Tailored nematic and magnetization profiles on two-dimensional polygons

Han, Yucen; Harris, Joseph; Walton, J.L.; Majumdar, Apala

doi:10.1103/physreve.103.052702

Cited by 13 publications

(8 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it gains stability for moderate values of λ, as L 2 increases, and ceases to exist for very large positive values of L 2 . We note some similarity with recent work on ferronematics [34], where the coupling between the nematic director and an induced spontaneous magnetisation stabilises interior nematic point defects, with L 2 = 0. It remains an open question as to whether elastic anisotropy or coupling energies (perhaps with certain symmetry and invariance properties) can stabilise interior nematic defects, and help us tune the locations, dimensionality and multiplicity of defects for tailor-made applications.…”

Section: Conclusion and Discussionsupporting

confidence: 84%

Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model

Han¹,

Harris²,

Zhang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the effects of elastic anisotropy on the Landau-de Gennes critical points for nematic liquid crystals, in a square domain. The elastic anisotropy is captured by a parameter, L2, and the critical points are described by three degrees of freedom. We analytically construct a symmetric critical point for all admissible values of L2, which is necessarily globally stable for small domains i.e., when the square edge length, λ, is small enough. We perform asymptotic analyses and numerical studies to discover at least 5 classes of these symmetric critical points -the W ORS, Ring ± , Constant and pW ORS solutions, of which the W ORS, Ring + and Constant solutions can be stable. Furthermore, we demonstrate that the novel Constant solution is energetically preferable for large λ and large L2, and prove associated stability results that corroborate the stabilising effects of L2 for reduced Landau-de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of L2, which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures.

show abstract

Section: Conclusion and Discussionsupporting

confidence: 84%

Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model

Han¹,

Harris²,

Zhang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The boundary of S R being parametrised by its arclength implies that, |γ | = 1 we can substituting in equation (10) to deduce that 2π =…”

Section: The Choice In the Parameterisationmentioning

confidence: 99%

“…• The three branches denoted Ortho, Meta and Para, correspond to permutations of the corner defect strengths: two of strength 1 3 and four of strength − 1 6 [10,8], these branches are present in the limit λ → ∞.…”

Section: Prediction Of Defect Strengthsmentioning

confidence: 99%

A conservation law for liquid crystal defects on manifolds

Pim¹

2021

Preprint

View full text Add to dashboard Cite

The analysis of nematics shells has recently become of great importance, with novel applications ranging from the creation of colloidal materials using DNA strands, to inventing contact lenses capable of changing their dioptre. In this piece, we analyse the orientation of a thin nematic film on the surface of a smooth manifold, specifically the strength of point defects located on the surface and the boundary. We model the orientation by a unit vector field which is orthogonal to the surface normal, in this model defects are points where the localised index is non-zero, this motivates us to derive a generalisation to the Poincare-Hopf theorem, which connects the total index of a vector field to the Euler characteristic of the surface, the sum of the interior angles and the integral of the boundary data. In liquid crystals one of the first models derived is the Oseen-Frank energy density, in this piece we consider the one constant approximation with respect to the curved geometry. The energy density diverges to infinity as one approaches a point defect of non-zero strength. Thus for a given manifold and vector field we derive a lower bound for the rate of energy divergence. This divergence rate is a function of the defect strengths and local curvatures, thus observable configurations of defects must minimise this rate of divergence, whilst also obeying the generalisation to the Poincare-Hopf theorem we derived earlier. Thus using these principle we create a heuristic method to predict the defect strengths of a nematic shell given purely geometrical parameters and boundary data. This is then contrasted with known results from both the experimental and numerical results within the liquid crystal community.

show abstract

“…A lot of interest has been devoted to carbon nanotubes that have an impact on LCs electro-optical properties ( Chen et al., 2007 ; Basu et al., 2010 , 2011 ; Petrov et al., 2013 ). Other studies on LC systems doped with quantum dots have shown the possibility to modify the dielectric, electro-optical properties of LCs as well as the pitch of cholesteric LCs ( Kumar et al., 2011 ; Cho et al., 2014 ; Rodarte et al., 2012 , 2014 ; Patranabish et al., 2021 ; Han et al., 2021 ).…”

Section: Introductionmentioning

confidence: 99%

Clustering in ferronematics—The effect of magnetic collective ordering

et al. 2021

View full text Add to dashboard Cite

Summary Clustering of magnetic nanoparticles can dramatically change their collective magnetic properties, and it consequently may influence their performance in biomedical and technological applications. Owing to tailored surface modification of magnetic particles such composites represent stable systems. Here, we report ferronematic mixtures that contain anisotropic clusters of mesogen-hybridized cobalt ferrite nanoparticles dispersed in liquid crystal host studied by different experimental methods—magnetization measurements, small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), and capacitance measurements. These measurements reveal non-monotonic dependencies of magnetization curves and the Fréedericksz transition on the magnetic nanoparticles concentration. This can be explained by the formation of clusters, whose structures were determined by SAXS measurements. Complementary to the magnetization measurements, SANS measurements of the samples were performed for different magnetic field strengths to obtain information on the orientation of the liquid crystal molecules. We demonstrated that such hybrid materials offer new avenues for tunable materials.

show abstract

Tailored nematic and magnetization profiles on two-dimensional polygons

Cited by 13 publications

References 38 publications

Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model

Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model

A conservation law for liquid crystal defects on manifolds

Clustering in ferronematics—The effect of magnetic collective ordering

Contact Info

Product

Resources

About