Lumped Pore Diffusion Model Research Articles

Competitive sorption of cis-DCE and TCE in silica gel as a model porous mineral solid

The competitive sorption of 1,2- cis-dichloroethene ( cis-DCE) and trichloroethene (TCE) was investigated by means of column experiments using a model porous mineral solid represented by silica gel. The experimental isotherms were obtained by employing a chromatographic method. The competitive sorption isotherms were modelled with the extended Freundlich and extended Langmuir isotherms, using the parameters from single-solute experiments. The breakthrough curves were modelled with the advection–dispersion transport equation coupled with the lumped pore diffusion model. The best results were obtained when the extended Freundlich isotherm was employed. The competitive sorption was revealed with the presence of an overshoot in the breakthrough curve of cis-DCE and a decrease in the degree of sorption of cis-DCE (20%) and TCE (12%). A linear dependency of the overshoot with an increase in the concentration of cis-DCE at a fixed concentration of TCE was observed, between 16% and 20%, and at least at concentrations <6 mg L −1 in the liquid phase. The displaced molecules of cis-DCE by TCE were accumulated through the column causing its overshoot; thus short columns may hinder its observation. Thermodynamic analysis shows an exothermic adsorption process of −34 to −41 kJ mol −1, which is enhanced by sorption in micropores. The Gibbs free energy is positive for cis-DCE in the multi-component case, due to its displacement by TCE.

Influence of microwave irradiation on the intraparticle diffusion of an insulin variant in reversed-phase liquid chromatography under linear conditions

The influence of microwave irradiation on the mass transfer kinetics of an insulin variant in reversed-phase liquid chromatography (RPLC) was investigated. The elution band profiles of insulin were obtained by the pulse-response method, under linear conditions. The RPLC column was placed in a microwave oven and the incremental change in the temperature of the column effluent stream at various microwave energies and mobile phase flow rates were measured. The microwave energy dissipated in the column was set at 15 and 30 W and the mobile phase flow rate was varied from 1.0 to 2.5 mL/min at a mobile phase composition of acetonitrile, water, and trifloroacetic acid (31:69:0.1, v/v/v). The experimental data were analyzed using the conventional method of moment analysis and the lumped pore diffusion model. Regardless of mobile flow rates, the effluent temperatures measured at 15 and 30 W microwave power input were 25 ± 1 and 30 ± 1 °C, respectively. The effect of microwave irradiation on the mass transfer of the variant insulin was determined by comparing the band profiles obtained under the same experimental conditions, at the same column temperature, with and without irradiation. The calculated intraparticle diffusion coefficient, D e, at 30 W (30 ± 1 °C) microwave irradiation was ca. 20% higher than without irradiation at 30 ± 1 °C. These preliminary results suggest that microwave irradiation may have a significant influence on the intraparticle diffusion of insulin in RPLC.

Influence of Microwave Irradiation on the Mass-Transfer Kinetics of Propylbenzene in Reversed-Phase Liquid Chromatography

The effect of microwave irradiation on the kinetics of mass transfer in reversed-phase liquid chromatography (RPLC) was studied by measuring its influence on the band profile of propylbenzene in a C18-silica column eluted with an aqueous solution of methanol and placed inside a microwave oven. The elution peaks were measured by the pulse-response method, under linear conditions. The amount of microwave energy induced into the column was varied based on the microwave input power. The experimental data were analyzed using the conventional method of moment analysis and the lumped pore diffusion model. With input powers of 15 and 30 W, the effluent temperatures were 25 ± 1 and 30 ± 1 °C, respectively. The effect of microwave irradiation on the mass transfer of the studied solute was determined by comparing the band profiles obtained under the same experimental conditions, at the same temperature, with and without irradiation. The values of the intraparticle diffusion coefficient, De, measured with microwave i...

Intraparticle mass transfer kinetics on molecularly imprinted polymers of structural analogues of a template

The intraparticle mass transfer kinetics of the structural analogues of a template on a Fmoc- L-Tryptophan (Fmoc- L-Trp) imprinted polymer (MIP) and on the corresponding non-imprinted polymer (NIP) were quantitatively studied using the lumped pore diffusion model (POR) of chromatography. The best equilibrium isotherm models of these compounds were used to calculate the high-concentration band profiles of different substrates on the MIP and the NIP with the POR model. These profiles were compared to experimental band profiles. The numerical values of the intraparticle pore and surface diffusion coefficients were adjusted to determine those that minimized the differences between calculated and experimental profiles. The results of this exercise show that surface diffusion is the dominant intraparticle mass transfer process for the substrates on the polymers and that the energetic heterogeneity of the surface should be considered in accounting for the surface diffusion of the L-enantiomers on the MIP. The surface diffusion coefficient increases with decreasing overall affinity of each substrate for the polymers.

Mass transfer kinetics on the heterogeneous binding sites of molecularly imprinted polymers

The mass transfer kinetics of the L- and D-Fmoc-Tryptophan (Fmoc-Trp) enantiomers on Fmoc- L-Trp imprinted polymer (MIP) and on its reference polymer (NIP), were measured using their elution peak profiles and the breakthrough curves recorded in frontal analysis for the determination of their equilibrium isotherms, at temperatures of 40, 50, 60, and 70 ∘ C . At all temperatures, the isotherm data of the Fmoc-Trp enantiomers on the MIP were best accounted for by the Tri-Langmuir isotherm model, while the isotherm data of Fmoc-Trp on the NIP were best accounted for by the Bi-Langmuir isotherm model. The profiles of the elution bands of various amounts of each enantiomer were acquired in the concentration range from 0.1 to 40 m M. These experimental profiles were compared with those calculated using the best values estimated for the isotherm parameters and the lumped pore diffusion model (POR), which made possible to calculate the intraparticle diffusion coefficients for each system. The results show that surface diffusion contributes predominantly to the overall mass transfer kinetics on both the MIP and the NIP, compared to external mass transfer and pore diffusion. The surface diffusion coefficients ( D s ) of Fmoc- L-Trp on the NIP does not depend on the amount bound ( q) while the values of D s for the two Fmoc-Trp enantiomers on the MIP increase with increasing q at all temperatures. These positive dependencies of D s on q for Fmoc-Trp on the MIP were fairly well modeled by indirectly incorporating surface heterogeneity into the surface diffusion coefficient. The results obtained show that the mass transfer kinetics of the enantiomers on the imprinted polymers depend strongly on the surface heterogeneity.

Measurement of intraparticle diffusion in reversed phase liquid chromatography

The intraparticle diffusion coefficient was measured using a method based on the fitting of a set of experimental chromatographic profiles to the lumped pore diffusion model. For this purpose, both the analytical solution of the model in the Laplace domain and a numerical method were used. There was an excellent agreement between the results given by the two methods. These results are compared to those obtained by moment analysis of the same set of chromatographic profiles and by the determination of the intraparticle diffusion coefficient from the second central moment of these bands. Nearly identical results were obtained with these two independent methods. The values of the intraparticle diffusion coefficient, D e , for rubrene in pure methanol was found to be 7.89×10 −7 cm 2/ s by the modeling method and 7.23×10 −7 cm 2/ s by the moment analysis method. These values increase with increasing water concentration, to 1.10×10 −6 and 1.24×10 −6 cm 2/ s , respectively, in a 96 :4 v/ v methanol/water solution and to 1.63×10 −6 and 2.38×10 −6 cm 2/ s , respectively, in a 90 :10 v/ v solution. These results confirm the validity and the consistency of the lumped pore model and the moment analysis theory. They show that both approaches describe correctly the mass transfer kinetics in the particles of packing material during the chromatographic process. Systematic determinations of the intraparticle diffusion coefficient can now be undertaken and the influence of various experimental parameters on this important property of packing materials can be investigated.

Prediction of the band profiles of the mixtures of the 1-indanol enantiomers from data acquired with the single racemic mixture

The adsorption isotherm data of R- and S-1-indanol and of their racemic mixture on cellulose tribenzoate were measured by frontal analysis. These data were then fitted to the Langmuir, the Bilangmuir, the Toth, and the Langmuir–Freundlich isotherm models. The single component data fitted well to both the Bilangmuir and the Toth models. Combined with the lumped pore diffusion model (POR) of chromatography, these isotherms were used to calculate overloaded elution profiles of the pure enantiomers. The calculated and the experimental profiles agree excellently in all cases if the former are derived from the Bilangmuir model. The competitive experimental data also gave excellent agreement with the Bilangmuir model. The simultaneous fit of all the data, for the single components and the racemic mixture, gave again superior agreement with the bilangmuir model. The overloaded elution profiles of samples of the racemic mixture calculated with the Bilangmuir isotherm model combined with the POR model of chromatography gave results in very good agreement with the experimental band profiles of large samples of the racemic mixture. This confirms that in numerous cases the whole set of competitive isotherms of two enantiomers can be derived from the experimental data obtained only with the racemic mixture.

Design of chromatographic separations on reversed phase

The accurate determination of adsorption isotherms is of key importance in the design and optimization of preparative chromatographic bulk separations and purifications. Issues to be considered involve other things: limited amount of test material, particularly in the case of the development of drugs; multicomponent mixture with widely different concentration levels of the main product and of the impurities. In this work, a rational procedure for the characterization of adsorption equilibria in reversed phase chromatography is proposed. This is applied to two different model separations, both involving an ascomycin derivative of industrial interest. The procedure is based on the peak fitting method and the use of a lumped pore diffusion model to simulate column dynamics. The accuracy of the obtained results is assessed thoroughly.

Adsorption equilibria of butyl- and amylbenzene on monolithic silica-based columns

The adsorption isotherms of butyl- and amylbenzene on silica monolithic columns were measured by frontal analysis. The external, internal and total porosities of these columns were determined by inverse size-exclusion chromatography. The adsorption isotherms are concave upward in the entire concentration range investigated. They were fitted to the anti-Langmuir model, an unusual model in liquid–solid and liquid–liquid phase equilibria. Band profiles under overloaded conditions were recorded. They were in good agreement with the profiles calculated using the lumped pore diffusion model of chromatography and these adsorption isotherms.

Comparative modeling of breakthrough curves of bovine serum albumin in anion-exchange chromatography

The experimental results of a previous study of the mass transfer kinetics of bovine serum albumin (BSA) in ion-exchange chromatography, under nonlinear conditions, were reevaluated using the general rate model of chromatography. Solutions of this model were obtained numerically. The influences of axial dispersion, the resistance to mass transfer from the bulk mobile phase to the surface of the packing particles, and the intraparticle mass transfer resistances on the profiles of the breakthrough curves of BSA were investigated. The results obtained are compared to those of a previous investigation of the same data, using the simple transport–dispersive model and the lumped pore diffusion model. The results obtained show that the use of an oversimplified model for the analysis of chromatographic data can lead to erroneous interpretations of the experimental data and to misunderstandings of the fundamentals of the processes involved. Finally, a theoretical comparison between the properties and the range of application of the three models is provided.

Modified Rouchon and Rouchon-like algorithms for solving different models of multicomponent preparative chromatography

Modified Rouchon and Rouchon-like algorithms were used to solve multicomponent equilibrium-dispersive chromatographic models as well as a more general lumped pore diffusion model. The modified algorithms enable remarkable reduction of computation time and avoid computation errors that result from the original Rouchon approach for some cases of multicomponent chromatography. A comparison is given between the general chromatographic model, the lumped pore diffusion model and the equilibrium-dispersive model.