https://chemical.eng.usm.my/bassim/PDF/adsorption%20isotherm.pdf

Insights into the modeling of adsorption isotherm systems

http://libir.tmu.edu.tw/bitstream/987654321/43034/1/4.pdf

Review of second-order models for adsorption systems.

http://repository.ust.hk/ir/bitstream/1783.1-645/1/323k.pdf

A comparison of chemisorption kinetic models applied to pollutant removal on various sorbents

Guidelines for the use and interpretation of adsorption isotherm models: A review.

/pdf/langmuir-freundlich-temkin-and-dubinin-radushkevich-2m29c7koi9.pdf

Langmuir, Freundlich, Temkin and Dubinin–Radushkevich Isotherms Studies of Equilibrium Sorption of Zn 2+ Unto Phosphoric Acid Modified Rice Husk

In activated chemisorption the plot of the reciprocal of the rate Z=(dq/dt)–1 against the time t is convex towards the Z axis at low t and concave at high t. This condition is satisfied if both the energy of activation, Et and the number of available sites, Nt decrease with the coverage q and if d2Et/dq2 < 0. Two models are considered:

Kinetics of activated chemisorption. Part 2.—Theoretical models

The kinetics of activated chemisorption are described by plots of the time t against the reciprocal of the rate of adsorption Z=(dq/dt)–1. The parameter t0 of the Elovich equation q=(1/b) ln ab+(1/b) ln (t+t0) where a, b and t0 are constants is estimated from the plot of t against Z. The plot of q against log(t+t0) is convex towards the q axis at low t indicating that the Elovich equation is not obeyed in that range. The “combined model” of Aharoni and Tompkins predicts a curvature in the wrong direction and is inapplicable without modification.

Kinetics of activated chemisorption. Part 1.—The non-elovichian part of the isotherm

The kinetics of chemisorption have been inadequately represented in the literature by second-order equations and by Elovich equations. The conditions at which non-valid equations become apparently applicable are discussed. Assumed isotherms are often congruent to the experimental one at a limited range of coverage and predict a correct value for the rate dq/dt and for the change of rate d2q/dt2 in that range; however, they have been applied beyond the range of validity by using plotting procedures that allow the location of the region of congruency to be adjusted and the effect of data outside this region to be attenuated. The second-order rate equation q∞/(q∞–q)=αt+ 1 where q∞ and α are constants, is congruent to the Elovich equation when q≈ 0.5q∞. Reciprocally, the Elovich equation q=c+(1/b)ln t where b and c are constant, is indistinguishable from a second-order equation when q≈ 2/b. Both equations can be fitted at certain conditions to data obeying the equation q=kt1/v where k and v are constants. Differential analysis shows that the experimental isotherms generally obey a complex function for which z=(dq/dt)–1 is sigmoid.

Kinetics of chemisorption. Deducing kinetic laws from experimental data

The heterogeneous-surface model applied in Part 2 to the kinetics, is now applied to the effects of temperature and pressure on the amount adsorbed. It predicts isobars with a maximum that is displaced towards higher temperatures at higher pressures. The low-temperature, pseudo-equilibrium isotherms obey the Freundlich equation. Increase in temperature or decrease in pressure produce desorption followed by readsorption. Temperature-programmed desorption gives one peak when heating is slow and two peaks when heating is rapid. When isotopes are successively adsorbed, the isotope adsorbed last is desorbed at lower temperature. The distribution of the adsorbate, according to the regions of various energy on the adsorbent, depends on temperature, pressure and time and is given by a discontinuous function with a maximum.

Kinetics of activated chemisorption. Part 3.—Amount and distribution of adsorbate at varying temperatures and pressures

A model is considered in which occlusion takes place in parallel in an array of micropores with different coefficients of diffusion. The rate equation for occlusion in a pore is approximated by a parabolic or by an exponential equation, and the rate for the overall process is obtained by summing the rates in the pores. The plot of Vt/V∞ against ln t, where Vt and V∞ are the amounts sorbed at times t and infinity, respectively, is sigmoid and has an intermediate part with greatest slope. The slope of this intermediate part is related to the heterogeneity of the system. If vE(E) is constant, where E is the energy of activation for diffusion and vE the pore volume for an energy between E and E+ dE, the reciprocal of the slope is equal to the difference between the highest and lowest E divided by RT. If E is constant the slope is close to 0.2.

Application of the Elovich equation to the kinetics of occlusion. Part 1.—Homogeneous microporosity

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Chaim Aharoni

Author Tools

Chat about Author