic liquid crystals within shallow rectangular wells. We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus.We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional Oseen-Frank framework, with strong tangent anchoring, and obtain explicit analytical expressions for the director fields and energies of the 'diagonal' and 'rotated' solutions reported in the literature. These expressions separate the leading-order defect energies from the bulk distortion energy for both families of solutions. The continuum Oseen-Frank study is complemented by a microscopic mean-field approach. We numerically minimize the mean-field functional, including the effects of weak anchoring, variable order and random initial conditions. In particular, these simulations suggest the existence of higher-energy metastable states with internal defects. We compare our theoretical results to experimental director profiles, obtained using two types of filamentous virus particles, wild-type fd-virus and a modified stiffer variant (Y21M), which display nematic ordering in rectangular chambers, as found by confocal scanning laser microscopy. We combine our analytical energy expressions with experimentally recorded frequencies of the different equilibrium states to obtain explicit estimates for the extrapolation length, defined to be the ratio of the nematic elastic constant to the anchoring coefficient, of the fd-virus. |
| Author | Koenderink, Gijsje H Aarts, Dirk G. A. L Alvarado, José Mulder, Bela M Dammone, Oliver J Lewis, Alexander H Howell, Peter D Garlea, Ioana Lettinga, M. P Majumdar, Apala |
| AuthorAffiliation | FOM Institute AMOLF Institute of Technology University of Bath Laboratory of Cell Biology Institut für Festkörperforschung Forschungszentrum Jülich Department of Chemistry Mathematical Institute Department of Mechanical Engineering University of Oxford Physical and Theoretical Chemistry Laboratory Department of Mathematical Sciences Wageningen University |
| AuthorAffiliation_xml | – name: Mathematical Institute – name: Department of Chemistry – name: Institut für Festkörperforschung – name: Laboratory of Cell Biology – name: University of Bath – name: FOM Institute AMOLF – name: Institute of Technology – name: University of Oxford – name: Department of Mechanical Engineering – name: Department of Mathematical Sciences – name: Forschungszentrum Jülich – name: Wageningen University – name: Physical and Theoretical Chemistry Laboratory |
| Author_xml | – sequence: 1 givenname: Alexander H surname: Lewis fullname: Lewis, Alexander H – sequence: 2 givenname: Ioana surname: Garlea fullname: Garlea, Ioana – sequence: 3 givenname: José surname: Alvarado fullname: Alvarado, José – sequence: 4 givenname: Oliver J surname: Dammone fullname: Dammone, Oliver J – sequence: 5 givenname: Peter D surname: Howell fullname: Howell, Peter D – sequence: 6 givenname: Apala surname: Majumdar fullname: Majumdar, Apala – sequence: 7 givenname: Bela M surname: Mulder fullname: Mulder, Bela M – sequence: 8 givenname: M. P surname: Lettinga fullname: Lettinga, M. P – sequence: 9 givenname: Gijsje H surname: Koenderink fullname: Koenderink, Gijsje H – sequence: 10 givenname: Dirk G. A. L surname: Aarts fullname: Aarts, Dirk G. A. L |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25154421$$D View this record in MEDLINE/PubMed |
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| Snippet | We theoretically and experimentally study nematic liquid crystal equilibria within shallow rectangular wells. We model the wells within a two-dimensional... |
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| SubjectTerms | alignment Anchoring cell-sized confinement Crystal defects de-gennes theory defects Exact solutions interfaces Liquid crystals Mathematical analysis Mathematical models Nematic phases surfaces Wells |
| Title | Colloidal liquid crystals in rectangular confinement: theory and experiment |
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