Analytical solutions for coagulation and condensation kinetics of composite particles

2013 ◽  
Vol 249 ◽  
pp. 38-45 ◽  
Author(s):  
Vladimir N. Piskunov
Keyword(s):  
Analytical Solutions ◽  
Composite Particles ◽  
Kinetics Of

scholarly journals Modelling Activity and Durability of Electrocatalysts from a Statistical Perspective

2021 ◽  
Author(s):  
Jun Huang
Keyword(s):  
Exponential Decay ◽  
Analytical Solutions ◽  
Electrocatalytic Activity ◽  
Active Sites ◽  
Simple Theory ◽  
Exact Analytical Solutions ◽  
Modelling Activity ◽  
Closing The Gap ◽  
The Mean ◽  
Kinetics Of

<p>We develop a theory to investigate how energetic nonhomogeneity of active sites determines the overall activity of an electrocatalyst and how the evolution of the nonhomogeneity determines the overall durability. The simple theory is amenable to exact analytical solutions and thus fosters an in-depth transparent analysis. It is revealed that nonhomogeneity does not necessarily diminish the electrocatalytic activity; instead, the highest overall activity is obtained with a suitable level of nonhomogeneity that is commensurate with the mean property. The evolution kinetics of nonhomogeneity is described by using the Fokker-Planck theory. Exponential decay of the activity is predicted theoretically and confirmed experimentally. The present work represents a first step toward closing the gap between model and practical electrocatalysts using statistical considerations.</p>

scholarly journals Enzyme kinetics of CRISPR molecular diagnostics

2021 ◽  
Author(s):  
Ashwin Ramachandran ◽  
Juan G. Santiago
Keyword(s):  
Reaction Time ◽  
Enzyme Kinetics ◽  
Molecular Diagnostics ◽  
Analytical Solutions ◽  
Rapid Testing ◽  
Kinetics Parameters ◽  
Diagnostic Assays ◽  
Degree Of Reaction ◽  
Significant Interest ◽  
Kinetics Of

AbstractCRISPR diagnostic assays have gained significant interest in the last few years. This interest has grown rapidly during the current COVID-19 pandemic where CRISPR diagnostics have been frontline contenders for rapid testing solutions. This surge in CRISPR diagnostics research prompts the following question: What exactly are the achievable limits of detection and associated assay times enabled by the kinetics of Cas12 and Cas13 enzymes? To address this question, we here present a model based on Michaelis-Menten enzyme kinetics theory applied to Cas enzymes. We use the model to develop analytical solutions for reaction kinetics and develop back-of-the­ envelope criteria to validate and check for consistency in reported enzyme kinetics parameters. We applied our analyses to all studies known to us which report Michaelis-Menten-type kinetics data for CRISPR associated enzymes. These studies include all subtypes of Cas12 and Cas13 and orthologs. We found all studies but one clearly violate at least two of our three rules of consistency. We further use our model to explore ranges of reaction time scales and degree of reaction completion for practically relevant target concentrations applicable to CRISPR-diagnostic assays.

Kinetics-Controllable Hetero-Precipitation Process on the Nanoscale Solid-Liquid Interface of Spherical Particles

2011 ◽  
Vol 688 ◽  
pp. 45-50
Author(s):  
Xiao Feng Wu ◽  
Yu Chao Liao ◽  
Ren Liang Yue ◽  
Yun Fa Chen
Keyword(s):  
Shell Thickness ◽  
Spherical Particles ◽  
Composite Particles ◽  
Precipitation Process ◽  
Square Root ◽  
Initial Concentration ◽  
First Order ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Kinetics Of

Based on the growth kinetics of the SiO2particles, we studied the kinetic hetero-precipitation process on the interface of polystyrene (PS) microscale particles. The nanoscale SiO2shell thickness increased with increasing time and was proportional to the square root of the initial concentration of TEOS precursor while governed by hetero-precipitation process. Moreover, the hetero-precipitation process followed the first-order growth mechanism of silica onto the surface of templating PS pariticles. Properly controlling the reagent concentrations could alleviate and even avoid, to a certain extent, aggregation among PS@SiO2particles that could otherwise have an adverse effect on the properties and applications of those composite particles and the corresponding SiO2hollow products.

Preparation of PVAc/CNT/Carbon Black Composite Particles

2013 ◽  
Vol 457-458 ◽  
pp. 262-265
Author(s):  
Gu Qin Wang ◽  
Yang Cui
Keyword(s):  
Sulfuric Acid ◽  
Nitric Acid ◽  
Emulsion Polymerization ◽  
Composite Particle ◽  
Chemical Reactivity ◽  
Polymerization Process ◽  
Composite Particles ◽  
Conductive Network ◽  
Polymerization System ◽  
Kinetics Of

Conductive PVAc/CNT/CB composite particles were prepared through emulsion polymerization. To get the good dispersity and chemical reactivity in the polymerization system, CNT was first modified with high concentrated nitric acid and sulfuric acid. And then in the polymerization process CNT and CB were evenly dispersed into the poly (vinyl acetate) matrix and a uniform and stable conductive network was obtained finally. A series of composite particle were prepared by changing the content of CNT. And the resistivity and structure of composite particles were determined by four-probe method and FTIR. Furthermore, the kinetics of emulsion polymerization was also investigated.

scholarly journals Modelling Activity and Durability of Electrocatalysts from a Statistical Perspective

2021 ◽  
Author(s):  
Jun Huang
Keyword(s):  
Exponential Decay ◽  
Analytical Solutions ◽  
Electrocatalytic Activity ◽  
Active Sites ◽  
Simple Theory ◽  
Exact Analytical Solutions ◽  
Modelling Activity ◽  
Closing The Gap ◽  
The Mean ◽  
Kinetics Of

<p>We develop a theory to investigate how energetic nonhomogeneity of active sites determines the overall activity of an electrocatalyst and how the evolution of the nonhomogeneity determines the overall durability. The simple theory is amenable to exact analytical solutions and thus fosters an in-depth transparent analysis. It is revealed that nonhomogeneity does not necessarily diminish the electrocatalytic activity; instead, the highest overall activity is obtained with a suitable level of nonhomogeneity that is commensurate with the mean property. The evolution kinetics of nonhomogeneity is described by using the Fokker-Planck theory. Exponential decay of the activity is predicted theoretically and confirmed experimentally. The present work represents a first step toward closing the gap between model and practical electrocatalysts using statistical considerations.</p>

An analysis of a second-order chemical reaction involving a single intermediate between reactants and products

1985 ◽  
Vol 63 (12) ◽  
pp. 3294-3297 ◽  
Author(s):  
Michael Jesse Blandamer ◽  
John Marshall William Scott ◽  
Danny Summers
Keyword(s):  
Differential Equations ◽  
Analytical Solutions ◽  
Initial Conditions ◽  
Nonlinear Ordinary Differential Equations ◽  
General Reaction ◽  
Initial Concentration ◽  
First Order ◽  
Numerical Integrations ◽  
Order Chemical Reaction ◽  
Kinetics Of

The differential equations which describe the kinetics of the general reaction[Formula: see text]are cast in a nondimensional form and analysed. The problem reduces to two first-order nonlinear ordinary differential equations containing three nondimensional constants together with two initial conditions. Composition–time curves are deduced for the general case. For the case when [Formula: see text], where [A]0 is the initial concentration of A, simple analytical solutions are obtained. Numerical integrations of the full equations are reported and the analytical solutions are found to represent accurate solutions to the nonlinear problem for sufficiently small values of k2.

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