The langmuir isotherm: A commonly applied but misleading approach for the analysis of protein adsorption behavior
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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.Keywords:
Langmuir adsorption model
Abstract The applicability of Freundlich and Langmuir adsorption isotherms to guide bleaching of vegetable oils was examined using rubber [ Hevea brasiliensis (Willd. ex Adr. Juss) Muell. Arg.] and melon [ Colocynthis vulgaris (Schrad)] seed oils at temperatures of 30, 55 and 80 C. Fuller’s earth, activated charcoal and a mixture thereof (1:1 ratio) were used as the decolorizing agents (adsorbents). The degree of bleaching was monitored spectrophotometrically. Plots of log(x/m) versus log X e (for Freundlich) and ( X e /x/m) versus X e (for Langmuir) were made; where x is the amount of coloring matter removed per unit mass of the adsorbent, m, and X e is the equilibrium concentration of the coloring matter. The results obtained show good agreement with Freundlich and Langmuir isotherms, indicating that the adsorption of the coloring matter from the oils proceeds by monolayer formation on the surface of the adsorbent. The specific adsorption (x/m) and the Freundlich and Langmuir constants were found to increase with temperature for a given oil/bleaching agent ratio, showing the formation of more active sites on the adsorbent with a rise in temperature.
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It was reported that adsorption of bacteria (E.coli K12 and S.aureus) on anion exchange resins (SuperQ and DEAE). Adsorption isotherms of E.coli K12 and S.aureus on SuperQ and DEAE at 30℃ and 37℃ were measured by static state method. The adsorption isotherms were correlated with the Freundlichand the Langmuir equations,respectively.The results showed that the Freundlich equation was well fitted with adsorption isotherms and the correlation coefficients were between 0.991 and 0.995.The exponents of Freundlich isotherms were between 0.3 and 0.4. The amount adsorbed at 30℃ was more than that at 37℃.The effect of pH on the amount adsorbed was measured also by static state method. The results showed that when pH was between 2.0 and 5.0,the amount adsorbed about adsorption of E.coli K12 and S.aureus on SuperQ was less than that when pH was more than 6.0 and 7.0.
Ion-exchange resin
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Isothermal process
Picoline
Langmuir adsorption model
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The boron (B) concentration in the soil solution is generally controlled by B adsorption and desorption reactions. With this background, a study was carried out to know the adsorption and desorption of boron using Freundlich, Langmuir and Temkin isotherms in cultivated soil of Himachal Pradesh. Eighty soil samples (0-0.15 m depth) were collected randomly from different locations across different districts of Himachal Pradesh and their B adsorption-desorption behaviour was studied. Among three different adsorption isotherms i.e. Freundlich, Langmuir and Temkin used to determine the B retention capacity of soils, Freundlich and Temkin isotherms represented better fit for fine textured soils, while Langmuir isotherm showed better fit for coarse textured soils. The results emanating from the study revealed that with increase in boron concentration, the boron adsorption by soils increases.
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Parameters from single-component isotherm models were used in multicomponent isotherm models to predict the aqueous phase sorption of trichloroethylene (TCE) in the presence of tetrachloroethylene (PCE) in four zeolites, Tenax, and three natural solids. The Langmuir, the Polanyi-Dubinin, and the Freundlich or the Langmuir-Freundlich isotherm models were used to simulate single-component sorption in zeolites. The Langmuir two-site, the Polanyi-Dubinin two-site, and the Freundlich or the Langmuir-Freundlich isotherm models were used to simulate single-component sorption in Tenax and natural solids. Two-site models have been used previously to model sorption in soils and sediments, and they combine an adsorption component (e.g., Langmuir) with a linear partitioning component. By using parameters from the different single-component isotherm models, the multicomponent Langmuir, the ideal adsorbed solution theory, and the Polanyi theory were each used to predict multicomponent sorption. In general, the ability to predict TCE sorption in the presence of PCE depended more on the choice of the single-component model than the multicomponent model, and better results were obtained when the Freundlich or the Langmuir-Freundlich isotherm was used for single-component sorption. This suggests that the more mechanistically based Langmuir and Polanyi-type models may not adequately describe the distribution of adsorption sites in some model and natural solids. The Freundlich or the Langmuir-Freundlich model, although empirical, has greater flexibility in characterizing sorbent heterogeneity and results in better multicomponent model predictions. However, this last statement is tenuous, because more solids must be tested against various model combinations.
Organic chemicals
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The humic acid (HA), extracted from soils by alkali and acid was used to study the adsorption mechanism of Co2+, Cd2+. The results show that the best pH ranges from 6 to 7 and the adsorption procedure is exothermic reaction. The adsorption of Co2+ on HA fits for Langmuire and Freundlich adsorption equation, the amount of adsorption at the temperature of 19℃、 35℃、 45℃ are 12.51, 9.52, 8.30 mg/g respectively. The adsorption of Cd2+ on HA fits for Langmuire and Freundlich adsorption equation at the temperature of 19℃、 35℃, the amount of adsorption are 33.90, 33.30 mg/g respectively; however, at 45℃ it mainly fits for Freundlich adsorption equation. The adsorption of Co2+ ,Cd2+ on HA is in the way of forming complex compound through second order complex reaction.
Exothermic reaction
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The need to minimize surfactant adsorption on rock surfaces has been a challenge for surfactant-based, chemical-enhanced oil recovery (cEOR) techniques. Modeling of adsorption experimental data is very useful in estimating the extent of adsorption and, hence, optimizing the process. This paper presents a mini-review of surfactant adsorption isotherms, focusing on theories of adsorption and the most frequently used adsorption isotherm models. Two-step and four-region adsorption theories are well-known, with the former representing adsorption in two steps, while the latter distinguishes four regions in the adsorption isotherm. Langmuir and Freundlich are two-parameter adsorption isotherms that are widely used in cEOR studies. The Langmuir isotherm is applied to monolayer adsorption on homogeneous sites, whereas the Freundlich isotherm suites are applied to multilayer adsorption on heterogeneous sites. Some more complex adsorption isotherms are also discussed in this paper, such as Redlich-Peterson and Sips isotherms, both involve three parameters. This paper will help select and apply a suitable adsorption isotherm to experimental data.
Sorption isotherm
Langmuir adsorption model
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본 연구에서는 국내에서 대표적으로 버려지는 폐벌목 중 잣나무에서 만든 활성탄을 이용하여 벤젠에 대한 정지(static)흡착 실험을 수행하였다. 7.999 kPa에 이르는 압력 범위 내에서 온도 조건을 변화시켜 가며 303.15, 318.15, 333.15 K에서 흡착실험을 진행하였다. 등온흡착곡선은 Langmuir 등온흡착식, Freundlich 등온흡착식, Toth 등온흡착식을 적용하여 비교하였다. 벤젠의 흡착량(q)을 측정한 결과 Langmuir 등온흡착식과 Toth 등온흡착식으로 적용한 등온흡착곡선의 정확도가 높은 것으로 나타났다. 그리고 Langmuir 등온흡착식의 $q_{max}$ 값을 이용하여 흡착제의 흡착량을 비교하였다. 또한, 폐벌목 활성탄과 상용활성탄의 세공 발달 여부를 비교하기 위해 주사전자현미경(scanning electron microscopy, SEM) 사진을 관찰하였다. SEM 사진 관찰 결과, 폐벌목 활성탄이 국내 외 상용활성탄(DARCO A.C., SPG-100 A.C.)에 비해 세공발달 정도가 우수하며, 벤젠흡착량(q)이 높은 것을 확인할 수 있었다. 본 연구 결과를 통해 폐벌목 활성탄의 상용화 가능성을 검증할 수 있었다. In this study, experiments on the static adsorption of benzene were carried out using activated carbon made from Pinus koraiensis which is normally discarded waste timber in South Korea. The experiment were performed at 303.15 K, 318.15 K and 333.15 K under the pressure up to 7.999 kPa. Isothermal adsorption curves were obtained using Langmuir isotherm, Freundlich isotherm and Toth isotherm for comparison. Based on the fitting, the adsorption quantity of Benzene (q), the isothermal adsorption curves obtained from Langmuir isotherm and Toth isotherm showed the higher accuracy. Although there was little difference in accuracy between result from Langmuir isotherm and that from Toth isotherm, the adsorption quantity of Benzene (q) was expressed in terms of Langmuir isotherm because less parameters were required for Langmuir isotherm than for Toth isotherm. Moreover SEM images of the activated carbon from Pinus koraiensis and the commercial activated carbon were taken to observe the pore size development. The results showed that the perforation development of activated carbon from Pinus koraiensis (waste timber) was better than that of commercial activated carbon (DARCO A.C., SPG-100 A.C.). Adsorption quantity of benzene on activated carbon from Pinus koraiensis was confirmed to be higher than that on commercial activated carbon. Therefore, we may conclude that it is feasible to commercialize the process to manufacturing activated carbon from waste timber.
Langmuir adsorption model
Pinus koraiensis
Isothermal process
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In environmental studies it is necessary to know the adsorption behavior of zinc by soils.This behavior can be evaluated by mathematical models described by Langmuir and Freundlich equations. The objective of this study was to evaluate Langmuir and Freundlich isotherms applied to zinc adsorption in surface samples of ten soil from Paraíba State, Brazil, with a wide range of chemical properties. In order to quantify the adsorbed zinc, 2 g of air-dried soil were equilibrated with 20 mL of a NaCl (0.01 mol L-1) solution containing different quantities of zinc (5, 20, 30, 40, 50, 60, 70, 90 mg L-1). Zinc adsorption by soils, with exception of the PAd, was well described by both Langmuir and Freundlich models. For Zn concentrations up to 30 mg L-1, applied in the soils, the two models estimated low values than the experimental values; above 70 mg L-1 of Zn, Freundlich model overestimated the experimental values.
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