Study of the competitive isotherm model and the mass transfer kinetics for a BET binary system

The competitive adsorption behavior of the binary mixture of phenetole (ethoxy-benzene) and propyl benzoate in a reversed-phase system was investigated. The adsorption equilibrium data of the single-component systems were acquired by frontal analysis. The same data for binary mixtures were acquired by the perturbation method. For both compounds, the single-component isotherm data fit best to the multilayer BET model. The experimental overloaded band profiles are in excellent agreement with the profiles calculated with either the general rate model or the modified transport-dispersive models. The competitive adsorption data were modeled using the ideal adsorbed solution (IAS) theory. The numerical values of the coefficients were derived by fitting the retention times of the perturbation pulses to those calculated using the IAS theory compiled with the coherence conditions. Finally, the elution profiles of binary mixtures were recorded. They compared very well with those calculated. As a characteristic feature of this case, an unusual retainment effect of the chromatographic band of the more retained component by the less retained one was observed. The combination of the General Rate Model and the adsorption isotherm model allowed an accurate prediction of the band profiles.     

Equilibrium theory based design of simulated moving bed processes for a generalized Langmuir isotherm

In the frame of the local equilibrium theory of chromatography, design criteria for complete separation of binary mixtures in simulated moving bed (SMB) separations are developed, presented and discussed. These apply to systems, whose retention behavior is characterized by a generalized Langmuir isotherm. By allowing for negative terms in the denominator of the classical Langmuir isotherm, this newly introduced adsorption model captures a broad class of competitive or synergistic adsorption, including anti-Langmuir behavior for both adsorbates, and mixed cases where one species behaves in a Lagmuirian and the other in an anti-Langmuirian manner. By extending classical equilibrium theory results for the binary Langmuir isotherm, and by generalizing the approach followed earlier to derive SMB design criteria for the binary and multi-component Langmuir isotherm, exact algebraic equations for the boundary of the complete separation region in the operating parameter space are derived for all possible generalized Langmuir isotherm. The effect of changing feed composition on the shape of the complete separation region and on the position of the optimal operating point is analyzed and discussed.     

A thermodynamically consistent explicit competitive adsorption isotherm model based on second-order single component behaviour

A competitive adsorption isotherm model is derived for binary mixtures of components characterized by single component isotherms which are second-order truncations of higher order equilibrium models suggested by multi-layer theory and statistical thermodynamics. The competitive isotherms are determined using the ideal adsorbed solution (IAS) theory which, in case of complex single component isotherms, does not generate explicit expressions to calculated equilibrium loadings and causes time consuming iterations in simulations of adsorption processes. The explicit model derived in this work is based on an analysis of the roots of a cubic polynomial resulting from the set of IAS equations. The suggested thermodynamically consistent and widely applicable competitive isotherm model can be recommended as a flexible tool for efficient simulations of fixed-bed adsorber dynamics.     

New thermodynamically consistent competitive adsorption isotherm in RPLC

A new equation of competitive isotherms was derived in the framework of the ideal adsorbed solution (IAS) that predicts multisolute adsorption isotherms from single-solute isotherms. The IAS theory makes this new isotherm thermodynamically consistent, whatever the saturation capacities of these single-component isotherms. On a Kromasil-C(18) column, with methanol-water (80/20 v/v) as the mobile phase, the best single-solute adsorption isotherm of both toluene and ethylbenzene is the liquid-solid extended multilayer BET isotherm. Despite a significant difference between the monolayer capacities of toluene (370 g/l) and ethylbenzene (170 g/l), the experimental adsorption data fit very well to single-component isotherms exhibiting the same capacities (200 g/l). The new competitive model was used for the modeling of the elution band profiles of mixtures of the two compounds. Excellent agreement between experimental and calculated profiles was observed, suggesting that the behavior of the toluene-ethylbenzene adsorbed phase on the stationary phase is close to ideal. For example, the concentrations measured for the intermediate plateau obtained in frontal analysis differ by less than 2% from those predicted by the IAS model.     

Band splitting in overloaded isocratic elution chromatography II. New competitive adsorption isotherms

The equations of two new binary competitive isotherms models are derived. The first of these models assumes that the isotherms of the two pure, single compounds have distinct monolayer capacities. Its derivation is based on kinetic arguments. The ideal adsorbed solution (IAS) framework was applied to derive the second model that is a thermodynamically consistent competitive isotherm. This second model predicts the competitive adsorption isotherm behavior of a mixture of two compounds that have single-component adsorption behavior following a BET and/or a Langmuir isotherms. Both models apply well to the binary adsorption of ethylbenzoate and 4-tert.-butylphenol on a Kromasil-C18 column (with methanol-water, 62:38, v/v, as the mobile phase). The best single-solute adsorption isotherms of these two compounds are the liquid-solid extended multilayer BET and the Langmuir isotherms, respectively. The kinetic and thermodynamic new competitive models were compared, regarding the accuracy of their prediction of the elution band profiles of mixtures of these two compounds. A better agreement between experimental and calculated profiles was observed with the kinetic model. The IAS model failed because the behavior of the ethylbenzoate/4-tert.-butylphenol adsorbed phase mixture is probably non-ideal. The most striking result is the qualitative prediction by these models of the peak splitting of 4-tert.-butylphenol during its elution in presence of ethylbenzoate.     

Solvent gradient operation of simulated moving beds. 2. Langmuir isotherms

Simulated Moving Bed separations of enantiomers or fine chemicals are usually carried out in the isocratic mode, i.e. by applying the same operating conditions (temperature, pressure, mobile phase composition, pH) in the whole SMB unit. However, it has been recently recognized that by properly modulating operating conditions in the SMB sections. i.e. Sections 1-4 normally, separation performance in terms of productivity and solvent consumption can be significantly improved. In this work, we study solvent gradient SMB (SG-SMB) operation, where the concentration of a modifier in the main solvent constituting the mobile phase is adjusted along the SMB unit, so as to have weaker retention of the species to be separated in the first two sections, and stronger retention in Sections 3 and 4. Overload chromatographic conditions are considered, where the adsorption behavior is characterized by a nonlinear competitive adsorption isotherm, e.g. a binary Langmuir isotherm. Design criteria to achieve complete separation are developed in the frame of the equilibrium theory of chromatography. The theoretical findings are discussed in view of typical effects of the modifier concentration on retention times and solubility of the species to be separated, and an overall assessment of the SG-SMB technology is attempted.     

High-performance liquid chromatography of substituted p-benzoquinones and p-hydroquinones. II. Retention behavior, quantitative structure-retention relationships and octanol-water partition coefficients

The retention behavior of methoxy-substituted p-benzoquinones and the corresponding hydroquinones in reversed-phase chromatography was examined on octylsilica and two octadecylsilica stationary phases and with five hydroorganic mobile phases containing acetonitrile, methanol or tetrahydrofuran and additionally in most cases (NH3OH)3PO4 used as a reducing and buffering agent. The retention order of benzoquinones and hydroquinones was the same on each stationary phase with either methanol or acetonitrile as the organic modifier. On the other hand, minor differences in the retention order were observed with the various stationary phases. In all cases, satisfactory quantitative structure-retention relationships (QSRRs) were found and the data suggest that the differences in the retention behaviour of octadecylsilicas used in this study are silanophilic interactions which, together with solvophobic interaction contribute to the retention of these eluites. Further analysis showed that QSRRs of sterically crowded molecules must take into account reduced surface area available for binding. The retention data obtained with use of aqueous tetrahydrofuran as mobile phase failed to give rise to satisfactory QSRRs. This was attributed to selective solvation of eluite by tetrahydrofuran and/or nearly equipotent binding of eluite and tetrahydrofuran to stationary phase.     

Retention of ionizable compounds in high-performance liquid chromatography. 14. Acid-base pK values in acetonitrile-water mobile phases

Using competitive frontal analysis, the binary adsorption isotherms of the enantiomers of 1-phenyl-l-propanol were measured on a microbore column packed with a chiral stationary phase based on cellulose tribenzoate. These measurements were carried out using only the racemic mixture. The experimental data were fitted to four different isotherm models: Langmuir, BiLangmuir, Langmuir-Freundlich and Tóth. The BiLangmuir and the Langmuir-Freundlich models accounted best for the competitive adsorption data. An excellent agreement between the experimental and the calculated overloaded band profiles for various samples of racemic mixture was obtained when the equilibrium dispersive model of chromatography was used together with the BiLangmuir competitive isotherm. The isotherm parameters measured under competitive conditions were used to calculate the overloaded band profiles of large samples of the pure S- and R-enantiomers, too. A satisfactory agreement between the experimental and calculated band profiles was observed when using in the computation the corresponding single component BiLangmuir isotherm derived from the binary isotherm previously determined. Thus oniy data derived from the racemic mixture are required for computer optimization of the preparative chromatography separation of the enantiomers.     

Sense and nonsense of high-temperature liquid chromatography

High-temperature liquid chromatography (HTLC) is recognized today as a valuable technique in reversed-phase high-performance liquid chromatography (RP-HPLC). Column temperature can play a role in reducing analysis time, modifying retention, controlling selectivity, changing efficiency or improving detection sensitivity. The different effects of high temperatures on reversed-phase separations, the practical limitations due to the instrumentation, the limits and the main advantages of HTLC, especially for the separation of polar and ionized compounds, are reviewed.     

Retention equilibrium and mass transfer characteristics in reversed-phase liquid chromatography using methanol-water mixtures

Pulse response experiments (i.e., elution chromatography) were made in reversed-phase liquid chromatography (RPLC) using a C18 silica gel column and methanol-water mixtures of different compositions (phi). The moment analysis of the elution peak profiles measured in the RPLC system provided some items of information about four parameters characterizing the retention equilibrium and the mass transfer kinetics in the column, i.e., adsorption equilibrium constant, isosteric heat of adsorption, surface diffusion coefficient and activation energy of surface diffusion. Characteristics of the chromatographic behavior were studied by analyzing the dependence of the four parameters on phi and the correlation between them. It was found that surface diffusion was one of the important processes of molecular migration having a significant contribution to the mass transfer kinetics in the column. Both the adsorption equilibrium constant and the surface diffusion coefficient varied depending on phi. The direction of their changes was approximately opposite, suggesting that the mass transfer in the manner of surface diffusion was restricted owing to the retention of the sample molecules on the stationary phase.     

Influence of preferential adsorption of mobile phase on retention behavior of amino acids on the teicoplanin chiral selector

The adsorption behavior of two amino acids, i.e., l,d-threonine and l,d-methionine has been investigated on the chiral stationary phase (CSP)column packed with teicoplanin bonded to a silica support. The study has been performed under non-linear conditions of adsorption isotherm for various types of organic modifiers (methanol, ethanol, propan-2-ol and acetonitrile) in the reversed-phase mode. A heterogeneous adsorption mechanism of amino acids has been identified that was strongly affected by the nature of organic modifier. Generally, isotherm non-linearity and retention decreased with decrease of the modifier content in the mobile phase exhibiting a minimum at water-rich mobile phases. These trends were suggested to result from a combined effect of the mobile as well as the adsorbed phase composition. To determine the composition of the adsorbed phase the excess adsorption of modifiers in aqueous solutions has been measured and their binary adsorption equilibria have been quantified and compared. Strongly non-ideal behavior of solvents in the mobile phase and the adsorbed phase has been accounted for by activity coefficients. The fraction of the modifiers in the adsorbed phase decreased in the sequence: methanol, ethanol, propan-2-ol and acetonitrile.     

苯酚与对氯酚竞争吸附数学模型研究

对氯苯酚;苯酚与对氯酚竞争吸附数学模型研究     

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。     

High-performance liquid chromatography of biotin and analogues

Biotin, analogues, and chemical intermediates were separated by high-performance liquid chromatography (HPLC) using reversed-phase and anion-exchange chromatographic conditions. Reversed-phase separations provided a wide range of retention times and resolution of nearly all the biotin compounds from mixtures of the analogues. Anion-exchange separations gave generally shorter retention times as compared to reversed-phase separations and greater resolution between biotin l- and d-sulfoxide. However, fewer analogues were resolved from mixtures of the compounds with anion-exchange HPLC.     

Synergistic effects in competitive adsorption of carbohydrates on an ion-exchange resin

Adsorption of the three carbohydrates sucrose, glucose and fructose from aqueous solutions was investigated on an ion-exchange resin. The adsorption equilibrium of single components, binary and ternary mixtures was quantified by frontal analysis and the adsorption-desorption method. The experiments covered a concentration range up to 600 g/L at 60 degrees C and 80 degrees C. Within this range the adsorption isotherms of carbohydrates exhibited anti-Langmuirian behavior. Data of mixture adsorption revealed reversed competitive (synergistic or cooperative) effects, i.e., an increase of the concentration of one component of the mixture enhanced the adsorption of others. To model such an adsorption behavior the anti-Langmuir model has been used. The isotherm parameters determined for single components were used to simulate the competitive adsorption equilibria through the IAS (ideal adsorbed solution) theory. Finally, dynamic concentration profiles of multicomponent mixtures have been recorded. The shapes of adsorption and desorption curves confirmed the observed competitive effects found in the equilibrium studies. The breakthrough curves measured were simulated using the equilibrium theory as well as a numerical solution of the equilibrium dispersive model.     

Adsorption/partition model of liquid chromatography for chemically bonded stationary phases of the aliphatic cyano, reversed-phase C8 and reversed-phase C18 types

A novel approach was introduced to modeling solute retention in the liquid chromatography systems, employing silica-based aliphatic chemically bonded stationary phases of the cyano, reversed-phase C8 and reversed-phase C18 types, and the mixed binary eluents most frequently used in the reversed-phase and normal-phase chromatography modes (i.e. using the methanol-water and the 2-propanol-n-hexane liquid mixtures, respectively). This approach takes notice of the mixed (adsorption/partition) mechanism of solute retention, in which both, the adsorptive and the dispersive forces contribute to the overall energetics of this process. Performance of our new model was compared with that of the widely recognized and on a routine basis applied Schoenmakers approach, and it was found out that both models perform with a practically equal and outstanding accuracy.     

A binary-like approach for the computer assisted method development of isocratic and programmed ternary solvent elutions in reversed-phase liquid chromatography

A specific tool to enable exploration of multisolvent isocratic and programmed elutions for the computer assisted method development of reversed-phase liquid chromatography separations is described. The tool is purposely identical to those used in the optimization of binary solvent systems, which are by far the most commonly used by chromatographers. Existing data from failed binary solvent optimization processes are reused to explore ternary solvent systems with a few additional isocratic and programmed runs. This allows the development of efficient retention models for ternary systems, although the work of the chromatographer remains identical to that for optimization of binary systems. The retention models are used to develop an unattended optimization process and finally, the chromatographer selects the most satisfactory solution for testing and implementing in routine analysis. The process is exemplified with a mixture of 12 compounds that cannot be separated satisfactorily in aqueous binary solvent systems with methanol and acetonitrile as modifiers.     

The significance of a second adsorption phase with weakly adsorbed species for the calculation of the surface concentrations of a mixture: methanol–DME and methanol–ethene adsorption in SAPO-34

With the calorimetric (adsorption heat versus coverage) curve also measured together with the adsorption isotherm, the simultaneous use of both curves showed that there were two phases of adsorption in the adsorption of methanol, dimethyl ether, ethene and propane in SAPO-34. The dual-site Langmuir equation gave good fits to the adsorption data to support the interpretation that a second (type 2) adsorption phase occurred in the high-pressure region in addition to a first (type 1) adsorption phase on the acid sites at lower pressures. Adsorption experiments and calculations using binary gas mixtures showed that due to the existence of two types of adsorption, the multicomponent Langmuir isotherm equation (Langmuir competitive adsorption model) calculated incorrect surface concentrations when the concentrations were high. In contrast, the ideal adsorbed solution theory (IAST) calculated correct surface concentrations in the adsorption of mixtures.     

Molecular Theory of Liquid Adsorption Chromatography

Abstract

A statistical-mechanical theory, based on a lattice model, has been developed to address the molecular mechanism of retention and selectivity in both normal-phase and reversedphase liquid adsorption chromatography. The model is a natural “competitive-equilibrium” one, where possible contributions from solvent-solvent and solute-solvent interactions, and, hence, from solution nonideality, are not neglected. Homogeneous and heterogeneous adsorbent surfaces, single-solvent and binary mixed-solvent mobile phases, and solute molecules of different size and shape are treated. Practical applications of the theory are presented to demonstrate its utility and significance.

For homogeneous adsorbents and neat solvents, the molecular energetics of retention and selectivity are examined, with special emphasis on the effects of solute size and shape, and, relatedly, the modes of solute adsorption. Separations of geometrical isomers and homologous series in real and simulated chromatographic processes are investigated, confirming predictions of the theory and the important role of solvent-solvent and solute-solvent interactions in reversed-phase systems. The implications of a more general retention equation for microscopically heterogeneous adsorbents are discussed. The dependence of capacity ratio on mobile-phase composition for binary solvents is analyzed in some detail. An often important contribution arising from solution nonideality is predicted theoretically. This is shown to be consistent with experimental results on normal-phase and reversed-phase systems.