Structure characterization of free-standing filaments drawn in the liquid crystal state

Abstract

Stable free-standing liquid filaments formed by some layered mesophases of bent-core mesogens are unique structures. Some of their physical properties have been analyzed in recent studies, but their microscopic structure and conditions for stability have still been unclear. We explore details of filament shapes and surface profiles of filaments drawn in liquid crystal phases of bent-core mesogens by AFM and SEM measurements, and we present a microscopic structure model. Conclusions on the stabilizing mechanisms are drawn. Qualitative differences in mechanical properties are found for different mesophases, even though the macroscopic appearance of the filaments is very similar.

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I. Introduction

Liquid crystalline phases of bent-core molecules have attracted considerable interest during recent years, in particular due to the unusual symmetry properties of the molecular arrangement, exotic optical textures, and in general due to their still insufficiently characterized phase structures. At least seven different mesophases B₁ to B₇ and several subphases of bent-core mesogens can be distinguished.¹ It is well known that a number of liquid crystal smectic phases can form free-standing planar films. Few phases of bent-core mesogens, however, are known to form freely suspended filaments instead, for example when material is pulled with a needle at a slow speed from the bulk phase. The filaments retain a uniform diameter during the pulling process; new material is constantly supplied from the meniscus. The first filament formation in banana phases has been reported for the B₇ phase by Link et al.² It has been shown later that B₂ (SmCP) materials are also able to form filaments.³ Another phase of bent-core molecules that was reported to form filaments is B₅.⁴

The formation of stable free-standing liquid filaments is a fascinating and most challenging phenomenon found in complex liquids. It should be noted that this feature is in clear contrast to the behavior of ordinary liquids. In such liquids, a cylindrical bridge remains stable against radial fluctuations only as long as its length to diameter ratio (slenderness ratio) is less than π.⁵ Filaments in non-Newtonian liquids can be stabilized by the pulling process, due to strain hardening. It has been observed in nature and also in technological processes that filaments with anisotropic structure are less susceptible to breakup due to Rayleigh-plateau instability than isotropic fluids.⁶ In our material, the dynamic properties are not essential for the filament stability. However, it seems clear that the smectic layer structure is one of the preconditions for the filament stability. The achievable slenderness ratio of free-standing filaments formed by mesophases of bent core molecules exceeds 1000. But still, it is not clear why only certain phases form free-standing filaments while other phases with smectic layers do not form similar fibers. Filament formation is also observed in ordinary smectic A phases embedded in a liquid environment.⁷ However there is no report of filaments formed by the classical smectic A or C phases in air.

In one of the very first studies about free-standing filaments of bent-core mesogens, Jákli et al. reported that sometimes the filaments are composed of bundles of twisted coiling strings. Dust particles stuck on the filament surface rotate during the change of the filament length and their direction of rotation is opposite for increasing and decreasing filament length.³ The following work of Eremin et al.⁸ confirmed the idea of the existence of bundles of fibrils by AFM imaging, with the difference that the fibrils did not appear twisted in these experiments. Optical images of the filaments showed axial stripes of the order of micrometres; their detailed appearance is wavelength dependent in transmission. The free-standing filaments have this features in common with the SmA filaments in alcohol.⁹ A typical filament segment is shown in Fig. 1. In transmission, parallel stripes along the filament axis of the order of 1 to 2 μm are resolved. Their dependence upon the illumination wavelength suggests influences of optical diffraction. In Fig. 1, one notices that the stripe texture follow, to some extent, the outer filament shape, pointing at diffraction effects, too. This is particularly evident near the filament thickness step. Thus, optical analysis seems inappropriate for a thorough microscopic analysis of the filament shapes. On the other hand, we will show later that irrespective of the optical artifacts, the texture reflects a structured surface of the filament.

Fig. 1 Transmission image of a filament detail illuminated with monochromatic light (589 nm). Two segments with diameters of 11.8 and 13.2 μm are visible. Usually, the filament diameter is homogeneous, in some special cases as shown in the picture one can prepare filaments with sections of different diameters.

The internal layer arrangement in the filaments has been probed by X-ray measurements earlier. X-ray images in one of the phases showed two sharp layer reflexes with the scattering vector perpendicular to the filament axis,⁸ no further reflexes were present. The smectic layers are wrapped cylindrically around one or more axial cores.

The filament appearance and stability depend very much on the phases and materials. B₇ and SmX† studies pointed out that filaments in these phases are stable and have an unlimited lifetime, with the difference that B₇ filaments are in general thinner (diameters smaller than 30 μm) than SmX filaments (up to 100 μm). In SmCP phases, filaments broke after few minutes or hours depending on what substances were used.⁸

Other studies of bent-core filaments showed that the filaments respond to an electric field with a lateral deflection.^3,10 The different mechanical behavior in both phases becomes obviously when an electric field applied perpendicular to the filament axis is switched off.¹⁰ While in some phases, filaments return to their straight equilibrium position with a damped oscillation, in other phases filaments straighten with a fast non-exponential relaxation. This is probably due to an in-plane structural order of B₇, leading to strong internal dissipation. One of the still open questions of the electro-mechanical experiments is the correct quantitative determination of the filament tension, which should essentially depend on the filament geometry. In the model presented in ref. 10 a simple cylindrical filament shape was assumed to relate this tension to the filament diameter and the surface tension of the compound.

In this paper, we present a detailed investigation of the filament shape and present a comparison between filaments in different phases. Optical methods, atomic force microscopy, and scanning electron microscopy are employed.

Before details of the experiments are introduced, a few remarks are necessary on the structure and nomenclature of the phases investigated (see Fig. 2). For both materials, the exact structures of the investigated mesophases (except SmCP) are not fully clear. In particular, for the high temperature phase of substance 1, assignments to B₇³ and SmCG¹¹ had been suggested. In earlier work, we have provisionally used the notation SmX.^4,8

Fig. 2 Phase transition and structures of the studied bent-core molecules.

In general, the structure of B₇ is only partially understood, although much progress has been achieved in the past few years. The microscopic structure is obviously not identical for all mesophases that are commonly subsumed under the nomenclature B₇. Rather, this notation refers to a class of mesophases, characterized by texture: in the melt, remarkable screw and wire structures, “banana leaf” and ribbon structures are observed. Free-standing films drawn in this phase often spontaneously decompose into filaments, and some textures are reminiscent of columnar mesophases.^11–17

Conclusions on the actual phase structure of the materials in Fig. 2 can be drawn from comparison with similar mesogens described in literature. Our substance 2 is a homologue of the compound labeled W1044 (alkyloxy chain length 8) in ref. 15, and for the latter, the structure of a layer interdigitated polar smectic phase has been proposed. This suggests that the mesophase of compound 2, denoted here as B₇, has a similar structure as described in ref. 15 for its homologue (see Fig. 1H in ref. 15). Fig. 3a sketches the proposed interdigitation structure of the mesophase of substance 2. X-ray bulk measurements of substance 2 give a complex multi-reflex spectrum.¹³ All mechanical properties measured in filaments of substance 2 are consistent with this structure interpretation. Interdigitation of the layers is a strong inhibitor for in-plane dynamic processes, particularly for shear flow normal to the interdigitation steps. One may expect that such a material is very stiff. If the disclinations of the layers follow the filament axis, it is evident that the pulling of filaments is possible with low efforts, while B₇ filaments behave very brittle at lateral deflections. Experiments described below confirm this assumption.

Fig. 3 (a) Sketch of the interdigitated layer structure of the mesophase of compound 2, based on the model proposed in ref. 15. (b) Sketch of the undulated layer structure of the PM-SmCP phase.^15,16 The molecular orientations are omitted in the pictures. Arrows indicate the barrier for the shear flow in (a), the unhinderd flow in (b).

The high temperature mesophase of compound 1 shows a much simpler X-ray spectrum, in ordered samples (filaments) only the first order layer reflex has been resolved.^4,8 The high temperature mesophase in a homologue of this material, labeled H87 (alkyloxy chain length 12) in ref. 15, has been interpreted as a tilted polar smectic phase with undulated layer structure. This phase is characterized by a modulated spontaneous polarization vector coupled to the layer undulations. We will therefore adopt the designation polarization modulated SmCP (PM-SmCP) in the following (see e.g.ref. 16). One of the striking differences in comparison with the interdigitated structure of substance 2 is the continuous layer structure, as sketched in Fig. 3b. This allows a certain liquid-like intralayer dynamics and may explain the differences in the mechanical behaviour of the filaments in the two phases.

In high-energy X-ray spectra of the PM-SmCP phase, multiple reflexes have been found, that correspond to the modulation of the smectic layer structure.¹⁶ In the bulk X-ray measurements of unoriented samples, the resolution is not sufficient to resolve these reflexes. The reason that our X-ray measurements performed on filaments of substance 1 did not show the off-axis peaks originating from layer undulations could be a resolution problem. Another interpretation is that in the filament geometry, not only the layer structure but also the wave vector of the undulations is oriented. It is natural to assume that these undulations are tangential on the filament column surface, as a consequence of the curvature of the layers in the columns. In that case, they do not appear in X-ray spectra in the geometry chosen in ref. 8.

II. Samples and experimental methods

The molecular structure and phase sequences of the mesogenic materials used in our experiments are presented in Fig. 2.

The filament-drawing device used in our experiments, depicted in Fig. 4, consists of a copper heating box for temperature control and protection against flow. The heating box has two quartz windows for optical observation and it includes two Teflon parts (T1, T2), which are moved by stepper motors. One of them controls the lateral displacement of support T1 and needle D1; the other one rotates T2. The filament is spanned between two glass needles (D1, D2). The position of T1 controls the distance between the needle tips and thus the length of the filament. T2 is rotatable and provides the option to turn the filament around its axis when T2 is coupled to T1 by the rigid metal connectors E. When the two metal rods E are removed, one can twist the filament by rotating only D2 at fixed needle D1. There is also an option to rotate the entire heating stage in the xz-plane by 90° so the filaments can be draw either horizontally or vertically.

Fig. 4 Experimental setup. The size of the box is approximately 8 cm × 8 cm × 8 cm.

The temperature is stabilized with a controller which has an accuracy of 0.1 K. We illuminate the filaments with parallel white or monochromatic unpolarized light. The observation axis (y) is perpendicular to the filament axis. Optical transmission images are recorded with a Nikon Coolpix 990 digital photo camera mounted on a Questar QM 100 long-range microscope.

Because the phases where the filaments can be drawn exist only far above room temperature, the methods of investigation, besides optical inspection, are limited. Atomic force microscopy (AFM) and scanning electron microscopy (SEM) have not been available at these temperatures. Therefore, after an optical analysis with the long-range microscope, the filaments have been cooled down into the crystalline phase where they become solid rods. That requires that the geometrical filament structure is not markedly changed by the phase transition. It turns out that the cooling can be performed slowly (few seconds to minutes) if the transition from the mesophases with the stable filament to the crystalline phase is direct. If there is an intermediate mesophase where the filament melts,⁸ the samples have to be quenched by evaporating liquid nitrogen into the heating box.

The surfaces of the solid rods obtained by these methods were imaged by an Oxford LEO 1550VP Field Emission Scanning Electron Microscope using the backscattering method.¹⁸ Using this technique, resolutions of the order of 5 nm are possible. The profile of the filament surface was also measured with a Digital Instruments NanoScope IIIa-Phase Atomic Force Microscope in the tapping mode.

III. Surface and internal structure

First, we discuss filaments drawn in the B₇ phase. In the compound investigated, B₇ crystallizes without other mesophases below. The overall optical filament appearance, in particular the stripe pattern, is preserved during cooling into the crystalline state (Fig. 5). This allows us to assume that the macroscopic shape of the filaments is preserved during the transition and we can infer from the crystalline measurements on the B₇ geometrical filament structure.

Fig. 5 (a) Stripe texture of a B7 filament of substance 2; (b) Tip of one part of the crystallized filament. The filament was drawn at 120 °C; the crystalline image has been taken at room temperature. Both pictures have been recorded at white light with the long-range microscope.

A typical B₇ filament of substance 2, showing the stripe texture, is depicted in Fig. 5a. Rotation of the filament reveals that its outer shape is, apart from surface corrugation, roughly that of a cylinder. During the transition into the crystalline phase, this particular filament broke and bent. One tip of the remaining filament is shown in Fig. 5b. Along the axis, the stripe texture is preserved.

The tip of the crystallized filament was imaged using SEM. As seen in Fig. 6, the surface of the crystallized B₇ filament appears corrugated. The structure factor (average distance of the ripples) of the corrugation revealed by SEM is comparable to the wavelength of the stripes observed optically. While the SEM gives a quite realistic picture of the surface structure, the optical image is blurred by diffraction artifacts.

Fig. 6 (a) The tip of one part of the crystallized filament shown in Fig. 5, observed by backscattered scanning electron microscopy (SEM); (b) The foot of the same part of the crystallized filament. Note the absence of a true meniscus at the base of the filament. Instead, the bulk surface seems to exhibit spaghetti-like structures growing out of the foot of the filament.

This result is confirmed with AFM measurements made on another crystallized filament with an exceptionally large diameter of 50 μm (Fig. 7a). Since the AFM cantilever cannot monitor steep slopes of the surface in the micrometre range, the surface profile is somewhat smoothed between the fibrils. The surface undulations are parallel to the fiber axis. Looking at these SEM and AFM pictures one can state that the typical filament is indeed composed of bundles of fibrils with diameters up to 2 μm. A proposed model based on the experimental surface data is drawn in Fig. 7b.

Fig. 7 (a) Height profile obtained by AFM in tapping mode of a 8 μm × 8 μm area of a typical crystallized B₇ filament of substance 2 with 50 μm diameter. The filament has been plased on a glass substrate with its axis along y; (b) The proposed model for the internal filament structure derived from the surface analysis.

The PM-SmCP filaments present a similar stripe texture like B₇ filaments. If the filament as a whole is rotated around its axis, the apparent diameter of the filament remains constant within the limits of optical resolution (∼0.1 μm). That demonstrates the global cylindrical shape of the filament as in the case of B₇. The stripe texture is shifting with the rotation (Fig. 8). This is one more evidence that the stripes primarily are not due to diffraction but reflect some surface roughness in the optical wavelength range as in B₇.

Fig. 8 Pictures of one segment of a PM-SmCP filament of substance 1 at 155 °C taken in white light in transmission with the long-range microscope. Image (b) is obtained after rotating the filament around its axis by 42°. The scale bars are 50 μm. The filament is cylindrical in good approximation.

An interesting phenomenon is observed during the transition from the PM-SmCP into the crystalline phase in substance 1, which is not a direct one but an intermediate SmCP phase is passed. In this case the filament slowly cooled from 155 °C starts to melt⁸ and the cylindrical shape is lost. The “melting” process is accompanied by a flow of material along the axis and disappearance of individual fibrils in the bundles. The filament becomes thinner and excess material flows along the axis into the bulk. The direction of flow appears to be chosen at random; it is not essentially influenced by gravitation (the material may also flow upward in vertical filaments).

During the transition into the crystalline phase, at slow cooling rate, sometimes the filament collapses, sometimes some part of the filament remains and the stripe texture (Fig. 9a) transforms into an “old-tree” texture (Fig. 9b).

Fig. 9 Transmission images of details of a PM-SmCP filament of substance 1. (a) in PM-SmCP at 155 °C and (b) after slow cooling into the crystalline phase at room temperature.

The filament shown in Fig. 10 has been broken after freezing, leaving a quite smooth edge (left side of Fig. 10a). Upon the melting of individual fibers, the overall cylindrical shape of the filament was lost, and the cross section has become irregular. Even on the molten rest of the crystallized PM-SmCP filament, remains of cylindrical fibrils are still visible at the exterior, with diameters of the order of a few micrometres (Fig. 10b, arrows).

Fig. 10 Crystallized PM-SmCP filament of substance 1 after slow cooling, monitored by backscattered SEM: (a) lateral surface of a filament part; (b) site of fracture magnified; the arrows point at the fibril structure.

The melting of individual fibers occurs within few seconds. In order to access the actual structure of the filament, it is necessary to quench it into the crystal state. Fast cooling of PM-SmCP filaments was possible using liquid nitrogen. When some liquid nitrogen is poured into the heating box, the temperature drops within few milliseconds. The transition in the crystalline phase occurs in this case sufficiently fast and the filament preserves at least partially the original optical stripe texture, alternating with the molten “old-tree” texture (Fig. 11a). At rapid cooling, the filament diameter and approximate cylinder shape is preserved.

Fig. 11 PM-SmCP filament of substance 1 quenched by injecting liquid nitrogen into the preparation box: (a) optical microscope image after quenching; (b) backscattered SEM image of the region where the striped texture is still preserved. The dashed line emphasizes the suggested surface profile.

Fig. 11b shows that the stripes represent surface corrugation parallel to the cylinder axis similar to the observations in B₇. Therefore, the model of layer arrangement proposed for B₇ filaments seems to be appropriate here as well.

IV. Mechanical deformation

The following experiment was designed to probe the mechanical response to a twist of the filament. Since these structures behave liquid like when they are stretched or pressed, it would be natural to assume that mechanically induced twist relaxes as quickly as lateral strain.

Removing the metal rods E in the experimental setup (Fig. 4) the filaments pulled between needles D1 and D2 can be twisted. We rotate D2 at fixed needle D1.

A typical PM-SmCP twisted filament is seen in Fig. 12. The fibrils in the bundles do not reorganize after twisting. The stripe texture reveals the twist of the individual fibrils.

Fig. 12 Pictures of a segment of a PM-SmCP filament of substance 1 (one quarter of its length) at 155 °C taken with white light in transmission with the long-range microscope. (a) Image of the freshly drawn undistorted filament. (b) Image obtained after twisting the complete filament by π/6. (c) Image obtained after twisting by 4π. The twist distributes homogeneously along the filament axis so that approximately half a turn is seen in the image.

Most of the individual fibrils seem to survive the twist, even a large twist of several full turns per millimetre. In addition to the winding of the fibrils about each other, the overall cylindrical filament shape flattens to a more band-like cross section.

The twist seems to be a reversible process in the case of PM-SmCP filaments. The untwisting of the filament leads to the reconstruction of the original filament shape. At the initial position, the filament looks like before twisting; the fibrils of the bundle are straight and parallel to each other again. More remarkably is the observation that the mechanically induced twist does not relax noticeably, even after hours, if the filament is not twisted back manually. The filament shown in Fig. 13 retains an 8π total twist even after 24 h. This indicates that, while the individual fibrils behave liquid-like with respect to length changes, there is no reorganization of these fibrils in the bundle without external forcing.

Fig. 13 Picture of a twisted PM-SmCP filament of substance 1 with 1.1 mm length and 47 μm diameter, taken with white light in transmission with the long-range microscope (a) immediately after twisting and (b) after 24 h. The detailed fibril arrangement is similar to that of Fig. 12c. There is practically no relaxation of the twist.

B₇ filaments are much more brittle than PM-SmCP filaments. They collapse at any attempt to twist them. This seems to be related with the existence of the interdigitated layer structure that is absent in PM-SmCP. Such a structure obviously makes the micro-fibers much more susceptible to rupture when they are distorted.

V. Discussion and summary

A first indication of the filament bundle structure in all mesophases that has been discussed earlier is their optical image. The optical observations of filaments in transmission have not given convincing evidence of the overall cylindrical shape of the filaments, although the minimization of surface energy suggests such a structure. In this work, we have improved the observation technique so that filaments could be monitored from all sides. During rotation of the filaments, the stripe texture is shifting. This behaviour evidences a true surface roughness, and possibly an internal bundle structure of the filaments, in all the observed mesophases.

By means of AFM and SEM measurements, we have demonstrated that filaments in two phases are actually not simple cylinders but do indeed represent composite fiber bundles. The same is obviously the case for the SmCP and B₅ filaments, judging from their optical appearance, even though there are no available AFM and SEM data.

SEM images of solidified filaments give a clear qualitative picture of the surface structure, even if one acknowledges that structural details may be influenced by the crystallization process. The SEM images reveal the global filament structure. In addition, details of the surface profile can be quantitatively probed by AFM. Although the AFM measurements are limited to small surface regions of filaments with large radii (small overall curvature), they supplement and fully confirm the SEM data.

A model for smectic A filaments growing in an isotropic phase was given by Todorokihara and Naito.⁹ The smectic layers, in this case, are wrapped around one core, and the filament should contain a disclination line along its axis. From optical simulations, the authors conclude that their filaments are actually tubes with an isotropic core of about 500 nm. Details of the computation are not given, but we conjecture that the optical behavior has been calculated by ray-optical techniques, which may be inappropriate for the correct description of submicrometre patterns. The stripe texture found by the authors is formally very similar to the optical appearance of our filaments.

We note that filaments immersed in the liquid phase have a much lower interface tension than our filaments in the gas phase. Therefore, the filaments described in this article are always straight, while the SmA structures in an isotropic solvent, as well as filaments of B₇ in the isotropic melt, may adopt screw like or other periodically deformed shapes.^15,17

If the free-standing filaments are represent of bundles, this suggests that during the filament formation, the growth of individual fibrils in diameter is limited. Such a limiting factor in the radial growth of fibrils could be the electrostatic self energy of the polar compound. Similar situations are encountered in systems with competing bulk and surface energy terms,¹⁹ for example, in circular domains of Langmuir films.^20,21 The polar properties of monolayers influence both the size distribution as well as the shapes of domains in Langmuir monolayers in the coexistence region of condensed and gas phases. In these systems, an equilibrium radius of circular domains is adopted as a consequence of the competition between the electrostatic self energy of the domains and the interface tension at the domain border.²⁰ If a similar mechanism is active here, it may be responsible for the limited growth of fibrils with cylindrical layer arrangement. The energy necessary to built up additional cylindrical layers around the fibril mantle increases with the radius of the fibril. At a certain diameter, it is favorable to grow a new fibril even on the cost of a new core defect. Since we have no data of the magnitude and even the direction of a spontaneous polarization in the investigated compounds, a speculation about details of these electric interaction forces seems inappropriate at the moment.

Interestingly, the response of the filaments to twist is qualitatively different in B₇ and PM-SmCP. The robustness of the PM-SmCP filaments compared with the B₇ filaments comes out there. This is a strong indication of the differences in the layer structures of both phases. It is astonishing that even though the PM-SmCP filaments have liquid-like behavior during the pulling process, a twisted filament will not relax after hours while a deformation along its axis will be restored in few minutes or seconds.

In particular, the option to twist individual fibrils and to preserve their state of twist even in the liquid crystal phase may be an essential feature when one thinks of application of such microstructures, e.g. after polymerization.

Acknowledgements

This study was supported by the DFG with grant STA 425/15 and by the European Regional Development Fund (ERDF). The authors are thankful to Lama Naji and Ines Grodrian for the AFM measurements.

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Footnote

† See following section for assignment of SmX.

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