Helicoidal dynamics of biaxial curved rods in twist-bend nematic phases unveiled by unsupervised machine learning techniques

Texture identification in liquid crystal-protein droplets using evaporative drying, generalized additive modeling, and K-means Clustering

Sessile drying droplets manifest distinct morphological patterns, encompassing diverse systems, viz., DNA, proteins, blood, and protein-liquid crystal (LC) complexes. This study employs an integrated methodology that combines drying droplet, image texture analysis (features from First Order Statistics, Gray Level Co-occurrence Matrix, Gray Level Run Length Matrix, Gray Level Size Zone Matrix, and Gray Level Dependence Matrix), and statistical data analysis (Generalized Additive Modeling and K-means clustering). It provides a comprehensive qualitative and quantitative exploration by examining LC-protein droplets at varying initial phosphate buffered concentrations (0x, 0.25x, 0.5x, 0.75x, and 1x) during the drying process under optical microscopy with crossed polarizing configuration. Notably, it unveils distinct LC-protein textures across three drying stages: initial, middle, and final. The Generalized Additive Modeling (GAM) reveals that all the features significantly contribute to differentiating LC-protein droplets. Integrating the K-means clustering method with GAM analysis elucidates how textures evolve through the three drying stages compared to the entire drying process. Notably, the final drying stage stands out with well-defined, non-overlapping clusters, supporting the visual observations of unique LC textures. Furthermore, this paper contributes valuable insights, showcasing the efficacy of drying droplets as a rapid and straightforward tool for characterizing and classifying dynamic LC textures.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

Active microrheology of colloidal suspensions of hard cuboids

By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.

All-atom simulations of bent liquid crystal dimers: the twist-bend nematic phase and insights into conformational chirality

The liquid crystal dimer 1,7-bis-4-(4'-cyanobiphenyl)heptane (CB7CB) is known to exhibit a nematic-nematic phase transition, with the lower temperature phase identified as the twist-bend nematic (N_TB) phase. Despite the achiral nature of the mesogen, the N_TB phase demonstrates emergent chirality through the spontaneous formation of a helical structure. We present extensive molecular dynamics simulations of CB7CB using an all-atom force field. The N_TB phase is observed in this model and, upon heating, shows phase transitions into the nematic (N) and isotropic phases. The simulated N_TB phase returns a pitch of 8.35 nm and a conical tilt angle of 29°. Analysis of the bend angle between the mesogenic units reveals an average angle of 127°, which is invariant to the simulated phase. We have calculated distributions of the chirality order parameter, χ, for the ensemble of conformers in the N_TB and N phases. These distributions elucidate that CB7CB is statistically achiral but can adopt chiral conformers with no preference for a specific handedness. Furthermore, there is no change in the extent of conformational chirality between the N_TB and N phases. Using single-molecule stochastic dynamics simulations in the gas phase, we study the dimer series CBnCB (where n = 6, 7, 8 or 9) and CBX(CH₂)₅YCB (where X/Y = CH₂, O or S) in terms of the bend angle and conformational chirality. We confirm that the bent molecular shape determines the ability of a dimer to exhibit the N_TB phase rather than its potential to assume chiral conformers; as |χ|_max increases with the spacer length, but the even-membered dimers have a linear shape in contrast to the bent nature of dimers with spacers of odd parity. For CBX(CH₂)₅YCB, it is found that |χ|_max increases as the bend angle of the dimer decreases, while the flexibility of the dimers remains unchanged through the series.

Long-time relaxation dynamics in nematic and smectic liquid crystals of soft repulsive colloidal rods

Understanding the relaxation dynamics of colloidal suspensions is crucial to identifying the elements that influence the mobility of their constituents, assessing their macroscopic response across the relevant time and length scales, and thus disclosing the fundamentals underpinning their exploitation in formulation engineering. In this work, we specifically assess the impact of long-ranged ordering on the relaxation dynamics of suspensions of soft repulsive rodlike particles, which are able to self-organize into nematic and smectic liquid-crystalline phases. Rods are modeled as soft repulsive spherocylinders with a length-to-diameter ratio L^{★}=5, interacting via the truncated and shifted Kihara potential. By performing dynamic Monte Carlo simulations, we analyze the effect of translational and orientational order on the diffusion of the rods along the relevant directions imposed by the morphology of the background phases. To provide a clear picture of the resulting dynamics, we assess its dependence on temperature, which can dramatically determine the response time of the system relaxation and the self-diffusion coefficients of the rods. The computation of the van Hove correlation functions allows us to identify the existence of rods that diffuse significantly faster than the average and whose concentration can be accurately adjusted by a suitable choice of temperature.

Re-entrant transition as a bridge of broken ergodicity in confined monolayers of hexagonal prisms and cylinders

The entropy-driven monolayer assembly of hexagonal prisms and cylinders was studied under hard slit confinement. At the conditions investigated, the particles have two distinct and dynamically disconnected rotational states: unflipped and flipped, depending on whether their circular/hexagonal face is parallel or perpendicular to the wall plane. Importantly, these two rotational states cast distinct projection areas over the wall plane that favor either hexagonal or tetragonal packing. Monte Carlo simulations revealed a re-entrant melting transition where an intervening disordered Flipped-Unflipped (FUN) phase is sandwiched between a fourfold tetratic phase at high concentrations and a sixfold triangular solid at intermediate concentrations. The FUN phase contains a mixture of flipped and unflipped particles and is translationally and orientationally disordered. Complementary experiments were conducted with photolithographically fabricated cylindrical microparticles confined in a wedge cell. Both simulations and experiments show the formation of phases with comparable fraction of flipped particles and structure, i.e., the FUN phase, triangular solid, and tetratic phase, indicating that both approaches sample analogous basins of particle-orientation phase-space. The phase behavior of hexagonal prisms in a soft-repulsive wall model was also investigated to exemplify how tunable particle-wall interactions can provide an experimentally viable strategy to dynamically bridge the flipped and unflipped states.

Unsupervised learning of sequence-specific aggregation behavior for a model copolymer

We apply a recently developed unsupervised machine learning scheme for local environments [Reinhart, Comput. Mater. Sci., 2021, 196, 110511] to characterize large-scale, disordered aggregates formed by sequence-defined macromolecules. This method provides new insight into the structure of these disordered, dilute aggregates, which has proven difficult to understand using collective variables manually derived from expert knowledge [Statt et al., J. Chem. Phys., 2020, 152, 075101]. In contrast to such conventional order parameters, we are able to classify the global aggregate structure directly using descriptions of the local environments. The resulting characterization provides a deeper understanding of the range of possible self-assembled structures and their relationships to each other. We also provide detailed analysis of the effects of finite system size, stochasticity, and kinetics of these aggregates based on the learned collective variables. Interestingly, we find that the spatiotemporal evolution of systems in the learned latent space is smooth and continuous, despite being derived from only a single snapshot from each of about 1000 monomer sequences. These results demonstrate the insight which can be gained by applying unsupervised machine learning to soft matter systems, especially when suitable order parameters are not known.

Microrheology of colloidal suspensions via dynamic Monte Carlo simulations

Understanding the rheology of colloidal suspensions is crucial in the formulation of a wide selection of industry-relevant products, such as paints, foods and inks. To characterise the viscoelastic behaviour of these soft materials, one can analyse the microscopic dynamics of colloidal tracers diffusing through the host fluid and generating local deformations and stresses. This technique, referred to as microrheology, links the bulk rheology of fluids to the microscopic dynamics at the particle scale. If tracers are subjected to external forces, rather than freely diffusing, it is called active microrheology. Motivated by the impact of microrheology in providing information on local structure in complex systems such as colloidal glasses, active matter or biological systems, we have extended the dynamic Monte Carlo (DMC) technique to investigate active microrheology in colloidal suspensions. The original DMC theoretical framework, able to accurately describe the Brownian dynamics of colloids at equilibrium, is here reconsidered and expanded to describe the effects of an external force pulling a tracer embedded in isotropic colloidal suspensions at different densities. To this end, we studied the dynamics of a spherical tracer dragged by a constant external force through a bath of spherical and rod-like particles of comparable size. We could extract valuable details on its effective friction coefficient, being constant at small and large values of the external force, but otherwise displaying a nonlinear behaviour that indicates the occurrence of a force-thinning regime. Our DMC simulation results are in excellent quantitative agreement with past Langevin dynamics simulations and theoretical works for the bath of spherical colloids. The bath of rod-like particles is studied in the isotropic phase, and displays an example where DMC is more convenient than Brownian or Langevin dynamics, in this case, in dealing with particle rotation.