Fibrous self-assembly of liquid crystal made by self-organisation

ABSTRACT Fibre structures of liquid crystals are of particular interest because they are expected to be used in optical fibres, optical devices, and lasers. Micrometre- sized liquid crystal self-assembly demonstrates new optical functions or interfacial interactions which cannot be observed in the bulk. Thermotropic liquid crystals organize fibres by phase transitions or shape changes. The fibrous self- assembly of liquid crystal made by self-organisation was reviewed in the study. We will also introduce the characteristics of these fibres as well as those of lyotropic myelin and lyotropic fibres. Theoretical research on the growth mechanism and physical properties of the fibres has also been summarized.


Introduction
The shape and dielectric constant of liquid crystal molecules are anisotropic. Depending on the shape anisotropy, liquid crystal molecules align spontaneously. Rod-shaped liquid crystal molecules, such as 4-cyano-4'-pentylbiphenyl (5CB), show a nematic phase, where almost all molecules align in the same direction but not in a crystal. A liquid crystal has been applied to a display because the voltage input can control direction of this alignment, and because a change in the alignment can control the brightness. Many papers have recently reported a new function demonstrated by micrometre-sized liquid crystal selfassembly, and researchers have focused on its application. Micrometre-sized self-assembly means, for example, droplet, core-shell, and fibre structures. Droplet structures consisting of nematic, cholesteric, and lyotropic liquids have been reported. The fabrication methods, tuning shapes, and applications are described in detail by Qu et al. [1].
Nematic liquid crystal droplets exhibit the whispering gallery mode (WGM). This is a unique resonance mode of light. In 2009, Humar et al. [2] reported that nematic liquid crystal droplets exhibit the WGM mode. They investigated the optical properties of a micro-resonator of nematic liquid crystal droplets in a polymer matrix. They found that the tuning range was significantly larger than typical solid-state micro-resonators. In 2011, Humar et al. [3] found that nematic liquid crystal droplets functioned as WGM lasers. The WGM laser spectra change depending on the molecular alignment in the droplet. Therefore, by observing the laser spectra, we can determine the change in the concentration of surfactants in millimolar order.
A report also focuses on the interaction at the liquid crystal droplet but not on the optical properties. Moreno-Razo et al. [4] investigated the pattern formation of surfactant molecules at the interface of a liquid crystal droplet using the numerical simulations. Following an increase in surfactant concentration, the pattern changes from dot to stripe. Whitmer et al. [5] experimentally and theoretically investigated the interaction between nanoparticles at the interface of liquid-crystal droplets. Two nanoparticles on the droplet surface are set at the two defects on the droplet surface.
Patel et al. [6] observed the precipitation of 5CB microdroplets by cooling a mixture of 5CB and methanol. The size and number of droplets were tuned by adjusting the cooling rate and depth of the temperature quenching. Thakur et al. [7] also observed the growth of nematic liquid crystal droplets in an isotropic liquid.
Previous studies have investigated cholesteric liquid crystal droplets. In 2010, Humar et al. [8] reported that cholesteric liquid crystal droplets functioned as omnidirectional microlasers. The wavelength of the laser depends on the chiral pitch of the cholesteric liquid crystal and is tuned on a scale of several tens of nanometres by temperature. Seč et al. [9] theoretically investigated the relationship between cholesteric pitch and radius of the droplet, where liquid crystal molecules align tangentially at the surface. The study indicated that the alignment changed from bipolar to radial spherical or diametric spherical structures following an increase in N (the number of pitches in a droplet).
The dynamic motion of cholesteric liquid crystal droplets has been reported. Bono et al. [10] investigated the rotational direction and speed in detail and presented a theoretical model to explain the experimental results. The droplet rotates in an isotropic phase at a temperature where cholesteric and isotropic phases coexist. Nishiyama et al. [11] also reported that the rotational motion of a cholesteric liquid-crystal droplet was caused by irradiation with ultraviolet (UV) light. It is well known that the chiral structure of a cholesteric liquid crystal droplet rotates when a temperature gradient is applied perpendicular to the chiral axis. However, it is yet to be known whether the rotation is caused by rigid body rotation or director rotation. Nishiyama et al. [11] revealed that the rotation was caused by rigid body rotation using the system used by Bono et al. [10].
Amphipathic compound with long alkyl chains is one of typical lyotropic liquid crystals. With an oil droplet covered with a surfactant thin film with a long alkyl chain, Guttman et al. [12] demonstrated that droplet shape has temperature-dependent facets. Sheng et al. [13] demonstrated colour change of a lyotropic droplet by applying a voltage.
In addition, the core-shell structure was also studied. Lopez-Leon et al. [14] investigated the positioning of colloids on the nematic shell, where the colloids were located at the defects in the shell, indicating that the thickness of the shell control the direction and number of defects. Uchida et al. [15] fabricated a cholesteric liquid crystal shell in which the chiral axis was perpendicular to the surface. Three types of laser modes have been presented by changing the combination of dyes and cholesteric liquid crystals.
Fibre structures are also attractive. It has attracted the attention of researchers because of its anisotropic shape and growth mechanism. We will summarise fibrous selfassembly in this study. The application of a fibre structure is also expected.
Some papers use the word 'filament', not 'fibre'. Thick and short fibres are often called fibres, and thin and long fibres are often called filaments. The study used the words employed by the original authors.
We show the artificial and spontaneous fibre organisation ( Figure 1). Artificial fibres are fabricated by confinement in a capillary [16], electrospinning [17], pulling procedures [18], and microfluidic devices [19,20] and were reviewed in [21]. In some cases, we observe fibrelike structures of liquid crystals in the phase transition. These structures are textures, which are observed with polarised microscopy and cannot be picked up. Here, we do not consider the texture but rather the rigid body as a fibre.
The final part of the Introduction reports a complex structure containing fibre structures. Takenaka et al. [22] fabricated a liquid crystal necklace structure made of 5CB and polyvinyl alcohol (PVA) (Figure 2(a)). The necklace structure contains 5CB droplets connected by liquid crystal fibres made of a mixture of 5CB and PVA ( Figure 2 (b,c)). The necklace structure is stable against to the phase transition and the alignment change of molecules in droplets. The elastic constant of the fibre was measured using two laser tweezers. The elastic constant was comparable to that of the PVA hydrogel. They also attempted light transfer between droplets; however, it was not observed. This was due to the fibre part being thin to transfer light, and the refractive index of 5CB was not sufficiently large.

Classification of spontaneous organisation in fibre structures
There are two types of spontaneously organised fibres: those organised during phase separation and those organised during shape change.

Fibres organised during phase separation
Certain liquid crystals exhibit a fibre structure when their phases change from isotropic to smectic [23]. The usual method of the fibre fabrication is as follows; the liquid crystal of the isotropic phase is dissolved in a solvent, following liquid precipitation by cooling as a smectic phase in a fibre shape. This system was first reported in 1910 by Friedel and Grandjean [24]. Pratibha et al. [25] reported that Meyer and Jones analysed this system in the 1970s. In the 1980s, Adamczyk et al. [26] and Arora et al. [27] reported similar phenomena.
Long-chain alcohols are the typical solvents used in this system. A combination of system with 4-Cyano-4'-n-octyloxybiphenyl (8OCB) and alcohol have often been studied. The isotropic phase of 8OCB was mixed with various types of alcohol, and the fibre-shaped precipitation of 8OCB resulted from cooling. In 1992, Pratibha et al. [25] investigated fibre organisation by using 8OCB and various alcohols with alkyl chains from C = 2 to 12. Consequently, long filaments can grow with long-chain alcohols.
Thus, dodecanol generated the longest fibres. In alcohols or alkanes with a similar structure, fibres can grow, however, the fibre grown with dodecanol is the longest. In addition, development of a theoretical model for fibre growth by considering elastic energy and interfacial tension was also reported. This model indicates that the fibre structure is more stable than the spherical structure from the viewpoint of free energy. After 1992, 8OCB and dodecanol systems were extensively studied. Pratibha et al. [28] experimentally and theoretically studied the system. Naito et al. [29] developed a theoretical model from the viewpoint of free energy and investigated the shape change of fibres. According to this model, the length of the fibres increases exponentially, implying the fibre grows at every point on the side. In addition, this model indicated that the straight length of the fibre was restricted because the fibre buckled and bent. By utilising the system of 8OCB and dodecanol, the theoretical results were experimentally demonstrated. Todorokihara et al. [30] also studied experimentally and theoretically the buckling instability that occurred in the system of 8OCB and dodecanol.
It has been reported that fibre organisation occurs in systems other than 8OCB and dodecanol. Adamczyk [31] and Kim et al. [32] grow fibres in silicone oil. Adamczyk [31] found that nematosmectogen 4-nitrophenyl-4'octyloxybenzoate (NPOOB) grew into fibres when precipitated in silicone oil by cooling. He observed experimentally and theoretically the development to fibre shape in detail. According to his theoretical analyses, fibre growth occurred, owing to the anisotropy of the interfacial tension between nematic/isotropic and smectic/nematic interfaces [31]. Kim et al. [32] used a semifluorinated liquid crystal that displayed two different smectic phases (smectic A and smectic E) for fibre growth. The fibres showed a repeated change in shape between fibres and emulsions. Although many reports related to spontaneously organised fibres have focused on the mechanism of anisotropic self-organisation, Kim et al. [32] indicated that the application of switchable emulsion could be realised with the fibres. For instance, on/off switching of laser irradiation can be controlled by tuning the temperature using a dye-containing liquid crystal.

Characterisation of lyotropic fibres
Amphiphilic molecules with long alkyl chains or lipid molecules are representative lyotropic liquid crystals and align with each other via hydrophobic interactions, between the long alkyl chains. Depending on the size of the hydrophobic and hydrophilic parts, amphiphilic molecules can form a variety of self-assemblies. For instance, when the size of the hydrophilic part is larger than that of the hydrophobic part, a hydrophilic emulsion structure appears. In contrast, when the size of the hydrophobic part is larger than that of the hydrophilic part, a hydrophobic emulsion structure appears. Membranes, sponges, and vesicle structures appear when the hydrophilic and hydrophobic parts have similar sizes [34].
The fibre structures in lyotropic liquid crystal systems have characteristic arrangements that are useful for identification. Ishimaru et al. [35] and Kageyama et al. [36] reported that, depending on pH, lyotropic fibre structures elongate or spiral in structure. The fibres that the lyotropic liquid crystals develop are called myelin. Although there have been many previous studies mentioning the shape of myelin, the detailed inner structures have not been sufficiently studied. Recently, however, the detailed inner structure of myelin has also been investigated. In 2015, Kageyama et al. [37] revealed the inner structure of myelins using small-angle X-ray scattering (SAXS). Benkowska-biernacka et al. [38] observed the cross-section of myelin using confocal and polarised microscopes. Recently, Khodaparast et al. [39] investigated the growth rate of myelin. The myelin structure, which grows from a multilamellar vesicle of sodium alkylbenzenesulfonate (NaLAS), was analysed by optical microscopy and small-angle neutron scattering (SANS). When the NaLAS solution was rapidly cooled (>10°C/ min), multilamellar structures appeared. In contrast, myelin structures appeared when the NaLAS solution was cooled slowly (<1°C/min). The growth rates of these were measured, it was found that the diameter of the NaLAS multilamellar vesicle increases proportionally to the square root of time and the length of myelin increased proportionally with time ( Figure 3). These results indicate that myelin grows at the edge and not on the side [39].
According to Naito et al. [29], the length of fibres which grow in a system of 8OCB and dodecanol increases exponentially. This indicates that the fibre grew on the side. Therefore, the growth mechanism of the myelin structure shown by lyotropic liquid crystal and that of the fibre structure of 8OCB and dodecanol are different.
Lastly, we introduce the recent paper which refers to the application of myelin structures. Van der Weijden et al. [40] fabricated fibres using tetra(ethylene glycol) monododecyl ether (C12E4OH) droplets on a water surface. The fibres extended following Marangoni flow and picked up an oleic acid liquid droplet. By balancing the Marangoni flow and shrinkage, myelin can be used for the positioning of materials.

Fibres organised in shape change
Fibres organised in shape change are similar to the myelin of lyotropic liquid crystals. Peddireddy et al. [16]  called the fibres organised in shape change as myelin. The difference between the myelin of the lyotropic liquid crystal and the myelin-like fibre of the thermotropic liquid crystal is explained in detail.
Toquer et al. [41] synthesised several surfactants with structure based on cetyltrimethylammonium bromide (CTAB) and mixed these surfactants with 5CB. The fibre structure grew from these mixtures by cooling and elongated with the addition of ethanol (Figure 4(a)). The temperature changes slowly, causing fibre elongation and shrinkage, following subsequent changes. A theoretical model was developed from the viewpoint of elastic energy and surface energy. The fibre structure was estimated to be a strong local minimum state of elastic energy. In simple terms, the elastic energy of fibres is larger than that of droplets with the same volume, causing local stability of the fibre structures owing to a large energy attributed to the hedgehog and hyperbolic hedgehog defect. Therefore, this large energy is necessary to change the shape from a fibre to a droplet (Figure 4(b)) [41].
In 2012, Peddireddy et al. [42] presented a fibre structure composed of 4-cyano-4-octylbiphenyl (8CB) and tetradecyltrimethylammonium bromide (TTAB) ( Figure 5). This is similar to the myelin structure, which appears at the interface of a lyotropic liquid crystal and water. The growth of this structure continued until the TTAB concentration decreased. Observations show that fibre growth from 8CB droplets dispersed in the TTAB solution. As a result, the fibre does not grow when a nematic 8CB droplet is dispersed in the TTAB solution. However, fibre can grow when a smectic 8CB droplet is dispersed in the TTAB solution. The fibre will grow at that specific point due to mechanical damage to the smectic 8CB structure in the dispersion process [42].
Peddireddy et al. [16] fabricated fibres with 8CB and CTAB in 2013. Investigating the growth rate and the diameter of the fibre, depending on the concentration of CTAB solution, the similarity and difference between the myelin of lyotropic liquid crystal and the myelin-like fibre of thermotropic liquid crystal were confirmed. In both systems, myelin/myelin-like fibre structures appear in a metastable state during the dissolution process of the solutes (lyotropic L alpha phase/thermotropic smectic phase) and are not soluble in the solvents (water/ surfactant solution). In addition, the bending elasticity was smaller than the compression elasticity in both systems. In other words, a flexible cylindrical structure in which multilayers are wrapped around the cylinder axis appears easily. In contrast, a clear difference can be observed in their microstructures. The lyotropic myelin structure contains two materials, water and surfactants, and exhibit a lamellar structure. However, the myelin-  like fibre structure of thermotropic liquid crystal is just composed of pure liquid crystal.
Peddireddy et al. [43] also indicated the difference in optical properties between the myelin of lyotropic liquid crystals and myelin-like fibre of thermotropic liquid crystals. The myelin of the lyotropic liquid crystal has a similar refractive index to that of the solvent surrounding the myelin. However, the myelin-like fibre of thermotropic liquid crystals have strong birefringence, with a larger refractive index than the surrounding surfactant solution. Therefore, the myelin-like fibre of the thermotropic liquid crystal demonstrates the property of a light guide and shows the laser oscillation of the WGM (Figures 6 and 7). Thus, this fibre is expected to be an optical device (an optical fibre or optical resonator) using soft materials.
Recently, Peddireddy et al. [44] fabricated a fibre in a system of 8CB and two types of surfactants (CTAB and the non-ionic surfactant monoolein (1-oleoyl-racglycerol)). In this system, the number of fibres which grew from one liquid crystal droplet is determined by the diameter of the smectic droplet, observing droplets with one to four fibres ( Figure 8) and the fibres made of smectic C liquid crystals had spiral structure. Gibaud et al. [45] demonstrated a helical ribbon-like fibre organised by a virus. This virus can be referred to as a lyotropic liquid crystal because it shows an aligned structure with an increase in density. Wei et al. [46] fabricated a droplet of a polydispersed nematic liquid crystal oligomer (NLCO) and observed the shape change of this droplet into a fibrous network. The theoretical model showed the experimental results, that is, the shape changes from a droplet to a fibrous network structure, caused by the change in the elastic energy and the surface energy of NLCO, attributed to the dispersity of the  oligomer chain length, temperature, and surfactant concentration. They succeeded in stabilising a fibrous network structure via photopolymerisation.

Theoretical discussions on the properties of fibres
Studies highlighting the growth of fibres organised during phase separation have discussed the stability of fibre structure in terms of surface tension and elasticity [25,28]. Other studies have investigated the morphology which could be observed in the phase transition [31,47,48].
E and Palffy-Muhoray [23] were focused on following three interesting properties of fibres in the phase transition; 'the thickness of a fibre is approximately constant', 'the length of a fibre increases exponentially', and 'thin fibres show buckling instability more easily than thick fibres'. The following three questions were asked: (1) What goes on at the isotropic-smectic A interfacial region and inside the filament? (2) How does the filament move and grow? (3) What is the origin of the buckling instability?
The detailed dynamics of the isotropic-smectic A phase transition were noted to answer these questions. An interface model was developed using the Navier -Stokes equations. The growth rate of the fibre and speed of penetration of molecules are discussed. The buckling instability of fibres organised in phase transition also have been discussed [23] and investigated by researchers using their model [30,49,50].
In contrast, the properties of general fibres which are not restricted to fibres organised in phase separation, have also been studied theoretically. The adsorption of surfactant molecules on the fibre surface, which affects the orientational order of the mesogens and anchoring, was reported by Sumer and Striolo [51]. Capillary instabilities in nematic liquid crystal fibres were reported by Cheong et al., considering the stability of the fibres [52,53].

Conclusions and future considerations
Liquid crystals have been used in displays because changes in the alignment of the liquid crystal molecules easily control the anisotropy of refractive index. However, micrometre-sized liquid crystal self-assembly demonstrates new functions which cannot be observed in bulk. Therefore, micrometre-sized liquid crystal self-assembly is expected to be applicable in optical devices, except for displays. As previously shown, liquid crystal fibre demonstrated light transfer and WGM [43]. These properties can apply fibrous selfassembly to optical fibres or liquid crystal lasers. An optical fibre made of liquid crystal would have useful properties which cannot be shown by an optical fibre made of polymer. To use liquid crystal fibres, it is necessary to stabilise them. This is because the liquid crystal fibre appears as a metastable structure. Recently, the stabilisation of fibres was demonstrated by photopolymerisation [46]. One of the most interesting structures is the liquid crystal necklace, which is a complex of nematic droplets and fibres. By maximising the optical characteristics shown by nematic droplets and fibres, optical microresonator can envisaged [22]. Further research on liquid crystal fibres is required for future applications