PREDICTION OF THE ASYMMETRIC PEAK PROFILE USING A MATHEMATICAL METHOD WITH A COMPETITIVE LANGMUIR ISOTHERM

The adsorption characteristics of a single component and a binary component in the stationary phase using preparative chromatography were investigated with a six-adsorption isotherm model. These analyses were based on the Langmuir model. Each parameter of the adsorption isotherm was obtained with the adsorption raw data that was calculated by frontal analysis (FA). The experimental data and the values calculated using the adsorption isotherm model were compared. The bi-Langmuir model showed good agreement for phenol while the tri-Langmuir model showed good agreement for caffeine. Each characteristic of adsorption was obtained from these results. The effect of competitive adsorption was investigated using the parameters of the adsorption isotherm model with a single component. There was good agreement between the experimental data and the calculated values.     

Prediction of the band profiles of the mixtures of the 1-indanol enantiomers from data acquired with the single racemic mixture

The adsorption isotherm data of R- and S-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. These data were then fitted to the Langmuir, the Bilangmuir, the Toth, and the Langmuir-Freundlich isotherm models. The single component data fitted well to both the Bilangmuir and the Toth models. Combined with the lumped pore diffusion model (POR) of chromatography, these isotherms were used to calculate overloaded elution profiles of the pure enantiomers. The calculated and the experimental profiles agree excellently in all cases if the former are derived from the Bilangmuir model. The competitive experimental data also gave excellent agreement with the Bilangmuir model. The simultaneous fit of all the data, for the single components and the racemic mixture, gave again superior agreement with the bilangmuir model. The overloaded elution profiles of samples of the racemic mixture calculated with the Bilangmuir isotherm model combined with the POR model of chromatography gave results in very good agreement with the experimental band profiles of large samples of the racemic mixture. This confirms that in numerous cases the whole set of competitive isotherms of two enantiomers can be derived from the experimental data obtained only with the racemic mixture.     

Separation of p-xylene from binary xylene mixture over silicalite-1 membrane: Experimental and modeling studies

The permeation of single component and binary mixture containing p-xylene and o-xylene through silicalite-1 membrane was studied experimentally in the temperature range of 150–250 °C at feed partial pressure of 0.26 kPa for p-xylene and 0.22 kPa for o-xylene. The model for single component flux based on the combination of dual-site Langmuir isotherm and Maxwell–Stefan formulation was derived. The adsorption parameters were estimated by minimizing the difference between the experimental flux and simulated flux. The heat of adsorption and entropy values obtained were in good agreement with the reported values. The effect of feed partial pressure in the range of 0.20–1.50 kPa on xylene flux was predicted using the adsorption parameters and compared with the experimental values. The Maxwell–Stefan diffusion model, in combination with the ideal adsorbed solution (IAS) theory and single-component adsorption parameters was used to predict the permeation flux of p-xylene and o-xylene for binary xylene mixture through the silicalite-1 membrane. The simulated results were in good agreement with the experimental data. The simulated adsorption isotherm in higher temperature range of 150–250 °C using the model and derived adsorption parameters could provide useful information for adsorption of xylene molecules on silicalite-1 membrane at a higher operating temperature.     

The prediction of adsorption equiliria for oxygen and nitrogen gas mixtures on 5a molecular sieves by ideal adsorbed solution theory(IAST)

Equilibria data for the adsorption of oxygen nitrogen and their binary mixtures were determined on 5A molecular sieve beads The single species isotherm data were approximated bv the Freundlich type isotherm in a piecewise manner. The binary equilibria were presented at the pressure of 1.5 atm abs and the three temperatures: 273, 283 and 293 K. The binary data were examined for values predicted by the ideal adsorbed solution theory using the piecewise Freundlich isotherms obtained from the single species isotherm data. Predicted equilibria data showed a good agreement with experimental values.     

Application of the general rate model with the Maxwell-Stefan equations for the prediction of the band profiles of the 1-indanol enantiomers

The adsorption isotherm data of R- and S-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. These experimental data were fitted to the single-component and the modified competitive Bilangmuir isotherms. The overloaded elution profiles of bands of the pure enantiomers and of the racemic mixture were calculated for different sample sizes, using the best competitive isotherm model and the General Rate Model of chromatography coupled with the generalized Maxwell-Stefan equation that describes the surface diffusion flux. The calculated and the experimental profiles were found to be in excellent agreement in all cases. The parameters of the model of the mass transfer kinetics were derived from the band profiles obtained for the pure enantiomers. The same values of these parameters give an excellent prediction of the profiles of multicomponent bands. The new model described here allows a satisfactory interpretation of the competitive mass transfer kinetics.     

Characterization of Ag(I), Co(II) and Cu(II) removal process from aqueous solutions using dolomite powder

Dolomite, a natural adsorbent, was used for removal of Ag(I), Cu(II) and Co(II) from aqueous solutions. Adsorption parameters including pH, temperature and contact time have been investigated to obtain adsorption mechanism. The results of experiments showed that adsorption of the metal ions increased by increasing pH values up to 5.5. The adsorption process was initially fast. Equilibrium isotherm data were analyzed using Langmuir, Freundlich and Dubinin-Radushkevich isotherm models. Maximum adsorption capacity of Ag(I), Cu(II) and Co(II) was 1.34, 1.63 and 2.84 mg/g at 20 oC, respectively. Kinetic models including Lagergren first-order and pseudo-second-order were used to test kinetic data. The results showed that pseudo-second-order has good agreement with experimental data. Thermodynamic parameters of the process were also investigated at different temperatures. The negative values of Gibbs free energy and enthalpy changes for Ag(I), Cu(II) and Co(II) indicated the spontaneous and exothermic nature of the adsorption process.     

A Modified Peng-Robinson Equation State for Prediction of Gas Adsorption Isotherm

This research proposes a modified two-dimensional Peng-Robinson equation model to predict adsorp-tion isotherm in adsorbate-adsorbent systems. The parameters of the proposed model are calculated by using the op-timization of experimental data for the different single gas adsorption systems at various temperatures. The experi-mental adsorption equilibrium data of adsorbate-adsorbent systems was compared with the calculated results in our proposed model and the two-dimensional Hill-deBoer equation model. The proposed model as indicated in the re-sults shows a better prediction of the experimental results compared with two others.     

Single and competitive isotherms of phenol ando-cresol by pulsed-input method

There is a considerable industrial interest in both the scale-up and optimization of chromatographic operations used in the purification of fine chemicals and biomolecules. One of the major factors affecting the adsorption operation is the adsorption isotherm. Reversed-phase high-performance liquid chromatography (RP-HPLC) was used to measure the adsorption isotherm of phenol ando-cresol. From the experimental results, the retention times were decreased with increasing sample sizes, and the front of the peak was very stiff, so Langmuir adsorption isotherm was applied. Also Early-eluting component, phenol, in a mixture of the two components elutes faster than that in a pure component. Pulsed-injection method (PIM) was used to determine the two parameters of the Langmuir isotherm. The resulting parameters, a and b, were used to calculate the elution profiles of phenol ando-cresol in pure and mixed state. The agreement between the experimental data and calculated elution profiles was fairly good in a mixture as well as a pure component.     

Batch Removal of Crystal Violet from Aqueous Solution by H2SO4 Modified Sugarcane Bagasse: Equilibrium,Kinetic, and Thermodynamic Profile

Batch adsorption studies were carried out using H₂SO₄ modified sugarcane bagasse (HMSB) for the removal of hazardous Crystal Violet (CV) dye from aqueous solutions. The effects of initial solution pH, adsorbent dose, and temperature on the adsorption process were investigated. The Langmuir isotherm model well described the equilibrium dye uptake while the pseudo-second-order kinetic model showed good agreement with the experimental kinetic data. Gibb's free energy change (ΔG⁰) was spontaneous for all interactions, and the adsorption process exhibited endothermic enthalpy values. Results suggest that HMSB is an effective adsorbent for the removal of CV from wastewater.     

表面活性剂在液固界面吸附的热力学

对已有的表面活性剂液固界面吸附等温线进行了系统的分类,并提出了非均匀表面两阶段吸附模型．用此模型导出的吸附等温方程式能很好地描述各种类型的吸附等温线.     

逆向法确定色氨酸对映体竞争型吸附等温线

引言 吸附等温线测定是研究色谱分离过程的关键,其准确性直接影响到色谱分离过程的准确程度,因此,选择适当的实验方法和数学模型来模拟吸附等温线是模拟色谱分离过程的一个重要环节.常用的几种方法包括:前沿分析法、特征点洗脱法、特征点前沿分析法以及扰动法[1-2].其中前沿分析法是最常用的方法,该方法简单,准确性高,可用于多组分竞争型吸附等温数据的测定,但其数据采集过程非常耗时,对原料的需求量大,且需要考察单组分吸附等温模型与吸附数据的拟合程度.     

Multicomponent adsorption isotherm modeling using thermodynamically inconsistent and consistent models

In this work, the multicomponent adsorption modeling of the experimental adsorption data of ternary system consisting of nitrobenzene (NI), phenol (PH) and aniline (AN) onto granulated activated carbon (GAC) was performed. The Redlich–Peterson and Freundlich isotherm models provided better fitting of the single component experimental data than the Langmuir isotherm model. The adsorption preference of GAC was found to be: NI > PH > AN. The ternary adsorption equilibrium data were analyzed by using thermodynamically consistent and inconsistent isotherm models as well as an artificial neural network model. Modified Redlich–Peterson and LeVan–Vermeulen models, and real adsorbed solution theory model provided satisfactory fit of the ternary system. Levenberg–Marquardt back-propagation or scaled conjugate gradient back-propagation algorithm with two neurons, either logsig or tansig transfer function in the hidden layer, and purelin transfer function in output layer were found to be the best network and gave an excellent prediction of experimental data.     

Equilibrium and Dynamic Adsorption of Bioethanol on Activated Carbon in the Liquid Phase

Equilibrium batch and dynamic column adsorption of bioethanol from the liquid phase on a commercial activated carbon was investigated. The effects of operational parameters, including flow rate, bed height, and initial solute concentration on the column breakthrough curve were studied. Axial dispersion was estimated by a tracer experimental breakthrough curve. Two mathematical models were developed to predict dynamic experimental results. The equilibrium results showed that the Toth isotherm could better predict the experimental adsorption data than the Langmuir model. The dynamic experimental results showed that increasing the flow rate decreases the column capacity. The macropore diffusion model and the linear driving force model were in good agreement with the experimental dynamic results.     

A mathematical model for multicomponent adsorption,desorption and displacement kinetics of ethane,propane and n-butane on activated carbon

A mathematical model allowing for macropore, surface and micropore diffusions is used to predict the multicomponent adsorption, desorption and displacement kinetics of gases on activated carbon using only information of single-component mass transfer and equilibrium. This model assumes the chemical potential gradient as the driving force for diffusion so that the concentration dependency of the surface diffusivity can be accounted for. The adsorbed species diffuse in both particle and microparticle (grain) coordinates. The local diffusion flux of the adsorbed species inside the microparticle is computed with the aid of the concept of an imaginary gas-phase concentration. The multicomponent adsorption equilibrium is calculated using the ideal adsorbed solution theory (IAST) and a single-component isotherm equation. To validate the model, experiments on equilibria as well as dynamics are carried out. Single-component adsorption equilibrium data are obtained by using a volumetric measurement rig. The dynamic responses of single and binary systems are collected via a differential adsorption bed, with ethane, propane and n-butane as adsorbates. The model predictions are found to be in good agreement with the experimental results and the role of concentration dependency of the diffusion of the adsorbed species is significant.     

Isotherms and thermodynamics studies for binary adsorption of methane and ethane on 4A molecular sieve zeolite

The temperature dependency of adsorption behavior for binary mixture of methane and ethane on 4A zeolite was investigated. The volumetric method has been adopted for determination of adsorption isotherm data in the temperature range 303–323 K and pressure up to 225 kPa. Extended Langmuir, modified extended Langmuir, and extended Freundlich isotherms were applied for prediction of binary adsorption data using pure component adsorption data. The data were also simulated by IAST model which showed the best correlation of experimental binary adsorption data along with extended Freundlich isotherm. The selectivity of 4A zeolite to adsorb gases was also studied. The result of this study showed that an increases in temperature increases selectivity for ethane to methane. The heats of adsorption for methane and ethane were also determined and found to be ?23.89 and ?36.78 kJ/mol, respectively, which indicate the exothermic and physisorption natures of adsorption.     

The adsorption of methane-ethane mixtures on activated carbon

The single component adsorption of methane and ethane and also the adsorption of binary mixtures of methane and ethane have been studied in a small fixed isothermal bed containing activated carbon. Results indicate that an empirical Langmuir isotherm fits the experimental data for single components. An extended form of the empirical Langmuir isotherm, in which the parameters are obtained from single component data, satisfactorily describes the adsorption of binary mixtures. The potential theory of Polanyi is also helpful in extending the experimental data. Breakthrough curves of both components from a diluted feed of methane and ethane could be predicted with good precision for the two activated carbons studied. Furthermore, the concentration waves of the components were sufficiently spaced to suggest that these carbons may be of use as a separating agent for methane-ethane mixtures.     

吸附热预测吸附等温线

实验测定了N2 在沸石分子筛、C2 H6 在活性炭、CO2 在硅胶上的吸附等温线 ,研究用Clausius Clapeyron方程求得等量吸附热、再利用所得的吸附热预测其它温度的吸附等温线数据的方法。将吸附热预测的等温线与实验值及插值法内插得到的吸附等温线数据进行了比较 ,结果表明吸附热预测值与实验值吻合较好。此外还对文献数据利用等量吸附热预测较高压力 ( 65 0kPa)下的等温线 ,均与文献中的实验值一致。为吸附工业操作需要不同温度下的等温线数据和吸附过程的模拟与设计提供了简便、准确的计算方法     

3,4-Dimethoxybenzaldehydethiosemicarbazone as corrosion inhibitor for aged 18 Ni 250 grade maraging steel in 0.5 M sulfuric acid

The corrosion inhibition of the aged 18 Ni 250 grade maraging steel in 0.5 M sulfuric acid by 3,4-dimethoxybenzaldehydethiosemicarbazone(DMBTSC) has been investigated by potentiodynamic polarization and electrochemical impedance spectroscopy(EIS) techniques. The inhibition efficiency increased with the increase in inhibitor concentration and decreased with the increase in temperature. Polarization curves indicated mixed type inhibition behavior affecting both cathodic and anodic corrosion currents. The thermodynamic parameters of corrosion and adsorption processes were evaluated. The adsorption of DMBTSC on the aged maraging steel surface was found to obey the Langmuir adsorption isotherm model, and the calculated Gibb’s free energy values confirm the spontaneous adsorption. The results obtained by the two techniques were in good agreement.     

逆向法测定酮洛芬对映体在Chiralpak AD柱上的吸附等温线

模拟移动床（SMB）色谱分离与纯化的操作过程复杂,对其进行设计与优化需要使用数值模拟方法,准确测定竞争型吸附等温线具有重要意义。采用逆向法确定了25℃下酮洛芬对映体在直链淀粉手性固定相（Chiralpak AD）上的竞争吸附等温线,先用高效液相色谱测得酮洛芬对映体在Chiralpak AD 柱上的过载流出曲线,再通过拟合实验测得的流出曲线确定吸附等温线模型及其参数。研究中采用平衡扩散模型描述酮洛芬对映体在色谱柱上流出的瞬态过程。参数拟合过程中,首先用非支配基因算法（NSGA-Ⅱ）在较广的参数空间内搜索吸附等温线模型参数,再以所得结果作为初值,使用Levenberg-Marquardt 算法（LMA）对参数进一步优化。比较了4种不同竞争吸附等温线模型对实验测得的流出曲线的拟合结果,其中五参数的Bi-Langmuir 模型拟合程度最好。测量了不同进料浓度和进料量条件下的流出曲线,并通过与模型预测结果的对照验证了所确定吸附等温线模型和参数。