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Tortuosity Computations of Porous Materials using the Direct Simulation Monte Carlo
Low-density carbon fiber preforms, used as thermal protection systems (TPS) materials for planetary entry systems, have permeable, highly porous microstructures consisting of interlaced fibers. Internal gas transport in TPS is important in modeling the penetration of hot boundary-layer gases and the in-depth transport of pyrolysis and ablation products. The gas effective diffusion coefficient of a porous material must be known before the gas transport can be modeled in material response solvers; however, there are very little available data for rigid fibrous insulators used in heritage TPS.The tortuosity factor, which reflects the efficiency of the percolation paths, can be computed from the effective diffusion coefficient of a gas inside a porous material and is based on the micro-structure of the material. It is well known, that the tortuosity factor is a strong function of the Knudsen number. Due to the small characteristic scales of porous media used in TPS applications (typical pore size of the order of 50 micron), the transport of gases can occur in the rarefied and transitional regimes, at Knudsen numbers above 1. A proper way to model the gas dynamics at these conditions consists in solving the Boltzmann equation using particle-based methods that account for movement and collisions of atoms and molecules.In this work we adopt, for the first time, the Direct Simulation Monte Carlo (DSMC) method to compute the tortuosity factor of fibrous media in the rarefied regime. To enable realistic simulations of the actual transport of gases in the porous medium, digitized computational grids are obtained from X-ray micro-tomography imaging of real TPS materials. The SPARTA DSMC solver is used for simulations. Effective diffusion coefficients and tortuosity factors are obtained by computing the mean-square displacement of diffusing particles.We first apply the method to compute the tortuosity factors as a function of the Knudsen number for computationally designed materials such as random cylindrical fibers and packed bed of spheres with prescribed porosity. Results are compared to literature values obtained using random walk methods in the rarefied and transitional regime and a finite-volume method for the continuum regime. We then compute tortuosity factors for a real carbon fiber material with a transverse isotropic structure (FiberForm), quantifying differences between through-thickness and in-plain tortuosities at various Knudsen regimes.
Tortuosity Effects in Lithium-Metal Host Anodes
Lithium (Li) metal is the ultimate anode material for Li batteries because of its highest capacity among all candidates. Recent research has focused on stable interphase and host materials to address its low stability and reversibility. Here, we discover that tortuosity is a critical parameter affecting the morphology and electrochemical performances of hosted Li anodes. In three types of hosts—vertically aligned, horizontally aligned, and random reduced graphene oxide (rGO) electrodes with tortuosities of 1.25, 4.46, and 1.76, respectively—we show that high electrode tortuosity causes locally higher current density on the top surface of electrodes, resulting in thick Li deposition on the surface and degraded cycling performance. Low electrode tortuosity in the vertically aligned rGO host enables homogeneous Li transport and uniform Li deposition across the host, realizing greatly improved cycling stability. Furthermore, using this principle of low tortuosity, the designed electrode shows through-electrode uniform morphology with anodic Coulombic efficiency of ~99.1% under high current and capacity cycling conditions.
Quantifying Uncertainty in Tortuosity Estimates for Porous Electrodes
Measuring tortuosity in porous electrodes is important for understanding rate capability and optimizing design. Here, we describe an approach to determine electrode tortuosities and quantify the associated uncertainties by fitting a P2D model to discharge profiles from a standard rate capability test. A dimensionless current is identified as a design-of-experiment parameter that can be used to identify experiments that return confident estimates of tortuosity, even when other model parameters are not known with certainty. This approach is applied to analysis of L i x V 3 O 8 (LVO) electrodes and L i x N i 0.33 M n 0.33 C o 0.33 O 2 (NMC) electrodes. The details of the assumptions made in these measurements and their impact on the reported uncertainties are discussed. We also perform an uncertainty analysis on the standard method for quantifying tortuosity in the literature: electrochemical impedance spectroscopy collected under blocking electrolyte conditions. We find that confident estimates can be obtained using this approach even when uncertainties in equivalent circuit model parameters are considered.
Tortuosity of lightning return stroke channels
Data obtained from photographs of lightning are presented on the tortuosity of return stroke channels. The data were obtained by making piecewise linear fits to the channels, and recording the cartesian coordinates of the ends of each linear segment. The mean change between ends of the segments was nearly zero in the horizontal direction and was about eight meters in the vertical direction. Histograms of these changes are presented. These data were used to create model lightning channels and to predict the electric fields radiated during return strokes. This was done using a computer generated random walk in which linear segments were placed end-to-end to form a piecewise linear representation of the channel. The computer selected random numbers for the ends of the segments assuming a normal distribution with the measured statistics. Once the channels were simulated, the electric fields radiated during a return stroke were predicted using a transmission line model on each segment. It was found that realistic channels are obtained with this procedure, but only if the model includes two scales of tortuosity: fine scale irregularities corresponding to the local channel tortuosity which are superimposed on large scale horizontal drifts. The two scales of tortuosity are also necessary to obtain agreement between the electric fields computed mathematically from the simulated channels and the electric fields radiated from real return strokes. Without large scale drifts, the computed electric fields do not have the undulations characteristics of the data.
Designing Low Tortuosity Electrodes through Pattern Optimization for Fast-Charging
The development of fast-charging technologies is crucial for expediting the progress and promotion of electric vehicles. In addition to innovative material exploration, reduction in the tortuosity of electrodes is a favored strategy to enhance the fast-charging capability of lithium-ion batteries by optimizing the ion-transfer kinetics. To realize the industrialization of low-tortuosity electrodes, a facile, cost-effective, highly controlled, and high-output continuous additive manufacturing roll-to-roll screen printing technology is proposed to render customized vertical channels within electrodes. Extremely precise vertical channels are fabricated by applying the as-developed inks, using LiNi 0.6 Mn 0.2 Co 0.2 O 2 as the cathode material. Additionally, the relationship between the electrochemical properties and architecture of the channels, including the pattern, channel diameter, and edge distance between channels, is revealed. The optimized screen-printed electrode exhibited a seven-fold higher charge capacity (72 mAh g -1 ) at a current rate of 6 C and superior stability compared with that of the conventional bar-coated electrode (10 mAh g -1 , 6 C) at a mass loading of 10 mg cm -2 . Finally, this roll-to-roll additive manufacturing can potentially be applied to various active materials printing to reduce electrode tortuosity and enable fast charging in battery manufacturing.
Tortuosity Engineering for Improved Charge Storage Kinetics in High-Areal-Capacity Battery Electrodes
The increasing demands of electronic devices and electric transportation necessitate lithium-ion batteries with simultaneous high energy and power capabilities. However, rate capabilities are often limited in high-loading electrodes due to the lengthy and tortuous ion transport paths with their electrochemical behaviors governed by complicated electrode architectures still elusive. Here, we report the electrode-level tortuosity engineering design enabling improved charge storage kinetics in high-energy electrodes. Both high areal capacity and high-rate capability can be achieved beyond the practical level of mass loadings in electrodes with vertically oriented architectures. The electrochemical properties in electrodes with various architectures were quantitatively investigated through correlating the characteristic time with tortuosity. The lithium-ion transport kinetics regulated by electrode architectures was further studied via combining the three-dimensional electrode architecture visualization and simulation. Finally, the tortuosity-controlled charge storage kinetics revealed in this study can be extended to general electrode systems and provide useful design consideration for next-generation high-energy/power batteries.
Low-Tortuosity Thick Electrodes with Active Materials Gradient Design for Enhanced Energy Storage
The ever-growing energy demand of modern society calls for the development of high-loading and high-energy-density batteries, and substantial research efforts are required to optimize electrode microstructures for improved energy storage. Low-tortuosity architecture proves effective in promoting charge transport kinetics in thick electrodes; however, heterogeneous electrochemical mass transport along the depth direction is inevitable, especially at high C-rates. In this work, we create an active material gradient in low-tortuosity electrodes along ion-transport direction to compensate for uneven reaction kinetics and the nonuniform lithiation/delithiation process in thick electrodes. The gradual decrease of active material concentration from the separator to the current collector reduces the integrated ion diffusion distance and accelerates the electrochemical reaction kinetics, leading to improved rate capabilities. Further, the structure advantages combining low-tortuosity pores and active material gradient offer high mass loading (60 mg cm –2 ) and enhanced performance. Comprehensive understanding of the effect of active material gradient architecture on electrode kinetics has been elucidated by electrochemical characterization and simulations, which can be useful for development of batteries with high-energy/power densities.
Ethane-CO2 Mixture Adsorption in Silicalite: Influence of Tortuosity and Connectivity of Pores on Selectivity
Selective adsorption using nanoporous materials is an efficient strategy for separating gas mixtures. In a nanoporous material, pores can exist in different shapes and can have different degrees of inter-connectivity. In recent studies, both pore connectivity and tortuosity have been found to affect the adsorption and dynamical properties of ethane and CO2 in silicalite differently. Here, using Monte Carlo simulations, we investigate if these two attributes can affect the selective adsorption of one component from a mixture of ethane and CO2 in silicalite. For this, the adsorption of an equimolar mixture of ethane and CO2 is simulated in 12 models of silicalite—SnZm (n, m = 0, 1, 2, 3 or 4; with n and m denoting, respectively, the fraction (out of 4) of straight and zigzag channels of silicalite that are available for adsorption)—differing in degrees of pore connectivity and tortuosity. The adsorption selectivity in this system is found to exhibit a reversal with the adsorption dominated by ethane at low pressures (below ~1 atm) and by CO2 at higher pressures (above ~10 atm). Pore connectivity is found to suppress the selective adsorption of CO2 at higher pressures and also shifts the selectivity reversal to higher pressures. The selectivity reversal results from a competition between the polarizability-affected adsorption at lower pressures and efficient packing at higher pressures. The efficient packing of CO2 is a compounded effect resulting from the larger effective pore volume available for CO2 due to its stronger interaction with the pore surface and smaller molecular volume. CO2 molecules show a preference to adsorb in non-tortuous pores, and this preference is found to be stronger in the presence of ethane. The effects of pore connectivity and tortuosity elucidated here should be applicable to a wide range of natural and engineered nanoporous materials, and this knowledge could be used to identify materials with better capability for separating and storing CO2 based on their pore attributes.
The influence of tortuosity on the spectrum of radiation from lightning return strokes
An investigation was made of the influence of tortuosity on the spectrum of radiation from lightning return strokes. The shape of the spectrum obtained by including effects of tortuosity was in keeping with data: The spectrum had a peak in the correct frequency regime followed by an initial decrease as the inverse of frequency. This spectrum was in better agreement with data than the spectrum predicted by the same model without tortuosity (i.e. the long straight channel), which decays at a rate proportional to 1/v squared.
Simulation of radiation from lightning return strokes - The effects of tortuosity
A Monte Carlo simulation has been developed for the electromagnetic fields radiated from a tortuous lightning channel. This was done using a piecewise linear model for the channel and employing for each element the field radiated by a traveling wave on an arbitrarily oriented filament over a conducting plane. The simulation reproduces experimental data reasonably well and has been used to study the effects of tortuosity on the fields radiated by return strokes. Tortuosity can significantly modify the radiated waveform, tending to render it less representative of the current pulse and more nearly unipolar than one would expect based on the theory for a long straight channel. In the frequency domain the effect of tortuosity is an increase in high frequency energy as compared with an equivalent straight channel. The extent of this increase depends on the mean length of the elements comprising the channel and can be significant.
Lithiation Gradients and Tortuosity Factors in Thick NMC111-Argyrodite Solid-State Cathodes
Achieving high energy density in all-solid-state lithium batteries will require the design of thick cathodes, and these will need to operate reversibly under normal use conditions. We use high-energy depth-profiling X-ray diffraction to measure the localized lithium content of Li 1-x Ni 1/3 Mn 1/3 Co 1/3 O 2 (NMC111) through the thickness of 110 μm thick composite cathodes. The composite cathodes consisted of NMC111 of varying mass loadings mixed with argyrodite solid electrolyte Li 6 PS 5 Cl (LPSC). During cycling at C/10, substantial lithiation gradients developed, and varying the NMC111 loading altered the nature of these gradients. Microstructural analysis and cathode modeling showed this was due to high tortuosities in the cathodes. This was particularly true in the solid electrolyte phase, which experienced a marked increase in tortuosity factor during the initial charge. Our results demonstrate that current distributions are observed in sulfide-based composites and that these will be an important consideration for practical design of all-solid-state batteries.
Effects of pore connectivity and tortuosity on the dynamics of fluids confined in sub-nanometer pores
Dynamical behavior of fluids under nano-pore confinement is studied extensively as it has important implications for several industrial as well as geological processes. Pore network in many porous materials exhibits a varied degree of inter connections. The extent of this pore connectivity may affect the structural and dynamical behavior of the confined fluid. However, studies of fluid confinement addressing these effects systematically are lacking. In this paper we report molecular dynamics simulation studies addressing the effects of pore connectivity on the dynamics of two representative fluids – CO 2 and ethane in silicalite by systematically varying the degree of pore connectivity through selectively blocking some pore space with immobile methane molecules. By selectively turning off the pore spaces in the shape of straight, or tortuous zigzag channels, we also probe the effects of pore tortuosity. In general, pore connectivity is found to facilitate both the translational as well as rotational dynamics of both fluids, while the intermolecular modes of vibration in both fluids remain largely unaffected. The effects of providing connections between a set of straight or zigzag channel-like pores are however more nuanced. Pore tortuosity facilitates the rotational motion, but suppresses the translational motion of CO 2 , while its effects on the rotational and translational motion of ethane are less pronounced. The intermolecular vibrational modes of both fluids shift to higher energies with an increase in the number of tortuous pores. The results reported here provide a detailed molecular level understanding of the effects of pore connectivity on the dynamics of fluids and thus have implications for applications like fluid separation.
Simulation of radiation from lightning return strokes: The effects of tortuosity
A Monte Carlo simulation has been developed for the electromagnetic fields radiated from a tortuous lightning channel. This was done using a piecewise linear model for the channel and employing for each element the field radiated by a traveling wave on an arbitrarily oriented filament over a conducting plane. The simulation reproduces experimental data reasonably well and had been used to study the effects of tortuousity on the fields radiated by return strokes. Tortuosity can significantly modify the radiated waveform, tending to render it less representative of the current pulse and more nearly unipolar than one would expect based on the theory for a long straight channel. In the frequency domain the effect of tortuosity is an increase in high frequency energy as compared with an equivalent straight channel. The extent of this increase depends on the mean length of the elements comprising the channel and can be significant.
Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media
We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.
Not all fugitives are bad: The case for using them to form low tortuosity - high porosity electrodes
This work focuses on the inclusion of an insoluble fugitive phase during slurry processing to form composite battery electrodes. The fugitive phases consist of natural derived products like alginic acid, sucrose, rice and potato starch, and carrageenans such as Irish Moss and synthetic pore-formers based on polymethyl methacrylate. The fugitive phases can be anaerobically thermally removed (350 °C) during binder crosslinking and electrode drying steps, resulting in electrodes with low tortuosities (approaching theoretical Bruggemann limits for spherical particles) and high porosities approaching 80%. The resulting ∼3 mg/cm 2 loaded electrodes suffer from poor electrical connectivity, lowering the effective material utilization, but represent an approach that could be utilized for the formation of solid-state batteries with infilling of materials into well-defined pores and optimized transport pathways.
Manufacturing Water‐Based Low‐Tortuosity Electrodes for Fast‐Charge through Pattern Integrated Stamping
Achieving high energy density and fast charging of lithium‐ion batteries can accelerate the promotion of electric vehicles. However, the increased mass loading causes poor charge transfer, impedes the electrochemical reaction kinetics, and limits the battery charging rate. Herein, this work demonstrated a novel pattern integrated stamping process for creating channels in the electrode, which benefits ion transport and increases the rate performance of the electrode. Meanwhile, the pressure applied during the stamping process improved the contact between electrode and current collector and also enhanced the mechanical stability of the electrode. Compared to the conventional bar‐coated electrode with the same thickness of 155 μm (delivered a discharge capacity of 16 mAh g −1 at the rate of 3 C), the stamped low‐tortuosity LiFePO 4 electrode delivered 101 mAh g −1 capacity. Additionally, water was employed as a solvent in this study. Owing to its eco‐friendliness, high scalability, and minimal waste generation, this novel stamping technique inspire a new method for the industrial‐level efficient roll to roll fabrication of fast‐charge electrodes.
Investigating the effect of screen-printed structured graphite electrodes with low tortuosity for high-capacity and fast-charging lithium-ion batteries
A flexible screen-printed graphite electrode was fabricated as an anode for developing fast-charging lithium-ion batteries with low tortuosity. A homogenous anode ink was prepared by mixing graphite as the active material, carbon black (C45) as the conductive additive, and polyvinylidene fluoride (PVDF) as the binder in N-Methyl-2-pyrrolidone (NMP) solvent. The ink was deposited on a flexible copper foil via a stainless-steel screen consisting of an array of pores, that act as secondary pore networks (SPNs), using the screen-printing process. Lithium-ion battery half-cells were assembled using the printed graphite anode, lithium metal foil as the counter electrode, and 1.2 M lithium hexafluorophosphate (LiPF 6 ) in ethyl carbonate: ethyl methyl carbonate (EC: EMC = 3:7) as the electrolyte. The effect of SPNs on the cell performance was investigated by performing formation, rate and cycling tests on the assembled cells, at different C-rates. It was observed that the cells consisting of SPNs with a pore size of 100 μm and edge-to-edge distance of 100 μm between the pores exhibited significantly higher specific capacities of 168 and 129 mAh/g when compared to reference cells without SPNs, which had capacities of 120 and 85 mAh/g, at high C-rates of 4 C and 6 C, respectively. The cells with SPNs also demonstrated excellent cycling performance with ~ 95% capacity retention after 100 cycles at 2 C.