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Abstract
The alignment of liquid crystals on surfaces plays a central role in optimizing their performances. In this work, a cutting-edge nano-lithography-based method to control the local orientation of a thermotropic liquid crystal is applied to easily available commercial standard materials and evaluated. Parallel nanogrooves on a substrate, created through 3D nanoprinting in a negative-tone photoresin optimized for two-photon polymerization are used for this purpose. Azimuthal anchoring energies of the order from 10−6 J/m2 to 10−5 J/m2 are found, depending on the spacing, width and depth of the grooves. In part, these values are larger than those reported previously for another photopolymer. Both uniform alignment and spatial patterns of different alignment directions can be realized. Electro-optic studies confirm the suitability of the method for electrically addressable photonic applications and indicate strong polar anchoring.
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1. Introduction
Liquid crystals, i. e. ordered fluids, are ubiquitous in nature and widely applied in technology, in particular for information displays and photonic devices [1,2]. Many of the technical applications are based on the anisometric (i.e. non-spherical) molecular shape and the anisotropic molecular properties (for example, anisotropy of the polarizability). If a large number of neighboring liquid crystal (LC) molecules is uniformly aligned, their effective macroscopic electrical and optical properties, for example electrical conductivity, dielectric permittivity and refractive index, also exhibit anisotropy. Therefore, the accurate control of the preferred alignment direction (which can be described by a pseudo-vector known as the director [1]) is essential for investigation and technical application of the anisotropic properties [1–3]. Consequently, various techniques for fabricating reliable alignment layers on the substrates confining the LC have been developed for thermotropic LCs, which can be electro-optically addressed and are widely used in LC displays [4–10]. These techniques include, for example, unidirectional rubbing of glass substrates [4], coating with a polymer and subsequent rubbing [5,6], oblique evaporation of silica on the substrate [7], formation of an anisotropic polymer film by linearly polarized photopolymerization [8], or sculpturing of the surface topography of the substrate on a micro- or nanoscopic scale by means of mechanic agitation [9,10], nanoimprinting lithography [11,12] or e-beam lithography [13]. The aligning effect of the substrates may be either attributed to molecular interactions at a flat substrate surface [8] or to the interplay of bulk elasticity and the surface topography at a surface relief [14,15].
A novel approach for the realization of nanostructures is 3D nanoprinting by laser direct writing. Here, two-photon polymerization can be used to realize tailored nanostructures with optical functionalities such as metasurfaces [16] or phase-only holograms [17,18]. In addition to the unique flexibility in fabricating such structures on unconventional substrates (for example, fibers [19,20]) or on the side surfaces of on-chip waveguides [21], the nanoprinting process allows the height of individual elements to be varied. This represents a new degree of freedom compared to conventional lithographic methods and can be used for optical applications (for example, achromatic metasurface-based lens on fiber [22]).
This work is motivated by the challenge of creating well-designed nano-structured surfaces as LC alignment layers by high-resolution nano-lithography through direct laser writing. For this purpose, we apply here the method of two-photon photopolymerization of a suitable photoresist [23], which shows a large versatility and extraordinarily high spatial resolution. So far, this method has been applied to thermotropic calamitic LCs [24], which are used for electro-optic applications, to thermotropic discotic LCs [25], which can be applied as organic semiconductors, to lyotropic LCs [26], i.e. solutions which appear frequently in living nature [2], and to colour filters based on LC elastomers [27]. A review article emphasizing the versatility and unusual opportunity to create photonic devices based on complex three-dimensional director fields was given by He et al. [28]. Here, we would like to contribute to this emerging field of LC research by measuring the azimuthal surface anchoring energy [29] on the photoresist material IP-Dip (Nanoscribe GmbH & Co. KG) and its dependence on geometrical parameters. We also show the impact of the various geometrical parameters on the anchoring energy and present electro-optical switching experiments to demonstrate the practical relevance of this concept. A typical thermotropic calamitic LC mixture is used, since we envisage electro-optic addressing in future studies.
The tailored nanostructured polymer surface consists of grooves in the nanometer range (Fig. 1) that define the local direction of the LC director at the surface of the structure. By changing the orientation of the nanogrooves in our samples, the optical properties of a thermotropic LC can be locally controlled, since the director aligns parallel to the grooves. This allows the creation of complex liquid crystal arrangements due to the unique flexibility of the nanoprinting process.
Fig. 1. (a) Illustration of the concept of aligning liquid crystals through nanopattered surfaces. (b) Atomic Force Microscope (AFM) image of a nano-structured checkerboard-like patterned surface (20 µm × 20 µm) containing nano-grooves of different orientations and geometric parameters. The lower plot shows the height distribution along a selected line. (c) Scanning-Electron-Microscopy (SEM) image of a nano-structured surface.
The nanostructured surfaces were fabricated by 3D nanoprinting (Nanoscribe 3D printer, model photonic professional GT2), using direct laser writing. This technology is based on the local polymerization of a polymer resin using two-photon absorption and generally enables high precision 3D microfabrication. The experiments were conducted on tailored nanostructured polymer surfaces with defined grooves arranged in checkboard pattern on the nanometer scale. The groove direction and the depth t, width w and spacing b of the grooves (Fig. 2) vary from field to field.
Fig. 2. (a) Top view of a writing field with the relevant parameters. L: length of a square-shaped writing field, w: width of a groove, b: width of a protrusion separating two grooves. (b) Side view of the nano-structured surface, t: depth of the grooves.
2. Experiments and results
2.1 Sample preparation and measurement of the azimuthal anchoring strength
The first investigation aims to achieve insights on how LC molecules interact with our nano-printed surfaces and what set of geometrical parameters of the nanogrooves lead to optimal orientations of the LC director n. In detail, a nano-groove-based surface with varying geometrical parameters (extension 90 µm × 90 µm) consisting of a number of square-shaped writing fields (15 µm × 15 µm) arranged in a checkerboard pattern was printed on a glass substrate [ Fig. 3 (a)]. Within each field, all nano-grooves have identical geometry and are characterized by a few key parameters (e. g., depth t, width w, and spacing b of the grooves). The size of the fields allows for a decent number of parallel grooves per field as long as the pitch Λ = (b + w) does not exceed 1 µm. For understanding the interaction of nano-grooves and LCs, the nano-structured substrate is inserted into a cell geometry that consist of a commercial LC-substrate [Fig. 3 (b), E.H.C Co.,Ltd. RP-B111P1N(LOW) 2.5 cm × 2.0 cm], on which a homogeneous unidirectional rubbed alignment layer of rubbed polyimide (PI) allows to anchor the director of LC molecules parallel to the substrate along the rubbing direction. The rubbed PI layer forms unidirectional nano-grooves, which dominate the orientation of the LCs. By using Mylar foil of defined height as a spacer, the substrates are placed at a distance of d ≈ 15 µm above the nano-structured surface [Fig. 3 (c)]. To demonstrate the properties of our concept, the widely used calamitic liquid crystal E7 (Merck, Darmstadt) has been chosen, consisting of four rod-like cyano-substituted biphenyls, 4-cyano-4’-pentylbiphenyl (51%), 4-cyano-4’- heptylbiphenyl (25%), 4-cyano-4’-octyloxybiphenyl (16%) and 4-cyano-4’’-pentylterphenyl (8%). The mixture has a wide temperature range for the nematic phase (from – 30 °C to + 61 °C) [30], which allows experiments to be performed at room temperature. Because of these advantages, E7 was chosen as sample used in this work. After filling the cell with E7 through capillary action, the quality of alignment using nano-grooves can be assessed by changes of the optical properties of the LC using polarizing optical microscopy, which was performed using a Leica DM4500 P microscope equipped with a white light source, 10× to 60× objectives, rotatable polarizer and analyser and an optional λ-waveplate.
Fig. 3. Sketches of the surfaces and sample configuration. (a) Top view of a nano-structured checkerboard-like surface, showing a tailored distribution of nano-grooves. Each field contains grooves of different geometric parameters. (b) Top view of a commercial substrate with unidirectional grooves. (c) Cross-sections view of a cell-type configuration with a nano-structured surface (top) and a commercial substrate (bottom).
In the polarizing optical microscopic measurements (Fig. 4), an alternating sequence of bright and dark regions could be clearly observed, which indicates different directions of the preferred local orientation of the LC molecules that is described by the director [1]. The local director is determined by the orientation of the nano-grooves of the structured top surface. In more detail, in half of the fields, the LC molecules twist in the cell due to the different orientations of the director at the upper and lower substrates. In these fields, the respective area observed through parallel polarizers appears dark. Note that intentionally the nano-groove arrays have different geometric parameters of the grooves (depth t and width w), so that the anchoring strength of the director in the different fields may be different. Indeed, this expectation is confirmed by the increasing image contrast of the fields towards the upper side in Fig. 4. Optical analysis of the data showed that twist angles close to 90° can be obtained for selected parameters of the nano-grooves.
Fig. 4. Polarizing optical microscope images of the liquid crystal cell filled with E7 (a) placed between parallel polarizers (horizontal, dark arrows above the figure) and (b) together with a full-wave retardation plate (with its slow axis oriented at an azimuthal angle of 45°, red arrow) between parallel polarizers, respectively.
Due to the different orientation of the anchoring molecules, the director field is either uniform (in areas, where the alignment direction (easy axis [1]) of the bottom substrate and the grooves on the nanostructured top substrate are parallel) or shows a twist deformation when the grooves are orthogonal (i.e., are rotated by 90 °). In the latter case of the twist, the free energy (F) is enhanced. In general, three basic types of elastic deformation, namely splay, twist and bend, can be distinguished. The competing effects of the surface anchoring and the bulk elasticity can be described by the free energy [1]
In the cell exhibiting a twisted director field (Fig. 5), the orientation of the director n is uniform in planes parallel to the substrates and depends only on the z-coordinate. Thus, its dependence on the position can be fully described by an azimuthal angle φ(z) [1]. The commercial EHC-substrate at the bottom (z = 0) is known to provide strong anchoring, i. e. φ (0) = φ0(0) = 0 ° at z = 0. The anchoring of the nanostructured top substrate (at z = d) with grooves rotated by 90 ° is unknown and to be analyzed. For strong anchoring at the nanopatterned surface (at z = d), an angle |φ(d)| close to φ0(d) = π/2, and for soft anchoring angles |φ(d)| < π/2 are expected. Since the anchoring is parallel to the substrate plane at both surfaces, only twist of the director field (characterized by n || curl n) is expected. Thus, the first and third term in the volume integral given in Eq. (1) can be ignored and the free energy is given by
Since φ(z) is independent on the coordinates x and y within one of the fields, integration over the surface area A [which is parallel to the (x, y)-plane] yields the simple equation
Fig. 5. (a) Schematic diagram of the twisted director field of rod-like liquid crystal molecules appearing for planar anchoring, if the azimuthal anchoring directions of the upper and lower surfaces deviate from each other by 90 degrees. (b) Azimuthal angle φ(z) of the twisted director field. Strong anchoring at the lower substrate ensures φ(0) = 0°. However, weak anchoring at the upper substrate (at z = d) may allow the azimuthal angle φ(d) to deviate from the easy axis φ0(d) = 90°.
It is very well known from solving the respective Euler-Lagrange equation for the integral in Eq. (3) [1] that the condition (dφ/dz) = const. needs to be fulfilled for minimizing the bulk free energy at given surface angles, i. e. (dφ/dz) = [φ(d)- φ(0)]/[d-0] =(φ(d))/d for the geometry and the boundary conditions given in Fig. 5. So, the free energy is given in this special case by
Consequently, minimizing the free energy yields the following relation between the director angle φ(d) and the anchoring energy Wφ, which includes the cell thickness d.
The LC E7 exhibits a twist elastic coefficient of K22 = 6.8 pN [21]. By measuring the polarization plane of the transmitted light, anchoring energies Wφ of each writing field can be determined. For this purpose, the sample is illuminated with linearly polarized light from below. The plane of polarization is parallel to the anchoring direction of the director at the lower substrate. In a twisted nematic cell as represented in Fig. 5, the waveguiding effect [32] is known to occur, i. e. the light propagating through the cell along the z-direction remains linearly polarized and its plane of polarization is gradually rotated, thereby always remaining parallel to the local optical axis, i. e. to the director. Consequently, the direction of the polarization of transmitted light indicates the azimuthal director orientation at the upper substrate. It can be easily detected by a second linear polarizer (the analyzer) placed in the microscope tube above the sample. According to the varying anchoring capabilities of the different fields, the azimuthal angle of the polarization plane of the analyzer needs to be adjusted to the darkest state at each field. If so, the deviation of the azimuthal angle of the polarizer α from the ideal azimuthal angle of 90 ° indicates the azimuthal angle φ(d) of the director.
The goal of this study is to find sets of parameters b, w, and t, for which maximum anchoring of the director of the molecules of the LCs can be achieved. For this purpose, various arrays of nano-grooves with parameters ranging from 200 nm to 800 nm are implemented. The nano-grooves are characterized by a groove width w, depth t, and spacing b [Fig. 3(c)].
The results of the twist angles (Table 1) are well reproducible for fields with the same geometry. The occurrence of both positive and negative values of α corresponds to the expectation that the twist of the director field can be either right-handed or left-handed. Observation with a full wave retardation plate (the azimuthal angle of its optical axis being 45°) inserted in the microscope tube confirms this expectation [Fig. 4 (b)]. According to the Michel-Levy color chart of uniaxially birefringent samples [33,34], insertion of a full wave retardation plate yields either a blue or yellow interference color, depending the question whether the retardations of the retarder and the birefringent sample enhance or reduce each other.
Table 1. Geometric parameters, twist angles, and anchoring energies for eighteen twisted fields with nano-grooves of different widths w, spacing b, and depths t. The angles α1 and α2 (two measurements per field) describe the deviation of the azimuthal angle of the analyzer at minimum light transmittance from π/2. Different signs of α1 and α2 indicate different twist directions (right- versus left-handed). The corresponding azimuthal angle φ(d) of the director is given by |φ(d)| = π/2 - |α|. The anchoring. energy Wφ is calculated from Eq. (5).
2.2 Dependence of the anchoring strength on in-plane geometric parameters
Generally the anchoring strength is overall much higher for fields with a groove depth of 300 nm compared to a field with a depth of 200 nm. For grooves of the same depth, a great difference between groove width w and spacing b reduces the anchoring energy. However, there is one exception. For a depth of t = 200 nm, decent anchoring strength was also observed when the groove width is w = 400 nm and the spacing is b = 200 nm.
The anchoring of fields with the same set of parameters were measured in different test cells, the determination of the angle φ(d) was repeated multiple times in each cell, and the averaged results are plotted in a color-coded diagram (Fig. 6). From the geometric combination of these green areas, it can be concluded: when the values of w, b, and t are approximately the same, the grooves anchor the LC molecules most efficient.
Fig. 6. Anchoring energy Wφ corresponding to different combinations of groove width w and spacing b, when the nano-groove depth is (a) t = 200 nm or (b) t = 300 nm. Areas marked in green indicate strong anchoring, areas marked in red weak anchoring.
An overview of the data given in Tab. 1 is also represented in Fig. 7, together with previous results by Lee et al. [24] that were previously measured for a different resist (Norland Optical Adhesive NOA 61). In addition to the study performed by Lee et al. [24], the parameters w and b were varied independently in our work. For comparison, the values of the anchoring energy are given as a function of the grating period Λ = w + b in Fig. 7. Our results for the anchoring strength of the resist IP-Dip (Nanoscribe GmbH & Co. KG) show that predominantly similar sizes yield high anchoring strength similarly observed for NOA 61 in the range 500 nm ≤ Λ ≤ 1 µm, partially exceeding the values reported by Lee et al. [24]. However, there are two distinct deviations: For t = 200 nm and w < b, the anchoring strength is lower than in other cases, i. e. polymer walls with a small thickness w and a relatively large spacing b promote the LC alignment to a reduced extent. More importantly, a large depth (t = 300 nm) and a spatially symmetric variation of the surface (w ≈ b) seem to promote the LC alignment extraordinarily.
Fig. 7. Dependence of the anchoring energy Wφ on the period Λ = w + b for (orange) t = 300 nm and w > b, (grey) t = 200 nm and w > b, (yellow) t = 300 nm and w = b, (light blue) t = 200 nm and w = b, (green) t = 300 nm and w < b, dark t = 200 nm and w < b. (blue). For comparison, the data reported by the authors of [24] in their text (for Λ = 519 nm) and in their Fig. 4 (for Λ = 1 µm to 4 µm, respectively) are reproduced in this diagram.
2.3 Dependence of the anchoring strength on the depth of the nanogrooves
So far, the discussion shows that it is important to understand how the depth impacts the anchoring effect when the groove depth is smaller or larger than 300 nm in case all other parameters remain identical. In the new experiment, the width of w and b are set equal, and then depth of the grooves is systematically varied (Fig. 8) to find the optimum set of parameters of the grooves.
Fig. 8. Anchoring energies Wφ for different combinations of groove width w (spacing b) and depth t, when the groove width w is the same as the spacing b. The color code indicating different anchoring energies is the same as in Fig. 6.
It is obvious from Fig. 8 that the anchoring energy increases with increasing nano-groove depth t, if width w and spacing b of the grooves have the same value. However, when both w and b are smaller than 200 nm, the anchoring effect is generally weak, no matter how deep the grooves are.
2.4 Spatial resolution of varying alignment directions
In addition to studying the maximum anchoring strength, another aim is to uncover the smallest possible size of a nano-groove array in which sufficient liquid crystal orientation can be achieved. This results in the smallest field size and lateral resolution of the nano-groove concept, an issue that has not been addressed in previous works [24]. Specifically, based on the above results, the size of the writing field can be reduced to about 200 nm to 500 nm (Fig. 9). Close inspection indicates, that fields as small as 2 µm by 2 µm are still sufficiently large to induce a uniform alignment distinguished from the neighboring field, i. e. a number of only 5 neighboring nano-grooves per field is sufficient to induce the intended liquid crystal orientation.
Fig. 9. Photograph of a sample containing fields of different sizes with alternating direction of the grooves, as seen in the polarizing microscope between parallel polarizers. (left) Without electric field E. (right) E = 35 V / (15 µm). Details about the electro-optic switching are given in the next section.
2.5 Electro-optic switching
In addition to the work by Lee et al. [24], the ability of the nano-groove arrays to serve as alignment layers also under the conditions of the electro-optic Freedericksz transition was tested for both twisted nematic and uniformly parallel aligned nematic layers. For this purpose, a switching test-cell was fabricated consisting of a printed substrate featuring nano-grooves in four fields [ Fig. 10 (a)] and a uniformly rubbed orienting counter-substrate. These two surfaces were positioned facing each other with a separation distance of 15µm. Owing to different groove directions, field 1 and field 4 of this test-cell establish a twisted nematic configuration, while the director is uniformly parallel in fields 2 and 3 [Fig. 10 (b)]. Both substrates are coated with a conductive layer of indium tin oxide (ITO) to facilitate applying an electric field perpendicular to the LC layer. The LC mixture E7 exhibits positive dielectric anisotropy. Thus, the director tends to align parallel to an applied electric field (Fréedericksz transition [1–3,36]). The electric field-induced reorientation of the director can be used to achieve the well-known electro-optic responses based on the twisted nematic (TN) effect [31] in twisted regions (fields 1 and 4) and based on the electrically addressed birefringence [1–3,36] in parallel nematic (PN) regions (fields 2 and 3), respectively.
Fig. 10. Electro-optic performance. (a) Orientation arrangement of nanoprinted areas with w = b = t = 300 nm. (b) Polarizing optical microscope (POM) image using parallel polarizer and analyzer. (c, d) Transmitted light intensity versus voltage for crossed polarizer and analyzer. (c) Twisted nematic field 4 (F4). (d) Field 3 (F3), aligned with its uniformly parallel director at an azimuthal angle of ϕ = 45° with respect to the plane of polarization of the incident light.
The twisted nematic (TN) configuration of E7 in the crossed polarizer-analyzer setup allows for transparency in the field-off state, because the plane of polarization of the linearly polarized incident light is continuously rotated by 90° owing to the nematic helix structure (waveguiding effect). This bright state switches to a dark state at sufficiently large voltage [Fig. 10 (c)]. This well-known TN switching behavior [31] occurs because the twist of the director field, and thus the rotation of the plane of polarization of the transmitted light disappear at high voltages, when the director aligns parallel to the electric field.
In contrast to the twisted nematic fields 1 and 4, the electric-field-induced realignment of the director in the uniformly parallel nematic (PN) fields 2 and 3 placed between crossed polarizers yield an electro-optic contrast only, when the azimuthal angle ϕ between the director and the plane of polarization of the incident light is non-zero [1–3,36]. When the applied voltage exceeds a threshold, the intensity of monochromatic transmitted light versus voltage follows a sinusoidal function [Fig. 10 (d)], which can be explained as follows. As the voltage increases, the polar angle ϑ between the director and the electric field direction decreases, thereby resulting in a decreasing difference between the effective extraordinary refractive index
It is important to note that the intensity of transmitted light is dependent on the wavelength λ. In the case of illumination with white light, the transmitted light is colored. The color impression varies strongly with the applied voltage [Fig. 11]. This well-known phenomenon appears for white light, because its spectral components with different wavelengths λ are transmitted to a different extent [Eqs. (8) and (9)].
Fig. 11. Interference colors appearing at specific voltages, when a nematic sample with uniformly parallel aligned director placed between crossed polarizers is illuminated with white light (here: field 2, azimuthal angle ϕ = 45°).
3. Discussion of the anchoring and its performance in electro-optic application
In summary, we have found values for the anchoring energy which are – with few exceptions (see Tab. 1) – of the order from 10−6 J/m2 to 10−5 J/m2, strongly depending on the groove pitch and depth. These values are between the weak azimuthal anchoring energies obtained for clean glass (10−7 J/m2) or oblique evaporation of SiO2 (10−6 J/m2) and the exceptionally large anchoring energy of an LC at a single crystal NaCl (001) surface (10−4 J/m2) [3]. Typical values given in Tab. 1 are comparable to azimuthal anchoring energies reported for polarized-light induced alignment (≈ 5 · 10−6 J/m2) [29]. Yet, for appropriate choice of the parameters w, b and t, the anchoring energies found in this study can reach the strong anchoring regime (Wφ > 10−5 J/m2), which has been reported for nano-structured poly(imide) [12]. Combining multiple measurements of nano-grooves from multiple test-cells, we finally identified two optimal sets of parameters: either a width and spacing of w = b = 200 nm and a depth of t = 400 nm or the same value w = b = t = 300 nm for all three parameters. According to Berreman’s theory [14], the azimuthal anchoring energy for a sinusoidal surface shape described by ζ(x, z) = u cos (q·z) can be estimated [1,14] to be
Using the values w = b = t = 300 nm and inserting the value of the bend elastic coefficient K33 ≈ 12.3 pN [35] in Eq. (9) yields an expected anchoring energy of approximately Wφ ≈ 1.6 · 10−4 J m-2, which is higher than the largest experimental value (Tab. 1). This difference can be attributed to the limited validity of the approximation [1,14], since the structure investigated has a rectangular surface topography in the parameter range q · u ≈ 1 .
4. Conclusion
The results confirm that nanostructured surfaces prepared using two-photon nanolithography can be used to align thermotropic liquid crystals, if the standard photoresist IP-Dip (Nanoscribe GmbH & Co. KG) is used. In agreement with earlier findings [24–28], the local direction of parallel grooves defines the orientation of the director, thereby allowing to create various liquid crystal arrangements. Our results indicate that a symmetric variation of the surface (w ≈ b) and a large depth of the grooves (t = 300 nm) are favourable to achieve large azimuthal anchoring energies (Wφ ≥ 10−5 J/m2). Owing to the large anchoring strength of the nanoprinted substrates, we expect that both aligning substrates in a typical LC cell can be replaced by nanostructured substrates, thereby making any conventional alignment layer obsolete. A single nanostructured surface may be used if a hybrid alignment is targeted. The electro-optic studies confirm that the alignment technique can be readily applied to electric switching effects and reveal a strong polar anchoring in addition to the strong azimuthal anchoring. We hope that these findings are helpful to explore this novel platform for research and applications of thermotropic LCs. Note that the ability to pattern LC alignment layers along all three spatial directions at the micro- and nanometer level represents a significant advantage over conventional alignment methods such as rubbing or even photoalignment. Among the large number of micro-and nano-scale liquid crystal photonic devices expected to be based on this novel alignment method [28], we envisage, for example, devices for modulating the state of polarization, beam-steering, compensating aberrations, or phase-shifting. Moreover, sophisticated types photonics devices can be envisioned for instance to access states of on the higher-order Poincare sphere [38,39].
Funding
Thueringer Universitaets- und Landesbibliothek Jena (Open Access Publication Fund); Deutsche Forschungsgemeinschaft (Excellence Strategy EXC 2051, Project-ID 390713860, Project No. 512648189); Universität Paderborn (Postdoc Scholarship for Young Researchers); Deutsche Forschungsgemeinschaft (SCHM2655/15-1, SCHM2655/21-1).
Acknowledgments
B. Z. would like to thank the President of Paderborn University for having received a scholarship for her postdoctoral research. We acknowledge support by the German Research Foundation Project-No. 512648189 and the Open Access Publication Fund of the Thueringer Universitaets- und Landesbibliothek Jena. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanýs Excellence Strategy – EXC 2051 – Project-ID 390713860.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data generated and analyzed in the presented research are given in the text of the manuscript, in Table 1 and represented in the figures.
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