Related Experiment Video
Updated: May 17, 2026
08:37
Forming, Confining, and Observing Microtubule-Based Active Nematics
Published on: January 13, 2023
Deformable homeotropic nematic droplets in a magnetic field
Ronald H J Otten1, Paul van der Schoot
1Theory of Polymers and Soft Matter and Eindhoven Polymer Laboratories, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. r.h.j.otten@gmail.com
The Journal of Chemical Physics
|October 23, 2012
Summary
We developed a theory for nematic droplets in magnetic fields, explaining their shapes and director fields. This helps understand experimental observations of these complex liquid crystal systems.
Area of Science:
- Soft Matter Physics
- Liquid Crystal Science
- Materials Science
Background:
- Nematic droplets exhibit complex shapes and internal structures.
- Surface anchoring and external fields significantly influence droplet behavior.
- Recent experiments show diverse tactoid shapes and director fields.
Purpose of the Study:
- To develop a Frank-Oseen elasticity theory for deformable nematic droplets.
- To investigate the influence of magnetic fields on droplet shape and director field.
- To rationalize experimentally observed structures in nematic droplets.
Main Methods:
- Application of Frank-Oseen elasticity theory.
- Analysis of nematic droplets with homeotropic surface anchoring.
- Inclusion of negative magnetic susceptibility in theoretical models.
- Development of a three-dimensional phase diagram.
Main Results:
- Small drops adopt a lens shape with homogeneous director fields.
- Larger drops show spherical shapes and radial director fields under weak magnetic fields.
- Strong magnetic fields induce split-core line defects and potential tactoid elongation.
- A phase diagram maps tactoid shape and director field based on anchoring, size, and field strength.
Conclusions:
- The Frank-Oseen theory successfully explains observed nematic droplet behaviors.
- Magnetic field strength and anchoring critically determine droplet morphology.
- Findings provide a theoretical basis for experimental observations in nematic-in-nematic systems.
Related Concept Videos
01:27Magnetic Fields
A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on any other moving charge or current that is present in the field. Like an electric field, the magnetic field is also a vector field. At any position, the direction of the magnetic field is defined as the direction in which the north pole of a compass needle points.
A magnetic field is defined by the force that a charged particle experiences...
A magnetic field is defined by the force that a charged particle experiences...
01:28Induced Electric Dipoles
A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...
01:24Potential Due to a Magnetized Object
Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...
The vector...
01:23Atomic Nuclei: Nuclear Relaxation Processes
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...
01:26Diamagnetism
Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the moments opposite to the field are induced. Such materials are called diamagnets. Diamagnetism is the response of the diamagnets when placed in an external magnetic field.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
01:31Ferromagnetism
Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic dipoles are rigidly aligned in the same direction within a domain by quantum mechanical coupling among the atoms. This coupling is so strong that even thermal agitation at room temperature cannot break it. The result is that each domain has a net dipole moment. However, some materials have weaker coupling, and are ferromagnetic at lower...