Transport of Carbamazepine,Ciprofloxacin and Sulfamethoxazole in Activated Carbon: Solubility and Relationships between Structure and Diffusional Parameters

The transport of carbamazepine, ciprofloxacin and sulfamethoxazole in the different pores of activated carbon in an aqueous solution is a dynamic process that is entirely dependent on the intrinsic parameters of these molecules and of the adsorbent. The macroscopic processes that take place are analyzed by interfacial diffusion and reaction models. Modeling of the experimental kinetic curves obtained following batch treatment of each solute at 2 µg/L in tap water showed (i) that the transport and sorption rates were controlled by external diffusion and intraparticle diffusion and (ii) that the effective diffusion coefficient for each solute, with the surface and pore diffusion coefficients, were linked by a linear relationship. A statistical analysis of the experimental data established correlations between the diffusional parameters and some geometrical parameters of these three molecules. Given the major discontinuities observed in the adsorption kinetics, the modeling of the experimental data required the use of traditional kinetic models, as well as a new kinetic model composed of the pseudo first or second order model and a sigmoidal expression. The predictions of this model were excellent. The solubility of each molecule below 60 °C was formulated by an empirical expression.     

Estimation of adsorption isotherm parameters with inverse method--possible problems

In recent years the inverse method (IM) has been frequently applied to estimate of isotherm parameters. The IM has been used for adsorption process modeling for one, two and even three component chromatography. This method requires only a few injections with various sample concentrations, so the solute consumption and time requirements are very modest. The successful estimation of isotherm parameters with IM depends on applied chromatography column model and a numerical method used to solve the model. For HPLC column the classical equilibrium-dispersive (ED) model can be used. This model is solved frequently with very fast Rouchon finite difference method. However, the accuracy of computations with Rouchon method is decreasing with increase of the number of analyzed components. The aim of this work is the comparison of the results obtained with inverse method when ED model was solved with Rouchon or orthogonal collocation on finite element (OCFE) scheme. Assuming that solution of ED model with OCFE method can be regarded as real a solution, it was found that the Rouchon scheme may not give satisfactory results even for column with 10,000 theoretical plates for three component chromatography. Moreover, the optimal conditions for separation, calculated with Rouchon method, can be remarkably different from that obtained with the OCFE method. The next aim of this work is the presentation of Craig method application to estimation of model parameters with IM.     

Adsorption of cyanuric acid on activated carbon from aqueous solution: effect of carbon surface modification and thermodynamic characteristics

The performance of a conventional and two surface-modified activated carbon samples was investigated for the sorption of cyanuric acid from aqueous solution by varying the process parameters such as initial concentration, pH, temperature, dose of adsorbents, and agitation time. The modified carbon samples obtained by acid and ammonia treatment of the conventional sample had a higher BET surface area (989 and 1010 m2 g-1, respectively) and higher specific mesopore surface area (27.36 and 33.21 m2 g-1, respectively) compared to the untreated material (820 and 18.25 m2 g-1). The solute removal was found to be favored at lower solute concentration, increased agitation time, increased adsorbent dose, and lower temperature. The modified adsorbents outperformed the conventional activated carbon for sorption of cyanuric acid especially at higher pH (>7.5) and with increasing temperature. The Freundlich model appears to fit the isotherm data better than the Langmuir model. The thermodynamic parameters (DeltaG degrees ads, DeltaH degrees, and DeltaS degrees) were evaluated showing that the sorption process was thermodynamically favorable, spontaneous, and exothermic. The findings can be used for predictive modeling for analysis and design adsorption systems for removal of cyanuric acid and other polar atrazine degradation products from environmental aqueous samples.     

Kinetics of adsorption and desorption of Pb(II) in aqueous solution on activated carbon by two-site adsorption model

The adsorption and desorption equilibrium and kinetics of lead ions from aqueous solutions on a granular activated carbon (GAC) were examined. Rapid increase followed by slow increase in Pb(II) amount on the GAC was observed as a function of time for the adsorption, while rapid decrease and consecutive very slow decrease was observed in desorption. Based on the experimental results, a two-site adsorption model was proposed for the adsorption and the desorption of Pb(II) under the study conditions. The Pb(II) adsorption on the GAC was estimated to have simultaneously occurred on the strong and the weak adsorption sites. Conventional Langmuir-type kinetic equations were introduced to quantitatively predict the adsorption and desorption with the two-site model by optimizing the parameters to fit the equilibrium and the kinetic experimental results. The equilibrium and kinetic experimental results could be represented by the equations by using one set of the common Langmuir parameters. Resultant kinetic parameters revealed that the adsorption equilibrium constant was two orders of magnitude greater for strong adsorption site than for weak adsorption site, though the maximum number of weak adsorption site was 1.5 times as great as that of strong adsorption site. The strong adsorption equilibrium constant resulted from a small desorption rate constant for the site. The equations were demonstrated to be applicable for predicting other desorption performances as well.     

Characterization and modeling of nonlinear hydrophobic interaction chromatographic systems

A general rate model was employed in concert with a preferential interaction quadratic adsorption isotherm for the characterization of HIC resins and the prediction of solute behavior in these separation systems. The results indicate that both pore and surface diffusion play an important role in protein transport in HIC resins. The simulated and experimental solute profiles were compared for two model proteins, lysozyme and lectin, for both displacement and gradient modes of chromatography. Our results indicate that a modeling approach using the generate rate model and preferential interaction isotherm can accurately predict the shock layer response in both gradient and displacement chromatography in HIC systems. While pore and surface diffusion played a major role and were limiting steps for proteins, surface diffusion was seen to play less of a role for the displacer. The results demonstrate that this modeling approach can be employed to describe the behavior of these non-linear HIC systems, which may have implications for the development of more efficient preparative HIC separations.     

Adsorption kinetics at the solid/solution interface: statistical rate theory at initial times of adsorption and close to equilibrium

The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system.     

毛细管气液色谱保留过程的研究

以ＰＥＧ２０Ｍ为代表研究了石英毛细管柱气液色谱保留过程,提出了利用毛细管柱测定分配和吸附常数的公式,并测定了９个温度下的分配和吸附常数。计算了８０℃和１２０℃下４支不同液膜厚度柱上吸附对保留的贡献。结果表明,在薄液膜的柱子上界面吸附对保留具有重要贡献;温度升高可以降低弱极性化合物（如正构烷烃和饱和醚）吸附对保留的贡献,但对其它化合物影响不明显。验证了正构烷烃、２－酮系列和正构伯醇的吸附常数的碳数规律。     

Machine learning method for simulation of adsorption separation: Comparisons of model’s performance in predicting equilibrium concentrations

In this work, we implemented different models for predicting adsorption separation of a dye from aqueous solution using porous materials. The equilibrium data of solute concentrations were collected from resources and used in the models for training and verification purposes to develop the models. For prediction of the equilibrium solute concentrations (Ce), we used tree models: Multi-layer Perceptron (MLP), Passive aggressive regression, and Decision Tree (DT) Regressor. In the modeling, we considered the adsorbent dosage as well as solution pH as the input parameters to the model, and the model was able to generate the output values, i.e., equilibrium concentrations based on the input variables. The evaluation of the models’ performances revelated that the final R² scores are 0.99, 0.98, 0.93 for DT, MLP and Passive-Aggressive, respectively and a very low RMSE of 0.055 for decision tree that shows this model is the best among models used in this study. Indeed, decision tree model is recommended among the other three models to be employed for correlation of adsorption equilibrium data.     

A Simple Frontal Analysis Equation to Determine the Adsorption Parameters of Solute Molecules on Different Adsorbents

A simple frontal analysis equation to determine the adsorption parameters of solute molecules on different adsorbents was presented. It gives the relationship between the average breakthrough time and the feed solute concentration, and by using its linear form, two important parameters, the thermodynamic equilibrium constant KSL for solute adsorption on the surface of adsorbent and the number nt of total adsorption sites distributed on the surface of adsorbent, can be simultaneously determined. The frontal analyses for some aromatic hydrocarbons on RP-C18 reversed-phase medium, and some protein molecules on RP-C18 reversed-phase, WCX-1 cation-exchange, PEG-400 hydrophobic and Chelating Sepharose Fast-flow separately chelated with Zn^2＋ or Cu^2＋ media, were separately carried out to test this equation and their adsorption parameters KSL and nt were separately obtained. The results show that all these frontal analysis data can be well described by this frontal analysis equation. For all of these frontal analysis systems, their parameters nt can separately approximately keep constant and they are independent of solute molecules used, while their parameters KSL are dependent upon both of the media packed in frontal analysis column and the solute molecules used.     

溶质在气相色谱中进样量和保留值关系的方程

考虑到气相中溶质分子和其它成分在固定相上的竞争吸附作用,提出了一个描述溶质在气相色谱中进样量和保留值的关系式.由此方程可以获得两个描述色谱体系特征的重要参数:溶质和其它成分在固定相表面竞争吸附的热力学平衡常数Ka和单位体积固定相所能吸附溶质的量NmS.当其它参数给定时,Ka的大小直接决定溶质进样量与保留值关系式的性质.通过试验对此方程进行了初步验证.     

A Mechanistic Approach to Modeling Single Protein Adsorption at Solid-Water Interfaces

A kinetic model for single component protein adsorption which can be readily extended to adsorption from multi-protein solutions was developed, and used to simulate adsorption of site-directed, structural stability mutants of bacteriophage T4 lysozyme. The model allows for two different adsorbed "states," distinguished by different binding strengths and different occupied areas. The presence of an increasing energy barrier to adsorption was incorporated into the model by formulating the adsorption rate constants as functions of time. Numerical analysis was performed using the Marquardt method. Estimated model parameters were consistent with the effect of structural stability on adsorption. In particular, kinetic parameters were such that adsorption into the more tightly bound, conformationally altered state was favored by less stable variants. Copyright 1999 Academic Press.     

Self-aggregation of cationic surfactants onto oxidized cellulose fibers and coadsorption of organic compounds

In this work, the adsorption of cationic surfactant and organic solutes on oxidized cellulose fibers bearing different amounts of carboxylic moieties was investigated. The increase in the amount of -COOH groups on cellulose fibers by TEMPO oxidation induced a general rise in surfactant adsorption. For all tested conditions, that is, cellulose oxidation level and surfactant alkyl chain length (C12 and C16), adsorption isotherms displayed a typical three-region shape with inversion of the substrate zeta-potential which was interpreted as reflecting surfactant adsorption and aggregation (admicelles and hemimicelles) on cellulose fibers. The addition of organic solutes in surfactant/cellulose systems induced a decrease in surfactant cac on the cellulose surface thus favoring surfactant aggregation and the formation of mixed surfactant/solute assemblies. Adsorption isotherms of organic solutes on cellulose in surfactant/cellulose/solute systems showed that solute adsorption is strictly correlated to (i) the surfactant concentration, solute adsorption increases up to the surfactant cmc, where solute partitioning between the cellulose surface and free micelles causes a drop in adsorption, and to (ii) solute solubility and functional groups. The specific shape of solutes adsorption isotherms at a fixed surfactant concentration was interpreted using a Frumkin adsorption isotherm, thus suggesting that solute uptake on cellulose fibers is a coadsorption and not a partitioning process. Results presented in this study were compared with those obtained in a previous work investigating solute adsorption in anionic surfactant/cationized cellulose systems to better understand the role of surfactant/solute interactions in the coadsorption process.     

Estimation of Adsorption Capacity for Dissociating and Non Dissociating Aromatic Compounds on Activated Carbon with Different Models

The process of adsorption of two dissociating and two non-dissociating aromatic compounds from dilute aqueous solutions on an untreated commercially available activated carbon (B.D.H.) was investigated systematically. All adsorption experiments were carried out in pH controlled aqueous solutions. The experimental isotherms were fitted into four different models (Langmuir homogenous Models, Langmuir binary Model, Langmuir-Freundlich single model and Langmuir-Freundlich double model). Variation of the model parameters with the solution pH was studied and used to gain further insight into the adsorption process. The relationship between the model parameters and the solution pH and pK_a was used to predict the adsorption capacity in molecular and ionic form of solutes in other solution.A relationship was sought to predict the effect of pH on the adsorption systems and for estimating the maximum adsorption capacity of carbon at any pH where the solute is ionized reasonably well.N₂ and CO₂ adsorption were used to characterize the carbon. X-ray Photoelectron Spectroscopy (XPS) measurement was used for surface elemental analysis of the activated carbon.     

Impact of carbon dioxide on the surface tension of 1-hexanol aqueous solutions

Effects of carbon dioxide presence on the surface tension and adsorption kinetics of 1-hexanol solutions were investigated. Experiments were performed at a range of carbon dioxide vapor pressures and varying concentrations of 1-hexanol aqueous solution. Both dynamic and steady-state surface tensions of 1-hexanol aqueous solution were found to decrease with carbon dioxide pressure, and a linear relationship was observed between the steady-state surface tension and carbon dioxide pressure. To explain the experiments, adsorption and desorption of the two species (1-hexanol and carbon dioxide) from two sides of the vapor-liquid interface were considered. A modified Langmuir isotherm, the modified Langmuir equation of state and the modified kinetic transfer equation were developed. The resulting steady-state and dynamic surface tension data were modeled using the modified Langmuir equation of state and the modified kinetic transfer equation, respectively. Equilibrium constants and adsorption rate constants of 1-hexanol and carbon dioxide were evaluated through a minimization procedure for CO₂ pressures ranging from 0 to 690 kPa. From the steady-state modeling, the equilibrium parameters for 1-hexanol and carbon dioxide adsorption from vapor phase and liquid phase were found unchanged at different pressures of carbon dioxide. From the dynamic modeling, the adsorption rate constants for 1-hexanol and carbon dioxide from vapor phase and liquid phase were found to decrease with carbon dioxide pressure. Some fluctuations in the fitting parameters of the dynamic modeling (adsorption rate constants) were observed. These fluctuations may be due to experimental errors, or more likely the limitations of the model used. A major limitation of the model is related to large differences in adsorption/desorption between initial and final stages of the process, and a single set of property parameters cannot describe both initial and final states of the system. Variations may occur depending on which set of data, of initial or final states, is used in the model predictions over the entire time range.     

Modelling the clarification of lactic acid fermentation broths by cross-flow microfiltration

This work is focused on modelling microfiltration for clarifying fermentation broths for the production of lactic acid. The hydraulic resistance-in-series model was used with membrane resistance, bacterial cell cake resistance, adsorption resistance and solute concentration polarisation resistance. Most of the model parameters were determined from independent experiments. This model was applied for microfiltrations operated either under constant transmembrane pressure or under constant permeate flux. Resistances due to adsorption and to solute concentration polarisation dominated. Bacterial cake resistance was found to be very low or equal to zero when microfiltration was below the critical flux.     

液-固吸附体系中扩展的Langmuir方程的推导和检验

从气-固吸附体系中推导出的Langmuir方程,近一世纪来只能经验性地描述液相吸附。本研究以液-固界面上的溶质计量置换模型为基础,考虑到液-固吸附体系中各组分之间的相互作用,从理论上推导出了在液-固体系中描述在不同溶剂浓度条件下的溶质吸附的扩展的Langmuir公式,并称其为扩展的Langmuir公式。将Langmuir公式中经验参数与液相色谱中的计量置换平衡中的参相关联,还将其扩展到在不同溶剂浓度条件下的溶质定量吸附的描述,为Langmuir方程在描述不同溶剂浓度条件下的组分吸附奠定了理论基础,扩大了Langmuir公式的应用。以不同溶剂浓度条件下所得到的吸附等温线数据对理论推导出的扩展的Langmuir公式进行了验证,并与计算置平衡中的参数相关联,表现用吸附等温线法计算的计量置换参数Z与用高效液相色谱法得到的Z值符合程度很好。     

A practical guide to the staggered herringbone mixer

An analytical model of mixing in the staggered herringbone mixer (SHM) was derived to estimate mixing parameters and provide practical expressions to guide mixer design and operation for a wide range of possible solutes and flow conditions. Mixing in microfluidic systems has historically been characterized by the mixing of a specific solute system or by the redistribution of flow streams; this approach does not give any insight into the ideal operational parameters of the mixer with an arbitrary real system. For Stokes-flow mixers, mixing can be computed from a relationship between solute diffusivity, flow rate, and mixer length. Confocal microscopy and computational fluid dynamics (CFD) modeling were used to directly determine the extent of mixing for several solutes in the staggered herringbone mixer over a range of Reynolds numbers (Re) and Péclet numbers (Pe); the results were used to develop and evaluate an analytical model of its behavior. Mixing was found to be a function of only Pe and downstream position in the mixer. Required mixer length was proportional to log(Pe); this analytical model matched well with the confocal data and CFD model for Pe<5 x 10(4), at which point the experiments reached the limit of resolution. For particular solutes, required length and mixing time depend upon Re and diffusivity. This analytical model is applicable to other solute systems, and possibly to other embodiments of the mixer, to enable optimal design, operation, and estimation of performance.     

Retention process in reversed phase TLC systems with polar bonded stationary phases

The retention of a solute in RP chromatography is a very complex process which depends on many factors. Therefore, the study of the influence of a mobile phase modifier concentration on the retention in different reversed phase chromatographic systems is very important for understanding the rules governing retention and mechanisms of substance separation in a chromatographic process. Composition changes and the nature of mobile phases enable tuning of the separated analytes' retention over a wide range of retention parameters and optimization of the chromatographic process as well. Optimization of the chromatographic process can be achieved by several different methods; one of them is the so-called interpretative strategy. The key approach adopted in this strategy is the implementation of adequate retention models that couple the retention of solute with the composition of a mixed mobile phase. The use of chemically bonded stationary phases composed of partially non-bonded silica matrix and organic ligands bonded to its surface in everyday chromatography practice leads to questions of the correct definition of the retention model and the dominant retention mechanism in such chromatographic systems. The retention model for an accurate prediction of retention factor as a function of modifier concentration and the heterogeneity of the adsorbent surface should be taken into consideration. In this work the influence of mobile-phase composition on the retention of sixteen model substances such as phenols, quinolines, and anilines used as test analytes in different RP-TLC systems with CN-, NH2-, and Diol-silica polar bonded stationary phases has been studied. The aim of this study is to compare the performance of three valuable retention models assumed as the partition, adsorption/partition, and adsorption mechanism of retention. All the models were verified for different RP-TLC systems by three statistical criteria. The results of investigations presented in this work demonstrate that the best agreement between the experimental and calculated Rf values was obtained by the use of new-generation retention models, which assume heterogeneity of adsorbent surface. The results reported here show that heterogeneity of the adsorbent surface may be important in analysis of the elution process in liquid chromatography. Consideration of the goodness of fit for the experimental data to the examined retention models is in conformity with the adsorption mechanism of retention on all polar bonded stationary phases in most eluent systems for most investigated compounds.     

液-固吸附体系中计量置换吸附模型的热力学研究

研究了液-固吸附体系中溶质计量置换吸附过程中的自由能变,推导出了新的表示溶质种类、溶质浓度和溶剂对Gibbs自由能变贡献的数学表达式,并阐明了该表达式中各种参数的物理意义.将用通常方法测定的自由能变分为与溶质吸附和溶剂解吸附有关的两个独立的自由能变,推导出了液-固吸附体系中溶质计量置换吸附模型的两个线性参数β_a和q/Z对绝对温度倒数的线性关系,又将吸附过程中溶质的焓变和熵变分成两个独立的分量.用文献中的实验数据,对本文推导出的公式进行了检验,理论结果与实验结果一致.     

A new model to describe the sorption of surfactants on solids in non-aqueous media

A new phenomenological model is developed to describe the sorption of surfactants on solids in non-aqueous media. This is based on the use of interaction parameters (delta) among solid, solute and solvent to assess the degree of the various interactions and computing an effective interaction parameter for the entire system represented by delta eff = abs{A|delta solid - delta solvent| + B|delta solute - delta solvent| - C|delta solid - delta solute|}. The effective interaction parameter determines the extent of adsorption that can occur in a given system. Interaction parameters typically account for dispersive interactions between the different components. This new model is used to describe the sorption behavior of a number of surfactant/solvent/solid systems.