Orientational Order Parameter Research Articles

Random close packing of semi-flexible polymers in two dimensions: Emergence of local and global order.

Through extensive Monte Carlo simulations, we systematically study the effect of chain stiffness on the packing ability of linear polymers composed of hard spheres in extremely confined monolayers, corresponding effectively to 2D films. First, we explore the limit of random close packing as a function of the equilibrium bending angle and then quantify the local and global order by the degree of crystallinity and the nematic or tetratic orientational order parameter, respectively. A multi-scale wealth of structural behavior is observed, which is inherently absent in the case of athermal individual monomers and is surprisingly richer than its 3D counterpart under bulk conditions. As a general trend, an isotropic to nematic transition is observed at sufficiently high surface coverages, which is followed by the establishment of the tetratic state, which in turn marks the onset of the random close packing. For chains with right-angle bonds, the incompatibility of the imposed bending angle with the neighbor geometry of the triangular crystal leads to a singular intra- and inter-polymer tiling pattern made of squares and triangles with optimal local filling at high surface concentrations. The present study could serve as a first step toward the design of hard colloidal polymers with a tunable structural behavior for 2D applications.

Molding Process Retaining Gold Nanoparticle Assembly Structures during Transfer to a Polycarbonate Surface.

The immobilization of gold nanoparticle (AuNP) linear surface assemblies on polycarbonate (PC) melt surface via molding is investigated. The order of the particle assemblies is preserved during the molding process. The assemblies on PC exhibit plasmonic coupling features and dichroic properties. The structure of the assemblies is quantified based on Scanning Electron Microscopy (SEM) and image analysis data using an orientational order parameter. The transfer process from mold to melt shows high structural fidelity. The order parameter of around 0.98 reflects the orientation of the lines and remains unaffected, independent of the injection direction of the melt relative to the particle lines. This is discussed in the frame of fountain flow during injection molding. The particles were permanently fixed and withstood the injection molding process, detachment of the substrate, and extraction in boiling ethanol. The plasmonic particles coupled strongly within the dense nanoparticle lines to produce anisotropic optical properties, as quantified by dichroic ratios of 0.28 and 0.52 using ultraviolet-visible-near-infrared (UV-Vis-NIR) spectroscopy. AuNP line assemblies on a polymer surface may be a basis for plasmonic devices like surface-enhanced Raman scattering (SERS) sensors or a precursor for nanowires. Their embedding via injection molding constitutes an important link between particle-self-assembly approaches for optically functional surfaces and polymer processing techniques.

Geometric phase analysis of magnetic skyrmion lattices in Lorentz transmission electron microscopy images

Magnetic skyrmions are quasi-particles with a swirling spin texture that form two-dimensional lattices. Skyrmion lattices can exhibit defects in response to geometric constraints, variations of temperature or applied magnetic fields. Measuring deformations in skyrmion lattices is important to understand the interplay between the lattice structure and external influences. Geometric phase analysis (GPA) is a Fourier-based image processing method that is used to measure deformation fields in high resolution transmission electron microscopy (TEM) images of crystalline materials. Here, we show that GPA can be applied quantitatively to Lorentz TEM images of two-dimensional skyrmion lattices obtained from a chiral magnet of FeGe. First, GPA is used to map deformation fields around a 5–7 dislocation and the results are compared with the linear theory of elasticity. Second, rotation angles between skyrmion crystal grains are measured and compared with angles calculated from the density of dislocations. Third, an orientational order parameter and the corresponding correlation function are calculated to describe the evolution of the disorder as a function of applied magnetic field. The influence of sources of artifacts such as geometric distortions and large defoci are also discussed.

Cholesteric liquid crystal phase variations within nanotubes: an in-depth analysis of the influences of twist radius and molecular pitch

ABSTRACT This study investigates the self-assembly and phase transitions of cholesteric liquid crystals (CLCs) when confined in nanotubes, specifically focusing on the variations in their molecular structures. A dissipative particle dynamics method was used to investigate how the changes in helix radius ( r LC ) and pitch ( P ) affect the behaviour of the LCs. For pitches of 24, 12, and 6, the orientation order parameter ( P 2 ) showed distinct trends during cooling. Smaller helix radii resulted in isotropic to nematic to smectic phase transitions, whereas larger radii resulted in a novel smectic phase with spiral structures (Sm s ). Circumferential local-order parameters ( P 2 r and P 2 z ) were introduced to better characterise the phases, and a disordered spiral-structure phase (Sm s 2 ) with local perturbations was observed. The transitions between isotropic, nematic, and smectic phases, highlighting the influence of the pitch and helix radius, were observed from the phase diagrams. Smaller pitches and radii prevented the formation of stable structures; however, specific combinations induced characteristic spiral structures in the smectic phase. These results provide new insights into the self-assembly of confined CLCs, which have potential applications in the design of photonic devices and LC-based sensors. This study advances our understanding of phase control in quasi-one-dimensional systems and highlights the importance of molecular variations in liquid crystal behaviour.

Emergent gauge symmetry in active Brownian matter.

We investigate a two-dimensional system of interacting active Brownian particles. Using the Martin-Siggia-Rose-Janssen-de Dominicis formalism, we built up the generating functional for correlation functions. We study in detail the hydrodynamic regime with a constant density stationary state. Our findings reveal that, within a small density fluctuations regime, an emergent U(1) gauge symmetry arises, originated from the conservation of fluid vorticity. Consequently, the interaction between the orientational order parameter and density fluctuations can be cast into a gauge theory, where the concept of "electric charge density" aligns with the local vorticity of the original fluid. We study in detail the case of a microscopic local two-body interaction. We show that, upon integrating out the gauge fields, the stationary states of the rotational degrees of freedom satisfy a nonlocal Frank free energy for a nematic fluid. We give explicit expressions for the splay and bend elastic constants as a function of the Péclet number (Pe) and the diffusion interaction constant (k_{d}).

A confined rod: mean field theory for hard rod-like particles

ABSTRACT In this paper, we model the configurations of a system of hard rods by viewing each rod in a cell formed by its neighbours. By minimising the free energy in the model and performing molecular dynamics, where, in both cases, the shape of the cell is a free parameter, we obtain the equilibrium orientational order parameter, free energy and pressure of the system. Our model enables the calculation of anisotropic stresses exerted on the walls of the cell due to shape change of the rod in photoisomerisation. These results are a key step towards understanding molecular shape change effects in photomechanical systems under illumination.

Neural network molecular dynamics study of LiGe2(PO4)3: Investigation of structure

Machine learning interatomic potential for LiGe2(PO4)3 in a form of a set of neural networks (DeePMD-model) was trained on DFT data. DFT simulations in GGA PBE approximation were performed for ordered and disordered LiGe2(PO4)3 supercell with 432 atoms which allowed the developed potential to describe crystalline, molten and glassy states. The developed DeePMD-potential was verified using literature and our experimental data demonstrating good agreement with it. Neural network molecular dynamic simulations indicate that P atoms have tetrahedral oxygen environment in both crystalline and glassy state. Coordination environment of Ge atoms is more complex. They have octahedral oxygen environment in crystalline state and mixed environment in glassy state: 4-, 5- and 6-coordinated Ge atoms were found. It was shown by calculation of orientational order parameters that in glassy LiGe2(PO4)3 4-coordinated Ge atoms have tetrahedral oxygen environment, while 6-coordinated Ge atoms have octahedral oxygen environment. Analysis of O-Ge-O angle distribution for 5-coordinated Ge atoms in glassy LiGe2(PO4)3 demonstrates that the environment of Ge atoms in this case is represented by various structures: square pyramids, trigonal bipyramids and transitional structures from 5-coordinated Ge atoms to tetrahedrons.

Optimization of the Domain Size in Stressed Liquid Crystals

The distributions of orientational and translational order parameters in liquid crystal polymer composites are studied using the methods of molecular-statistical physics. A model is considered in which the composite consists of liquid crystal (LC) domains separated by flat polymer sheets. The perturbation of the orientational and translational order parameters, which is caused by an arbitrary flat polymer sheet in a planar LC layer, is estimated. The effective distance over which this disturbance propagates is estimated. It is shown that it is proportional to the square root of the splay elastic constant of LC. It has been shown that in certain temperature ranges the polymer can induce a more ordered liquid crystal phase near itself (smectic phase inside of nematic phase and nematic phase – inside of isotropic liquid phase). In this case, the orientational order parameter of LC near the polymer can be significantly higher than far from it, and the “perturbation” of the order parameters can propagate over a distance of up to several micrometers with a sharp peak at a distance of the order of one micrometer. Based on the original theory, the methods have been proposed for optimizing the sizes of domains in stressed liquid crystals obtained by mechanical treatment in liquid crystal polymer composites.

Photosynthetically-powered phototactic active nematic liquid crystal fluids and gels

One of the most ancient forms of life dating to ~3.5 billion years ago, cyanobacteria are highly abundant organisms that convert light into energy and motion, often within conjoined filaments and larger colonies that attract a great deal of interest but their active nematic behavior remained unexplored. Here we demonstrate how light causes a spontaneous self-assembly of two- and three-dimensional active nematic states of cyanobacterial filaments, with a plethora of topological defects. We quantify light-controlled evolutions of orientational and velocity order parameters during the transition between disordered and orientationally ordered states of photosynthetic active matter, as well as the subsequent active nematic’s fluid-gel transformation. Patterned illumination and foreign inclusions with different shapes interact with cyanobacterial active nematics in nontrivial ways while inducing interfacial boundary conditions and fractional boojum defects. Our phototactic model system promises opportunities to systematically explore fundamental properties and technological utility of the liquid crystalline active matter.

Manifestation of the hexatic phase in confined two-dimensional systems with circular symmetry

Quasi-two-dimensional systems play an important role in the manufacture of various devices for the needs of nanoelectronics. Obviously, the functional efficiency of such systems depends on their structure, which can change during phase transitions under the influence of external conditions (for example, temperature). Until now, the main attention has been focused on the search for signals of phase transitions in continuous two-dimensional systems. One of the central issues is the analysis of the conditions for the nucleation of the hexatic phase in such systems, which is accompanied by the appearance of defects in the Wigner crystalline phase at a certain temperature. However, both practical and fundamental questions arise about the critical number of electrons at which the symmetry of the crystal lattice in the system under consideration will begin to break and, consequently, the nucleation of defects will start. The dependences of the orientational order parameter and the correlation function, which characterize topological phase transitions, as functions of the number of particles at zero temperature have been studied. The calculation results allows us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, 187, considered as an example.

Theoretical models for the nematic twist-bend phase and the Landau de Gennes theory of Longa and Tomczyk

ABSTRACT We present a critical analysis of the existing phenomenological theories of the nematic twist-bend phase including the models proposed by Dozov and Selinger and the more general Landau de Gennes theory of L. Longa and W. Tomczyk. The role of the flexoelectric polarisation is considered in detail as well as the stabilisation of the nanoscale helical structure of the twist-bend phase. In particular we focus into the mechanism of the reduction of the bend elastic constant determined by negative flexoelectric corrections and discuss why the splay elastic constant is not reduced at all. A molecular theory of elasticity of bent-core nematics, which also enables one to describe the reduction of the bend elastic constant, is considered in detail as well. Finally we consider two different tensor orientational order parameters of the twist-bend phase which describe all kinds of uniaxial and local biaxial ordering of bent-core molecules in the twist-bend phase.

A close look at the hydration layer and at the premelting layer of K-feldspar

In this work, we perform molecular dynamics simulations to investigate the structural properties of water at the interface with K-feldspar. We aim at understanding the modifications induced on water structure by the presence of this mineral. We analysed both the hydration layer of K-feldspar in supercooled water and the premelting layer at the interface between K-feldspar and hexagonal ice. We studied the density profile, the orientational tetrahedral order parameter, the distribution of the cos ⁡ ( γ ) function, the hydrogen bond distribution, the number of water molecules belonging to different phases close to the surface of the feldspar. We focused on the interplay between high-density water and low-density water to inquire on local modifications of water structure with respect to the bulk phase. We investigated four different pressures where the structure of bulk water spans from high-density liquid (locally more disordered) to low-density liquid (locally more ordered). The investigation showed that both the hydration and the premelting layers present a low-density liquid water component and similarities as a function of pressure with the corresponding bulk. We also find that the premelting layer shows structural features intermediate between the liquid and the crystalline state acting as a matching layer.

Deviation from the prediction of the Maier-Saupe theory of mixtures of charged discotic Gay-Berne and Lennard-Jones particles

ABSTRACT We report an analysis of the orientational order and orientational distribution functions of mixtures of discotic charged Gay-Berne (GB) and Lennard-Jones (LJ) particles as models of ionic liquid crystals and colloidal suspensions. We have studied three different stoichiometries (GB:LJ of 1:2, 1:1 and 2:1), with the opposite charges on the two particles selected to guarantee electroneutrality. We have found that for relatively low values of the scaled charge the dependence of the fourth-rank orientational order parameter, <P 4>, on the second-rank orientational order parameter, <P 2>, is in very good agreement with the prediction of the Maier-Saupe theory. In contrast, for relatively high values of the charge a deviation is observed which is in opposite directions for mixtures with an excess for GB particles and mixtures with an excess of LJ particles.

Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom

We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of the model and the associated closed set of equations of state involving four order parameters, proving the integrability and exact solvability of the model. The equations of state are specified via a suitable representation of the orientational order parameters, which imply two-order parameter reductions in the absence of external fields. A detailed exact analysis of the equations of state reveal a rich phase diagram where isotropic versus uniaxial versus biaxial phase transitions are explicitly described, including the existence of triple and tricritical points. Results on the discrete models are qualitatively consistent with their continuum analogue. This observation suggests that, in more general settings, discrete models may be used to capture and describe phenomena that also occur in the continuum for which exact equations of state in closed form are not available.

Chiral induction of helical mesophase by amphiphilic chlorin e6 derivatives and their metal complexes: Effect of chiral and achiral aliphatic chains

An experimental and theoretical study of structure and properties of chiral amphiphilic chlorin e6 13(N)-methylamide-15-methyl,17-alkyl esters (17-pentadecyl 1 and 17-phytyl 2) and their Ni complexes (Ni-1 and Ni-2) and their helical twisting efficiency in liquid crystal were carried out. Quantum chemical simulation of their structure was performed, the adequacy of which was established by comparing the calculated and experimental UV/Vis, CD, 1H and 13C NMR spectra as well as optical rotation angles. Low values of g-factors of dissymmetry for macroheterocycle (MHC) with the phytol substituent were experimentally revealed. The reason for this effect, associated with the transfer of the chirality from the stereogenic centers of the substituent to macrocyclic chromophore in the associate, was established by quantum-chemical calculation. Using polarization microscopy, the formation of chiral nematic phases was detected by doping a mixture of cyanobiphenyls with macroheterocycles 1, 2, Ni-1 and Ni-2. The values of the clearance temperature and helical pitch were measured, the slopes of phase diagrams β and helical twisting power (HTP) were calculated. The orientation order parameters of dopants in liquid crystal (LC) were determined by polarization spectroscopy. The dielectric properties of LC–MHC systems were studied within the chiral nematics and isotropic phases, and the values of the Kirkwood’s correlation factors were calculated. Using quantum chemical simulation of MHC solvates, the features of the influence of aliphatic chains structure and complex formation on the physical properties of induced mesophases were established.

Structures and energies of twist grain boundaries in Mg[formula omitted]SiO4 forsterite

In this work, we investigate twist grain boundary (GB) energies and structures in Mg2SiO4 forsterite using atomistic simulations. We first present a new bond orientational order parameter allowing to highlight disordered regions in this low-symmetry crystal for which classical visualization tools are ineffective. Then we examine three GB planes, (010), (120) and (001), corresponding to the most favorable free surfaces of this crystal. We show that twist GB follow the same energy ordering as corresponding free surfaces. In addition, except for some misorientation angles and for the (120) GB plane, GB energies and structures are quite insensitive to microscopic translational degrees of freedom. The dislocation composition of low-angle twist GB can be related to γ-surfaces in the corresponding planes, and are in good agreement with first-principle calculations. It is also shown that the dislocation core structures in low angle twist GB can strongly differ from the ones of intracrystalline dislocations.

Study of the positional and orientational contributions to the Helmholtz free energy of a finite hard-disk system. A molecular dynamics analysis of its hexatic transition

Based on an equilibrium thermodynamic scheme, this work studies the separation of the Helmholtz free energy of a hard-disk system into its positional and orientational contributions. For the positional part, an accurate two dimensional version of the Carnahan-Starling equation of state is proposed, while a simple ansatz of the one particle partition function for the orientational part is proposed. The latter expression, which contains information about the probability of the norm of the six-fold orientational order parameter, is obtained through molecular dynamics simulations. Perhaps due to finite size effects, the ordering of the fluid is not a sudden phenomenon: the fluid-hexatic phase transition is preceded by a linear increase in the orientational contribution to the pressure of the fluid. A similar result is obtained for the hexatic-solid phase transition. Thus, the hexatic first-order phase transition is located between two linear ordering processes, consistent with the KTHNY theory. The proposed separation also predicts the existence of first order fluid-hexatic phase transition by using two procedures: the first, based on a purely bimodal probability density function, produces a pressure with a van del Waals-like first-order phase transition, while the second, considering density fluctuations, results in a flattened pressure phase transition.

Peptoid-based macrodiscs of variable lipid composition for structural studies of membrane proteins by oriented-sample solid-state NMR

Solid-state Nuclear Magnetic Resonance (NMR) in combination with magnetically aligned discoidal lipid mimics allows for studying the conformations of membrane proteins in planar, lipid-rich bilayer environments and at the physiological temperature. We have recently demonstrated the general applicability of macrodiscs composed of DMPC lipids and peptoid belts, which yield magnetic alignment and NMR spectroscopic resolution comparable or superior to detergent-containing bicelles. Here we report on a considerable improvement in the magnetic alignment and NMR resolution of peptoid-based macrodiscs consisting of a mixture of the zwitterionic and negatively charged lipids (DMPC/DMPG at the 85% to 15% molar ratio). The resulting linewidths are about 30% sharper due to the higher orientational order parameter likely arising from the stabilizing electrostatic repulsion between the discs. Moreover, highly aligned, detergent-free macrodiscs can be formed with a longer-chain lipid, DPPC. Interestingly, the spectra of Pf1 in the two lipid mimetics are almost indistinguishable, which would mean that the overall transmembrane helix tilt might be governed not only by the hydrophobic matching but also possibly by the interactions of the flanking lysine and arginine residues at the membrane interface.

Novel properties of high-performance multi-component mixture for Vertically Aligned mode LCDs

ABSTRACT Vertically Aligned mode Liquid Crystal Displays (VALCDs) which have generated huge research interest due to their excellent contrast and wide viewing angle require materials with negative dielectric anisotropy. This work highlights the systematic development of a fifteen-component mixture from pure liquid crystalline compounds comprising laterally fluorinated bi-, tri- phenyl, tolane, bicyclohexane compounds and non-mesogenic compounds exhibiting negative dielectric anisotropy. The temperature dependence of birefringence (Δn), dielectric anisotropy (Δε), threshold voltage (Vth), bend elastic constant (K33), relaxation time (τ0) and rotational viscosity (γ1) as a function of temperature of this fifteen-component nematic mixture have been reported. This mixture exhibits a high Figure of Merit (FoM) which is desirable for reducing the device response time. Additionally, the orientational order parameter (OOP) values, activation energy (Ea), visco-elastic co-efficient (γ1/K33) and material parameters (A 0 ) have also been reported. The effect of pretilt angle in the alignment layers on the threshold voltage (Vth) and switching time (τ0) to ascertain the applicability of this material in Vertically Aligned mode Liquid Crystal Displays (VALCDs) have also been discussed.

Influence of the dispersed silver nanoparticles size and concentration on the properties of 6CB nematic

ABSTRACT We study the effects of concentration and size of the doped silver nanoparticles on material properties of 6CB nematic: 4-hexyl-4’-cyanobiphenyl using electrical, dielectric measurements along with the polarising microscopy methods. We show that the dispersed NPs do not affect the nematic-isotropic liquid transition temperature. We report that the doped NPs decrease the dielectric anisotropy, elasticity and viscosity of the material. We attribute this behaviour to the fact that the dispersed NPs lower the orientational order parameter of the nematic. However, the threshold voltage stays almost unaffected by the doped NPs and the switching-off time is decreased only at certain NPs concentration. Using our measured data, we test the validity of the predicted by the classical Maier-Saupe theory, linear dependence of the elasticity vs the square root of the order parameter. We show that while for the pure sample the mentioned dependence follows the classical prediction, the dispersed samples elasticity shows anomalous behaviour. We report that the mentioned dependence predicted by Gelbart-Ben Shaul theory fits well with the doped samples measured data.