Session L44: Focus Session: Nano to Mesoscale Structure in Ordered Soft Matter: Liquid Crystal Phases

Nano to Meso-scale Structure in Liquid Crystals: the Cybotactic Nematic Phase of Bent-core Mesogens

The extent of molecular order and the resulting broken symmetry determine the properties and mesophase type of liquid crystals (LCs). Thermotropic bent-core mesogens (BCMs) represent a new class of LCs exhibiting substantially different physical properties than traditional linear (calamitic) materials. In recent years BCMs have become the focus of intense experimental and theoretical investigation, with several exciting new developments. These include chiral mesophases composed of achiral BCMs, giant flexoelectricity, biaxial nematic ($N)$ order, a ferroelectric response in the $N$ phase, and a large flow birefringence. A key issue that is currently widely debated concerns the actual nature of the $N$ phase of BCMs which gives rise to some of the above mentioned effects and is unambiguously identified by a peculiar low-angle X-ray diffraction pattern (the ``four-spot pattern''). The consensus emerging is that this $N$ phase of BCMs constitutes a new type of mesophase, namely, a cybotactic nematic ($N_{cyb})$ phase unrelated to pretransition cybotaxis, in agreement with experimental [1-3] and theoretical findings [4]. This $N_{cyb}$ phase is composed of nanometer-size clusters of BCMs exhibiting a relatively high degree of internal order---orientational as well as translational order (strata) imposed by close packing the BCM nonlinear shape. This peculiar supramolecular structure of the $N_{cyb}$ mesophase of BCMs---evanescent, biaxial clusters of tilted and stratified nonlinear mesogens percolating the nematic fluid---accounts for their unusual properties, e.g., biaxial order [4], ferroelectric response [1], and extraordinary field-induced effects [5]. In this talk I will give an overview of the most recent developments and the current state of research on this subject. \\[4pt] [1] O. Francescangeli \textit{et al}., Adv. Funct. Mater. \textbf{19},2592 (2009). \\[0pt] [2] O. Francescangeli and E.T. Samulski, Soft Matter \textbf{6}, 2413 (2010) \\[0pt] [3] O. Francescangeli \textit{et al}., Soft Matter \textbf{7}, 895 (2011). \\[0pt] [4] A.G. Vanakaras and D.J.Photinos, J. Chem. Phys. \textbf{128}, 154512 (2008). \\[0pt] [5] O. Francescangeli \textit{et al}., Phys. Rev. Lett. \textbf{107}, 207801 (2011).   

Nanoscale Positional Order Correlations: Swarms, Cybotactic Groups, Clusters, and Pretransitional Fluctuations in Liquid Crystals

Short-range molecular associations in organic liquids were first described as ``cybotactic'' groups [1] followed by the development of the swarm theory [2] to explain the structure, strong light scattering, and flow behavior of the nematic (N) liquid crystal phase. However, these ideas became inconsequential with the advent of the Oseen-Frank's continuum theory [3]. In 1970, de Vries reinvoked \textit{cybotactic} groups for the N phase of bis-(4'-n-octyloxybenzal)-2-chloro-l,4-phenylenediamine. These were eventually understood to be SmC pretransitional fluctuations, i.e., small correlated regions of the lower symmetry phase near the transition. Thermotropic biaxial mesophases have resurrected the faith in \textit{cybotacticity} in the guise of a new word - ``clusters''. Previous x-ray studies of normal organic fluids, and calamitic, lyotropic, and bent-core mesogens show that these clusters fall into three groups depending on the relative contributions of normal liquid structure and pretransitional fluctuations. A comparison with other organic and inorganic fluids will also be made.\\[4pt] [1] G.W. Stewart, Phys. Rev. \textbf{35}, 726 (1930).\\[0pt] [2] L.S. Ornestein and W. Kast, Trans. Farad. Soc. \textbf{29}, 931 (1933).\\[0pt] [3] FC Frank, Discuss. Faraday Soc. \textbf{25}, 19 (1958); W. Oseen, Ark. Mat., Astron. Fys. \textbf{19}, 1 (1925).   

Randomized Grain Boundary Liquid Crystal Phase

The formation of macroscopic, chiral domains, in the B4 and dark conglomerate phases, for example, is a feature of bent-core liquid crystals resulting from the interplay of chirality, molecular bend and molecular tilt. We report a new, chiral phase observed in a hockey stick-like liquid crystal molecule. This phase appears below a smectic A phase and cools to a crystal phase. TEM images of the free surface of the chiral phase show hundreds of randomly oriented smectic blocks several hundred nanometers in size, similar to those seen in the twist grain boundary (TGB) phase. However, in contrast to the TGB phase, these blocks are randomly oriented. The characteristic defects in this phase are revealed by freeze-fracture TEM images. We will show how these defects mediate the randomized orientation and discuss the intrinsic mechanism driving the formation of this phase. This work is supported by NSF MRSEC Grant DMR0820579 and NSF Grant DMR0606528.   

Resonant X-ray Scattering Studies of Smectic and Columnar Bent-Core Liquid Crystal Phases

Resonant X-ray scattering provides a direct probe of orientational structures in liquid crystals with periodicities that range from molecular dimensions (0.1 nm) to dimensions that can be observed with visible light (1.0 micron). We have recently applied this technique to study the orientational ordering of bent-core molecules in the smectic B$_{2}$ phase and the columnar B$_{1}$ phase. Using resonant scattering ``forbidden'' reflections due to glide or screw symmetry elements can be measured and an analysis of their polarization state enabled us to identify a chiral anticlinic antiferroelecrtic B$_{2}$ phase (Smectic C$_{A}$P$_{A}$) coexisting with an achiral synclinic antiferroelectric B$_{2}$ phase (Smectic C$_{S}$P$_{A}$) [1]. We were also able to determine the structure of a columnar B$_{1}$ phase and study the transition mechanism between the B$_{1}$ and B$_{2}$ phases [2]. \\[4pt] [1] V. Ponsinet, et al., Phys. Rev. E 84, 011706 (2011).\\[0pt] [2] C. Folcia, et al., Phys. Rev. E 84, 010701R (2011).   

Polyhedral Liquid Crystalline Vesicles

Vesicles with internal liquid-crystalline order can assume a variety of shapes depending on the ratio of the Frank moduli to the bending rigidity. Using both analytic and numerical tools one can we show that the possible low free energy morphologies include nano-fibers, faceted tetrahedral vesicles, ellipsoidal vesicles and cylindrical vesicles. The tetrahedral vesicle is a particularly fascinating example of a faceted liquid-crystalline membrane. Faceted liquid vesicles may lead to the design of supra-molecular structures with tetrahedral symmetry and new classes of nano-carriers.   

Packing Cheerios: Simulation studies of torus-shaped hard particles

We perform simulation studies of hard torus-shaped particles under compression or in granular flow. A major challenge in performing simulations of non-spherical hard particles is determination of possible overlap between particle pairs. To simplify this calculation, we model a torus particle as an assembly of overlapping hard spheres arranged in a ring, and implement GPU acceleration to create an efficient Monte Carlo algorithm. For particles shaped approximately like Cheerios, with major radius $R$=1 and minor radius $r$=0.6, the hexagonal columnar crystal structure has packing fraction of about 2/3, but---as easy to observe in your cereal box---the system is easily trapped in a glassy disordered state. Preliminary simulation studies of the disordered state formed via rapid compression show short-range orientational correlations in which neighboring particles are either parallel or at right angles. We also examine structures that form when particles rain down onto a flat surface. Results are compared with the known liquid crystal phases of oblate ellipsoids and experiments on discotic colloidal phases.   

Effect of CNTs and Induced Chirality on Smectic- Smectic Liquid Crystal Phase Transitions

High-resolution calorimetry results are presented of carbon nanotubes (CNTs) and the liquid crystal (LC) 9OO4 nano-colloidal dispersions as a function of temperature, scan rate, and CNT concentration ($0$, $0.025$, $0.05$, $0.20$ wt/$\%$). The CNT used have an enantiomeric excess that has been shown to induce chirality into this LC. The pure LC exhibits the phase sequence $I$-$N$-Sm$A$-Sm$C$-Sm$B$-$Cr$ on cooling with the expected heat capacity $C_p$ signatures, except for the Sm$A$-Sm$C$ transition, manifesting a double-$C_p$ peak $\sim 2$~K apart at low effective scan rates ($< 0.5$~K~min$^{-1}$). The introduction of CNTs results in the $I$-$N$, $N$-Sm$A$, and Sm$A$-Sm$C$ double $C_p$ features shifting to higher temperatures by $\sim 1$~K and remain sharp. However, the Sm$C$-Sm$B$ and Sm$B$-$Cr$ transitions shift to lower temperatures by $\sim 3-4$~K and broaden dramatically with increasing CNT content. We interpret these observations as a consequence of the $\pi$-$\pi$ interactions between the phenyl rings of 9OO4 and the graphene surfaces that induces bulk chirality, and the pinning of the director parallel to the CNT long-axis far from the surface. The balance of these two mechanisms may stabilize phases that lack any in-smectic-plane ordering.   

Mesophase behavior and effect of polydispersity in assemblies of polyhedral particles

Mesophase behavior of polyhedral particles is uniquely linked to the inherent interactions embedded in their geometrical shape. A two-parameter model based on particle shape anisotropy and order of symmetry has been proposed for predicting phase behavior of polyhedral particles. The focus of the current work is to explore the phase behavior of a distinct class of polyhedral shapes, which emerge at different growth stages of PbSe nanocrystal formation. The~body of knowledge~that is emerging from these studies~may prove useful in designing optimal self-assembly strategies for many desired nanostructures; e.g., as~in our ongoing efforts in understanding the nanocrystal~superlattice~formation for solar cell applications. Moreover the effect of particle size polydispersity is explored by simulating the assembly of two representative shapes exhibiting totally different mesophase behavior. It is found that while mesophases are quite resilient to particle size anisotropy, the ordered structures are a complex function of the polydispersity and geometric attributes.   

Submolecular organization of de Vries smectics with tuned frustration between SmA- and SmC- promoting elements

Structure-property relationships and the SmA-SmC (AC) transition were investigated with x-ray diffraction in de Vries smectics compounds with tuned frustration between SmA and SmC promoting elements in the molecules. These are isometric analogues of a compound with a 2-phenylpyrimidine core that combines a trisiloxane-terminated alkoxy side-chain with a chloro-terminated alkoxy side-chain. The results reveal the local molecular structure in which, both siloxane and hydrocarbon segments are segregated and oriented parallel to the director in the SmA phase. But the siloxane segments oriented at an angle ($\sim $14$^{\circ})$ different from the remaining hydrocarbon part of the molecule. This provides the first direct evidence of a kinked molecular conformation and nano-segregation of the molecule in the SmC phase. The two parts of the molecule possess different orientational order, siloxane part being more disordered, in both phases. The rate of change of the tilt angle with temperature appears to be different in the three compounds investigated.