Adsorption in columns packed with porous adsorbent particles having partially fractal structures

A mathematical model is constructed and solved that could describe the dynamic behavior of the adsorption of a solute of interest in single and stratified columns packed with partially fractal porous adsorbent particles. The results show that a stratified column bed whose length is the same as that of a single column bed, provides larger breakthrough times and a higher dynamic utilization of the adsorptive capacity of the particles than those obtained from the single column bed, and the superior performance of the stratified bed becomes especially more important when the superficial velocity of the flowing fluid stream in the column is increased to accommodate increases in the system throughput. This occurs because the stratified column bed provides larger average external and intraparticle mass transfer and adsorption rates per unit length of packed column. It is also shown that increases in the total number of recursions of the fractal and the ratio of the radii between larger and smaller microspheres that make up the partially fractal particles, increase the intraparticle mass transfer and adsorption rates and lead to larger breakthrough times and dynamic utilization of the adsorptive capacity of the particles. The results of this work indicate that highly efficient adsorption separations could be realized through the use of a stratified column comprised from a practically reasonable number of sections packed with partially fractal porous adsorbent particles having reasonably large (i) total number of recursions of the fractal and (ii) ratio of the radii between larger and smaller microspheres from which the partially fractal particles are made from. It is important to mention here that the physical concepts and modeling approaches presented in this work could be, after a few modifications of the model, applied in studying the dynamic behavior of chemical catalysis and biocatalysis in reactor beds packed with partially fractal porous catalyst particles.     

Modeling and simulation of the dynamic behavior of monoliths. Effects of pore structure from pore network model analysis and comparison with columns packed with porous spherical particles

A mathematical model is presented that could be used to describe the dynamic behavior, scale-up, and design of monoliths involving the adsorption of a solute of interest. The value of the pore diffusivity of the solute in the pores of the skeletons of the monolith is determined in an a priori manner by employing the pore network modeling theory of Meyers and Liapis [J. Chromatogr. A, 827 (1998) 197 and 852 (1999) 3]. The results clearly show that the pore diffusion coefficient, Dmp, of the solute depends on both the pore size distribution and the pore connectivity, nT, of the pores in the skeletons. It is shown that, for a given type of monolith, the film mass transfer coefficient, Kf, of the solute in the monolith could be determined from experiments based on Eq. (3) which was derived by Liapis [Math. Modelling Sci. Comput., 1 (1993) 397] from the fundamental physics. The mathematical model presented in this work is numerically solved in order to study the dynamic behavior of the adsorption of bovine serum albumin (BSA) in a monolith having skeletons of radius r(o) = 0.75x10(-6) m and through-pores having diameters of 1.5x10(-6)-1.8x10(-6) m [H. Minakuchi et al., J. Chromatogr. A, 762 (1997) 135]. The breakthrough curves of the BSA obtained from the monolith were steeper than those from columns packed with porous spherical particles whose radii ranged from 2.50x10(-6) m to 15.00x10(-6) m. Furthermore, and most importantly, the dynamic adsorptive capacity of the monolith was always greater than that of the packed beds for all values of the superficial fluid velocity, Vtp. The results of this work indicate that since in monoliths the size of through-pores could be controlled independently from the size of the skeletons, then if one could construct monolith structures having (a) relatively large through-pores with high through-pore connectivity that can provide high flow-rates at low pressure drops and (b) small-sized skeletons with mesopores having an appropriate pore size distribution (mesopores having diameters that are relatively large when compared with the diameter of the diffusing solute) and high pore connectivity, nT, the following positive results, which are necessary for obtaining efficient separations, could be realized: (i) the value of the pore diffusion coefficient, Dmp, of the solute would be large, (ii) the diffusion path length in the skeletons would be short, (iii) the diffusion velocity, vD, would be high, and (iv) the diffusional response time, t(drt), would be small. Monoliths with such pore structures could provide more efficient separations with respect to (a) dynamic adsorptive capacity and (b) required pressure drop for a given flow-rate, than columns packed with porous particles.     

The dynamic behavior of a stratified column bed packed with porous adsorbent particles having partially fractal structures and a nonuniform ligand density distribution

The dynamic behavior of adsorption in a single column and in stratified column beds packed with porous adsorbent particles having partially fractal structures is studied when all columns have the same total length and the spatial ligand density distribution in the porous microspheres from which the porous adsorbent particles are made, is either uniform or nonuniform and such that the concentration of the immobilized ligands (active sites) increases monotonically from the center of the microspheres to their outer surface. The total number of immobilized ligands in the porous adsorbent particles has the same value whether the spatial ligand density distribution is uniform or nonuniform. The results in this study clearly show that for a given value of the superficial velocity of the flowing fluid stream in the column (for a given value of throughput) the breakthrough time is significantly increased when the radius of the microspheres is decreased, the total number of sections of the stratified column bed is increased, and the spatial ligand density distribution employed in the microspheres is nonuniform. Furthermore, when the superficial velocity of the flowing fluid stream in the column is increased (throughput is increased) the effect that (i) the reduction in the radius of the microspheres and (ii) the increase in the number of sections of the stratified column bed have on providing robust and effective dynamic adsorptive capacity and smaller reductions on the breakthrough time is substantially larger than that realized through the use of the nonuniform ligand density distribution. Similar trends are also observed in the dynamic behavior of adsorption in the systems studied here when the value of the concentration of the adsorbate in the flowing fluid stream entering the column (inlet concentration) has such a high magnitude that the value of the equilibrium concentration of the adsorbate in the adsorbed phase determined from the equilibrium Langmuir isotherm that would correspond to the inlet concentration of the adsorbate in the flowing fluid stream is, for all practical purposes, at its saturation limit.     

Perfusion chromatography: Effect of micropore diffusion on column performance in systems utilizing perfusive adsorbent particles with a bidisperse porous structure

A mathematical model describing single-component and multi-component adsorption in columns with bidisperse perfusive or bidisperse purely diffusive adsorbent particles is constructed and presented. The model is used to study the adsorption of lysozyme onto monocional anti-lysozyme in columns with bidisperse porous adsorbent particles. The influence of the effective pore diffusion coefficient of the adsorbate in the microparticles (microspheres) and the effects of particle size and intraparticle convective flow on column performance are examined. The results for the systems studied indicate that the systems with bidisperse perfusive particles provide a higher dynamic utilization of the adsorptive capacity of the column than the systems having bidisperse purely diffusive particles.     

Why Does the Linear Driving Force Model for Adsorption Kinetics Work?

The Linear Driving Force (LDF) model for gas adsorption kinetics is frequently and successfully used for analysis of adsorption column dynamic data and for adsorptive process designs because it is simple, analytic, and physically consistent. Yet, there is a substantial difference in the characteristics of isothermal batch uptake curves on adsorbent particles by the LDF and the more rigorous Fickian Diffusion (FD) model. It is demonstrated by using simple model systems that the characteristics of the adsorption kinetics at the single pore or the adsorbent particle level are lost in (a) evaluating overall uptake on a heterogeneous porous solid, (b) calculating breakthrough curves from a packed adsorbent column, and (c) establishing the efficiency of separation by an adsorptive process due to repeated averaging of the base kinetic property. That is why the LDF model works in practice.     

Novel general expressions that describe the behavior of the height equivalent of a theoretical plate in chromatographic systems involving electrically-driven and pressure-driven flows

Novel general expressions are constructed and presented that describe the behavior of the height equivalent of a theoretical plate (plate height), H, as a function of the linear velocity, Vx, along the axis, x, of the column and the kinetic parameters that characterize the mass transfer and adsorption mechanisms in chromatographic columns. Open tube capillaries as well as columns packed with either non-porous or porous particles are studied. The porous particles could have unimodal or bimodal pore-size distributions and intraparticle convective fluid flow and pore diffusion are considered. The expressions for the plate height, H, presented in this work could be applicable to high-performance liquid chromatography (HPLC) and capillary electrochromatography (CEC) systems, and could be used together with experimental plate height, H, versus linear velocity, Vx, data to determine the values of the parameters that characterize intraparticle convective fluid flow and pore diffusion. Furthermore, chromatographic systems under unretained as well as under retained conditions are examined. The experimental values of the plate height, H, versus the linear velocity, Vx, for a CEC system involving charged porous silica C8 particles and an uncharged analyte are compared with the theoretical results for the plate height, H, obtained from the expressions presented in this work. The agreement between theory and experiment is good, and the results indicate that the magnitude of the intraparticle electroosmotic flow (EOF) in the pores of the particles is substantial while the pore diffusion coefficient was of small magnitude. But the overall intraparticle mass transfer resistance in these particles was low because of the significant contribution of the intraparticle EOF. Simulation results are also presented (i) for a hybrid HPLC-CEC system, and (ii) for different CEC systems involving open capillaries as well as packed columns having non-porous or porous particles. The analysis of the results indicates (a) the reasons for the superior performance exhibited by the hybrid HPLC-CEC system over the performance obtained when the system is operated only in the HPLC mode, and (b) the operational configuration and the properties that the structure of the porous particles would have to have in CEC systems involving uncharged or charged analytes under unretained or retained conditions in order to obtain high CEC efficiency (low values of the plate height, H).     

Analysis of mass transport models for protein adsorption to cation exchanger by visualization with confocal laser scanning microscopy

The mass transfer of bovine serum albumin (BSA) to a cation exchanger, SP Sepharose FF, has been studied by finite batch adsorption experiments. The uptake curve was simulated with three mass transport models (i.e., effective pore diffusion model, surface diffusion model and Maxwell-Stefan model) incorporating the particle size distribution of the adsorbent particles. All the three models can simulate the uptake curves reasonably well. However, how well these models could simulate the real concentration profile within the adsorbent particle cannot be verified by the fitness of the models to the uptake curve. Thus, confocal laser scanning microscopy (CLSM) was used to visualize protein uptake to the porous adsorbent particles during the batch experiments. Using a fluorescent dye-labeled bovine serum albumin (BSA) for the dynamic adsorption experiments, the radial concentration profiles of the labeled BSA molecules into individual adsorbent particles at different times were obtained from the CLSM images. The protein distribution profiles within various particle diameters at different time were compared with the radial protein distributions predicted from the models. It reveals that surface diffusion model describes the intraparticle protein concentration profiles better than the other two models.     

Adsorption in a stratified column bed packed with porous particles having partially fractal structures and a distribution of particle diameters

Stratified column bed systems whose sections are formed by packing adsorbent particles with a partially fractal structure are proposed and studied. The simulation results clearly show that the breakthrough times and the shape of the breakthrough curves obtained from stratified column beds are significantly larger and sharper than those obtained from conventional columns. The stratified column beds provide, to the designer and user of chromatographic column systems, more degrees of freedom with respect to the number of parameters and variables that could be controlled in the design, construction, and operation of efficient chromatographic adsorption systems. Furthermore, the results suggest that the stratified column beds could provide a higher dynamic adsorptive capacity than conventional columns when it is required to increase the column throughput.     

Evaluation of new high-density ion exchange adsorbents for expanded bed adsorption chromatography

New adsorbents Q HyperZ and CM HyperZ composed of hydrogel-filled porous zirconium oxide particles were evaluated for expanded bed adsorption applications in the present work. The HyperZ adsorbents have wet density of 3.16 g ml(-1), particle size of 44.5-100.8 microm and average sphere diameter of 67 microm. The bed expansion as the function of flow velocity and fluid viscosity was measured and correlated with Richardson-Zaki equation. The suitable expansion factor was considered less than 2.5, while the corresponding flow velocity was about 450 cmh(-1). Liquid mixing in the bed was determined to evaluate the stability of expanded bed. The Bodenstein numbers tested were higher than 40 and the axial mixing coefficients (D(ax)) were between 0.5 and 9.7x10(-6)m(2)s(-1), which demonstrated that a stable expanded bed could be formed under suitable operation conditions. Bovine serum albumin (BSA) and lysozyme were used as model proteins to estimate the adsorption capacities of Q and CM HyperZ, respectively. The maximum equilibrium adsorption of Q and CM HyperZ could reach 45.7 and 27.2 mg g(-1) drained adsorbents, respectively. It was found that yeast cells had little influence on the adsorption capacities of the two adsorbents tested. The dynamic adsorption capacity of BSA at 10% breakthrough with Q HyperZ was 35.9 mg g(-1) drained adsorbent at flow velocity of 100 cm h(-1) for packed bed adsorption. The values for expanded bed adsorption were 34.4 mg g(-1) drained adsorbent at flow velocity of 200 cm h(-1), 33.6 mg g(-1) drained adsorbent at 300 cm h(-1) and 31.7 mg g(-1) drained adsorbent 400 cm h(-1). The results demonstrated that Q HyperZ and CM HyperZ are suitable for expanded bed adsorption of biomolecules.     

Modeling and Analysis of the Electrokinetic Mass Transport and Adsorption Mechanisms of a Charged Adsorbate in Capillary Electrochromatography Systems Employing Charged Nonporous Adsorbent Particles

Mass-transfer systems based on electrokinetic phenomena (i.e., capillary electrochromatography (CEC)) have shown practical potential for becoming powerful separation methods for the biotechnology and pharmaceutical industries. A dynamic mathematical model, consisting of the momentum balance and the Poisson equations, as well as the unsteady-state continuity expressions for the cation and anion of the background electrolyte and of a positively charged analyte (adsorbate), is constructed and solved to determine quantitatively the electroosmotic velocity, the electrostatic potential, the concentration profiles of the charged species in the double layer and in the electroneutral core region of the fluid in the interstitial channels for bulk flow in the packed chromatographic column, and the axial current density profiles as the adsorbate adsorbs onto the negatively charged fixed sites on the surface of the nonporous particles packed in the chromatographic column. The frontal analysis mode of operation is simulated in this work. The results obtained from model simulations provide significant physical insight into and understanding of the development and propagation of the dynamic profile of the concentration of the adsorbate (analyte) and indicate that sharp, highly resolved adsorption fronts and large amounts of adsorbate in the adsorbed phase for a given column length can be obtained under the following conditions: (i) The ratio, gamma(2, 0), of the electroosmotic velocity of the mobile liquid phase at the column entrance after the adsorption front has passed the column entrance to the electrophoretic velocity of the anion is very close to -1. The structure of the equations of the model and model simulations indicate that a stable adsorption front cannot develop when gamma(2, 0) is less than -1 unless the value of the mobility of the cation is less than the value of the mobility of the analyte, which may be a rare occurrence in practical CEC systems. (ii) The ratio of the mobility of the cation to the mobility of the analyte is less than two orders of magnitude. This effect becomes more significant as the value of the equilibrium adsorption constant, K(A, 3), of the analyte increases. (iii) The concentration of the analyte relative to the concentration of the cation is increased (feed solutions with less dilute concentrations of the analyte are employed). Therefore, to obtain good performance for CEC systems operated in the frontal analysis mode (well-resolved adsorption fronts and high adsorbate amounts in the adsorbed phase), one can choose an electrolyte whose cation has a mobility that is not more than one or two orders of magnitude greater than the mobility of the analyte and whose anion has a mobility such that the value of gamma(2, 0) is close to -1; one can then bring the value of gamma(2, 0) closer to -1 by decreasing the particle diameter, d(p), and/or making the value of the surface charge density, delta(0), of the particles more negative (in effect, making the value of the zeta potential, zeta(p), at the surface of the particles more negative at time t=0) to change the value of the velocity, |(x=0), of the electroosmotic flow (EOF) at the column entrance (|(x=0) is determined after the adsorption front has passed the column entrance). This approach could provide conditions in the column that avoid overloading of the adsorbate. One can obtain faster breakthrough times at the sacrifice of resolution and utilization of the adsorptive capacity of the packed bed if one employs a cation whose mobility is very large relative to the mobility of the analyte and/or an anion that provides a value of gamma(2, 0) significantly greater than -1. If it is possible, one can increase the concentration of the analyte in the feed stream to avoid sacrificing resolution and adsorptive capacity of the packed bed and still decrease the time at which breakthrough occurs. Also, the dynamic behavior of the axial current density, i(x), profiles indicates that the magnitude of i(x) and/or the change in the value of i(x) across the adsorption front could serve as a measurement for the rate of propagation of the adsorption front through the column. Furthermore, the effect of the decreased magnitude of the velocity of the EOF in the region of the column where the analyte is present in the adsorbed phase could act to decrease the effect of tailing when CEC systems are operated in the pulse injection mode (analytical electrochromatography) because the higher velocity of the fluid upstream of the migrating adsorption zone may compress the tail of the peak. Copyright 2001 Academic Press.     

Pore size distributions of ion exchangers and relation to protein binding capacity

The pore structure of chromatographic media directly influences macromolecular transport and adsorption, and consequently separation resolution and loading capacity in chromatographic separations. The pore size distribution (PSD) is therefore a central structural characteristic of chromatographic materials and a critical determinant of chromatographic behavior. In this work the PSDs of a set of commercial anion exchangers were determined by inverse size-exclusion chromatography (ISEC). The PSDs were further utilized to develop relations to functional properties of adsorbents, such as intraparticle diffusivity, and static and dynamic binding capacities. We find that the detailed PSD is useful in semi-quantitative understanding of chromatographic behavior. However, more accurate prediction of column behavior requires more thorough knowledge of the pore structure, specifically the connectivity of the pore network, as well as improved understanding of the function of grafted resins.     

The interplay of diffusional and electrophoretic transport mechanisms of charged solutes in the liquid film surrounding charged nonporous adsorbent particles employed in finite bath adsorption systems

A model that describes the diffusive and electrophoretic mass transport of the cation and anion species of a buffer electrolyte and of a charged adsorbate in the liquid film surrounding nonporous adsorbent particles in a finite bath adsorption system, in which adsorption of the charged adsorbate onto the charged surface of the nonporous particles occurs, is constructed and solved. The dynamic behavior of the mechanisms of this model explicitly demonstrates (a) the interplay between the diffusive and electrophoretic molar fluxes of the charged adsorbate and of the species of the buffer electrolyte in the liquid film surrounding the nonporous adsorbent particles, (b) the significant effect that the functioning of the electrical double layer has on the transport of the charged species and on the adsorption of the charged adsorbate, and (c) the substantial effect that the dynamic behavior of the surface charge density has on the functioning of the electrical double layer. It is found that at equilibrium, the value of the concentration of the charged adsorbate in the fluid layer adjacent to the surface of the adsorbent particles is significantly greater than the value of the concentration of the adsorbate in the finite bath, while, of course, the net molar flux of the charged adsorbate in the liquid film is equal to zero at equilibrium. This result is very different than that obtained from the conventional model that is currently used to describe the transport of a charged adsorbate in the liquid film for systems involving the adsorption of a charged adsorbate onto the charged surface of nonporous adsorbent particles; the conventional model (i) does not consider the existence of an electrical double layer, (ii) assumes that the transport of the charged adsorbate occurs only by diffusion in the liquid film, and (iii) causes at equilibrium the value of the charged adsorbate in the liquid layer adjacent to the surface of the particles to become equal to the value of the concentration of the charged adsorbate in the liquid of the finite bath. Furthermore, it was found that a maximum can occur in the dynamic behavior of the concentration of the adsorbate in the adsorbed phase when the value of the free molecular diffusion coefficient of the adsorbate is relatively large, because the increased magnitude of the synergistic interplay between the diffusive and electrophoretic molar fluxes of the adsorbate in the liquid film allows the adsorbate to accumulate (to be entrapped) in the liquid layer adjacent to the surface of the adsorbent particles faster than the concentrations of the electrolyte species, whose net molar fluxes are significantly hindered due to their opposing diffusive and electrophoretic molar fluxes, can adjust to account for the change in the surface charge density of the particles that arises from the adsorption of the charged adsorbate. The results presented in this work also have significant implications in finite bath adsorption systems involving the adsorption of a charged adsorbate onto the surface of the pores of charged porous adsorbent particles, because the diffusion and the electrophoretic migration of the charged solutes (cations, anions, and charged adsorbate) in the pores of the adsorbent particles will depend on the dynamic concentration profiles of the charged solutes in the liquid film surrounding the charged porous adsorbent particles. The results of the present work are also used to illustrate how the functioning of the electrical double layer could contribute to the development of inner radial humps (concentration rings) in the concentration of the adsorbate in the adsorbed phase of charged porous adsorbent particles.     

Flow-through particles for the high-performance liquid chromatographic separation of biomolecules: perfusion chromatography

This paper reports a new technique for reducing resistance to stagnant mobile phase mass transfer without sacrificing high adsorbent capacity or necessitating extremely high pressure operation. The technique involves the flow of liquid through a porous chromatographic particle, and has thus been termed "perfusion chromatography". This is accomplished with 6000-8000 A pores which transect the particle. Data from electron microscopy, column efficiency, frontal analysis and theoretical modelling all suggest that mobile phase will flow through these large pores. In this manner, solutes enter the interior of the particles through a combination of convective and diffusional transport, with convection dominating for Peclet numbers greater than one. The implications of flow through particles on bandspreading, resolution and dynamic loading capacity are examined. It is shown that the rate of solute transport is strongly coupled to mobile phase velocity such that bandspreading, resolution of proteins and dynamic loading capacity are unaffected by increases in mobile phase velocity up to several thousand centimeters per hour. The surface area of this very large-pore diameter material is enhanced by using a network of smaller, 500-1500 A interconnecting pores between the throughpores. Scanning electron micrographs show that the pore network is continuous and that no point in the matrix is more than 5000-10,000 A from a through-pore. As a consequence, diffusional path lengths are minimized and the large porous particles take on the transport characteristics of much smaller particles but with a fraction of the pressure drop. Capacity and resolution studies show that these materials bind and separate an amount of protein equivalent to that of conventional high-performance liquid chromatography as well as low performance agarose-based media at greater than 10-100 times higher mobile phase velocity with no loss in resolution.     

Determination of the intraparticle electroosmotic volumetric flow-rate, velocity and Peclet number in capillary electrochromatography from pore network theory

The results obtained from the pore network model employed in this work, clearly show that the magnitudes of the intraparticle electroosmotic volumetric flow-rate, Qintrap, and velocity, (v(intrap,x)), in the pores of the charged porous silica particles considered in this study are greater than zero. The intraparticle Peclet number, Pe(intra, of a solute in these charged porous silica particles would be greater than zero, and, in fact, the magnitude of the intraparticle Peclet number, Pe(intrap), of lysozyme is greater than unity for all the values of the pore connectivity, nT, of the intraparticle pores and of the applied electric potential difference per unit length, Ex, along the axis of the capillary column considered in this work. Furthermore, the values of the intraparticle electroosmotic volumetric flow-rate, Qintrap, and velocity, (v(intrap,x)), as well as the magnitude of the pore diffusion coefficient, Dp, of the solute increase as the value of the pore connectivity, nT, of the intraparticle pores increases. The intraparticle electroosmotic flow can contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (i) decreasing the intraparticle mass transfer resistance, (ii) decreasing the dispersive mass transfer effects, and (iii) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained.     

Chromatography in pore networks II — The role of structure and adsorption in the band broadening

Summary The complex intraparticle structure typical of chromatographic column packings has been analyzed by use of an equivalent network model which emphasizes pore size distribution and connectivity. Special attention is given as to the way in which diffusion and adsorption interact and display modified peak spreading characteristics according to the morphology of the pore space. This study reveals a very significant increase in the column band broadening over that expected from physical adsorption which can arise from particular distributions of pore sizes. This has implications for designing packings which take advantage of the separating power due to adsorption but do not compromise the resolution of the chromatographic system.     

漆酚醛树脂多孔微球对有机物的吸附性能

研究了由悬浮缩聚法制备的多孔漆酚醛树脂微球对乙二胺、二乙烯三胺和茶碱,以及苯、二甲苯、氯仿和四氯化碳等气体的吸附性能,并研究了吸附时间对乙二胺、二乙烯三胺和茶碱吸附性能的影响。结果表明,树脂中的酚羟基因能与胺基产生酸碱之间的作用而吸附乙二胺和二乙烯三胺,其吸附量分别为320.9mg/g、222.2mg/g;该多孔微球亦能吸附有机物气体,尤其对氯仿、四氯化碳的吸附性能较佳,其吸附量分别为248.1mg/g和119.7mg/g。     

Mass transfer and fluid flow visualization in packed and fluidized beds by the adsorption method

Mass transfer coefficient (j _D ) between fluid and column wall in liquid packed and fluidized beds of spherical inert particle has been studied experimentally using adsorption method. Experiments were conducted in column 40 mm in diameter for packed and fluidized beds. In all runs mass transfer rates were determined in presence of spherical glass particles 2.06 mm in diameter. This paper introduced adsorption method as very suitable method for studies of mass transfer and for fluid flow visualization. The adsorption method is based on the dynamic adsorption of an organic dye onto a surface covered with a thin layer of a porous adsorbent. Local and average mass transfer coefficients were determinated from the surface color intensity of the foils of silica gel. Correlation j _D = f(Re) was derived using mass transfer coefficients data. The article is published in the original.     

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.     

Role of convection and diffusion in a single pore with adsorptive walls

The importance of intraparticle convection during and after the pressurization step of a pressure swing adsorption process is assessed by considering a single, cylindrical, closed-end pore with adsorptive walls exposed to a binary mixture of an adsorbable component and an inert gas. Gas-phase mass transfer is comprised of pore diffusion and convection, and surface diffusion occurs in the adsorbed phase. Concentration, velocity, and flux profiles are obtained inside the pore both during and after pressurization. Solutions are obtained analytically for the limiting cases of no adsorption, no diffusion, and no inert gas. Complete solutions of the material balance equations are obtained by orthogonal collocation. The pressurization rate, the adsorptive capacity of the pore wall, and the gas-phase mole fraction are varied over a wide range to study the relative importance of convection and diffusion under different conditions. Results show that convection makes a large contribution to transport in the pore except when the adsorbable component has a small mole fraction.     

Hydrophobic interaction chromatography of proteins. IV. Protein adsorption capacity and transport in preparative mode

The adsorption isotherms of four model proteins (lysozyme, α-lactalbumin, ovalbumin, and BSA) on eight commercial phenyl hydrophobic interaction chromatography media were measured. The isotherms were softer than those usually seen in ion-exchange chromatography of proteins, and the static capacities of the media were lower, ranging from 30 to 110 mg/mL, depending on the ammonium sulfate concentration and the protein and adsorbent types. The protein-accessible surface area appears to be the main factor determining the binding capacity, and little correlation was seen with the protein affinities of the adsorbents. Breakthrough experiments showed that the dynamic capacities of the adsorbents at 10% breakthrough were 20-80% of the static capacities, depending on adsorbent type. Protein diffusivities in the adsorbents were estimated from batch uptake experiments using the pore diffusion and homogeneous diffusion models. Protein transport was affected by the adsorbent pore structures. Apparent diffusivities were higher at lower salt concentrations and column loadings, suggesting that adsorbed proteins may retard intraparticle protein transport. The diffusivities estimated from the batch uptake experiments were used to predict column breakthrough behavior. Analytical solutions developed for ion-exchange systems were able to provide accurate predictions for lysozyme breakthrough but not for ovalbumin. Impurities in the ovalbumin solutions used for the breakthrough experiments may have affected the ovalbumin uptake and led to the discrepancies between the predictions and the experimental results.