Continuum percolation of congruent overlapping spherocylinders

Rapid Tissue Perfusion Using Sacrificial Percolation of Anisotropic Networks

Tissue engineering has long sought to rapidly generate perfusable vascularized tissues with vessel sizes spanning those seen in humans. Current techniques such as biological 3D printing (top-down) and cellular self-assembly (bottom-up) are resource intensive and have not overcome the inherent tradeoff between vessel resolution and assembly time, limiting their utility and scalability for engineering tissues. We present a flexible and scalable technique termed SPAN - Sacrificial Percolation of Anisotropic Networks, where a network of perfusable channels is created throughout a tissue in minutes, irrespective of its size. Conduits with length scales spanning arterioles to capillaries are generated using pipettable alginate fibers that interconnect above a percolation density threshold and are then degraded within constructs of arbitrary size and shape. SPAN is readily used within common tissue engineering processes, can be used to generate endothelial cell-lined vasculature in a multi-cell type construct, and paves the way for rapid assembly of perfusable tissues.

Numerical modeling of the effects of the shape and aspect ratio of 3D curved fiber on the percolation threshold and electrical conductivity of conductive polymer composites

For designing conductive polymer composites (CPCs), understanding how the fiber curvature affects the percolation behavior of curved conductive fibers is essential for determining the effective electrical conductivity σeff of the CPCs. In this work, CPCs were considered as a polymer matrix filled with the random packing of overlapped curved spherocylinders. The geometries of the curved spherocylinders were defined, and inter-curved spherocylinder contact-detecting and system-spanning fiber cluster searching algorithms were developed. The finite-size-scaling method was used to explore how the aspect ratio α and bending central angle θ of a curved spherocylinder affect the percolation threshold ϕc of an overlapped curved spherocylinder system in 3D space. The findings suggest that ϕc decreases as α increases and increases initially before declining as θ increases. An empirical approximation formula was proposed to quantify the effect of the curved spherocylinder's morphology, characterized by the dimensionless excluded volume Vdex of the curved spherocylinder, on ϕc. The new rigorous bound for ϕc of the soft-curved spherocylinder system was further proposed. A random resistor network model was constructed, and the reliability of this model was validated by comparing the simulations and published data. Finally, a fitting formula was developed to assess the impacts of the normalized reduced density (η - ηc)/ηc and Vdex on the σeff of CPCs. A distinct linear correlation between σeff and (η - ηc)/ηc was constructed, denoted as σeff ∼ [(η - ηc)/ηc]t(α,θ). An empirical approximation model was proposed to establish the relationship between the fiber shape and conductivity exponent t. Our study may provide a theoretical hint for the design of CPCs.

Improved Performance in Li-S Batteries Due to In Situ CuS Formation from Cu Nanowires

Lithium-sulfur batteries offer theoretical capacities of 800-1600 mAh g-1 of active material and are therefore one of the most promising new battery chemistries currently under intensive study. However, the low electronic conductivity of the sulfur and the discharge products imposes energy penalties during the discharge and charge steps. In addition, the reduction of sulfur during discharge forms soluble polysulfides, which will diffuse to, and react with, the lithium metal anode. To address these two challenges, copper nanowires were introduced into the composite cathode to improve the electronic conductivity of the cathode and to provide electrostatic anchoring points for the formed polysulfide anions. The addition of the conductive copper nanowires resulted in the in situ formation of copper sulfide, which was shown to decrease the resistivity of the SEI layer on the anode, as manifested by diminished lithium plating and stripping overpotentials. Higher copper loadings exacerbated the dissolution of the copper sulfide during deep discharge and increased the concentration of displaced capping ligands in the electrolyte. Both phenomena generate species that react at the lithium anode, resulting in a more resistive SEI layer.

Computational design of anisotropic stealthy hyperuniform composites with engineered directional scattering properties

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)1359-645410.1016/j.actamat.2017.09.053] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ[over ̃]_{_{V}}(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ[over ̃]_{_{V}}(k)=0 for k∈Ω, i.e., complete suppression of scattering in an "exclusion" region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the global symmetry of the resulting media, they can still possess structures at a local level that are nearly isotropic. Both the isotropic and anisotropic hyperuniform microstructures associated with the elliptical-disk, square, and rectangular Ω possess phase-inversion symmetry over certain range of volume fractions and a percolation threshold ϕ_{c}≈0.5. On the other hand, the directionally hyperuniform microstructures associated with the butterfly-shaped and lemniscate-shaped Ω do not possess phase-inversion symmetry and percolate along certain directions at much lower volume fractions. We also apply our general procedure to construct stealthy nonhyperuniform systems. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures via the shape, size, and symmetries of Ω, which is crucial to engineering directional optical, transport, and mechanical properties of two-phase composite media.

Percolation threshold and electrical conductivity of conductive polymer composites filled with curved fibers in two-dimensional space

Quantifying the influence of fiber curvature on the percolation behavior of flexible conductive fiber and further on the electrical conductivity of conductive polymer composites (CPCs) is crucial for the design of CPCs. This study considers CPCs as a random packing of soft curved discorectangles (CDCRs) in a polymer matrix. The geometry of CDCR is developed, and an inter-CDCR contact detection algorithm is used to generate a random packing structure of CDCRs. The effects of aspect ratio α and bending central angles θ of CDCR on the percolation threshold ϕc of the overlapped CDCR system in a two-dimensional plane are then investigated using the finite-size scaling method. The result reveals that ϕc decreases monotonically as α grows and increases monotonically as θ rises. A shape-independent power law formula, denoted as ϕc = 2.2015 A-0.8172dex is developed to quantify the relationship between the Adex and ϕc. A comparison of our numerical simulations, published data, and predictions verifies the reliability and universality of the fitting model. Subsequently, a resistor network searching algorithm (RNSA) is proposed to construct the random resistor network model (RRNM). A power law model, denoted as is developed to evaluate the effects of the normalized reduced density (η - ηc)/ηc on the effective conductivity σeff of CPC. Comparing our predictions with data from the literature and our simulation verifies the reliability of our RNSA and the fitting model. This paper's methodology and findings may provide a theoretical hint for the CPC's design.

Effect of sample height and particle elongation in the sedimentation of colloidal rods

We study theoretically the effect of a gravitational field on the equilibrium behaviour of a colloidal suspension of rods with different length-to-width aspect ratios. The bulk phases of the system are described with analytical equations of state. The gravitational field is then incorporated via sedimentation path theory, which assumes a local equilibrium condition at each altitude of the sample. The bulk phenomenology is significantly enriched by the presence of the gravitational field. In a suspension of elongated rods with five stable phases in bulk, the gravitational field stabilizes up to fifteen different stacking sequences. The sample height has a non-trivial effect on the stable stacking sequence. New layers of distinct bulk phases appear either at the top, at the bottom, or simultaneously at the top and the bottom when increasing the sample height at constant colloidal concentration. We also study sedimentation in a mass-polydisperse suspension in which all rods have the same shape but different buoyant masses.

3D aggregation of cells in packed microgel media

In both natural and applied contexts, investigating cell self-assembly and aggregation within controlled 3D environments leads to improved understanding of how structured cell assemblies emerge, what determines their shapes and sizes, and whether their structural features are stable. However, the inherent limits of using solid scaffolding or liquid spheroid culture for this purpose restrict experimental freedom in studies of cell self-assembly. Here we investigate multi-cellular self-assembly using a 3D culture medium made from packed microgels as a bridge between the extremes of solid scaffolds and liquid culture. We find that cells dispersed at different volume fractions in this microgel-based 3D culture media aggregate into clusters of different sizes and shapes, forming large system-spanning networks at the highest cell densities. We find that the transitions between different states of assembly can be controlled by the level of cell-cell cohesion and by the yield stress of the packed microgel environment. Measurements of aggregate fractal dimension show that those with increased cell-cell cohesion are less sphere-like and more irregularly shaped, indicating that cell stickiness inhibits rearrangements in aggregates, in analogy to the assembly of colloids with strong cohesive bonds. Thus, the effective surface tension often expected to emerge from increased cell cohesion is suppressed in this type of cell self-assembly.

Percolation thresholds for discorectangles: Numerical estimation for a range of aspect ratios

Using Monte Carlo simulation, we have studied the percolation of discorectangles. Also known as stadiums or two-dimensional spherocylinders, a discorectangle is a rectangle with semicircles at a pair of opposite sides. Scaling analysis was performed to obtain the percolation thresholds in the thermodynamic limits. We found that (i) for the two marginal aspect ratios ɛ=1 (disc) and ɛ→∞ (stick) the percolation thresholds coincide with known values within the statistical error and (ii) for intermediate values of ɛ the percolation threshold lies between the percolation thresholds for ellipses and rectangles and approaches the latter as the aspect ratio increases.

Absorbing-active transition in a multi-cellular system regulated by a dynamic force network

Collective cell migration in 3D extracellular matrix (ECM) is crucial to many physiological and pathological processes. Migrating cells can generate active pulling forces via actin filament contraction, which are transmitted to the ECM fibers and lead to a dynamically evolving force network in the system. Here, we elucidate the role of this force network in regulating collective cell behaviors using a minimal active-particle-on-network (APN) model, in which active particles can pull the fibers and hop between neighboring nodes of the network following local durotaxis. Our model reveals a dynamic transition as the particle number density approaches a critical value, from an "absorbing" state containing isolated stationary small particle clusters, to an "active" state containing a single large cluster undergoing constant dynamic reorganization. This reorganization is dominated by a subset of highly dynamic "radical" particles in the cluster, whose number also exhibits a transition at the same critical density. The transition is underlaid by the percolation of "influence spheres" due to the particle pulling forces. Our results suggest a robust mechanism based on ECM-mediated mechanical coupling for collective cell behaviors in 3D ECM.

Continuum percolation of congruent overlapping polyhedral particles: Finite-size-scaling analysis and renormalization-group method

The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction ϕ_{c} or the critical reduced number density η_{c}), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that ϕ_{c} (or η_{c}) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more "spherical." We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of ν=0.88 reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.

Continuum percolation-based tortuosity and thermal conductivity of soft superball systems: shape dependence from octahedra via spheres to cubes

Understanding the effect of particle shape on the percolation threshold, tortuosity and thermal conductivity of soft (geometrical overlapping) particle systems is very crucial for the design and optimization of such materials, including colloids, polymers, and porous and fracture media. In this work, we first combine the excluded-volume theory with the Monte Carlo simulations to determine the percolation threshold for a family of soft superballs, the shape of which interpolates between octahedra and cubes via spheres. Then, we propose two continuum percolation-based models to respectively obtain the tortuosity and effective thermal conductivity of soft superball systems considering their percolation behavior, where monodisperse overlapping superballs are uniformly distributed in a homogeneous solid matrix. Specifically, both models cover the whole feasible range of superball volume fractions, including near the percolation threshold. Comparison with extensive experimental, numerical and theoretical results confirms that the present models are capable of precisely predicting the percolation threshold, tortuosity and thermal conductivity of such systems. Furthermore, we apply the proposed models to probe the influence of particle shape on these important parameters. Our results show that the decreasing percolation threshold and tortuosity as soft particles become more anisotropic is consistent with increasing conductivity. It suggests that the anisotropic-shaped inclusion phase is more conducting than the spherical inclusion phase. The present theoretical strategies and conclusions may provide sound guidance for the synthesis of colloidal and polymer superballs.

Geometrical percolation threshold of congruent cuboidlike particles in overlapping particle systems

With the advances in artificial particle synthesis, it is possible to create particles with unique shapes. Particle shape becomes a feasible parameter for tuning the percolation behavior. How to accurately predict the percolation threshold by particle characteristics for arbitrary particles has aroused great interest. Towards this end, a versatile family of cuboidlike particles and a numerical contact detection algorithm for these particles are presented here. Then, combining with percolation theory, the continuum percolation of randomly distributed overlapping cuboidlike particles is studied. The global percolation threshold ϕ_{c} of overlapping particles with broad ranges of the shape parameter m in [1.0,+∞) and aspect ratio a/b in [0.1, 10.0] is computed via a finite-size scaling technique. Using the generalized excluded-volume approximation, an analytical formula is proposed to quantify the dependence of ϕ_{c} on the parameters m and a/b, and its reliability is verified. The results reveal that the percolation threshold ϕ_{c} of overlapping cuboidlike particles is heavily dependent on the shapes of particles, and much more sensitive to a/b than m. As the cuboidlike particles become spherical (i.e., m=1.0 and a/b=1.0), the maximum threshold ϕ_{c,max} can be obtained.