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.     

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.     

Determination of the single component and competitive adsorption isotherms of the 1-indanol enantiomers by the inverse method

The inverse method of isotherm determination consists in calculating the numerical values of the coefficients of an isotherm model that give a set of chromatographic profiles in best possible agreement with the set of experimental profiles available. This method was applied to determine the adsorption isotherms of the 1-indanol enantiomers on a cellulose tribenzoate chiral stationary phase. Both single-component and competitive isotherms were determined by using no more than one or two overloaded band profiles. The isotherms determined from the overloaded band profiles agreed extremely well with the isotherms determined by frontal analysis. Several isotherm models were used and tested. The best-fit isotherm was selected by means of statistical evaluation of the results. The results show that the adsorption is best characterized with a model describing heterogeneous adsorption with bimodal adsorption energy distribution.     

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.     

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.     

Predicting adsorption isotherms using a two-dimensional statistical associating fluid theory

A molecular thermodynamics approach is developed in order to describe the adsorption of fluids on solid surfaces. The new theory is based on the statistical associating fluid theory for potentials of variable range [A. Gil-Villegas et al., J. Chem. Phys. 106, 4168 (1997)] and uses a quasi-two-dimensional approximation to describe the properties of adsorbed fluids. The theory is tested against Gibbs ensemble Monte Carlo simulations and excellent agreement with the theoretical predictions is achieved. Additionally the authors use the new approach to describe the adsorption isotherms for nitrogen and methane on dry activated carbon.     

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.     

Characterization of soil particle surfaces using adsorption excess isotherms

Measurement of adsorption excess isotherms of methanol-benzene mixtures was applied to the characterization of soil particle surfaces. The sorption capacity and Gibbs energy of sorption of the solid-liquid interface were determined for montmorillonite, three types of soil, and their humin fractions. The soils were found to be less polar or less hydrophilic than the clay, and the humin fraction of soils was found to be less hydrophilic than the whole soils. The soil and humin samples have heterogeneous surfaces which can be divided in two regions on the basis of their relative polarity. The x-axis intersection of the straight section of isotherm assigns the relative proportions of the hydrophilic and hydrophobic regions of the surface.     

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.     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

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.     

Efficient simulation of binary adsorption isotherms using transition matrix Monte Carlo

Molecular simulations of binary adsorption in porous materials are a useful complement to experimental studies of mixture adsorption. Most molecular simulations of binary adsorption are performed using grand canonical Monte Carlo (GCMC) to independently examine a range of state points of interest. A disadvantage of this approach is that it only yields information at a discrete set of state points; therefore, if a complete isotherm is required for arbitrary conditions, some type of data fitting or interpolation must be used in combination with the GCMC data. We show that the transition matrix Monte Carlo (TMMC) method of Shen and Errington (Shen, V. K.; Errington, J. R. J. Chem.Phys. 2005, 122, 064508) is well-suited to simulation of binary adsorption in porous materials. At the completion of a TMMC simulation, the adsorption isotherm for all possible bulk phase compositions and pressures is available without data fitting or interpolation. It is also straightforward to use results from TMMC to compute derivatives of the isotherm such as the mixture thermodynamic correction factors, partial differential ln f(i)/partial differential ln c(j), again without data fitting or interpolation. This approach should be useful in contexts where information on the full adsorption isotherm is needed, such as the design of adsorption- or membrane-based separations.     

pH-dependent adsorption isotherms of hydrolyzable metal ions interacting with various surfaces,explained by a single curve

It was shown on several examples from the literature, including some own data, that complicated adsorption dependence on pH for hydrolyzable metal ions, can be explained with one single curve, Λ = b [MeL_x^{p min}]_eqn^a, with a and b uniquely determined. Other authors have used presentation Λ = b[Me]_{TOT, eqn}^a, with a and b pH dependent. In presented model, it is assumed that the species with the smallest charge is adsorbed the most. Its concentration can be calculated as [MeL_x^pmin]=β_xL^x[Me]_TOT,eqn/(1+ϵβ_nLⁿ) where n is the number of ligand in the complex MeL_n^p and x is the n value for which is the carge p the smallest one. The value of a varies from 0.1 to 1.0. The hydrolysis mechanisms can satisfactorily explain studied adsorption data. For future studies it is emphasized the necessity of good and complete β_n constants, of more comparable data about the influence of other ligands and of the types of adsorbent.     

Neural network modelling of adsorption isotherms

This paper examines the possibility to use a single neural network to model and predict a wide array of standard adsorption isotherm behaviour. Series of isotherm data were generated from the four most common isotherm equations (Langmuir, Freundlich, Sips and Toth) and the data were fitted with a unique neural network structure. Results showed that a single neural network with a hidden layer having three neurons, including the bias neuron, was able to represent very accurately the adsorption isotherm data in all cases. Similarly, a neural network with four hidden neurons, including the bias, was able to predict very accurately the temperature dependency of adsorption data.     

Differential heats of adsorption and adsorption isotherms of alcohols on silicalite

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2117–2120, September, 1989.     

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.     

Effect of temperature on competitive adsorption of the solute and the organic solvent in reversed-phase liquid chromatography

In analysis of the temperature effect on chromatographic separations the influence of the adsorption of organic solvent on the retention properties of solute is generally not taken into account. In fact, adsorption behavior of solutes is strongly affected by competitive adsorption of organic solvents, which is temperature dependent. In this work changes of adsorption equilibrium of an organic solvent as well as a solute with temperature have been analyzed. Data of the excess adsorption of methanol from aqueous solutions on octadecyl-bonded silica have been acquired at different temperature. Experiments have been performed over a relatively narrow temperature range corresponding to typical chromatographic conditions, i.e., 10-50 degrees C. The competitive adsorption equilibria of model solutes (i.e., two homologous compounds: cyclopentanone and cyclohexanone) have been measured at different temperature and composition of the mobile phase. Temperature alterations to the retention properties were found to result from combined effects of changes in adsorption behavior of the organic solvent and of the solute. The influence of temperature on the separation selectivity has been considered.