Cylindrical Confinement Research Articles

Compaction and clustering of a heterogeneous polymer by biomolecular crowding.

Inspired by bacterial chromosome organization, we study the compaction and clustering of a heterogeneous ring polymer in a crowded medium using molecular dynamics simulations. The polymer consists of several large monomers interspersed along the backbone and small intervening monomers. In a crowded medium, the entropy of crowding particles or crowders favors the collapse of chain molecules, such as chromosomes. Our study shows that the compaction transition of heterogeneous polymers by crowders is well-correlated with the clustering of large monomers: when the large monomers are sufficiently large, both occur concomitantly in the same narrow (biologically relevant) range of the volume fraction of crowders. It also indicates that cylindrical confinement makes crowding effects more effective. The results presented here suggest that phase separation and clustering are essential features of bacterial chromosome organization.

Free energy and extension of stiff polymer chains confined in nanotubes with diverse cross-sectional shapes

The statistical mechanics of stiff polymer chains confined within narrow tubes is a foundational topic in polymer physics, extensively analyzed in prior research. For cylindrical, rectangular, and slit-like confinements, the chains’ free energy and extension adhere to a scaling law consistent with the Odijk theory. While this scaling law may not apply to tubes with different cross-sectional geometries, there is a lack of research examining the behavior of stiff chains in tubes with intricate cross-sectional shapes. In this study, we investigate the partition function of a stiff chain confined within an elliptic tube using the path integral approach, deriving a deflection length in a concise closed form through dimensional analysis. This length scale facilitates straightforward expressions for the chain's free energy and extension. Notably, we discover a shape-independent property of these expressions applicable to tubes with a wide variety of cross-sectional geometries. Extensive numerical simulations are conducted using a biased chain-growth Monte Carlo method, incorporating the Pruned and Enriched Rosenbluth algorithm, to validate the theoretical predictions on the confinement free energy and extension of chains in tubes with differing shapes.

Characterization of a radially emitting spray jet in a cylindrical inertial electrostatic confinement plasma source based on particle in cell simulation

This paper investigates the outflow mechanism of a cylindrical inertial electrostatic confinement plasma source using Particle in Cell plasma simulations. Various phenomena such as ion-wall interactions, impact ionization, excitation, and secondary electron generation are considered. Together with a fine time and cell resolution to reveal relevant phenomena. The results indicate a high electron and ion density in front of the cathode at the widest grid opening, which suggests the formation of a cascade-like charge carrier emission, commonly referred to as the “spray jet”. Initially, a virtual anode is formed within the cathode grid and is shifted toward the grid opening as time elapsed. Ions are accelerated in the plasma sheath around the cathode and collide with the cathode grids or oscillate through the grid opening. Electrons are accelerated and ionize the background gas at the plasma sheath edge. While the electron flow is disordered within the cathode it forms a cascade-like quasi-neutral plasma at the outlet of the plasma source. Through the formation of a virtual anode the discharge becomes self-sustained. With this simulation results the working principle of the inertial electrostatic confinement plasma source can be derived.

Coarse-grained molecular simulation of the effect of liquid crystal molecular pitch on structure in cylindrical confinement.

Blue phases (BPs) consist of three-dimensional self-assembled structures formed by a double-twisted columnar arrangement of liquid crystal molecules. Although their unique optical and structural properties render BPs particularly useful for applications such as liquid crystal displays, BPs typically appear in a narrow temperature range between the isotropic and nematic phases. This thermodynamic instability impedes their practical applicability. However, the simulations we present here showed that, in a quasi-one-dimensional system confined to nanospace, a phase equivalent to the BP appears and persists between the nematic and smectic phases. Confinement to a nanotube (NT) with a relatively small radius enables the BP to be maintained over a wide temperature range, whereas for an NT with a relatively larger radius, the BP appears only in a very narrow temperature range between the aforementioned phases. We additionally showed that the pitch of the BP is dependent on and can be controlled by adjusting the radius of the NTs. This finding has significant implications for the potential application of these materials in fields such as photonics and chiral separation technologies.

Prismatic Confinement Induces Tunable Orientation in Plasmonic Supercrystals.

Throughout history scientists have looked to Nature for inspiration and attempted to replicate intricate complex structures formed by self-assembly. In the context of synthetic supercrystals, achieving such complexity remains a challenge due to the highly symmetric nature of most nanoparticles (NPs). Previous works have shown intricate coupling between the self-assembly of NPs and confinement in templates, such as emulsion droplets (spherical confinement) or tubes (cylindrical confinement). This study focuses on the interplay between anisotropic NP shape and tunable "prismatic confinement" leading to the self-assembly of supercrystals in cavities featuring polygonal cross sections. A multiscale characterization strategy is employed to investigate the orientation and structure of the supercrystals locally and at the ensemble level. Our findings highlight the role of the mold interface in guiding the growth of distinct crystal domains: each side of the mold directs the formation of a monodomain that extends until it encounters another, leading to the creation of grain boundaries. Computer simulations in smaller prismatic cavities were conducted to predict the effect of an increased confinement. Comparison between prismatic and cylindrical confinements shows that flat interfaces are key to orienting the growth of supercrystals. This work shows a method of inducing orientation in plasmonic supercrystals and controlling their textural defects, thus offering insight into the design of functional metasurfaces and hierarchically structured devices.

Confinement-induced self-assembly of a diblock copolymer within a non-uniform cylindrical nanopore.

The self-assembly of a diblock copolymer melt confined within a non-uniform cylindrical nanopore is studied using the self-consistent field theory. The non-uniformity manifests in the form of a converging-diverging cylindrical nanopore. The axial variation in pore diameter presents a range of curvatures within the same confinement pore as opposed to a single curvature in a uniform-diameter cylindrical pore. The introduction of multiple curvatures leads to the formation of novel microstructures not accessible in uniform cylindrical confinement. The well-known equilibrium structures like a single helix, double helices, and concentric lamella under cylindrical confinement transition into new morphologies such as hyperboloidal phases, microstructures containing rings with a bead, rings with spheres, and a squeezed helical phase as the pore diameter varies axially. The converging-diverging geometry of the confining pore renders the helical phases seen in the cylindrical pore less favorable. A phase diagram in the parametric space of the block fraction and the ratio of the smallest and largest pore radii has been constructed to depict the order-order transition of various microstructures. The ratio of radii, a measure of the non-uniformity of the pore, along with the pore length brings out some interesting morphologies. The mechanism of these structural transitions is understood as the interplay between the variation in pore curvature attributed to the non-uniformity, the spontaneous curvature of the block copolymer interface, and the enthalpic interaction between the segregated blocks.

Transition Paths of Ordered Phases in a Diblock Copolymer under Cylindrical Confinement

Transition Paths of Ordered Phases in a Diblock Copolymer under Cylindrical Confinement

Sensitive determination of rare earth elements in liquid samples by spatial confinement assisted surface enhanced laser-induced breakdown spectroscopy

The rapid determination of rare earth elements (REEs) in liquid samples holds significant importance for various applications such as the exploration and development of REEs resources, quality control of the extraction process, regeneration and recycling of REEs, and monitoring of nuclear industry wastewater. This study employed spatial confinement assisted surface-enhanced laser-induced breakdown spectroscopy (SC-SE-LIBS) for REEs determination in liquid samples. Investigations were conducted into the impact of different material substrates, sample pretreatment methods, and spatial confinement cavity diameters on detection performance. The results reveal that the graphite substrate yields superior spectral signal intensity compared to other materials (Zn, Al, and Ni). The groove-constrained liquid–solid conversion (GCLSC) pretreatment method significantly enhances spectral stability and detection accuracy. The most favorable signal enhancement is achieved using a cylindrical spatial confinement cavity (CSCC) with an 8 mm diameter. Employing the optimized experimental conditions, quantitative analysis of six REEs (La, Ce, Pr, Nd, Gd, Y) in liquid samples was performed using analytical lines at wavelengths of La Ⅱ 394.91 nm, Ce Ⅱ 401.24 nm, Gd Ⅱ 404.99 nm, Nd Ⅱ 406.11 nm, Pr Ⅱ 417.94 nm, and Y Ⅱ 488.37 nm. The obtained calibration curves exhibited R2 fit coefficients above 0.99, with corresponding limits of detection (LoDs) of 0.021 μg/mL, 0.104 μg/mL, 0.312 μg/mL, 0.241 μg/mL, 0.036 μg/mL, and 0.045 μg/mL, respectively.

Helical structures of achiral liquid crystals under cylindrical confinement.

Confined liquid crystals (LCs) exhibit complex and intriguing structures, which are fascinating fundamental problems in soft matter. The helical structure of cylindrical cavities is of great importance in LC studies, particularly for their application in optical devices. In this study, we employ molecular dynamics simulations to explore the behavior of achiral smectic-B LCs confined in narrow cylindrical cavities, where geometric frustration plays an important role. By increasing the cylinder size, LCs exhibit a transition from multi-helical to layered structures. Notably, we observe two stable structures, namely the helical structure and the layered structure, at moderate cylinder size. We also investigate the effects of the arrangement of cylindrical wall particles (hexagonal or square array) and anchoring strength on the LC structure. Our findings reveal that both the hexagonal array and strong anchoring strength promote the formation of helical structures. Our study provides novel insights into the confinement physics of LCs and highlights the potential for achieving helical structures in achiral LCs, which will expand the future applications of LCs.

Conformation and Dynamics of Ring Polymer Chains under Cylindrical Confinement

AbstractUsing coarse‐grained molecular dynamics simulations, the conformation and dynamic behavior of ring polymer chains in ring/linear blends confined into cylinders are studied. By changing the particle number density, polymer chain bending energy and length, the spatial distribution of rings in the constrained binary polymer blends is investigated. An ordered tubular structure composed of several quasi‐parallel rings is observed. The mean square displacement of the center‐of‐mass of ring chains and its diffusion coefficient are analyzed. The results indicate that the diffusion behavior of rings is transformed from inhibition to promotion as the increase of linear chain bending energy. This study provides a new way to further understand the special conformation and dynamic behavior of ring polymer chains in constrained systems.

Second harmonic generation on crystalline organic nanoclusters under extreme nanoconfinement in functionalized silica–benzil composites

We demonstrate a series of organic–inorganic nanocomposite materials combining the mesoporous silica (PS) and benzil (BZL) nanocrystals embedded into its nanochannels (6.0–13.0 nm in diameter) by capillary crystallization. One aims to design novel, efficient nonlinear optical composite materials in which inactive amorphous host PS-matrix provides a tubular scaffold structure, whereas nonlinear optical functionality results from specific properties of the deposited guest BZL-nanocrystals. A considerable contraction of the BZL melt during its crystallization inside the silica nanochannels results in a formation of the texture consisting of (221)- and (003)-oriented BZL nanoclusters (22 nm in length), separated by voids. Specificity of the textural morphology similarly to the spatial confinement significantly influences the nonlinear optical features of composite PS:BZL materials being explored in the second harmonic generation (SHG) experiment. The light polarization anisotropy of the SHG response appears to be considerably reduced at channel diameters larger than 7 nm apparently due to the multiple scattering and depolarization of the light on randomly distributed and crystallographically oriented BZL-nanoclusters. The normalized SHG response decreases nonlinearly by more than one order of magnitude as the channel diameter decreases from 13.0 to 6.0 nm and vanishes when spatial cylindrical confinement approaches the sizes of a few molecular layers suggesting that the embedded BZL clusters indeed are not uniformly crystalline but are characterized by more complex morphology consisting of a disordered SHG-inactive amorphous shell, covering the channel wall, and SHG-active crystalline core. Understanding and controlling of the textural morphology in inorganic–organic nanocrystalline composites as well as its relationships with nonlinear optical properties can lead to the development of novel efficient nonlinear optical materials for the light energy conversion with prospective optoelectronic and photonic applications.

Double-enhanced LIBS system with N2 atmosphere and cylindrical cavity confinement for quantitative analysis of Sr element in soil

To effectively improve the quality of laser-induced plasma spectra and the detection accuracy of laser-induced breakdown spectroscopy (LIBS) simultaneously for Sr element in soil, the dual mechanism of N2 atmosphere combined with cylindrical cavity confinement for laser-induced Sr plasma emission enhancement was proposed and investigated in this paper, and a multi-spectral fusion internal standard analysis model was established. Optimum enhancement effect can be achieved under the conditions of 2 mm diameter and 6 mm height of the confinement cavity in N2 atmosphere, where the enhancement factor was about 3.25, the signal-to-noise ratio reached 710.28, and the LIBS spectrum quality was the best; the relative standard deviation value (2.64%) was the smallest, and the LIBS signal reproducibility was the best. For the samples in this study, the limit of detection of the sample Sr elements under the dual enhancement mechanism was 34.60 mg kg−1, which was 40.43% lower than the limit of detection (LOD) without enhancement mechanism (58.08 mg kg−1), and the R 2 of the multispectral fusion internal standard model was 1.23% higher and the relative error was 3.41% lower than that of the internal standard method. The results showed that the dual enhancement mechanism combining N2 atmosphere and cylindrical cavity confinement improved the spectral quality, signal reproducibility, and detection sensitivity.

Theory and Simulations of Ionic Liquids in Nanoconfinement.

Room-temperature ionic liquids (RTILs) have exciting properties such as nonvolatility, large electrochemical windows, and remarkable variety, drawing much interest in energy storage, gating, electrocatalysis, tunable lubrication, and other applications. Confined RTILs appear in various situations, for instance, in pores of nanostructured electrodes of supercapacitors and batteries, as such electrodes increase the contact area with RTILs and enhance the total capacitance and stored energy, between crossed cylinders in surface force balance experiments, between a tip and a sample in atomic force microscopy, and between sliding surfaces in tribology experiments, where RTILs act as lubricants. The properties and functioning of RTILs in confinement, especially nanoconfinement, result in fascinating structural and dynamic phenomena, including layering, overscreening and crowding, nanoscale capillary freezing, quantized and electrotunable friction, and superionic state. This review offers a comprehensive analysis of the fundamental physical phenomena controlling the properties of such systems and the current state-of-the-art theoretical and simulation approaches developed for their description. We discuss these approaches sequentially by increasing atomistic complexity, paying particular attention to new physical phenomena emerging in nanoscale confinement. This review covers theoretical models, most of which are based on mapping the problems on pertinent statistical mechanics models with exact analytical solutions, allowing systematic analysis and new physical insights to develop more easily. We also describe a classical density functional theory, which offers a reliable and computationally inexpensive tool to account for some microscopic details and correlations that simplified models often fail to consider. Molecular simulations play a vital role in studying confined ionic liquids, enabling deep microscopic insights otherwise unavailable to researchers. We describe the basics of various simulation approaches and discuss their challenges and applicability to specific problems, focusing on RTIL structure in cylindrical and slit confinement and how it relates to friction and capacitive and dynamic properties of confined ions.

Emergence and Stability of Hierarchical Structures under Cylindrical Confinement

Front Cover: In article number 2200076, Tiancheng Chen and Yuci Xu study the self-assembly of A(BC)2B multiblock copolymer in a nanopore using the self-consistent field theory. Obtain the hierarchical concentric ring (HCk), hierarchical perforated cylinder (HPk), hierarchical helix (HHk), and hierarchical disk (HDk) in research. Then discuss the stability of hierarchical structures by exploring the influence of pore size and χAB on k.

Emergence and Stability of Hierarchical Structures under Cylindrical Confinement

AbstractFocusing on the formation of hierarchical structure under cylindrical confinement, the self‐assembly of A(BC)2B multiblock copolymer of chain length N in a nanopore with size R is studied using the self‐consistent field theory. The hierarchical concentric ring (HCk), hierarchical perforated cylinder (HPk), hierarchical helix (HHk), and even hierarchical disk (HDk) is obtained with different number of mid‐thin layers k via a proposed design principle. The results show that large pore size and χAB favor the hierarchical structure with more k, while χBC prefers hierarchical structure with less k, consistent with the results of hierarchical structure in bulk. By investigating the effect of the volume fraction of the tail A block (fA), the phase transition sequence, HCk → HPk → HHk → HDk is explored, which shares the same transition of multiblock copolymer in bulk with Lk → Gk → Ck → Sk. Finally, the phase diagram with respect to the fA and R is explored, where the stability regime of these hierarchical structures is well understood. The results provide a compelling panacea for the fabrication of hierarchical 3D nanostructures under confinement.

Self-assembly of cellulose nanocrystals confined to square capillaries.

Biological systems exploit restricted degrees of freedom to drive self-assembly of nano- and microarchitectures. Simplified systems, such as colloidal nanoparticles that behave as lyotropic liquid crystalline mesophases in confined geometric spaces, may be used to mimic biological structures. Cellulose nanocrystals (CNCs) are colloidally stable nanoparticles that self-assemble into chiral nematic (ChN) liquid crystalline mesophases. To date, the self-assembly of ChN mesophases of CNCs has been studied under confinement conditions within curved surfaces or under drying conditions that impose curvatures that can be exploited to control ChN ordering; however, their self-assembly has not been investigated in geometries with square cross-sections under static conditions. Here, we show that because of surface anchoring on perpendicular surfaces, the ChN CNC phase is unable to bend with the 90° angle of the square capillary under increasing confinement. Instead, the ChN phase forms radial layers in the shape of concentric squircle shells. With increasing layer distance from the capillary wall, the squircles transition into concentric cylinder shells. In larger capillaries, the radial shell layers appear as a continuous spiral pattern that engulfs fragmented ChN pseudolayers, a defect to accommodate the cylindrical confinement of the mesophase. These results are useful for understanding the fundamentals of self-assembling systems and development of new technologies.

Shape-Mediated Oriented Assembly of Concave Nanoparticles under Cylindrical Confinement.

This contribution describes the self-assembly of colloidal nanodumbbells (NDs) with tunable shapes within cylindrical channels. We present that the intrinsic concave geometry of NDs endows them with peculiar packing and interlocking behaviors, which, in conjunction with the adjustable confinement constraint, leads to a variety of superstructures such as tilted-ladder chains and crossed-chain superlattices. A mechanistic investigation, corroborated by geometric calculations, reveals that the phase behavior of NDs under strong confinement can be rationalized by the entropy-driven maximization of the packing efficiency. Based on the experimental results, an empirical phase diagram is generated, which could provide general guidance in the design of intended superstructures from NDs. This study provides essential insight into how the interplay between the particle shape and confinement conditions can be exploited to direct the orientationally ordered assembly of concave nanoparticles into unusual superlattices.

Influence of boundary condition on the sound velocity in granular assembly: Spiral tube versus cylinder

The properties of elastic wave propagation in granular assemblies have become a subject of immense interest in recent years, however, the influence of different confinements on the sound velocity is seldom investigated. This study provides a method to determine the contact point between spherical, super-ellipsoidal particles and complex boundaries, in order to investigate how the anisotropy induced by particle shape or boundary affects velocity. Taking cylinder and spiral tube confinements as examples, the falling process of spherical and super-ellipsoidal assemblies are simulated to verify the validation by the discrete element method (DEM). The convergence of the kinetic energy during the falling process and the equilibrium state with zero residual kinetic energy guarantees the stability and correctness. On the basis, elastic wave propagation of spherical and super-ellipsoidal systems in spiral tube and cylindrical confinements under different pressures are modelled, and sound velocities are calculated. The effective medium theory (EMT), granular solid hydrodynamics (GSH), and elastic stiffness are used to interpret the relationship between velocity and stress in cylindrical confinement. However, the results in the spiral tube deviate from EMT and GSH, which means the boundary affects velocity significantly. The difference of velocity between spiral tube and cylinder is qualitatively explained from the perspective of anisotropy of contact force distribution in the system. The simulation results show that anisotropy introduced by the curved surface affects the acoustic properties greatly. The method used for spiral boundary is also suitable for other complicated confinements.

Emergence of Multi-strand Helices from the Self-Assembly of AB-Type Multiblock Copolymer under Cylindrical Confinement

Emergence of Multi-strand Helices from the Self-Assembly of AB-Type Multiblock Copolymer under Cylindrical Confinement

Simulating Microswimmers Under Confinement With Dissipative Particle (Hydro) Dynamics

In this work we study microwimmers, whether colloids or polymers, embedded in bulk or in confinement. We explicitly consider hydrodynamic interactions and simulate the swimmers via an implementation inspired by the squirmer model. Concerning the surrounding fluid, we employ a Dissipative Particle Dynamics scheme. Differently from the Lattice-Boltzmann technique, on the one side this approach allows us to properly deal not only with hydrodynamics but also with thermal fluctuations. On the other side, this approach enables us to study microwimmers with complex shapes, ranging from spherical colloids to polymers. To start with, we study a simple spherical colloid. We analyze the features of the velocity fields of the surrounding solvent, when the colloid is a pusher, a puller or a neutral swimmer either in bulk or confined in a cylindrical channel. Next, we characterise its dynamical behaviour by computing the mean square displacement and the long time diffusion when the active colloid is in bulk or in a channel (varying its radius) and analyze the orientation autocorrelation function in the latter case. While the three studied squirmer types are characterised by the same bulk diffusion, the cylindrical confinement considerably modulates the diffusion and the orientation autocorrelation function. Finally, we focus our attention on a more complex shape: an active polymer. We first characterise the structural features computing its radius of gyration when in bulk or in cylindrical confinement, and compare to known results obtained without hydrodynamics. Next, we characterise the dynamical behaviour of the active polymer by computing its mean square displacement and the long time diffusion. On the one hand, both diffusion and radius of gyration decrease due to the hydrodynamic interaction when the system is in bulk. On the other hand, the effect of confinement is to decrease the radius of gyration, disturbing the motion of the polymer and thus reducing its diffusion.