arXiv subjects

Eugene C. Gartland Jr

Publications and source records attributed to Eugene C. Gartland Jr.

4 recordsLinked to original sources

arXiv2024

Anomalous behavior of electric-field Fréedericksz transitions

Fréedericksz transitions in nematic liquid crystals are re-examined with a focus on differences between systems with magnetic fields and those with electric fields. A magnetic field can be treated as uniform in a liquid-crystal medium; while a nonuniform director field will in general cause nonuniformity of the local electric field as well. Despite these differences, the widely held view is that the formula for the threshold of local instability in an electric-field Fréedericksz transition can be obtained from that for the magnetic-field transition in the same geometry by simply replacing the magnetic parameters by their electric counterparts. However, it was shown in [Arakelyan, Karayan, and Chilingaryan, Sov. Phys. Dokl., 29 (1984) 202-204] that in two of the six classical electric-field Fréedericksz transitions, the local-instability threshold should be strictly greater than that predicted by this magnetic-field analogy. Why this elevation of the threshold occurs is carefully examined, and a simple test to determine when it can happen is given. This "anomalous behavior" is not restricted to classical Fréedericksz transitions and is shown to be present in certain layered systems (planar cholesterics, smectic-A) and in certain nematic systems that exhibit periodic instabilities.

cond-mat.soft↗

arXiv2021

A model liquid crystal cell in an RC circuit

A nematic liquid-crystal cell subject to an electric field created by electrodes held at constant potential is modeled as a variable capacitor in an RC circuit. The state of the system is characterized in terms of the director field in the cell and the charge on the electrodes. A dynamical system is developed that couples director dynamics in the cell (with no fluid flow) and charge dynamics in the circuit. The dynamical equations are derived from expressions for the total potential energy of the system and a dissipation involving a single rotational viscosity for the director plus Joule heating associated with current in the circuit. An effort is made to quantify effects, in particular the widely differing time scales for the processes involved, and numerical illustrations are given. The exercise illuminates aspects of the modeling of equilibrium states of such a system.

cond-mat.soft↗

arXiv2019

Forces and Variational Compatibility for Equilibrium Liquid Crystal Director Models with Coupled Electric Fields

Expressions are obtained for force and couple densities and stress tensors in macroscopic models for nematic liquid crystals subjected to electric fields. The coupling between the liquid crystal orientational properties and the electric field is taken into account via a free energy of Oseen-Frank type expressed as an integral functional of the director field and the electric potential field. The variational model here also allows for a gravitational field and a magnetic field, and the differences among these three common types of force fields (gravitational, magnetic, and electric) are discussed. Also included in the free energy is a surface anchoring potential, and its effect on boundary traction and couple stress is explored. The electric field is assumed to arise from electrodes held at constant potential. Flexoelectric effects are included, and as a consequence, the material is no longer a linear dielectric medium. It is shown that the equilibrium solutions of the Euler-Lagrange equations satisfy appropriate expressions of force balance and torque balance, obtained from a virtual-work principle, and a connection is made between this and ideas related to Noether's Theorem. The development here builds from theories of Ericksen related to the notion of "variational compatibility," and this connection is made. Comparisons are also made to the extensive literature in physics and continuum mechanics on electromagnetic field/matter interaction.

cond-mat.soft↗

arXiv2017

Scalings and Limits of Landau-deGennes Models for Liquid Crystals: A Comment on Some Recent Analytical Papers

Some recent analytical papers have explored limiting behaviors of Landau-deGennes models for liquid crystals in certain extreme ranges of the model parameters: limits of "vanishing elasticity" (in the language of some of these papers) and "low-temperature limits." We use simple scaling analysis to show that these limits are properly interpreted as limits in which geometric length scales (such as the size of the domain containing the liquid crystal material) become large compared to intrinsic length scales (such as correlation lengths or coherence lengths, which determine defect core sizes). This represents the natural passage from a mesoscopic model to a macroscopic model and is analogous to a "London limit" in the Ginzburg-Landau theory of superconductivity or a "large-body limit" in the Landau-Lifshitz theory of ferromagnetism. Known relevant length scales in these parameter regimes (nematic correlation length, biaxial coherence length) can be seen to emerge via balances in equilibrium Euler-Lagrange equations associated with well-scaled Landau-deGennes free-energy functionals.

cond-mat.soft↗