Imaging of affinity microcontact printed proteins by using liquid crystals

This paper reports the design of surfaces on which thermotropic liquid crystals can be used to image affinity microcontact printed proteins. The surfaces comprise gold films deposited onto silica substrates at an oblique angle of incidence and then functionalized with a monolayer formed from 2-mercaptoethylamine. Ellipsometric measurements confirm the transfer of anti-biotin IgG to these surfaces from affinity stamps functionalized with biotinylated bovine serum albumin (BSA), while control experiments performed using anti-goat IgG confirmed the specificity of the IgG capture on the stamp. On these surfaces, anti-biotin IgG caused nematic phases of 4-cyano-4'-pentylbiphenyl (5CB, Delta epsilon = epsilon(parallel) - epsilon(perpendicular) > 0) to assume orientations that were parallel to the surfaces (planar anchoring) but with azimuthal orientations that were distinct from those assumed by the liquid crystals on the amine-terminated surfaces not supporting IgGs. Following incubation of these samples for >8 h at 36 degrees C, we observed that the amine-terminated regions of the surface not supporting IgG cause 5CB to undergo a transition from planar to perpendicular (homeotropic). Because N-(4-methoxybenzylidene)-4-butylaniline (MBBA) (Delta epsilon < 0) does not undergo a similar transition in orientation, this transition is consistent with the effects of an electrical double layer formed at the amine-terminated surface on the liquid crystal. Following the transition to homeotropic anchoring, the liquid crystals provide high optical contrast between regions of the surface supporting and not supporting IgG. We conclude that amine-terminated surfaces (I) uniformly align liquid crystals when not supporting proteins and (II) have sufficiently high surface free energy to capture proteins delivered to the surface from an affinity stamp, and thus they form the basis of a useful class of surfaces on which affinity microcontact printed proteins can be imaged using liquid crystals.     

液晶/水界面上的氢键作用诱导液晶取向转变

本文提出液晶/水界面上氢键作用可以诱导热致型液晶(戊基联苯氰,简称: 5CB)发生取向转变.当液晶5CB膜接触酚类(如对硝基苯酚)水溶液的时候,由于酚类物质的酚羟基与液晶5CB分子中的氰基在液晶水界面上形成了氢键,在氢键的作用下使得液晶5CB由平行取向转变成了垂直取向.此外,还利用了液晶传感器可视化了酚类物质与牛血清蛋白(BSA)之间的相互作用.本文的研究结果可为研究液晶/水界面上的界面现象提供新的思路,并且有望开发出基于氢键作用的液晶生物化学传感技术.     

Enantiomeric interactions between liquid crystals and organized monolayers of tyrosine-containing dipeptides

We have examined the orientational ordering of nematic liquid crystals (LCs) supported on organized monolayers of dipeptides with the goal of understanding how peptide-based interfaces encode intermolecular interactions that are amplified into supramolecular ordering. By characterizing the orientations of nematic LCs (4-cyano-4'-pentylbiphenyl and TL205 (a mixture of mesogens containing cyclohexane-fluorinated biphenyls and fluorinated terphenyls)) on monolayers of l-cysteine-l-tyrosine, l-cysteine-l-phenylalanine, or l-cysteine-l-phosphotyrosine formed on crystallographically textured films of gold, we conclude that patterns of hydrogen bonds generated by the organized monolayers of dipeptides are transduced via macroscopic orientational ordering of the LCs. This conclusion is supported by the observation that the ordering exhibited by the achiral LCs is specific to the enantiomers used to form the dipeptide-based monolayers. The dominant role of the -OH group of tyrosine in dictating the patterns of hydrogen bonds that orient the LCs was also evidenced by the effects of phosphorylation of the tyrosine on the ordering of the LCs. Overall, these results reveal that crystallographic texturing of gold films can direct the formation of monolayers of dipeptides with long-range order, thus unmasking the influence of hydrogen bonding, chirality, and phosphorylation on the macroscopic orientational ordering of LCs supported on these surfaces. These results suggest new approaches based on supramolecular assembly for reporting the chemical functionality and stereochemistry of synthetic and biological peptide-based molecules displayed at surfaces.     

Orientational behavior of thermotropic liquid crystals on surfaces presenting electrostatically bound vesicular stomatitis virus

We report the orientational behavior of nematic phases of 4-cyano-4'-pentylbiphenyl (5CB) on cationic, anionic, and nonionic surfaces before and after contact of these surfaces with solutions containing the negatively charged vesicular stomatitis virus (VSV). The surfaces were prepared on evaporated films of gold by either adsorption of poly-L-lysine (cationic) or formation of self-assembled monolayers (SAMs) from HS(CH2)2SO3- (anionic) or HS(CH2)11(OCH2CH2)4OH (nonionic). Prior to treatment with virus, we measured the initial orientation of 5CB (delta epsilon = epsilon(parallel) - epsilon(perpendicular) > 0) to be parallel to the cationic surfaces (planar anchoring) but perpendicular (homeotropic) after equilibration for 5 days. A similar transition from planar to homeotropic orientation of 5CB was observed on the anionic surfaces. Only planar orientations of 5CB were observed on the nonionic surfaces. Because N-(4-methoxybenzylidene)-4-butylaniline (MBBA, delta epsilon = epsilon(parallel) - epsilon(perpendicular) < 0) exhibited planar alignment on all surfaces, the time-dependent alignment of 5CB on the ionic surfaces is consistent with a dipolar coupling between the 5CB and electrical double layers formed at the ionic interfaces. Treatment ofpoly-L-lysine-coated gold films (cationic) with purified solutions of VSV containing 10(8)-10(10) plaque-forming units per milliliter (pfu/mL) led to the homeotropic alignment of 5CB immediately after contact of 5CB with the surface. In contrast, treatment of anionic surfaces and nonionic surfaces with solutions of VSV containing approximately 10(10) pfu/mL did not cause immediate homeotropic alignment of 5CB. These results and others suggest that homeotropic alignment of 5CB on cationic surfaces treated with VSV of titer > or = 10(8) pfu/mL reflects the presence of virus electrostatically bound to these surfaces.     

Measurement of the azimuthal anchoring energy of liquid crystals in contact with oligo(ethylene glycol)-terminated self-assembled monolayers supported on obliquely deposited gold films

We report measurements of the orientations and azimuthal anchoring energies of the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) on polycrystalline gold films that are deposited from a vapor at an oblique angle of incidence and subsequently decorated with organized monolayers of oligomers of ethylene glycol. Whereas the gold films covered with monolayers presenting tetra(ethylene glycol) (EG4) lead to orientations of 5CB that are perpendicular to the plane of incidence of the gold, monolayers presenting tri(ethylene glycol) (EG3) direct 5CB to orient parallel to the plane of incidence of the gold during deposition of the gold film. We also measure the azimuthal anchoring energy of the 5CB to be smaller on the surfaces presenting EG3 (3.2 +/- 0.8 microJ/m2) as compared to EG4 (5.5 +/- 0.9 microJ/m2). These measurements, when combined with other results presented in this paper, are consistent with a physical model in which the orientation and anchoring energies of LCs on these surfaces are influenced by both (i) short-range interactions of 5CB with organized oligomers of ethylene glycol at these surfaces and (ii) long-range interactions of 5CB with the nanometer-scale topography of the obliquely deposited films. For surfaces presenting EG3, these short- and long-range interactions oppose each other, leading to small net values of anchoring energies that we predict are dependent on the level of order in the EG3 SAM. These measurements provide insights into the balance of interactions that control the orientational response of LCs to biological species (proteins, viruses, cells) on these surfaces.     

Influence of surfactant tail branching and organization on the orientation of liquid crystals at aqueous-liquid crystal interfaces

We have examined the influence of two aspects of surfactant structure--tail branching and tail organization--on the orientational ordering (so-called anchoring) of water-immiscible, thermotropic liquid crystals in contact with aqueous surfactant solutions. First, we evaluated the influence of branches in surfactant tails on the anchoring of nematic liquid crystals at water-liquid crystal interfaces. We compared interfaces that were laden with one of three linear surfactants (sodium dodecyl sulfate, sodium dodecanesulfonate, and isomerically pure linear sodium dodecylbenzenesulfonate) to interfaces laden with branched sodium dodecylbenzenesulfonate. We carried out these experiments at 60 degrees C, above the Krafft temperatures of all the surfactants studied, and used the liquid crystal TL205 (a mixture of cyclohexane-fluorinated biphenyls and fluorinated terphenyls), which forms a nematic phase at 60 degrees C. Linear surfactants caused TL205 to assume a perpendicular orientation (homeotropic anchoring) above a threshold concentration of surfactant and parallel orientation (planar anchoring) at lower concentrations. In contrast, branched sodium dodecylbenzenesulfonate caused planar anchoring of TL205 at all concentrations up to the critical micelle concentration of the surfactant. Second, we used sodium dodecanesulfonate and a commercial linear sodium dodecylbenzenesulfonate to probe the influence of surfactant tail organization on the orientations of liquid crystals at water-liquid crystal interfaces. Commercial linear sodium dodecylbenzenesulfonate, which comprises a mixture of ortho and para isomers, has been previously characterized to form less ordered monolayers than sodium dodecanesulfonate at oil-water interfaces at room temperature. We found sodium dodecanesulfonate to cause homeotropic anchoring of both TL205 and 4'-pentyl-4-cyanobiphenyl (5CB, nematic at room temperature), whereas commercial linear sodium dodecylbenzenesulfonate caused predominantly planar and tilted orientations of both TL205 and 5CB. These results, when combined, lead us to conclude that (1) interactions between the aliphatic tails of surfactants and liquid crystals largely dictate the orientations of liquid crystals at aqueous-liquid crystal interfaces, (2) the interactions that orient the liquid crystals at these interfaces are sensitive to the branching and degree of disorder in the surfactant tails, and (3) differences in the chemical composition of TL205 and 5CB, most notably fluorination of TL205, lead to subtle differences in the orientations of these two nematic liquid crystals.     

向列相液晶4-氰基-4'-庚基联苯和4-氰基-4'-戊基联苯在准固态染料敏化太阳电池中的应用

将两种向列相液晶,4-氰基-4'-庚基联苯和4-氰基-4'-戊基联苯,引入到染料敏化太阳电池(DSC)用偏氟乙烯-六氟乙烯共聚物基准固态电解质中,以期提高DSC的光电转化效率.研究了液晶的引入对电解质中I-/I3-的氧化还原行为、DSC中TiO2/电解质界面的暗反应以及DSC光伏性能的影响.结果表明,尽管液晶的引入会降低电解质中I-/I3-的传输并且使得DSC中暗反应加快,但是DSC的短路电流密度却显著地提高,使DSC的光电转化效率增加.这可能是由于液晶的引入改善了DSC中的界面接触以及增加染料的光吸收引起的.     

Low-frequency dilational elasticity of the nematic 4'-pentyl-4-biphenylcarbonitrile (5CB)/water interface

Axisymmetric oscillating pendant drop shape analysis has been used to study the interfacial rheology of the liquid crystal 4'-pentyl-4-biphenylcarbonitrile (5CB) in water with homeotropic anchoring. Nearly spherical 5CB droplets were subjected to low frequency (1-5 mHz) volume oscillations, and the increase in tension with surface dilation was used to calculate the complex modulus. The droplet interface response is completely elastic, with no relaxations occurring on the experimental time scale. This surprising result is attributed to droplet storage of elastic energy in the form of distorted orientational distributions within the bulk (Frank elasticity) and on the surface (anchoring elasticity).     

Weak surface anchoring energy of 4-cyano-4'-pentyl-1,1'-biphenyl on perfluoropolyether Langmuir-Blodgett films

Functional director alignment layers are needed for high performance liquid crystal displays (LCDs). Reported herein is a novel polymer material for LC alignment, namely, perfluoropolyether (PFPE), which exhibits a weak surface anchoring energy for bend deformation and is amenable to simple fabrication of grooved surfaces by soft lithography, a surface topography desired for multistable LCDs. Liquid crystal optical cells fabricated using Langmuir-Blodgett films of PFPE (of variable thickness) exhibited weak surface anchoring energies on the order of 10(-5) Jm2 for the nematic liquid crystal 4-cyano-4'-pentyl-1,1'-biphenyl with no dependence on film thickness.     

Alignment and ordering mechanisms at a liquid crystal–solid interface

Abstract

The role of surface coupling agents on the aligning and ordering mechanisms at a liquid crystal–solid interface are examined with deuterium nuclear magnetic resonance. The cylindrical channels of alumina membranes 0·2 μm in diameter are chemically modified using an aliphatic acid (C _n H_2n+1 COOH) as a surface coupling agent and filled with the liquid crystal compound 4′-pentyl-4-cyanobiphenyl deuteriated in the α position of the hydrocarbon chain (5CB-αd ₂). The preferred anchoring direction at the cavity wall and its strength are found to depend on the length of the aliphatic chain of the surface coupling agent which determine the nematic director field in the pores. The planar polar configuration with homeotropic anchoring conditions is stable for agents with n ≥7 while chain lengths n ≤6 support a uniform axial configuration with planar anchoring at the cavity wall. The pretransitional orientational ordering at the cavity wall above the clearing temperature is strongly reflected in the spectra. The radical changes in the quadrupole splitting as the length of the aliphatic chain of the surface coupling agent is varied indicates strong coupling between the 5CB molecules and the n = 15 surface, while shorter chain lengths reveal substantially reduced degrees of coupling.     

Liquid crystal-based sensors for the detection of heavy metals using surface-immobilized urease

In this study, a new method for the detection of heavy metals in aqueous phase was developed using liquid crystals (LCs). When UV-treated nematic LC, 4-cyano-4'-pentyl biphenyl (5CB) that was confined in the urease-modified gold grid was immersed in a urea solution, an optical response from bright to dark was observed under a polarized microscope, indicating that a planar-to-homeotropic orientational transition of the LC occurred at the aqueous/LC interface. Since urease hydrolyzes urea to produce ammonia, which would be ionized into ammonium and hydroxide ions, the main product of the photochemically degraded 5CB, 4-cyano-4'-biphenylcarboxylic acid (CBA), was deprotonated and self-assembled at the interface, inducing the orientational transition in the LC. Due to the high sensitivity and rapid response of this system, detection of heavy metal ions was further exploited. The divalent copper ion, which could effectively inhibit the activity of urease, was used as a model heavy metal ion. The optical appearance of the LC did not change when urea was in contact with the copper nitrate hydrate-blocked urease. After the copper-inhibited urease was reactivated by EDTA, a bright-to-dark shift in the optical signal was regenerated, indicating an orientational transition of the LC. This type of LC-based sensor shows high spatial resolution due to its optical characteristics and therefore could potentially be used to accurately monitor the presence of enzyme inhibitors such as heavy metal ions in real-time.     

Liquid crystal anchoring transitions induced by thermal motion

The thermal motion of a substrate is shown to have strong effects on the orientation of liquid crystal molecules in contact with it. Using an invertedpendulum model, we find that the orientation of the liquid crystal molecules can have a sequence of transitions between planar and homeotropic orientations. Analytical expressions for stability conditions for the homeotropic orientations are found for both monochromatic and some multiple-mode thermal motions, and, in both homeotropic and planar anchoring cases. Numerical simulations confirm the analytical model calculations and show that strong interactions between molecules favour processes of dynamic stabilization and destabilization of the homeotropic orientation.     

Anchoring of a nematic liquid crystal on a wettability gradient

We have studied the anchoring of the nematic liquid crystal 5CB (4'-n-pentyl-4-cyanobiphenyl) as a function of the surface wettability, thickness of the liquid crystal layer, and temperature by measuring the birefringence of a hybrid aligned nematic cell where the nematic material was confined between octadecyltriethoxysilane-treated glass surfaces, with one surface linearly varying in its hydrophobicity. A homeotropic-to-tilted anchoring transition was observed as a function of the lateral distance along the hydrophobicity gradient, typically in a region corresponding to a water contact angle of approximately 64 degrees. The effect of the nematic layer thickness was measured simultaneously by preparing a wedge cell where the thickness varied along the direction perpendicular to the wettability. The detailed behavior of the onset of birefringence was found to be consistent with a dual-easy-axis model that predicts a discontinuous anchoring transition from homeotropic to planar. The anchoring was independent of temperature, except within 1 degrees C of the nematic-to-isotropic transition temperature (T(NI)). As the temperature approached T(NI), the tendency for planar anchoring gradually increased relative to that for homeotropic anchoring.     

Anchoring energies of liquid crystals measured on surfaces presenting oligopeptides

We report a methodology that permits quantitation of the azimuthal anchoring energy of the nematic liquid crystal 4-cyano-4'-pentyl-biphenyl on surfaces patterned with oligopeptides. The oligopeptide (IYGEFKKKC), an optimized substrate for the Src protein kinase, was covalently immobilized via the terminal cysteine to monolayers of amine-terminated tetra(ethylene glycol) formed on gold films. The measurements of anchoring energies, which were based on a torque-balance method, revealed a systematic decrease in anchoring energy from 3.7 +/- 0.6 microJ/m2 with increasing surface density of oligopeptide. We calculate that a mass density of oligopeptide of less than 1 ng/cm2 can lead to a measurable change in the anchoring energy of the nematic liquid crystal. These results suggest that measurements of anchoring energies of liquid crystals on surfaces may offer the basis of quantitative and label-free methods for detecting biomolecules on surfaces.     

Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events

We report a study of the orientations of nematic liquid crystals (LCs) in contact with peptide-modified, oligoethylene glycol-containing, self-assembled monolayers (SAMs). The SAMs were formed on gold films that were prepared by physical vapor deposition at an oblique angle of incidence. Two peptides were investigated: the optimized substrate for the Src protein kinase (IYGEFKKKC) and the synthetic equivalent of that peptide after kinase modification (IpYGEFKKKC). Polarization modulation-infrared reflectance absorbance spectroscopy (PM-IRRAS) was used to characterize the relative areal densities and orientations of these peptides at the interface. We conclude that the presence/absence of a phosphate group can influence the maximum packing density of immobilized peptide. We evaluated the orientations of the nematic liquid crystal 5CB in contact with these peptide-modified surfaces by using polarized microscopy. The time required for the nematic phase of 5CB to exhibit long-range orientational ordering (uniform alignment) was found to increase with increasing areal densities of immobilized peptide. We also found that the specific binding event between anti-phosphotyrosine IgG and the surface-immobilized phosphopeptide leads to an increase in the time required for the liquid crystal to achieve uniform anchoring (exceeding the experimentally accessible time scales). These results, when combined, suggest that the areal density and size of biomolecules at an interface can influence the time required for liquid crystals in contact with nanostructured surfaces to exhibit long-range orientational order. Finally, we illustrate the potential utility of this system by demonstrating that liquid crystals can be used to amplify and report protein binding events occurring on a spatially resolved peptide array.     

Influence of simple electrolytes on the orientational ordering of thermotropic liquid crystals at aqueous interfaces

We report orientational anchoring transitions at aqueous interfaces of a water-immiscible, thermotropic liquid crystal (LC; nematic phase of 4'-pentyl-4-cyanobiphenyl (5CB)) that are induced by changes in pH and the addition of simple electrolytes (NaCl) to the aqueous phase. Whereas measurements of the zeta potential on the aqueous side of the interface of LC-in-water emulsions prepared with 5CB confirm pH-dependent formation of an electrical double layer extending into the aqueous phase, quantification of the orientational ordering of the LC leads to the proposition that an electrical double layer is also formed on the LC-side of the interface with an internal electric field that drives the LC anchoring transition. Further support for this conclusion is obtained from measurements of the dependence of LC ordering on pH and ionic strength, as well as a simple model based on the Poisson-Boltzmann equation from which we calculate the contribution of an electrical double layer to the orientational anchoring energy of the LC. Overall, the results presented herein provide new fundamental insights into ionic phenomena at LC-aqueous interfaces, and expand the range of solutes known to cause orientational anchoring transitions at LC-aqueous interfaces beyond previously examined amphiphilic adsorbates.     

Oscillating Poiseuille flow in photo-aligned liquid crystal cells

We present an experimental study of thin liquid crystal (LC) layers under the action of a harmonically varied pressure gradient. Optical measurements were performed to register the linear oscillations of a nematic director related to homeotropic and homeoplanar (hybrid) initial states. In the latter case one of the inner surfaces of the rectangular channels was treated by ultraviolet light to provide a relatively weak planar anchoring. The optical response of hybrid and homeotropic LC cells under an oscillating pressure gradient was investigated in relation to on the amplitude and frequency of the pressure gradient. A hydrodynamic model is developed taking into account the LC polar anchoring strength and the surface viscosity responsible for a fast LC surface dynamics. Our estimates show that the thickness of the boundary layer corresponding to the surface viscosity does not exceed 10^-6 m, and further experiments are needed with thinner LC cells and higher frequency oscillations to achieve a more precise value. An oscillating Poiseuille flow in the hybrid cell was found to be useful for characterizing elastic and viscous properties of a weakly anchoring LC surface layer in a fast surface dynamic process.     

Ordering transitions in nematic liquid crystals induced by vesicles captured through ligand-receptor interactions

We report that phospholipid vesicles incorporating ligands, when captured from solution onto surfaces presenting receptors for these ligands, can trigger surface-induced orientational ordering transitions in nematic phases of 4'-pentyl-4-cyanobiphenyl (5CB). Specifically, whereas avidin-functionalized surfaces incubated against vesicles composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) were observed to cause the liquid crystal (LC) to adopt a parallel orientation at the surface, the same surfaces incubated against biotinylated vesicles (DOPC and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(biotinyl) (biotin-DOPE)) caused the homeotropic (perpendicular) ordering of the LC. The use of a combination of atomic force microscopy (AFM), ellipsometry and quantitative fluorimetry, performed as a function of vesicle composition and vesicle concentration in solution, revealed the capture of intact vesicles containing 1% biotin-DOPE from buffer at the avidin-functionalized surfaces. Subsequent exposure to water prior to contact with the LC, however, resulted in the rupture of the majority of vesicles into interfacial multilayer assemblies with a maximum phospholipid loading set by random close packing of the intact vesicles initially captured on the surface (5.1 ± 0.2 phospholipid molecules/nm(2)). At high concentrations of biotinylated lipid (>10% biotin-DOPE) in the vesicles, the limiting lipid loading was measured to be 4.0 ± 0.3 phospholipid molecules/nm(2), consistent with the maximum phospholipid loading set by the spontaneous formation of a bilayer during incubation with the biotinylated vesicles. We measured the homeotropic ordering of the LC on the surfaces independently of the initial morphology of the phospholipid assembly captured on the surface (intact vesicle, planar multilayer). We interpret this result to infer the reorganization of the phospholipid bilayers either prior to or upon contact with the LCs such that interactions of the acyl chains of the phospholipid and the LC dominate the ordering of the LC, a conclusion that is further supported by quantitative measurements of the orientation of the LC as a function of the phospholipid surface density (>1.8 molecules/nm(2) is required to cause the homeotropic ordering of the LC). These results and others presented herein provide fundamental insights into the interactions of phospholipid-decorated interfaces with LCs and thereby provide guidance for the design of surfaces on which phospholipid assemblies captured through ligand-receptor recognition can be reported via ordering transitions in LCs.     

Oscillating Poiseuille flow in photo‐aligned liquid crystal cells

We present an experimental study of thin liquid crystal (LC) layers under the action of a harmonically varied pressure gradient. Optical measurements were performed to register the linear oscillations of a nematic director related to homeotropic and homeoplanar (hybrid) initial states. In the latter case one of the inner surfaces of the rectangular channels was treated by ultraviolet light to provide a relatively weak planar anchoring. The optical response of hybrid and homeotropic LC cells under an oscillating pressure gradient was investigated in relation to on the amplitude and frequency of the pressure gradient. A hydrodynamic model is developed taking into account the LC polar anchoring strength and the surface viscosity responsible for a fast LC surface dynamics. Our estimates show that the thickness of the boundary layer corresponding to the surface viscosity does not exceed 10^?6 m, and further experiments are needed with thinner LC cells and higher frequency oscillations to achieve a more precise value. An oscillating Poiseuille flow in the hybrid cell was found to be useful for characterizing elastic and viscous properties of a weakly anchoring LC surface layer in a fast surface dynamic process.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.