Influence of particle diameter distribution on protein recovery in the expanded bed adsorption process

The General Rate model has been developed and solved to describe protein adsorption in an expanded bed. The model takes into account axial and local variation of particle size distribution (PSD), external and intra-particle mass transfer resistances, and dispersion in liquid phase. The influence of PSD on breakthrough profiles has been analysed. The simulation results show that for a significantly high expanded bed the lower part of the breakthrough curve profiles, calculated for local particle size distribution (LPSD) and for axial average particle size distribution (APSD) are very similar. However, the upper part of breakthrough profiles calculated for LPSD approaches inlet concentration much more slowly than those calculated for APSD. The retention times of the lower part of uptake curves calculated with average particle diameter are constantly shorter than those obtained from LPSD. For the calculation of the dynamic capacity (DC), the LPSD can be replaced by APSD for large expanded bed heights. Using breakthrough profiles calculated for average particle size, DC values are constantly underestimated.     

Measurement and modeling of the equilibrium behavior of the Tröger's base enantiomers on an amylose-based chiral stationary phase

The binary isotherms of the two enantiomers of Tr?ger's base were measured on a system made of pure 2-propanol as the mobile phase and of Chiralpak AD, a chiral stationary phase (CSP) based on amylose tri-(3,5-dimethylphenyl carbamate). The experimental data were acquired using both frontal analysis and the perturbation method. The results obtained are most unusual. The adsorption of the more-retained (-)-enantiomer is not competitive: the amount adsorbed onto the CSP at equilibrium with a constant concentration of the (-)-enantiomer is independent of the concentration of the (+) enantiomer. On the other hand, the adsorption of the less-retained enantiomer is cooperative: the amount of this (+)-enantiomer adsorbed by the CSP at equilibrium with a constant concentration of this enantiomer increases with increasing concentration of the (-)-enantiomer. Such a phenomenon has hardly ever been reported. A model equation is proposed that accounts well for all these isotherm data.     

Non-linear electrical effect in graded-electron concentration silicon

A gradient of carrier concentration in semiconductors can create a double-frequency internal electric field which is parallel to this gradient and perpendicular to the applied a.c. field. This warm-carrier effect was measured in silicon specimens with a gradient of electron concentration, at 77 and 300 K, under applied fields from 1 to 10 V m^-1 and within the frequency range of 0.3–20 kHz. A comparison between experimental data and a theoretical model is discussed.     

Phase diagram of silicon from atomistic simulations

In this Letter we present a calculation of the temperature-pressure phase diagram of Si in a range of pressures covering from -5 to 20 GPa and temperatures up to the melting point. The phase boundaries and triple points between the diamond, liquid, beta-Sn, and Si34 clathrate phases are reported. We have employed efficient simulation techniques to calculate free energies and to numerically integrate the Clausius-Clapeyron equation, combined with a tight-binding model capable of an accuracy comparable to that of first-principles methods. The resulting phase diagram agrees well with the available experimental data.     

Adsorption of naproxen enantiomers from solutions on chemically modified cellulose. The effect of a polar component of a liquid phase

The influence of mobile phase composition (hexane-ethanol with the addition of 0.1 vol.% of trifluoroacetic acid) on the adsorption of the naproxen enantiomers on a chiral adsorbent Chiralcel OJ-H was investigated. Methods of linear and nonlinear chromatography were used to investigate adsorption thermodynamics at infinite dilution and to measure adsorption isotherms for solutions containing 10 and 20 vol.% of ethanol. It was found that two groups of adsorption sites coexist on the surface of the adsorbent in contact with the mentioned solvent, strong and weak ones, with the strong adsorption sites contributing mainly to the adsorption of naproxen. The effect of ethanol content on the retention of naproxen consists of the change in the number of the strong adsorption sites and regulating solvation property of a solvent.     

The influence of mobile phase demixion on thin-layer chromatographic enantioseparation of ibuprofen and naproxen

In our earlier article we presented the results of tracing the enantioseparation of the two test analytes (ibuprofen and naproxen) by means of video densitometry and scanning densitometry. In that way we demonstrated an excellent performance of this combined approach to the thin-layer chromatographic detection in the area of enantioseparation. In this paper we study an impact of the four different mobile phases on the enantioseparation of the scalemic mixtures of ibuprofen and naproxen on the silica gel layers impregnated with L-arginine as chiral selector. The main component of all the investigated mobile phases is 2-propanol. Mobile phase 1 consists of pure 2-propanol, while mobile phases 2-4 contain, respectively, ca. 0.66, 1.32, and 1.98 g/L of glacial acetic acid in 2-propanol. Acetic acid is used to protonate L-arginine, as the involved retention mechanism consists of the ion pair formation between L-arginine in the cationic form and the chiral 2-arylpropionic acids (2-APAs), ibuprofen and naproxen, in the anionic form. It is shown that in the absence of glacial acetic acid no enantioseparation can be obtained. Then with adding of 0.66 g/L glacial acetic acid partial enantioseparation of the naproxen and ibuprofen antimers is obtained, with a simultaneous effect of the mobile phase demixion. With the amount of acetic acid increasing, the effect of demixion becomes increasingly perceptible. In that case the displacement effect is observed (and mathematically modeled), which results in compressing of the antimer pairs by the second front of mobile phase. The obtained results allow a deeper insight into the mechanism of enantioseparation with the two test 2-APAs. A combined impact of the crystalline chirality of silica gel and the molecular chirality of L-arginine on the vertical and the horizontal enantioseparation of ibuprofen and naproxen is also discussed.     

Estimation of adsorption isotherm parameters with inverse method--possible problems

In recent years the inverse method (IM) has been frequently applied to estimate of isotherm parameters. The IM has been used for adsorption process modeling for one, two and even three component chromatography. This method requires only a few injections with various sample concentrations, so the solute consumption and time requirements are very modest. The successful estimation of isotherm parameters with IM depends on applied chromatography column model and a numerical method used to solve the model. For HPLC column the classical equilibrium-dispersive (ED) model can be used. This model is solved frequently with very fast Rouchon finite difference method. However, the accuracy of computations with Rouchon method is decreasing with increase of the number of analyzed components. The aim of this work is the comparison of the results obtained with inverse method when ED model was solved with Rouchon or orthogonal collocation on finite element (OCFE) scheme. Assuming that solution of ED model with OCFE method can be regarded as real a solution, it was found that the Rouchon scheme may not give satisfactory results even for column with 10,000 theoretical plates for three component chromatography. Moreover, the optimal conditions for separation, calculated with Rouchon method, can be remarkably different from that obtained with the OCFE method. The next aim of this work is the presentation of Craig method application to estimation of model parameters with IM.     

Kinetic Models of the Polymerization of an AB2 Monomer

Two mean‐field kinetic models of the polymerization of an AB₂ monomer that lead to hyperbranched polymers are presented. The first model deals with branched molecules only and constitutes a new version of the Flory theory. Its modification, which takes into account ring formation, is the second model. Preliminary results of the application of the models are shown and discussed.     

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.