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Model and native membranes

A membrane has a number of mechanical degrees of freedom: area stretching, thickness compression, shear deformation, chain tilting, and, notably, curvature deformation. The last one, curvature, is just a liquid crystal degree of freedom since membrane curvature is equivalent to a splay of lipid chains (under the condition that chains remain parallel to the local normal in each point of the curved bilayer).

Mechanoelectricity is a fundamental property of biomolecular layers relating their mechanical and electrical degrees of freedom. It is closely related to mechanosensitivity, electromotility and mechanotransduction, basic properties of living systems [11]. Understanding of mechanism of mechanosensitivity would open the way for construction of artificial bioelectronic mechanosensors [3], [29].

Flexoelectricity stands for a reciprocal relationship between electric and mechanical degree of freedom of a membrane, i.e., curvature-induced membrane polarization (direct flexoeffect) or voltage-induced membrane curvature (converse flexoeffect) [1], [7], [17], [23], [28], [30].

Experimentally, the way to probe BLM flexoelectricity is to subject a membrane to a pressure differential, either static or dynamic, or both. BLM models used by us comprise the classic Mueller-Rudin-Tien-Wescott method of BLM painting a over a hydrophobic hole, as well as the tip-dip method where a microsize BLM is patch-clamped inside a hydrophilic borosilicate glass micropipette [4].

Current registration regime.

Our first experiments, aimed specifically at registering the flexoelectricity of BLMs from biological lipids (bacterial phosphatidylethanolamine (PE) were performed in the current registration regime by using a low impedance current-to-voltage converter. The influence of some modifiers of the surface charge and surface dipole, as well as of the membrane conductivity, upon the value of the effect was also studied.

Voltage registration regime.

Further experiments on membrane flexoelectricity were performed in the regime of voltage registration (open external circuit) by using a high impedance selective nanovoltmeter. These experiments provided a check of surface charge contribution in the presence of univalent or divalent (uranyl acetate, UA) ions [3].

Stroboscopic Interferometry.

Initially, BLM curvatures were evaluated indirectly from the second harmonic capacitance responses by assuming, necessarily, completely spherical deformation of an initially flat BLM. A new development was later concentrated on the actual membrane shape under oscillating pressure. Both direct or converse flexoelectric effect (figure 1) have been studied using this method [5], [12], [13].

Figure 1: Converse flexocoefficient of a bovine brain phosphatidyl serine (+UA 2+ ) BLM vs. oscillation frequency of a.c. transmembrane potential. Conditions: 25 mg PS in 1 ml n-decane at 25 C; BLM modified by 1 mM UA in bathing electrolyte (0.1 M KCl); membrane radius was 143 m; the amplitude (peak-to-peak) of the applied a.c. potential was 600 mV. Each point was averaged over at least six successive extreme deviations of the BLM and the relative error in f was typically 9%.

Patch Clamp Technique and Direct Flexoeffect of Native and Model Membranes.

A patch clamp method was originally developed for the investigation of single ion channels. To this aim, small patches of native membranes were sealed at the tips of glass micropipettes. The patch clamp method is well described in the literature. With the development of the tip-dip technique formation of model phospholipid membranes on patch clamp pipettes from lipid monolayers also became possible. Thus, the method became available for reconstituted channel studies as well. A novel application of the patch clamp technique is provided by us after combining it with oscillation pressure technique. This gave us the possibility to time-modulate the membrane curvature on a m m scale and, thus, to study the flexoelectric properties of model and native membranes by using phase-sensitive registration methods [6], [8], [9], [11], [23], [29]. Flexoelectric response of a native membrane of a locust muscle in the higher frequency range is demonstrated on figure 2.

Figure 2: Flexoelectric recordings from an inside?out patch excised from locust muscle membrane in standard locust saline. Pipette resistance was 6.7 MW. Seal resistance was 0.5 GW . Patch capacitance components were = 7.5 pF and = 0.8 pF. Upper traces: flexoelectric response (F) of the patch at 3 different frequencies (345 Hz, 446 Hz and 512 Hz) in the high frequency range. Lower traces: driving pressure signals ( P ). Current bar of 10 pA and pressure bar of 5 torr apply to all measurements. Flexoelectric signals were strong enough to be directly recorded from the List amplifier output. No voltage dependence of the 1st harmonic was observed (i.e., patch oscillated around its flat state). At 345 Hz, with 2.4 torr (pp) driving pressure a first harmonic flexoresponse of 9 pA(RMS), phase - 72 ° was observed. The control pick-up response after rupturing the patch and taking the pipette tip out of the saline was much lower (0.23 pA).

Some of our results on flexoelectricity of different membrane compositions are summarized in table 1.

Lipid; Electrolyte	Partial charge per lipid head b (%)	Flexocoefficient [ x 10 E-19 C]
1. Phosphatidyl ethanolamine from E.coli; 50 mM KCl	- 3.7%	- 25.5 ( ± 72.5%)
2. Phosphatidyl choline from egg yolk; 0.1M NaCl	- 0.4%	+26.5 ( ± 50%)
3.Phosphatidyl choline from egg yolk; 0.1M NaCl + 1 mM UO22+	ca. 100%	20( ± 10%)
4. Phosphatidyl choline from egg yolk; 0.1M KCl	- 18.8%	13 ( ± 0.2%)
5. Glyceryl mono-oleate (synthetic); 0.1M KCl	0	0.43 ( ± 0.5%)
6. Phosphatidyl serine from bovine brain; 0.1M KCl	ca. - 100%	20 ( ± 25%)
7. Phosphatidyl serine from bovine brain; 0.1 M KCl + 1mM UO22+	ca. 100%	151 (± 19%)
8. Diphytanoyl phosphatidyl choline (synth.); 0.15 M KCl	0	0.31 ( ± 29%)
9. Locust muscle membrane; standard locust saline	> 100%	25 ( ± 50%)

Table 1: Flexoelectric coefficients of BLMs (1 - 7) and membrane patches (8 - 9) made from different lipids under various ionic conditions. 1 - 3 and 8 - 9: electrical estimation of curvature; 4 - 7: interferometric measurement of curvature, sign determination of f not attempted. All experiments except 7 concern the direct flexoeffect. All data refer to the high frequency range above 200 - 300 Hz, i.e., to the blocked flexocoefficient .

Black lipid membranes covered by in-situ synthesised semiconductor nanosized CdS particles ("nanomembranes") serve as models of photosensitive native cell membranes, where CdS crystallites mimic membrane proteins. Nanomembranes are known to display photoelectric effects. Like some biomembranes, they are capable of transformation of the optical energy into electrical one.

Periodic variations of membrane curvature with such membranes lead us to the discovery [16] of a new effect, named "photoflexoelectricity" (figure 3).

Figure 3: Flexoelectric response of a GMO BLM coated with CdS nanoparticles, oscillating at 700 Hz under zero current clamp. The first harmonic of the membrane potential is measured. The increase of the flexoelectric signal after light flashing shows exponential rise kinetics and reversible decay.

The flexoelectric amplitude increments and the phase shifts caused by illumination of BLMs with increasing amount of particles generated on the membrane were studied . The dark response decreased as the amount of CdS particles increased (as judged from the visual appearance), but the difference (light-dark) became more and more pronounced. At the same time, a tendency towards larger phase shift at higher photoflexoelectric response was observed. The frequency dependence of the effect was found to be nearly linear in both the light and dark state.

A mechanism of photoflexoelectricity in nanomembranes was proposed and compared to the experiment [16], [17], [19].

First observation of helielectricity in tilted lecithin multilamellar phases chiralized by the addition of cholesterol has been performed using the oscillation drop method [39]. This finding provides another mechanoelectric mechanism for native membranes, where cholesterol is a basic lipid constituent. The piezoelectric signal was obtained in the tilted gel and ripple phases only, vanishing in the fluid phase. This peculiar liquid crystal ferroelectricity produces a permanent polarization parallel to the membrane plane and normal to the tilt plane. The tilt may be locally existing even in the fluid phase due to integral membrane proteins. Modulating mechanically the tilt angle, e.g. by shear (as in the cited experiments) the in-plane polarization is also modulated and depolarizing currents are induced along the two membrane surfaces.

Pore formation in the lipid bilayer.

All the mechanisms, considered so far, have neither imply the existence of conducting defects in the membrane, nor their emergence under mechanical stress. Instead, membranes were rather considered as elastic and flexoelectric two-dimensional continua. The theory of pore formation was developed earlier [1], in connection to the steric and electric asymmetry of pore-forming molecules. It is natural to expect that ion conducting defects (pores, channels) could be stress-sensitive sites and there is much evidence about this nowadays. For example, stretch sensitivity of cyanotoxin-induced pores was studied by us in details [6], [8], [15], [20], [22]. The defect-forming action of DNA as related to electrotranfection (i.e., the electrically-mediated transmembrane DNA transport) was also investigated [10], [14]. Pore formation by photoactive amphiphilic spiropiranes (which change their steric asymmetry under UV illumination) is another interesting subject of our studies [26].

Ion channels.

A broad class of ion channels in native membranes are found mechanosensitive, i.e., capable of mechanical control of the ion flow through them [11]. In particular, we found that two potassium ion channels of locust muscle membranes (a small and a big channel) are mechanosensitive, although in a different way [6], [24]. While small channel displays the common, fully reversible pattern of increase of open probability by lateral stress, the big channel's response is hysteretic and irreversible. We speculated that it may be a demonstration of a new type of curvature-gated channels.

In all our studies on membranes the role of membrane mechanics is recognized as a very important one. The existence of mechanical degree of freedom in a membrane permits to describe it as a machine. Besides, electric and optical degrees of freedom are quite common. An opto-mechano-electric membrane offers a great number of possible combinations between its three degrees of freedom (serving either as inputs or outputs). Above all, due to the ultimate existence of these degrees of freedom in some native membranes, new hints about the structure-function relationship in photosynthetic membranes, retinal rods and discs, and other photoactive membranes could be obtained.

In a physical system with more degrees of freedom (e.g., mechanical, electrical and optical, comprising the horizontal plane of the pyramid in figure 4) the possible energy interconversion effects, involving 2 or 3 degrees of freedom simultaneously, can be classified in the way proposed in figure 4. More complicated combinations (e.g. of 4 degrees of freedom) could also be envisaged.

Figure 4: Possible mechanisms of energy interconversion in flexible, electro-, photo-, chemi- and termo-active membranes. Effects involving two degrees of freedom of the membrane system can be marked by 2 letters (e.g., ME and EM, the direct and converse flexoeffect) and those involving 3 degrees of freedom by 3 letters (e.g., OME, opto-mechano-electric effect, viz. photoflexoelectric effect).

Black lipid membranes decorated with nanoparticles of photo-semiconductors, "nanomembranes", represent a new model system having the three degrees of freedom into consideration. Like some biomembranes, they are then capable of the transformation of the three types of energy one into another. As mentioned above, a new effect, called photoflexoelectricity, was recently observed by us in nanomembranes, and earlier in photoactive BLM containing bacteriorodopsin or retinal-acetate.

The vast majority of the combined 3-degrees' effects in figure 4 has not been demonstrated yet, and represents a promising field for future studies. Chemical degree of freedom is inherent to all the others, for all the values of elastic moduli, spontaneous curvature, flexoelectric coefficient, etc., depend crucially on the membrane chemistry. Same conclusion holds for the thermal degree of freedom, also included in figure 4. Photochemical and thermochemical reactions provide further pathways. These can as well be coupled to mechanical, and/or electrical degrees of freedom, etc., etc.

A very important feature of a membrane system having two or more degrees of freedom: the possibility of occurrence of deterministic chaos in it, should be pointed out. According to the Bendixon-Poincare theorem, a dynamic system can be chaotic in a 3D or higher-dimensional phase space. Each degree of freedom provides one generalized coordinate and one generalized force. Therefore, even a flexoelectric membrane (4D phase space) does possess all the necessary features for the arising of dissipative, self-organizing structures. These should have played a very important role already at the level of prebiotic evolution of matter.

Starting from 1975 the knowledge of bioflexoelectricity has been steadily developed by us. Earlier results have been reported in the 30th Anniversary Jubilee Collection of ISSP (2002) Theory and experiment of lyotropic and biomembrane flexoelectricity is further revisited and reviewed. It is made clear that bioflexoelectricity provides a reciprocal relationship between electricity and mechanics in soft lyotropic and living systems, e.g., between curvature and polarization in a biomembrane. New experimental evidence of model and biomembrane flexoelectricity (including direct and converse flexoelectric effect) is reported by us. Biological implications of flexoelectricity are underlined. New groups from US (the teams of F.Sachs in Buffalo, NY and B.Brownell in Houston, TX) joined recently this exciting field of studies with new experimental techniques and theoretical models of some processes, in cooperation with us. Bioflexoelectricity enables membrane structures to function like soft micro- and nanomachines, sensors and actuators, thus providing important input to nanoionics applications. Nanobio-examples include membrane transport, membrane contact, mechanosensitivity, electromotility, hearing, etc. [37-45]. It was discovered thatchirality of lipids makes fluid lamellar phases piezoelectric (Figure 1) [42].

Figure 1: Temperature dependences of the piezoelectric signals measured at 80 Hz mechanical excitations in heating for the left L-DPPC/EG, right D- DPPC/EG/ and 50/50 wt.% racemic mixtures. The amplitude of the signal [42].

Langmuir-Blodgett (LB) films are organized molecular films deposited on solid substrates by the method of Langmuir-Blodgett: transferring of an amphiphilic molecular monolayer of controlled density spread at an air-water interface by slowly pulling (or pushing) the substrate normally through the interface. This procedure can be repeated many times. Thus a multilayer can result. Another way of transfer provides the method of Langmuir-Shaefer - horizontal lifting of the monolayer by touching it with a hydrophobic substrate from above. LB films are usually deposited in a centrosymmetric manner (Y type), but with certain substances polar LB films can be built up, facing the substrate either with hydrophilic heads (Z type) or with hydrophobic tails (X type). The LB method permits a straightforward way of variation of surface molecular density by compressing or expanding the precursor monolayer.

However, single monolayers or multilayers of some amphiphilic molecules can be obtained even easier by simple dipping of substrates in very diluted solutions (self-assembly method). A variation of the surface density of the adsorbed surfactant molecules can be achieved by varying t heir bulk concentration and the speed of withdrawal.

The general design and performance of a new Langmuir-Blodgett trough, produced in the Laboratory, are given in [32], [33]. Some factors important to LB film quality like vibrations generated within the trough, unevenness of motion of the barrier or substrate holder, control of constant pressure during deposition are evaluated in [35]. The problems arising during and after the transfer of lipid monolayers to solid substrates showing two-dimensional patterns are discussed in [31]. Experiments with LB films from dimiristoylphosphatidylethanolamine and a fluorescently marked lipid were performed for different speeds of monolayer compression and support pulling. Horizontal lifting was also attempted.

Self-assembled (SA) multiplayers of stearic acid and of the phospholipid dipalmitoyl L-a-phosphatidic acid (DPPA) were investigated by polarized FTIR-ATR spectroscopy. It has been shown that SA films of stearic acid consist of well-ordered crystalline assemblies with hydrocarbon chains in all-trans conformation. The detailed molecular organization depends on the concentration of layers-forming solutions. This offers some possibilities for controlling SA-structure [37]. SA-multilayers of DDPA consist of well-ordered and packed in all-trans configuration molecules in a hexagonal crystalline lattice. Incorporation of the peptide gramicidin D results in a largely unperturbed lipid lattice (on the infrared length scale). This implies strongly that peptide aggregation occurs, as was also found for the same peptide in Langmuir-Blodgett multilayers of the same lipid [38].

SA and LB films of DPPA/gramicidin were also prepared on the surface of platinum wires and studied by means of impedance spectroscopy [21]. Selective ac conductance of K vs. Na ions was demonstrated at 0.5 Hz ac measuring voltage.

Organized layers of biphilic biomolecules (lipids, fatty acids, surfactants; monomer or polymer ones) on solid supports are used for a long time as orienting substrates for nematic liquid crystals ( NLC ) . They are known to influence NLC orientation in a specific way depending on surface density of molecules, number of monomolecular layers, surface charge and/or dipole of the hydrophilic head group, hydrophobic tail(s) length, temperature etc. This phenomenon is known as liquid crystal anchoring: homeotropic, planar or tilted one.

A complete theory of surface nematic anchoring was developed [42], including steric, dielectric, flexoelectric and surface polarization coupling mechanisms [44], [46]. In the last three cases surface electric field due to the adsorption of surface charges on the substrates is of ultimate importance. The extent of penetration of surface electric field inside a nematic is shorter than believed, due to the important surface screening. This leads to a substantial dehancement of dielectric coupling.

In the case of lower anchoring strength and strictly planar or homeotropic anchoring it is possible with relatively little energy to rotate the director on the surface to an orthogonal position. This is a situation of unstable equilibrium known as anchoring breaking. The concept of anchoring breaking is important for the new display generation.

Steric aspect.

Earlier understanding was that planar NLC anchoring by rubbing or evaporation is due to the creation of a surface relief (grooves, tips, tilted prisms) which then interacts with the orientational elasticity of the nematic. More recent insight in the ordoelectric aspect (see below) of NLC-substrate interaction focuses on the strong disorder a double evaporated, fractal, surface can induce in the interfacial nematic layer, leading to a very characteristic conical anchoring under the magic angle.

It is well known that homeotropic NLC anchoring by LB films is strongly dependent on LB film surface density. It could be approximated by the monolayer density on the air-water interface of the Langmuir through, although some modification could take place during the deposition. Expanded LB films usually result in much better homeotropic orientation than compressed ones: nematic molecules enter the holes in the film and in this way the whole nematic becomes anchored. At close packing of the alkyl chains the homeotropic orientation is lost completely.

Biphilic aspect.

Biphilic asymmetry of lyotropic mesogens used for LB film formation is well known and forms the basis for their self-assembly. Some time ago we recognized also the importance of biphilic asymmetry of the thermotropic (nematic, smectic, discotic) mesogens. If the end substituents of a nematic molecule differ strongly in their polarity and lipophilicity (e.g. alkyl-cyanobiphenyls) they will be oriented in a polar fashion at the contact with the substrate while entering the holes in the LB film. Since usually biphilic asymmetry is coupled with both dipolar and steric molecular asymmetry, a surface polarized and sterically stressed nematic layer will be formed at the contact LB-NLC.

Dielectric aspect.

The molecules forming LB film may be either dipolar, or charged, or both. Thus, the film will create an exponentially decaying electric field due to the double layer created by the charges or to the residual electric field of the super-lattice of vacancies in the head group dipolar lattice. Here, important surface screening effect was recognized [44], [46] and described by the Schmiedel screening length l_s=2ee_okT/q_es, q_e being the proton charge, s, the surface charge density and e, the average dielectric constant of the NLC. Compared to the familiar Debye length of bulk screening, this new length of surface screening is one order of magnitude less. Therefore, dielectric contribution to anchoring energy is, in fact, small enough.

Flexoelectric aspect.

Since our discovery of the gradient flexoelectric effect it is known that a nonhomogeneous electric field gives rise also to bulk flexoelectric energy depending on the product of the field gradient dE/dz and the total flexoelectric coefficient e=e_1z+e_3x. This term can also be integrated out as a surface one. In this way another material property of the nematic, its flexoelectricity [52], enters the picture [41], [42].

Ordoelectric aspect.

If the order parameter S_s of NLC at the interface takes a different value from the bulk one, S_b, then the so-called ordoelectric polarization will arise according to Durand et al. It will be confined in the interfacial layer (of a length x) of the order parameter variation (DS = S_b - S_s). The depolarizing electric field from the ordopolarization will interact with itself and will give rise to an ordoelectric self-energy, also of surface type.

All the energies discussed above depend on the orientation of the NLC with respect to the substrate. If this orientation varies in space, the bulk elastic terms should also be considered. The simplest case of homogeneous NLC orientation is reduced to an energy functional containing surface terms only [42].

The surface torque balance equation predicts a rich variety of surface transitions depending on all the parameters taking part in the description. The delicate balance of surface torques could even result in "re-entrant sequences" planar-homeotropic-planar or homeotropic-planar-homeotropic at continuous variations of surface density of charges.

Dynamic aspects of anchoring.

All the aspects considered above deal with the case of static surface-bulk equilibrium. In a dynamic situation when interfacial orientation of NLC changes with time there will be an additional torque in the torque-balance equation originating from surface viscosity k and proportional to the rate of q change. Clearly, at periodical variations of q this term will be important in the higher frequency region. Surface dissipation of energy is an important, but weakly explored, aspect of surface interactions, which governs the speed of switching of the new generation of surface-driven displays [51].

Dynamic aspects of NLC anchoring were investigated experimentally in a few papers of ours [48], [49], [50].

Photoflexoelectric effect in homeotropic MBBA/azodye nematic layers in horizontal electric field subjected to UV illumination was investigated. About 10 % reversible increase of the flexoresponse (i.e., the increment of transmitted light intensity between crossed polarisers due to an in-plane electric field) was found under epi-UV-illumination, with relaxation times of the order of 15 s (figure 5). The d.c. voltage dependencies of both dark and light flexoresponses followed the predictions of the theory. An UV-dependent amplification of the amplitude of flexo-oscillations (excited by an a.c. voltage) was also registered. The relative importance of bulk and surface contributions to the photoflexoresponse was discussed [45].

Figure 5: Transmitted light intensity through a 100 mm homeotropic MBBA/ azodye layer with 1% at various in-plane electric fields (E = U / l ), where U is the indicated voltage and l, the interelectrode distance, is 2mm) and under UV focused epi-illumination (140 mW) on and off. Microscope NU2 (Zeiss). Crossed polarisers. Orange transmitted light (590 nm), epi-UV light (334 nm, nonpolarised). Lock-in registration of transmitted light (SR830 DSP Lock-in amplifier with SR540 optical chopper at 260 Hz). The moments of UV and voltage switching on and off are indicated by arrows.

Langmuir-Blodgett (LB) technique was used for deposition of of monolayer lipid films of dipalmitoyl phospathidylcholine (DPPC) on glass with variable surface density of lipid molecules [46], [48]. In a certain range of surface density these surfaces oriented homeotropically the highly polar nematic liquid crystal (NLC) of 4-cyano-4'-n-pentylbiphenyl (5CB). Anchoring energy values were obtained by magnetic Freedericksz transition. Optical transmission curves of liquid crystal (LC) layers sandwiched between orienting lipid monolayers were recorded versus magnetic field with high accuracy. They were further converted into optical retardation and fitted by a complete theory of the transition containing anchoring strength as a parameter. Independent measurements of refractive indices of 5CB were also performed by the prism method. Anchoring energies thus obtained showed for the first time a non-monotonic behaviour with increasing packing density of DPPC monolayers and a pronounced minimum around 0.82 nm 2 per molecule. This was explained by the complete theory of surface anchoring outlined above, including steric, electric, flexoelectric, and notably, surface polarization coupling mechanisms. The last one stands for surface polarized layers at the liquid crystal interfaces interacting with surface electric field due to lipid molecules. The competition of these mechanisms leads to an initial dehancement followed by an enhancement of the anchoring strength at monotonically increasing DPPC packing densitiy. Surface polarization evaluated from the experimental data is in a good correspondence to molecular parameters.

Anchoring interaction of MBBA and MBBA + 5CB nematic layers with monomolecular films of CTAB on ITO glass supports is studied by videomicroscopy in the presence of an electric field [43]. In DC-electric field some new effects were observed: (i) polarity dependent breaking of anchoring and switching to two oblique states in dielectrically stable planar cells; (ii) a polarity dependent flow-induced metastable anchoring transition in homeotropic cells to a planar or tilted alignment after the field is switched off. The results are discussed in terms of a surface transition assisted by electric transport of biphilic CTAB ions and by a surface memorization of the flow-induced planar alignment.

Homeotropic nematic layers of MBBA oriented by self-assembled (SA) monolayers of CTAB were studied [49] by phase-sensitive flexoelectric spectroscopy method [48]. Higher frequency part of the viscoelastic spectra provided information about surface dissipation of orientational energy. Temperature dependence of surface viscosity was revealed for the first time (figure 6). Influence of area density of CTAB monolayer was also investigated.

Homeotropic nematic layers of MBBA, oriented by SA layers (on glass substrates) of dilauroyl phosphatidyl choline (DLPC), cetyl trimethyl-amonium bromide (CTAB) and silane orienting agent (ODS-E), were also studied by flexoelectric spectroscopy method [50]. DLPC solutions in chloroform provided SA multilayers with different thickness on dipped glass substrates, depending on bulk DLPC concentration. CTAB solutions in water provided, on the other hand, SA monolayers, with surface density depending on pulling speed of substrates. Finally, ODS-E solutions provided orienting layers that can be cross-linked at elevated temperatures.The viscoelastic spectra of these layers contained information about surface dissipation of orientational energy under variable structure of orienting layers that may, or may not, dissolve partially in the nematic. Results are summarized in table 2.

Figure 6: Temperature dependence of surface viscosity of MBBA homeotropic nematic layer in contact with loose self-organized films of CTAB. B ulk concentration of CTAB 1.6 * 10^-5 M, 2 cm/min pulling velocity of the glass substrate, 100 mm thickness of LC layer.

Liquid crystal	Chromolan	DLPC	ODS-E	CTAB
MBBA	2.1	2.0	3.8	1.7
BMAOB	2.3	-	-	-

Table 2: Surface viscosity ( k * 10⁸/ J.s.m ^-2 ) at room temperature of two liquid crystals, MBBA and BMAOB, homeotropically oriented by the indicated surfactants.

Polymer Dispersed Liquid Crystal.

The linear electro-optic response of polymer dispersed liquid crystal films (PDLC) has been studied. Nematic micrometer variable size droplets of E7 were formed in a NOA 65 photopolymer by photopolymerization induced phase separation (PIPS) [69] and in polymethylmetacrylate by solvent induced phase separation (SIPS) [70].
Dielectric and flexoelectric oscillation of the director orientation in the droplets were excited by an a.c. driving voltage in the range 1Hz to 3 kHz. Both the linear and quadratic electro-optical response of the PDLC films were studied by the flexoelectric spectroscopy method and by laser light diffraction.
The temperature dependence of the first harmonic electrooptic spectra was obtained. Peculiar picks and double peaks in the spectra were found at temperatures close to the clearing point, especially in samples with narrow distributions of droplet size. A flexoelectric origin of the first harmonic spectra in confined nematic systems is discussed. The temperature and voltage dependence of the 1st and 2nd harmonic electro-optic spectra (amplitude and phase of the transmitted light vs frequency) were obtained, and strikingly deep minima in all spectra were found. These minima were interpreted as resulted from a spatial filtering (i.e. selective diffraction) of the time-modulated components of the transmitted light [71].
Single-layered optical material of linear-gradient microscale PDLC are investigated as well. The formation of the PDLC structure, as well as the droplet gradient, are fully controlled by the PDLC cell geometry and UV laser [72].
The electro-optical light-switching properties of wedge-formed microscale droplet-gradient single layers of PDLC are examined. Related to the wedge dimension, the liquid-crystal droplets in the layers reach several tens of micrometers [73].
Also composite films formed by pulsed UV laser are investigated. In this case two morphology types, namely a bipolar and a hybrid alignment of liquid crystal droplets are obtained. The specific structural properties of the produced PDLC layers, such as the droplet shape uniformity and alignment, as well as the droplet size control through the film thickness, facilitate the efficient control on the electro-optical response, thus being of practical interest for EO device applications [74].
The flexoelectro-optical behaviour of composite layers of E7 dispersed in a transparent polymer matrix, prepared between glass substrates with Teflon nanolayers initially deposited, was investigated. Thus, LC-polymer composite layers with well ordered and aligned droplet morphology were obtained, with dispersed LC droplets spherical in shape [75].

Homeotropic Nematic Layers and Planar Nematic Layers.

Homeotropic nematic layers of MBBA and BMAOB have been studied by a phase-sensitive flexoelectric spectroscopy method. They have been oriented by films (with different degree of desorbtion) of DLPC, CTAB and Chromolan self-assembled onto the cell glass plates. The viscoelastic spectra contain information about the surface dissipation of the orientational energy for different aligning films that partially desorb from the surface and dissolve in the nematic, producing a gradient of concentration of the surfactant. A new type of flexoelectric effect dependent on the space derivative of flexo-coefficients has been identified. This effect consists of a bulk flexo-torque source that substantially influences the apparent liquid crystal anchoring. Static and dynamic cases have been analyzed for a steplike surfactant distribution. Resulting spectra have been successfully compared with the experiment, yielding information about the surfactant gradient. A theoretical treatment of the first harmonic has been implemented. The temperature dependence of the thickness of the desorbed subsurface layer of the Various flexo-dielectric domains such as cross-like domains, π-walls, longitudinal flexo-dielectric walls, etc. were observed for voltages below 8 V. Our interpretation is that all surfactant was revealed. The surface viscosity was also obtained from the theoretical fits to the spectra. These results provide new insights on the interfacial physics of nematic liquid crystals and solid surfaces interaction, where flexoelectricity and desorption play a fundamental role [68, 76, 78]. Experimental values of the flexocoefficient difference |e∗| = |e₁z − e₃x| of a BMAOB/“swallow-tail” mixture as a function of the concentration of a “swallow-tail” compound are analysed. The fact that the extrapolated value of this difference is somewhat lower than originally expected is explained by a theory showing that the strong steric asymmetry of “swallow-tail” molecules gives a comparable contribution to both flexocoefficients [79].
Planar nematic layers of 5CB oriented by ‘sliding on’ nanolayers of PTFE were studied by electro-optic methods. Deposited layers were characterized by AFM, spectroscopic ellipsometry and polarizing videomicroscopy. It was found that at 100°C presumably single PTFE chains (4 nm thickness) are deposited. By ellipsometry measurements c. 0.1° pretilt angle of the nematic layer was determined. In planar nematic layers low frequency flexoelectric splay oscillations were excited. An overall 1/f shape of the oscillation spectrum was found in the range 1 to 1000 Hz, giving no evidence of a surface viscosity effect in this range [80]. By using a drop method it was established that the preferred director alignment is tilted opposite to the sliding direction. In some of these samples an unusual modulated domain pattern after switching off a prolonged a.c. excitation was observed for the first time. A possible relation between the domain origin and loosely deposited PTFE layers was suggested [81].
Parallel surface-induced flexoelectric domains (flexo-dielectric walls) have been further studied using new tools – a shadowgraph technique and computer processing of the most important images and in an additional applied magnetic field in the Z direction. The electro-magneto-optical curves have a resonance character due to competition between the flexoelectric, dielectric and magnetic torques [82, 83]. The d.c. voltage threshold and wave number of the flexoelectric domains of have been obtained experimentally in BMAOB layers with strong-strong and strong-weak anchoring, under the joint action of increasing d.c. and a.c. voltages. [84]. Further, their characteristics for the case of one arbitrary nematic have been calculated. It was suggested the optimal values of the material parameters of the nematic for the creation of the variable-grating mode widely studied in the world [85]. These domains have been experimentally obtained in BMAOB. The fitting of the experimental points with the theoretical curves permitted to obtain various material parameters of the nematic [86]. The solution of the Euler–Lagrange equations for the director components of the flexoelectric domains has been for the first time found with the aid of matrix calculations for the case of a planar nematic layer under the simultaneous action of an d.c. and a.c. voltages [87]. A discussion of the eventual applications of this solution is also presented [88]. Based on the formulated expressions, we present and analyze computer calculations for a planar nematic layer with anisotropic elasticity and both negative and positive dielectric anisotropy under the action of a homogeneous flexoelectrically deforming d.c. electric field [89]. Correction of the theoretical results presented in Eur. Phys. J. E 31 179 (2010) is made for the case of weak anisotropic elasticity [90].
Experimental observations on the flexoelectoro behaviour of the bent-core- in the nematic phase with a positive dielectric anisotropy were performed for the first time these flexoelectric domains arise by the inhomogeneity of the electric field created by injection of ions from one of the electrodes [91]. It was reported on the converse flexoelectric effect in two bent-core nematic liquid crystals with opposite dielectric anisotropies. The bend flexocoefficient for both the compounds is of the usual order of magnitude as in calamitics, unlike in a previously investigated bent-core nematic for which giant values of the bend flexocoefficient are reported. In order to resolve this discrepancy, we propose a molecular model with nonpolar clusters showing quadrupolar flexoelectricity. The study also includes measurements on surface polarization instabilities in the dielectrically positive material; the splay flexocoefficient thereby deduced is also of the conventional order [92]. Various low temperature nematic mixtures possessing a positive dielectric anisotropy, were investigated. The strength of the flexoelectricity in the mixtures was studied [93].
The flexo-surface polarization term |e_3x + m_p|= 5.1 pC/m and the flexoelectric sum |e_1z + e_3x|= 15 pC/m were measured for the case of the nematic E7. The inclusion of minute amounts of single-walled carbon nanotubes (SWCNTs) with a concentration below 10-3 wt. % changes the results obtained as follows: |e_3x + m_p|= 14.7 pC/m and |e_1z + e_3x|= 78.7 pC/m, respectively. The value of the anchoring energy was found to be 0.4x10^-6 J/m² for the pure nematic E7 and 0.78x10^-6 J/m² for the E7/SWCNTs mixture [94]. The SWCNT influence on the behaviour of the gradient flexoelectric and surface polarization induced domains arising in a homeotropic nematic E7 layer oriented by the lipid SOPC, or without the lipid, has been studied. Appropriate dynamic light transmitted curves have been recorded and typical microphotographs have been taken [95].
A digitalized version of the standard method of conoscopy was developed to register the bend deformation of molecular orientation in homeotropic nematic layers caused by an in-plane applied DC electric field, and influenced by UV light illumination. Two guest-host systems prepared by mixing of a nematic liquid crystal and some novel photochromic liquid crystalline materials with single azo-bond or two azo-bonds, with or without a longitudinal dipole moment, were studied. A marked, reversible UV increase of the flexoelectrooptic effect was found in case of guest molecules with a longitudinal dipole moment. The corresponding change in the thermal behaviour of the dielectric properties of the mixtures was also evidenced. A lowering of the bend elastic constant upon photoisomerization was observed for the first time, a feature ascribed to the formation of the bent-shaped cis isomers [96 – 99]. Detailed temperature investigations of the bend converse flexoelectric effect in POPDOB, a nearly symmetrically substituted mesogen with a rich polymorphism, specifically exhibiting the nematic-smecticA (N-SmA) transition, were carried out. The pretransitional behaviour of the flexoelectric effect on approaching the SmA phase suggests a quadrupolar origin of the flexoeffect [100].

Superparamagnetic fero/feri oxide nanoparticles covered by β-cyclodextrine were synthesised and investigated by ultramicroscopy in dark field regime. By ultrafiltration of the suspesion through a nanopore filter their size was confirmed. Magnetic nature of particles was confirmed by observing a striking process of aggregation in magnetic field [101]. The route for obtaining of hydrophobic superparamagnetic particles contrast and tracing agents for magnetic resonance imaging (MRI) has been examined. A new contrast agent for liver MRI was propose. The effect and the degree of change in the rabbit liver MRI signal by using the experimental contrast substance was studied. The contrast agent prepared by us substantially reduces the MR intensity of liver parenchyma during T₂ magnetic resonance imaging. The shortening of T₂ relaxation time is about 50% with the 80 nm size of the nanoparticles used. Our initial experiments demonstrate that liver tissue difference of signals before and after contrasting is sufficient for the detection of focal liver lesions and is potentially usable for their diagnosis [102 and 103].

Second harmonic generation, optical microscopy, and AFM are used for the investigation of the thin films of azobenzene and trans-stilbene derivatives. Film morphology is studied at micron and submicron scale. The approach allows one to estimate the size and integral ordering of the crystalline molecular aggregates [105].
Dry components of different red and white wines were investigated by application of thin layer nematic liquid crystal. A change in the orientation of the liquid crystal was observed over the wine residue region. Differences between the structures of investigated pure wine samples and samples with inclusions were observed. The optical analyses of deformed liquid crystal layer were realized by polarizing microscopy. The method gives possibilities for quick detection of wine inclusions and wine imitation [106, 107].