Langmuir adsorption isotherm model

Electrochemical impedance spectroscopy was used to determine the effect of isomers of 2,5-bis( -pyridyl)-l,3,4-thiadiazole 36 (n 2 or 3) on the corrosion of mild steel in perchloric acid solution <2002MI197>. The inhibition efficiency was structure dependent and the 3-pyridyl gave better inhibition than the 2-pyridyl. X-ray photoelectron spectroscopy helped establish the 3-pyridyl thiadiazoles mode of action toward corrosion. Adsorption of the 3-pyridyl on the mild steel surface in 1M HCIO4 follows the Langmuir adsorption isotherm model and the surface analysis showed corrosion inhibition by the 3-pyridyl derivative is due to the formation of chemisorbed film on the steel surface. 

A final area of difficulty is in the application of data analysis to specific models of adsorption isotherms. This difficulty results from the fact that different models for adsorption isotherms generate plots of surface versus dissolved concentration that have characteristic shapes. If a plot of observational data results in a curve with a shape similar to that generated by a model, this result is often taken as proof that the particular model applies. Unfortunately, this assumption has been made for situations where many of the basic requirements of the model are violated in the system under study. The Langmuir adsorption isotherm model has suffered considerable abuse by geochemists in this regard. It should be remembered that "shapes" of adsorption isotherms are far from proof that a specific model applies. 

The concentration-dependent binding of Ru(dcb)-based sensitizers is well described by the Langmuir adsorption isotherm model from which adduct formation constants of 10 have typically been abstracted [123, 132]. While it is often stated that monolayer coverage of the sensitizers is achieved, this is difficult to prove. The colloidal nature of the films makes absolute surface area determinations almost impossible. There is no evidence for multilayer formation, so the surface coverage is at most monolayer and probably sub-monolayer in most cases. The surface coverage for sensitzers in a 1 cm geometric area is typically 10 mol, where 10 mol cm would be expected for a close-packed monolayer of 14 A diameter sensitizers on a flat surface. 

Hwang et al. synthesized poly(vinylphosphonic acid-co-methaciylic acid) microbeads by suspension polymerization, and they investigated the adsorption properties with indium. The maximum adsorption predicted by the Langmuir adsorption isotherm model was greatest at a 0.5 mol ratio of vinylphosphonic acid. The adsorption capacity of indium was... 

Interestingly, while the adsorption of polyelectrolytes onto BaS04 does not conform to the usual assumptions of the Langmuir adsorption isotherm model, the Langmuir model nevertheless provides a good fit to these experimental results as it does in many other cases of polymer adsorption. The Langmuir adsorption isotherm can be written in linear form as shown in Equation 1. 

Langmuir and Freundlich adsorption models can be used to describe the adsorption behavior of dispersants on an abrasive surface. The Langmuir adsorption isotherm model assumes that the particle surface is homogeneously covered by the monolayer dispersant. It is expressed as follows ... 

Berger et al. [34] measured the surface stress changes and kinetics by micromechanical sensors during the self-assembly process of HS-(CH2) i-CH3 for n = 4, 6, 8,12, and 14 on gold, where n is the number of carbon atoms in the alkyl chain. The sensor deflection was shown to be a function of time for experiments with alkanethi-ols of various chain lengths (fig. 7.4a) and has been fitted to a Langmuir adsorption isotherm model as... 

Parameters of the Langmuir Adsorption Isotherm Model Coupled with the Van t Hoff s Relationship Model... 

Adsorption capacities of different adsorbent was compared by Choi et al. (2009) modeling using Langmuir adsorption isothermal model (Eq. 2.1) and three stage kinetic model as shown in Eqs. (2.2) and (2.3) below. 

For nonlinear systems, however, the evaluation of the flow rates is not straightforward. Morbidelli and co-workers developed a complete design of the binary separation by SMB chromatography in the frame of Equilibrium Theory for various adsorption equilibrium isotherms the constant selectivity stoichiometric model [21, 22], the constant selectivity Langmuir adsorption isotherm [23], the variable selectivity modified Langmuir isotherm [24], and the bi-Langmuir isotherm [25]. The region for complete separation was defined in terms of the flow rate ratios in the four sections of the equivalent TMB unit ... 

As noted in Chapter 1, the most simple and theoretically sound model for drug-receptor interaction is the Langmuir adsorption isotherm. Other models, based on receptor behavior (see Chapter 3), are available. One feature of all of these models (with the exception of some instances of the... 

The multicomponent Langmuir adsorption isotherm given in Eq. (7) is the simplest model for the description of non-linear, multicomponent, adsorption equilibrium. At high concentration, the model predicts saturation of the stationary phase and overload of the chromatographic column. At low concentration (high dilution) the behavior can be correctly described by the non-competitive linear adsorption isotherm ... 

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

This model of adsorption was suggested by Irving Langmuir and is referred to as the Langmuir adsorption isotherm . The aim of this experiment is to test the validity of this isotherm equation and to measure the surface area per gram of charcoal, which can easily be obtained from the measured value, if the area per solute molecule is known. 

The Adsorption of Hydrolyzed Al(III). O Melia and Stumm (12) have shown that specific adsorption of hydrolyzed Fe(III) species accounts for the observed coagulation and restabilization of silica dispersions. A model was formulated on the basis of the Langmuir adsorption isotherm and was shown to explain the observations adequately. The authors derive a relationship between the surface area concentration of the dispersed phase S (in meter2/liter and the applied coagulant ion concentration Cte (in M) necessary to reach a certain fraction of surface coverage. The extent of destabilization or of restabilization can be concluded from the amount of surface coverage on the colloidal particle ... 

Equations D3.5.30 and D3.5.32 are both very valuable. They state that the rate of adsorption can be obtained from plots of the interfacial tension versus either tA- (for t—>0) or lth (for the long-term solution f— >). With these two equations the tool to extract the adsorption rate from experimentally obtained surface tension-time curves is at hand. It should be noted that instead of the Gibbs model, one could use one of the previously mentioned adsorption isotherms such as the Langmuir adsorption isotherm to convert interfacial tension to interfacial coverage data. The adsorption isotherms may be obtained by fitting equilibrium surface tension data versus surfactant concentration. 

The kinetic derivation has the disadvantage that it refers to a certain model. The Langmuir adsorption isotherm, however, applies under more general conditions and it is possible to derive it with the help of statistical thermodynamics [8,373], Necessary and sufficient conditions for the validity of the Langmuir equation (9.21) are ... 

In Langmuir model, the maximal adsorption is that of a monolayer. Langmuir adsorption isotherms all saturate at high vapor pressures. This is unrealistic for many cases. In order to consider the adsorption of multilayers, Brunauer, Emmett, and Teller extended the Langmuir theory and derived the so-called BET adsorption isotherm [378], The basic idea in the BET theory was to assume a Langmuir adsorption for each of the layers (Fig. 9.8). 

Mg2+ influences calcite dissolution rates the same way, but not to the same extent as Ca2+. The inhibition effects of Mg2+ can be described in terms of a Langmuir adsorption isotherm. Sjoberg (1978) found he could model results for the combined influences of Ca2+ and Mg2+ in terms of site competition consistent with ion exchange equilibrium. The inhibition effects of Mg2+ in calcite powder runs increase with increasing Mg2+ concentration and as equilibrium is approached. 

This effect is relatively small until the total magnesium ion concentrations reach about 1000 ppm. o The effect of Mg2+ concentration on limestone dissolution rate can be explained by a surface adsorption model. The adsorption of Mg2+ reduces the limestone dissolution rate because the surface is partially blinded by the adsorbed magnesium ions. The competitive adsorption of calcium and magnesium ions was described by a mathematical model based on the Langmuir adsorption isotherm. The model was used to explain the sensitivity of limestone dissolution rate to magnesium ion concentration under limestone DA operating conditions. 

A frequently used adsorption model that allows for adsorption in multilayers has been introduced by Brunauer, Emmett and Teller [10] and is known as the BET equation. With the exception of the assumption that the adsorption process terminates at monolayer coverage, these authors have retained all the other assumptions made in deriving the Langmuir adsorption isotherm. Hence all objections to the application of the Langmuir equation apply here, too. 

In literature the existing experimental data base of supercritical adsorption equilibria is limited and most of the data have been modelled with one of three common adsorption isotherm models - the Langmuir, the Freundlich and the Toth. The models define adsorption isotherms with a similar shape and they have 2 or 3 adjustable parameters which allow an accurate correlation. 

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