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.     

Effect of the flow rate on the measurement of adsorption data by dynamic frontal analysis

The adsorption data of propyl benzoate were acquired by frontal analysis (FA) on a Symmetry-C18 column, using a mixture of methanol (65%, v/v) and water as the mobile phase, at three different flow rates, 0.5, 1.0 and 2.0 mL/min. The exact flow rates Fv were measured by collecting the mobile phase in volumetric glasses (deltaFv / Fv < or = 0.2%). The extra-column volumes and the column hold-up volume were accurately measured at each flow rate by tracer injections. The detailed effect of the flow rate on the value of the amount adsorbed was investigated. The best isotherm model accounting for the adsorption data was the same BET isotherm model at all three flow rates. Only slight differences (always less than 5%) were found between the three different sets of isotherm parameters (saturation capacity, q(s), equilibrium constant on the adsorbent, b(s) and equilibrium constant on successive layers of propyl benzoate, bL). The reproducibility of the same isotherm parameters measured by the inverse method (IM) is less satisfactory, leading to R.S.D.s of up to 10%. A flow rate increase is systematically accompanied by a slight increase of the amount adsorbed. This phenomenon is consistent with the influence of the pressure on the equilibrium constant of adsorption due to the difference between the partial molar volumes of the solute and the adsorbate. The larger average pressure along the column that is required to achieve a larger flow rate causes a larger amount of solute to be adsorbed on the column at equilibrium. This result comforts the high sensitivity and versatility of the FA method for isotherm determination under any kind of situation.     

Systematic errors in the measurement of heat by flow microcalorimetry

It is shown that a number of systematic errors must be considered when performing heat measurements by flow microcalorimetry because the nature of the flow technique is such that substantial heat loss can be incurred. The conventional procedure of electrical calibration is found to be an inadequate correction parameter. Equations to account for the effects of thermal disequilibrium are derived from the basic principles incorporated in the Tian equation. The predicted relationships are tested by simple experiments and shown to be correct. The various correction parameters are measured for a wide range of flow rate and heat input conditions. A composite equation is presented which allows for the correction of heat loss while deconvoluting electrical heat from a heat of reaction. The total heat output rate from a flow calorimeter can be calculated for most experimental conditions by reference to this equation and to the tabulated correction values.     

Study of structural and thermodynamic characteristics of adsorption layers by the density functional method: Local density in adsorption layer on planar solid surface and adsorption isotherms

The local density profiles in Lennard-Jones adsorption layers, as well as the excess (Gibbs) and absolute adsorption values, are calculated by the density functional method (weighting factor approximations). The substrate is described using the single-particle potential corresponding to the Lennard-Jones potential integrated over the half space occupied by the substrate. The Steele potential is used as a single-particle potential to consider methane adsorption on the surface of nonporous graphite as a specific system. The calculations are performed for both sub- and supercritical temperature regions. It is established that the density profiles are characterized by the existence of one to three maxima, which reflect the positional order of molecules in adsorption layers, i.e., the layered structure of an adsorbate.     

Experimental determination of adsorption energies, adsorption isotherms, probability density functions, and lateral molecular interactions on CXHY/CaO systems

Reversed-flow gas chromatography (RF-GC) is extended to the measurements of the probability density function for the adsorption energies as well as the differential energies of adsorption due to lateral interactions of molecules adsorbed on different heterogeneous solid surfaces. All these calculations are based on a non-linear adsorption isotherm model as it is well accepted that the linear one is inadequate for substances such as these used in this work. Thus, some new important physicochemical parameters have been obtained for the characterization of the heterogeneous systems studied. The adsorbent used in this study was calcium oxide. The adsorption of many significant hydrocarbons was investigated. With these systematic experiments under conditions which are similar to the atmospheric ones, an extrapolation of the results obtained to "real" atmospheres with a high degree of confidence is possible.     

Thermodynamic parameters analysis of ethidium bromide and mitoxantrone binding with DNA by adsorption isotherms

Analysis of the adsorption isotherms by virtue of experimentally obtained data of anti-tumorous compound mitoxantrone and ethidium bromide binding with DNA has been carried out. The obtained data showed that throughout the comparatively simple linear isotherm, the more precise values of the binding constant K and number of nucleotides n, per binding site were received. Based on the values of K, those for the enthalpy changes at complex-formation of these ligands with DNA were obtained.

     

Breakthrough curves and elution profiles of single solutes in case of adsorption isotherms with two inflection points

The shape of breakthrough curves and elution profiles depends strongly on the course of the specific equilibrium functions characterizing the chromatographic system. For a highly efficient system the equilibrium theory provides a methodology how to predict the band profiles. The concept is frequently applied to analyze single component systems characterized by isotherms possessing simple shapes (Langmuir or anti-Langmuir behaviour). However, adsorption isotherms often possess more complicated shapes and have inflection points in their courses. This leads to the development of composite concentration waves and results in complex shapes of breakthrough curves and elution profiles. In this paper, the equilibrium theory is used to predict breakthrough curves for a chromatographic system characterized by an adsorption isotherm with two inflection points. The results obtained are validated by comparing with numerical solutions of the equilibrium dispersive model.     

Impact of an error in the column hold-up time for correct adsorption isotherm determination in chromatography I. Even a small error can lead to a misunderstanding of the retention mechanism

The impact of a realistic error in the column hold-up time on the determination of the adsorption isotherm model was systematically investigated. Frontal analysis and the inverse method were used for the accurate determination of the adsorption isotherm. The true retention times of the breakthrough curves were used with a known hold-up time as reference. The adsorption isotherms were calculated using the same procedure that is used for real experimental adsorption isotherms, where the true hold-up time is unknown. The raw data were analyzed with calculations of adsorption energy distributions (AEDs), Scatchard plots, fitting to different rival adsorption models and finally their ability to predict true profiles. The results show that for a true Langmuir and bi-Langmuir model with an underestimated hold-up time the error may lead to a more heterogeneous model and for overestimated cases false adsorption processes like multi-layer adsorption or solute-solute interaction are assumed. The Scatchard plots for data obtained using a Langmuir adsorption isotherm are nonlinear and the AEDs show clear deviations from Langmuir behavior already at small deviations from the true hold-up time at a moderate surface coverage. The inverse method confirms the result that was obtained from the frontal analysis procedure.     

Influence of the errors made in the measurement of the extra-column volume on the accuracies of estimates of the column efficiency and the mass transfer kinetics parameters

The influences of the errors made in the measurement of the extra-column volume of an instrument on the accuracies of the estimates made of the column efficiency and of the parameters of the mass transfer kinetics were investigated from an experimental point of view. A standard HP1090 apparatus (extra-column volume, approximately 50 micro L) was used to measure the efficiency of a Sunfire-C(18) RPLC column (column hold-up volume, approximately 1.50 mL). The first and second moments of the peaks of phenol (a retained compound) and of thiourea (a practically non-retained compound) were measured at six different temperatures between 22 and 78 degrees C, for flow rates between 0.10 and 4.70 mL/min (i.e., for linear velocities between 0.025 and 1.179 cm/s). Each series of measurements was successively made with the instrument being fitted with and without the column. The experimental HETP data must be corrected for the solute dispersion in the connected tubes in order properly to assess the true column efficiency. Even with a modern, high performance instrument, the dispersion of a non-retained compound is essentially due to the band broadening phenomena that take place in the extra-column volumes, the sum of all these extra-column band broadening contributions accounting for more than 80% of the total band broadening measured. The contribution of the sampling device is particularly deleterious since, for a 2 mu L injection, the maximum solute concentration in the peak that enters into the column is nearly ten-fold lower than that of the sample. Nevertheless, the impact of the extra-column volumes on the estimates of the kinetic parameters (e.g., molecular diffusion coefficient D(m) and effective particle diffusivity D(e)) remains negligible. Obviously, the relative error made on the column efficiency of a retained compound depends much on its retention factor. It decreases from 8 to 1% when the retention factor increases from 5 to 17.     

Improvement in the generation of adsorption isotherm data in the elution by characteristic points method--the ECP-slope approach

The elution by characteristic points (ECP) method is a very rapid and precise method for determination of the phase system equilibrium of phase systems in broad solute concentration ranges. Thus, the method is especially suitable for rapid characterization of high efficient separation systems. One important source of error, the effects by the post-loop dispersion, was eliminated in a recent investigation. In this study, the systematic error caused by the selection of the integration starting point at concentration equal to 0 is eliminated. This is done by developing and validating a new procedure for isotherm data generation; the ECP-slope method. The method generates raw slope data of the adsorption isotherm instead of raw adsorption data by integrations as the classical ECP does. Both numerical and experimental data were used for the comparison of the classical ECP approach with the slope-ECP method.     

Assessment of systematic errors in measurement of vapor pressures by thermogravimetric analysis

The present study explores the application of the diffusion limited evaporation theory to the estimation of vapor pressure from TG experimental data. A simplified method was developed to calculate the apparent values of the vapor pressure of pure substances from TG data, based on isothermal TG runs with crucibles having different surface areas available for evaporation. Antoine parameters are estimated through a numerical procedure based on a non-linear least square algorithm. The procedure also evaluates the substance diffusivity in nitrogen. The methodology developed might be used for a preliminary screening of the vapor pressure of pure compounds, due to the limited amounts of sample that are necessary and to the limited time frame required for the experimental runs. However, the estimation of diffusivity and vapor pressures values by the TG technique is possible with limited accuracy. Possible sources of error were thoroughly investigated and discussed.     

Numerical analysis of nitrogen adsorption isotherms on active carbons by an employment of the new LBET class models

The reported research concerns properties of the new LBET class models designed to describe the heterogeneous adsorption on microporous carbonaceous materials. In particular, the new adsorption models were used for the analysis of the microporous structure of two active carbons on the basis of nitrogen adsorption isotherms. This paper gives more information on the properties of the proposed identification technique.     

Binding of caffeic acid to human serum albumin by the retention data and frontal analysis

A new mathematical model and frontal analysis were used to characterize the binding behavior of caffeic acid to human serum albumin (HSA) based on high‐performance affinity chromatography. The experiments were carried out by injecting various mole amounts of the drug onto an immobilized HSA column. They indicated that caffeic acid has only one type of binding site to HSA on which the association constant was 2.75 × 10⁴/m . The number of the binding site involving the interaction between caffeic acid and HSA was 69 nm . The data obtained by the frontal analysis appeared to present the same results for both the association constant and the number of binding sites. This new model based on the relationship between the mole amounts of injection and capacity factors assists understanding of drug–protein interaction. The proposed model also has the advantages of ligand saving and rapid operation. Copyright © 2014 John Wiley & Sons, Ltd.     

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.