In Silico Measurement of Elastic Moduli of Nematic Liquid Crystals

Atomistic analysis of nematic phase transition in 4-cyano-4'-n-alkyl biphenyl liquid crystals: Sampling for the first-order phase transition and the free-energy decomposition

Molecular dynamics simulations were conducted using the generalized replica exchange method (gREM) on the 4-cyano-4'-n-alkyl biphenyl (nCB) system with n = 5, 6, 7, and 8, which exhibits a nematic-isotropic (NI) phase transition. Sampling near the phase transition temperature in systems undergoing first-order phase transitions, such as the NI phase transition, is demanding due to the substantial energy gap between the two phases. To address this, gREM, specifically designed for first-order phase transitions, was utilized to enhance sampling near the NI phase transition temperature. Free-energy calculations based on the energy representation (ER) theory were employed to characterize the NI phase transition. ER evaluates the insertion free energy of the nCB molecule for both nematic and isotropic phases, revealing a change in the temperature dependence across the NI phase transition. Further decomposition into energetic and entropic terms quantitatively shows the balance between these contributions at the NI phase transition temperature.

Improving Machine Learned Force Fields for Complex Fluids through Enhanced Sampling: A Liquid Crystal Case Study

Machine learned force fields offer the potential for faster execution times while retaining the accuracy of traditional DFT calculations, making them promising candidates for molecular simulations in cases where reliable classical force fields are not available. Some of the challenges associated with machine learned force fields include simulation stability over extended periods of time and ensuring that the statistical and dynamical properties of the underlying simulated systems are correctly captured. In this work, we propose a systematic training pipeline for such force fields that leads to improved model quality, compared to that achieved by traditional data generation and training approaches. That pipeline relies on the use of enhanced sampling techniques, and it is demonstrated here in the context of a liquid crystal, which exemplifies many of the challenges that are encountered in fluids and materials with complex free energy landscapes. Our results indicate that, whereas the majority of traditional machine learned force field training approaches lead to molecular dynamics simulations that are only stable over hundred-picosecond trajectories, our approach allows for stable simulations over tens of nanoseconds for organic molecular systems comprising thousands of atoms.

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.

Structures, thermodynamics and dynamics of topological defects in Gay-Berne nematic liquid crystals

Topological defects are a ubiquitous phenomenon across different physical systems. A better understanding of defects can be helpful in elucidating the physical behaviors of many real materials systems. In nematic liquid crystals, defects exhibit unique optical signatures and can segregate impurities, showing their promise as molecular carriers and nano-reactors. Continuum theory and simulations have been successfully applied to link static and dynamical behaviors of topological defects to the material constants of the underlying nematic. However, further evidence and molecular details are still lacking. Here we perform molecular dynamics simulations of Gay-Berne particles, a model nematic, to examine the molecular structures and dynamics of +1/2 defects in a thin-film nematic. Specifically, we measure the bend-to-splay ratio K₃/K₁ using two independent, indirect measurements, showing good agreement. Next, we study the annihilation event of a pair of ±1/2 defects, of which the trajectories are consistent with experiments and hydrodynamic simulations. We further examine the thermodynamics of defect annihilation in an NVE ensemble, leading us to correctly estimate the elastic modulus by using the energy conservation law. Finally, we explore effects of defect annihilation in regions of nonuniform temperature within these coarse-grained molecular models which cannot be analysed by existing continuum level simulations. We find that +1/2 defects tend to move toward hotter areas and their change of speed in a temperature gradient can be quantitatively understood through a term derived from the temperature dependence of the elastic modulus. As such, our work has provided molecular insights into structures and dynamics of topological defects, presented unique and accessible methods to measure elastic constants by inspecting defects, and proposed an alternative control parameter of defects using temperature gradient.

Simulating the nematic-isotropic phase transition of liquid crystal model via generalized replica-exchange method

The nematic-isotropic (NI) phase transition of 4-cyano-4'-pentylbiphenyl was simulated using the generalized replica-exchange method (gREM) based on molecular dynamics simulations. The effective temperature is introduced in the gREM, allowing for the enhanced sampling of configurations in the unstable region, which is intrinsic to the first-order phase transition. The sampling performance was analyzed with different system sizes and compared with that of the temperature replica-exchange method (tREM). It was observed that gREM is capable of sampling configurations at sufficient replica-exchange acceptance ratios even around the NI transition temperature. A bimodal distribution of the order parameter at the transition region was found, which is in agreement with the mean-field theory. In contrast, tREM is ineffective around the transition temperature owing to the potential energy gap between the nematic and isotropic phases.

Impurity-induced nematic-isotropic transition of liquid crystals

Complex fluids made of liquid crystals (LCs) and small molecules, surfactants, nanoparticles or 1D/2D nanomaterials show novel and interesting features, making them suitable materials for various applications starting from optoelectronics to biosensing. While these additives (impurities) introduce new features in the complex fluids, they may also alter the phase transition behaviour of LCs depending on the physiochemical properties of the added impurity. This article reports on the phase transition of 4-cyano-4'-alkylbiphenyl (nCB) LCs in the presence of an associative impurity, i.e., water and a non-associative impurity, i.e., hexane employing computational methods and experiments. In particular, all-atom (AA) simulations and coarse-grained (CG) models were designed for two complex systems, i.e., 6CB + water and 6CB + hexane and corresponding spectrophotometry experiments were performed using a homologous LC, i.e., 5CB. Results from the simulations and experiments elucidate that the phase transition of LCs depends on the mixing/demixing phenomenon of the impurity in the LC. While associative liquids like water which do not mix with LCs do not influence the nematic-to-isotropic phase transition of LCs, hexane, being a non-associative liquid, mixes well with LCs and induces a sharp impurity-induced nematic-to-isotropic phase transition. Upon application of both AA and CG simulations, we could reach the conclusion that the mixing/demixing phenomenon in an LC + impurity system influences the entropy of the system and hence the observed phase transitions are entropy-driven.

Programming emergent symmetries with saddle-splay elasticity

The director field adopted by a confined liquid crystal is controlled by a balance between the externally imposed interactions and the liquid's internal orientational elasticity. While the latter is usually considered to resist all deformations, liquid crystals actually have an intrinsic propensity to adopt saddle-splay arrangements, characterised by the elastic constant [Formula: see text]. In most realisations, dominant surface anchoring treatments suppress such deformations, rendering [Formula: see text] immeasurable. Here we identify regimes where more subtle, patterned surfaces enable saddle-splay effects to be both observed and exploited. Utilising theory and continuum calculations, we determine experimental regimes where generic, achiral liquid crystals exhibit spontaneously broken surface symmetries. These provide a new route to measuring [Formula: see text]. We further demonstrate a multistable device in which weak, but directional, fields switch between saddle-splay-motivated, spontaneously-polar surface states. Generalising beyond simple confinement, our highly scalable approach offers exciting opportunities for low-field, fast-switching optoelectronic devices which go beyond current technologies.

Novel elastic response in twist-bend nematic models

Bent-shaped liquid crystals have attracted significant attention recently due to their novel mesostructure and the intriguing behavior of their elastic constants, which are strongly anisotropic and have an unusual temperature dependence. Though theories explain the onset of the twist-bend nematic phase (NTB) through spontaneous symmetry breaking concomitant with transition to a negative bend (K3) elastic constant, this has not been observed as yet in experiments. There, the small bend elastic constant has a strongly non-monotonic temperature dependence, which first increases after crossing the isotropic (I)-nematic (N) transition, then dips near the nematic (N)-twist-bend (NTB) transition before it increases again as the transition is crossed. The molecular mechanisms responsible for this exotic behavior are unclear. Here, we utilize density of states algorithms in Monte Carlo simulation applied to a variant of the Lebwohl-Lasher model which includes bent-shaped-like interactions to analyze the mechanism behind elastic response in this novel mesostructure and understand the temperature dependence of its Frank-Oseen elastic constants.

Nematic order in solutions of semiflexible polymers: Hairpins, elastic constants, and the nematic-smectic transition

Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent bead-spring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the director is well described by a Gaussian, irrespective of whether the chains are rod-like or rather flexible. However, the related concept of "deflection length" is shown to make sense only in the latter case for rather dilute solutions since otherwise the deflection length is of the order of about two bond lengths only. When the solution is semi-dilute, a substantial renormalization of the persistence length occurs, while this effect is absent in the isotropic phase even at rather high monomer densities. The effective radii of the "tubes" confining the chains in the related description of orientational ordering are significantly larger than the distances between neighboring chains, providing evidence for a pronounced collective character of orientational fluctuations. Hairpins can be identified close to the isotropic-nematic transition, and their probability of occurrence agrees qualitatively with the Vroege-Odijk theory. The corresponding theoretical predictions for the elastic constants, however, are not in good agreement with the simulations. We attribute the shortcomings of the theories to their neglect of the coupling between local density and orientational fluctuations. Finally, we detected for this model a transition to a smectic phase for reduced monomer densities near 0.7.

Self-assembly of semiflexible polymers confined to thin spherical shells

Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to elucidate the nature of orientational ordering in different parameter regimes. Previous simulations have revealed the emergence of bipolar and quadrupolar topological defects on the surface when the entire cavity was filled with a concentrated polymer solution [Phys. Rev. Lett., 2017, 118, 217803]. In contrast, spherical shell confinement restricts the appearance of a bipolar order. Instead, only the extent of the quadrupolar order changes with chain stiffness, as evidenced by the relative motion of topological defects. In the case of monolayers, we observe a nematic to smectic transition accompanied by a change in the nematic grain-size distribution as the contour length was decreased.