Adaptive plasticity of auxetic Kirigami hydrogel fabricated from anisotropic swelling of cellulose nanofiber film.

Hydrogels are flexible materials that typically accommodate elongation with positive Poisson's ratios. Auxetic property, i.e., the negative Poisson's ratio, of elastic materials can be macroscopically implemented by the structural design of the continuum. We realize it without mold for hydrogel made of cellulose nanofibers (CNFs). The complex structural design of auxetic Kirigami is first implemented on the dry CNF film, i.e., so-called nanopaper, by laser processing, and the CNF hydrogel is formed by dipping the film in liquid water. The CNF films show anisotropic swelling where drastic volumetric change mainly originates from increase in the thickness. This anisotropy makes the design and fabrication of the emergent Kirigami hydrogel straightforward. We characterize the flexibility of this mechanical metamaterial made of hydrogel by cyclic tensile loading starting from the initial end-to-end distance of dry sample. The tensile load at the maximum strain decreases with the increasing number of cycles. Furthermore, the necessary work up to the maximum strain even decreases to the negative value, while the work of restoration to the original end-to-end distance increases from the negative value to the positive. The equilibrium strain where the force changes the sign increases to reach a plateau. This plastic deformation due to the cyclic loading can be regarded as the adaptive response without fracture to the applied dynamic loading input.

Highly anisotropic swelling-based gelation of dry film of cellulose nanofibers enables development of emergent hydrogel Kirigami with auxetic behavior. Furthermore, adaptive response to the iterative loading condition is found.

Analytical model of critical buckling transition for smectic liquid crystal based on the viscoelastic scaling of coarse-grained molecular dynamics.

The buckling transition of smectic liquid crystals (LCs) is important not only as fundamental physics but also for the rational design of devices to make use of their optical and mechanical properties. However, there exists a huge gap between the specific knowledge and universal analytical formulation. We have conducted coarse-grained molecular dynamics (CGMD) simulations with the force field optimized for the description of buckling phenomena including topological defects to link the molecular nature and continuum formulation. The simulations reveal the viscoelastic characteristics where the critical strain and the compression modulus highly depend on the strain rate as well as the number of layers. Therefore, we formulate the scaling model whose coupling constants depend on both strain rate and domain size. The model reproduces the CGMD results as well as experimental and theoretical values in existing literature. Furthermore, we elucidate from this model that the critical buckling behavior is determined by the competition between the suppression of compression-induced flow and the undulation fluctuation of layers. The framework consisting of the CGMD simulation and the scaling model enables us to estimate the buckling characteristics of smectic LCs reflecting their molecular structures in a wide range from the low-frequency regime that can be verified by experiments to the high-frequency regime beyond the reach of it.

Swelling-based gelation of wet cellulose nanopaper evaluated by single particle tracking.

Nanopapers fabricated from cellulose nanofibers (CNFs) drastically swell to form hydrogels when they are in contact with water. This gelation makes contrast with conventional papers that simply deform without drastic volume increase. While the volume increase is qualitatively obvious from the macroscopic visual inspection, its quantitative understanding is nontrivial because of the difficulty in the detection of the boundary between the nanopaper hydrogel and the residual or extra water. In this study, we use single particle tracking (SPT) to reveal the swelling-based gelation phenomenon of cellulose nanopapers. The diffusive dynamics of probe particles uncovers the transient process of swelling, and equilibrium analysis reveals the dependence of volume increase fundamentally dependent on the amount of water to be in contact with the nanopapers. Comparison with the aqueous CNF dispersion without drying reveals the difference in the texture of the nanopaper hydrogels from them.

Resilient Mechanical Metamaterial Based on Cellulose Nanopaper with Kirigami Structure.

Nanopapers fabricated from cellulose nanofibers (CNFs) are flexible for bending while they are rather stiff against stretching, which is a common feature shared by conventional paper-based materials in contrast with typical elastomers. Cellulose nanopapers have therefore been expected to be adopted in flexible device applications, but their lack of stretching flexibility can be a bottleneck for specific situations. The high stretching flexibility of nanopapers can effectively be realized by the implementation of Kirigami structures, but there has never been discussion on the mechanical resilience where stretching is not a single event. In this study, we experimentally revealed the mechanical resilience of nanopapers implemented with Kirigami structures for stretching flexibility by iterative tensile tests with large strains. Although the residual strains are found to increase with larger maximum strains and a larger number of stretching cycles, the high mechanical resilience was also confirmed, as expected for moderate maximum strains. Furthermore, we also showed that the round edges of cut patterns instead of bare sharp ones significantly improve the mechanical resilience for harsh stretching conditions. Thus, the design principle of relaxing the stress focusing is not only important in circumventing fractures but also in realizing mechanical resilience.

Derivation of coarse-grained force fields for buckling-induced topological defects of liquid crystals.

Microscopic details of buckling-induced topological defects are required for molecular design of smectic liquid crystals to control buckling instability of the layers. In this study, we present a multiobjective optimization method to derive the coarse-grained (CG) force fields with sufficiently precise buckling characteristics including the molecular details for molecular dynamics (MD) simulations. We perform CGMD simulations of buckling deformation at sample points in the CG force field parameter space, from which the response surfaces of objective functions such as the scalar orientational order parameters, critical angles of layer collapse, and radial distribution functions are estimated. Since not all objective functions can be optimized simultaneously, we use a genetic algorithm to calculate the Pareto set of optimal solutions. We select the models with different molecular head-tail symmetries to study buckling deformation. The extracted CG model successfully reproduces the buckling deformation in terms of the collapse of smectic layers through the generation of dislocations with dipole disclinations. We also find that the molecular symmetry is a dominant factor to control the class of the buckling-induced dislocations.

Partial structural order of gel-forming material detected as multimodal subdiffusion by logarithmic measure.

Fibrous nanomaterials suspended in liquid form gel structures when the binding sites between the components reach sufficient number densities. Cellulose nanofibers (CNFs) are one of such nanomaterials, and transparent papers are fabricated by drying their aqueous dispersions. It is therefore important to characterize the wet state, but the specific fluorescent marker molecules are not available for arbitrary CNFs. We report an approach based on the single particle tracking of Brownian probe particles. We focus on the nonuniformity in the Brownian motion to detect the partial structural order between sol and gel, which is nontrivial to characterize. The simple logarithmic measure of diffusive behavior reveals the multimodal nature of Brownian motion depending on the CNF concentration. The subdiffusive behavior by the overall mean squared displacements alone does not tell whether it is caused by confinement in the local environment by CNFs, or binding to single CNFs possibly diffusing in the dispersion. However, the particle-size dependence clarifies that it is not caused by binding but the confinement effect. Furthermore, the logarithmic measure approach enables the detection of overlapping distributions through their heads rather than tails. The detection of partial structural order by rheological non-uniformity of the system with a simple approach will contribute to the further understanding of gel forming materials in general.

Spatio-temporally controlled suppression of the coffee-ring phenomenon by cellulose nanofibers.

Sessile droplets of colloidal dispersions tend to exhibit the coffee-ring phenomenon in the drying process. The suspended particles are transported especially at the final stage of the drying process, which is called the rush hour. Conventional inkjet printers require the ink liquid to have a sufficiently low viscosity for inkjet discharge, but such liquids tend to be subject to the coffee-ring effect. The coffee-ring effect is an issue for conventional printing applications and drawing wires in printed electronics. We show by microscopy movie data analysis based on single particle tracking that the addition of a small amount of cellulose nanofibers (CNFs) to the colloidal dispersion works in such a way that the initial low concentration satisfies the low viscosity requirement, and the three-dimensional structural order of the CNFs formed during the final stage of droplet drying owing to the high concentration hinders the transport of particles to the periphery, suppressing the coffee-ring effect. This is a spatio-temporally controlled process that makes use of the inherent process of ordinary ink printing situations by the simple protocol. This is also an approach to seamlessly link the ink and substrate since CNFs are regarded as a promising substrate material for flexible devices in printed electronics because of their fine texture that keeps conductive nanoparticles on the surface.

Fundamentals of the logarithmic measure for revealing multimodal diffusion.

We develop a theoretical foundation for a time-series analysis method suitable for revealing the spectrum of diffusion coefficients in mixed Brownian systems, for which no prior knowledge of particle distinction is required. This method is directly relevant for particle tracking in biological systems, in which diffusion processes are often nonuniform. We transform Brownian data onto the logarithmic domain, in which the coefficients for individual modes of diffusion appear as distinct spectral peaks in the probability density. We refer to the method as the logarithmic measure of diffusion, or simply as the logarithmic measure. We provide a general protocol for deriving analytical expressions for the probability densities on the logarithmic domain. The protocol is applicable for any number of spatial dimensions with any number of diffusive states. The analytical form can be fitted to data to reveal multiple diffusive modes. We validate the theoretical distributions and benchmark the accuracy and sensitivity of the method by extracting multimodal diffusion coefficients from two-dimensional Brownian simulations of polydisperse filament bundles. Bundling the filaments allows us to control the system nonuniformity and hence quantify the sensitivity of the method. By exploiting the anisotropy of the simulated filaments, we generalize the logarithmic measure to rotational diffusion. By fitting the analytical forms to simulation data, we confirm the method's theoretical foundation. An error analysis in the single-mode regime shows that the proposed method is comparable in accuracy to the standard mean-squared displacement approach for evaluating diffusion coefficients. For the case of multimodal diffusion, we compare the logarithmic measure against other, more sophisticated methods, showing that both model selectivity and extraction accuracy are comparable for small data sets. Therefore, we suggest that the logarithmic measure, as a method for multimodal diffusion coefficient extraction, is ideally suited for small data sets, a condition often confronted in the experimental context. Finally, we critically discuss the proposed benefits of the method and its information content.

Spatiotemporal Dynamics of Laser-Induced Molecular Crystal Precursors Visualized by Particle Image Diffusometry.

We have succeeded in label-free visualization of spatiotemporal dynamics of laser-induced crystal precursors in aqueous solutions. The tracking-free evaluation of the diffusion-coefficient field for the observation domain with tens of micrometers on a side from microscopy movie data is realized by particle image diffusometry (PID). PID revealed the time fluctuation of coverage composition with the nonuniform space distribution of diffusion coefficients by the prenucleation clusters. Furthermore, the results indicate the existence of a loose aggregation domain of prenucleation clusters where the order of viscosity corresponds to that of honey.

Soft trapping lasts longer: Dwell time of a Brownian particle varied by potential shape.

It is often regarded that the dwell time (or residence time, escape time, trapping duration) of trapped Brownian particles is described by the multiplication of two separate factors, i.e., the diffusive traveling time of the trapping domain size without taking into account the trapping force, and the stochastic event of overcoming the trapping energy by thermal one instantaneously. However, we show that the ratio of dwell time to the typical traveling time for the trapping domain size depends on the shape of the force field. The shape of the trapping potential affects this ratio even if the trapping energy gap is the same and the smooth potential has a single minimum. Our finding suggests the possible application of the potential shape to realize the desired trapping characteristics.

Characterization of aqueous cellulose nanofiber dispersions from microscopy movie data of Brownian particles by trajectory analysis.

Cellulose nanofibers (CNFs) are promising for various applications such as substrates of flexible devices and reinforcement materials. Most of these applications require control of the drying process of the aqueous CNF dispersions. However, the existing reports examine the surface of dried materials because scanning electron microscopy (SEM) and atomic force microscopy (AFM) are not compatible with either the wet conditions or structure inside the materials. We report the characterization of these aqueous dispersions by the use of optical microscopy although it cannot be used directly to observe CNFs. We add a small portion of colloidal particles into the samples and obtain their trajectory data. The trajectories of Brownian motion include information on the surrounding environments. We analyze the microscopy movie data from the viewpoint of statistical mechanics, and reveal the mesoscale characteristics beyond viscosity. In particular, the possible non-uniformity of the dispersion is quantitatively examined through the framework of the generalized diffusion.

Estimation of diffusive states from single-particle trajectory in heterogeneous medium using machine-learning methods.

We propose a novel approach to analyze random walks in heterogeneous medium using a hybrid machine-learning method based on a gamma mixture and a hidden Markov model. A gamma mixture and a hidden Markov model respectively provide the number and the most probable sequence of diffusive states from the time series position data of particles/molecules obtained by single-particle/molecule tracking (SPT/SMT) method. We evaluate the performance of our proposed method for numerically generated trajectories. It is shown that our proposed method can correctly extract the number of diffusive states when each trajectory is long enough to be frame averaged. We also indicate that our method can provide an indicator whether the assumption of a medium consisting of discrete diffusive states is appropriate or not based on the available amount of trajectory data. Then, we demonstrate an application of our method to the analysis of experimentally obtained SPT data.

Negative thermophoresis of nanoparticles interacting with fluids through a purely-repulsive potential.

Thermophoretic forces acting on nanoparticles are investigated using molecular dynamics simulation. We assume the Lennard-Jones (LJ) potential for the interaction between fluid molecules. On the other hand, the interaction between the nanoparticle and the surrounding fluid molecules are assumed to be either LJ or Weeks-Chandler-Andersen (WCA) potential, where the latter is purely-repulsive. The effect of the interaction potential on the thermophoretic force is investigated for various situations. It is found that the thermophoretic force basically acts in the direction from the hotter side to the colder side of the nanoparticle. However, when the surrounding fluid is in the liquid phase, the force acts in the reversed direction for the case of the WCA potential. It is clarified that the sign reversal is caused by the different structures observed in the distribution of repulsive forces acting on the nanoparticle.

Suspended particle transport through constriction channel with Brownian motion.

It is well known that translocation events of a polymer or rod through pores or narrower parts of micro- and nanochannels have a stochastic nature due to the Brownian motion. However, it is not clear whether the objects of interest need to have a larger size than the entrance to exhibit the deviation from the dynamics of the surrounding fluid. We show by numerical analysis that the particle injection into the narrower part of the channel is affected by thermal fluctuation, where the particles have spherical symmetry and are smaller than the height of the constriction. The Péclet number (Pe) is the order parameter that governs the phenomena, which clarifies the spatio-temporal significance of Brownian motion compared to hydrodynamics. Furthermore, we find that there exists an optimal condition of Pe to attain the highest flow rate of particles relative to the dispersant fluid flow. Our finding is important in science and technology from nanopore DNA sequencers and lab-on-a-chip devices to filtration by porous materials and chromatography.

Suppressing the coffee-ring effect of colloidal droplets by dispersed cellulose nanofibers.

We report that the addition of a small amount of cellulose nanofibers (CNFs) into an aqueous dispersion of colloidal particles suppresses the coffee-ring effect when the dispersion dries on a solid substrate, as revealed by the computational analysis of experimental time-series images and by particle image velocimetry. The addition of CNFs is much more effective than the increase of colloidal particle concentration at the same weight percentage; it is also more environment friendly than the use of typical molecular surfactants. This finding is promising for the fabrication of metamaterials from colloidal dispersions and for ink printing in electronics, where CNFs can also serve as a substrate for flexible devices.

Faster Convergence of Diffusion Anisotropy Detection by Three-Step Relation of Single-Particle Trajectory.

We focus on the issue of limited number of samples in the single particle tracking (SPT) when trying to extract the diffusion anisotropy that originates from the particle asymmetry. We propose a novel evaluation technique of SPT making use of the relation of the consecutive three steps. More specifically, the trend of the angle comprised of the three positions and the displacements are plotted on a scatter diagram. The particle anisotropy dependence of the shape of the scatter diagram is examined through the data from the standard numerical model of anisotropic two-dimensional Brownian motion. Comparison with the existing method reveals the faster convergence in the evaluation. In particular, our proposed method realizes the detection of diffusion anisotropy under the conditions of not only less number of data but also larger time steps. This is of practical importance not only when the abundant data is hard to achieve but also when the rotational diffusion is fast compared to the frame rate of the camera equipment, which tends to be more common for smaller particles or molecules of interest.

Departure of microscopic friction from macroscopic drag in molecular fluid dynamics.

Friction coefficient of the Langevin equation and drag of spherical macroscopic objects in steady flow at low Reynolds numbers are usually regarded as equivalent. We show that the microscopic friction can be different from the macroscopic drag when the mass is taken into account for particles with comparable scale to the surrounding fluid molecules. We illustrate it numerically by molecular dynamics simulation of chloride ion in water. Friction variation by the atomistic mass effect beyond the Langevin regime can be of use in the drag reduction technology as well as the electro or thermophoresis.

Coarse-grained picture of Brownian motion in water: Role of size and interaction distance range on the nature of randomness.

The Brownian motion of a particle in a fluid is often described by the linear Langevin equation, in which it is assumed that the mass of the particle is sufficiently large compared to the surrounding fluid molecules. This assumption leads to a diffusion coefficient that is independent of the particle mass. The Stokes-Einstein equation indicates that the diffusion coefficient depends solely on the particle size, but the concept of size can be ambiguous when close to the molecular scale. We first examine the Brownian motion of simple model particles based on short-range interactions in water by the molecular dynamics method and show that the diffusion coefficient can vary with mass when this mass is comparable to that of the solvent molecules, and that this effect is evident when the solute particle size is sufficiently small. We then examine the properties of a water molecule considered as a solute in the bulk solvent consisting of the remainder of the water. A comparison with simple solute models is used to clarify the role of force fields. The long-range Coulomb interaction between water molecules is found to lead to a Gaussian force distribution in spite of a mass ratio and nominal size ratio of unity, such that solutes with short-range interactions exhibit non-Gaussian force distribution. Thus, the range of the interaction distance determines the effective size even if it does not represent the volume excluded by the repulsive force field.

Evaluation of bacterial motility from non-Gaussianity of finite-sample trajectories using the large deviation principle.

Motility of bacteria is usually recognized in the trajectory data and compared with Brownian motion, but the diffusion coefficient is insufficient to evaluate it. In this paper, we propose a method based on the large deviation principle. We show that it can be used to evaluate the non-Gaussian characteristics of model Escherichia coli motions and to distinguish combinations of the mean running duration and running speed that lead to the same diffusion coefficient. Our proposed method does not require chemical stimuli to induce the chemotaxis in a specific direction, and it is applicable to various types of self-propelling motions for which no a priori information of, for example, threshold parameters for run and tumble or head/tail direction is available. We also address the issue of the finite-sample effect on the large deviation quantities, but we propose to make use of it to characterize the nature of motility.

Detection of diffusion anisotropy due to particle asymmetry from single-particle tracking of Brownian motion by the large-deviation principle.

We show that the diffusion anisotropy due to the asymmetry of the particle can be extracted from the trajectory data without the information of the particle orientation. The subject of analysis is typical in single-particle tracking (SPT) experiments, and the analysis is based on the large-deviation principle in mathematics. We consider the model system of Langevin equations in two dimensions where a particle diffusion shows anisotropy depending on a single parameter defined by the two diffusion coefficients in the perpendicular directions of the frame fixed to the particle. We show how the large-deviation quantities depend on this parameter so that it can be used for the detection of the diffusion anisotropy. We also illustrate how the discreteness of the sampling interval in the SPT and the finiteness of the number of samples influence the results of the analysis.