Towards Femtoscan-Assisted Analysis of Liquid Crystal Self-Organization on Diﬀerent Polymer and Glass Surfaces for Lab-on-a-Chip and Lab-on-a-Dish Applications, Including Optoﬂuidic and Flexoelectric Ones

In this paper, starting with an introductory review of the applications of liquid crystals and polymer-dispersed liquid crystal systems in (bio)sensors and microﬂuidics, the possibilities of visualizing self-organization products of liquid crystalline media or ﬁeld-induced instabilities of liquid crystalline systems are considered. In particular illustrated cases, it is proposed to use FemtoScan software-containing metrological complexes to visualize instabilities in liquid crystalline systems and products of self-organization in liquid crystalline media


Introduction
It is well known that liquid crystals (LCs) are widely used in the development of different physical sensors, including chipbased ones [1] and lab-on-a-chip analytical systems [2].Such LC and polymer composite structures can be used for physical [3] and chemical or biochemical sensing.Examples of LC-based physical sensors include: 1. Liquid crystal temperature sensors [4][5][6][7] (based on different principles -from optical to electrical [8,9] and phase transition-based ones [10]), including fiber-optic liquid crystalline temperature sensors [11][12][13] optical fiber sensor networks [27], liquid crystal optical phased arrays and modulators [28,29], fiber-and film-based spectral multiplexers [30,31], etc. 6. Liquid crystals in optical sensors of mechanical forces and motion [32,33].Such systems in microfluidic polymer chips can also be used with voltage-expandable liquid crystal surfaces or liquid crystal pumps [34,35] or liquid crystal polymer microactuators, including 3D-printed artificial cilia and artificial muscles [36][37][38][39] (electrocontrollable, thermocontrollable or photo controllable ones).7. LC-based and LC-containing image sensors and transceivers [40], including spectrally multiplexed ones and multispectral/hyperspectral ones [41] for smart regenerative medicine of the future -for the artificial retina design [42].Many optical sensors and transducers can also be used for multi-angle holographic detection [43,44] [56] and cholesteric liquid crystal detectors of organic vapors [57].Such devices can be spatially sensitive/2D positionsensitive [58].As examples of biochemical sensors based on liquid crystals and liquid crystal polymer composites (including biochemical sensing devices with in situ-formed liquid crystal thin films [59,60] and microdroplets [61]) one can mention: 1. DNA biosensors on solid surfaces and liquid-crystalline DNAbased biosensors [62][63][64].2. Different enzyme sensor assays and microarrays [65,66], for example, liquid-crystal protease assays [67][68][69].3. Microfluidic immunoassays with liquid crystals on the polymer biosensing chips [70].4. Liquid crystal-based aptasensors [71][72][73].5. Protein determination systems based on molecularly imprinted polymer recognition combined with birefringence liquid crystal detection [74] and liquid crystal microdroplets coated with block liquid crystalline polymers by protein adsorption for sensor applications [75].Some LC-assisted protein detection techniques (including on-chip detection) can also be implemented using surface plasmon resonance principles [76].6. Toxicological tests, including neurotoxicity sensors with liquid crystal components (for example, sensors for detecting organophosphorous nerve agents using liquid crystals supported on chemically functionalized surfaces [77][78][79][80][81][82] or neurochemical applications of liquid crystals sensor for organoamine detection.Polymer microfluidic devices with liquid crystal components and devices based on LC polymers can be used for optical detection [83,84].For example, concentric polymer-dispersed liquid crystal rings can be used for light intensity modulation [85].The production of interferometric sensors based on the wavelength detuning by a liquid crystalline polymer waveplate can also be implemented [86] [110][111][112][113][114].This potential source of artifacts before 2000 th has been eliminated by measuring area-averaged values, leveling the role of single microstructures or liquid-crystal texture elements.However, this approach is inapplicable when microanalysis with positional sensitivity is required. Unfortunately, morphological and textural inhomogeneities and features of the spatial distribution of mesophases in contact with various substrates (metal, polymer, and glass) used in the sensor design affect the metrological qualities of the sensors.They change not only the area-averaged analytical signal, but also its spatial distribution.The boundaries of the blurring effects of metrological signals received from liquid crystal transducers are determined by soft matter physics, that is, the partial ordering of the medium.Therefore, it is necessary not only to take into account the contribution of this (changing in response to the primary sensor signal/properties of the analyzed medium) ordering to the overall result of the analysis, but also to take into account the phenomena of microstructural self-organization and physicochemical transitions in a liquid crystal system (including LC-containing sensor sandwich systems) with positional sensitivity corresponding to the level of its structural (self) organization.In this regard, in this work, we attempt to perform a morphometric operando analysis of structural changes in a sensor based on a liquid crystal matrix on glass and polymer substrates using 3D visualization.The resulting crystals/dendrites under chemical analytics and biochemical physics detection conditions can lead to artifacts in detecting analytes and biological/biochemical/cytological structures.Therefore, we also consider examples in which the resulting products of selforganization are "artifacts" from the point of view of obtaining the final analytical signal [115,116].

Materials and Methods
We used propionic acid cholesteryl ester liquid crystal (REACHEM, catalog number 070140) dissolved in chloroform (reagent grade, Chimmed, Russia).This solution was poured onto the polymer substrates made of low-density polyethylene (LDPE), in particular, those adapted for working with agar media.The latter was chosen due to the fact that visualizing sensory LC-containing systems on a chip (for which the above experiments were performed in 2018) was intended for experimental biophysical and biomedical problems.The same LCs were studied on glass substrates (as prototypes of glass microfluidic chips) [117].
The measurements were performed using an inverted microscope with a modular illuminator designed by O.V. Gradov and a modified DIC/NIC microscope.A series of raw focal scans before multi-layer image processing and stacking are given in the supplement.Image analysis was performed using FemtoScan software, designed, in particular, to analyze scanning probe and superresolution microscopy data.

Results
First, unification of scales and selection of the optimal mesh for 3D visualization of LC textures and crystalline mesostructures on the surface of a polymer substrate were performed.The optimal mode was established between undersampling and oversampling, when the main features of the 3D texture are already visible, but it is not overloaded with details.At the same time, we did not allow false super-resolution when the sampling increases due to bootstrap or interpolation.An example of scale selection is shown in Figure 1.Figures 1-a -1-e demonstrate undersampling, Figures 1-g -1-h are optimal in terms of detail, while in Figures 1-i -1-l oversampling is observed.(Self-organization on a chip using optimal Bezier meshes we considered earlier within the context of morphological evolution in the d'Arcy-Thompson model in the technical papers [118,119]).Using this approach, we analyzed the spatial level of self-organization, from mesoscopic to nano level.These results are a kind of resolvometry for LC medium in response to the external factors that induce self-organization (either the nature of the surface or signals from the external environment).Laplace-type, Lambertian, and Lommel-Seeliger-like [120] shadow photometric mapping methods were used for pseudo-3D visualization.Pseudocolor mode enabled texture visualization, as in DIC/NIC and Hoffman and Rheinberg contrast techniques.An example of this is given in Figure 2. Optical density gradient fitting (including optimization in different spectrozonal channels) for 2D and 3D pseudocolor maps was also available, as shown in Figure 3.This figure and the following figures (Figure 4 -Figure 6) show the examples of linear artifacts observed in the evaporation and cooling zones.In general, it was possible to achieve optimal visualization for probe types of microscopy (for example, AFM) and for interference methods such as modulation interference microscopy (examples of such visualizations are given in Figure 4).
Correlation spectral analysis methods based on 2D Fourier spectra (2D FFT) were applied for original monochrome grayscale images and their 2D-to-3D transforms.Previously, we implemented this using QAVIS software based on the FFTW library.However, in Femtoscan technologies, a separate module works inside the GUI program shell for these purposes.An example of its use for the original image and the same image processed according to the above-described procedure is presented in Figure 5. Figure 6 shows a variety of visualizations of 2D Fourier spectra for a similar image from another area of the same sample.
For the characterization of the image elements by 2D FFT, there are ISC and IFC (integral spatial characteristics and frequency characteristics) calculation techniques and section techniques.We previously implemented these techniques on the basis of the software developed by a group of colleagues from the Pacific Oceanological Institute of the Far Eastern Branch of the Russian Academy of Sciences.Femtoscan does not have such features, but QAVIS can work directly with video memory with images opened in any software, including any version of Femtoscan.Thus, estimation of ISC and IFC is also possible for this kind of measurement protocol.

Figure 7 Section profiling and morphometric measurements
of LC structures on a chip.
However, the Femtoscan GUI has an option for grain analysis and comparative sectioning.An example of this module application is shown in Figure 7.
Macroscopic analysis of the sample surface in Petri dishes was also performed using a polariscope with the subsequent processing of video flow frames by the Sobel-Feldman gradient operator (filter).The results are shown at the link: https://www.youtube.com/watch?v=iApqY4FRY7o (Figure 8, Figure 9).Figure 8 provided the polarization pattern image without another processing, mapping or analysis; and Figure 9 provided the Sobel-Feldman gradient map for this pattern.In this case LC layer was used as the biochemical immobilization layer analog for the prototyping of lab-on-a-dish design.Another example of such a pattern (with its Sobel-Feldman map visualization) is provided in the video "Orientation effect detection in liquid crystals using Sobel filter (Sobel-Feldman operator).

Conclusions
Femtoscan allows selecting the optimal metrological mesh for analyzing self-organization and phase transitions in liquid crystals on the substrates, potentially applicable in the analytical chip design, controlling and eliminating the possible artifacts.
Femtoscan usage is compatible with Lommel-Seeliger-like techniques and edge detection techniques in multi-angle detection, which allows using together with multi-angle detection techniques on a chip containing liquid crystal structures and related elements [121,122].
Femtoscan is compatible with the correlation-spectral analysis techniques of the structures on a chip (for example, on a chip for the analysis of liquid crystal facies [123,124]), which allows integrating the analysis and separation (AI-clustering for their further recognition based on machine learning results) of differently organized mesophases with various textures.This can be applied to several biological and fossilization taphonomic problems [125][126][127]

Page 6/ 23 Figure 1
Figure1 (a-l) Selection of the optimal LC surface visualization mode between undersampling and oversampling.

Figure 2
Figure 2 Laplace-type, lambertian and Lommel-Seeliger-like shadow photometric maps of the LC surface: a) grayscale monochrome image, b) visualization optimal for DIC/NIC and Rheinberg contrast; c-d) two versions of shadow-like visualizations (optimal for different shlieren techniques).

Figure 3
Figure 3 Optical density gradient fitting for 2D (b) and 3D pseudo-color (a) photometric maps.

Figure 5
Figure 5 Correlation spectral analysis based on 2D Fourier spectra (c, d) applied for original monochrome grayscale image (a) and its volume (2D-to-3D) transform (b).

Figure 6
Figure 6 Examples of 2D Fourier spectra (b-d) of the original LC surface image (a).

Figure 8
Figure 8Polarization pattern images (registered using polariscope) of the lab-on-a-dish LC immobilization layer prototype without any digital image processing or mapping.

Figure 9
Figure 9Sobel-Feldman[3 × 3]  gradient maps of the polarization pattern images (registered using polariscope) of the lab-on-a-dish LC immobilization layer prototype.