Adsorption technology has been widely applied for water and wastewater treatment due its low cost and easy operation. Understanding the adsorption kinetic could help to design the adsorption system. ...The pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic models were usually used, however their specific theoretical meanings and the application conditions were still unclear. In addition, for a practical adsorption system, the kinetic process is complex, which may include both the PFO and PSO kinetic process. Therefore, it is necessary to develop a general kinetic model to describe the whole adsorption process more accurately. In this paper, based on the Langmuir kinetics, and the theoretical analysis of the PFO and PSO models, a general form of adsorption kinetic model was developed. The experimental data from our previous studies and literature were used to fit the mixed-order (MO) model. The results showed that it is capable of describing both the PFO and PSO kinetic process and suitable for whole adsorption process, suggesting that it can describe the kinetics of whole adsorption process better. The MO kinetic model can be solved by using 4–5 order Runge-Kutta method, and the solving program as well as the method illustration was provided in Appendixes, which can be used by the readers who are interested in this model.
•A general kinetic model was developed based on the Langmuir kinetics.•It is a general form of the first- and second-order kinetics.•This model is suitable for describing whole adsorption process.•The solving program and method illustration were provided in Appendixes.
Catalysts are widely used to increase reaction rates. They function by stabilizing the transition state of the reaction at their active site, where the atomic arrangement ensures favourable ...interactions
. However, mechanistic understanding is often limited when catalysts possess multiple active sites-such as sites associated with either the step edges or the close-packed terraces of inorganic nanoparticles
-with distinct activities that cannot be measured simultaneously. An example is the oxidation of carbon monoxide over platinum surfaces, one of the oldest and best studied heterogeneous reactions. In 1824, this reaction was recognized to be crucial for the function of the Davy safety lamp, and today it is used to optimize combustion, hydrogen production and fuel-cell operation
. The carbon dioxide products are formed in a bimodal kinetic energy distribution
; however, despite extensive study
, it remains unclear whether this reflects the involvement of more than one reaction mechanism occurring at multiple active sites
. Here we show that the reaction rates at different active sites can be measured simultaneously, using molecular beams to controllably introduce reactants and slice ion imaging
to map the velocity vectors of the product molecules, which reflect the symmetry and the orientation of the active site
. We use this velocity-resolved kinetics approach to map the oxidation rates of carbon monoxide at step edges and terrace sites on platinum surfaces, and find that the reaction proceeds through two distinct channels
: it is dominated at low temperatures by the more active step sites, and at high temperatures by the more abundant terrace sites. We expect our approach to be applicable to a wide range of heterogeneous reactions and to provide improved mechanistic understanding of the contribution of different active sites, which should be useful in the design of improved catalysts.
Atomistic simulations play a central role in many fields of science. However, their usefulness is often limited by the fact that many systems are characterized by several metastable states separated ...by high barriers, leading to kinetic bottlenecks. Transitions between metastable states are thus rare events that occur on significantly longer timescales than one can simulate in practice. Numerous enhanced sampling methods have been introduced to alleviate this timescale problem, including methods based on identifying a few crucial order parameters or collective variables and enhancing the sampling of these variables. Metadynamics is one such method that has proven successful in a great variety of fields. Here we review the conceptual and theoretical foundations of metadynamics. As demonstrated, metadynamics is not just a practical tool but can also be considered an important development in the theory of statistical mechanics.
The stochasticity of molecular motion results in the existence of multiple kinetically relevant pathways in many biomolecular mechanisms. Because it is highly demanding to characterize them for ...complex systems, mechanisms are often described with a single-pathway perspective. However, kinetic network analysis and sub-ensemble experimental insight are increasingly demonstrating not only the existence of competing pathways but also the importance of kinetic selection in biology. This review focuses on advances in multiscale kinetic analysis of proteins, which connects molecular level information from simulations to macroscopic data to characterize mechanistic reaction networks and the reactive flux through them. We describe a range of methods used and highlight several examples where kinetic modeling has revealed functional importance of pathway heterogeneity.
High‐speed plasma jets downstream of Earth's bow shock are high velocity streams associated with a variety of shock and magnetospheric phenomena. In this work, using the Magnetosphere Multiscale ...mission, we study the properties of a jet found downstream of the Quasi‐parallel bow shock using high‐resolution (burst) data. By doing so, we demonstrate how the jet is an inherently kinetic structure described by highly variable velocity distributions. The observed distributions show the presence of two plasma population, a cold/fast jet and a hotter/slower background population. We derive partial moments for the jet population to isolate its properties. The resulting partial moments appear different from the full ones which are typically used in similar studies. These discrepancies show how jets are more similar to upstream solar wind beams compared to what was previously believed. Finally, we explore the consequences of our results and methodology regarding the characterization, origin, and evolution of jets.
Plain Language Summary
Typically, particles from the Sun get strongly decelerated when they interact with the magnetic field of Earth, forming a shock wave. Magnetosheath (MSH) jets are fast streams of particles appearing downstream of this shock, with typically higher velocities and densities than the background population. In this work, we show how jets behave after they are created at the shock wave. We describe the variability of their properties and how this is connected to the background MSH population they interact with. Through that, we reveal new insights regarding their origin, evolution, and motivate on a new approach to study jets and similar phenomena in the future.
Key Points
Ions in an observed jet exhibit complex distribution functions, with a cold/fast jet beam and hotter/slower background population
Jet interaction with the background magnetosheath is studied by comparing partial moments of the jet population with the full ion moments
The derived properties of the cold/fast population connect the jet's origin to upstream solar wind and foreshock structures
Ocean circulation receives its energy input at basin scales while dissipates at microscopic mixing scale. How this energy is transferred across different lengthscales is of paramount importance for ...understanding the ocean circulation equilibration and variability. Advancement in high‐resolution numerical simulations in recent years has significantly improved our understanding of kinetic energy (KE) cascades from basin to kilometer scales, although observational evidence to verify the simulated processes remains limited. Using repeat ship‐board velocity measurements along 165°E across the equatorial, subtropical and subarctic Pacific Ocean, we show that the length scale separating the inverse and forward cascades, LS, falls in the 8 ∼ 300 km range and it does not scale straightforwardly with the baroclinic deformation radius. Balanced and unbalanced oceanic motions co‐exist in this range but contribute oppositely to the directional energy cascades. LS is observed to depend on the relative strengths of these motions, as well as by their interaction.
Plain Language Summary
This paper investigates how nonlinear interactions in the turbulent upper ocean transport kinetic energy (KE) across different spatial scales. This investigation is important because the energy input that drives the ocean circulation has scales at tens of thousand kilometers, whereas the oceanic mixing and dissipation take place below the centimeter scales. How oceanic KE is transported from one scale to another is neither fully understood nor adequately observed, and this is particularly true in the oceanic meso‐submesoscales in the 1 ∼ 300 km range. By using repeat shipboard Acoustic Doppler Current Profiler surveys from 2004 to 2020 in the western Pacific Ocean, we examined the cross‐scale KE transfers in dynamically different regimes of tropics, subtropics and high latitudes. We found that the KE can transfer both up‐scales and down‐scales due to the co‐existence of balanced geostrophic motions and unbalanced wave motions. The length scale that separates the bi‐directional KE transfers is geographically dependent. It is controlled by the relative strengths of co‐existing balanced and unbalanced motions, as well as by how the unbalanced wave motions are dynamically generated.
Key Points
Nonlinear interaction in upper ocean transfers kinetic energy both up‐ and down‐scales
Upper ocean balance and unbalanced motions contribute oppositely to energy cascade
Bi‐directional energy cascade depends on relative importance of balanced versus unbalanced motions and characteristics of the unbalanced motions
•Kinetic analysis of waste biomass (sawdust) was investigated through deconvolution.•Activation energy is determined by Straink (SR) and Friedman (FR) kinetic methods.•Reaction mechanism is evaluated ...by employing integral master plot method.•Thermodynamic parameters (ΔH, ΔS, and ΔG) were also determined.•Deconvolution kinetic analysis is suitable for complex decomposition processes.
Non-isothermal kinetics involved during the slow pyrolysis of waste biomass (sawdust) was investigated. The slow pyrolysis profile of sawdust was distinguished into three reactions corresponding to each pseudo component (hemicellulose, cellulose & lignin) through the deconvolution process. Kinetic triplets (activation energy, reaction mechanism & pre-exponential factor) were estimated for each pseudo component. The Straink (SR) and Friedman (FR) iso-conversional kinetic models were used to calculate the activation energy of pseudo-cellulose (SR = 162.90 kJ/mol, FR = 165.67 kJ/mol), pseudo-hemicellulose (SR = 156.25 kJ/mol, FR = 158.47 kJ/mol) and pseudo-lignin (SR = 301.62 kJ/mol, FR = 316.72 kJ/mol). The reaction mechanism involved during the slow pyrolysis of waste sawdust was identified through integral master plot method. The results revealed that the two-dimensional contract area (R2) and second order reaction (F2) reaction mechanism dominates slow pyrolysis of pseudo-cellulose and pseudo-hemicellulose, respectively. However, no exact reaction mechanism was observed for pseudo-lignin. The pre-exponential factor was determined with the help of the activation energy and reaction mechanism. Thermodynamic parameters i.e. change in enthalpy (ΔH), entropy (ΔS) and Gibb’s free energy (ΔG) were also determined for pseudo-cellulose (ΔH=157.54kJ/mol, ΔS=-17.615 J/mol and ΔG=168.64 kJ/mol) and pseudo-hemicellulose (ΔH=151.28kJ/mol, ΔS=6.61 J/mol and ΔG=147.12 kJ/mol).
The recent technological evolution of reaction monitoring techniques has not been paralleled by the development of modern kinetic analyses. The analyses currently used disregard part of the data ...acquired, thus requiring an increased number of experiments to obtain sufficient kinetic information for a given chemical reaction. Herein, we present a simple graphical analysis method that takes advantage of the data‐rich results provided by modern reaction monitoring tools. This analysis uses a variable normalization of the time scale to enable the visual comparison of entire concentration reaction profiles. As a result, the order in each component of the reaction, as well as kobs , is determined with just a few experiments using a simple and quick mathematical data treatment. This analysis facilitates the rapid extraction of relevant kinetic information and will be a valuable tool for the study of reaction mechanisms.
Overlaid concentration profiles: The order in any component of a reaction is determined by visual comparison of variably normalized concentration profiles. Variable time normalization analysis (VTNA) is easy and quick to perform, is run under synthetically relevant conditions, and provides information on the entire reaction course.
In this paper, two main ideas of chemical kinetics are distinguished, i.e., a hierarchy and commensuration. A new class of chemical kinetic models is proposed and defined, i.e., egalitarian kinetic ...models (EKM). Contrary to hierarchical kinetic models (HKM), for the models of the EKM class, all kinetic coefficients are equal. Analysis of EKM models for some complex chemical reactions is performed for sequences of irreversible reactions. Analytic expressions for acyclic and cyclic mechanisms of egalitarian kinetics are obtained. Perspectives on the application of egalitarian models for reversible reactions are discussed. All analytical results are illustrated by examples.
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