Determination of competitive isotherms of enantiomers by a hybrid inverse method using overloaded band profiles and the periodic state of the simulated moving-bed process

A procedure for determination of adsorption isotherms in simulated moving-bed (SMB) chromatography is presented. The parameters of a prescribed adsorption isotherm model and rate constants are derived using a hybrid inverse method, which incorporates overloaded band profiles of the racemic mixture and breakthrough data from a single frontal experiment. The latter are included to reduce the uncertainty on the estimated saturation capacity, due to the dilution of the chromatograms with respect to the injected concentrations. The adsorption isotherm model is coupled with an axially dispersed flow model with finite mass-transfer rate to describe the experimental band profiles. The numerical constants of the isotherm model are tuned so that the calculated and measured band profiles match as much as possible. The accuracy of the isotherm model is then checked against the cyclic steady state (CSS) of the target SMB process, which is readily and cheaply obtained experimentally on a single-column set-up. This experiment is as expensive and time consuming as just a few breakthrough experiments. If necessary, the isotherm parameters are adjusted by applying the inverse method to the experimental CSS concentration profile. The method is successfully applied to determine the adsorption isotherms of Tr?gers base enantiomers on Chiralpak AD/methanol system. The results indicate that the proposed inverse method offers a reliable and quick approach to determine the competitive adsorption isotherms for a specific SMB separation.     

Experimental determination of single solute and competitive adsorption isotherms

In order to design and to optimise preparative liquid chromatography, the knowledge of the underlying thermodynamic functions, i.e. the adsorption isotherms, is of large importance. Usually these functions can not be predicted and various techniques have been suggested to determine them experimentally. In this paper, several important methods to measure adsorption equilibrium data are discussed and evaluated. The main focus is set on dynamic methods analysing concentration profiles that could be detected at the outlet of fixed-beds packed with the stationary phase of interest. The theoretical background of the different methods is explained using classical equilibrium theory and the equilibrium dispersion model. Each method is illustrated based on experimental data collected in our laboratory. Based on these personal experiences recommendations are given regarding the potential and the applicability of the methods discussed.     

Quantification of single solute and competitive adsorption isotherms using a closed-loop perturbation method

A modification of the classical method of perturbation chromatography for measuring isotherms of the adsorption of dissolved components is suggested. The general principle of the method consists in analyzing responses of the chromatographic system to small perturbations at different equilibrium concentrations. Essential advantages of the method are: (a) only retention times or volumes have to be measured and no detector calibration is required and (b) experiments with mixtures can be performed and analyzed efficiently. The modification suggested in this paper is the application of a closed-loop arrangement allowing the efficient exploitation of the sample. Experimental data for four different chromatographic systems are presented to illustrate the method. With the determined adsorption isotherms elution profiles could be predicted satisfactorily.     

Prediction of single component adsorption isotherms on microporous adsorbents

The adsorption of gases on microporous solids is a fundamental physical interaction which occurs in many technical processes, e.g. the heterogeneous catalysis or the purification of gases. In this context the adsorption equilibrium can determine the velocity and/or the capacity of the process. Therefore, it has to be known for designing purposes. The aim of this work has been the a priori prediction of the adsorption equilibria of arbitrary gases on microporous solids like zeolites and active carbon based only on the molecular properties of the adsorptive and the adsorbent. The adsorption isotherm is described completely from the Henry region over the transition zone to the saturation region. The quality of the model permits a first approximation of the planned process without further experimental effort.     

Determination of single component isotherms and affinity energy distribution by chromatography

Adsorption isotherm data were acquired by frontal analysis (FA) and large sample-size band profiles were recorded for phenol and caffeine. For both compounds, the isotherm data fit well to the Langmuir, Toth, and Bi-Langmuir models of adsorption. The Langmuir model must be dismissed because it does not predict accurately the overloaded band profiles. However, profiles calculated using the unimodal Toth and the bimodal Bi-Langmuir models are indistinguishable. The expectation-maximization procedure was used to calculate directly the affinity energy distribution (AED) from the raw FA data points. For both compounds, the AED converges to a bimodal distribution at high numbers of iterations. This result, which shows the high sensitivity of the EM method, suggest that the Bi-Langmuir model makes better physical sense than the Toth model. This model also permits a detailed investigation of the properties of active sites, a feature often evoked in chromatography but so far rarely the topic of a quantitative investigation.     

Comparison of the binary equilibrium isotherms of the 1-indanol enantiomers on three high-performance liquid chromatography columns of different sizes

The competitive isotherm data for the enantiomers of 1-indanol were measured on three columns, a microbore column (15 cm x 0.1 cm), a conventional analytical column (15 cm x 0.46 cm), and a semi-preparative column (20 cm x 1.0 cm), packed with Chiralcel OB. The sets of isotherm data measured on each one of these three columns could be fitted well by a bi-Langmuir isotherm model. The experimental elution band profiles of mixtures of the 1-indanol isomers were recorded on the three columns. The isotherm model, combined with the equilibrium dispersive model of chromatography, gave calculated profiles that are in excellent agreement with the experimental profiles in all cases investigated. It was found that the value of the inner diameter of the column is an important parameter in the calculation of the isotherm parameters from the measured isotherm data. In order to use isotherm data obtained on one column to account for the phase equilibrium on another one, the inner diameters of these columns must be measured accurately. The diameters of the three columns were all slightly off their nominal value. Without correction, an important systematic error was made on the isotherm data obtained with the microbore column while only negligible errors were made on the data obtained with the other two columns. After due correction for this effect, the relative difference between the isotherm data for the microbore and the semi-preparative column is still, on the average, about 10%, a difference that might be explained by the limited precision of the measurement of the microbore column diameter. The relative difference between the isotherm data for the analytical and the semi-preparative columns was about 1%, a reasonable value, since the two columns came from different batches of the same packing material.     

Accurate and rapid estimation of adsorption isotherms in liquid chromatography using the inverse method on plateaus

The inverse method (IM) is an attractive approach for estimating adsorption isotherm parameters in liquid chromatography (LC), mainly due to its experimental simplicity and low sample consumption. This article presents a new experimental approach, the inverse method on plateaus (IMP), which uses elution profiles on concentration plateaus together with IM. This approach enabled us to obtain very accurate adsorption isotherms that agreed well with those estimated by means of frontal analysis over the entire concentration range under consideration. IMP is recommended when accurate adsorption isotherm estimates are required, and standard IM is insufficient.     

Determination of competitive adsorption isotherm parameters of pindolol enantiomers on alpha1-acid glycoprotein chiral stationary phase

In this paper, inverse method (IM) was used to determine the binary competitive adsorption isotherm of pindolol enantiomers by a least-square fitting of the proposed model to the experimentally measured elution curves of racemic pindolol. The isotherm parameters were determined by minimizing the least-square error using an adaptation of genetic algorithm, non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG). An equilibrium dispersive (ED) model combined with bi-Langmuir isotherm was used in predicting the elution profiles. The determined parameters show good agreement with the experimental profiles at various experimental conditions such as sample volume, concentration and flow rates of the racemic mixture. Robustness and validity of the isotherm parameters were also verified by frontal analyses at various step inputs. Results from both the pulse tests and the frontal analysis indicate that adsorption isotherm derived from the inverse method is quite reliable. This method requires relatively less number of experiments to be performed and therefore, lower experimental costs confirming that inverse method is an attractive alternative approach of experimental technique in determining the competitive adsorption isotherm for binary systems.     

Theoretical study of the accuracy of the pulse method,frontal analysis,and frontal analysis by characteristic points for the determination of single component adsorption isotherms

The adsorption isotherms of selected compounds are our main source of information on the mechanisms of adsorption processes. Thus, the selection of the methods used to determine adsorption isotherm data and to evaluate the errors made is critical. Three chromatographic methods were evaluated, frontal analysis (FA), frontal analysis by characteristic point (FACP), and the pulse or perturbation method (PM), and their accuracies were compared. Using the equilibrium-dispersive (ED) model of chromatography, breakthrough curves of single components were generated corresponding to three different adsorption isotherm models: the Langmuir, the bi-Langmuir, and the Moreau isotherms. For each breakthrough curve, the best conventional procedures of each method (FA, FACP, PM) were used to calculate the corresponding data point, using typical values of the parameters of each isotherm model, for four different values of the column efficiency (N=500$N=500$, 1000, 2000, and 10,000). Then, the data points were fitted to each isotherm model and the corresponding isotherm parameters were compared to those of the initial isotherm model. When isotherm data are derived with a chromatographic method, they may suffer from two types of errors: (1) the errors made in deriving the experimental data points from the chromatographic records; (2) the errors made in selecting an incorrect isotherm model and fitting to it the experimental data. Both errors decrease significantly with increasing column efficiency with FA and FACP, but not with PM.     

Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies

In order to estimate single solute adsorption isotherms, the nonlinear frequency response (FR) of a chromatographic column is analyzed experimentally and evaluated using the concept of higher order frequency response functions (FRFs) based on the Volterra series and generalized Fourier transform. In this case study, it has been investigated the adsorption of ethyl benzoate on octadecyl silica from a mixture of methanol and water (60:40) as a solvent. Experiments are performed using a standard gradient HPLC unit. For estimation of adsorption isotherms by the nonlinear FR method the column inlet concentration is changed in a nearly sine waveform around several steady-state concentrations. Using this method the first three local derivatives of a single solute adsorption isotherm are estimated from the low frequency asymptotes of the corresponding functions, i.e. the phase and first order derivative of the FRFs. For an accurate estimation of isotherm coefficients periodical experiments should be preformed for frequencies below a certain critical frequency. This is the frequency needed for approaching the low frequency asymptotic behaviour of the corresponding functions close enough, so that errors due to the non-feasibility of experiments with zero frequency can be neglected. Unfortunately, depending on the properties of the system, it can happen (as for the system investigated here) that experiments for the critical frequency would be too long and cannot be realized. In order to study the loss of accuracy of the nonlinear FR method, when it is applied for non-optimal frequencies, experiments are performed for frequencies approximately one order of magnitude higher than the critical frequency required to evaluate the FRF phases. The obtained isotherm model coefficients are compared with the ones estimated using conventional frontal analysis as a reference method. The isotherms determined by two methods are similar, however a closer look reveals that peaks predicted under overloading conditions differ.     

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.     

Determination of adsorption isotherms of proteins by H-root method: comparison between open micro-channels and conventional packed columns

This communication compares the accuracy of a micro open parallel plate system (microOPPS) with a conventional packed column for predicting isotherm data by using the H-root method (HRM). HRM is restricted to compounds obeying the Langmuir isotherm model. The performance of the two chromatographic systems was simulated by using comprehensive mathematical models. Operating conditions were varied and their effects on the accuracy of predictions was evaluated. Better accuracy in the isotherm predictions was obtained with the packed column due to its higher efficiency. However, good predictions can be obtained with the microOPPS with the advantage of significantly lower sample consumption.     

Competitive ion-exchange adsorption of proteins: competitive isotherms with controlled competitor concentration

The competitive adsorption processes inevitably present in chromatographic separations of complex mixtures have not been extensively studied. This is partly due to the difficulty of measuring true competitive isotherms, in which all system parameters (including competitor concentrations) are held constant. We report a novel approach to determining competitive protein adsorption isotherms in which the competitor concentration is held constant across the entire isotherm. By using the heme prosthetic group in cytochrome b5 as a quantitative spectrophotometric label, competitive isotherms between cytochrome b5 and alpha-lactalbumin can be constructed. Similarly, manganese-substituted protoporphyrin IX heme replacement allows the non-perturbing labeling of individual cytochrome b5 conservative surface charge mutants by replacement of a single atom in the interior of the protein. This labeling allows the study of competition between cytochrome b5 charge mutants of identical size and shape, which differ only in charge arrangement. Using these techniques, the effect of competing species on equilibrium behavior and the apparent heterogeneity of anion-exchange adsorbents in the presence of competitors can be quantitatively studied by fitting the data to two popular single-component binding models, the Temkin and the Langmuir-Freundlich (L-F) isotherms.     

Adsorbent screening for biobutanol separation by adsorption: kinetics, isotherms and competitive effect of other compounds

Butanol, considered as one of the best renewable alternatives for gasoline, has attracted significant attention in recent years. However, biobutanol production via fermentation is plagued by the low final product concentration due to product inhibition. It is possible to enhance productivity by selectively removing biobutanol from the fermentation broth. Adsorption is one of the most promising and energy-efficient techniques for butanol separation and recovery. In the present study, different adsorbents were tested by performing kinetic and equilibrium experiments to find the best adsorbent for butanol separation. Activated carbon (AC) F-400 showed the fastest adsorption rate and the highest adsorption capacity amongst ACs and zeolites tested. AC F-400 also showed the highest affinity toward butanol and to a lesser extent for butyric acid whereas its adsorption capacity for the other main components present in acetone–butanol–ethanol fermentation broths was very low. In addition, the butanol adsorption capacity was not affected by the presence of ethanol, glucose and xylose while the presence of acetone led to a slight decrease in adsorption capacity at low butanol concentrations. On the other hand, the presence of acids (acetic acid and butyric acid) showed a significant effect on the butanol adsorption capacity over a wide range of butanol concentration and this effect was more pronounced for butyric acid.     

Determination of the energetic topography of bivariate heterogeneous surfaces from adsorption isotherms

The reversible adsorption process occurring on patchwise heterogeneous bivariate surfaces is studied by Monte Carlo simulation and mean-field approximation. These surfaces are characterized by a collection of deep and shallow adsorbing patches with a typical length scale l. Patches can be either arranged in a deterministic chessboard structure or in a random way. Previous studies showed that the topography of a given surface can be obtained from the knowledge of the corresponding adsorption isotherm and a reference curve. In the present work, we discuss the advantages and disadvantages of using different reference curves. One of the main consequences of this analysis is to provide an improved method for the determination of the energetic topography of the surface from adsorption measurements.