Internal Concentration Gradients Research Articles

A practical semi-empirical model for predicting the SoH of lithium-ion battery: A novel perspective on short-term rest

In this paper, the semi-empirical battery degradation prediction model proposed considers electrochemical degradation characteristics and represents degradation effects under various conditions, including different states of charge (SoC) areas. This model is specifically designed to address degradation during cycling and short-term rest periods in lithium-ion batteries using liquid electrolytes. Cycle aging incorporates the impact of solid electrolyte interphase (SEI) growth, a known dominant factor, and the model for short-term resting periods captures potential aging impacts on subsequent cycles due to internal material concentration gradients, moving away from the traditionally used calendar life approach. The derivation of the model presented in this paper is based on 14 data sets under different SoC conditions and 8 data sets under various Crates, explaining the degradation effects at 10 % SoC intervals and three different Crate points. Moreover, the model's performance was validated through capacity prediction for two data sets experimented with dynamic operational schedules of actual energy storage systems (ESS), including various conditions. The results showed a root mean square error (RMSE) of 0.564 and a mean absolute percentage error (MAPE) of 0.346. The superiority of this model is demonstrated by comparing its performance with four other types of degradation models derived through the same process in the validation data.

Utility of Minimal Physiologically Based Pharmacokinetic Models for Assessing Fractional Distribution, Oral Absorption, and Series-Compartment Models of Hepatic Clearance.

Minimal physiologically based pharmacokinetic (mPBPK) models are physiologically relevant, require less information than full PBPK models, and offer flexibility in pharmacokinetics (PK). The well-stirred hepatic model (WSM) is commonly used in PBPK, whereas the more plausible dispersion model (DM) poses computational complexities. The series-compartment model (SCM) mimics the DM but is easier to operate. This work implements the SCM and mPBPK models for assessing fractional tissue distribution, oral absorption, and hepatic clearance using literature-reported blood and liver concentration-time data in rats for compounds mainly cleared by the liver. Further handled were various complexities, including nonlinear hepatic binding and metabolism, differing absorption kinetics, and sites of administration. The SCM containing one to five (n) liver subcompartments yields similar fittings and provides comparable estimates for hepatic extraction ratio (ER), prehepatic availability (Fg ), and first-order absorption rate constants (ka ). However, they produce decreased intrinsic clearances (CLint ) and liver-to-plasma partition coefficients (Kph ) with increasing n as expected. Model simulations demonstrated changes in intravenous and oral PK profiles with alterations in Kph and ka and with hepatic metabolic zonation. The permeability (PAMPA P) of the various compounds well explained the fitted fractional distribution (fd ) parameters. The SCM and mPBPK models offer advantages in distinguishing systemic, extrahepatic, and hepatic clearances. The SCM allows for incorporation of liver zonation and is useful in assessing changes in internal concentration gradients potentially masked by similar blood PK profiles. Improved assessment of intraorgan drug concentrations may offer insights into active moieties driving metabolism, biliary excretion, pharmacodynamics, and hepatic toxicity. SIGNIFICANCE STATEMENT: The minimal physiologically based pharmacokinetic model and the series-compartment model are useful in assessing oral absorption and hepatic clearance. They add flexibility in accounting for various drug- or system-specific complexities, including fractional distribution, nonlinear binding and saturable hepatic metabolism, and hepatic zonation. These models can offer improved insights into the intraorgan concentrations that reflect physiologically active moieties often driving disposition, pharmacodynamics, and toxicity.

Osmotic-Enhanced-Photoelectrochemical Hydrogen Production Based on Nanofluidics

Osmotic-Enhanced-Photoelectrochemical Hydrogen Production Based on Nanofluidics

Theoretical Analysis of Mass Transfer Behavior in Fixed-Bed Electrochemical Reactors: Akbari-Ganji’s Method

The theoretical model for a packed porous catalytic particle of the slab, cylindrical, and spherical geometries shape in fixed-bed electrochemical reactors is discussed. These particles have internal mass concentration and temperature gradients in endothermic or exothermic reactions. The model is based on a nonlinear reaction–diffusion equation containing a nonlinear term with an exponential relationship between intrinsic reaction rate and temperature. The porous catalyst particle’s concentration is obtained by solving the nonlinear equation using Akbari-Ganji’s method. A simple and closed-form analytical expression of the effectiveness factor for slab, cylindrical, and spherical geometries was also reported for all values of Thiele modulus, activation energy, and heat reaction. The accordance with results of a reliable numerical method shows the good accuracy that their approximate solution yields.

Bevel Structure Based XPS Analysis as a Non-Destructive Chemical Probe for Complex Interfacial Structures of Organic Semiconductors.

The bevel structure of organic multilayers produced by finely controlled Ar gas cluster ion beam sputtering preserves both the molecular distribution and chemical states. Nevertheless, there is still an important question of whether this method can be applicable to organic multilayer structures composed of complex or ambiguous interfaces used in real organic optoelectronic devices. Herein, various bevel structures are fabricated from different types of organic semiconductors using a solution-based deposition technique: complicatedly intermixed electron-donor and electron-acceptor bulk heterojunction structure, thin film structure with an internal donor-acceptor concentration gradient, and multi-layered structure with more than three layers. For these organic material combinations listed above, the bevel structure is fabricated with finely tuned Ar gas cluster ion beam sputtering. The location-dependent X-ray photoelectron spectroscopy (XPS) results obtained for each bevel structure exactly correspond to the XPS depth profiles. This result demonstrates that the bevel structure analysis is a powerful method to distinguish subtle differences in chemical component distributions and chemical states of organic semiconductors even with complex or ambiguous interfaces. Ultimately, due to its reliability as verified by this study, the proposed bevel structure analysis is expected to greatly expand other analytical techniques with a limited spatial or depth resolution.

Kinetic modeling of heterogeneous esterification reaction using initial reaction rate analysis: data extraction and evaluation of mass transfer criteria.

This data article provides detailed guidance to obtain heterogeneous reaction rate expressions and the corresponding initial reaction rates and their application. Explanation is provided to deal with specific criteria to rule out internal and external concentration gradients, so that the usage of intrinsic catalytic data is guaranteed. Overall, the main goal is to provide an easy tool to evaluate both aforementioned results by simple plug-and-play of available reaction data.

Disruption of Electrospinning due to Water Condensation into the Taylor Cone.

The well-known problems of electrospinning hygroscopic polymer fibers in humid air are usually attributed to water condensing onto the jet mid-flight: water enters the jet as an additional solvent, hindering solidification into well-defined fibers. Here, we show that fiber fusion and shape loss seen at the end of the process may actually stem from water already condensing into the Taylor cone from where the jet ejects, if the solvent is volatile and miscible with water, for example, ethanol. The addition of water can radically change the solvent character from good to poor, even if water on its own is an acceptable solvent. Moreover, and counterintuitively, the water condensation promotes solvent evaporation because of the release of heat through the phase transition as well as from the exothermic mixing process. The overall result is that the polymer solution develops a gel-like skin around the Taylor cone. The situation is significantly aggravated in the case of coaxial electrospinning to make functional composite fibers if the injected core fluid forms a complex phase diagram with miscibility gaps together with the polymer sheath solvent and the water condensing from the air. The resulting phase separation coagulates the polymer throughout the Taylor cone, as liquid droplets with different compositions nucleate and spread, setting up strong internal flows and concentration gradients. We demonstrate that these cases of uncontrolled polymer coagulation cause rapid Taylor cone deformation, multiple jet ejection, and the inability to spin coaxial fiber mats, illustrated by the example of coaxial electrospinning of an ethanolic polyvinylpyrrolidone solution with a thermotropic liquid crystal core, at varying humidities.

Influence of the Catalyst Particle Size on the Aqueous Phase Reforming of n-Butanol Over Rh/ZrO2.

Butanol is a by-product obtained from biomass that can be valorized through aqueous phase reforming. Rh/ZrO2 catalysts were prepared and characterized, varying the size of the support particles. The results showed a relatively mild effect of internal mass transport on butanol conversion. However, the influence of internal transport limitations on the product distribution was much stronger, promoting consecutive reactions, i.e., dehydrogenation, hydrogenolysis, and reforming of propane and ethane. Hydrogen consuming reactions, i.e., hydrogenolysis, were more strongly enhanced than hydrogen producing reactions due to internal concentration gradients. Large support particles deactivated faster, attributed to high concentrations of butyraldehyde inside the catalyst particles, enhancing deposit formation via aldol condensation reactions. Consequently, also the local butyric acid concentration was high, decreasing the local pH, enhancing Rh leaching. The influence of internal transfer limitation on product distribution and stability is discussed based on a reaction scheme with three main stages, i.e., (1) formation of liquid intermediates via dehydrogenation, (2) formation of gas via decarbonylation/decarboxylation reactions, and (3) hydrocarbon hydrogenolysis/reforming/dehydrogenation.

Enhanced transport in Gas-Liquid-Solid catalytic reaction by structured wetting properties: Nitrite hydrogenation

This work presents a new approach to improve mass transfer in and around catalyst particles in three-phase operation with micro-structured catalysts, containing hydrophilic and hydrophobic domains. Partially hydrophilic catalysts were prepared via physical mixing of hydrophobic perfluorinated octyltrichloro silane (FOTS)/γ-Al2O3 domains and hydrophilic Pd/γ-Al2O3 domains, resulting in manipulation of water wetting, both at the external surface and the pores inside the support particles. The modified catalysts were characterized with elemental analysis, XRF, N2 physisorption and light microscopy after selective dyeing hydrophobic and hydrophilic domains. The catalysts are tested for hydrogenation of nitrite in water, which is an extremely fast reaction whereas the product distribution (N2 versus NH4+) is also easily influenced by internal concentration gradients. Noticeably, the partially hydrophilic catalyst is more active and produces more ammonium compared to hydrophilic catalyst. This work demonstrates that this way of structuring the catalyst enables influencing the internal concentration gradients for aqueous systems. For the case of nitrite hydrogenation, we show that structured catalysts achieve the same rate per gram Pd at lower hydrogen pressure compared to classical hydrophilic catalysts. This results in formation of less ammonia, which is of practical importance for cleaning of drinking water.

Kinetic investigations of the steam reforming of methanol over a Pt/In2O3/Al2O3 catalyst in microchannels

A kinetic study of methanol steam reforming over bimetallic Pt/In2O3/Al2O3 catalyst was carried out. The kinetic measurements were performed in a microstructured monolithic reactor with an external recycle free of temperature and concentration gradients. By the help of residence time distribution measurements it could be verified that the reactor showed the behaviour of an ideal continuous stirred tank reactor (CSTR). The absence of external and internal concentration gradients could be proven by corresponding experiments and theoretical diagnostic criteria.The kinetic measurements performed by variation of the reactant inlet partial pressures revealed that in the temperature range from 310°C to 355°C the molar rate of methanol consumption mainly depends on the methanol partial pressure, especially at higher temperatures, whereas there is only minor dependence on the water partial pressure. Carbon dioxide has no inhibiting effect, whereas hydrogen showed a weak inhibiting effect.Two power laws and three Langmuir-Hinshelwood rate equations were created for the modelling of the kinetic data. Power laws could not be fitted to the measured values. Therefore the uses of Langmuir-Hinshelwood rate laws with temperature dependent sorption constants are inevitable for the modelling. The model discrimination revealed that the rate law derived from a mechanism, which assumes the dehydrogenation of an adsorbed methoxy-species as rate determining step, described the measured kinetic data second best. Optimum agreement between observed and predicted molar rates of methanol consumption was obtained when applying a Langmuir-Hinshelwood rate law assuming dissociative methanol and molecular water adsorption on the catalyst surface. Dissociative adsorption of water and methanol at the same active site may be excluded. This leads to a better evaluation of the models that assume molecular water adsorption at the same site where methanol ties or the ones with no participation of water in the rate determining step (RDS) under discrimination.

The Approximate Analytical Solution of Non-Linear Equation for Simultaneous Internal Mass and Heat Diffusion Effects

For the first time a mathematical modelling of porous catalyst particles subject to both internal mass concentration gradients as well as temperature gradients, in endothermic or exothermic reactions has been reported. This model contains a non-linear mass balance equation which is related to rate expression. This paper presents an approximate analytical method (Modified Adomian decomposition method) to solve the non-linear differential equations for chemical kinetics with diffusion effects. A simple and closed form of expressions pertaining to substrate concentration and utilization factor is presented for all value of diffusion parameters. These analytical results are compared with numerical results and found to be in good agreement.

On New High Order Quasilinearization Approaches to the Nonlinear Model of Catalytic Reaction in a Flat Particle

A novel computational approach known as pseudospectral quasilinearization (SQLM) is employed to tackle the two-point boundary value problem describing the reactivity behaviour of porous catalyst particles subject to both internal mass concentration gradients and temperature gradients, in endothermic or exothermic catalytic reactions. A comparison with the numerical results generated using the inbuilt MATLAB boundary value solver, <span style="font-family:monospace">bvp4c</span>, for different values of the governing physical parameters is performed and an excellent agreement is achieved. A systematic way of improving the convergence of the SQLM is also presented.

Support effect on selectivity of nitrite reduction in water

Palladium catalysts on various supports were studied for the hydrogenation of aqueous nitrite solution. The effects of reaction parameters such as nitrite and hydrogen concentration, pH and reaction temperature on the selectivity were discussed. Internal concentration gradients are influencing the selectivity significantly. Gradients of protons and nitrite are responsible for increasing ammonia selectivity. Carbon based catalysts were more selective towards ammonia as compared to oxidic supports. We propose that electron conductivity of carbon supports influences internal concentration gradients of both hydrogen and protons, favouring ammonia selectivity.

Structure formation mechanisms in consolidating pigment coatings—Simulation and visualisation

Microstructure development in consolidating pigment coating layers was studied in terms of particle flocculation and clustering mechanisms utilising a 3D particle dynamics model. The model includes hydrodynamic forces, colloidal interactions as well as the Brownian motion. The influence of colloidal interactions and drying strategy on the coating layer thickness development and internal solid concentration gradients, was investigated. A low particle surface potential resulted in the formation of porous particle networks, which impeded the shrinkage of the coating layer. At higher surface potentials particles arranged into denser structures, whereby the solids concentration profile could be controlled by the drying. Low electrostatic double layer thicknesses allowed sharp concentration gradients to form as result of the applied drying strategy. At high double layer thicknesses, the structure formation was similar regardless of drying strategy. This work elucidates the combined effect of drying conditions and colloidal suspension properties on coating microstructure development. Furthermore, the results aid in the understanding of how coating suspension additives may influence the structure development of the coating layer.

Modelling of micro/nano-scale concentration and temperature gradients in porous supported catalysts

Meso-scale mathematical model of local reaction and transport processes in a porous catalyst with bimodal pore-size distribution is used for the evaluation of internal concentration and temperature gradients. The model takes into account reaction steps on active sites (microkinetics), diffusion of reactants in both macro- and meso-pores (molecular and Knudsen diffusion), and heat generation and transport. The processes are modelled within a 3D domain ( ≈ 10 × 10 × 10 μ m 3 ) of computer-reconstructed porous catalyst. Methods of digital reconstruction, based on the analysis of electron microscope images (SEM and TEM) are employed. The methodology is demonstrated on CO oxidation on Pt / γ - Al 2 O 3 . Overall reaction rate and effectiveness factor are studied in dependence on the morphological properties of the catalyst—macro- and meso-porosity, the sizes of support γ - Al 2 O 3 particles, and characteristic diameter of the pores. Relative importance of diffusion in macro- and meso-pores and reaction heat effects are discussed. The volume-averaged parameters (e.g. effectiveness factor) calculated at this detailed spatial scale can be used as input values for simulations at a larger scale. Parametric study is performed for different γ - Al 2 O 3 particles sizes, mixing ratios and levels of sintering, and local optima of effectiveness factor are found.

Analysis of thermal effects in infrared and interference microscopy: n-Butane-5A and methanol–ferrierite systems

Recently, infrared and interference microscopy methods have been increasingly applied to measure internal concentration gradients and hence the uptake of different adsorbates in zeolite crystals. In contrast to conventional macroscopic batch uptake techniques, these microscopic/mesoscopic methods measure changes associated with single zeolite crystals. The analysis of data from these measurements to determine micropore diffusivities has been performed on the basis of the assumption that isothermal conditions prevail during both the adsorption and desorption experiments. This assumption is critically examined in this paper for the case of methanol diffusion in ferrierite crystals during adsorption and desorption to vacuum. It is shown by both detailed simulation as well as an order of magnitude analysis of time constants for heat transfer and diffusion that the temperature changes in the system are negligible during adsorption due to the high conductive heat transfer rate. However, during desorption to a vacuum, heat conduction is minimal so that heat transfer occurs only by radiation. Temperature changes as large as 5–7 K are therefore to be expected at the beginning of the desorption process. However, since the time constant for the desorption process is of the order of hundreds of seconds, this temperature transient dissipates rapidly and has no significant impact on the overall desorption process. Even for the worst case scenario considered here, for both interference and infrared microscopy methods, the systems can be considered as essentially isothermal.

Further quantification of the role of internal unstirred layers during the measurement of transport coefficients in giant internodes of Chara by a new stop-flow technique

A new stop-flow technique was employed to quantify the impact of internal unstirred layers on the measurement of the solute permeability coefficient (P(s)) across the plasma membrane of internodes of the giant-celled alga Chara corallina using a cell pressure probe. During permeation experiments with rapidly permeating solutes (acetone, 2-propanol, and dimethylformamide), the solute concentration inside the cell was estimated and the external medium was adjusted to stop solute transport across the membrane, after which responses in turgor were measured. This allowed estimation of the solute concentration right at the membrane. Stop-flow experiments were also simulated with a computer. Both the stop-flow experiments and simulations provided quantitative data about internal concentration gradients and the contribution of unstirred layers to overall measured values of P(meas)(s) for the three solutes. The stop-flow experimental results agreed with stop-flow simulations assuming that solutes diffused into a completely stagnant cell interior. The effects of internal unstirred layers on the underestimation of membrane P(s) declined with decreasing P(s). They were no bigger than 37% in the presence of the most rapidly permeating solute, acetone (P(meas)(s) =4.2 x 10(-6) m s(-1)), and 14% for the less rapidly permeating dimethylformamide (P(meas)(s) =1.6x10(-6) m s(-1)). It is concluded that, even in the case of rapidly permeating solutes such as isotopic water and, even when making pessimistic assumptions about the internal mixing of solutes, an upper limit for the underestimation of P(s) due to internal unstirred layers was 37%. The data are discussed in terms of recent theoretical estimates of the effect of internal unstirred layers and in terms of some recent criticism of cell pressure probe measurements of water and solute transport coefficients. The current stop-flow data are in line with earlier estimations of the role of unstirred layers in the literature on cell water relations.

Internal Concentration Gradients of Guest Molecules in Nanoporous Host Materials: Measurement and Microscopic Analysis

Evolution of internal concentration profiles of methanol in 2-D pore structure of ferrierite crystal was measured in the pressure range of 0 to 80 mbar with the help of the recently developed interference microscopy technique. The measured profiles showed that both a surface barrier and internal diffusion controlled the kinetics of adsorption/desorption. Furthermore, they indicated that in the main part of the crystal, the z-directional 10-ring channels were not accessible to methanol and that the transport of methanol mainly occurred via 8-ring y-directional channels. The roof-like part of the crystal was almost instantaneously filled/emptied during adsorption/desorption, indicating accessible 10-ring channels in this section. The measured profiles were analyzed microscopically with the direct application of Fick's second law, and the transport diffusivity of methanol in ferrierite was determined as a function of adsorbed phase concentration. The transport diffusivity varied by more than 2 orders of magnitude over the investigated pressure range. Transport diffusivities, calculated from measured profiles from small and large pressure step changes, were all found to be consistent. Simulated concentration profiles obtained from the solution of Fick's second law with the calculated functional dependence of diffusivities on concentration compared very well with the measured concentration profiles, indicating validity and consistency of the measured data and the calculated diffusivities. The results indicate the importance of measuring the evolution of concentration profiles as this information is vital in determining (1) the direction of internal transport, (2) the presence of internal structural defects, and (3) surface/internal transport barriers. Such detailed information is available neither from common macroscopic methods since, they measure changes in macroscopic properties and use model assumptions to predict the concentration profiles inside, nor from microscopic methods, since they only provide information on average displacement of diffusing molecules.

Simulation of an isothermal hydrodesulfurization small reactor with different catalyst particle shapes

In this work we examine the effect of different catalyst particle shapes (sphere, pellet, cylinder, 2-lobe, 3-lobe, and 4-lobe) on the characteristics and behavior of hydrodesulfurization catalyst and reactor, such as liquid holdup, external and internal concentration gradients, sulfur content in the product, and pressure drop. The analysis was based on experimental information obtained in a small hydrodesulfurization reactor using straight-run gas oil as feed and a tri-lobular commercial catalyst sample at typical commercial operating conditions. An isothermal reactor model is described in detail, which was validated with experimental information and then applied to study the effect of the different particle shapes on HDS reaction.

Characterization of sub-stoichiometric tungsten trioxide (WO 3− X) using impedance spectroscopy

Tungsten oxide electroceramic materials are routinely used in metal oxide semiconductor (MOS) gas sensors and photoelectric devices due to their gasochromic and photoelectrochromic properties. Hexagonal tungsten oxide bronze phases are ideal intercalation hosts for Li + cations and are therefore utilised as electrode materials in lithium ion batteries. Previous research has been largely concentrated on thin and thick films due to these applications. This work aims to fill the voids in the electrical characterization of dense non-stoichiometric WO 3− X polycrystalline materials. The electrical properties of which are mainly attributed to grain boundary phases and internal oxygen concentration gradients (OCGs) across grain boundaries and inter-connecting pores. The sintering regime of WO 3− X was optimised to produce fully sintered pellets with varying grain sizes and oxygen stoichiometry. Impedance spectroscopy (IS) was used to electrically characterize the microstructure, in addition to conventional electron microscopy characterization. This technique is especially valuable since it allows the deconvolution of the total impedance response of materials into their constituent components, e.g., Z bulk, Z gb, and Z el, according to their characteristic time constants.