NOTE: End date changed to 12/1/2022 per NSSC information (Ed., 1/26/22)

Perhaps most important use of topological defects is that they can serve as traps for micro- and nanoparticles (NPs), as the presence of the particles reduces or eliminates the divergent energy associated with the defect core. In other words, nanoparticles (NPs) migrate within the LC in the direction of increasing stress associated with the liquid crystal's orientational order, as the presence of the particles provides relief from the large stresses that would be present at LC singularities. The incorporation of NPs into liquid crystals and their subsequent behavior in and around defects finds applications in areas such as energy harvesting, photonic structures, mirrorless lasing, micro-patterned LC devices, and chiral metamaterials for photonics and communications applications. They also may have applications in pharmaceuticals, as an alternative means of drug delivery.

A patterned surface defect of integer "strength" can decompose into a pair of surface defects and disclination lines of half strength. For certain liquid crystals subjected to an applied AC electric field E, these half-integer defects are observed to wobble azimuthally for E > than some threshold field and, for sufficiently large fields, to co-revolve around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency, where the threshold field for full co-revolution scales as the square root of frequency. Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency “phase diagram” compellingly suggests that the defects’ fluctuations and eventual co-revolutions are coupled strongly to the presence of the electrohydrodynamic (EHD) instability. We have spent considerable effort to map the director field in the EHD instability and compare this to the director field of the defect pair in the absence of an electric field. As of this writing, we are at the cusp of showing that the EHD instability “carries” along the defect pair in its co-revolution motion. We also have examined the effects of chirality (the absence of mirror symmetry) on the motion, both in terms of mixing a chiral dopant into the liquid crystals (LC) and by patterning the substrate with a 2D chiral easy axis.

A thin film of Smectic-A liquid crystal was deposited on a polymer-coated substrate that had been scribed with closely spaced (200 m separation) lines over a small square of side L, where L=85 µm. Because of the small size of the patterned region, material could be transported to form either a hill (for a thin film) or divot (for a thick film) that contains an "oily streak" LC texture above the scribed square. (The oily streak texture involves a series of half cylinders that are comprised of the smectic liquid crystal layers.) Optical measurements of the topography of the free surface of the film vs. average film thickness suggest that the oily streak layer attempts to adopt a preferred thickness that depends on the nature of the molecule, the temperature, and the surface tension at the air interface. We hypothesized that the oily streak has a preferred “Goldilocks” thickness z0: If the film is thinner than z0, liquid crystal material would flow into the patterned region to create a hill above the pattern; if the film is thick, then material would flow out of the region to create a divot. Competing against either hill or divot formation is surface tension, which attempts to keep the film surface flat. We developed a model in which we determine the energy cost of the oily streak layer if its thickness differs from the preferred thickness z0. Moreover, the model allows us to estimate the energy cost of the oily streak region for thickness deviations from z0. A manuscript has just been submitted for publication.

We measured the behavior of a chirally-doped nematic mixture of of different helical pitches for a liquid crystal that aligns parallel to an applied electric field. Initially the liquid crystal molecules are "surface-stabilized" in the homeotropic configuration, where the molecules lie perpendicular to the cell walls.. By applying an in-plane magnetic field perpendicular to the director, we find a "Freedericksz" threshold field Hth above which the sample begins to undergo a combination of bend and twist distortions, and for which Hth decreases as the chiral helical pitch p decreases. For sufficiently tight pitch or sufficiently thick sample, the extrapolated Freedericksz threshold goes to zero. A similar experiment had been performed for a negative dielectric anisotropy LC using an electric field, but the current situation is of lower symmetry and therefore considerably more complex. We developed a theoretical model for this symmetry-broken configuration, finding good agreement with the experiment. Additionally, the new magnetic results are compared to the previous electric field 2*pi-degenerate experiments. As of this writing a manuscript is being prepared, which we expect to submit for publication in early 2023.

Skyrmions are broken-symmetry excitations with particle-like characteristics and which are topologically protected. In practice, this configuration involves a series of concentric circles in which the liquid crystal molecules are perpendicular to the circles in the center, i.e., at r = 0. Moving radially outward, the polar angle increases to 90 degrees (in the plane of the circles), while the azimuthal component of the director is tangent to the circles, forming a clockwise or counterclockwise circumnavigation. Theoretically, a quasi-2D lattice of half-skyrmions can be the stable ground state for a chiral liquid crystal in a cell with homeotropic (vertical) boundary conditions. We have begun to study these structures by patterning a substrate for the skyrmion’s director field and examining the resulting behavior (with and without applied electric field) using fluorescent confocal microscopy. Our goal is to investigate how the natural pitch of the chiral liquid crystal is affected by the cell thickness and the patterned pitch length. Additionally, we aim to understand defect formation when one substrate is patterned for half- or full-skyrmion director fields. That is, for a given chiral liquid crystal helical pitch, is the skyrmion stable over a range of spatial periodicities that can be imposed by a surface patterning technique? And if so, what is the nature of the required defect near the opposing substrate?

NOTE: End date changed to 12/1/2022 per NSSC information (Ed., 1/26/22)

Perhaps most important use of topological defects is that they can serve as traps for micro- and nanoparticles (NPs), as the presence of the particles reduces or eliminates the divergent energy associated with the defect core. In other words, nanoparticles (NPs) migrate within the LC in the direction of increasing stress associated with the liquid crystal's orientational order, as the presence of the particles provides relief from the large stresses that would be present at LC singularities. The incorporation of NPs into liquid crystals and their subsequent behavior in and around defects finds applications in areas such as energy harvesting, photonic structures, mirrorless lasing, micro-patterned LC devices, and chiral metamaterials for photonics and communications applications. They also may have applications in pharmaceuticals, as an alternative means of drug delivery.

Much of our effort went into working with the groups in Boulder and Kent, in conjunction with the NASA Glenn team, on the Science Requirements Document (SRD).

Continued from the previous year, we have been investigating film thickness measurement techniques, and have focused on an approach involving illumination with a quasi-white light source (but having a known spectral distribution) and imaging of the reflected light using the R, G, and B channels of a CCD (charge-coupled device) camera, also of known spectral response. Previously, we modeled the intensity vs. film thickness for each of the channels, and developed a calculational technique to extract the film thickness and avoid the ambiguity of an intensity that is periodic in film thickness by using multiple color sensors in the detector. Moreover, this approach is superior to the laser illumination approach as it allows us to image an area, and extract the local film thickness when islands, divots, or steps in thickness are present. An automated image processing macro was developed to extract intensity values from film images. This work was conducted partially at Case and partially remotely during the spring of 2021. We investigated the use of one or multiple LEDs (light-emitting diodes) for illumination, which would obviate the need to account for the illumination spectrum of the quasi-white light. Reflection intensity measurements are being conducted on films of various thickness that contain steps and islands, and have spent considerable time accurately measuring the refractive indices of the relevant liquid crystals at appropriate temperatures and wavelengths. Using Dr. Tin's film holder, we have been drawing films at various spreader speeds in order to assess empirically how the approximate film thickness and stability is related to the speed. We have found that there is little correlation between spreading speed and film thickness, suggesting that the actual flight experiments will need to be performed by creating a film of arbitrary thickness, measuring the thickness, performing the experiment, breaking the film, and then creating another film of arbitrary thickness.

A patterned surface defect of strength m = +1 and its associated disclination lines can decompose into a pair of surface defects and disclination lines of strength m = +½. For a negative dielectric anisotropy liquid crystal subjected to an applied ac electric field E, these half-integer defects are observed to wobble azimuthally for E > some threshold field and, for sufficiently large fields, to co-revolve antipodally around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency, where the threshold field for full co-revolution scales as sqrt (frequency). Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency “phase diagram” compellingly suggests that the defects’ fluctuations and eventual co-revolutions are coupled strongly to the presence of the hydrodynamic instability, resulting in a Lehmann-like mechanism that drives the co-revolution.

Perhaps most important use of topological defects is that they can serve as traps for micro- and nanoparticles (NPs), as the presence of the particles reduces or eliminates the divergent energy associated with the defect core. In other words, nanoparticles (NPs) migrate within the LC in the direction of increasing stress associated with the liquid crystal's orientational order, as the presence of the particles provides relief from the large stresses that would be present at LC singularities. The incorporation of NPs into liquid crystals and their subsequent behavior in and around defects finds applications in areas such as energy harvesting, photonic structures, mirrorless lasing, micro-patterned LC devices, and chiral metamaterials for photonics and communications applications. They also may have applications in pharmaceuticals, as an alternative means of drug delivery.

We have been investigating film thickness measurement techniques, and have focused on an approach involving illumination with a quasi-white light source (but having a known spectral distribution) and imaging of the reflected light using the R, G, and B channels of a CCD (charge-coupled device) camera, also of known spectral response. We have modeled the intensity vs. film thickness for each of the channels, and developed a calculational technique to extract the film thickness and avoid the ambiguity of an intensity that is periodic in film thickness by using multiple color sensors in the detector. Moreover, this approach is superior to the laser illumination approach as it allows us to image an area, and extract the local film thickness when islands, divots, or steps in thickness are present. We also have written software to account for ancillary effects, such as the angular spread of the light and noise. An automated image processing macro was developed to extract intensity values from film images. This work was conducted partially at Case and partially remotely during the summer of 2020, with undergraduate Rachel Margulies working with Dr. Padetha Tin at NASA (as well as with the Principal Investigator-PI Charles Rosenblatt at Case).

Currently we are investigating the possibility of using one or multiple LEDs (light emitting diodes) for illumination, which would obviate the need to account for the illumination spectrum of the quasi-white light. Reflection intensity measurements are being conducted on films of various thickness that contain steps and islands.

We have continued some of the work from the previous year in order to finalize the materials to be used aboard ISS. We have been adjusting the voltage parameters to our inkjet head to optimize the droplet size and speed for methanol and IPA (isopropyl alcohol). This has resulted in a decrease in the size of the islands created, which is essential for our fluorescent carbon dot experiment to study topological defects in smectic-C films using the liquid crystals 9OO4 and ZA-284. But importantly, the control of the ejected methanol droplets from the inkjet printer allows us to study the creation of islands and divots in the film. (The solvent evaporates quickly and is chosen to have poor solubility with the liquid crystal. Thus, the island formation is due to the impulse force of the droplet.) In particular, the diameter and thickness of the islands and divots are being examined as functions of the film’s original thickness and the droplet speed. We have performed 1g studies of island and divot formation, and have concluded that we will use only normal incidence for the experiments aboard the ISS. Moreover, we have decided to perform the island/divot experiments using the liquid crystal ZA-284 and methanol.

Using Dr. Tin’s film holder, which for us has been an improvement over Prof. Yokoyama’s design last year, and which relies on two plates with holes having razor-sharp edges passing over each other, we have been drawing films at various spreader speeds in order to assess empirically how the approximate film thickness and stability is related to the speed. We have found that there is little correlation between spreading speed and film thickness, suggesting that the actual flight experiments will need to be performed by creating a film of arbitrary thickness, measuring the thickness, performing the experiment, breaking the film, and then creating another film of arbitrary thickness.

We examined electric field induced transition from a strength m = +1 partially escaped radial topological defect to a pair of split (m = ½) defects, and the same transition in the reversed direction. We found the transitions to be discontinuous (first order), and developed a theory for the phenomenon. In the course of the experiments we discovered the phenomenon of co-rotation of the split defects about a common point. This work is continuing.

Perhaps most important use of topological defects is that they can serve as traps for micro- and nanoparticles (NPs), as the presence of the particles reduces or eliminates the divergent energy associated with the defect core. In other words, nanoparticles (NPs) migrate within the LC in the direction of increasing stress associated with the liquid crystal's orientational order, as the presence of the particles provides relief from the large stresses that would be present at LC singularities. The incorporation of NPs into liquid crystals and their subsequent behavior in and around defects finds applications in areas such as energy harvesting, photonic structures, mirrorless lasing, micro-patterned LC devices, and chiral metamaterials for photonics and communications applications. They also may have applications in pharmaceuticals, as an alternative means of drug delivery.

1. Tailoring the size and speed of the solvent droplets [methanol and isopropyl alcohol (IPA)] emanating from the ink jet printer head in order to minimize the creation of islands in the smectic film

2. Measuring the film thickness as a function of spreader speed using a prototype film holder loaned to us by Prof. Hiroshi Yokoyama

3. Determining the parameters for incident UV light on the fluorescent carbon dots

4. Examining the feasibility of adding an additional experiment in which the focus will be on the creation of islands and divots in the smectic film due to impact from a droplet emanating from the inkjet printer.

Inkjet printers operate on the basis of several pulses applied to piezoelectrics, where the duration and pulse heights determine the velocity and diameter at which droplets of liquid are expelled from the aperture. We have been adjusting these parameters in order to optimize the droplet size and speed for methanol, our original choice of solvent for the carbon dots, and more recently for IPA. Using both 70 and 50 micrometers diameter aperture inkjet heads, we have been able to achieve a droplet speed of order 10 cm s-1, one to two orders of magnitude slower than the canonical speeds stated by the manufacturer. This has resulted in a decrease in the size of the islands created, an important requirement for our original project goals, that is, deposition of fluorescent carbon dots on a film and examination of the carbon dot aggregation at topological defects in the smectic-C phase and dispersal when the film is cooled into the smectic-A phase. Because the liquid crystals (9OO4 and ZA-261) chosen for the project have relatively high smectic-A phase temperatures, we have decided to do these experiments with IPA, which has a higher boiling temperature than methanol and therefore is more stable when the experiments are performed at temperatures of order 60-65oC. Recently we have added a new goal, viz., the creation of islands and divots in smectic-A films by bombardment of solvent droplets. (The solvent evaporates quickly and is chosen to have poor solubility with the liquid crystal. Thus, the island formation is due to the impulse force of the droplet.) In particular, the diameter and thickness of the islands and divots are being examined as functions of the film’s original thickness and the droplet speed. We also examined a number of alternate liquid crystals that possessed the appropriate surface tensions for spreading and stability in the presence of our solvents. We eventually settled on Lemieux’s group’s ZA-284, which has a smectic-A temperature in the 40oC range and thus allows us to use methanol as the solvent. Lemieux has synthesized a batch of this liquid crystal for us, and it now has been incorporated into the program.

Using Prof. Yokoyama’s film holder, we have been drawing films at various spreader speeds in order to assess empirically how the film thickness is related to the speed. Here we have been using a spectroscopic technique with two lasers at 632 and 515 nm on reflection in order to determine the film thickness, and also measuring the reflectivity of thin films using the thickness-square technique, i.e., where the reflected intensity is approximately proportional to film thickness squared. We have found that there is little correlation between spreading speed and film thickness from approximately 15 nm up to 100 nm, suggesting that the actual flight experiments will need to be performed by creating a film of arbitrary thickness, measuring the thickness, performing the experiment, breaking the film, and then create another film of arbitrary thickness. To be sure, however, the thickness may be a function of the quantity of liquid crystal on the spreader, which will need to be investigated.

We are in the process of examining the illumination of the quantum dots utilizing a 2W LED source at wavelength 450 nm. We have set up a lens system for collimation of the light, and currently are measuring the intensity required to detect the dots at low concentrations, i.e., the sorts of concentrations that we expect to be using in the smectic-C thin film experiments.

In related projects:

1. We are continuing with our switching (“rewiring”) of in-plane line defects. Here we are attempting to use a single pair of in-plane electrodes (rather than orthogonal pairs of electrodes), coupled with a “dual frequency” liquid crystal in which the sign of the dielectric constant is a function of frequency.

2. We have demonstrated how certain types of in-plane disclination lines connecting half-integer strength surface topological defects can be switched to vertical disclinations using an electric field and a negative dielectric constant liquid crystal. On applying the field, the director is “squeezed” into the two-dimensional xy-plane, which excludes certain types of in-plane defect pairings.

Perhaps most important use of topological defects is that they can serve as traps for micro- and nanoparticles (NPs), as the presence of the particles reduces or eliminates the divergent energy associated with the defect core. In other words, nanoparticles (NPs) migrate within the LC in the direction of increasing stress associated with the liquid crystal's orientational order, as the presence of the particles provides relief from the large stresses that would be present at LC singularities. The incorporation of NPs into liquid crystals and their subsequent behavior in and around defects finds applications in areas such as energy harvesting, photonic structures, mirrorless lasing, micro-patterned LC devices, and chiral metamaterials for photonics and communications applications. They also may have applications in pharmaceuticals, as an alternative means of drug delivery.

1. We switched the shape of the liquid crystal (LC) film from a hollow bubble to a flat film of thickness approximately 100 nm (30 layers of smectic LC). This was done because of the inability to track defect motion on the bubble surface, whereas a flat film is amenable to camera tracking software.

2. We found that using an initial mixture of LC and FCDs to create the film resulted in aggregation of the FCDs. Instead, we switched to a system whereby the smectic LC film is created and then an inkjet printer head is used to deposit a mixture of FCDs and solvent onto the film. The solvent then evaporates, leaving the FCDs to incorporate into the film. We also investigated the efficacy of the inkjet deposition angle onto the film, finding little difference when varying the angle from 90 degrees (perpendicular to the film) down to 45 degrees. We have designed and have 3D-printed a holder for the inkjet nozzle that will provide better protection against damage, and facilitate angular and positional control.

3. We investigated various solvents for the FCD / solvent mixture, and found that methanol is an effective and safe choice. The FCDs do not aggregate in the methanol, and the FCDs prefer the LC to the methanol after deposition onto the LC film.

4. We investigated the optical properties of several LCs and molecules attached to the FCDs to make sure that we do not see any unwanted artifacts in our fluorescent signal.

5. We examined how best to eliminate unwanted smectic "islands" from the film. We found that our original plan of using air blowers to push islands to the periphery would not be adequate. Instead, we found that the new film holder design by Hiroshi Yokoyama (Kent State U.) could create stable island-free films. We have adopted the new design.

6. We have been looking into the issue of cosmic ray artifacts on the LC and the imaging system. Since the number of high energy electrons is small, we don't expect them to have a deleterious effect on the LC. For the few spurious cosmic ray events on the CCD array, they tend to affect only 1 or 2 random pixels for short bursts (~ nanoseconds), so artifacts in the video will be easy to eliminate using post-data-collection processing. There is a well developed literature on how to handle this.

7. One problem has been the lack of robustness of the Microfab inkjet printer heads. We have found that they are damaged easily, and have been working on methods to avoid having the heads become clogged with the solvent NP/mixture.

Perhaps most important use of topological defects is that they can serve as traps for micro- and nanoparticles (NPs), as the presence of the particles reduces or eliminates the divergent energy associated with the defect core. In other words, nanoparticles (NPs) migrate within the LC in the direction of increasing stress associated with the liquid crystal's orientational order, as the presence of the particles provides relief from the large stresses that would be present at LC singularities. The incorporation of NPs into liquid crystals and their subsequent behavior in and around defects finds applications in areas such as energy harvesting, photonic structures, mirrorless lasing, micro-patterned LC devices, and chiral metamaterials for photonics and communications applications. They also may have applications in pharmaceuticals, as an alternative means of drug delivery.

Phase 1 involves optimizing the size, composition, and functionalization of the carbon-dots; the choice of liquid crystal; and the concentration of fluorescent carbon dots inside the liquid crystal. Co-Investigator (Co-I) Torsten Hegmann has chosen a variety of C-dots and coated them with various molecules (called ligands), in order to control the carbon dots' tendency to remain in the orientationally ordered LC or to move to the defect sites. Co-I Robert Lemieux has supplied us with a variety of LCs that have a range of phase transitions and temperatures suitable for use in the OASIS module. We have been testing these combinations to determine the most appropriate set of materials. These tests involve both closed cells that have been patterned with arrays of topological defects using the stylus of an AFM, as well as a newly-constructed sample holder that facilitates flat, free-standing films. For the closed cells we first had been using a fluorescence microscope in which the sample was illuminated at 480 nm in order to observe the fluorescent C-dots and their relationship to the defect patterns. More recently we have been using a confocal fluorescence microscope, with illumination at 405 nm, which allows us to obtain not only x and y information about the location of the fluorescent C-dots, but also information about the vertical (z) position of the dots as well. Our initial results suggest that the dots tend to aggregate in the center of the cell, away from the two bounding surfaces (one coated with polyvinyl alcohol and the other with polymethyl methacrylate). As part of phase 1 we also have been examining the optical requirements of the experiment, and have found an appropriate method for illuminating the bubbles aboard the ISS by using an LED at 450 nm for epi-illumination in conjunction with a long pass filter with a band edge at 475 nm that allows the fluorescent light, but not the incident light, to reach the detector. We still need to determine the intensity required of the light source.

Phase 2 is aimed at free-standing films, with no top and bottom substrates. This more closely mimics the conditions of the smectic bubbles that will be investigated in the OASIS module. We have constructed the free-standing film holder and have begun to examine the location of the C-dots within the smectic-C films. Our early investigations indicate that the presence of islands in the films tends to attract C-dots. As a result, we are now searching for ways to both minimize the presence of islands and to calibrate the C-dot density in a film of known thickness in order to account for artifacts due to the presence of any remaining islands.

Co-I Philip Taylor has been leading the theoretical part of the project. He has been examining two-dimensional nematic films in which there are a pair of s = ±½ defects that are free to move within the 2D surface. Additionally, he has trapped (theoretically, of course) a nanoparticle at the core of each defect. His simulations suggest that larger nanoparticles tend to remain associated with the defect cores as the defects move within the surface; smaller particles do not remain trapped. This result is important for one of the long term goals of the project, viz., how particles affect the motion of defects in the film.

As part of Phase 1, we examined a patterned array of s = ±1 topological defects in a closed nematic cell as a function of applied voltage and cell thickness. These defects did not contain carbon-dots, as the experiment was meant to understand the mechanisms by which defects decompose into "daughter defects" of weaker topological strength. We found that thicker cells tend to exhibit an escape of the nematic director as a means of mitigating the elastic energy cost near the defect cores, whereas thinner cells tend to favor splitting of the integer defects into pairs of half-integer strength defects. On heating the cells into the isotropic phase and recooling into the nematic, the relaxation mechanism of some defects was found to reverse. This is consistent with the system’s symmetry, which requires a first order transition between the two relaxation mechanisms. This work has been submitted for publication.