Mathematical analysis of affinity membrane chromatography

A mathematical model including convection, diffusion and Freundlich adsorption is developed. To examine the validity of the model, the affinity membranes were prepared by coating chitosan on the nylon membranes, a ligand of poly-L-lysine was bound to the chitoan-coating membranes, and the adsorption behavior of bilirubin through the stacked affinity membranes was investigated. The agreements between the theoretical and experimental results are exceptional. Using our new model, we show that: (1) As Pe increases, the breakthrough curves become sharper. For Pe greater than 30, the effect of axial diffusion is insignificant; (2) As m increases, the time of total saturation is delayed and the loading capacity at the point of breakthrough is increased; (3) As n decreases, the time of total saturation is delayed and the loading capacity at the point of breakthrough is increased; (4) As r increases, both the time of total saturation and the loading capacity at the point of breakthrough are increased; (5) adsorption rate influences the time of total saturation strongly but contributes little to the loading capacity.     

In situ determination of adsorption kinetics of proteins in a finite bath

A method for fast in situ measurement of adsorption kinetics based on a finite bath was developed. We modified the conventional finite bath by replacing the external loop by a dip probe which enables in situ measurement of the concentration change in the contactor. Deposition of adsorbent particles on the reflection surface of the dip probe compromised measurements. Different membranes, a polyamide, a polypropylene and a nylon membrane were tested to protect the internal reflection surface of the dip probe from fouling with adsorbent particles. The nylon membrane provided efficient protection and high mass transfer evaluated by response time experiments. Unspecific adsorption of the model protein on the membrane could also be excluded. To corroborate the measurements of the dip probe the results were compared to a conventional finite bath and to a shallow-bed. The uptake curves for human polyclonal IgG at different concentrationes (0.1-3 g/l) on rProtein A Sepharose FF and MabSelect were used as model system. The effective diffusion coefficients were determined using a pore diffusion model. These values were in good agreement for all methods.     

Monitoring of mouse immunoglobulin G by flow-injection analytical affinity chromatography

A flow-injection analytical affinity chromatographic (FIAAC) system was developed for the on-line monitoring of mouse immunoglobulin G (IgG). Protein A or anti-mouse IgG antibodies immobilized on oxirane beads were filled in a miniature column. The IgG-containing samples and standards were passed through the column and detected fluorimetrically after elution with citrate buffer (pH 3 or 2.5). The on-line monitoring of mouse IgG 2a during a 7-day cultivation of hybridoma cells in a perfusion reactor by FIAAC is presented. A chemical barrier was used to prevent contamination of the reactor from the FIAAC.     

On the application of quantitative models of diffusion-controlled adsorption kinetics at fluid interfaces

The model of diffusion-controlled adsorption kinetics can be solved by different mathematical procedures. For the most important case of a Langmuir isotherm, useful solutions are summarized and extended and the ranges of application are given. New approximations are presented which can be applied to most experiments in practice.Nomenclature a _i coefficients of the collocation solution - a _L Langmuir parameter - a interaction parameter of the Frumkin isotherm - _n coefficients of a power series - c surfactant bulk concentration - c ₀ equilibrium bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - _t8 maximum surface concentration - ( _x ) Gamma function - t time - dimensionless time Dedicated to the 60th birthday of G. Kretzschmar.     

Modeling investigation of membrane biofouling phenomena by considering the adsorption of protein, polysaccharide and humic acid

The importance of solute adsorption in the biofouling membrane has been clearly verified for the performance of membrane bioreactor (MBR). In order to quantify the mechanism of static adsorption in biofouling during of MBR process, we characterize membrane biofouling caused by model solutions containing a protein (bovine serum albumin, BSA), a humic substance (humic acid, HA) and a polysaccharide (alginic acid, Alg) on commercial hydrophilic polyethersulfone (PES) membrane. For static adsorption experiments, membranes were immersed in well-defined model solutions in three temperatures (298, 308 and 318 K) to obtain equilibrium data. To determine the characteristic parameters for this process, 7 isotherm models were applied to the experimental data. Three error analysis methods; the coefficient of nonlinear regression (R(2)), the sum of the squared errors (SSE) and standard deviation of residuals (S(yx)), were used to evaluate the data and determine the best fit isotherm for each model solutions. The error values demonstrated that the Sips isotherm model provided the best fit to the experimental data. AFM images were used for determination of changes in membrane surface after adsorption. These images confirmed the results obtained from adsorption isotherm study. Thermodynamic parameters such as standard free energy (Δ(r)G(θ)), enthalpy (Δ(r)H(θ)) and entropy (Δ(r)S(θ)) changes were determined; these adsorption processes were found to be feasible and endothermic but not spontaneous. The distribution of the substances adsorbed on PES surface were more chaotic than that in the aqueous solutions. Parameters obtained in this study can be used to determine the "fouling potential" of a given feed stream and a membrane.     

IgG adsorption on a new protein A adsorbent based on macroporous hydrophilic polymers. I. Adsorption equilibrium and kinetics

Experimental determination and modeling of IgG binding on a new protein A adsorbent based on a macroporous resin were performed. The new adsorbent consists of polymeric beads based on hydrophilic acrylamido and vinyl monomers with a pore structure optimized to allow favorable interactions of IgG with recombinant protein A coupled to the resin. The particles have average diameter of 57 μm and a narrow particle size distribution. The IgG adsorption equilibrium capacity is 46 mg/cm³ and the effective pore diffusivity determined from pulse response experiments for non-binding conditions is 8.0 × 10⁻⁸ cm²/s. The IgG adsorption kinetics can be described with the same effective diffusivity by taking into account a heterogeneous binding mechanism with fast binding sites, for which adsorption is completely diffusion controlled, and slow binding sites for which adsorption is controlled by the binding kinetics. As a result of this mechanism, the breakthrough curve exhibits a tailing behavior, which appears to be associated with the slow binding sites. A detailed rate model taking into account intraparticle diffusion and binding kinetics is developed and is found capable of predicting both batch adsorption and breakthrough behavior over an ample range of experimental conditions. The corresponding effective diffusivity is independent of protein concentration in solution over the range 0.2–2 mg/cm³ and of protein binding as a result of the large pore size of the support matrix. Overall, the small particle size and low diffusional hindrance allow capture of IgG with short residence times while attaining substantial dynamic binding capacities.     

A review on experimental studies of surfactant adsorption at the hydrophilic solid-water interface

The progresses of understanding of the surfactant adsorption at the hydrophilic solid-liquid interface from extensive experimental studies are reviewed here. In this respect the kinetic and equilibrium studies involves anionic, cationic, non-ionic and mixed surfactants at the solid surface from the solution. Kinetics and equilibrium adsorption of surfactants at the solid-liquid interface depend on the nature of surfactants and the nature of the solid surface. Studies have been reported on adsorption kinetics at the solid-liquid interface primarily on the adsorption of non-ionic surfactant on silica and limited studies on cationic surfactant on silica and anionic surfactant on cotton and cellulose. The typical isotherm of surfactants in general, can be subdivided into four regions. Four-regime isotherm was mainly observed for adsorption of ionic surfactant on oppositely charged solid surface and adsorption of non-ionic surfactant on silica surface. Region IV of the adsorption isotherm is commonly a plateau region above the CMC, it may also show a maximum above the CMC. Isotherms of four different regions are discussed in detail. Influences of different parameters such as molecular structure, temperature, salt concentration that are very important in surfactant adsorption are reviewed here. Atomic force microscopy study of different surfactants show the self-assembly and mechanism of adsorption at the solid-liquid interface. Adsorption behaviour and mechanism of different mixed surfactant systems such as anionic-cationic, anionic-non-ionic and cationic-non-ionic are reviewed. Mixture of surface-active materials can show synergistic interactions, which can be manifested as enhanced surface activity, spreading, foaming, detergency and many other phenomena.     

A kinetics,isotherms, and thermodynamic study of diclofenac adsorption using activated carbon prepared from olive stones

The objective of this work was to study the efficiency of activated carbon prepared from agricultural waste (olive stones; OS) on diclofenac (DCF) adsorption in aqueous solutions. The prepared charcoals were characterized by Fourier transform infrared (FTIR), scanning electron microscopy (SEM)/Energy Dispersive X-Ray Analyser (EDX), and Brunauer–Emmett–Teller (BET) analysis techniques. The results show that DCF adsorption is favorable in acid medium and low temperature. The adsorption kinetics follows a pseudo-second-order kinetic model. The adsorption was found to be spontaneous (ΔG°?相似文献   

Influence of surface heterogeneity on hydrogen adsorption on activated carbons

This study presents an experimental and theoretical analysis of the effect of surface heterogeneity on the capacity of 20 commercial activated carbons to adsorb hydrogen at 77 and 258 K and for maximum pressures of 20 bar. Some of the samples have been subjected to surface modification by impregnation or by surface oxidation prior to the hydrogen adsorption measurements. All the activated carbons have been analyzed by N₂ adsorption at 77 K using the thermodynamic isotherm presented in a previous study. The hydrogen adsorption capacity of the activated carbons has been well correlated to the micropore volume and the characteristic m₂ parameter of the thermodynamic isotherm accounting for the energy heterogeneity of the material. On the basis of the model presented here, we discuss how surface heterogeneity, in addition to the adsorption strength, might affect the ability of activated carbons and related materials to adsorb hydrogen.     

Method of the Green functions in the kinetics of adsorption from micellar surfactant solutions

The kinetics of adsorption from micellar surfactant solutions is considered theoretically from a uniform point of view. Three boundary value problems for the adsorption on flat and on spherical interface are solved analytically by means of the method of the Green functions. In this way the bulk concentration and the adsorption of surfactant monomers are expressed as functions of time. The contribution of the micelles (surfactant aggregates) to the diffusion of the monomers is accounted for as pseudo-first order reaction. The adsorption from surfactant solutions without micelles turns out to be the particular case of the problems considered here. Being general in form, the derived equations can be applied also to other practical problems in heterogeneous chemical kinetics, adsorption of gases, heat transfer, etc.     

Effects of ligand density and pore size on the adsorption of bovine IgG with DEAE ion-exchange resins

Immunoglobulin G is an important plasma protein with many applications in therapeutics and diagnostics, which can be purified effectively by ion exchange chromatography. The ligand densities and pore properties of ion-exchange resins have significant effects on the separation behaviors of protein, however, the understandings are quite limited. In this work, with bovine immunoglobulin as the model IgG, the adsorption isotherms and adsorption kinetics were investigated systematically with series of diethylaminoethyl ion-exchange resins with different ligand densities and pore sizes. The Langmuir equation and pore diffusion model were used to fit the experimental data. The influences of ligand density and pore size on the saturated adsorption capacity, the dissociation constant and the effective diffusivity were discussed. The adsorption capacities increased with the increase of ligand density and the decrease of pore size, and an integrative parameter was proposed to describe the combined effects of ligand density and pore size. It was also found that the effective pore diffusion coefficient of the adsorption kinetics was influenced by pore sizes of resins, but was relatively independent on the ligand densities of resins. For a given protein, the ligand density and pore size should be optimized for improving the protein adsorption.     

On the importance of the purity of surfactant solutions in determining their adsorption kinetics

By means of a theoretical experiment it is demonstrated, that a barrier in the adsorption kinetics of a surfactant can be simulated by the presence of surface-active impurities. Hence, the application of models for the diffusion-kinetic-controlled and/or kinetic controlled adsorption presumes the proof of the surface chemical purity of the surfactant solution under investigation.     

Alternative sample-introduction technique to avoid breakthrough in gradient-elution liquid chromatography of polymers

Gradient-elution liquid chromatography (GELC) is a powerful tool for the characterization of synthetic polymers. However, gradient-elution chromatograms often suffer from breakthrough phenomena. Breakthrough can be averted by using a sample solvent as weak as the mobile phase. However, this approach is only applicable to polymers for which a sufficiently strong solvent exists which is at the same time a weak eluent. Finding such a solvent for a given polymer can be laborious or may even be impossible. Besides, when working with comprehensive two-dimensional LC the effluent of the first dimension is the injection solvent of the second dimension. In this case, it is not possible to avoid breakthrough by adjusting the eluent strength of the second-dimension injection solvent. Therefore, another strategy to avert breakthrough has to be implemented. In this work, we successfully avoided breakthrough in GELC by mixing the mobile phase not before, but after the autosampler. This was demonstrated measuring a blend of poly(methyl methacrylate) standards with different molecular-weights as model mixture with comprehensive two-dimensional GELC × size-exclusion chromatography. The strategy is thought to be applicable to all substances with a sufficiently strong dependence of retention on mobile-phase composition. This typically applies to large molecules (synthetic and natural polymers) and allows efficient refocusing. Unretained and barely retained substances are not refocused and therefore suffer in the proposed setup from peak broadening.     

Chromatographic study of the adsorption kinetics of albumin on monoclonal and polyclonal immunoadsorbents

Summary High-performance liquid chromatography (HPLC) has been used to study the adsorption kinetics of proteins on immunoadsorbents. The adsorption rate constant of human serum albumin (HSA) on monoclonal and polyclonal anti-HSA antibodies immobilized on a silica HPLC support was determined by saturating the column with repeated pulse injections. Studies on polyclonal immunodsorbents of different capacities enable evaluation of the contribution of transport to the binding sites. The adsorption properties of two different monoclonal anti-HSA antibodies immobilized on a chromatographic support were characterized by different approaches. The location of the epitope on the HSA molecule was determined by enzyme-linked immunoassay (ELISA) with albumin fragments. The chromatographic method was used to determine the column capacity and the adsorption rate constant of HSA on the immunoadsorbent. To compare the affinity of the antibodies for the antigen, an indirect ELISA method was used to determine the equilibrium constant of antigen-antibody association in solution Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th september, 1996.     

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.     

Adsorption of Zinc and Cyanide from Cyanide Effluents on Anionic Ion-exchange Resin

The adsorption of zinc and cyanide from cyanide effluents onto strong and weak basic anion exchange resins was studied in a batch adsorption system. Factors influencing the adsorption rates such as resin selection, resin amounts, contact time and temperature were studied and scanning electron microscopy-energy disperse spectroscopy(SEM-EDS) was used in the analysis. The present study shows that the adsorption capacity of resin 201×7 is better than that of resin 301. The adsorption process was relatively fast and came to equilibrium after 60 min. The kinetic data were analyzed with three models and the pseudo-second-order kinetic model was found to agree with the experimental data well. The equilibrium data could also be described well by Langmuir isotherm model. Thermodynamic parameters such as enthalpy change(ΔH⁰), free energy change(ΔG⁰) and entropy change(ΔS⁰) were calculated and the adsorption process was spontaneous and endothermic.     

Effects of supercritical CO2 exposure on diffusion and adsorption kinetics of CH4, CO2 and water vapor in various rank coals

The physico-chemical effects caused by supercritical CO₂ (ScCO₂) exposure is one of the leading problems for CO₂ storage in deep coal seams as it will significantly alter the flow behaviors of gases. The main objective of this study was to investigate the effects of ScCO₂ injection on diffusion and adsorption kinetics of CH₄, CO₂ and water vapor in various rank coals. The powdered coal samples were immersed in ScCO₂ for 30 days using a high-pressure sealed reactor. Then, the diffusion and adsorption kinetics of CH₄, CO₂ and water vapor in the coals both before and after exposure were examined. Results indicate that the diffusivities of CH₄ and CO₂ are significantly increased due to the combined matrix swelling and solvent effect caused by ScCO₂ exposure, which may induce secondary faults and remove some volatile matters that block the pore throats. On the other hand, the diffusivities of water vapor are reduced due to the elimination of surface functional groups with ScCO₂ exposure. It is concluded that density of the surface function groups is the controlling factor for water vapor diffusion rather than the pore properties. The unipore model and pseudo-first-order equation can simulate the diffusion and adsorption kinetics of CH₄ and CO₂ very well, but the unipore model is not capable of well describing water vapor diffusion. The effective diffusivity (D_e), diffusion coefficient (D) and adsorption rates (k₁) of CH₄ and CO₂ are significantly increased after ScCO₂ exposure, while the values of water vapor are decreased notably. Thus, the injection of ScCO₂ will efficiently improve the transport properties of CH₄ and CO₂ but hinder the movement of water molecules in coal seams.