Three-dimensional Percolation Research Articles

Numerical study of leakage rate in reciprocating seal with non-Gaussian topography characteristics using percolation mechanism

The topography significantly affects the leakage prevention of the sealing surface. However, the topography effect on sealing performance is not yet fully understood. The leakage mechanism cannot be revealed by average flow model using a statistical distribution to characterize the surface. This paper proposes a new leakage analysis method for reciprocating seals based on the percolation theory. The contact and lubrication analysis of non-Gaussian surfaces with different characteristics is conducted to establish three-dimensional percolation channels. The leakage rate can be calculated from the flow velocity across the cross-section at the critical constriction in the channel. The results show that compared with experimental data, the simulation results of the percolation model are more accurate than those of the average flow model.

Robust-Dense Composite Cathode with Improved Three-Dimensional Ionic Percolation Network and Electrode/Electrolyte Interface for the Development of All-Solid-State Sodium Batteries

All solid-state sodium batteries (AS3Bs) attract immense attention due to their excellent energy and power density, cycle life and thermal security [1]. However, the practical realization of AS3Bs is greatly affected by low to moderate ionic conductivity of the solid electrolyte, unstable electrode/electrolyte interface and poor ion and electron transport between the cathode active materials [2,3]. The unstable electrode/electrolyte interface with point contact leads to huge charge transfer resistance, stress generation and the delamination of the electrode/electrolyte interface during electrochemical reactions. The ion percolation network in the cathode structure is also a critical part. Liquid electrolyte fills the pores present in the cathode and leads to a good Na+ percolation network; however, Na+ percolation cannot be possible in the case of AS3Bs due to the non-fluidity nature of solid electrolyte. This results in low capacity contribution from the cathode owing to fewer cathode active material utilization during electrochemical cycling [4]. Due to the above mentioned issues, the long-cycle stability of AS3Bs is poor.Here we have first prepared Mg doped Na1+3xZr2(SixP1-xO4)3 (NZSP-0.05Mg) with improved ionic conductivity (4.1 mS cm-1 25 ℃) by minimizing the secondary impurity phase. Further, we have utilized an innovative approach to develop a composite cathode by directly firing sodium vanadium fluoro phosphates (NVPF) with Na3.1Zr1.95Mg0.05Si2PO12 (NZSP-0.05Mg) solid electrolyte in the optimized size and weight ratio leading to the robust and dense structure with 3D ionic and electronic percolation network. Additionally, the pores present in the composite cathode is addressed by incorporating polymer electrolyte which further improves the ionic percolation network. The intimate contact between the solid electrolyte and the electrodes was further improved by using a composite solid electrolyte, and the full cell is fabricated by using NVPF composite cathode, composite solid electrolyte and Na metal. The cell delivers a discharge capacity of 103 mAh g-1 after 500 cycles with a Coulombic efficiency of 98 % at 0.1 C and shows excellent capacity retention of 67 mAh g-1 at 2C. The post-mortem XPS analysis confirms the electrochemical stability between the NVPF composite cathode and CSE as well as the Na metal and CSE. Our research provides a new prospective for the preparation of composite cathode and full cell design which can be utilized in solid state sodium and lithium batteries. This work can contribute to a safer battery with long cycle life.

A new method of the hydrocarbon secondary migration research: Numerical simulation

A three-dimensional invasion percolation simulation model is introduced and integrated into a novel three-dimensional geological modeling framework based on the “unit element” theory to study secondary hydrocarbon migration. Leveraging the computational efficiency inherent in the invasion percolation theory, the simulation method is effectively applied to basin-scale hydrocarbon migration using finely discretized grids. Sensitivity analysis demonstrates the substantial influence of geological parameters including structural configuration, sedimentary facies, and pressure, on simulation results. Noteworthy observations from this study encompass: (1) The intricate influence of sedimentary facies and petrophysical properties characteristics on hydrocarbon migration and accumulation patterns within structural and lithological traps. Favorable petrophysical attributes in the carrier beds enhance the likelihood of accumulation in the structural traps, while lithological traps are prevalent in less conducive carrier beds. (2) The significant impact of sand bodies exhibiting favorable petrophysical attributes, such as channels, on migration and accumulation profiles. This underscores the necessity of incorporating sedimentary facies and rock attributes into oil and gas resource exploration. (3) The pronounced effects of overpressure magnitude and direction on hydrocarbon migration and accumulation dynamics. (4) Optimal strategies for oil and gas resource exploration necessitate a comprehensive assessment of rock attributes, overpressure considerations, and sedimentary facies. The practical implementation of this methodology is demonstrated in an actual exploration project within China's Junggar Basin. The simulation results closely align with established oil recovery data and facilitate predictive identification of promising exploration areas. This indicates the methodology is applicable to all petroleum systems similar to Junggar Basin. Through practical applications, the development of a scientifically rigorous three-dimensional geological model for the study area, coupled with numerical simulations of oil and gas migration, facilitates the elucidation of accumulation patterns. This approach aids in identifying pivotal factors such as sand body distribution, internal structural composition, permeability attributes, and fracture behavior, which collectively influence oil and gas migration. Furthermore, by correlating insights obtained from oil and gas discoveries in wells, a deeper understanding of carrier bed properties and their geological evolution is attained.

Critical properties of the optical field localization in a three-dimensional percolating system: Theory and experiment

We systematically study the optical field localization in an active three-dimensional (3D) disordered percolating system with light nanoemitters incorporated in percolating clusters. An essential feature of such a hybrid medium is that the clusters are combined into a fractal radiation pattern, in which light is simultaneously emitted and scattered by the disordered structures. Theoretical considerations, based on systematic 3D simulations, reveal nontrivial dynamics in the form of propagation of localized field bunches in the percolating material. We obtain the length of the field localization and dynamical properties of such states as functions of the occupation probability of the disordered clusters. A transition between the dynamical states and narrow point-like fields pinned to the emitters is found. The theoretical analysis of the fractal field properties is followed by an experimental study of the light generation by nanoemitters incorporated in the percolating clusters. The experimental results corroborate theoretical predictions.

Expandable Li Percolation Network: The Effects of Site Distortion in Cation-Disordered Rock-Salt Cathode Material

Cation-disordered rock-salt (DRX) materials receive intensive attention as a new class of cathode candidates for high-capacity lithium-ion batteries (LIBs). Unlike traditional layered cathode materials, DRX materials have a three-dimensional (3D) percolation network for Li+ transportation. The disordered structure poses a grand challenge to a thorough understanding of the percolation network due to its multiscale complexity. In this work, we introduce the large supercell modeling for DRX material Li1.16Ti0.37Ni0.37Nb0.10O2 (LTNNO) via the reverse Monte Carlo (RMC) method combined with neutron total scattering. Through a quantitative statistical analysis of the material's local atomic environment, we experimentally verified the existence of short-range ordering (SRO) and uncovered an element-dependent behavior of transition metal (TM) site distortion. A displacement from the original octahedral site for Ti4+ cations is pervasive throughout the DRX lattice. Density functional theory (DFT) calculations revealed that site distortions quantified by the centroid offsets could alter the migration barrier for Li+ diffusion through the tetrahedral channels, which can expand the previously proposed theoretical percolating network of Li. The estimated accessible Li content is highly consistent with the observed charging capacity. The newly developed characterization method here uncovers the expandable nature of the Li percolation network in DRX materials, which may provide valuable guidelines for the design of superior DRX materials.

Porous single crystalline-like titanium dioxide monolith with enhanced photoelectrochemical performance

Macro-sized porous single crystalline-like (PSC-like) TiO2 is endowed with unique structural advantages due to its structural consistency and porosity in a large area, which would significantly enhance its photoelectrochemical function. However, there are significant technical challenges in the growth of porous single crystalline-like monoliths. The consistency of structure dominates the structure so that the grain boundary is reduced to the minimum, which is in contradiction with the three-dimensional percolation structure. Here we report a lattice reconstruction strategy based on solid-solid transformation to grow porous single crystal-like anatase TiO2 dominated by (200) and (101) facets at 2 cm scale. In comparison with the traditional definition of porous single crystal, it has two different lattice orientations, but still has good photoelectrochemical properties. The band gap engineering introduces Ti3+ gap into the lattice to generate TinO2n−1 with Magneli phase, limiting the created active structure to the lattice with two-dimensional surface, which would open a new avenue to create highly active surfaces to capture photons and transport electrons stably. The PSC-like TinO2n−1 provides enhanced exciton lifetime (3–5 ns) as a photocatalytic catalyst and shows significant visible light absorption. The independent PSC-like TinO2n−1 delivers high photocurrent of 1.8–5.5 mA · cm−2 at room temperature and does not decay for 10 h.

Step-by-Step Modeling and Experimental Study on the Sol–Gel Porous Structure of Percolation Nanoclusters

Non-conventional crystallization techniques have been developed in recent years. Non-conventional crystallization techniques use primary structural elements (for example, clusters) rather than atoms and molecules. Modern nanomaterial science is going through great changes as an entirely new approach of non-conventional growth mechanisms is emerging due to cluster coupling, catalyzing interest in cluster physics. The formation of fractal and percolation clusters has increased. We carried out step-by-step modeling and an experimental study of the formation of fractal and percolation clusters based on tin dioxide and silicon dioxide and formed by sol–gel technology. In this paper, the growth of fractal aggregates (clusters) from sol particles SnO2 and SiO2 based on the modified models of diffusion-limited and cluster–cluster aggregation is discussed. A percolation model using simulated fractal clusters of SnO2 and SiO2 particles is proposed. Experimental data on the sol–gel percolation structure of porous nanocomposites are presented. The modeling of SnO2 and SiO2 particles, which also consist of clusters (the next step in the hierarchy), is shown. We propose a generalized hierarchical three-dimensional percolation cluster model that allows calculating the surface area, knowing the experimental sizes of macropores and taking into account the micro- and mesopores (sizes less than a few nanometers).

In situ Observation of Porosity Formation in Porous Single-crystalline TiO2 Monolith for Enhanced and Stable Catalytic CO Oxidation.

Introducing pores in single crystals creates a new type of porous materials that incorporate porosity and structural coherence. Herein, we use in situ transmission electron microscopy to disclose the porosity formation by converting KTiOPO4 (KTP) single crystals into porous single-crystalline (PSC) TiO2 monoliths in a solid-solid transformation. The isolated crystalline nuclei of TiO2 clusters with identical lattice orientation on KTP surface moves TiO2 /KTP interface toward mother phase for growing PSC TiO2 monoliths. The relative density in PSC TiO2 monoliths dominates porosity while the macroscopic dimensions remain unchanged in the transformation. The single-crystalline nature of porous architecture stabilizes oxygen vacancy to activate lattice oxygen while the three-dimensional percolation enhances species diffusion. PSC TiO2 monoliths with deposited Pt clusters show enhanced and stable catalytic CO oxidation in air at ∼75 °C for 200 hours of operation.

A novel method for the 3D inhomogeneous percolation on the Lattice with its application

This article anticipates the puzzle of acquiring a three-dimensional inhomogeneous site percolation on an irregular Bethe Lattice (TDIBL). In this work, we explore a TDIBL with the intent to realize the right tradeoff among different percolating variates, namely, cluster size distribution (CSD), critical occupation probability (COP), percolating probability (PP), and mean cluster size (MCS). The variates results are acquired using the generating function (GF) and generalized recursive approaches (GRA). The findings revealed that, for inhomogeneous site percolation (ISP) on the proposed model, the high fraction of probabilities (occupation and distribution probabilities) boosts the intensity of the process, which will enlarge the mean degree of the system in the percolation process. Moreover, numerical simulation and sensitivity analysis will also enhance our understanding of the percolating process via 2D and 3D. Their corresponding shape profiles of earned findings are drawn to perceive their dynamics amongst the options of entailed parameters. Furthermore, exhausting the above scheme, we discuss the transmission behavior of the novel corona-virus 2019 (COVID-19) and present particular disease-control schemes courtesy of groups with numerous infection probabilities and find the effect according to the age distribution. We recognize that this endeavor is timely, that it will be about curiosity, and that it will include scientists working with diverse percolation approaches.

High-precision anomalous dimension of three-dimensional percolation and spatial profile of the critical giant cluster.

In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile ϕ, which is obtained by raising the solution of the Yamabe equation to the scaling dimension Δ_{ϕ}. The latter can be fixed from outcomes of numerical simulations, from which we obtain Δ_{ϕ}=0.47846(71) and the corresponding value of the anomalous dimension η=-0.0431(14). The comparison with values of η determined by using scaling relations is discussed. A test of hyperscaling is also performed.

Oxyfluoride Cathode for All-Solid-State Fluoride-Ion Batteries with Small Volume Change Using Three-Dimensional Diffusion Paths

All-solid-state fluoride-ion batteries (FIBs) are expected to become the next generation of battery systems owing to their outstanding energy storage characteristics. However, the volume expansion of the cathode that accompanies the insertion of fluoride ions remains an urgent issue to be addressed. Even if an intercalation-type cathode is applied in FIBs, fluoride-ion insertion into the interstitial sites of two-dimensional materials such as LaSrMnO4 still leads to non-negligible volume expansion. Here, we report a novel intercalation-type material, Sr3Fe2O5F2, possessing the Ruddlesden–Popper structure as a cathode material for FIBs that features not only interstitial sites but also anion vacancies as three-dimensional (3D) percolation sites to accommodate fluoride ions. This material exhibits a relatively high capacity of 118 mAh g–1 and good cycling stability over 70 cycles. Fe2+/Fe3+ redox reactions are responsible for charge compensation during the charging and discharging processes. The crystal structure during the charging process changes from Sr3Fe2O5F0.46 to Sr3Fe2O5F2 by using the 3D percolation sites with an extremely small volume change of approximately 0.17% and thereafter changes to Sr3Fe2O5F3 with a P4/mmm symmetry by using interstitial sites with a large volume change of approximately 11%. Our findings should pave the way for the design of new cathodes with excellent cycling stability and minimal volume expansion based on the percolation mechanism.

Percolative superconductivity in electron-doped Sr1−xEuxCuO2+y films

Electron-doped infinite-layer Sr$_{1-x}$Eu$_{x}$CuO$_{2+y}$ films over a wide doping range have been prepared epitaxially on SrTiO$_3$(001) using reactive molecular beam epitaxy. In-plane transport measurements of the single crystalline samples reveal a dome-shaped nodeless superconducting phase centered at $x$ $\sim$ 0.15, a Fermi-liquid behavior and pronounced upturn in low temperature resistivity. We show that the resistivity upturn follows square-root temperature dependence, suggesting the emergence of superconductivity via a three-dimensional percolation process. The percolative superconductivity is corroborated spectroscopically by imaging the electronic phase separation between superconducting and metallic phases with low-temperature scanning tunneling microscopy. Furthermore, we visualize interstitial and apical oxygen anions that rapidly increase in number as $x>$ 0.12, and elucidate their impacts on the superconductivity and normal-state resistivity.

Smart multi-responsive aramid aerogel fiber enabled self-powered fabrics

Wearable electronics and systems with self-powered real-time responses to various stimuli, such as mechanical, electrical, thermal and optical signals，are eagerly desired, however still remain great challenges. Herein, smart fibers with multi-response to external stimuli are developed via wet spinning porous aramid aerogel nanofibers while utilized as a three-dimensional hierarchical percolating skeleton for silver nanowires (AgNWs) interwoven MXene conductive network. The coaxial AgNWs/MXene@ aramid aerogel nanofibers with entangled heterostructures effectively avoid “trade-off” effect between high electrical conductivity and mechanical flexibility of smart fibers. Meanwhile, the hierarchical porous structure of aerogel conductive fibers induced strong capillary force and confinement to polyethylene glycol, which has a wide range of phase transition temperature and huge enthalpy to store tremendous thermal energy. After further encapsulated with transparent fluorosilicone resin, the stabilized smart fiber exhibits excellent self-cleaning properties with water and oil repellent. Furthermore, the woven aerogel fabrics coupled with thermoelectric generator realized efficient reversible energy conversion and storage as well as solar-thermal-electrical power generation for all-weather electricity power supply, which could drive the operation of wearable electronics and car models without batteries, providing an efficient strategy for outdoor travel and lunar rover continuous operating. The smart aramid aerogel fibers and fabrics hold great promise for next generation of self-powered wearable systems.

Prediction of sealing interface leakage based on porous medium model considering effective porosity

To explore the influence of surface topography on sealing performance and improve the prediction accuracy of leakage, a porous medium leakage model considering effective porosity is proposed. Based on the measured point cloud data from two rough surfaces, a three-dimensional percolation grid model is developed to simulate the sealing interface. By using the connected domain labelling algorithm, the effective porosity of the sealing interface is obtained. An experiment is implemented to measure the leak rate of sealing interface. It is shown that the proposed leakage model predicts the leak rate of a sealing interface consisting of two rough surfaces accurately, which is convenient for engineering applications.

Probing the Lithium Substructure and Ionic Conductivity of the Solid Electrolyte Li4PS4I

In search of high-performance solid electrolytes, various materials have been discovered in the past, approaching or even exceeding the ionic conductivity of conventional liquid electrolytes. Among the reported classes of superionic electrolytes for solid-state battery applications, lithium thiophosphates appear to be the most promising owing to their high ionic conductivity and mechanical softness. A recent example is the Li4PS4I phase (P4/nmm). Surprisingly, this material shows a comparatively low ionic conductivity at room temperature ranging from 10-4 to 10-5 S cm-1 despite having favorable structural characteristics. Because of discrepancies between experiment and theory regarding the Li-ion conductivity and polymorphism in Li4PS4I, we herein examine the crystal structure over a broad temperature range using ex situ and in situ X-ray and neutron powder diffraction techniques. We demonstrate the absence of polymorphic transitions, with a lithium redistribution at low temperatures though, and confirm the relatively poor room-temperature ionic conductivity despite the presence of a three-dimensional (3D) percolation network for facile charge transport.

Evaluation Analysis on Leakage Performance for Beam Seal With Two Sealing Areas

As a special type of aviation hydraulic pipe joint, a beam seal comprises two annular sealing areas. This paper presented a leakage model for an annular sealing area based on a developed three-dimensional percolation grid model and the porous medium theory. Both average contact pressure and true contact width of the beam seal were simulated using the finite element method. An experimental study of beam seal verified the accuracy of the numerical results. Considering that the two sealing areas and the groove in the beam seal form an isolated sealing system, a leakage model of the beam seal is proposed based on the leakage model for annular sealing area. We evaluated the effects of the roughness of the surface, preload and fluid pressure on the leak rate of the beam seal. Furthermore, the geometry of the beam seal was modified to improve its sealing performance. This study provides an evaluation method for optimizing the design and improving the sealing performance of the beam seal.

The mediated rheological properties of emulsions stabilized by thread-like mesoporous silica nanoparticles in combination with CTAB.

The combination of hydrophilic particles and surfactants provides a simple method to stabilize Pickering emulsions. The type and concentration of the particles and surfactants play important roles in the microstructure and rheological properties of the resulting emulsions. Herein, stable n-octane-in-water Pickering emulsions with tunable rheological properties were prepared using thread-like mesoporous silica nanoparticles (TMSNPs) and cetyltrimethylammonium bromide (CTAB) as emulsifiers. The CTAB concentration (CCTAB) highly affected the properties of emulsions, which were divided into three regions according to the results of large-amplitude oscillatory shear responses. In the low CCTAB range (0.03 mmol L-1 ≤ CCTAB ≤ 0.1 mmol L-1), the emulsions gelled with a high storage modulus . With CCTAB increasing, the value of emulsions, measured by the small-amplitude oscillatory shear, decreased from approximately 1000 Pa at 0.03 mmol L-1 to 100 Pa at 0.3 mmol L-1 and then to 40 Pa at 3 mmol L-1. A three-dimensional percolation structure formed by cross-linking of TMSNPs in the emulsion continuous phase was observed via cryo-SEM in the low CCTAB range but not in the intermediate and high CCTAB ranges. The mechanisms showing the synergistic stability and rheological properties of these emulsions were investigated. It is attributed to the unique morphology of TMSNPs and the competitive adsorption of CTAB molecules at the oil-water interface and on the nanoparticle surface in different CCTAB ranges. Moreover, owing to the porosity and hydrogen-bonding interactions between the TMSNPs and the confinement effect of the flocculated oil droplets, the viscoelasticity of the emulsions could be mediated by adding a trace amount of acid/base. This study provides a new strategy to regulate the rheological properties of emulsions. It also expands the Pickering emulsion systems with tunable rheological properties.

Structure and electrical properties of polymer composites based on tungsten oxide varistor ceramics

Composites based on nonlinear tungsten oxide ceramics and a polyethylene matrix with a volume fraction of ceramic filler from 10 vol % to 43 vol % were studied. It was shown that composites are an isotropic mixture of WO3 grains in a polymer matrix. The current-voltage characteristics of the composites were nonlinear. Composites have a high positive temperature coefficient of resistance up to 15.8 K-1 in the temperature range of 40–75 °C. It is shown that the temperature coefficient of resistance is positive and increases with increasing electric field strength. The decrease in the electrical conductivity of composites with increasing temperature is explained by the expansion of the polymer matrix and the rupture of the current-conducting channels between the conducting grains of the varistor ceramics. The dependence of the electrical conductivity of the composite on the volume fraction of varistor ceramics is well described within the framework of a three-dimensional percolation model for a two-phase system.

Effects of disorder on Harris-criterion violating percolation.

We present the results of computer simulations on a class of percolative systems, called protected percolation, that violates the Harris criterion. The Harris criterion states whether the critical behavior at a phase transition from a disordered state to an ordered state will be altered by impurities. We incorporate impurities into our simulations to test whether the critical exponents for protected percolation are altered by impurities. We find that the critical exponents for three-dimensional protected percolation simulations indeed change with impurities in the form of missing sites and immortal sites. On the other hand, the critical exponents for both standard percolation and protected percolation in two dimensions are stable against impurities.

3D Simulation Modeling for the Electrical Conductivity of Carbon Nanotube Networks in Polymer Nanocomposites

In this paper, we developed a three-dimensional percolation model to investigate the effects of the concentration and morphology of CNTs (carbon nanotubes) on the electrical conductivity of the nanocomposites. In the model, we judged the connections between CNTs by range search algorithm based on KD-Tree structure. At the same time, DIJKSTRA-Melissa algorithm was applied to efficiently find all the conductive paths instead of finding conductive network in traditional methods. From the simulation results, CNTs with higher aspect ratio were easier to form the conductive network. In a certain range of CNT’s concentration, the relationship between the conductivity of the conductive network and the carbon nanotubes was basically consistent with the classical percolation theory. To verify our simulation model, the morphological, electrical properties of Carbon nanotubes (CNTs)/poly(dimethyl siloxane) (PDMS) nanocomposites with different aspect ratio (AR) of MWNTs were systematically studied. In conclusion, these unique advantageous properties could be exploited to suggest potential applications of artificial electronic skin.