Quantifying local stiffness and forces in soft biological tissues using droplet optical microcavities.

Mechanical properties of biological tissues fundamentally underlie various biological processes and noncontact, local, and microscopic methods can provide fundamental insights. Here, we present an approach for quantifying the local mechanical properties of biological materials at the microscale, based on measuring the spectral shifts of the optical resonances in droplet microcavities. Specifically, the developed method allows for measurements of deformations in dye-doped oil droplets embedded in soft materials or biological tissues with an error of only 1 nm, which in turn enables measurements of anisotropic stress inside tissues as small as a few pN/µm2. Furthermore, by applying an external strain, Young's modulus can be measured in the range from 1 Pa to 35 kPa, which covers most human soft tissues. Using multiple droplet microcavities, our approach could enable mapping of stiffness and forces in inhomogeneous soft tissues and could also be applied to in vivo and single-cell experiments. The developed method can potentially lead to insights into the mechanics of biological tissues.

Photonic eigenmodes and transmittance of finite-length 1D cholesteric liquid crystal resonators.

Cholesteric liquid crystals exhibit a periodic helical structure that partially reflects light with wavelengths comparable to the period of the structure, thus performing as a one-dimensional photonic crystal. Here, we demonstrate a combined experimental and numerical study of light transmittance spectra of finite-length helical structure of cholesteric liquid crystals, as affected by the main system and material parameters, as well as the corresponding eigenmodes and frequency eigenspectra with their Q-factors. Specifically, we have measured and simulated transmittance spectra of samples with different thicknesses, birefringences and for various incident light polarisation configurations as well as quantified the role of refractive index dispersion and the divergence of the incident light beam on transmittance spectra. We identify the relation between transmittance spectra and the eigenfrequencies of the photonic eigenmodes. Furthermore, we present and visualize the geometry of these eigenmodes and corresponding Q-factors. More generally, this work systematically studies the properties of light propagation in a one-dimensional helical cholesteric liquid crystal birefringent profile, which is known to be of interest for the design of micro-lasers and other soft matter photonic devices.

Single-Layer and Double-Layer Filtration Materials Based on Polyvinylidene Fluoride-Co-hexafluoropropylene Nanofibers Coated on Melamine Microfibers.

In this work, we demonstrate selected optimization changes in the simple design of filtration masks to increase particle removal efficiency (PRE) and filter quality factor by combining experiments and numerical modeling. In particular, we focus on single-layer filters fabricated from uniform thickness fibers and double-layer filters consisting of a layer of highly permeable thick fibers as a support and a thin layer of filtering electrospun nanofibers. For single-layer filters, we demonstrate performance improvement in terms of the quality factor by optimizing the geometry of the composition. We show significantly better PRE performance for filters composed of micrometer-sized fibers covered by a thin layer of electrospun nanofibers. This work is motivated and carried out in collaboration with a targeted industrial development of selected melamine-based filter nano- and micromaterials.

Slow light by dual-periodic self-similar dielectric multilayered films.

We demonstrate the emergence of slow-light in dual-periodic dielectric one-dimensional photonic crystals with self-similar features at different length scales. Specifically, using numerical modelling, we explore self-similar photonic crystals which are formed as effective combinations of dual periodic stacks of dielectric layers and show that the emergent photonic band diagram can be widely designed by different structural parameters. The width and the position of bandgaps can be designed to work over a wide range of bands and frequencies. The proposed design also leads to the emergence of flat bands and major slow-light regimes, with possible group refractive index of light as large as 103 and in a range of bands.

Nematronics: Reciprocal Coupling between Ionic Currents and Nematic Dynamics.

Adopting a spintronics-inspired approach, we study the reciprocal coupling between ionic charge currents and nematic texture dynamics in a uniaxial nematic electrolyte. Assuming quenched fluid dynamics, we develop equations of motion analogously to spin torque and spin pumping. Based on the principle of least dissipation of energy, we derive the adiabatic "nematic torque" exerted by ionic currents on the nematic director field as well as the reciprocal motive force on ions due to the orientational dynamics of the director. We discuss several simple examples that illustrate the potential functionality of this coupling. Furthermore, using our phenomenological framework, we propose a practical means to extract the coupling strength through impedance measurements on a nematic cell. Exploring further applications based on this physics could foster the development of nematronics-nematic iontronics.

Defect Line Coarsening and Refinement in Active Nematics.

Active matter is naturally out of equilibrium which results in the emergence of diverse dynamic steady states, including the omnipresent chaotic state known as the active turbulence. However, much less is known how active systems dynamically depart out of these configurations, such as get excited or damped to a different dynamic steady state. In this Letter, we demonstrate the coarsening and refinement dynamics of topological defect lines in three-dimensional active nematic turbulence. Specifically, using theory and numerical modeling, we are able to predict the evolution of the active defect density away from the steady state due to time-dependent activity or viscoelastic material properties, establishing a single length scale phenomenological description of defect line coarsening and refinement in a three-dimensional active nematic. The approach is first applied to growth dynamics of a single active defect loop, and then to a full three-dimensional active defect network. More generally, this Letter provides insight into the general coarsening phenomena between dynamical regimes in 3D active matter, with a possible analogy in other physical systems.

Neural networks determination of material elastic constants and structures in nematic complex fluids.

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

Continuous generation of topological defects in a passively driven nematic liquid crystal.

Synthetic active matter is emerging as the prime route for the realisation of biological mechanisms such as locomotion, active mixing, and self-organisation in soft materials. In particular, passive nematic complex fluids are known to form out-of-equilibrium states with topological defects, but their locomotion, activation and experimental realization has been developed and understood to only a limited extent. Here, we report that the concentration-driven flow of small molecules triggers turbulent flow in the thin film of a nematic liquid crystal that continuously generates pairs of topological defects with an integer topological charge. The diffusion results in the formation of counter-rotating vortex rolls in the liquid crystal, which above a velocity threshold transform into a turbulent flow with continuous generation and annihilation of the defect pairs. The pairs of defects are created by the self-amplifying splay instability between the vortices, until a pair of oppositely charged defects is formed.

Topological defect-propelled swimming of nematic colloids.

Topological defects on colloids rotating in nematic liquid crystals form far-from-equilibrium structures that perform complex swim strokes in which the defects periodically extend, depin, and contract. These defect dynamics propel the colloid, generating translation from rotation. The swimmer's speed and direction are determined by the topological defect's polarity and extent of elongation. Defect elongation is controlled by a rotating external magnetic field, allowing control over particle trajectories. The swimmers' translational motion relies on broken symmetries associated with lubrication forces between the colloid and the bounding surfaces, line tensions associated with the elongated defect, and anisotropic viscosities associated with the defect elongation adjacent to the colloid. The scattering or effective pair interaction of these swimmers is highly anisotropic, with polarization-dependent dimer stability and motion that depend strongly on entanglement and sharing of their extended defect structures. This research introduces transient, far-from-equilibrium topological defects as a class of virtual functional structures that generate modalities of motion and interaction.

Numerical modeling of optical modes in topological soft matter.

Vector and vortex laser beams are desired in many applications and are usually created by manipulating the laser output or by inserting optical components in the laser cavity. Distinctly, inserting liquid crystals into the laser cavity allows for extensive control over the emitted light due to their high susceptibility to external fields and birefringent nature. In this work we demonstrate diverse optical modes for lasing as enabled and stablised by topological birefringent soft matter structures using numerical modelling. We show diverse structuring of light-with different 3D intensity and polarization profiles-as realised by topological soft matter structures in radial nematic droplet, in 2D nematic cavities of different geometry and including topological defects with different charges and winding numbers, in arbitrary varying birefringence fields with topological defects and in pixelated birefringent profiles. We use custom written FDFD code to calculate emergent electromagnetic eigenmodes. Control over lasing is of a particular interest aiming towards the creation of general intensity, polarization and topologically shaped laser beams.

Controllable shifting, steering, and expanding of light beam based on multi-layer liquid-crystal cells.

Shaping and steering of light beams is essential in many modern applications, ranging from optical tweezers, camera lenses, vision correction to 3D displays. However, current realisations require increasingly greater tunability and aim for lesser specificity for use in diverse applications. Here, we demonstrate tunable light beam control based on multi-layer liquid-crystal cells and external electric field, capable of extended beam shifting, steering, and expanding, using a combination of theory and full numerical modelling, both for liquid crystal orientations and the transmitted light. Specifically, by exploiting three different function-specific and tunable birefringent nematic layers, we show an effective liquid-crystal beam control device, capable of precise control of outgoing light propagation, with possible application in projectors or automotive headlamps.

Topological liquid crystal superstructures as structured light lasers.

Liquid crystals (LCs) form an extremely rich range of self-assembled topological structures with artificially or naturally created topological defects. Some of the main applications of LCs are various optical and photonic devices, where compared to their solid-state counterparts, soft photonic systems are fundamentally different in terms of unique properties such as self-assembly, self-healing, large tunability, sensitivity to external stimuli, and biocompatibility. Here we show that complex tunable microlasers emitting structured light can be generated from self-assembled topological LC superstructures containing topological defects inserted into a thin Fabry-Pérot microcavity. The topology and geometry of the LC superstructure determine the structuring of the emitted light by providing complex three-dimensionally varying optical axis and order parameter singularities, also affecting the topology of the light polarization. The microlaser can be switched between modes by an electric field, and its wavelength can be tuned with temperature. The proposed soft matter microlaser approach opens directions in soft matter photonics research, where structured light with specifically tailored intensity and polarization fields could be designed and implemented.

Long-term stability predictions of therapeutic monoclonal antibodies in solution using Arrhenius-based kinetics.

Long-term stability of monoclonal antibodies to be used as biologics is a key aspect in their development. Therefore, its possible early prediction from accelerated stability studies is of major interest, despite currently being regarded as not sufficiently robust. In this work, using a combination of accelerated stability studies (up to 6 months) and first order degradation kinetic model, we are able to predict the long-term stability (up to 3 years) of multiple monoclonal antibody formulations. More specifically, we can robustly predict the long-term stability behaviour of a protein at the intended storage condition (5 °C), based on up to six months of data obtained for multiple quality attributes from different temperatures, usually from intended (5 °C), accelerated (25 °C) and stress conditions (40 °C). We have performed stability studies and evaluated the stability data of several mAbs including IgG1, IgG2, and fusion proteins, and validated our model by overlaying the 95% prediction interval and experimental stability data from up to 36 months. We demonstrated improved robustness, speed and accuracy of kinetic long-term stability prediction as compared to classical linear extrapolation used today, which justifies long-term stability prediction and shelf-life extrapolation for some biologics such as monoclonal antibodies. This work aims to contribute towards further development and refinement of the regulatory landscape that could steer toward allowing extrapolation for biologics during the developmental phase, clinical phase, and also in marketing authorisation applications, as already established today for small molecules.

Topics in the mathematical design of materials.

We present a perspective on several current research directions relevant to the mathematical design of new materials. We discuss: (i) design problems for phase-transforming and shape-morphing materials, (ii) epitaxy as an approach of central importance in the design of advanced semiconductor materials, (iii) selected design problems in soft matter, (iv) mathematical problems in magnetic materials, (v) some open problems in liquid crystals and soft materials and (vi) mathematical problems on liquid crystal colloids. The presentation combines topics from soft and hard condensed matter, with specific focus on those design themes where mathematical approaches could possibly lead to exciting progress. This article is part of the theme issue 'Topics in mathematical design of complex materials'.

Anisotropic electrostatic screening of charged colloids in nematic solvents.

The physical behavior of anisotropic charged colloids is determined by their material dielectric anisotropy, affecting colloidal self-assembly, biological function, and even out-of-equilibrium behavior. However, little is known about anisotropic electrostatic screening, which underlies all electrostatic effective interactions in such soft or biological materials. In this work, we demonstrate anisotropic electrostatic screening for charged colloidal particles in a nematic electrolyte. We show that material anisotropy behaves markedly different from particle anisotropy. The electrostatic potential and pair interactions decay with an anisotropic Debye screening length, contrasting the constant screening length for isotropic electrolytes. Charged dumpling-shaped near-spherical colloidal particles in a nematic medium are used as an experimental model system to explore the effects of anisotropic screening, demonstrating competing anisotropic elastic and electrostatic effective pair interactions for colloidal surface charges tunable from neutral to high, yielding particle-separated metastable states. Generally, our work contributes to the understanding of electrostatic screening in nematic anisotropic media.

Spectral energy analysis of bulk three-dimensional active nematic turbulence.

We perform energy spectrum analysis of the active turbulence in a 3D bulk active nematic using continuum numerical modelling. Specifically, we calculate the spectra of the two main energy contributions - kinetic energy and nematic elastic energy - and combine this with the geometrical analysis of the nematic order and flow fields, based on direct defect tracking and calculation of autocorrelations. We show that the active nematic elastic energy is concentrated at scales corresponding to the effective defect-to-defect separation, scaling with activity as ∼ζ0.5, whereas the kinetic energy is largest at somewhat larger scales of typically several 100 nematic correlation lengths. Nematic biaxiality is shown to have no role in active turbulence at most length scales, but can affect the nematic elastic energy by an order of magnitude at scales of the active defect core size. The effect of an external aligning field on the 3D active turbulence is explored, showing a transition from an effective active turbulent to an aligned regime. The work is aimed at providing a contribution towards understanding active turbulence in general three-dimensions, from the perspective of main energy-relevant mechanisms at different length scales of the system.

Collective photonic response of high refractive index dielectric metasurfaces.

Sub-wavelength periodic nanostructures give rise to interesting optical phenomena like effective refractive index, perfect absorption, cloaking, etc. However, such structures are usually metallic which results in high dissipative losses and limitations for use; therefore, dielectric nanostructures are increasingly considered as a strong alternative to plasmonic (metallic) materials. In this work, we show light-matter interaction in a high refractive index dielectric metasurface consisting of an array of cubic dielectric nano-structures made of very high refractive index material, Te in air, using computer modelling. We observe a distinct band-like structure in both transmission and reflection spectra resulting from the near-field coupling of the field modes from neighboring dielectric structures followed by a sharp peak in the transmission at higher frequencies. From the spatial distribution of the electric and magnetic fields and a detailed multipole analysis in both spherical harmonics and Cartesian components, the dominant resonant modes are identified to be electric and magnetic dipoles. Specifically at lower frequency (60 THz) a novel anapole-like state characterized by strong-suppression in reflection and absorption is observed, reported very recently as 'lattice-invisibility' state. Differently, at higher frequency (62 THz), strong absorption and near-zero far field scattering are observed, which combined with the field profiles and the multipole analysis of the near-fields indicate the excitation of an anapole. Notably the observed novel modes occur in the simple geometry of dielectric cubes and are a result of collective response of the metasurfaces. Periodicity of the cubic metasurface is shown as the significant material tuning parameter, allowing for the near-field and far-field coupling effects of anapole metasurface. More generally, our work is a contribution towards developing far-fetching applications based on metamaterials such as integrated devices and waveguides consisting of non-radiating modes.

Topological-Defect-Induced Surface Charge Heterogeneities in Nematic Electrolytes.

We show that topological defects in an ion-doped nematic liquid crystal can be used to manipulate the surface charge distribution on chemically homogeneous, charge-regulating external surfaces, using a minimal theoretical model. In particular, the location and type of the defect encodes the precise distribution of surface charges and the effect is enhanced when the liquid crystal is flexoelectric. We demonstrate the principle for patterned surfaces and charged colloidal spheres. More generally, our results indicate an interesting approach to control surface charges on external surfaces without changing the surface chemistry.

Control of viscosity in biopharmaceutical protein formulations.

Controlling the viscosity of concentrated protein solutions - usually reducing - is an open challenge, with major recent relevance in protein formulations for biopharmaceutical, medical, food, and other applications. The addition of viscosity-reducing additives generally not only changes the viscosity of the protein solutions but also the actual secondary/tertiary structure of the proteins, which is usually highly undesirable, and can be even toxic in systems, such as for biopharmaceutical applications. Therefore, it is of major importance to be able to establish control over the combination of viscosity-affecting additives and adequate protein stability, usually at high protein concentrations. Here, we demonstrate the control and manipulation of the viscosity profile of a selected protein solution (monoclonal antibody of immunoglobulin gamma type IgG) of direct biopharmaceutical relevance, by identifying elementary viscosity contributions via selected additives that target different protein-protein interactions. Specifically, a combined study of viscosity control and protein aggregation is performed with viscosity characterized by microfluidic measurements and protein aggregation by size-exclusion chromatography, where aggregation data is further supplemented with conformational stability measurements via thermal and chemical protein denaturation. A dissection of contributions to total viscosity - steric, electrostatic, hydrophobic, van der Waals - is performed. A novel mechanism of the impact of electrostatic interactions on the viscosity of IgG solutions is proposed based on interacting charged protein patches subjected to orientational alignment under flow birefringence. More generally, we show a control over the interplay of viscosity, potency and stability in a distinct protein system, as a general contribution to understanding the viscosity in different colloidal, biological, and soft materials.

Three-Dimensional Active Defect Loops.

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge ±1/2 profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology. To address the general formation of defect loops in three dimensions, we show their creation via bend instability from different initial elastic distortions.