Viscoelasticity of nematic liquid crystals at a glance

The Casimir-like effect induced by active nematics

We consider an active nematic phase and use hydrodynamical equations of it to model the activity as an internal field. The interaction of this field with the nematic director in a confined geometry is included in the Hamiltonian of the system. Based on this model Hamiltonian and the standard field theoretical approach, the Casimir-like force induced between the boundaries of such a confined film is discussed. The force depends on the geometrical shape and the dynamical character of the constituents of our active phase, as well as the anchoring conditions. For homeotropically aligned rod-like particles which in principle tend to align along a planar flow field, extensile activity enhances the attraction present in a thin nematic film. As the film thickness increases the force reduces. Beyond a critical thickness, a planar flow field instantaneous to a bend distortion sets in. Near but below the threshold of this activity-induced instability, the force crosses zero and repulsively diverges right at the critical threshold of this so-called flow instability. For contractile rods, in the same geometry as above, the structure is stable and the Casimir-like force diminishes by an exponential factor as a function of the film thickness. On the other side for a planar director alignment, rod-like contractile particles can induce opposite shear flows at the boundaries creating a splay distortion for the director between the plates. In this configuration, we obtain the same universal pretransitional behavior for the force as above. Vice versa, for extensile rod-like particles in this geometry, the director fluctuations become massive and the Casimir-like force diminishes again by an exponential factor as the film thickness increases. The effect of the active field on thermal fluctuations of the director and the fluctuation-induced Casimir force per area is derived through a "semi"-dynamical approach as well. However, the results of the calculation due to a mathematical sum over the fluctuating modes do not lead to an approved closed form.

Dynamics and Topology of Symmetry Breaking with Skyrmions

We observe that pretransitional order parameter fluctuations of a skyrmion-forming chiral nematic liquid crystal are slowed down for 4 orders of magnitude, if confined to ≲100  nm thin layers. Fluctuating fragments of half-skyrmions are observed in a narrow temperature interval and are explained by thermally activated hopping between the various energy states. Skyrmion fluctuations are accompanied by imbalanced topological charge: positive charges appear at higher temperatures and dominate in the fluctuating region until skyrmions fully condense and negative charges appear at lower temperatures.

Dynamics of anisotropic colloidal systems: What to choose, DLS, DDM or XPCS?

Investigation of the dynamics of colloids in bulk can be hindered by issues such as multiple scattering and sample opacity. These challenges are exacerbated when dealing with inorganic materials. In this study, we employed a model system of Akaganeite colloidal rods to assess three leading dynamics measurement techniques: 3D-(depolarized) dynamic light scattering (3D-(D)DLS), polarized-differential dynamic microscopy (P-DDM), and x-ray photon correlation spectroscopy (XPCS). Our analysis revealed that the translational and rotational diffusion coefficients captured by these methods show a remarkable alignment. Additionally, by examining the q-ranges and maximum volume fractions for each approach, we offer insights into the best technique for investigating the dynamics of anisotropic systems at the colloidal scale.

Mesoscopic Characterization of the Early Stage of the Glucono-δ-Lactone-Induced Gelation of Milk via Image Analysis Techniques

We provide a method for quantifying the kinetics of gelation in milk acidified with glucono-δ-lactone (GDL) using image analysis techniques, particle image velocimetry (PIV), differential variance analysis (DVA) and differential dynamic microscopy (DDM). The gelation of the milk acidified with GDL occurs through the aggregation and subsequent coagulation of the casein micelles as the pH approaches the isoelectric point of the caseins. The gelation of the acidified milk with GDL is an important step in the production of fermented dairy products. PIV qualitatively monitors the average mobility of fat globules during gelation. The gel point estimated by PIV is in good agreement with that obtained by rheological measurement. DVA and DDM methods reveal the relaxation behavior of fat globules during gelation. These two methods make it possible to calculate microscopic viscosity. We also extracted the mean square displacement (MSD) of the fat globules, without following their movement, using the DDM method. The MSD of fat globules shifts to sub-diffusive behavior as gelation progresses. The fat globules used as probes show the change in matrix viscoelasticity caused by the gelling of the casein micelles. Image analysis and rheology can be used complementarily to study the mesoscale dynamics of the milk gel.

Hidden traces of chirality in the fluctuations of a fully unwound cholesteric

Confinement and hydrodynamic interactions often play an important role in the fluctuation dynamics of soft matter systems, which can typically be studied using light scattering techniques. With experimental and theoretical methodologies, I demonstrate here that chirality is an additional critical parameter that leads to diverging decay times and correlation lengths in chiral liquid crystal cells with a fully unwound cholesteric helix. This study combines light scattering measurements made in a tailored microscope geometry and theoretical calculations of the decay dynamics of chiral orientational fluctuations-including hydrodynamics-to establish the existence of two soft chiral modes of fluctuations driving the destabilization of the unwound cholesteric. Despite the achirality of the equilibrium state of unwound cholesterics, this study indicates that chirality hides itself in the orientational fluctuation modes and plays a major role in their dynamics, which can be exploited to locally measure the strength of chirality in frustrated chiral liquid crystal cells.

Liquid crystal phase formation and non-Newtonian behavior of oligonucleotide formulations

Viscosity behavior of liquid oligonucleotide therapeutics and its dependence on formulation properties has been poorly studied to date. We observed a high increase in viscosity and solidification of therapeutic oligonucleotide formulations with increasing oligonucleotide concentration creating challenges during drug product manufacturing. In this study, we characterized the viscosity behavior of three different single strand DNA oligonucleotides based on oligonucleotide concentration and formulation composition. We subsequently studied the underlying mechanism for increased viscosity at higher oligonucleotide concentrations by dynamic light scattering (DLS), 1H nuclear magnetic resonance (NMR), differential scanning calorimetry (DSC), and polarized light microscopy. Viscosity was highly dependent on formulation composition, oligonucleotide sequence, and concentration, and especially dependent on the presence and combination of different individual ions, such as the presence of sodium chloride in the formulation. In samples with elevated viscosity, the viscosity behavior was characterized by non-Newtonian, shear-thinning flow behavior. We further studied these samples by DLS and 1H NMR, which revealed the presence of supra-molecular assemblies, and further characterization by polarized light and DSC characterized these assemblies as liquid crystals in the formulation. The present study links the macroscopic viscosity behavior of oligonucleotide formulations to the formation of supra-molecular assemblies and to the presence of liquid crystals, and highlights the importance of formulation composition selection for these therapeutics.

Uncertainty quantification and estimation in differential dynamic microscopy

Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present statistical analysis that quantifies the noise, reduces the computational order, and enhances the robustness of DDM analysis. We propagate the image noise through the Fourier analysis, which allows us to comprehensively study the bias in different estimators of model parameters, and we derive a different way to detect whether the bias is negligible. Furthermore, through use of Gaussian process regression (GPR), we find that predictive samples of the image structure function require only around 0.5%-5% of the Fourier transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with uncertainty quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization.

Deformation profiles and microscopic dynamics of complex fluids during oscillatory shear experiments

Oscillatory shear tests are widely used in rheology to characterize the linear and non-linear mechanical response of complex fluids, including the yielding transition. There is an increasing urge to acquire detailed knowledge of the deformation field that is effectively present across the sample during these tests; at the same time, there is mounting evidence that the macroscopic rheological response depends on the elusive microscopic behavior of the material constituents. Here we employ a strain-controlled shear-cell with transparent walls to visualize and quantify the dynamics of tracers embedded in various cyclically sheared complex fluids, ranging from almost-ideal elastic to yield stress fluids. For each sample, we use image correlation processing to measure the macroscopic deformation field, and echo-differential dynamic microscopy to probe the microscopic irreversible sample dynamics in reciprocal space; finally, we devise a simple scheme to spatially map the rearrangements in the sheared sample, once again without tracking the tracers. For the yield stress sample, we obtain a wave-vector dependent characterization of shear-induced diffusion across the yielding transition, which is accompanied by a three-order-of-magnitude speed-up of the dynamics and by a transition from localized, intermittent rearrangements to a more spatially homogeneous and temporally uniform activity. Our tracking free approach is intrinsically multi-scale, can successfully discriminate between different types of dynamics, and can be automated to minimize user intervention. Applications are many, as it can be translated to other imaging modes, including fluorescence, and can be used with sub-resolution tracers and even without tracers, for samples that provide intrinsic optical contrast.

Measuring capillary wave dynamics using differential dynamic microscopy

The interface between two fluids is roughened by thermally excited capillary waves. By using colloid-polymer systems which exhibit liquid-gas phase separation, the time and length scales of capillary waves become accessible to optical microscopy methods. Here, we study such a system using bright-field optical microscopy combined with a novel extension of differential dynamic microscopy. With differential dynamic microscopy, we analyze images in order to determine the decay time of interfacial fluctuations spanning wavevectors from 0.1 to 1 μm-1. We find capillary velocities on the order of 0.1 μm s-1 that depend on the sample composition in expected ways and that match values from the literature. This work demonstrates the first application of differential dynamic microscopy to the study of interfacial dynamics.

Cross-differential dynamic microscopy

We demonstrate the use of a dual-camera-equipped microscope for the study of the wavevector-dependent dynamics of soft matter. Contrary to the standard differential dynamic microscopy (DDM) in which a series of digital video images is acquired with a single camera at a constant frame rate, we use two randomly triggered cameras to acquire two sequences of images of the same region in the sample. From the two data sets we calculate cross-image differences and Fourier analyze them as a function of time delay between the two images. We show that this technique can greatly decrease the time delay, which allows us to measure fast dynamics at larger wavevectors that could not have been performed with a single camera setup.

Anisotropic Diffusion and Phase Behavior of Cellulose Nanocrystal Suspensions

In this paper, we use dynamic light scattering in polarized and depolarized modes to determine the translational and rotational diffusion coefficients of concentrated rodlike cellulose nanocrystals in aqueous suspension. Within the range of studied concentrations (1-5 wt %), the suspension starts a phase transition from an isotropic to an anisotropic state as shown by polarized light microscopy and viscosity measurements. Small-angle neutron scattering measurements also confirmed the start of cellulose nanocrystal alignment and a decreasing distance between the cellulose nanocrystals with increasing concentration. As expected, rotational and translational diffusion coefficients generally decreased with increasing concentration. However, the translational parallel diffusion coefficient was found to show a local maximum at the onset of the isotropic-to-nematic phase transition. This is attributed to the increased available space for rods to move along their longitudinal axis upon alignment. This increased parallel diffusion coefficient thus confirms the general idea that rodlike particles gain translational entropy upon alignment while paying the price for losing rotational degrees of freedom. Once the concentration increases further, diffusion becomes more hindered even in the aligned regions due to a reduction in the rod separation distance. This leads once again to a decrease in translational diffusion coefficients. Furthermore, the relaxation rate for fast mode translational diffusion (parallel to the long particle axis) exhibited two regimes of relaxation behavior at concentrations where significant alignment of the rods is measured. We attribute this unusual dispersive behavior to two length scales: one linked to the particle length (at large wavevector q) and the other to a twist fluctuation correlation length (at low wavevector q) along the cellulose nanocrystal rods that is of a larger length when compared to the actual length of rods and could be linked to the size of aligned domains.

Perspective: Differential dynamic microscopy extracts multi-scale activity in complex fluids and biological systems

Differential dynamic microscopy (DDM) is a technique that exploits optical microscopy to obtain local, multi-scale quantitative information about dynamic samples, in most cases without user intervention. It is proving extremely useful in understanding dynamics in liquid suspensions, soft materials, cells, and tissues. In DDM, image sequences are analyzed via a combination of image differences and spatial Fourier transforms to obtain information equivalent to that obtained by means of light scattering techniques. Compared to light scattering, DDM offers obvious advantages, principally (a) simplicity of the setup; (b) possibility of removing static contributions along the optical path; (c) power of simultaneous different microscopy contrast mechanisms; and (d) flexibility of choosing an analysis region, analogous to a scattering volume. For many questions, DDM has also advantages compared to segmentation/tracking approaches and to correlation techniques like particle image velocimetry. The very straightforward DDM approach, originally demonstrated with bright field microscopy of aqueous colloids, has lately been used to probe a variety of other complex fluids and biological systems with many different imaging methods, including dark-field, differential interference contrast, wide-field, light-sheet, and confocal microscopy. The number of adopting groups is rapidly increasing and so are the applications. Here, we briefly recall the working principles of DDM, we highlight its advantages and limitations, we outline recent experimental breakthroughs, and we provide a perspective on future challenges and directions. DDM can become a standard primary tool in every laboratory equipped with a microscope, at the very least as a first bias-free automated evaluation of the dynamics in a system.

Dark field differential dynamic microscopy enables accurate characterization of the roto-translational dynamics of bacteria and colloidal clusters

Micro- and nanoscale objects with anisotropic shape are key components of a variety of biological systems and inert complex materials, and represent fundamental building blocks of novel self-assembly strategies. The time scale of their thermal motion is set by their translational and rotational diffusion coefficients, whose measurement may become difficult for relatively large particles with small optical contrast. Here we show that dark field differential dynamic microscopy is the ideal tool for probing the roto-translational Brownian motion of anisotropic shaped particles. We demonstrate our approach by successful application to aqueous dispersions of non-motile bacteria and of colloidal aggregates of spherical particles.

Image windowing mitigates edge effects in Differential Dynamic Microscopy

Differential Dynamic Microscopy (DDM) analyzes traditional real-space microscope images to extract information on sample dynamics in a way akin to light scattering, by decomposing each image in a sequence into Fourier modes, and evaluating their time correlation properties. DDM has been applied in a number of soft-matter and colloidal systems. However, objects observed to move out of the microscope's captured field of view, intersecting the edges of the acquired images, can introduce spurious but significant errors in the subsequent analysis. Here we show that application of a spatial windowing filter to images in a sequence before they enter the standard DDM analysis can reduce these artifacts substantially. Moreover, windowing can increase significantly the accessible range of wave vectors probed by DDM, and may further yield unexpected information, such as the size polydispersity of a colloidal suspension.

Time correlation functions in the Lebwohl-Lasher model of liquid crystals

Time correlation functions in the Lebwohl-Lasher model of nematic liquid crystals are studied using theory and molecular dynamics simulations. In particular, the autocorrelation functions of angular momentum and nematic director fluctuations are calculated in the long-wavelength limit. The constitutive relations for the hydrodynamic currents are derived using a standard procedure based on non-negativity of the entropy production. The continuity equations are then linearized and solved to calculate the correlation functions. We find that the transverse angular momentum fluctuations are coupled to the director fluctuations and are both propagative. The propagative nature of the fluctuations suppresses the anticipated hydrodynamic long-time tails in the single-particle autocorrelation functions. The fluctuations in the isotropic phase are, however, diffusive, leading to t^{-d/2} long-time tails in d spatial dimensions. The Frank elastic constant measured using the time correlation functions are in good agreement with previously reported results.

Investigation of moderately turbid suspensions by heterodyne near field scattering

Light scattering has proven to be a very powerful technique to characterize soft matter systems. However, many samples are turbid and hence suffer from multiple scattering which can affect the signal considerably. Multiple scattering can be reduced by diluting the sample or changing the solvent, but often this alters the sample and hence is precluded. Here we study the dynamics of a model system. In particular, we investigate the effects of moderate multiple scattering on small-angle heterodyne near field scattering (HNFS). Varying the particle concentration and size we change the degree of multiple scattering, which is quantified by the transmission of light. In dependence of the degree of multiple scattering, we analyze the statistical properties of the HNFS signal, which is the difference between two intensity patterns separated by a delay time. The distribution of intensity differences follows a Gaussian distribution if single scattering dominates and a Laplace distribution in the presence of extreme multiple scattering. We also investigate the effects of multiple scattering on the measured intermediate scattering function and the hydrodynamic radius of the particles. Reliable data are obtained for sample transmissions down to about 0.7. This is confirmed by a comparison with results from a far field cross-correlation instrument that suppresses multiple scattering contributions. Therefore, HNFS represents a technically simple but powerful method to investigate samples that are moderately multiple scattering.

Assessing the Collective Dynamics of Motile Cilia in Cultures of Human Airway Cells by Multiscale DDM

The technique of differential dynamic microscopy is extended here, showing that it can provide a powerful and objective method of video analysis for optical microscopy videos of in vitro samples of live human bronchial epithelial ciliated cells. These cells are multiciliated, with motile cilia that play key physiological roles. It is shown that the ciliary beat frequency can be recovered to match conventional analysis, but in a fully automated fashion. Furthermore, it is shown that the properties of spatial and temporal coherence of cilia beat can be recovered and distinguished, and that if a collective traveling wave (the metachronal wave) is present, this has a distinct signature and its wavelength and direction can be measured.

Structure and dynamics of concentration fluctuations in a non-equilibrium dense colloidal suspension

Linearised fluctuating hydrodynamics describes effectively the concentration non-equilibrium fluctuations (NEF) arising during a diffusion process driven by a small concentration gradient. However, fluctuations in the presence of large gradients are not yet fully understood. Here we study the giant concentration NEF arising when a dense aqueous colloidal suspension is allowed to diffuse into an overlying layer of pure water. We use differential dynamic microscopy to determine both the statics and the dynamics of the fluctuations for several values of the wave-vector q. At small q, NEF are quenched by buoyancy, which prevents their full development and sets an upper timescale to their temporal relaxation. At intermediate q, the mean squared amplitude of NEF is characterised by a power law exponent -4, and fluctuations relax diffusively with diffusion coefficient D1. At large q, the amplitude of NEF vanishes and equilibrium concentration fluctuations are recovered, enabling a straightforward determination of the osmotic compressibility of the suspension during diffusion. In this q-range we also find that the relaxation of the fluctuations occurs with a diffusion coefficient D2 significantly different from D1. Both diffusion coefficients exhibit time-dependence with D1 increasing monotonically (by about 15%) and D2 showing the opposite behaviour (about 17% decrease). At equilibrium, the two coefficients coincide as expected. While the decrease of D2 is compatible with a diffusive evolution of the concentration profile, the increase of D1 is still not fully understood and may require considering nonlinearities that are neglected in current theories for highly stressed colloids.

Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy

We probe the roto-translational Brownian motion of optically anisotropic particles suspended in water with a simple and straightforward optical microscopy experiment that does not require positional or rotational particle tracking. We acquire a movie of the suspension placed between two polarizing elements and we extract the translational diffusion coefficient D T and the rotational diffusion coefficient D R from the analysis of the temporal correlation properties of the spatial Fourier modes of the intensity fluctuations in the movie. Our method is successfully tested with a dilute suspension of birefringent spherical colloidal particles obtained by polymerizing an emulsion of droplets of liquid crystal in a nematic phase, whose roto-translational dynamics is found to be well described by theory. The simplicity of our approach makes our method a viable alternative to particle tracking and depolarized dynamic light scattering.

Dark-field differential dynamic microscopy

Differential dynamic microscopy (DDM) is an emerging technique to measure the ensemble dynamics of colloidal and complex fluid motion using optical microscopy in systems that would otherwise be difficult to measure using other methods. To date, DDM has successfully been applied to linear space invariant imaging modes including bright-field, fluorescence, confocal, polarised, and phase-contrast microscopy to study diverse dynamic phenomena. In this work, we show for the first time how DDM analysis can be extended to dark-field imaging, i.e. a linear space variant (LSV) imaging mode. Specifically, we present a particle-based framework for describing dynamic image correlations in DDM, and use it to derive a correction to the image structure function obtained by DDM that accounts for scatterers with non-homogeneous intensity distributions as they move within the imaging plane. To validate the analysis, we study the Brownian motion of gold nanoparticles, whose plasmonic structure allows for nanometer-scale particles to be imaged under dark-field illumination, in Newtonian liquids. We find that diffusion coefficients of the nanoparticles can be reliably measured by dark-field DDM, even under optically dense concentrations where analysis via multiple-particle tracking microrheology fails. These results demonstrate the potential for DDM analysis to be applied to linear space variant forms of microscopy, providing access to experimental systems unavailable to other imaging modes.

Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters

Nanoparticle dynamics impact a wide range of biological transport processes and applications in nanomedicine and natural resource engineering. Differential dynamic microscopy (DDM) was recently developed to quantify the dynamics of submicron particles in solutions from fluctuations of intensity in optical micrographs. Differential dynamic microscopy is well established for monodisperse particle populations, but has not been applied to solutions containing weakly scattering polydisperse biological nanoparticles. Here we use bright-field DDM (BDDM) to measure the dynamics of protein-rich liquid clusters, whose size ranges from tens to hundreds of nanometers and whose total volume fraction is less than 10(-5). With solutions of two proteins, hemoglobin A and lysozyme, we evaluate the cluster diffusion coefficients from the dependence of the diffusive relaxation time on the scattering wave vector. We establish that for weakly scattering populations, an optimal thickness of the sample chamber exists at which the BDDM signal is maximized at the smallest sample volume. The average cluster diffusion coefficient measured using BDDM is consistently lower than that obtained from dynamic light scattering at a scattering angle of 90°. This apparent discrepancy is due to Mie scattering from the polydisperse cluster population, in which larger clusters preferentially scatter more light in the forward direction.

Chiral structures and defects of lyotropic chromonic liquid crystals induced by saddle-splay elasticity

An experimental and theoretical study of lyotropic chromonic liquid crystals (LCLCs) confined in cylinders with degenerate planar boundary conditions elucidates LCLC director configurations. When the Frank saddle-splay modulus is more than twice the twist modulus, the ground state adopts an inhomogeneous escaped-twisted configuration. Analysis of the configuration yields a large saddle-splay modulus, which violates Ericksen inequalities but not thermodynamic stability. Lastly, we observe point defects between opposite-handed domains, and we explain a preference for point defects over domain walls.

Propagating director bend fluctuations in nematic liquid crystals

We show, by molecular simulation, that for a range of standard, coarse-grained, nematic liquid crystal models, the director bend fluctuation is a propagating mode. This is in contrast to the generally accepted picture of nematic hydrodynamics, in which all the director modes (splay, twist, bend, and combinations thereof) are overdamped. By considering the various physical parameters that enter the equations of nematodynamics, we propose an explanation of this effect and conclude that propagating bend fluctuations may be observable in some experimental systems.

Magneto-optic and converse magnetoelectric effects in a ferromagnetic liquid crystal

We have studied the response of ferromagnetic liquid crystals to external magnetic and electric fields, and compared it to the usual response of nematic liquid crystals (NLCs). We have observed effects, which are not present in a pure NLC and are a consequence of the coupling between the nematic director and the magnetization. The electro-optic effect, which is in the ferromagnetic phase the same as in the pure NLC, is accompanied by a converse magnetoelectric effect. The magneto-optic effect differs completely from the one observed in the pure NLC, where it is a quadratic effect and it only appears when a magnetic field larger than a critical field is applied perpendicular to the director. In the ferromagnetic NLC in addition to the response to the perpendicular field, there is also a qualitatively different response to the parallel field. Contrary to the pure NLC no critical field needs to be exceeded for the system to respond to a perpendicular field, but a critical field needs to be exceeded to observe a response to the field parallel to the director and antiparallel to the magnetization. The critical field is in this case two orders of magnitude smaller than the critical field of the magnetic Frederiks transition in the pure NLC. The experimental observations are well described by a simple macroscopic theory.