Spontaneous Twisting of Achiral Hard Rod Nematics.

Since Onsager's seminal work, hard rods have been taken as a prototype of nematic liquid crystals, characterized by uniaxial order and a uniform director field as a ground state. Here, using Onsager theory to calculate the free energy in the presence of arbitrary deformations, we find that hard rod nematics have an intrinsic tendency to twist around their ordering axis (double twist), driven by a mechanism in which the orientational fluctuations of particles play a key role. The anisotropic hard core potential used here is arguably the simplest form of interaction able to originate spontaneous breaking of mirror symmetry in a 3D fluid. Our results are discussed in relation to the recent discovery of a double twisted ground state in cylindrically confined lyotropic chromonic liquid crystals.

Modeling of minimal systems based on ATP-Zn coordination for chemically fueled self-assembly.

Following nature's example, there is currently strong interest in using adenosine 5'-triphosphate (ATP) as a fuel for the self-assembly of functional materials with transient/non-equilibrium behaviours. These hold great promise for applications, e.g. in catalysis and drug delivery. In a recent seminal work [Maiti et al., Nat. Chem., 2016, 8, 725], binding of ATP to the metallosurfactant zinc hexadecyl-1,4,7-triazacyclononane ([ZnC16 TACN]2+) was exploited to produce ATP-fueled transient vesicles. Crucial to the complex formation is the ability of ATP to bind to the metal ion. As a first step to unveil the key elements underlying this process, we investigate the interaction of ATP with Zn2+ and with methyl-1,4,7-triazacyclononane ([ZnCH3 TACN]2+), using all-atom molecular dynamics simulations. The free energy landscape of the complex formation is sampled using well-tempered metadynamics with three collective variables, corresponding to the coordination numbers of Zn2+ with the oxygen atoms of the three phosphate groups. We find that the structure of the ternary complex is controlled by direct triphosphate coordination to zinc, with a minor role played by the interactions between ATP and CH3 TACN which, however, may be important for the build-up of supramolecular assemblies.

On the elusive saddle-splay and splay-bend elastic constants of nematic liquid crystals.

The elastic behavior of nematics is commonly described in terms of the three so-called bulk deformation modes, i.e., splay, twist, and bend. However, the elastic free energy contains also other terms, often denoted as saddle-splay and splay-bend, which contribute, for instance, in confined systems. The role of such terms is controversial, partly because of the difficulty of their experimental determination. The saddle-splay (K24) and splay-bend (K13) elastic constants remain elusive also for theories; indeed, even the possibility of obtaining unambiguous microscopic expressions for these quantities has been questioned. Here, within the framework of Onsager theory with Parsons-Lee correction, we obtain microscopic estimates of the deformation free energy density of hard rod nematics in the presence of different director deformations. In the limit of a slowly changing director, these are directly compared with the macroscopic elastic free energy density. Within the same framework, we derive also closed microscopic expressions for all elastic coefficients of rodlike nematics. We find that the saddle-splay constant K24 is larger than both K11 and K22 over a wide range of particle lengths and densities. Moreover, the K13 contribution comes out to be crucial for the consistency of the results obtained from the analysis of the microscopic deformation free energy density calculated for variants of the splay deformation.

Microscopic modelling of nematic elastic constants beyond Straley theory.

Recent findings on various classes of nematics, whose microscopic structure differs from the prototypical rod-like shape, evidence unusual elastic properties, which challenge existing theories. Here we develop a theoretical and numerical methodology for the calculation of Frank elastic constants, accounting for the coupling between the molecular shape and each specific deformation mode. This is done in the framework of Onsager-Straley's second-virial theory, using a non-local form of the orientational distribution function. The comparison between two benchmark systems, a straight and a bent rod, allows us to illustrate the distinct features of this approach, which include additional order parameters induced by the deformation and, related to this, an ideal contribution to the deformation free energy. Then, using a simple system that can be seen as a minimalist model of liquid crystal trimers, we discuss the impact of different molecular conformations on elastic constants.

Interplay of Particle Morphology and Director Distortions in Nematic Fluids.

The existing microscopic theories for elasticity of nematics are challenged by recent findings on systems, whether bent molecules or semiflexible polymers, which do not comply with the model of rigid rodlike particles. Here, we propose an extension of Onsager-Straley second-virial theory, based on a model for the orientational distribution function that, through explicit account of the director profile along a particle, changes in the presence of deformations. The elastic constants reveal specific effects of particle morphology, which are not captured by the existing theories. This paves the way to microscopic modeling of the elastic properties of semiflexible liquid crystal polymers, which is a longstanding issue.

Correction: Thermo-orientation in fluids of arbitrarily shaped particles.

Correction for 'Thermo-orientation in fluids of arbitrarily shaped particles' by Andrea Gardin et al., Phys. Chem. Chem. Phys., 2019, 21, 104-113.

Thermo-orientation in fluids of arbitrarily shaped particles.

Recent nonequilibrium Molecular Dynamics (NEMD) simulations revealed preferential orientation, induced by a temperature gradient, in fluids of uncharged dumbbell-like particles. The magnitude of this phenomenon, called thermo-orientation, was found to be linear in the applied temperature gradient and to increase with the difference in shape or mass between the two beads of the particles. The underlying mechanism and the microscopic determinants of the phenomenon are not obvious. Here, after examination of the general symmetry requirements for thermo-orientation, we have extended the NEMD simulations to uncharged particles of various shapes and mass distribution, including chiral cases. The numerical results are rationalized by a microscopic model, based on the assumption of local equilibrium. This allows us to correlate the thermo-orientation response of arbitrarily shaped particles to quantities that characterize their shape and mass distribution.

Cholesteric and screw-like nematic phases in systems of helical particles.

Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C2 symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. First, the real nature of the lower density nematic phase, expected to be cholesteric. Second, the influence that the latter, once allowed to form, may have on the existence and stability of the screw-like nematic phase. To address these questions, we have performed Monte Carlo and molecular dynamics numerical simulations of helical particle systems confined between two parallel repulsive walls. We have found that the removal of the periodicity constraint along one direction allows a relatively-long-pitch cholesteric phase to form, in lieu of the uniform nematic phase, with helical axis perpendicular to the walls while the existence and stability of the screw-like nematic phase are not appreciably affected by this change of boundary conditions.

Chiral self-assembly of helical particles.

The shape of the building blocks plays a crucial role in directing self-assembly towards desired architectures. Out of the many different shapes, the helix has a unique position. Helical structures are ubiquitous in nature and a helical shape is exhibited by the most important biopolymers like polynucleotides, polypeptides and polysaccharides as well as by cellular organelles like flagella. Helical particles can self-assemble into chiral superstructures, which may have a variety of applications, e.g. as photonic (meta)materials. However, a clear and definite understanding of these structures has not been entirely achieved yet. We have recently undertaken an extensive investigation on the phase behaviour of hard helical particles, using numerical simulations and classical density functional theory. Here we present a detailed study of the phase diagram of hard helices as a function of their morphology. This includes a variety of liquid-crystal phases, with different degrees of orientational and positional ordering. We show how, by tuning the helix parameters, it is possible to control the organization of the system. Starting from slender helices, whose phase behaviour is similar to that of rodlike particles, an increase in curliness leads to the onset of azimuthal correlations between the particles and the formation of phases specific to helices. These phases feature a new kind of screw order, of which there is experimental evidence in colloidal suspensions of helical flagella.

Density functional theory of nematic elasticity: softening from the polar order.

Recent experiments have evidenced some unconventional features in the elasticity of nematics, which cannot be explained by standard microscopic theories. Here, in the framework of a second-virial density functional theory, we have developed a general approach, relaxing the usual assumption that the angular distribution of particles with respect to their local director is unaffected by the deformation. We show that, for particles with polar symmetry, a new contribution to the splay and bend deformation free energy arises, associated with the onset of polar order. Calculations for conical and bent-shaped particles reveal dramatic softening of the splay and the bend mode, respectively, which eventually may lead to spontaneous deformation.

Understanding the twist-bend nematic phase: the characterisation of 1-(4-cyanobiphenyl-4'-yloxy)-6-(4-cyanobiphenyl-4'-yl)hexane (CB6OCB) and comparison with CB7CB.

The synthesis and characterisation of the nonsymmetric liquid crystal dimer, 1-(4-cyanobiphenyl-4'-yloxy)-6-(4-cyanobiphenyl-4'-yl)hexane (CB6OCB) is reported. An enantiotropic nematic (N)-twist-bend nematic (NTB) phase transition is observed at 109 °C and a nematic-isotropic phase transition at 153 °C. The NTB phase assignment has been confirmed using polarised light microscopy, freeze fracture transmission electron microscopy (FFTEM), (2)H-NMR spectroscopy, and X-ray diffraction. The effective molecular length in both the NTB and N phases indicates a locally intercalated arrangement of the molecules, and the helicoidal pitch length in the NTB phase is estimated to be 8.9 nm. The surface anchoring properties of CB6OCB on a number of aligning layers is reported. A Landau model is applied to describe high-resolution heat capacity measurements in the vicinity of the NTB-N phase transition. Both the theory and heat capacity measurements agree with a very weak first-order phase transition. A complementary extended molecular field theory was found to be in suggestive accord with the (2)H-NMR studies of CB6OCB-d2, and those already known for CB7CB-d4. These include the reduced transition temperature, TNTBN/TNI, the order parameter of the mesogenic arms in the N phase close to the NTB-N transition, and the order parameter with respect to the helix axis which is related to the conical angle for the NTB phase.

Entropy-Driven Chiral Order in a System of Achiral Bent Particles.

Why should achiral particles organize into a helical structure? Here, using theory and molecular dynamics simulations we show that at high concentration crescent-shaped particles interacting through a purely repulsive potential form the twist-bend nematic phase, which features helical order of the twofold symmetry axes of particles, with doubly degenerate handedness. Spontaneous breaking of the chiral symmetry is driven by the entropic gain that derives from the decrease in excluded volume in the helical arrangement. Crucial to this purpose is the concave shape of particles. This study is based on a general formulation of the Onsager theory, which includes biaxiality and polarity of phase and particles, in addition to the space modulation of order. Molecular dynamics simulations corroborate the theoretical predictions and provide further insights into the structure of the helical phase.

From the molecular structure to spectroscopic and material properties: computational investigation of a bent-core nematic liquid crystal.

We present a computational investigation of the nematic phase of the bent-core liquid crystal A131. We use an integrated approach that bridges density functional theory calculations of molecular geometry and torsional potentials to elastic properties through the molecular conformational and orientational distribution function. This unique capability to simultaneously access different length scales enables us to consistently describe molecular and material properties. We can reassign (13)C NMR chemical shifts and analyze the dependence of phase properties on molecular shape. Focusing on the elastic constants we can draw some general conclusions on the unconventional behavior of bent-core nematics and highlight the crucial role of a properly-bent shape.

Molecular geometry, twist-bend nematic phase and unconventional elasticity: a generalised Maier-Saupe theory.

It has been found that bent-shaped achiral molecules can form a liquid crystal phase, called the Twist-Bend Nematic (NTB), which is locally polar and spontaneously twisted having a tilted director, with a conglomerate of degenerate chiral domains with opposite handedness and pitch of a few molecular lengths. Here, using a major extension of the Maier-Saupe molecular field theory, we can describe the transition from the nematic (N) to the NTB phase. We provide a consistent picture of the structural and elastic properties in the two phases, as a function of the molecular bend angle, and show that on approaching the transition there is a gradual softening of the bend mode in the N phase. This points to the crucial role of the molecular shape for the formation of modulated nematic phases and their behaviour.

Self-assembly of hard helices: a rich and unconventional polymorphism.

Hard helices can be regarded as a paradigmatic elementary model for a number of natural and synthetic soft matter systems, all featuring the helix as their basic structural unit, from natural polynucleotides and polypeptides to synthetic helical polymers, and from bacterial flagella to colloidal helices. Here we present an extensive investigation of the phase diagram of hard helices using a variety of methods. Isobaric Monte Carlo numerical simulations are used to trace the phase diagram; on going from the low-density isotropic to the high-density compact phases a rich polymorphism is observed, exhibiting a special chiral screw-like nematic phase and a number of chiral and/or polar smectic phases. We present full characterization of the latter, showing that they have unconventional features, ascribable to the helical shape of the constituent particles. Equal area construction is used to locate the isotropic-to-nematic phase transition, and the results are compared with those stemming from an Onsager-like theory. Density functional theory is also used to study the nematic-to-screw-nematic phase transition; within the simplifying assumption of perfectly parallel helices, we compare different levels of approximation, that is second- and third-virial expansions and a Parsons-Lee correction.

Left or right cholesterics? A matter of helix handedness and curliness.

Using an Onsager-like theory, we have investigated the relationship between the morphology of hard helical particles and the features (pitch and handedness) of the cholesteric phase that they form. We show that right-handed helices can assemble into right- (R) and left-handed (L) cholesterics, depending on their curliness, and that the cholesteric pitch is a non-monotonic function of the intrinsic pitch of particles. The theory leads to the definition of a hierarchy of pseudoscalars, which quantify the difference in the average excluded volume between pair configurations of helices having (R) and (L)-skewed axes. The predictions of the Onsager-like theory are supported by Monte Carlo simulations of the isotropic phase of hard helices, showing how the cholesteric organization, which develops on scales longer than hundreds of molecular sizes, is encoded in the short-range chiral correlations between the helical axes.

Communication: from rods to helices: evidence of a screw-like nematic phase.

Evidence of a special chiral nematic phase is provided using numerical simulation and Onsager theory for systems of hard helical particles. This phase appears at the high density end of the nematic phase, when helices are well aligned, and is characterized by the C2 symmetry axes of the helices spiraling around the nematic director with periodicity equal to the particle pitch. This coupling between translational and rotational degrees of freedom allows a more efficient packing and hence an increase of translational entropy. Suitable order parameters and correlation functions are introduced to identify this screw-like phase, whose main features are then studied as a function of radius and pitch of the helical particles. Our study highlights the physical mechanism underlying a similar ordering observed in colloidal helical flagella [E. Barry, Z. Hensel, Z. Dogic, M. Shribak, and R. Oldenbourg, Phys. Rev. Lett. 96, 018305 (2006)] and raises the question of whether it could be observed in other helical particle systems, such as DNA, at sufficiently high densities.

Structure and Dynamics of ATP and the ATP-Zn2+ Complex in Solution.

Despite the crucial role of ATP in life and artificial life-like applications, fundamental aspects relevant to its function, such as its conformational properties and its interaction with water and ions, remain unclear. Here, by integrating linear and two-dimensional infrared spectroscopy with ab initio molecular dynamics, we provide a detailed characterization of the vibrational spectra of the phosphate groups in ATP and in its complex with Zn2+ in water. Our study highlights the role of conformational disorder and solvation dynamics, beyond the harmonic normal-mode analysis, and reveals a complex scenario in which electronic and environmental effects tune the coupling between phosphate vibrations. We identify ßγ-bidentate and αßγ-tridentate modes as the preferential coordination modes of Zn2+, as was proposed in the literature for Mg2+, although this conclusion is reached by a different spectral interpretation.

Mechanically Adaptive Metal-Coordinated Electrogel Membranes.

Achieving specific mechanical properties of hydrogels, especially when used as thin films, can be crucial in diverse applications, including tissue engineering and bioelectronics. Here, a novel electrochemical approach for fabricating uniform and robust hydrogel films based on carboxymethyl cellulose cross-linked by Fe3+ ions (Fe-CMC), exhibiting tunable, dynamic properties is introduced. High modulation of the mechanical properties of the film is achieved by applying multiple electrochemical pulses of oxidative voltage during hydrogel deposition. Our study shows also a remarkable effect of the ionic strength on the properties of the electrodeposited hydrogel films. We found that switching from a salt solution to water enhanced the stiffness of the hydrogels, thereby regulating the permeability of the films. These results are supported by molecular dynamics (MD) simulations, showing that an increase in the ionic strength induces a weakening of the Fe-CMC interactions, ultimately affecting the network strength. Finally, the robustness of these electrodeposited hydrogel films enables their delamination from the electrode without any damage, thereby expanding their potential applications as freestanding smart membranes. By providing fundamental insights into the dynamics of metal-coordinated bonds and their response at the macroscopic scale, we have demonstrated the versatility of electrochemical gelation for the fabrication of robust hydrogel films with tunable mechanical properties, which could serve as smart platforms for a variety of biomedical applications.

Enantiotopic discrimination and director organization in the twist-bend nematic phase.

Extending a molecular field model for the orientational order in the nematic phase, we calculate the (2)H-NMR splittings for the achiral solute 8CB-d2 in the twist-bend nematic phase formed by the achiral liquid crystal dimer CB7CB. We give an explanation for the enantiotopic discrimination observed in the spectra and comparison with experimental data allows us to provide quantitative estimates of the order parameters (pitch and conical angle) that characterize the director modulation of the twist-bend nematic phase.