Calculations of the energy distribution from perturbation peak data--a new tool for characterization of chromatographic phases

The calculation of the adsorption energy distribution (AED) was recently introduced as an important tool for the chromatographic community for characterization of modern phases. The AED-calculations, provides model-independent information about the numbers of different adsorption sites and their respective energy-levels, prior to the selection of an adsorption isotherm model which narrows the number of possible rival models. The selection of a proper model for the fitting of the determined raw data is crucial; if the wrong model is selected misleading information about the retention mechanism may be drawn. The AED-calculations require raw adsorption isotherm data (i.e. data points) which is unfortunately not obtained by the newly validated perturbation peak method. In this study, we developed mathematical expression allowing the use of the raw tangential slope provided by the perturbation peak method for AED calculations. The approach worked excellently and was verified against both computer-generated adsorption isotherm data as well as experimentally determined data, using three different experimental systems. It was found that the calculations of the AED, as based on perturbation peak data, converts faster and are not more sensitive to experimental noise as compared to the classical AED calculations using raw adsorption isotherm data.     

Influence of the column radial heterogeneity on the determination of single-component isotherms by the elution by characteristic point method

The influence of the column radial heterogeneity on the determination of equilibrium isotherm data by the elution by characteristic point (ECP) method is studied using nondimensional numerical calculations and taking into account typical radial distributions of the mobile phase flow velocity and the column efficiency across a column. Overloaded elution peaks were calculated with the equilibrium-dispersive model as a function of four dimensionless parameters, the number of theoretical plates at the center of the column, the Langmuir equilibrium constant, the retention and the loading factors. The influence of the mass transfer resistances and the radial heterogeneity of the column on the ECP data was analyzed by comparing the true isotherm and the one estimated from the diffuse profile of overloaded peaks. The results provide information on the accuracy of the ECP method. The error made increases with increasing degree of radial heterogeneity. This error can be corrected by using the results of the nondimensional numerical calculations, allowing a further extension of the applicability of the ECP method.     

Theoretical study of the accuracy of the elution by characteristic points method for bi-langmuir isotherms

The bi-Langmuir equation has recently been proven essential to describe chiral chromatographic surfaces and we therefore investigated the accuracy of the elution by characteristic points method (ECP) for estimation of bi-Langmuir isotherm parameters. The ECP calculations was done on elution profiles generated by the equilibrium-dispersive model of chromatography for five different sets of bi-Langmuir parameters. The ECP method generates two different errors; (i) the error of the ECP calculated isotherm and (ii) the model error of the fitting to the ECP isotherm. Both errors decreased with increasing column efficiency. Moreover, the model error was strongly affected by the weight of the bi-Langmuir function fitted. For some bi-Langmuir compositions the error of the ECP calculated isotherm is too large even at high column efficiencies. Guidelines will be given on surface types to be avoided and on column efficiencies and loading factors required for adequate parameter estimations with ECP.     

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.     

Determination of chromatographic separation parameters of tryptophan enantiomers on a Chirosil-SCA chiral stationary phase by using the inverse method based on the initial guesses estimated from elution by characteristic point method

An effective chiral stationary phase (CSP) for enantioseparation of amino acids was established previously by bonding (18-crown-6)-2, 3, 11, 12-tetracarboxylic acid to silica gel. This CSP has recently been commercialized under the name of Chirosil-SCA. As a first step for developing a Chirosil-SCA simulated moving bed chromatographic process for separation of tryptophan enantiomers, the adsorption isotherm and mass-transfer parameters of each tryptophan enantiomer on the Chirosil-SCA CSP were determined in this study while using only water as a mobile phase. For this task, inverse method (IM) was applied on the basis of the initial guesses estimated from elution by characteristic point (ECP) method, which was found to be more advantageous in the aspects of both accuracy and computational efficiency than the case of utilizing individually only IM or ECP method. The results revealed that the adsorption behavior of each tryptophan enantiomer on the Chirosil-SCA could be well described by the Langmuir-Freundlich isotherm. The model predictions based on the determined parameter values were in close agreement with the experimental chromatograms from a series of single-component or mixture pulse tests that were performed under various feed concentrations and flow rates. It was also found that the Langmuir-Freundlich isotherm parameters of each enantiomer were largely affected by temperature. Such a marked dependence of the parameters on temperature was investigated quantitatively. The results of such an investigation indicated that as the temperature decreases, the adsorption affinities of both enantiomers become higher and the heterogeneity of the Chirosil-SCA becomes more pronounced.     

Effect of the ionic strength of salts on retention and overloading behavior of ionizable compounds in reversed-phase liquid chromatography I. XTerra-C18

The influence of the salt concentration (potassium chloride) on the retention and overloading behavior of the propranolol cation (R'-NH2+ -R) on an XTerra-C18 column, in a methanol:water solution, was investigated. The adsorption isotherm data were first determined by frontal analysis (FA) for a mobile phase without salt (25% methanol, v/v). It was shown that the adsorption energy distribution calculated from these raw adsorption data is bimodal and that the isotherm model that best accounts for these data is the bi-Moreau model. Assuming that the addition of a salt into the mobile phase changes the numerical values of the parameters of the isotherm model, not its mathematical form, we used the inverse method (IM) of chromatography to determine the isotherm with seven salt concentrations in the mobile phase (40% methanol, v/v; 0, 0.002, 0.005, 0.01, 0.05, 0.1 and 0.2 M). The saturation capacities of the model increase, q(s,1) by a factor two and q(s,2) by a factor four, with increasing salt concentration in the range studied while the adsorption constant b1 increases four times and b2 decreases four times. Adsorbate-adsorbate interactions vanish in the presence of salt, consistent with results obtained previously on a C18-Kromasil column. Finally, besides the ionic strength of the solution, the size, valence, and nature of the salt ions affect the thermodynamic as well as the mass transfer kinetics of the adsorption mechanism of propranolol on the XTerra column.     

The direct inverse method: A novel approach to estimate adsorption isotherm parameters

A novel method to estimate adsorption isotherm parameters is presented and its applicability is studied through synthetic as well as experimental data. This approach assumes a linear dependency of the UV absorption intensity on the solute concentration in the fluid phase, at least in certain ranges of the UV spectra. It was demonstrated that by fitting the absorption profiles, i.e. the new direct inverse method, and by fitting the concentration profiles, i.e. the classical inverse method, very similar adsorption isotherm parameters can be obtained. The findings presented in this work have as important implication the elimination of the requirement of converting a measured absorption intensity into a concentration value, i.e. the elimination of the calibration of the UV signal.     

Adsorption isotherm models for basic dye adsorption by peat in single and binary component systems

Colored effluents from textile industries are a problem in many rivers and waterways. Prediction of dye adsorption capacities is important in design considerations. The sorption of three basic dyes, namely Basic blue 3, Basic yellow 21, and Basic red 22, onto peat is reported. Equilibrium sorption isotherms have been measured for the three single-component systems. Equilibrium was achieved after 21 days. The experimental isotherm data were analyzed using Langmuir, Freundlich, Redlich-Peterson, Tempkin, and Toth isotherm equations. A detailed error analysis has been undertaken to investigate the effect of using different error criteria for the determination of the single-component isotherm parameters and hence obtain the best isotherm and isotherm parameters which describe the adsorption process. The linear transform model provided the highest R(2) regression coefficient with the Redlich-Peterson model. The Redlich-Peterson model also yielded the best fit to experimental data for all three dyes using the nonlinear error functions. An extended Langmuir model has been used to predict the isotherm data for the binary systems using the single component data. The correlation between theoretical and experimental data had only limited success due to competitive and interactive effects between the dyes and the dye-surface interactions.     

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.     

Expanding the elution by characteristic point method for determination of various types of adsorption isotherms

Important improvements have recently been made on the elution by characteristic point (ECP) method to increase the accuracy of the determined adsorption isotherms. However, the method has so far been limited/used for only type I adsorption isotherms (e.g. Langmuir, Tóth, bi-Langmuir). In this study, general strategies are developed to expand the ECP method for the determination of more complex adsorption isotherms including such containing inflection points. We will exemplify the methodology with type II, type III and type V isotherms. Guidelines are given for how to determine such isotherms using the ECP method and for the experimental considerations that must be taken into account or that may be eliminated in the particular case.     

Comparison of the adsorption equilibrium of a few low-molecular mass compounds on a monolithic and a packed column in reversed-phase liquid chromatography

Adsorption isotherm data were acquired by frontal analysis for several low-molecular mass compounds (3-phenyl 1-propanol, 4-tert.-butylphenol, butylbenzene, and butyl benzoate) on a classical packed column and a monolithic column using methanol-water RP-HPLC conditions. These columns have similar characteristics (C18-bonded silica, close specific surface areas and bonding densities). In each case, the isotherm model best accounting for the data was the same on both columns. The solute polarity determines the class of this model. For the two -OH compounds it was a Langmuirian adsorption isotherm. The hydrocarbon data were best modeled by an anti-Langmuir convex-downward isotherm model. The adsorption data for the aromatic ester exhibited a nearly linear behavior, depending on the methanol concentration of the mobile phase. A slightly convex downward isotherm was obtained at high methanol concentrations while the best fitting was obtained with a liquid-solid extended multilayer B.E.T. isotherm model at low concentrations. The validation of these models is discussed in detail. In all cases, similar values of the adsorption-desorption constants were found, underlining the closeness of the adsorption energies on both columns. By contrast, the adsorption capacity of the monolithic column was found to be approximately 1.4 greater than that of the packed column in spite of the close values of the surface areas of the silica in both columns.     

Characterization of an unusual adsorption behavior of racemic methyl-mandelate on a tris-(3,5-dimethylphenyl) carbamoyl cellulose chiral stationary phase

An interesting adsorption behavior of racemic methyl mandelate on a tris-(3,5-dimethylphenyl)carbamoyl cellulose chiral stationary phase was theoretically and experimentally investigated. The overloaded band of the more retained enantiomer had a peculiar shape indicating a type V adsorption isotherm whereas the overloaded band of the less retained enantiomer had a normal shape indicating a type I adsorption behavior. For a closer characterization of this separation, adsorption isotherms were determined and analyzed using an approach were Scatchard plots and adsorption energy distribution (AED) calculations are combined for a deeper analysis. It was found that the less retained enantiomer was best described by a Tóth adsorption isotherm while the second one was best described with a bi-Moreau adsorption isotherm. The latter model comprises non-ideal adsorbate-adsorbate interactions, providing an explanation to the non-ideal adsorption of the more retained enantiomer. Furthermore, the possibility of using the Moreau model as a local model for adsorption in AED calculations was evaluated using synthetically generated raw adsorption slope data. It was found that the AED accurately could predict the number of adsorption sites for the generated data. The adsorption behavior of both enantiomers was also studied at several different temperatures and found to be exothermic; i.e. the adsorbate-adsorbate interaction strength decreases with increasing temperature. Stochastic analysis of the adsorption process revealed that the average amount of adsorption/desorption events increases and the sojourn time decreases with increasing temperature.     

Adsorption behavior of the (+/-)-Tröger's base enantiomers in the phase system of a silica-based packing coated with amylose tri(3,5-dimethyl carbamate) and 2-propanol and molecular modeling interpretation

The binary adsorption isotherms of the enantiomers of Tr?ger's base in the phase system made of Chiral Technologies ChiralPak AD [a silica-based packing coated with amylose tri(3,5-dimethyl carbamate)] as the chiral stationary phase (CSP) and 2-propanol as the mobile phase were measured by the perturbation method. The more retained enantiomer exhibits a S-shaped adsorption isotherm with a clear inflection point, the concentration of the less retained enantiomer having practically no competitive influence on this isotherm: In the entire range of concentrations studied, dq2/dC1 approximately 0. By contrast, the less retained enantiomer has a Langmuir adsorption isotherm when pure. At constant mobile phase concentrations, however, its equilibrium concentration in the adsorbed phase increases with increasing concentration of the more retained enantiomer and dq1/dC2 > 0. This cooperative adsorption behavior, opposed to the classical competitive behavior, is exceedingly rare but was clearly demonstrated in this case. Two adsorption isotherm equations that account for these physical observations were derived. They are based on the formation of an adsorbed multi-layer, as suggested by the isotherm data. The excellent agreement between the experimental overloaded elution profiles of binary mixtures and the profiles calculated with the equilibrium-dispersive model validates this binary isotherm model. The adsorption energies calculated by molecular mechanics (MM) and by molecular dynamics (MD) indicate that the chiral recognition arising from the different interactions between the functional groups of the CSP and the molecules of the Tr?ger's base enantiomers are mainly driven by their Van der Waals interactions. The MD data suggest that the interactions of the (-)-Tr?ger's base with the CSP are more favored by 8+/-(5) kJ/mol than those of (+)-Tr?ger's base. This difference seems to be a contributing factor to the increased retention of the - enantiomer on this chromatographic system. The modeling of the data also indicates that both enantiomers can form high stoichiometry complexes while binding onto the stationary phase, in agreement with the results of the equilibrium isotherm studies.     

New method for the determination of adsorption space volume for sorbents with an arbitrary porous structure from excess gas adsorption isotherm measurements

A new method for the determination of adsorption space volume has been proposed, which is applicable to adsorbents with an arbitrary porous structure, including nonporous adsorbents with open surfaces. The method is based on the use of an experimental excess adsorption isotherm measured over a wide range of pressures in the equilibrium gaseous phase (as a rule up to 100–150 MPa) and the absolute adsorption isotherm equation with unspecified parameters in the most general form, given by statistical physics. The method has been tested for a number of adsorption systems, and it has been found that the result was always unambiguous, correct, and stable in the sense of input data.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2381–2385, December, 1995.     

Thermodynamic analysis of the heterogenous binding sites of molecularly imprinted polymers

The thermodynamic interactions of two polymers, one Fmoc-L-Trp-imprinted (MIP), the other one an unimprinted reference (NIP), with the two Fmoc-tryptophan enantiomers were studied by frontal analysis, which allows accurate measurements of the adsorption isotherms. These isotherms were acquired at temperatures of 40, 50, 60, and 70 degrees C, for sample concentrations ranging between 0.005 and 40 mM. The mobile phase used was acetonitrile with one percent acetic acid as an organic modifier. Within the measured concentration ranges, the tri-Langmuir isotherm model accounts best for the isotherm data of both enantiomers on the MIP, the bi-Langmuir model for the isotherm data of Fmoc-L-Trp on the NIP. These isotherm models were selected using three independent processes: statistical tests on the results from regression of the isotherm data to different isotherm models; calculation of the affinity energy distribution from the raw isotherm data; comparison of the experimental and the calculated band profiles. The isotherm parameters obtained from these best selected isotherm models showed that the enantiomeric selectivity does not change significantly with temperature, while the affinity of the substrates for both the MIP and the NIP decrease considerably with increasing temperatures. These temperature effects on the binding performance of the MIP were clarified by considering the thermodynamic functions (i.e., the standard molar Gibbs free energy, the standard molar entropy of adsorption, and the standard molar enthalpy of adsorption) for each identified type of adsorption sites, derived from the Van't Hoff equation. This showed that the entropy of transfer of Fmoc-L-Trp from the mobile to the MIP stationary phase is the dominant driving force for the selective adsorption of Fmoc-L-Trp onto the enantioselective binding sites. This entropy does not change significantly with increasing temperatures from 40 to 70 degrees C.     

2-异戊基环戊酮虚拟模板印迹微球的制备及其吸附性能

以2-异戊基环戊酮为虚拟模板,采用沉淀聚合法制备了粒径20~50 μm的分子印迹微球。 用傅里叶变换红外光谱(FTIR)和扫描电子显微镜(SEM)研究了分子印迹微球的表面化学特征及粒径分布,测试了印迹聚合物对玫瑰醚的吸附动力学、等温吸附性能及吸附选择性。 考察了分子印迹固相萃取玫瑰醚的应用效能。 结果表明:分子印迹聚合物(MIPs)对玫瑰醚的吸附可在25 min达到平衡,具有较快的吸附动力学,一级动力学模型更适合描述其吸附动力学行为。 Freundlich模型最适合描述MIPs对玫瑰醚的等温吸附行为,聚合物材料最大的印迹位点数目为149.3 μmol/g。 聚合物对玫瑰醚的平均吸附能为166 kJ/mol,表明主要为化学吸附。 虚拟模板印迹聚合物对玫瑰醚的选择因子相对于香叶醇和香茅醇分别为3.710和5.636,且对含玫瑰醚的混合物中的目标化合物仍具有较高的选择吸附能力(竞争吸附量为18.02 mg/g)。 在优化洗涤(1 mL乙腈+1 mL乙腈和水混合溶剂(体积比9.5:0.5)+2 mL乙腈、甲醇和水混合溶剂(体积比8:1:2)和洗脱(3 mL甲醇和醋酸混合溶剂(体积比9:1))条件下,通过分子印迹固相萃取可实现玫瑰醚的有效分离和富集,回收率为96.23%。     

Adsorption from binary solvent mixtures onto silica gel by HPLC frontal analysis

Summary The chromatographic technique of frontal analysis is applied to measuring adsorption from binary liquid mixtures by silica gel. The complete adsorption isotherm of a solvent mixture is obtained by measuring the break-through curves for a series of small concentration steps of the mobile phase. This method offers a direct way to determine the composition of the stationary phase in liquid-solid chromatography with mixed mobile phases. The surface excess isotherms of all binary systems formed by benzene, cyclohexane, and 1,2-dichloroethane, at the solution-silica gel interface at 25 °C are presented. The data of the three systems are shown to be thermodynamically mutually consistent.     

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.     

Adsorption of the enantiomers of 3-chloro-1-phenyl-propanol on silica-bonded chiral quinidine carbamate

The interactions of 3-chloro-1-phenyl-propanol with a quinidine carbamate-bonded chiral stationary phase under NPLC conditions were studied by measuring the adsorption isotherm data of its enantiomers by frontal analysis, modeling these data with a suitable isotherm model, and comparing the experimental overloaded elution band profiles with those calculated with this isotherm and the equilibrium dispersive model of liquid chromatography. The affinity energy distribution was calculated from the adsorption isotherm data. The results show that the surface of the adsorbent is heterogeneous and exhibits a bimodal adsorption energy distribution. This fact is interpreted in terms of the presence of two different types of adsorption sites on the stationary phase, nonselective and enantioselective sites. Albeit the bi-Langmuir isotherm model successfully accounts for the single-component data corresponding to both enantiomers, the competitive bi-Langmuir isotherm model does not allow an accurate prediction of the overloaded band profiles of the racemic mixture. Thermodynamic data are drawn for explanation. Some aspects of the retention mechanism are discussed in the light of the data obtained.     

Comparison of the adsorption mechanisms of pyridine in hydrophilic interaction chromatography and in reversed-phase aqueous liquid chromatography

The adsorption isotherms of pyridine were measured by frontal analysis (FA) on a column packed with shell particles of neat porous silica (Halo), using water–acetonitrile mixtures as the mobile phase at 295 K. The isotherm data were measured for pyridine concentrations covering a dynamic range of four millions. The degree of heterogeneity of the surface was characterized by the adsorption energy distribution (AED) function calculated from the raw adsorption data, using the expectation-maximization (EM) procedure. The results showed that two different retention mechanisms dominate in Per aqueous liquid chromatography (PALC) at low acetonitrile concentrations and in hydrophilic interaction chromatography (HILIC) at high acetonitrile concentrations. In the PALC mode, the adsorption mechanism of pyridine on the silica surface is controlled by hydrophobic interactions that take place on very few and ultra-active adsorption sites, which might be pores on the irregular and rugose surface of the porous silica particles. The surface is seriously heterogeneous, with up to five distinct adsorption sites and five different energy peaks on the AED of the packing material. In contrast, in the HILIC mode, the adsorption behavior is quasi-homogeneous and pyridine retention is governed by its adsorption onto free silanol groups. For intermediate mobile phase compositions, the siloxane and the silanol groups are both significantly saturated with acetonitrile and water, respectively, causing a minimum of the retention factor of pyridine on the Halo column.