Kinetic and equilibrium studies of Cs-137 sorption on calcium-doped Prussian blue
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Prussian blue
Langmuir adsorption model
Caesium
Isothermal process
The adsorption performances of four adsorbents,CAS,DTCS,CTS and DTC-CTS for heavy metals(Cu,Pb,Zn) are investigated,and the selectivity of adsorbents for heavy metal ions is determined by isothermal adsorption equations.The results show that the calculation results by Langmuir-Freundlich isothermal equation are well fitted with the experimental data for the four adsorbents.Associating with the calculated results by Langmuir isothermal equation,the selectivity of adsorbents in the actual process of multi-metal-ion system can be predicted by the Langmuir-Freundlich isothermal equation,therefore much experiment can be saved.
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Langmuir adsorption model
Langmuir equation
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Langmuir adsorption model
Langmuir equation
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Langmuir adsorption model
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Standard isotherm equations do not estimate capacity (Qmax) and distribution coefficient (Kd) for complex or non-Langmuir-shaped isotherm plots. In this study, two mycotoxins, that is, aflatoxin B1 (AfB1) and cyclopiazonic acid (CPA), were mixed with kaolinite and a naturally acidic montmorillonite clay (LPHM) at 25 °C, respectively. Isotherm data gave S-type plots. The data were fitted to the models of Langmuir (LM) and multi-Langmuir (MLM); however, these models did not provide a good fit for data that displayed multisite adsorption or multiple plateaus. While a published modification of the Langmuir equation (QKLM), which defines an effective partition coefficient as a function of the surface coverage, was able to fit simple isotherm plots from all categories (H, L, S, C), it did not fit complex or multisite isotherm plots. Importantly, an equation that enables the estimation of Qmax and Kd for both S-shaped and multisite isotherm plots has not yet been reported. Since the LM, MLM, and QKLM did not provide adequate fitting of the data, several modifications of the LM were developed: shifted Langmuir, shifted squared Langmuir, shifted cubed Langmuir, shifted exponential Langmuir, exponential Langmuir, and shifted modified Langmuir. These equations were used to derive information about the adsorption of mycotoxins to clay and to gain insight into the molecular mechanism(s) and site(s) of adsorption. The objectives of this study were to present a series of modified Langmuir equations that can be used to estimate the Qmax and Kd of a specific adsorption site and to relate Qmax to available adsorption area.
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The Langmuir isotherm is a widely used model for analyzing adsorption equilibrium data. This study evaluated the efficiency and accuracy of all four linear forms of the Langmuir isotherm and its non-linear form using 67 experimental data sets selected from the literature. The results showed that only if all four linear forms simultaneously show high accuracy, then the non-linear form also shows high accuracy, and therefore it can be said that the process probably follows the Langmuir isotherm. On the contrary, when at least one of the four linear forms of the Langmuir isotherm has low accuracy, it means that the non-linear form also has low accuracy, and it can be concluded that this process does not follow the Langmuir isotherm. This research suggests that all four linear forms of the Langmuir isotherm should be evaluated simultaneously to conclude whether the studied system follows the Langmuir isotherm or not. In other words, relying on only one of the four linear forms of the Langmuir isotherm to model adsorption and calculate the Langmuir constant and maximum adsorption capacity is an incomplete approach, contrary to the conventional approach.
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The Langmuir adsorption isotherm provides one of the simplest and most direct methods to quantify an adsorption process. Because isotherm data from protein adsorption studies often appear to be fit well by the Langmuir isotherm model, estimates of protein binding affinity have often been made from its use despite that fact that none of the conditions required for a Langmuir adsorption process may be satisfied for this type of application. The physical events that cause protein adsorption isotherms to often provide a Langmuir-shaped isotherm can be explained as being due to changes in adsorption-induced spreading, reorientation, clustering, and aggregation of the protein on a surface as a function of solution concentration in contrast to being due to a dynamic equilibrium adsorption process, which is required for Langmuir adsorption. Unless the requirements of the Langmuir adsorption process can be confirmed, fitting of the Langmuir model to protein adsorption isotherm data to obtain thermodynamic properties, such as the equilibrium constant for adsorption and adsorption free energy, may provide erroneous values that have little to do with the actual protein adsorption process, and should be avoided. In this article, a detailed analysis of the Langmuir isotherm model is presented along with a quantitative analysis of the level of error that can arise in derived parameters when the Langmuir isotherm is inappropriately applied to characterize a protein adsorption process.
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A graphical method for evaluating the Langmuir favorable adsorption is proposed in this work. The conditional Langmuir constant (KLN), a new parameter related to the Langmuir equilibrium constant (KL), can be used to predict the shapes of Langmuir favorable adsorption isotherms. On the dimensionless Langmuir isotherm diagram, all the Langmuir favorable adsorptions (0 < RL < 1) are further divided into three subgroups: favorable adsorption, very favorable adsorption, and highly favorable or pseudoirreversible adsorption, with two critical Langmuir constants (KLN1 and KLN2) as the demarcation point. The feasibility of the method is demonstrated by analyzing 14 adsorption systems. The graphical method is effective and intuitional, and can be used for the favorable evaluation of any Langmuir isotherms. This method shows the advantage that the parameter KLN does not depend on the initial adsorbate concentration (co) over RL method.
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Adsorption processes are typically designed with the aid of process simulators. Here, the extended Langmuir model and derivates are frequently used when dealing with type I isotherms (Langmuirian). The extended Langmuir model captures competition effects based on low-coverage Henry selectivity. However, it does not account for adsorbate size effects, where smaller adsorbates can be preferred at a higher pressure. Still, in simulators, the extended Langmuir model is predominantly used over the implicit ideal adsorbed solution theory (IAST), which does predict a size effect. In this work, we define and explore two models, having an explicit form and aimed at introducing an adsorbate size effect. The aim is twofold: First, the extended Langmuir and new model predictions are compared to IAST to demonstrate the adsorbate size effect. Second, all models are tested in a process simulator case study where the performance results as well as execution time are considered. A temperature swing adsorption (TSA) process simulation case study with a 10-component mixture was performed at high loading: the extended Langmuir model shows large recovery differences over the models which do incorporate a size effect. Explicit models can be executed quicker than IAST (FASTIAS), although the manner of implementation in the process simulator is important. The new models may improve the extended Langmuir predictions with respect to (IAST) size effects and also have their limitations.
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Langmuir Probe
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