Modulated nematic structures induced by chirality and steric polarization

What kind of one-dimensional modulated nematic structures (ODMNS) can form nonchiral and chiral bent-core and dimeric materials? Here, using Landau-deGennes theory of nematics, extended to account for molecular steric polarization, we study a possibility of formation of ODMNS, both in nonchiral and intrinsically chiral liquid crystalline materials. Besides nematic and cholesteric phases, we find four bulk ODMNS for nonchiral materials, two of which have not been reported so far. These new structures are longitudinal ($N_{LP}$) and transverse ($N_{TP}$) periodic waves where the polarization field being periodic in one dimension stays parallel and perpendicular, respectively, to the wave vector. The other two phases have all characteristic features of the twist-bend nematic phase ($N_{TB}$) and the splay-bend nematic phase ($N_{SB}$), but their fine structure appears more complex than that considered so far. The presence of molecular chirality converts nonchiral $N_{TP}$ and $N_{SB}$ into new $N_{TB}$ phases. Interestingly, the nonchiral $N_{LP}$ phase can stay stable even in the presence of intrinsic molecular chirality. Exemplary phase diagrams provide further insights into the relative stability of these new modulated nematic structures.Comment: 5 pages, 5 figure

Noise-induced synchronization in the Fahy-Hamann model

We study the noise-induced synchronization in a system of particles moving in Fahy–Hamann potential [S. Fahy, D.R. Hamann,Phys.Rev.Lett. 69, 761 (1992)] and subjected to generalized Langevin forces. We investi- gate the synchronization dependence on system’s parameters and on mem- ory range. The results show that while in general memory acts against synchronization, for intermediate memory ranges the opposite effect can be observed. Generally the synchronization transition is found to depend on memory range, temperature and dissipation in the system. PAC

Synchronization of Kuramoto oscillators with distance-dependent delay

We investigate the synchronization process in a Kuramoto model of phase-coupled oscillators with distance-dependent delay. The oscillators occupy the nodes of a two-dimensional square lattice subjected to periodic boundary conditions. The mean-field interactions with velocity-dependent delays propagate along the lattice sites. This gives rise to a non-uniform distribution of delays and lattice dimensionality dependence, which is not present in mean-field models without delays. We find that the 'coupling strength-delay' phase diagram does not show up reentrant behavior present in models with uniform delay. A number of dynamic patterns, reported earlier for a generalized Kuramoto model with non-mean-field distance-dependent interactions, is also found

Ambidextrous chiral domains in nonchiral liquid-crystalline materials

Recently, we studied equilibrium properties of the Lebwohl–Lasher model with quadrupolar and octupolar interactions in the large twist limit. A complete mean field analysis of the model and Monte Carlo simulations were presented to show a global stabilization of new structures like tetrahedratic, nematic tetrahedratic, and chiral nematic tetrahedratic phases of Td, D2d, and D2 symmetry, respectively. Here, by means of Monte Carlo simulation on two-dimensional system, we show that the model can also give a molecular interpretation of macroscopic regions with opposite optical activity (ambidextrous chirality), observed in achiral bent-core systems, and recently in ferrocenomesogens and flexible liquid crystal dimers. The resulting superstructures include short- and long-range twist deformations

Molecular dynamics simulation of the Lennard-Jones polymers in a good solvent

We carried out united-atom Langevin dynamics simulations of poly- mer’s equilibrium state in a good solvent. Our primary goal was a pedagog- ical exposition of fundamental equilibrium properties of isolated polymers in dilutions with amodel that containsmany features of realmaterials. The polymer was chosen to be a three-dimensional chain of N identical beads (monomers) without internal structure. Each monomer interacted with its two neighbors by a harmonic potential, which modeled a chemical bond. Additionally all monomers within a chain were assumed to interact through the Lennard–Jones (LJ) potential. Interaction with solvent and with other polymers was introduced using Langevin forces. Analyzing internal energy per polymer and radius of gyration as function of temperature we observed a rapid globule to coil phase transition. Also we studied elastic properties of single polymer chain for temperatures below the transition and identified three regions with different elastic behavior. Typical chain lengths in our simulations ranged from 100 to 1000 monomers. The elaborated software package can easily be modified to study e.g. the effect of polymer stiffness on thermodynamic behavior

Nematic twist--bend phase in an external field

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 Landau--de Gennes theory we find that for compounds with positive anisotropy the helix unwinds to a polar uniaxial nematic, however negative material anisotropy gives rise to a rich sequence of new nematic phases obtained via mechanism of flattening the conical spiral

Phases with splay modulation in a system of hard wedges composed of balls

We studied equilibrium systems composed of wedge-shaped monodisperse molecules using hard-particle Monte Carlo simulations. Each model molecule was built of six co-linear tangent spheres of linearly decreasing diameters. Thus, the shape was unequivocally described by a single parameter $d$: the ratio of the smallest and largest sphere diameters. The phases of the systems were analyzed as a function of $d$ and packing density $\eta$. As interactions were purely of the excluded-volume type, the emergent phases were governed solely by the configurational entropy. For $\eta < 0.5$, apart from the isotropic liquid, we observed standard nematic and smectic A liquid crystalline phases. For $\eta > 0.5$, however, apart from ordinary non-polar hexagonal crystal, two new frustrated polar crystalline phases with splay modulation appeared: antiferroelectric splay crystal ($\text{Cr}_\text{S}\text{P}_\text{A}$) and ferroelectric splay crystal ($\text{Cr}_\text{S}\text{P}_\text{F}$). All configurations were studied in terms of nematic, smectic, and hexatic order parameters, as well as the radial distribution function and the polarization correlation function

Stability of Biaxial Nematic Phase for Systems with Variable Molecular Shape Anisotropy

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean field model of Mulder and Ruijgrok [Physica A {\bf 113}, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems - a mixture of potassium laurate, 1-decanol, and $D_2O$, where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimeric- or tetrapod-like molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, the stability of the biaxial nematic phase can be either enhanced or depressed, relative to the uniaxial nematic phases. In the former case the splitting of the Landau point into two triple points with a direct phase transition line from isotropic to biaxial phase is observed.Comment: 18 pages containing 6 figure