A Twist-Bend Chiral Helix of 8nm Pitch in a Nematic Liquid Crystal of Achiral Molecular Dimers
Dong Chen, Jan H. Porada, Justin B. Hooper, Arthur Klittnick, Yongqiang Shen, Eva Korblova, Dmitry Bedrov, David M. Walba, Matthew A. Glaser, Joseph E. Maclennan, Noel A. Clark
Freeze Fracture Transmission Electron Microscopy (FFTEM) study of the nanoscale structure of the so-called "twist-bend" nematic (NX) phase of the cyanobiphenyl (CB) dimer molecule CB(CH2)7CB reveals a stripe texture of fluid layers periodically arrayed with a bulk spacing of d ~ 8.3 nm. Fluidity and a rigorously maintained spacing produce long-range-ordered fluid layered focal conic domains. Absence of a lamellar x-ray reflection at wavevector q ~ 2π/8 nm-1 or its harmonics in synchrotron-based scattering experiments indicates that this periodic structure is achieved with no detectable associated modulation of the electron density, and thus has nematic molecular ordering. A search for periodic ordering with d ~ 8nm in CB(CH2)7CB using atomistic molecular dynamic computer simulation yielded equilibration of a conical twist-bend helixed nematic ground state, of the sort first proposed by Meyer, and envisioned in systems of bent molecules by Dozov and Memmer, We identify θ ~ 33 degree as the cone angle, and p ~ 8nm as the full pitch of the helix, the shortest ever found in a nematic fluid.
We present a molecular simulation study of the structure of linear dendronized polymers. We use excluded volume interactions in the context of a generic coarse-grained molecular model whose geometrical parameters are tuned to represent a poly(para-phenylene) backbone with benzyl ether, Frechet type dendrons. We apply Monte Carlo sampling in order to investigate the formation of packing-induced chiral structures along the polymer backbone of these chemically non-chiral systems. We find that helical structures can be formed, usually with defects consisting of domains with reversed helical handed…
The chiral, heliconical (twist-bend) nematic ground state is reported in an achiral, rigid, bent-core mesogen (UD68). Similar to the nematic twist-bend (NTB) phase observed in bent molecular dimers, the NTB phase of UD68 forms macroscopic, smectic-like focal-conic textures and exhibits nanoscale, periodic modulation with no associated modulation of the electron density, i.e., without a detectable lamellar x-ray reflection peak. The NTB helical pitch is pTB ~ 14 nm. When an electric field is applied normal to the helix axis, a weak electroclinic effect is observed, revealing 50 um-scale left- a…
In many biological materials with a hierarchical structure there is an intriguing and unique mechanism responsible for the 'propagation' of order from the molecular to the nano- or micro-scale level. Here we present a much simpler molecular system built of achiral mesogenic dimeric molecules that shows a similar complexity with four levels of structural chirality (i) layer chirality, (ii) helicity of a basic 4-layer repeating unit, (iii) a helix with a pitch of several layers and (iv) mesoscopic helical filaments. As seen in many biological systems, there is a coupling between chirality at dif…
Resonant x-ray scattering shows that the bulk structure of the twist-bend liquid crystal phase, recently discovered in bent molecular dimers, has spatial periodicity without electron density modulation, indicating a lattice-free heliconical nematic precession of orientation that has helical glide symmetry. In situ study of the bulk helix texture for the dimer CB7CB shows an elastically-confined temperature-dependent minimum helix pitch, but a remarkable elastic softness of pitch in response to dilative stresses. Scattering from the helix is not detectable in the higher temperature nematic phas…
We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free-energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Sky…
Using a novel Se-labelled dimer mixed with DTC5C7 aligned by magnetic field, the twist-bend nematic phase (Ntb) in dimers was studied by hard X-ray resonant scattering and by small and wide angle X-ray scattering (SAXS, WAXS). Resonant diffraction spots indicated a helix with a 9-12 nm pitch in the Ntb phase. Unprecedentedly high helix orien-tation enabled deconvolution of global and local order parameters. This, combined with simultaneous resonant and non-resonant SAXS and WAXS data, allowed us to construct a modified model of the Ntb phase matching twisted molecular conformations and the loc…
Certain nematic liquid crystals, e.g., those formed by banana-shaped molecules, can exhibit a low-temperature twist-bend nematic (Ntb) phase. Upon addition of chiral dopants, a chiral version of the twist-bend phase (N*tb) can be observed below the conventional chiral nematic (N*) phase, while under electric field the N* phase is transformed into a specific state known as "heliconical cholesteric". In this work, we have studied the well-known Ntb-forming system CB7CB:CB6OCB with addition of 5CB and chiral dopants (ChD) using optical microscopy, differential scanning calorimetry (DSC), and meas…
Nematic twist--bend is the fifth nematic phase recognized in nature. This phase exhibits spiral orientational order, thus it is a chiral structure and it can be stabilized in systems composed of achiral molecules. The microscopic origin of this spontaneous chiral symmetry breaking is to a large extent unknown but phenomenologically it appears stabilized by assuming coupling between steric polar and orientational orderings. Understanding of how external fields affect the stability of this phase is of great intellectual interest and of relevance to potential applications. Within mesoscopic Landa…
Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. 96, 207802 (2006)] that isolated, square-well homopolymers can spontaneously break chiral symmetry and freeze into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics, combined with an optimized parallel tempering scheme, to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of th…
How change in molecular structure can affect relative stability and structural properties of the twist-bend nematic phase (N$_\text{TB}$)? Here we extend the mean-field model [C. Greco et al., Soft Matter, 2014, 10, 9318] for bent-shaped achiral molecules, to study the influence of arm molecular biaxiality and the value of molecule's bend angle on relative stability of N$_\text{TB}$. In particular we show that by controlling biaxiality of molecule's arms up to four ordered phases can become stable. They involve locally uniaxial and biaxial variants of N$_\text{TB}$, together with the uniaxial …
The nematic twist-bend ($\mathrm{N_{TB}}$) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The $\mathrm{N_{TB}}$ phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The $\mathrm{N_{TB}}$ structure thus provides another fascinating example of spontaneous chiral symmetry break…
By means of extensive replica-exchange simulations of generic coarse-grained models for helical polymers, we systematically investigate the structural transitions into all possible helical phases for flexible and semiflexible elastic polymers with self-interaction under the influence of torsion barriers. The competing interactions lead to a variety of conformational phases including disordered helical arrangements, single helices, and ordered, tertiary helix bundles. Most remarkably, we find that a bending restraint entails a clear separation and stabilization of the helical phases. This aids …
Mesogenic dimers in the twist-bend nematic phase exhibit much higher flexoelectric polarization than in their uniform nematic phase. In order to theoretically investigate this data, we extend the symmetry based linear elastic theory of the twist-bend nematic phase developed in Phys. Rev. E 92, 030501(R) 2015, by including flexoelectricity under the action of an external electric field perpendicular to the helical axis. We show that at the nematic towards twist-bend nematic transition, a new flexoelectric mode becomes active. Consequently, the present model predicts the increase of the effectiv…
Periodic structures of phases with orientational order of molecules, but homogenous electron density distribution: a short pitch cholesteric, blue phase and twist-bend nematic phase, were probed by a resonant soft x-ray scattering (RSoXS) at the carbon K-edge. The theoretical model shows that in case of a simple heliconical nematic structure two resonant signals corresponding to the full and half pitch band should be present, while only the full pitch band is observed in experiment. This suggests that the twist-bend nematic phase has complex structure with a double-helix, built of two interloc…
The interplay between bending of the molecule axis and appearance of disruptions in circular DNA molecules, with $\sim 100$ base pairs, is addressed. Three minicircles with different radii and almost equal content of AT and GC pairs are investigated. The DNA sequences are modeled by a mesoscopic Hamiltonian which describes the essential interactions in the helix at the level of the base pair and incorporates twisting and bending degrees of freedom. Helix unwinding and bubble formation patterns are consistently computed by a path integral method that sums over a large number of molecule configu…
The ground state of twist-bend nematic liquid crystals is a heliconical molecular arrangement in which the nematic director precesses uniformly about an axis, making a fixed angle with it. Both precession senses are allowed in the ground state of these phases. When one of the two \emph{helicities} is prescribed, a single helical nematic phase emerges. A quadratic elastic theory is proposed here for each of these phases which features the same elastic constants as the classical theory of the nematic phase, requiring all of them to be positive. To describe the helix axis, it introduces an extra …
We have numerically studied a liquid composed of achiral, bent-shaped molecules built of tangent spheres. The system is known to spontaneously break mirror symmetry, as it forms a macroscopically chiral, twist-bend nematic phase [Phys. Rev. Lett. 115, 147801 (2015)]. Here, we have examined the full phase diagram of such liquid and observed several phases characterized by orientational and/or translational ordering of molecules. Apart from conventional nematic, smectic A, and the above-mentioned twist-bend nematic phase, we have identified antiferroelectric smectic A phase. For large densities …
We present a theoretical study of director fields in toroidal geometries with degenerate planar boundary conditions. We find spontaneous chirality: despite the achiral nature of nematics the director configuration show a handedness if the toroid is thick enough. In the chiral state the director field displays a double twist, whereas in the achiral state there is only bend deformation. The critical thickness increases as the difference between the twist and saddle-splay moduli grows. A positive saddle-splay modulus prefers alignment along the short circle of the bounding torus, and hence stimul…
We review the physics underlying Meyer's conjecture of how macroscopic-scale twist and bend conspire within the Frank-Oseen elasticity theory of nematics to create a heliconical arrangement of the uniaxial, apolar nematic director, the so-called "twist bend nematic" $\rm N_{TB}$. We show that since 2011 a second, lower-temperature nematic phase observed in odd methylene-linked cyanobiphenyl dimers discovered by Toriumi and called $\rm N_X$, has been incorrectly identified as $\rm N_{TB}$. Moreover, as more quantitative data on the $\rm N_X$ emerged, Meyer's simple prediction has been distorted…
The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered macroscopically chiral heliconical winding of molecular scale pitch, in absence of positional ordering. Here we characterize the structure of the ground state of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB over a wide range of concentrations and temperatures, showing that the contour length along the molecular direction for a single turn of the helix is approximately equal to 2πRmol, where Rmol is the radius of bend cu…
The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's elastic theory for nematic liquid crystals by including gradients of the nematic strain tensor in the elastic deformation energy. The invariants of the elastic tensor fields, up to the fourth order in the nematic director spatial derivatives, are calculated. An alternative approach that consists in the extension of the linear elastic energy to higher powers of …
The base pair fluctuations and helix untwisting are examined for a circular molecule. A realistic mesoscopic model including twisting degrees of freedom and bending of the molecular axis is proposed. The computational method, based on path integral techniques, simulates a distribution of topoisomers with various twist numbers and finds the energetically most favorable molecular conformation as a function of temperature. The method can predict helical repeat, openings loci and bubble sizes for specific sequences in a broad temperature range. Some results are presented for a short DNA circle rec…
Dielectric spectroscopy of a twist bend nematic phase of an achiral bent core liquid crystalline compound under DC bias is used to investigate its response to electric field. Two collective relaxation processes are revealed, these are assigned to distortions of helicoidal structure by the external bias field. Frequency of the mode depends primarily on the helicoidal angle and has anomalous, softening- like behaviour at the nematic to the twist bend nematic transition. A coupling of dielectric anisotropy with electric field gives rise to a new equilibrium periodic structure in the time scale in…
Strongly dipolar mesogenic compounds with a chiral center located in a lateral alkyl chain were synthesized, and shown to form the ferroelectric nematic phase. The presence of molecular chirality induced a helical structure in both the N and NF phases, but with opposite helix sense in the two phases. The relaxation frequency of the polar fluctuations was found to be lower for the chiral NF phase than for its achiral, non-branched counterpart with the same lateral chain length.
A state of matter in which molecules show a long-range orientational order and no positional order is called a nematic liquid crystal. The best known and most widely used (for example, in modern displays) is the uniaxial nematic, with the rod-like molecules aligned along a single axis, called the director. When the molecules are chiral, the director twists in space, drawing a right-angle helicoid and remaining perpendicular to the helix axis; the structure is called a chiral nematic. In this work, using transmission electron and optical microscopy, we experimentally demonstrate a new nematic o…
The free energy of antiferroelectric liquid crystal which takes into account polar order explicitly is presented. Steric, van der Waals, piezoelectric and flexoelectric interactions to the nearest layers and dipolar electrostatic interactions to the nearest and to the next nearest layers induce indirect tilt interactions with chiral and achiral properties, which extend to the third and to the fourth nearest layers. Chiral indirect interactions between tilts can be large and induce helicoidal modulations even in systems with negligible chiral van der Waals interactions. If indirect chiral inter…
The simplest model of DNA mechanics describes the double helix as a continuous rod with twist and bend elasticity. Recent work has discussed the relevance of a little-studied coupling $G$ between twisting and bending, known to arise from the groove asymmetry of the DNA double helix. Here, the effect of $G$ on the statistical mechanics of long DNA molecules subject to applied forces and torques is investigated. We present a perturbative calculation of the effective torsional stiffness $C_\text{eff}$ for small twist-bend coupling. We find that the "bare" $G$ is "screened" by thermal fluctuations…
We analytically derive the effective layer elastic energy of smectic-A and smectic-C liquid crystals by adiabatic elimination of the orientational degree of freedom from the generalized Chen-Lubensky model. In the smectic-A phase, the effective layer bending elastic modulus is calculated as a function of the wavelength of the layer undulation mode. It turns out that an unlocking of the layer normal and the director reduces the layer bending rigidity for wavelengths smaller than the director penetration length. In the achiral smectic-C phase, an anisotropic bending elasticity appears due to the…
The recently discovered twist-bend nematic phase, $\rm N_{tb}$, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, $\textbf{n}$, on a conical helix with a tilt angle $θ$ and helical pitch $P$. The stability of the $\rm N_{tb}$ phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of helical axis, $\bf t$. In the present communication, we investigate the influence of an external bulk field (magnetic or electric) on t…
$α$-helices stand out as common and relatively invariant secondary structural elements of proteins. However, $α$-helices are not rigid bodies and their deformations can be significant in protein function ({\it e.g.} coiled coils). To quantify the flexibility of $α$-helices we have performed a structural principal-component analysis of helices of different lengths from a representative set of protein folds in the Protein Data Bank. We find three dominant modes of flexibility: two degenerate bend modes and one twist mode. The data are consistent with independent Gaussian distributions for each m…
The understanding of self-organization in the twist-bend nematic $(N_\text{TB})$ phase, identified in 2011 in liquid crystal dimers, is at the forefront of soft matter research worldwide. This new nematic phase develops structural chirality in the isotropic $(I)$ and the uniaxial nematic $(N_\text{U})$ phases, despite the fact that the molecules forming the structure are chemically achiral. Molecular, shape-induced flexopolarization provides a viable mechanism for a qualitative understanding of $N_\text{TB}$ and the related phase transitions. The key question that remains is whether with this …
The dielectric spectra of the twist bend nematic phase of the bent shaped achiral liquid crystal dimer are studied for the determination of the different relaxation modes. The two molecular processes were assigned one to the precessional rotation of the longitudinal components of the cyanobiphenyl groups and the second to the spinning rotation of the transverse component of the dimer. The low frequency peak shows a peculiar temperature behavior at the twist bend nematic to nematic transition. This peak can be assigned to a collective fluctuation of the tilt angle of the coarse grained director…
Being capable of characterizing DNA local bending is essential to understand thoroughly many biological processes because they involve a local bending of the double helix axis, either intrinsic to the sequence or induced by the binding of proteins. Developing a method to measure DNA bend angles that does not perturb the conformation of the DNA itself or the DNA-protein complex is a challenging task. Here, we propose a joint theory-experiment high throughput approach to rigorously measure such bend angles using the Tethered Particle Motion (TPM) technique. By carefully modeling the TPM geometry…
This article re-examines a classic question in liquid-crystal physics: What are the elastic modes of a nematic liquid crystal? The analysis uses a recent mathematical construction, which breaks the director gradient tensor into four distinct types of mathematical objects, representing splay, twist, bend, and a fourth deformation mode. With this construction, the Oseen-Frank free energy can be written as the sum of squares of the four modes, and saddle-splay can be regarded as bulk rather than surface elasticity. This interpretation leads to an alternative way to think about several previous re…
The model of the deformation of DNA macromolecule is developed with the accounting of two types of components of deformation: external and internal. External components describe the bend, twist and stretch of the double helix. The internal component - the conformational mobility inside of the double helix. In the work the deformation of DNA macromolecule is considered taking into account the coupling of the external component (of deformation) with the internal component (of conformational change). Under the task consideration the macromolecule twist-stretch coupling and coupling between twist …
We present a comprehensive set of measurements of optical, dielectric, diamagnetic, elastic and viscous properties in the nematic (N) phase formed by a liquid crystalline dimer. The studied dimer, 1,7-bis-4-(4-cyanobiphenyl) heptane (CB7CB), is composed of two rigid rod-like cyanobiphenyl segments connected by a flexible aliphatic link with seven methyl groups. CB7CB and other nematic dimers are of interest due to their tendency to adopt bent configurations and to form two states possessing a modulated nematic director structure, namely, the twist bend nematic, NTB, and the oblique helicoidal …
Helical molecules change their twist number under the effect of a mechanical load. We study the twist-stretch relation for a set of short DNA molecules modeled by a mesoscopic Hamiltonian. Finite temperature path integral techniques are applied to generate a large ensemble of possible configurations for the base pairs of the sequence. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. Simulating a broad range of twisting conformation, we compute the helix structural parameters by averaging over the ensemble of base pairs con…
The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining "layer" compression and bending ought to be char…
We study the effects of chirality at the segment scale on the thermodynamics of block copolymer melts using self consistent field theory. In linear diblock melts where segments of one block prefer a twisted, or cholesteric, texture, we show that melt assembly is critically sensitive to the ratio of random coil size to the preferred pitch of cholesteric twist. For weakly-chiral melts (large pitch), mesophases remain achiral, while below a critical value of pitch, two mesocopically chiral phases are stable: an undulated lamellar phase; and a phase of hexagonally-ordered helices. We show that the…
We study a minimal extension of the worm-like chain to describe polypeptides having alpha-helical secondary structure. In this model presence/absence of secondary structure enters as a scalar variable that controls the local chain bending modulus. Using this model we compute the extensional compliance of an alpha-helix under tensile stress, the bending compliance of the molecule under externally imposed torques, and the nonlinear interaction of such torques and forces on the molecule. We find that, due to coupling of the ``internal'' secondary structure variables to the conformational degrees …
We investigate the statistical mechanics of a torsionally constrained polymer. The polymer is modeled as a fluctuating rod with bend stiffness A kT and twist stiffness C kT. In such a model, thermal bend fluctuations couple geometrically to an applied torque through the relation Lk = Tw + Wr. We explore this coupling and find agreement between the predictions of our model and recent experimental results on single lambda-DNA molecules. This analysis affords an experimental determination of the microscopic twist stiffness (averaged over a helix repeat). Quantitative agreement between theory and …
It is well-established that many physical properties of DNA at sufficiently long length scales can be understood by means of simple polymer models. One of the most widely used elasticity models for DNA is the twistable worm-like chain (TWLC), which describes the double helix as a continuous elastic rod with bending and torsional stiffness. An extension of the TWLC, which has recently received some attention, is the model by Marko and Siggia, who introduced an additional twist-bend coupling, expected to arise from the groove asymmetry. By performing computer simulations of two available version…
Heliconical cholesteric liquid crystals are expected to be more sensitive to torque induced by light field since their structure allows both bend and twist in molecular orientations, differently from the conventional cholesterics in which only twist deformation is involved, requiring much higher fields. We report here a demonstration of tuning the helical pitch in heliconical cholesterics induced by an optical torque. Experimental observations are in agreement with expectations of the classical theory extended to include the effect of the optical field. A dual control of the helical pitch is a…
The occurrence of coiled or helical morphologies is common in nature, from plant roots to DNA packaging into viral capsids, as well as in applications such as oil drilling processes. In many examples, chiral structures result from the buckling of a straight fiber either with intrinsic twist or to which end moments have been applied in addition to compression forces. Here, we elucidate a generic way to form regular helicoidal shapes from achiral straight filaments transported in viscous flows with free ends. Through a combination of experiments using fluorescently labeled actin filaments in mic…
The thermodynamic properties of DNA circular molecules are investigated by a new path integral computational method which treats in the real space the fundamental forces stabilizing the molecule. The base pair and stacking contributions to the classical action are evaluated separately by simulating a broad ensemble of twisted conformations. We obtain, for two short sequences, a free energy landscape with multiple wells corresponding to the most convenient values of helical repeat. Our results point to a intrinsic flexibility of the circular structures in which the base pair fluctuations move t…
We present a simplified molecular model of mesogenic dimers consisting of two identical uniaxial mesogenic cores separated by a fixed-length spacer and allowed to assume only two, statistically equivalent, conformations which are non-planar and of opposite handedness. In the mean-field approximation, with additive interactions among the mesogenic cores, the model yields up to three positionally disordered phases, one isotropic and two nematic. The low temperature nematic phase ($\mathrm{N_X}$) has a local two-fold symmetry axis which is also a direction of molecular polar ordering and is tight…
