Magnetic Field Control of Liquid Crystal-Enabled Colloid Electrophoresis

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Summary:

Torres-Andres et al. use a combination of a strong magnetic field and an AC electric field for controlled transport of non-spherical micron-sized particles in a nematic liquid crystal. The electric field is used both to actuate the particles and to induce the LC Fredericksz transition from an initially homeotropic to a planar orientation. A homogeneous magnetic field (generated by a Hallbach array of magnets) is used to align the director along the field lines. In a different configuration, a ring magnet is employed to create a +1 topological defect with a radial configuration.

The authors demonstrate that when propelled, the particles move (more or less) along the director, whose orientation can be modified by the rotation of the magnet array. In the case of the ring magnet and +1 defect, the particles are drawn towards the defect. Due to inter-particle repulsion, the particles don’t form a closely packed cluster, but rather orbit around the defect (“rotating mill”).

 

Suggestions:

1. In the section 2.2. Particles-LC Mixture it is not clear how many steps were needed to exchange the solvent from ethanol to pure water. Please also state why one can not directly replace ethanol with water.
2. Check the spelling in the manuscript: Trek amplifier (not Treck), evaporate (not evapoate), magetic field (not cield).
3. In Figure 1 you show that magnetic field influences the motion of the particles, however it is not clear how good is this control. Could you add a few snapshots of particles when magnetic has a constant direction, i.e. not only between t=0s and t=10s but to t=100s? Also a distribution of particle velocities as in Figure 6c would be beneficial.
4. In the text you claim that "the presence of irregularities in the ITO glass surfaces, disclination lines"  alters the uniform motion of particles. Could you please add a POM image (with P and A at 45 degrees to the B field) to show the readers the uniformity of the director field?
5. What is magnetic field density of the ring magnet in the sample? In the text (l. 191, page 5) you state "115 mT measured at the center of the magnet". In the caption of Figure 5 you state "The magnetic field acquires a value of 115 mT at the cell mid-plane." Isn't the cell mid-plane (=LC layer) at least 2 mm (spacer)+ 1.1 mm (glass) away from the magnet? Could you estimate the in-plane and out-of-plane components of the B field in the LC?
6. Figure 6: How come that the number fraction of particles with horizontal velocity u>0 remains constant at 65% as the cluster is dissolved? The long-range hydrodynamic interactions should be significantly reduced as inter-particle distance increases. Would you get fraction of positive u's 0.5 if you turned off the magnetic field and turned it back on at t=100s?
7. What is the large black blob that is seen in Figure 6a (and in SM_5.avi) that is travelling from upper-right side of the image to lower-left side? Hi-res resolution POM images of this situation would be beneficial.

Author Response

We thank the reviewer for their comments and useful suggestions. Please, see attached file. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Since the mechanism of electrokinetics based on liquid crystal-enabled colloid electrophoresis was introduced by the Lavrentovich group more than 10 years ago, numerous studies were performed using various methods to control the nematic director field. The authors are the first to study these phenomena controlled by applying a magnetic field. The paper is well written; nevertheless, a few points should be improved before publication. Below are particular remarks.

Lines 28-30
When listing the driving mechanisms for swimming, it would be good to add light driving.

Line 94
Stress that the phi refers to cell thickness.

Line 99
When introducing LC, it would be good to stress that the negative dielectric anisotropy is needed to allow electric field-induced structural transition in a degenerate planar state and a positive magnetic anisotropy to allow orientation along the magnetic field.

Line 100
What kind of surface anchoring is provided by polystyrene particles?

Line 115
In what range is the field strength provided, and how does it compare with the one needed for the Fredericks transition?
Colloids are mainly in the same plane (Figs and videos). Is this the effect of narrow focus as the cell is thick? Or is there a strong surface repulsion due to surface anchoring?

Lines 118-119
Homogenous instead of the fixed external magnetic field! Add schematics like for the toroidal case.

Lines 148-155
How uniform is the planarity of the nematic field through the cell thickness? It depends on the uniformity of the magnetic field and surface anchoring strength. If the nematic director is not planar, particles can be driven toward the surface, where viscous friction increases and velocities slow down. 

Lines 170-174
Are differences in Fig 2 due to the variation of the director due to the magnetic field effect on the planarity of the director?

Fig. 1
The inset showing details around a colloidal particle is too tiny!
Is the surface expected to have a nonslip boundary condition? That is crucial for colloids that come close to the surface.
Is the E field high enough to provide planar alignment without a magnetic field?

Lines 188-238
In this case, experiments show that the magnetic effect close to the toroid is stronger than the electric field effect. Therefore, close to the defect, the director is no longer planar, which means the particles are driven towards the surface where friction is higher due to nonslip conditions! A simple simulation can easily illustrate the director field in the case of a toroidal magnet. The approaching of colloids to the surface should influence their velocity profiles and the formation of the rotating mill!

Lines 240-271
Also, in this part, the effect of the non-planar director is relevant and needs to be considered in the promise at the end of this section.

Author Response

We thank the reviewer for their comments and useful suggestions. Please, see attached file. 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents interesting and well-executed experimental work on the magnetic control of liquid-crystal-enabled electrophoresis (LCEEP). The authors demonstrate both unidirectional and collective control of particle motion using reconfigurable magnetic fields, which is timely and relevant to the field of soft matter and active colloids. However, I have several comments and suggestions that should be addressed before the manuscript can be recommended for publication:

 

1 Figure 1b lacks a scale bar or any scale reference, which is essential for readers to evaluate particle displacement and overall field of view.

 

2 In Figure 2, the dependence of particle speed on electric field strength and frequency is briefly described. While a quadratic dependence on field amplitude and a specific trend with frequency are mentioned, the underlying mechanisms—such as how the AC field couples with director distortions or ionic flows—are not clearly explained. Furthermore, it would be useful to comment on whether there is a plateau or optimal range of voltage beyond which the particle speed saturates.

 

3 The description of rotating particle mills (pages 7–9) is visually compelling, but the mechanisms driving particle clustering and rotation—e.g., elastic repulsion, director-mediated interactions, or hydrodynamic coupling—are only qualitatively discussed. A more detailed theoretical or quantitative insight would greatly strengthen this section.

 

4 In the discussion surrounding Equation (1), the influence of the applied AC electric field on the observed vorticity and speed profiles is not explicitly analyzed. Clarifying how the field strength modulates the observed collective dynamics would enhance the physical interpretation.

 

5 The manuscript requires careful language revision to correct typographical and grammatical errors. Examples include:

     Page 4, line 174: "magnetif cield alignment" → "magnetic field alignment".

     Page 9, line 275: The phrase “less robust than the ring magnet technique, although providing enhanced control opportunities” is awkward and redundant.

     Page 10, line 319: "FPU fellowship (No. ???)" should be completed or removed.

 

6 I suggest that the authors include citations to two recent and relevant studies that would help contextualize and broaden the scientific scope of the manuscript:

     Light: Science & Applications 11.1 (2022): 270, which provides a comprehensive overview of self-assembled optical structures in liquid crystals and their manipulation through external stimuli. This is particularly relevant when discussing the formation of defect-induced microstructures (Section 3.2).

     Physical Review Research 2.1 (2020): 013178, which reports a symmetry-breaking mechanism for AC electrophoresis in nematic liquid crystals, leading to particle motion via director perturbations (“directrons”). This complements the current discussion on the nonlinear and threshold-dependent behavior of LCEEP.

Author Response

We thank the reviewer for their comments and useful suggestions. Please, see attached file. 

Author Response File: Author Response.pdf