Mechanism and kinetics of protein transport in chromatographic media studied by confocal laser scanning microscopy. Part I. The interplay of sorbent structure and fluid phase conditions

An experimental study on the interplay of sorbent structure and fluid phase conditions (pH) has been carried out examining adsorption and transport of bovine serum albumin (BSA) and a monoclonal antibody (IgG 2a) on SP Sepharose Fast Flow and SP Sepharose XL. SP Sepharose Fast Flow is characterised by a relatively open pore network, while SP Sepharose XL is a composite structure with ligand-carrying dextran chains filling the pore space. Both adsorbents have similar ionic capacity. Protein transport and adsorption profiles were evaluated using confocal laser scanning microscopy. Under all investigated conditions, BSA uptake could be adequately explained by a pore diffusion mechanism. The adsorption profiles obtained for IgG 2a, however, indicated that changes in fluid phase conditions as well as a change in the solid phase structure could result in a more complex uptake mechanism as compared to pore diffusion alone. This mechanism results in a fast transport of proteins into the adsorbent, followed by an overshoot of protein in the center of the sorbent and a setback towards a homogeneous adsorption profile.     

A heterogeneous model for gas transport in carbon molecular sieves

A dual resistance model with distribution of either barrier or pore diffusional activation energy is proposed in this work for gas transport in carbon molecular sieve (CMS) micropores. This is a novel approach in which the equilibrium is homogeneous, but the kinetics is heterogeneous. The model seems to provide a possible explanation for the concentration dependence of the thermodynamically corrected barrier and pore diffusion coefficients observed in previous studies from this laboratory on gas diffusion in CMS. The energy distribution is assumed to follow the gamma distribution function. It is shown that the energy distribution model can fully capture the behavior described by the empirical model established in earlier studies to account for the concentration dependence of thermodynamically corrected barrier and pore diffusion coefficients. A methodology is proposed for extracting energy distribution parameters, and it is further shown that the extracted energy distribution parameters can effectively predict integral uptake and column breakthrough profiles over a wide range of operating pressures.     

A parallel pore and surface diffusion model for predicting the adsorption and elution profiles of lispro insulin and two impurities in gradient-elution reversed phase chromatography

Lispro insulin (LPI), a widely used insulin analog, is produced on tons per year scale. Linear gradient reversed phase chromatography (RPC) is used in the production to separate LPI from two impurities, which differ from LPI by a single amino acid residue. A chromatography model for the ternary separation in this RPC process is unavailable from the literature. In this study, a parallel pore and surface diffusion model is developed and verified for LPI and the two impurities. The LPI can be recovered with high yield (≥95%) and high purity (>99.5%). A new method, which requires a small amount of materials and an order of magnitude fewer experiments, has been developed to estimate the solvent-modulated isotherm parameters. A modified reversed phase modulator model is developed to correlate the adsorption isotherms of LPI and impurities. A strategy has been developed for estimating the intrinsic pore diffusivity and surface diffusivity. Since the adsorption affinities decrease by more than three orders of magnitude as organic fraction (φ) increases from 0.19 to 0.40, the apparent diffusivities based on a pore diffusion model or a surface diffusion model can also vary by several orders of magnitude. For this reason, a pore diffusion model or a surface diffusion model with a constant apparent diffusivity cannot predict closely the chromatograms over the same range of organic fractions, concentrations, and loadings. The parallel pore and surface diffusion model with constant diffusivities can predict closely the frontal and elution profiles over a wide range of organic fractions (0.19-0.40), LPI concentrations (0.05-18 g/L), linear velocities (<10 cm/min), and loading volume (0.0004-13 CV). For large loading stepwise and linear gradient elution, the peaks of LPI and the impurities are strongly focused by self-sharpening and gradient focusing effects as a result of the steep decrease of adsorption affinity from the loading φ (0.19) to elution φ (≥0.27). When the ratio of diffusion rate to convection rate is greater than 10, spreading due to diffusion is largely compensated by the focusing effects. As a result, a pore diffusion model with a constant pore diffusivity can predict closely the elution profiles in stepwise and linear gradient elution. The experimental yield values (≥95%) can be predicted to within ±1% by the model.     

Experimental verification of sample-solvent induced modifier-solute peak interactions in biochromatography

In a previous theoretical analysis based on equilibrium theory it has been shown how differences in the sample and elution modifier concentrations can lead to unexpected behavior of the solute eluted peaks such as retention time distortion, peak deformation and peak doubling. All these features are verified experimentally in this work using the polypeptide calcitonin and a variant of a specific monoclonal antibody as chromatographic model systems. For both experimental systems, the retention time distortion can be predicted with high accuracy by the solution of the equilibrium theory model. For the polypeptide, the predictions from the theory about the occurrence of peak deformation and double peaks has been successfully verified by a series of tailored experiments with positive as well as negative modifier perturbations.     

Hypercross-linked polystyrene and its potentials for liquid chromatography: a mini-review

A recently introduced method [Biotechnol. Prog. 13 (1997) 429] for determining intraparticle mass transfer parameters in high speed liquid chromatography is considered in the present study for the case where the eluite adsorbs onto the stationary phase. The validity of the method was verified theoretically using simulated elution profiles and then applied to experimental data obtained using columns packed with either a macroporous or a gel-filled gigaporous stationary phase. For this purpose, experimental measurements were made using alpha-lactalbumin and bovine serum albumin as eluites at several retention factors. Apparent intraparticle diffusivities measured for the gel-filled gigaporous stationary phase were seen to increase with the retention factor, which indicates that for this material surface diffusion is a significant mechanism of mass transfer under retained conditions. Data obtained on the macroporous stationary phase revealed that the intraparticle diffusivity was independent of the retention factor, which suggests that pore diffusion remains the principal mass transfer mechanism even under conditions where proteins are adsorbed on the column packing.     

Methane adsorption and diffusion in a model nanoporous carbon: an atomistic simulation study

A constricted slit model was introduced to improve, one step further, the performance of the simple slit model in prediction of the adsorption and diffusion behavior of simple molecules in the nanoporous carbons (NPCs). The grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations are performed to study the adsorption and diffusion behavior of methane within the constricted slit models. The models are called slit-1, 2, and 3 with constriction heights 5, 7, and 9 Å respectively. For comparison, we used the slit-0 name for the simple slit without constriction. Adsorption results show that at low pressures, the constriction increases the adsorbed amount irrespective of its height. Slit-2 with a constriction height as a molecular diameter has the greatest heat of adsorption and has highest loading at pressures up to 3,000 kPa. At high pressures, when all pores are filled, the adsorption trend is in line with the pore volumes of slits where slit-0 with higher pore volume is dominant. The density profiles in the models were calculated and examined. The spatial distribution of adsorbed methane molecules was examined by various radial distribution functions calculated by MD. Also, MD simulation results show that the diffusion coefficient of methane decreases in constricted slits. The calculated diffusion coefficients in slit-2 in the direction of the constriction are one order of magnitude smaller than the calculated one in the simple slit model but it is far from the experimental values in the NPCs.     

Characterization and modeling of nonlinear hydrophobic interaction chromatographic systems

A general rate model was employed in concert with a preferential interaction quadratic adsorption isotherm for the characterization of HIC resins and the prediction of solute behavior in these separation systems. The results indicate that both pore and surface diffusion play an important role in protein transport in HIC resins. The simulated and experimental solute profiles were compared for two model proteins, lysozyme and lectin, for both displacement and gradient modes of chromatography. Our results indicate that a modeling approach using the generate rate model and preferential interaction isotherm can accurately predict the shock layer response in both gradient and displacement chromatography in HIC systems. While pore and surface diffusion played a major role and were limiting steps for proteins, surface diffusion was seen to play less of a role for the displacer. The results demonstrate that this modeling approach can be employed to describe the behavior of these non-linear HIC systems, which may have implications for the development of more efficient preparative HIC separations.     

Theoretical modeling of water vapor transport in cellulose-based materials

The theory of mass transport in porous media is of fundamental importance for different applications such as food, paper packaging, textiles, and wood for building materials. In this study, a theoretical water vapor transport model has been developed for cellulose-based materials, such as paper and regenerated cellulose film. Pore diffusivities were determined from the dynamic moisture breakthrough experiments comprising a stack of paper sheets and regenerated cellulose films in a configuration similar to a packed adsorption column. Other mass transfer parameters were determined from transient moisture uptake rate measurements. The model incorporates pore and surface diffusion as a lump parameter into a variable effective diffusion coefficient. The mass transport, involving both pore and surface diffusions, is evaluated independently. The theoretical water vapor transmission rates (WVTRs) obtained from the model were compared with experimentally determined WVTRs measured under steady-state conditions. The theoretical model, based on intrinsic diffusion, stipulates higher WVTR values compared to the experimental results. However, the theoretical water vapor transfer rates agree well with the experimental results when external mass transfer resistance is incorporated in the model.     

Finite-element model of interaction between fungal polysaccharide and monoclonal antibody in the capsule of Cryptococcus neoformans

Many microorganisms such as bacteria and fungi possess so-called capsules made of polysaccharides which protect these microorganisms from environmental insults and host immune defenses. The polysaccharide capsule of Cryptococcus neoformans, a human pathogenic yeast, is capable of self-assembly, composed mostly of glucuronoxylomannan (GXM), a polysaccharide with a molecular weight of approximately 2,000,000, and has several layers with different densities. The objective of this study was to model pore-hindered diffusion and binding of the GXM-specific antibody within the C. neoformans capsule. Using the finite-element method (FEM), we created a model which represents the in vivo binding of a GXM-specific antibody to a C. neoformans cell taking into account the intravenous infusion time of antibody, antibody diffusion through capsular pores, and Michaelis-Menten kinetics of antibody binding to capsular GXM. The model predicted rapid diffusion of antibody to all regions of the capsule where the pore size was greater than the Stokes diameter of the antibody. Binding occurred primarily at intermediate regions of the capsule. The GXM concentration in each capsular region was the principal determinant of the steady-state antibody-GXM complex concentration, while the forward binding rate constant influenced the rate of complex formation in each region. The concentration profiles predicted by the model closely matched experimental immunofluorescence data. Inclusion of different antibody isotypes (IgG, IgA, and IgM) into the modeling algorithm resulted in similar complex formation in the outer capsular regions, but different depths of binding at the inner regions. These results have implications for the development of new antibody-based therapies.     

Couple axial gradients of potential and concentration in a cylindrical pore electrode: an impedance model

The impedance of a cylindrical pore electrode in the case where the potential gradient due to the electrolyte resistivity is coupled to the axial concentration gradient of reacting species has been calculated semi-analytically from the approximate solution reported previously for the steady-state concentration and current profiles in the pore. Complex plane impedance plots, computed by an iteration technique for the transmission line, indicate: (i) a quasi-semi-circular diffusion loop at low frequencies due to diffusion control; and (ii) a high frequency loop in which the frequency dispersion is strongly dependent on the electrode parameters (electrolyte resistivity, diffusion coefficient of the reacting species, pore depth, Tafel coefficient of the electrochemical reaction and overall current flowing through the pore).     

Model study of the effect of pore structure and condensation on multilayer adsorbate transport in porous media

A single-pore model approach to multilayer adsorbate transport in mesoporous media, previously shown to be capable of interpreting the observed behavior of relative vapor permeability PHs/PHL (or of the corresponding surface diffusion coefficient Ds), has been incorporated in a model pore network. The resulting more sophisticated model can simulate realistically the effect on PHs/PHL or Ds (i) of salient structural features of the porous medium (notably pore size dispersion and network connectivity) and (ii) of vapor condensation, which inevitably accompanies multilayer adsorbate transport in reality. An extensive generic parametric study of these effects has been performed on this basis. The results indicate that the aforementioned effects are ordinarily unlikely to induce substantial deviations of observed PHs/PHL behavior from the single-pore model benchmark. Thus, the utility of this simple model as a good basis for data analysis is confirmed, while the network model offers the possibility of exploiting external structural and other available information for a more refined interpretation of PHs/PHL behavior in particular mesoporous solid-vapor systems.     

Theoretical simulation of chromatographic separation based on random diffusion in the restricted space

The diffusion behavior of particles in the chromatography is a fundamental issue of chromatographic dynamics. The understanding of the diffusion behaviors is particularly critical to optimize the operation conditions, improve the chromatographic performance and design a new separation device. Many of the present simulations focus on chromatographic thermodynamics, and very few aim at the overall diffusion and separation process. In order to dynamically trace the trajectory of the diffusing particles and to perform simulations of the whole chromatographic process, we have developed a model based on the framework of random walk in the restricted space and performed the simulation of a single particle diffusion in the gas chromatography. The simulation parameters were determined by comparing with the experimental data. The elution profiles of n-alkanes under different flow rates were accurately simulated with the method. The results show that the relative difference between the measures and the simulations are less than 2% and 10% for the retention time and the peak width, respectively. The simulation method shows great significance for the optimization of separation conditions and the development of novel technologies of chromatographic separation.     

Numerical modeling of elution peak profiles in supercritical fluid chromatography. Part I—Elution of an unretained tracer

When chromatography is carried out with high-density carbon dioxide as the main component of the mobile phase (a method generally known as “supercritical fluid chromatography” or SFC), the required pressure gradient along the column is moderate. However, this mobile phase is highly compressible and, under certain experimental conditions, its density may decrease significantly along the column. Such an expansion absorbs heat, cooling the column, which absorbs heat from the outside. The resulting heat transfer causes the formation of axial and radial gradients of temperature that may become large under certain conditions. Due to these gradients, the mobile phase velocity and most physico-chemical parameters of the system (viscosity, diffusion coefficients, etc.) are no longer constant throughout the column, resulting in a loss of column efficiency, even at low flow rates. At high flow rates and in serious cases, systematic variations of the retention factors and the separation factors with increasing flow rates and important deformations of the elution profiles of all sample components may occur. The model previously used to account satisfactorily for the effects of the viscous friction heating of the mobile phase in HPLC is adapted here to account for the expansion cooling of the mobile phase in SFC and is applied to the modeling of the elution peak profiles of an unretained compound in SFC. The numerical solution of the combined heat and mass balance equations provides temperature and pressure profiles inside the column, and values of the retention time and efficiency for elution of this unretained compound that are in excellent agreement with independent experimental data.     

Application of the general rate model and the generalized Maxwell-Stefan equation to the study of the mass transfer kinetics of a pair of enantiomers

The general rate model of chromatography can be coupled with the generalized Maxwell-Stefan equation that describes the surface diffusion flux. The resulting model is useful to describe the behavior of two enantiomers during their separation on chiral phases, cases in which the mass transfer kinetics is known to be sluggish. A case in point is the modeling of the elution profiles of the racemic mixture of the two enantiomers of 1-phenyl-1-propanol on cellulose tribenzoate coated on silica, a popular chiral stationary phase. The competitive equilibrium isotherm behavior of the two enantiomers on the chiral stationary phase was described using the competitive Tóth isotherm model. An excellent agreement between the experimental and the calculated profiles was observed in the whole range of experimental conditions investigated, at low and high column loadings.     

Predicting gas transport in formed zeolite adsorbents from NMR studies

The self-diffusion of nitrogen, methane, and carbon monoxide within a 5A zeolitic adsorbent has been examined with use of pulsed field gradient (PFG) NMR. In all cases, the diffusion process is well-described by a refined version of the long-range diffusion model (LRDM), adapted here for use with pelletized adsorbents, which uses exclusively adsorbent porosity and isotherm data as inputs. Correlation of the experimental data with this model yields tortuosity factors that are characteristic of the adsorbate and reflect the longer diffusive path a molecule must take due to the winding nature of the pore structure. It is demonstrated that the diffusion model can be used to accurately predict the diffusion coefficients for a ternary gas mixture within a 5A zeolite. To fully characterize the diffusive process, the surface excess on the PFG NMR samples has been obtained by a novel gas-phase NMR technique that is well-suited for measuring pure and multicomponent isotherms.     

Experimental investigation of the difference in B-term dominated band broadening between fully porous and porous-shell particles for liquid chromatography using the Effective Medium Theory

The difference in B-term diffusion between fully porous and porous-shell particles is investigated using the physically sound diffusion equations originating from the Effective Medium Theory (EMT). Experimental data of the B-term diffusion obtained via peak parking measurements on six different commercial particle types have been analyzed (3 porous and 3 non porous). All particles were investigated using the same experimental design and test analytes, over a very broad range of retention factor values. First, the B-term reducing effect of the solid core (inducing an additional obstruction compared to fully porous particles) has been quantified using the Hashin-Shtrikman expression, showing that the presence of a solid core can account for a reduction of about 11% when the core diameter makes up 63% of the total particle diameter (Halo and Poroshell-particles) and a reduction of 16% when the core diameter makes up 73% (Kinetex). Remaining differences can be attributed to differences in the microscopic structure of the meso-porous material (meso-pore diameter, internal porosity or relative void volume). The much lower B-term diffusion of Halo and Kinetex particles compared to the fully porous Acquity particles (some 20-40% difference, of which about 10-15% can be attributed to the presence of the solid core) can hence largely be attributed to the much smaller internal porosity and the smaller pore size of the meso-porous material making up the shell of these particles.     

Determination of lattice and grain boundary diffusion coefficients in protective alumina scales on high temperature alloys using SEM,TEM and SIMS

Grain and grain boundary diffusion coefficients in alumina scales on FeCrAl-based ODS alloys have been determined. The boundary diffusion-coefficients have been derived by combining gravimetrically determined growth rate data with SEM and TEM analyses of the oxide scale microstructure. The diffusion coefficients determined have been used as input parameters for a computer model describing the oxygen isotope exchange between grain and grain boundary in the alumina scale which forms during a two-stage oxidation using (18)O-tracers. This comparison of the calculated tracer profiles with profiles determined experimentally by SIMS allows the estimation of the lattice diffusion coefficient of oxygen in the alumina scale.     

Pore network modelling: determination of the dynamic profiles of the pore diffusivity and its effect on column performance as the loading of the solute in the adsorbed phase varies with time

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous ion-exchange particles and along the length of the column as the loading of the adsorbate molecules on the surface of the pores occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. The pore size distribution of the porous adsorbent particles and the chemistry of the adsorption sites were unchanged in the simulations. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by: (i) the superficial fluid velocity in the column, (ii) the diameter of the adsorbent particles and (iii) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as: (a) the particle diameter and the superficial fluid velocity in the column decreased, and (b) the column length and the pore connectivity increased. In preparative chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

Diffusion in hierarchical mesoporous materials: applicability and generalization of the fast-exchange diffusion model

Transport properties of cyclohexane confined to a silica material with an ordered, bimodal pore structure have been studied by means of pulsed field gradient nuclear magnetic resonance. A particular organization of the well-defined pore structure, composed of a collection of spatially ordered, spherical mesopores interconnected via narrow worm-like pores, allowed for a quantitative analysis of the diffusion process in a medium with spatially ordered distribution of the fluid density for a broad range of the gas-liquid equilibria. The measured diffusion data were interpreted in terms of effective diffusivities, which were determined within a microscopic model considering long-range molecular trajectories constructed by assembling the alternating pieces of displacement in the two constituting pore spaces. It has further been found that for the system under study, in particular, and for mesoporous materials with multiple porosities, in general, this generalized model simplifies to the conventional fast-exchange model used in the literature. Thus, not only was justification of the applicability of the fast-exchange model to a diversity of mesoporous materials provided, but the diffusion parameters entering the fast-exchange model were also exactly defined. The equation resulting in this way was found to nicely reproduce the experimentally determined diffusivities, establishing a methodology for targeted fine-tuning of transport properties of fluids in hierarchical materials with multiple porosities.