Geometrical Confinement Research Articles

Optimizing Circular Rotations in Confined Systems via Enhanced Self-Driven Speed of Active Nematics

Abstract Active matter exhibits collective motions at various scales. Geometric confinement has been identified as an effective way to control and manipulate active fluids, with much attention given to external factors. However, the impact of the inherent properties of active particles on collective motion under confined conditions remains elusive. Here, we use a highly tunable active nematics model to study active systems under confinement, focusing on the effect of self-driven speed of active particles. We identify three distinct states characterized by unique particle and flow fields within confined active nematic systems, among which circular rotation emerges as a collective motion involving rotational movement in both particle and flow fields. The theoretical phase diagram shows that increasing the self-driven speed of active particles significantly enhances the region of circular rotation state and improves its stability. Our results provide insights into the formation of high quality vortices in confined active nematic systems.

Collective phase transitions in confined fish schools

The collective patterns that emerge in schooling fish are often analyzed using models of self-propelled particles in unbounded domains. However, while schooling fish in both field and laboratory settings interact with domain boundaries, these effects are typically ignored. Here, we propose a model that incorporates geometric confinement, by accounting for both flow and wall interactions, into existing data-driven behavioral rules. We show that new collective phases emerge where the school of fish "follows the tank wall" or "double mills." Importantly, confinement induces repeated switching between two collective states, schooling and milling. We describe the group dynamics probabilistically, uncovering bistable collective states along with unintuitive bifurcations driving phase transitions. Our findings support the hypothesis that collective transitions in fish schools could occur spontaneously, with no adjustment at the individual level, and opens venues to control and engineer emergent collective patterns in biological and synthetic systems that operate far from equilibrium.

Nanoscopically Confined 1,4-Polybutadiene Melts: Exploring Confinement by Alumina Nanorod and Nanopore Systems.

We present molecular dynamics simulations of a chemically realistic model of 1,4-polybutadiene (PBD) in contact with curved alumina surfaces. We contrast the behavior of PBD infiltrated into alumina pores with a curvature radius of about three times the radius of gyration of the chains to its behavior next to a melt dispersed alumina rod of equal absolute curvature. These confinement types represent situations occurring in polymer melts loaded with nanoparticles due to nanoparticle aggregation. While there are observable differences in structure and dynamics due to the different types of geometric confinement, the main effects stem from the strong attraction of PBD to the alumina surfaces. This strong attraction leads to a deformation of the chains in contact to the surfaces. We focus on temperatures well above the bulk glass transition temperature, but even at these high temperatures, the layers next to the alumina surfaces show glass-like relaxation behavior. We analyze the signature of this glassy behavior for neutron scattering or nuclear magnetic resonances experiments.

Enhanced non-equilibrium Peltier cooling through electron gas expansion: A Monte Carlo simulation study

We demonstrate enhanced Peltier cooling at the nanoscale using geometrical constriction. This nozzle structure leads to electron expansion under an applied bias, which in turn results in additional cooling. This extra cooling enhances the overall Peltier effect when the electrons are out of equilibrium with the lattice. An ensemble Monte Carlo simulation is used to demonstrate the non-equilibrium expansion of an electron gas using nanoscale trapezoidal geometric confinement. The proposed device operates under steady-state conditions, providing enhanced cooling compared to a one-dimensional flat geometry. We observe a five-fold increase in both the maximum cooling temperature and cooling power density, reaching more than 5 kW/cm2, when comparing the trapezoidal geometry to the regular flat geometry.

Mechanical reinforcement and confinement in elastomeric corn starch/bentonite nanocomposites

The mechanical reinforcement of plasticized corn starch (CS) films induced by bentonite nanoclay was investigated using dynamic mechanical analysis and rheology. Dynamic temperature scans revealed mechanical reinforcement from cryogenic to high temperatures, and two mechanical relaxations named α and α’. The lower temperature relaxation α was associated with long range cooperative molecular motions typical of the glass transition and it was associated to glycerin-rich domains, ranging from −60 °C to −40 °C. The mechanical relaxation α′ was detected in the range −30 °C to −10 °C and it may be associated to phase separated starch-rich domains. The morphology was a function of bentonite concentration, at cbentonite<3 wt% the nanoplatelets were exfoliated and c ≥ 3 wt% they were intercalated. Strikingly, at 3 wt% bentonite content the elastic modulus E′ increased drastically. The viscoelastic properties showed that the geometrical confinement exerted by the nanoplatelets also induced a decrease of fractional free volume fg and of apparent molecular weight between crosslinks Mc,app, and an increase of the activation energy Ea of the α’ relaxation. Spatial confinement in the intercalated morphology appears to be the source of mechanical reinforcement of CS/bentonite nanocomposites.

Achieving exceptional high-temperature strength in a cast Mg alloy via LPSO honeycomb shell

Conventional casting Mg alloys tend to lose strength quickly when exposed to elevated temperatures (200–300 °C). Here, we report a cast Mg alloy decorated by honeycomb LPSO structure via high pressure die casting, with an impressive strength of 191 MPa at 300 °C, exceeding all traditional cast Mg based alloys and common Al-Si alloys. Such remarkable strength ascribes to the strong geometric confinement of the LPSO cellular shell to grain boundaries and dislocations, coupled with extra strain hardening derived from <a> dislocation interactions with stacking faults. In addition, non-basal <a> and <c> dislocations avoid macro-plastic instability at high strains.

Geometric frustration and pairing-order transition in confined bacterial vortices

Dense systems of active matter exhibit highly dynamic collective motion characterized by intermingled vortices, referred to as active turbulence. The interaction between these vortices is key to controlling turbulent dynamics, and a promising approach for revealing the rules governing their interaction is geometric confinement. In this study, we investigate the vortex-pairing patterns in confined bacterial suspensions as a model frustrated system in which a perfect antiferromagnetic state is prohibited. We find that three-body vortex interactions exhibit anomalous pairing-order transition from corotational vortex pairing to counterrotating patterns with frustration. Although an active matter system is in nonequilibrium, our theory based on bending energy accounts for significant features, including pattern transition and a shift of the transition point in frustrated systems. Moreover, the interplay between the chirality in collective motion and frustration in vortex pairing creates a collective rotational flow under the broad geometric conditions of a confined space. Our results show that frustrated vortex patterning promotes a geometric approach for arranging active turbulence in microfluidic systems. Published by the American Physical Society 2024

Cryogenic Atom Probe Tomograph to Resolve Confined Electrochemical Interfaces

Atom Probe Tomography (APT) is an analysis technique capable of providing a 3-dimensional, element-sensitive map of needle-shaped samples (where the tip radius is about 50 nm) with sub-nanometre resolution [1]. APT analysis is carried out at temperatures in the range of 25-75 K to limit the thermal motion of surface atoms which improves the spatial and mass resolution. As a result, this enables the analysis of frozen liquids, and by extension solid-liquid interfaces, by so-called “cryo-APT”. While this was historically challenging, recent advancements in UHV-cryogenic transfer and sample preparation methods now make it possible for the atomic scale analysis of interfacial species in electrochemical systems [2-4].In this study, we will attempt to explore the effect of nanoscale geometrical confinement on the distribution of interfacial ions for the first time and to resolve the electric double layer, using cryo-APT. We will describe the workflow for cryo-APT sample preparation to study confined solid-liquid interfaces, using nanoporous gold as a template material with a frozen sodium iodide solution inside its pores. APT reconstructions will allow 3-dimensional mapping of aqueous interfacial species, helping to develop our understanding of the structure of the electric double layer under nanoscale geometrical confinement. The attached Figure shows an SEM image of the later stages of cryo-FIB milling of an APT tip of frozen deionised water and 50 mM sodium iodide and a segment of the related APT atom map reconstruction.

Measuring colloidomer hydrodynamics with holographic video microscopy.

In-line holographic video microscopy records a wealth of information about the microscopic structure and dynamics of colloidal materials. Powerful analytical techniques are available to retrieve that information when the colloidal particles are well separated. Large assemblies of close-packed particles create holograms that are substantially more challenging to interpret. We demonstrate that Rayleigh-Sommerfeld back propagation is useful for analyzing holograms of colloidomer chains, close-packed linear assemblies of micrometer-scale emulsion droplets. Colloidomers are fully flexible chains and undergo three-dimensional configurational changes under the combined influence of random thermal forces and hydrodynamic forces. We demonstrate the ability of holographic reconstruction to track these changes as colloidomers sediment through water in a horizontal slit pore. Comparing holographically measured configurational trajectories with predictions of hydrodynamic models both validates the analytical technique for this valuable class of self-organizing materials and also provides insights into the influence of geometric confinement on colloidomer hydrodynamics.

Stabilizing and Accelerating Secondary Flow in Ultralong Spiral Channel for High-Throughput Cell Manipulation.

Efficient cell manipulation is essential for numerous applications in bioanalysis and medical diagnosis. However, the lack of stability and strength in the secondary flow, coupled with the narrow range of practical throughput, severely restricts the diverse applications. Herein, we present an innovative inertial microfluidic device that employs a spiral channel for high-throughput cell manipulation. Our investigation demonstrates that the regulation of Dean-like secondary flow in the microchannel can be achieved through geometric confinement. Introducing ordered microstructures into the ultralong spiral channel (>90 cm) stabilizes and accelerates the secondary flow among different loops. Consequently, effective manipulation of blood cells within a wide cell throughput range (1.73 × 108 to 1.16 × 109 cells/min) and cancer cells across a broad throughput range (0.5 × 106 to 5 × 107 cells/min) can be achieved. In comparison to previously reported technologies, our engineering approach of stabilizing and accelerating secondary flow offers specific performance for cell manipulation under a wide range of high-throughput manner. This engineered spiral channel would be promising in biomedical analysis, especially when cells need to be focused efficiently on large-volume liquid samples.

Electron-related properties in a GaAs/GaAlAs Ultra-thin Core/Shell Film through external field direction for energy and photonic devices

In this paper, we investigate electron-related properties in GaAs/GaAlAs Ultra-thin Core/Shell Film Quantum dot (UTFQD), examining the effects of external electric fields, impurity position, and aluminum fraction. Using the finite element method (FEM) within the effective mass approximation, we numerically solve the Schrödinger equation to study electron probability density, polarizability, and diamagnetic susceptibility. Our results reveal that electric fields can shift electron probability density due to the Stark effect. Without an electric field, the density centers near the shell's core. However, with electric fields, the density shifts opposite to the field's direction. Moreover, polarizability and diamagnetic susceptibility are influenced by impurity position and aluminum fraction. Polarizability increases with electric field intensity, indicating a transition from geometrical confinement to the Stark effect. Diamagnetic susceptibility rises with more aluminum, indicating stronger electron confinement. These findings suggest that adjusting electric fields, impurity position, and aluminum fraction in GaAs/GaAlAs core/shell QDs can control electron behavior, providing flexibility for photonic devices. This study offers a foundation for optimizing quantum dot-based components in photonics.

Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones.

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the timescales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a rich phase diagram of multidefect dynamics, including exotic periodic orbits of one or two +1/2 flank defects, depending on activity and nonquantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we present detailed understanding of (i) defect unbinding, (ii) defect absorption, and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.

Controlling Chaos: Periodic Defect Braiding in Active Nematics Confined to a Cardioid.

This work examines self-mixing in active nematics, a class of fluids in which mobile topological defects drive chaotic flows in a system comprised of biological filaments and molecular motors. We present experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the defects. Notably, we show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state of exactly three defects with no defect creation or annihilation. We characterize the golden braid state using different measures of topological entropy and the Lyapunov exponent. In particular, topological entropy measured from the stretching rate of material lines agrees well with an analytical computation from braid theory. Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic active turbulent state.

Stepwise ordering under nano-scale confinement in thin silica films

The phase transition from an amorphous 2D structure to a crystalline 3D structure under confinement is a fascinating and challenging problem in materials science and condensed matter physics. This work reports the Field Emission Scanning Electron Microscopy (FESEM) and energy dispersive analysis of X-rays (EDAX), X-ray diffraction (XRD), X-ray reflectivity (XRR), Fourier Transform Infrared Spectroscopy (FTIR) studies on pristine silica thin films. Silica was deposited on pristine Al (001) substrate (Alfa-Aesar) from tetraethyl orthosilicate (TEOS) precursor and thin films were spin-coated at different spinning frequencies under ambient conditions. The samples are highly porous and in-plane porosity varies from 30% to 60% as analyzed from both the FESEM and XRR and with increasing spinning frequency pores become more ordered. XRR shows that the samples are composed of two layers, a thick layer of aluminum oxide (Al2O3) as buffer layer and a layer of SiO2 on the top of the film. XRR shows sharp ordering rather than any layering. The film thickness varies from 90[Formula: see text]Å to 200[Formula: see text]Å and it shows a linear decay in the thickness of silica layer. In between 1000 and 1500[Formula: see text]rpm, XRR shows a sharp drop in the thickness of silica layer where thickness of this layer falls below the unit-cell dimension indicating higher-ordered crystallization under strained condition. XRD shows that there are no crystalline peaks coming from silica at lower rpm except the peaks of Al coming from the substrate. At 1000, 1200 and 1500[Formula: see text]rpm there is peak corresponding to the quartz, highly crystalline phase of SiO2 and where the substrate is slightly modified Al2O3. Reflection from (101) plane is prominent in all the films and it gives indication of formation 3D crystalline phase. Whereas FTIR shows that the Si–O stretching modes exhibit sharper and more defined reflectance peak compared to the broad bands observed in the samples in lower rpm. Observations suggest a clear indication of progressive ordering under confinement. To one extent, the results of XRR and FESEM will suggest the mechanism of transition from 2D amorphous to 3D crystalline phase under geometrical confinement effect and total confinement effect arising from thinning of the films with the increasing rpm, interfacial effect and on the other hand XRD and FTIR results will explain high ordering under confinement without any layering.

Electronic transport properties in GaAs/AlGaAs finite superlattice of cylindrical quantum wires

In this paper, we have studied a theoretical and numerical investigation of the electronic properties of finite cylindrical quantum wires (CQWRs), constituted by the periodic alteration of two semiconductor materials of CQWRs GaAs/AlGaAs in the axial direction, the structure sandwiched between two substrates GaAs. The electronic band structure and the electronic transmission spectrum are obtained by means of Green’s function approach, taking into account the impact of connection barriers. Our results reveal that the electronic energy levels of CQWRs consist of alternating passbands and bandgaps. The coincidence of incoming electronic waves with these discrete electronic energy levels leads to electron transport during the CQWRs superlattice. We employed an effective mass model dependent on the cell position in the axial direction to solve the Schrodinger equation. This model was adjusted to reflect variations in the confining potentials while accounting for changes in the radial direction. When the radius of the structure is relatively small the electronic states tend towards higher energies due to geometrical confinement. On the other hand, as the radius increases, the passbands and bandgaps move to lower energies. Similarly, the pseudogaps turn into full gaps, and their width increases, and this feature is also observed when the number of cells increases. This property is due to the interaction between the neighboring electrons and the eigenstates of the CQWRs. In addition, the passbands and band gaps shift to high energy when the barrier concentration increases, and the width of band gaps increases also. Finally, we have demonstrated the theoretical design of an optoelectronic device for filtering electronic waves by geometrical and physical parameters, whose electronic band structure of this finite CQWRs superlattice can be controlled.

Self-Assembly of Ionic Superdiscs in Nanopores.

Discotic ionic liquid crystals (DILCs) consist of self-assembled superdiscs of cations and anions that spontaneously stack in linear columns with high one-dimensional ionic and electronic charge mobility, making them prominent model systems for functional soft matter. Compared to classical nonionic discotic liquid crystals, many liquid crystalline structures with a combination of electronic and ionic conductivity have been reported, which are of interest for separation membranes, artificial ion/proton conducting membranes, and optoelectronics. Unfortunately, a homogeneous alignment of the DILCs on the macroscale is often not achievable, which significantly limits the applicability of DILCs. Infiltration into nanoporous solid scaffolds can, in principle, overcome this drawback. However, due to the experimental challenges to scrutinize liquid crystalline order in extreme spatial confinement, little is known about the structures of DILCs in nanopores. Here, we present temperature-dependent high-resolution optical birefringence measurement and 3D reciprocal space mapping based on synchrotron X-ray scattering to investigate the thermotropic phase behavior of dopamine-based ionic liquid crystals confined in cylindrical channels of 180 nm diameter in macroscopic anodic aluminum oxide membranes. As a function of the membranes' hydrophilicity and thus the molecular anchoring to the pore walls (edge-on or face-on) and the variation of the hydrophilic-hydrophobic balance between the aromatic cores and the alkyl side chain motifs of the superdiscs by tailored chemical synthesis, we find a particularly rich phase behavior, which is not present in the bulk state. It is governed by a complex interplay of liquid crystalline elastic energies (bending and splay deformations), polar interactions, and pure geometric confinement and includes textural transitions between radial and axial alignment of the columns with respect to the long nanochannel axis. Furthermore, confinement-induced continuous order formation is observed in contrast to discontinuous first-order phase transitions, which can be quantitatively described by Landau-de Gennes free energy models for liquid crystalline order transitions in confinement. Our observations suggest that the infiltration of DILCs into nanoporous solids allows tailoring their nanoscale texture and ion channel formation and thus their electrical and optical functionalities over an even wider range than in the bulk state in a homogeneous manner on the centimeter scale as controlled by the monolithic nanoporous scaffolds.

A new method for determining the ogden parameters of soft materials using indentation experiments

A full understanding of the material properties of skin tissue is crucial for exploring its tribo-mechanical behaviour. It has been widely accepted that the mechanical behaviour of skin tissue for both small and large deformations can be accurately described using a hyperelastic model, such as the one developed by Ogden. However, obtaining these Ogden parameters for in-vivo skin by in-vivo experiments no matter the indentation or suction tests is a significant challenge. The mathematical model used to describe the material behaviour during the test should consider not only the material nonlinearity but also the geometrical confinement of the tissue, the large deformations induced, and the fact that the specimens are relatively thin.A range of contact models is available to describe the contact behaviour during the indentation test. However, none of them can be used for hyperelastic materials with small thickness under large deformations. Simultaneously explaining material nonlinearity and geometric nonlinearity, either through theoretical equations or numerical calculations, poses a significant challenge.In this research, we propose a pragmatic method to obtain Ogden parameters for in-vivo skin tissue by combining experimental indentation results and numerical simulations. The indentation tests were used to obtain the force-indentation depth curves, while the numerical simulations were used to obtain the strain fields. The method assumes the material behaviour of specimens can be linearized in each small deformation increment, and the contact model developed by Hayes can be applied to accommodate each increment. Then, the linear elastic behaviour in each increment can be described by the elastic modulus E which were obtained using Hayes model, and the principal stresses in each increment were subsequently obtained using Hooke's law. By combining all stress fields, overall stress-strain curves can be constructed, from which the hyperelastic Ogden parameters can be obtained. A second numerical simulation of the hyperelastic indentation was then performed using the obtained Ogden parameters, allowing a comparison of the experimental and simulated relationships between force and indentation.

Fluid entrapment during forced imbibition in a multidepth microfluidic chip with complex porous geometry

Understanding and controlling fluid entrapment during forced imbibition in porous media is crucial for many natural and industrial applications. However, the microscale physics and macroscopic consequences of fluid entrapment in these geometric-confined porous media remain poorly understood. Here, we introduce a novel multidepth microfluidic chip, which can mitigate the depth confinement of traditional two-dimensional (2-D) microfluidic chips and mimic the wide pore size distribution as natural-occurring three-dimensional (3-D) porous media. Based on microfluidic experiments and direct numerical simulations, we observe the fluid-entrapment scenarios and elucidate the underlying complex interaction between geometric confinement, capillary number and wettability. Increasing depth variation can promote fluid entrapment, whereas increasing capillary number and contact angle yield the opposite effect, which seemingly contradicts conventional expectations in traditional 2-D microfluidic chips. The fluid-entrapment scenario in depth-variable microfluidic chips stems from microscopic interfacial phenomena, classified as snap-off and bypass events. We provide theoretical analyses of these pore-scale events and validate corresponding phase diagrams numerically. It is shown that increasing depth variation triggers snap-off and bypass events. Conversely, a higher capillary number suppresses snap-off events under strong imbibition, and an increased contact angle inhibits bypass events under imbibition. These macroscopic imbibition patterns in microfluidic porous media can be linked with these pore-scale events by improved dynamic pore-network models. Our findings bridge the understanding of forced imbibition between 2-D and 3-D porous media and provide design principles for newly engineered porous media with respect to their desired imbibition behaviours.

Interfacial molecular structure and orientation evolution of the polystyrene under confinement during annealing revealed by sum frequency generation vibrational spectroscopy

The geometrical confinement directly affects many crucial properties of polymer thin films by interfacial interactions. A key to understanding the role of these interfacial interactions is to specifically probe the confined interface at the molecular level and in situ. However, the direct and nondestructive detection of interfacial polymer structures under confinement is very difficult. In this study, specific interface-sensitive sum frequency generation (SFG) spectroscopy was applied to study the deuterated PS (d8-PS) film confined between hydrogenated poly (methyl methacrylate) (PMMA) films at the molecular level and in situ. The results showed that the ordering/orientation of the PS chain (backbone and phenyl group) evolved at the buried d8-PS/PMMA interface during annealing. The tilt angle of the PS phenyl group increased while the twist angle decreased with elevated annealing temperature. Both overall SFG ssp and ppp intensities decreased after annealing at 433 K for 24 h, indicating that PS chains entangled with or penetrated the PMMA chains at the confined interface. This study qualitatively and quantitatively revealed the interfacial structure and structural evolution of the PS chain confined between PMMA films in situ during annealing, which is beneficial to the molecular-level understanding of the interfacial chain conformational relaxation of polymers under confinement.

Electronic states in GaAs/AlGaAs/GaAs core/shell cylindrical quantum wires

Cylindrical quantum wires (CQWRs) based on GaAs/ AlxBGa1−xBAs /GaAs core/shell semiconductors are multilayer semiconductor nanostructures that exhibit interesting electronic properties. In this study, we explore in detail the electronic band structure and electronic transmission spectrum in these core/shell CQWRs in relation to various parameters such as inner and outer shell radius and aluminum-doping rate. Using Green’s function formalism, an advanced theoretical approach to solving Schrödinger’s equation in the effective mass approximation, taking into account the confinement potential of the cylindrical geometry. The results show that as the difference between the outer and inner radii of the shell increases, the number of electronic states increases due to the weakening of geometric confinement. In addition, as the concentration of Aluminum in the shell increases, the electronic states move to higher energies, due to the increase in confinement by the height of the potential. This study aims to provide an overview of the electronic states in core/shell nanowires, due to modification in Al molar concentration and shell size; they offer advantages such as better electronic transmission. We can control the electronic band structure of this nanowire, which can be used to fabricate high-performance electronic devices such as transistors, diodes and sensors.