1.1 Lyotropic Chromonic Liquid Crystals

Lyotropic liquid crystals (LCs) represent an extended family of dispersed systems that possesses a long-range orientational order (the prefix lyo- means “to loosen, dissolve” in Greek) [1, 2]. The basic building units of such systems are usually super-molecular assemblies of high aspect ratio dispersed in solvent (usually water). Examples include: amphiphiles that form wormlike micelles, double-strain DNA (ds-DNA) molecules, tobacco mosaic viruses (TMV) representing rigid protein polymer rods, and cylindrical stacks of disk-like molecules in water solution. Molecules in the last category are usually drugs or dyes molecules that have a polyaromatic center and ionizable groups at the periphery. The liquid crystal phases formed by such molecules in water solution are called lyotropic chromonic liquid crystals, or LCLCs [3,4,5,6,7]. Classical examples include antiasthma drug disodium cromoglycate (DSCG), food and textile dyes Sunset Yellow (SSY), Allura red, Tartrazine, Blue 27, Violet 20, Fig. 1.1, and many more. An extended family of chromonics also includes ds-DNA assemblies [4,5,6,7,, 8] which share many structural features with the classical LCLCs such as SSY and DSCG, including: repeating distance of molecules along the aggregate’s axis being 0.34 nm, diameter of aggregates being 1–2 nm, persistence length being on the order of tens of nanometers, and so on.

Fig. 1.1
figure 1

Molecular structures of some lyotropic chromonic liquid crystal materials

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In lyotropic LC, the underlying mechanism for a dispersion of elongated objects to achieve an orientationally ordered state is very different from that of thermotropic LCs. In thermotropic LCs, the basic building units are molecules of covalently fixed shape. The ordered phases (nematic, smectic, etc.) occur at a lower temperature when the molecular interactions favoring parallel arrangement of neighboring molecules win over entropy. In lyotropic LCs, the orientational order occurs when the building units sacrifice orientational freedom and align with neighbors to gain translational entropy. For example, in an Onsager-type system [9] composed of identical rigid rods, the isotropic-to-nematic phase transition occurs only if the volume fraction of the rods in the system is larger than a threshold value, \(\phi > \phi_{\text{nem}} = 4.5D/L\), where \(L\) and \(D\) are the length and diameter of the rods, respectively. Temperature does not play a role here, leaving the volume fraction \(\phi\), or equivalently, the mass concentration \(c\), being the only tuning parameter. In comparison, the phase behavior of lyotropic chromonic liquid crystals can be controlled by both concentration and temperature, due to the very different underlying mechanism of how the basic building unites of the LCLCs, the cylindrical aggregates, are formed. When LCLC molecules are dissolved in water, the hydrophobic aromatic centers stack on top of each other. At the same time, positive ions at the periphery of the molecules are disassociated, leaving behind negative charged aggregates, with a maximum charge density \(\tau^{\hbox{max} } e = 6e / {\text{nm}}\), Fig. 1.2. The effective interaction, counting both the attraction of the aromatic centers (\(E_{0}\)) and electrostatic repulsions of the periphery (\(E_{e}\)) is characterized by the so-called scission energy \(E = E_{0} - E_{e} \approx 10k_{B} T\), an energy needed to break one aggregate into two. The equilibrium average length of chromonic aggregates, as described more in detail later in this thesis, is determined by \(E,\) \(\bar{L} \propto \exp \left({\frac{E}{{2k_{B} T}}} \right)\) [3, 4, 10, 11]. At lower temperature, the length of the aggregates increases [12], thus an ordered phase is preferred over isotropic phase. Moreover, keeping \(c\) and \(T\) the same, but increasing the ionic concentration in the system screens the repulsion between molecules in the aggregates, decreases \(E_{e}\), thus increases \(\bar{L}\), promoting a more ordered phase. On the contrary, adding NaOH enhances the disassociation of sodium ions, increases \(E_{e}\), thus decreases \(\bar{L}\), destabilizes the ordered phase. Phase dependence of LCLCs on \(c\), \(T\), \(c_{ion}\), pH value, presence of crowding agents, etc. are experimentally studied in Ref. [12, 13], and also in Chaps. 2–4 in this thesis.

Fig. 1.2
figure 2

Molecular structure and schematic of a SSY-water LCLC. a Molecular structure and schematic of the disassociation of sodium ions from a single molecule in water. b Schematic of SSY assembly in water (represented by the blue background) to form nematic LCLC; aromatic centers stack on top of each other while the sodium ions are disassociated, leaving the aggregates negatively charged

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Another important difference between LCLCs and the Onsager-type lyotropic LCs composed of rigid rods (such as water suspension of TMV [14]) is that LCLC aggregates are flexible. The flexibility of LCLC aggregates is characterized by the persistence length \(\lambda_{p}\), a length over which unit vectors tangential to the aggregates lose correlation. Since \(E\) is on the order of \(10k_{B} T\), the aggregates may be bent easily by thermal fluctuations. In a similar system composed of ds-DNA molecules face-to-face assembled with a scission energy \(E \approx (4 - 8)k_{B} T\), the persistence length is estimated to be 50 nm [8]. The flexibility of the aggregates can be influenced by ion concentration which controls the Debye screening length \(\lambda_{D}\). Since the bend deformation brings negative surface charges closer and causes stronger electrostatic repulsion, a decreased \(\lambda_{D}\) at higher ionic concentration relieves the repulsion, and makes the aggregates more flexible. Similar effects of ionic contents on flexibility of biomolecules are of prime importance in biological processes such as DNA wrapping around nucleosomes, packing inside bacteriophage capsids, biding to proteins and so on [15, 16].

Despite the growing interests of the LCLCs, very little is known about their elastic and viscous properties. Knowledge of viscoelastic constants, such as the Frank elastic moduli in the nematic phase and the viscosities associated with different flow geometries, is of essential importance to understand both static and dynamic phenomena such as template assisted alignments [17,18,19,20], behavior of LCLCs in samples with various thickness [21,22,23], LCLC-guided orientation of nanoparticles [24], shape of LCLC tactoids [25, 26], effect of spontaneously broken chiral symmetry [27, 28], and flow behavior of LCLC [29]. LCLCs also provide a model system to study how these macroscopic viscoelastic properties are connected with microscopic features such as the contour length \(L\) and the persistence length \(\lambda_{p}\), which can help our understanding of the biological systems such as DNA assemblies, where very often direct measurements of microscopic properties are not easily available.

1.2 Active Colloids and Collective Behavior

If liquid crystals can be described as “passive” matters, there is another kind of systems, known as “active matters”, composed of self-driven individuals that use stored or locally harvested energy to drive systematic movement [30]. A distinctive feature of active matter, as compared to non-equilibrium state of a passive system (e.g. LC director reorientation driven by external field), is that the energy input that drives the system out of equilibrium is local, often at the level of each particles, rather than at the boundaries of the system. A particular interesting subset of active matter is active colloids. Colloids are suspensions of particles whose sizes range from 10 nm to 100 μm, usually in fluid or gas. They are prevalent in our daily life (e.g., milk, ink, blood) and play critical roles in many industries (e.g., food, printing, medicine, nanotechnology) [31]. Interactions between colloids are governed by various forces, such as steric repulsion, electrostatic and magnetic forces, van der Waals forces, entropic forces, hydrodynamic forces, etc. [32]. Colloidal science has been a traditionally important field of research. A large body of work has been dedicated to the equilibrium self-assembled colloidal structures [33, 34], which have important potential in applications such as photonic band gap (PBG) structures [35,36,37]. Bringing activity into colloidal particles gives rises to new fascinating phenomena, including: activity induced crystallization at low density [38], self-organization of microtubules driven by molecular motor [39], spontaneous and constant creation, annihilation and self-propulsion of topological defects [40, 41], reduction of viscosity in active particle suspension [42, 43] and so on. Self-assembled active colloids also open new doors to produce materials with functions not available in equilibrium conditions, such as self-healing [44, 45], self-propulsion [46,47,48], formation of unusual shapes (reconfigurable snakes, asters, etc.) and transport of cargo [48, 49].

The simplest way to create an active colloid is to suspend microorganisms in water; examples include bacteria [50] such as Escherichia coli (E-coli) [51] and Bacillus subtilis, green algae such as Chlamydomonas reinhardtii [52] and sperm cells [53]. These self-motile microorganisms are also called microswimmers. Depending on the direction of flow field along the axis of swimming, they are classified as “puller” or “pusher” types [30, 54]. For example, bacteria such as E-coli and Bacillus subtilis are pushers, since they pump fluid away from them along the direction of propulsion, by rotating helicoidal flagella, Fig. 1.3a. Chlamydomonas reinhardtii is a puller, as it pulls fluid towards its body along the direction of motion, by stoking two arm-like flagella, Fig. 1.3b. The pair of forces that drive the fluid motion are pointing inward (puller) or outward (pusher), corresponding to a positive or negative force dipole on the swimmer body, respectively [30]. Since the self-motile swimmers are not driven by an external field (electric, magnetic, flow field, etc.), the net force is zero. Inspired by the biological microswimmers, researchers developed synthetic microswimmers in a variety of forms [55,56,57], including bimetallic rods that use chemical reaction with hydrogen peroxide [58], water droplets that use Marangoni effect to drive themselves in oil [59], metallic-dielectric Janus spherical particles propelled by an electric field [60], high-speed bilayer microtubes [61], magnetic field [48, 49] or light driven [38] microspheres, silicon dioxide swimmers with nanostructured helical shape [62], and so on.

Fig. 1.3
figure 3

“Pusher” versus “puller” swimmers. a shows a pusher swimmer, best represented by rod-shaped bacteria such as E-coli or Bacillus subtilis [51]. The forces (shown with red arrows) that drive the flow are pointing outwards along the swimming direction \({\mathbf{v}}\). b shows a puller swimmer, best represented by green algae Chlamydomonas reinhardtii [52]. Black arrows on bacteria bodies show direction of motion of bacteria parts. Grey curved arrows show schematic flow field

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In this thesis, we deal with a typical “pusher” microswimmer, bacteria Bacillus subtilis. Bacillus subtilis is a rod-shaped bacterium 5–7 μm in body length and 0.7 μm in diameters. It has about 20 pieces of helicoidal 10-μm long flagella filaments attached to the bacterial body. In isotropic media, the bacteria swim in the so called “run-and-tumble” fashion [63, 64]. During an approximately 1 s “run” phase, the flagella form a bundle at one end of the bacterial body and rotate counter-clock wise (ccw, viewing behind a swimming-away bacterium along the body axis), thus powering unidirectional “head-forward” motion. In the following tumble phase of about 0.1 s, one or a few of the flagella reverse their rotation to clock wise (cw) and leave the bundle, causing bacterium to “tumble” and change its orientation randomly. Then flagella rotate ccw again, forming the bundle and power the forward motion in a new direction. The motility of this aerobic bacterium can be controlled by the amount of dissolved oxygen.

One spectacular phenomenon observed in an isotropic Bacillus subtilis suspension is the spontaneous collective motion [54, 64,65,66]: at high enough concentration (~2% by volume), bacteria swarm together with their velocity field correlated over ~10 times body length and with a up to 4 fold increase in speed as compared to individual bacterium at a dilute concentration [67, 68]. In fact, collective motion can be found in many active matter systems [69,70,71,72] of different sizes, ranging from microscopic organisms such as bacteria swarms, to macroscopic creatures such as fish schools, birds flocks and herds of mammals, Fig. 1.4. In the collective motion mode, bacteria suspension exhibit unusual properties such as greatly reduced viscosity [42, 52] and increased diffusivity [73, 74]. A very interesting phenomenon is the unidirectional rotation of asymmetric millimeter size gears [75, 76] driven by the chaotic motion of swimming bacteria, Fig. 1.4a. By contrast, in an equilibrium system of suspension of passive particles, this rotation cannot be observed since it is against the second law of thermodynamics. However, in condensed bacterial suspension, even though the motion of individual particles is still random and looks very much like Brownian motion of passive particles, one can still harvest energy, a signature that the system is not in the equilibrium states.

Fig. 1.4
figure 4

Collective motion at different scales and in different media. a High density suspension of Bacillus subtilis powers unidirectional rotation of asymmetric gears (with reprint permission of Fig. 2 of “Swimming bacteria power microscopic gears.” Proceedings of the National Academy of Sciences 107(3):969–974 by Sokolov A., Apodaca M. M, Grzybowski B. A., & Aranson I. S. (2010)). b School of fish. (http://www.coralreefphotos.com/big-school-of-fish-schooling-fish-school-of-bogas/) c Flock of birds. (http://www.howitworksdaily.com/why-do-birds-flock-together/) d Herd of migration animals in South Sudan, Africa. (http://www.reuters.com/article/us-sudan-wildlife-idUSN1225815120070612)

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Collective motion in active matter systems results in ordered states with polar [77, 78] or nematic [79,80,81,82] symmetry. For example, in a system composed of microtubules, crowding agents and molecular motors, Dogic and his collaborators [40, 41] demonstrate that at high enough concentration, microtubules absorbed on flat oil-water interface undergo a transition to the nematic phase. When the activity is turned on with adenosine triphosphate (ATP) supply, one observes constant creation and annihilation of topological defects of charge 1/2 and −1/2, distinctive from the uniform alignment of director observed in the equilibrium nematic phase. However, in this system, the nematic order and activity are both tightly connected to the parallel aligned microtubules. As a result, one sees only one steady state, i.e., active nematic with topological defects. In this thesis, we take advantage of the non-toxic lyotropic chromonic liquid crystal disodium cromoglycate [83] and mix in active particles, the bacteria Bacillus subtilis. By varying the bacterial concentration and oxygen supply, we independently (and continuously) change the activity of the system from zero to high values. As a result, our system exhibits three major steady states: (i) equilibrium uniform nematic embedding small amount of active particles in their inactive form (non-swimming), (ii) active nematic with uniform bend modulation, and (iii) active nematic with topological defects. We also demonstrate that LCLCs have the ability to control the motion of active particles through the spatially varying director field, and to visualize the fluid motion induced by 24 nm thick bacterial flagella. The studies of this system that we call a living liquid crystal are presented in Chap. 5.

1.3 Scope and Objectives of the Dissertation

The scope of this dissertation is two-fold. First, we aim to understand the elastic and viscous properties of LCLCs, and how factors such as temperature, concentration and ionic contents influence them. Second, we study the interaction between self-propelled particles (bacteria Bacillus subtilis) and the long-range nematic order provided by DSCG LCLC. The studies involve various experimental techniques, such as magnetic field induced Frederiks transition, dynamic light scattering (DLS), polarizing optical microscopy, LC-PolScope and video-microscopy.

The objectives of the dissertation are to study experimentally: (i) the temperature and concentration dependence of Frank elastic moduli of Sunset Yellow LCLC, using magnetic Frederiks transition technique; (ii) the ionic-content dependences of elastic moduli and rotation viscosity of Sunset Yellow LCLC, using the same technique; (iii) elasticity, viscosity and orientational fluctuation of DSCG LCLC using dynamic light scattering technique; (iv) the interaction between active self-propelling bacteria and the nematic order in the living liquid crystal.

The dissertation is organized as follows.

Chapter 2 describes the experimental study of Frank elastic constants of SSY LCLC, probed by Frederiks transition in a magnetic field. In this study, we observed unusual anisotropy of elastic properties. Namely, the splay \(K_{1}\) and bend \(K_{3}\) constants are found to be 10 times larger than the twist constant \(K_{2}\). \(K_{1}\) has the strongest temperature dependence among all three. We explain our findings through the idea of semiflexible aggregates, whose length dramatically increases as temperature decreases or concentration increases.

Chapter 3 is an extension of the study in Chap. 2 in two aspects: (1) we aim to understand how ionic content in the system influences the properties of LCLC; (2) we measure rotation viscosity \(\gamma_{1}\) by the relaxation of twist deformation in a magnetic field, in addition to the Frank elastic moduli. Here we fix the concentration of SSY but vary the type and concentration of ionic components and temperature. Using the same magnetic Frederiks transition technique, we find that the ionic content influences the elastic constants in dramatic and versatile ways. For example, the monovalent salt NaCl decreases \(K_{3}\) and \(K_{2}\), but increases \(\gamma_{1}\), while pH agent NaOH decreases all of them.

Chapter 4 deals with LCLC material DSCG. DSCG is not only the earliest and most studied LCLC material, but also a bio-compatible one [83] with optical transparency in visible wavelength, an advantage for optical study and applications [84]. Dynamic light scattering technique allows one to extract both elastic moduli and viscosity coefficients at the same time. The results obtained are rather astonishing. In addition to anisotropy of elastic constants, \(K_{1} \approx K_{3} \approx 10K_{2}\), which is similar to SSY LCLC, the viscosity of bend deformation \(\eta_{bend} \approx \eta_{{_{bend} }}^{5CB}\) can be up to 4 orders of magnitude smaller than \(\eta_{splay}\) and \(\eta_{twist}\). The temperature dependences of \(K_{1}\), \(\eta_{splay}\) and \(\eta_{twist}\) are exponential. Again, we explain our findings through the idea of semi-flexible aggregates whose lengths strongly depend on \(T\). We also find an additional mode in the DLS experiments, which we attribute to the diffusion of stacking faults of the aggregates.

In Chap. 5, we combine two fundamentally different systems, the nematic DSCG LCLC and bacteria Bacillus subtilis, in order to create the living liquid crystal in which the activity and orientational order can be tuned independently. The coupling between the active particles and long-range nematic order results in intriguing dynamic phenomena, including (i) nonlinear trajectories of bacterial motion guided by a non-uniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a non-flowing equilibrium uniform state into a flowing out-of-equilibrium one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence enabled visualization of micro-flow generated by the nanometers thick bacterial flagella.

Chapter 6 summarizes the results in this dissertation.

The following publications cover the topics discussed in the dissertation:

[1]: Shuang Zhou, Yu. A. Nastishin, M.M. Omelchenko, L. Tortora,1 V. G. Nazarenko, O. P. Boiko, T. Ostapenko, T. Hu, C. C. Almasan, S. N. Sprunt, J. T. Gleeson, and O. D. Lavrentovich, “Elasticity of Lyotropic Chromonic Liquid Crystals Probed by Director Reorientation in a Magnetic Field”, Phys. Rev. Lett., 109, 037801 (2012)

[2]: Shuang Zhou, Adam J. Cervenka, and Oleg D. Lavrentovich, “Ionic-content dependence of viscoelasticity of the lyotropic chromonic liquid crystal sunset yellow” Phys. Rev. E, 90, 042505 (2014)

[3]: Shuang Zhou, Krishna Neupane, Yuriy A. Nastishin, Alan R. Baldwin, Sergij V. Shiyanovskii, Oleg D. Lavrentovich and Samuel Sprunt, “Elasticity, viscosity, and orientational fluctuations of a lyotropic chromonic nematic liquid crystal disodium cromoglycate”, Soft Matter, 10, 6571 (2014).

[4]: Shuang Zhou, Andrey Sokolov, Oleg D. Lavrentovich, and Igor S. Aranson, “Living liquid crystals”, Proc. Natl. Acad. Sci. U. S. A., 111, 1265 (2014)

The research also results in the following publication:

[5]: Andrey Sokolov, Shuang Zhou, Oleg D. Lavrentovich, and Igor S. Aranson, “Individual behavior and pairwise interactions between microswimmers in anisotropic liquid”, Phys. Rev. E, 91, 013009 (2015)

and two more publications that are currently being prepared or submitted:

[6]: Shuang Zhou, Andrey Sokolov, Igor Aranson, Oleg D. Lavrentovich, “Controlling dynamic states of active bacterial suspensions through surface alignment of a nematic liquid crystal environment”, submitted

[7]: Shuang Zhou, Sergij V. Shiyanovskii, Heung-Shik Park, Oleg D Lavrentovich, “Fine structure of the topological defect cores studied for disclinations in lyotropic chromonic liquid crystals”, Nat Comm, accepted