Diffusion Time Constants Research Articles

Synthesis of nanosheet epitaxial growth ZSM-5 zeolite with increased diffusivity and its catalytic cracking performance

The introduction of microporous substrate in the nanosheet zeolite reduces the “acid wall” barrier. The diffusional time constant of RP-120 is increased by 32%, and its TOF is increased by 54%.

Analysis of the Effect of Surface Diffusion on Effective Diffusivity of Oxygen in Catalyst Layer By Direct Simulation Monte Carlo

Because in the catalyst layers (CLs) of polymer electrolyte fuel cells (PEFCs) platinum (Pt) is used as catalyst, we need to reduce the amount of Pt for cost reduction. In order to maintain the same output even when the amount of Pt is reduced, it is necessary to increase the current density per unit area of Pt surface. At high current density, mass transport is a major factor in voltage drop. Therefore, improving the oxygen transport properties in CLs will lead to cost reduction of PEFCs. Although the transport properties of oxygen in the porous structure of CLs have been studied, the effect of surface diffusion, which is the motion of an oxygen molecule on the ionomer thin film, on transport properties has not yet been clarified. The purpose of the present study is to analyze how the motion of an oxygen molecule on the ionomer thin film affects the oxygen transport properties in the CLs of PEFCs.We used the direct simulation Monte Carlo (DSMC) method. In this study, a computational system was constructed based on an actual catalyst layer sample. The three dimensional structure of the sample was obtained as sequential slice images using a focused ion beam-scanning electron microscope (FIB-SEM). In order to examine the effect of surface diffusion on the transport properties of oxygen molecules, the simulation was performed using a various conditions of the surface diffusion. The behavior of surface diffusion was determined by a surface diffusion coefficient (D s) and a time constant (τ).Figure 1 shows the results of the effective diffusion coefficient of oxygen in the CL. The red line shows the effective diffusion coefficient of oxygen in the calculation without considering the surface diffusion, which is 2.75×10-6 m2/s. The plot marks shows the each surface diffusion coefficient. As the surface diffusion coefficient increases, the effective diffusion coefficient of oxygen increases. When the surface diffusion coefficient is small, the increase in the time constant results in the decrease in the effective diffusion coefficient of oxygen. When surface diffusion coefficient is large, the increase in the time constant leads to the larger effective diffusion coefficient of oxygen. However, when the surface diffusion coefficient is large, as the time constant increases, the effective diffusion coefficient of oxygen has a peak value and then decreases. Although the surface diffusion coefficient becomes larger, the effective diffusion coefficient does not continue to increase. This trend occurs presumably due to the tortuosity of the three dimensional structure. When an oxygen molecule moves along the bended three dimensional structure, the distance of the motion of the oxygen molecule become larger than the straight-line distance between the start and end points. This is the reason why the effective diffusion coefficient does not continue to increase.Fig. 1: Effective diffusion coefficient of oxygen in the catalyst layer as a function of the time constant of the surface diffusion. The difference in plot marks shows the difference in the surface diffusion coefficient. The red line shows the effective diffusion coefficient of oxygen in the calculation without considering the surface diffusion. Figure 1

Equilibrium adsorption and kinetic study of CO2 and N2 on synthesized carbon Black–Zeolite composite

In this study, the preparation of a composite of zeolite-carbon black (CB) for enhancing the CO2 adsorption capacity of zeolites has been investigated. The composites were prepared by adding 5 wt% CB to zeolite 13X crystals via a hydrothermal synthesis method. The standard instrumental analysis techniques, including X-ray diffraction, scanning electron microscopy, thermogravimetric analysis, differential thermal analysis, and obtaining N2 adsorption/desorption isotherms at 77 K, were used to characterize the as-prepared composite. The adsorption isotherms of CO2 and N2 on the composite were measured by a volumetric method at 283, 303, and 323 K and up to 2.2 bar. Employing the Sips and Toth isotherm models, it was found that the Toth model has the best adaptability to the experimental isotherms data. The isosteric heats of adsorption were evaluated with the Clausius-Clapeyron equation. The binary adsorption isotherm and selectivity of CO2 over N2 were predicted using the ideal adsorbed solution theory. The adsorption kinetics of CO2 and N2 on the composite were determined by the non-isothermal kinetic model. The microporous diffusional time constants obtained from correlating the kinetic model with the experimental uptake curves were also compared with those of zeolite 13X. The results show the significant improvements in the adsorption capacity and rate by adding around 5 wt% CB to zeolite 13X.

Adsorption kinetics and equilibria of two methanol samples with different water content on activated carbon

To investigate the influence of fluid purity on the adsorption properties, adsorption kinetics and adsorption equilibria of two methanol samples with different water content on an activated carbon were studied. The purity of the methanol samples was 98.5% and 99.9%. Measurements were conducted at 298 K and 318 K using a magnetic suspension balance and cover a wide p/p0 range. To determine effective diffusion time constants and mass transfer coefficients, adsorption kinetics were evaluated using an isothermal and a nonisothermal Fickian diffusion model, and the linear driving force model. The pressure dependence of the kinetic parameters was studied and discussed. A small influence of sample purity on the adsorption equilibria was observed, as the purer methanol sample showed slightly higher equilibrium loadings than the less pure sample. However, significantly faster adsorption kinetics were observed for the purer sample at all temperature and pressure conditions. Compared to the less pure sample, the determined effective diffusion time constants and the mass transfer coefficients were up to 98% and 35% higher, respectively.

Magnetic diffusion, inductive shielding, and the Laplace transform

In the quasistatic limit, a time-varying magnetic field inside a conductor is governed by the diffusion equation. Despite the occurrence of this scenario in many popular physics demonstrations, the concept of magnetic diffusion appears not to have garnered much attention itself as a subject for teaching. We employ the model of a thin conducting tube in a time-varying axial field to introduce magnetic diffusion and connect it to the related phenomenon of inductive shielding. We describe a very simple apparatus utilizing a wide-band Hall-effect sensor to measure these effects with a variety of samples. Quantitative results for diffusion time constants and shielding cutoff frequencies are consistent with a single, sample-specific parameter given by the product of the tube radius, thickness, and electrical conductivity. The Laplace transform arises naturally in regard to the time and frequency domain solutions presented here, and the utility of the technique is highlighted in several places.

Time adapted linear driving force model for gas adsorption onto solids

• Frequently used models cannot predict kinetics data for all adsorption pairs. • Introduces a time adapted linear driving force model for adsorption kinetics. • Validates the proposed model with experimental data of various adsorbent-adsorbate pairs. • Proposed model can successfully predict the entire adsorption process. • Diffusion time constant has been calculated for all the studied pairs. Adsorption systems are promising for sustainable energy applications, like a low-grade thermal energy-driven heat pump, gas storage, water desalination, and thermal energy storage. The dynamic uptake of adsorbate onto the porous adsorbent plays a crucial role in determining the performance of these adsorption systems. This paper presents a new kinetics model to precisely describe the adsorption dynamics for different adsorbate – adsorbent pairs. A detailed mathematical derivation of this model, along with validation for several adsorption pairs, is presented in this paper. The most significant drawback of traditional kinetics models such as Fickian diffusion, linear driving force, and semi-infinite model has been their time-dependent deviation from experimental data. The proposed model can predict the adsorption dynamics accurately both during the initial unsaturated condition as well as during the later period when the adsorbent is near its saturated condition. Thus, one can use this model for predicting the adsorption system performance for both short and long cycle times.

Understanding How Degree of Crystallinity Affects Electrochemical Kinetics of Sodium‐Ion in Brown TiO2 Nanotubes

AbstractSodium‐ion batteries (SIBs) have attracted significant attention as an emerging alternative to lithium‐ion batteries (LIBs). The charge and discharge performance of the electrode material are affected by various intrinsic parameters, including Na‐ion diffusion coefficient, ionic conductivity, concentration, etc., which are further related to the structure and crystallinity of the material. Herein, the kinetics of Na‐ion intercalation into low and high crystalline brown TiO2 nanotubes are studied by using galvanostatic intermittent titration technique (GITT) and electrochemical impedance spectroscopy (EIS) techniques. Various parameters such as intercalation capacity, partial sodium ion conductivity , diffusion time constant ( ), characteristic diffusion length ), etc., are analyzed during sodiation/de‐sodiation, and the dependence of these parameters with the degree of crystallinity of the material is discussed. The chemical diffusion coefficients ( ) are determined at different intercalation and de‐intercalation potentials, which showed similar behaviour within a range of 10−15–10−18 cm2 s−1, with a slightly higher value for high crystalline brown TiO2. The correlation between the diffusion behavior of Na‐ions in high and low crystalline brown TiO2 nanotubes and their degree of crystallinity provides insights into the electrochemical performance of TiO2 anodes.

Adsorption of CO2, N2 and CH4 on a Fe-based metal organic framework, MIL-101(Fe)-NH2

MIL-101(Fe)-NH2 was synthesized using solvothermal method to assess the selective adsorption of CO2 over N2 and CH4. The BET surface area of adsorbent sample was 915 m2.g-1. The adsorption capacities of CO2, N2 and CH4 on MIL-101(Fe)-NH2 at 4 MP and 298 K were achieved equal to 13, 3.8 and 5 mmol.g-1 respectively. Khan adsorption equilibrium model was applied to correlate the adsorption isotherms of pure gases. In addition to Khan model, the adsorption isotherm of CO2, which showed type II behavior, was also obtained by BET model as well as a newly presented hybrid model, which resulted in excellent agreement with the experimental data. Moreover, the selectivity of CO2 over N2 and CH4 was estimated by Ideal Adsorbed Solution Theory (IAST). Comparison of the achieved results from IAST method with experimental data verified the accuracy of this method in the lower pressure. The selectivity coefficient was about 2.2 for CO2 over N2 and CH4 at 16 bar. The achieved results from a classical micropore diffusion model showed that the diffusion coefficient of the pure gases was approximately constant with pressure. Moreover, the estimated values for diffusion time constants (DC/rC2 × 103) for CO2, N2 and CH4 were obtained equal to 1.178, 1.118, and 0.802 respectively. The adsorption kinetic data were also correlated with empirical models. Ultimately, the results showed that pseudo-nth order empirical model achieved the best agreement with the experimental data, and it can be successfully applied for kinetic modeling of gas adsorption by MIL-101(Fe)-NH2 MOF.

Enrichment of Oxygen-Containing Low-Concentration Coalbed Methane with CMS-3KT as the Adsorbent.

A type of carbon molecular sieve (CMS-3KT) was used as the adsorbent for the CH4 enrichment of a methane/oxygen/nitrogen (CH4/O2/N2) mixture using micro-positive pressure vacuum pressure swing adsorption (∼120 kPa). The adsorption isotherms of individual CH4, O2, and N2 on CMS-3KT were studied and fitted. The results indicated the important influence of the adsorbent surface heterogeneity on the adsorption equilibrium process. In addition, the interaction of adsorbent–adsorbate in this process was studied from the measured adsorption heat. The adsorption uptake curves were fitted linearly with a classical micropore model for evaluating the kinetics-based separation possibility of CH4/O2/N2, and the corresponding diffusion time constants of CH4, O2, and N2 were calculated. Based on the results of adsorption equilibrium and kinetics, breakthrough experiments were employed to explore the upper limit value of methane concentration in feed gas such that methane can be enriched feasibly but difficultly. The breakthrough experiments were performed on the CH4/O2/N2 mixture with CH4 concentration ranging from 1 to 30%. Regarding industrial application, the O2 removal and CH4 enrichment performance of ultra-low-concentration methane (CH4 < 5%) were evaluated according to the results of the breakthrough experiment. The results indicated that the proposed method was promising for enriching O2-containing ultra-low-concentration CBM.

Emulating neural functions utilizing the larger time constants found in the operation of molecular-gap atomic switches

Using hardware to emulate biological functions is essential for the realization of more sophisticated brain-type information processing. For this purpose, up to now, various nonvolatile devices have been used to emulate complex functions such as spike-timing dependent plasticity. However, little research has been conducted on more complicated neural functions. In this study, we demonstrate neural functions such as paired-pulse facilitation (PPF) and paired-pulse depression (PPD), utilizing the larger time constant of the ionic diffusion found in molecular-gap atomic switches. Both the PPF and PPD emulated in this study are dependent on pulse intervals that are the same as those found in biological synapses. Simulations of how pulsed bias changes ion concentration at the subsurface, which in turn determines the precipitation/dissolution of metal atoms, provide a good explanation of the mechanisms of the PPF and the PPD observed in this study.

High-contrast fluorescence polarization microscopy through stimulated emission

In this work, we demonstrate the contrast enhancement through polarization-resolved pump-probe microscopy, implemented by measuring the spontaneous fluorescence loss induced by stimulated emission. The pump-probe measurement is compared with the conventional fluorescence polarization microscopy. The anisotropy values thus obtained are 0.11 and 0.01, respectively. The contrast improvement is attributed to the multiphoton mechanism in sharpening the point-spread function and the polarization resolving. In addition, the pump-probe technique promises higher temporal resolution in lifetime measurements than time-correlated single-photon counting, enabling more precise determination of the fluorescent molecules’ rotational diffusion time constant, which is often in the sub-nanosecond regime.

Core‐shell structured HZSM‐5@mesoSiO2 catalysts with tunable shell thickness for efficient n‐butane catalytic cracking

AbstractA series of core‐shell HZSM‐5@mesoSiO2 with tunable shell thickness from 10 to 70 nm was prepared and studied for n‐butane catalytic cracking. With introducing of SiO2 shell, the catalytic performance of HZSM‐5@mesoSiO2 was largely enhanced, and n‐butane conversion rate per Al site reached to 2.43 min−1 over HZSM‐5@mesoSiO2(1:4) at 675°C which is nearly twice to that of HZSM‐5 (1.34 min−1). The diffusion property of n‐butane over as‐prepared sample was quantified by measuring the diffusional time constants using zero length column chromatography technique (ZLC). Combining with chemical reaction kinetic analysis, the quantitative relationship between diffusion property and catalytic performance was effectively established for the first time in n‐butane catalytic cracking. Positive linear correlation between diffusional time constant (D/R2) and n‐butane conversion rate per Al site could be found, which confirms that diffusion enhancement by hierarchical structure is an effective strategy to improve the activity of HZSM‐5 in catalytic cracking.

Comparative simulation study of methanol production by CO2 hydrogenation with 3A, 4A and 5A zeolites as adsorbents in a PSA reactor

In this work, the performance of 3A, 4A and 5A zeolites in a PSA reactor to obtain methanol by CO2 hydrogenation has been compared by numerical simulation. Henry's constants of adsorption and the reciprocal diffusion time constants of water and methanol in these adsorbents have been measured in the reaction temperature range (200–350 °C) to simulate their performance using a zeolite/Cu-ZnO-Al2O3 catalyst mixture. A new cycle has been proposed for PSA reactors including a complete recirculation of heavy product, without using a purge. The best performance is obtained with 3A zeolite, having the lower water and methanol affinities facilitating bed regeneration. With the proposed process, methanol can be produced from CO2 hydrogenation at 250 °C and 50 bar with a conversion of 99.6% in one step, a selectivity of 83–96%, and productivities of 0.023–0.13 mol m3 s−1. The process has minimal loss of H2 in the form of water (1 mol H2O/mole converted CO2).

Further Understanding of Uncertainties in the Impedance Spectrum of the Polymer Electrolyte Fuel Cell due to Inductive Effects and Oxygen Diffusion Time Constant

In this study, uncertainties during the assessment of the electrochemical impedance spectrum of the polymer electrolyte fuel cell (PEFC) attributed to inductive artefacts at high frequencies and inductive loops at low frequencies as well as oxygen diffusion time constant are discussed. A validated impedance model represented as an equivalent electrical circuit of a PEFC allowed the simulation of the effect of inductive artefacts, inductive loops and oxygen diffusion time constant on electrochemical impedance spectroscopy (EIS) measurements represented in the Nyquist plot. This study considers EIS measurements reported in previous studies and provides an insight into the EIS measurements with positive imaginary components at high frequencies attributed to the intrinsic inductance of the measurement cables during EIS tests and at low frequencies attributed to electrochemical mechanisms (e.g. side reactions with intermediate species) during PEFC operation. In addition, an overview of overlapping mechanisms (charge transfer and oxygen transport resistances during the oxygen reduction reaction) on the PEFC impedance spectrum attributed to oxygen diffusion across the cathode catalyst layer is presented. EIS measurements with positive imaginary components and with overlapping effects could yield to ambiguities when studying or relating electrochemical mechanisms (ion conduction, capacitance, charge transfer and mass transport resistances) of the PEFC through a defined single frequency or a single measured value represented in the Nyquist complex-impedance plot.

Modeling Capacity and Power Fade of Cylindrical NCA-Si Graphite Battery Cell in Electric Vehicles

The energy storage device in most electric vehicles today are lithium-ion batteries. Particularly, Tesla electric vehicles uses the lithium ion chemistry of nickel cobalt aluminum oxide (NCA) and graphite electrodes. Their aging and lifetime are critical issues that must be addressed for a successful large-scale commercialization of electrified vehicles. Therefore, the present work focus on the study of possible aging mechanisms that contribute to the capacity fade and impedance increase of NCA and Si-graphite battery cells in a modeling framework. The batteries are subjected to partial cycling at different state-of-charge (SOC) ranges to imitate different driving behaviors. By predicting the aging parameters from separated electrodes through model, it is possible to understand the responsible aging mechanisms in such applications.The NCA/Si-graphite cylindrical cells were calendar-aged and cycle-aged between SOC of 20-50 %, 35-65 %, 60-90 % and 20-95 % until end of test (EOT) is reached. The cells electrochemical characterization methods include electrochemical impedance spectroscopy (EIS) at 100-cycle interval to measure the impedance behavior and slow cycle discharge to measure the capacity available.We use two models in analyzing the aging behavior through fitting and validation with experimental data – time-based model for capacity fade and frequency-based model for impedance increase. They are physics-based Doyle-Fuller-Newman (DFN) model, which is based on porous electrode theory. The models account for (electrochemical) aging processes within the electrode. Specifically, the solid-electrolyte interface (SEI) build-up, surface and particle cracking; and electrolyte oxidation on the cathode particle interface. These lead to the loss of lithium inventory (LLI) and loss of active material (LAM), contributing to the capacity fade. The same aging mechanisms are represented in the impedance model in the form of charge transfer resistance, interfacial resistance and diffusion time constant. The challenge in modeling the full cell impedance is the superimposition of aging parameters of roughly the same time constants, making it quite hard for the deconvolution of anode and cathode aging. The deduced aging mechanisms from the modeling work are supported by experimental observation, e.g. scanning electron microscope (SEM). For example, micro-cracks and isolation of particles observed from SEM explain the high possibility of increase in LAM and structural change. Overall, modeling of the battery’s capacity and power fade can deepen our understanding of aging processes, allow lifetime prediction, or optimal battery design.

Hydrogen storage in AB2 hydride alloys: Diffusion processes analysis

AB2 alloys have been extensively studied as Ni-MH battery anodes. In the hydriding process, hydrogen diffusion inside the crystal lattice is the determining step, so a comparison between gas phase and electrochemical environment was carried out. As concern, we have found structural changes as a consequence of hydriding in terms of segregation of different stable phases and variations in unit cell parameters in each alloy. Maximum hydrogen storage capacity and hydrogen molar volume for studied alloys were evaluated by PCT curves at different temperatures. Resulting values were compared with electrochemical PCT (ECT plots). Results obtained for both methods were similar, with a hydrogen molar volume value close to 30 cm3 mol−1 being higher for AB2M0 in accordance with the reported capacity values. Diffusion time constants were determined from GITT, achieved data were similar to previously reported by EIS and HRD. AB2M1 alloy showed the best kinetic behavior, depicting a time constant value an order of magnitude lower than AB2M0. This fact could be attributed to the diffusion coefficient and/or the hydrogen diffusion length mean path. No significant differences in thermodynamic parameters were observed between both alloys, therefore, the diffusion coefficients should be similar. Thus, differences in time diffusion constants were attributed to dissimilar mean lattice diffusion paths associated with changes in crystalline structures as a result of the hydriding process.

The zero length column technique to measure adsorption equilibrium and kinetics: lessons learnt from 30 years of experience

The zero length column technique has been developed over the past 30 years as a versatile experimental method to measure adsorption equilibrium and kinetics. In this review we discuss in detail the theory that forms the basis for the technique in order to understand how to design and operate efficiently a system. Experimental checks that should be performed to ensure the correct interpretation of the dynamic response are presented and examples are used to identify how to avoid major errors in determining diffusion time constants. The review concludes with an overview of all experimental studies available in the literature to date and a set of recommendations that should help improve the standard in the reported equilibrium and kinetic properties.

Assessing mass transfer rates in porous adsorbents using gas adsorption microcalorimetry

A novel method to estimate mass transfer kinetics in porous adsorbents using gas adsorption microcalorimetry is described. By fitting an appropriate model to experimental microcalorimetric peaks, both the LDF constant and the effective diffusion time constant could be estimated. Results are shown for an activated carbon and zeolite 13X. The experimental apparatus consisting of a microcalorimeter coupled to a controlled gas dosing system was described in the model by four control volumes: the dosing vessel, the dead volume, the measuring cell and the composite wall surrounding the cell. The proposed model was able to accurately describe the microcalorimetric peaks obtained upon each gas injection. The sensitivity of the model solution to the diffusion parameters was analyzed and adequate ranges of experimental conditions allowing for accurate parameter estimation could be determined. Mass transfer parameters found by this technique are in agreement with those reported in the literature by other experimental techniques.

Three-Dimensional Si Anodes with Fast Diffusion, High Capacity, High Rate Capability, and Long Cycle Life.

There are many interfaces in conventional nanostructured silicon anodes for LIBs, including (1) the solid-electrolyte interface (SEI), (2) interfaces between Si nanoparticles (NPs) and binders, and (3) interface between the current collector and active materials (CCAMI). Interfacial layers (e.g., graphene, activated carbon) coated on conventional Cu foil current collectors are often used to improve charge transfer and reduce CCAMI resistance. Indeed, our detailed studies show that the introduction of interfacial graphene layers results in an ∼20-60% increase in capacity after 500 cycles at 0.1 C. While the capacity is enhanced by inclusion of interfacial layers or conductive additives, they do not resolve problems associated with the diffusion of Li+ ions in the anode. Such electrodes that cannot accommodate the fast diffusion of Li+ ions are prone to plating. Here, we show that the use of freestanding and scalably produced carbon nanotube (CNT) Bucky paper or Bucky sandwich electrodes containing Si NPs (diameter of ∼100 nm) exhibits up to ∼1200 and 1900% increases in the gravimetric capacity after 500 cycles at 0.1 C, respectively, when discharged to 0.1 V. Using detailed electrochemical impedance spectroscopy, we show that the diffusion time constants in the Bucky paper and Bucky sandwich electrodes are increased by 2 orders of magnitude compared to that in the bare Cu foil. Furthermore, we demonstrate that the Bucky paper and Bucky sandwich electrodes can withstand high rates up to 4 C and show long cycle life up to ∼500 cycles at 0.1 C. Finally, we show that the Bucky sandwich electrode architecture with smaller diameter Si NPs (∼30 nm) leads to capacities as high as ∼1490 mAh/g (∼1635 mAh/g) at 0.1 C up to 100 cycles when discharged to 0.1 V (0.01 V).

Kinetic advantage of forming respiratory supercomplexes

Components of respiratory chains in mitochondria and some aerobic bacteria assemble into larger, multiprotein membrane-bound supercomplexes. Here, we address the functional significance of supercomplexes composed of respiratory-chain complexes III and IV. Complex III catalyzes oxidation of quinol and reduction of water-soluble cytochrome c (cyt c), while complex IV catalyzes oxidation of the reduced cyt c and reduction of dioxygen to water. We focus on two questions: (i) under which conditions does diffusion of cyt c become rate limiting for electron transfer between these two complexes? (ii) is there a kinetic advantage of forming a supercomplex composed of complexes III and IV? To answer these questions, we use a theoretical approach and assume that cyt c diffuses in the water phase while complexes III and IV either diffuse independently in the two dimensions of the membrane or form supercomplexes. The analysis shows that the electron flux between complexes III and IV is determined by the equilibration time of cyt c within the volume of the intermembrane space, rather than the cyt c diffusion time constant. Assuming realistic relative concentrations of membrane-bound components and cyt c and that all components diffuse independently, the data indicate that electron transfer between complexes III and IV can become rate limiting. Hence, there is a kinetic advantage of bringing complexes III and IV together in the membrane to form supercomplexes.