Analysis of diffusion models for protein adsorption to porous anion-exchange adsorbent

The ion-exchange adsorption kinetics of bovine serum albumin (BSA) and gamma-globulin to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments. Various diffusion models, that is, pore diffusion, surface diffusion, homogeneous diffusion and parallel diffusion models, are analyzed for their suitabilities to depict the adsorption kinetics. Protein diffusivities are estimated by matching the models with the experimental data. The dependence of the diffusivities on initial protein concentration is observed and discussed. The adsorption isotherm of BSA is nearly rectangular, so there is little surface diffusion. As a result, the surface and homogeneous diffusion models do not fit to the kinetic data of BSA adsorption. The adsorption isotherm of gamma-globulin is less favorable, and the surface diffusion contributes greatly to the mass transport. Consequently, both the surface and homogeneous diffusion models fit to the kinetic data of gamma-globulin well. The adsorption kinetics of BSA and gamma-globulin can be very well fitted by parallel diffusion model, because the model reflects correctly the intraparticle mass transfer mechanism. In addition, for both the favorably bound proteins, the pore diffusion model fits the adsorption kinetics reasonably well. The results here indicate that the pore diffusion model can be used as a good approximate to depict protein adsorption kinetics for protein adsorption systems from rectangular to linear isotherms.     

Characterization and modeling of monolithic stationary phases: application to preparative chromatography

Two different approaches, the rectangular pulse method and a new method, the frontal velocity analysis method are applied to the determination of competitive isotherms for two systems on ODS-silica. Both sets of experimental data are found to fit well to the competitive-Langmuir isotherm equation. The data obtained from the rectangular pulse method and the frontal velocity analysis method are in general agreement with each other and the best coefficients of the competitive isotherms obtained with the two methods are close. This shows that the simpler and easier method, the frontal velocity analysis method can be used to determine binary competitive isotherms.     

Adsorption integral equation via complex approximation with constraints: kernel of general form

For the monolayer adsorption on a homogeneous surface, including arbitrary range lateral interactions, the isotherm can be written as a power series of the Langmuir isotherm. If this isotherm is used as the kernel in the adsorption integral equation, this integral equation can be solved in an analytical form. Because the global isotherm is usually known as a set of experimental values, the use of a numerical method is inevitable. A new numerical method for solving the adsorption integral equation with a kernel of general form is developed. It is based on recent results concerning the structure of the local isotherm and on the ideas of complex approximation with constraints, and allows reduction of the problem under consideration to a linear‐quadratic programming problem. Results of numerical experiments are presented. The method can be useful for the evaluation of the adsorption energy distribution from experimental data. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1058–1066, 2001     

The kinetics of adsorption in the case of a rectangular isotherm and variable concentration of the adsorbent at the grain boundary

Conclusions The kinetics of adsorption in cylindrical and spherical grains was investigated in the case of a rectangular isotherm and variable concentration of the absorbent in the flux.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 526–528, March, 1972.     

Adsorption isotherms on nicotinamide-imprinted polymer stationary phase

The molecular-imprinted technique is applied for the preparation of a polymer selector by using methacrylic acid as functional monomer, ethyleneglycol dimethacrylate as the cross-linker, 2,2'-azobisisobutyronitrile as the initiator, and nicotinamide as the template. The adsorption isotherms of nicotinamide and nicotinic acid and the competitive adsorption isotherms of nicotinamide and nicotinic acid on the imprinted stationary phase are determined using rectangular pulse frontal analysis and static method. Aqueous solution is used as the mobile phase in frontal analysis. It is found that the adsorption data fit well to both Langmuir and Freundlich isotherm models.     

Protein adsorption equilibria and kinetics to a poly(vinyl alcohol)-based magnetic affinity support

A poly(vinyl alcohol)-based magnetic gel entrapping Fe3O4 colloids has been prepared by an emulsification-crosslinking method. The gel was modified with Cibacron blue 3GA, and thus a magnetic affinity support was produced. The adsorption equilibrium studies showed that the adsorption isotherm of lysozyme was nearly rectangular, with a capacity of 254 mg/ml, while the adsorption isotherm of bovine serum albumin obeyed the Henry's law. Uptake kinetics of the two proteins was investigated and analyzed with a pore diffusion model and a homogeneous diffusion model. Experimental results showed that the magnetic affinity gel had magnetic responsiveness and favorable properties in protein adsorption, and was mechanically and chemically stable.     

Kinetic Study of the Mass Transfer of Bovine Serum Albumin on Cibacron Blue Cellulose Membranes by Using the Multi-Plate and Transport Models

The mass transfer kinetics of bovine serum albumin on Cibacron blue F3GA cellulose affinity membranes has been investigated. It was found that the multi-plate (MP) and transport models successfully described experimental breakthrough curves obtained by single-step frontal analysis. The correlation between the two models was used to estimate the rate coefficients of mass transfer from experimental data. The flow rate was found to have little effect on the performance of affinity membrane separations. The improvement of the performance by increasing the thickness of the membranes was limited. The transport model was simplified by approximating the very sharp Langmuir isotherm determined by a rectangular isotherm and an analytical solution obtained although this was found to be unsuited to describe the experimental data.     

Equilibrium in an ideal adsorption layer during multiplet adsorption

The equilibrium in an ideal adsorption layer during adsorption of a mixture of substances whose molecules can occupy one or m elementary sites is examined. It is shown that the isotherm for any adsorbate in the mixture can be readily found if the isotherm is known for one of the adsorbed substances whose molecules occupy m elementary surface sites in the absence of other adsorbates. The form of the isotherm for multiplet adsorption depends on the distribution of the elementary sites on the surface.     

一种改进的休克尔分子轨道模型预测纯碳环分子稳定结构

从动力学和统计热力学角度介绍了BET方程中C的物理意义,分析了C的大小对吸附等温线形状的影响,推导了吸附等温线上拐点、B点位置和C大小的关系以及达到单程吸附量时C与相对压力、覆盖表面分数的关系。文章用数学方法介绍了保证C为正值的方法,解释了数据分析中的一个常见现象,还从BET方程的数学形式及物理意义探讨了C的下限。     

General expression of the linear potential sweep voltammogram in the case of diffusionless electrochemical systems

The equation of the linear potential sweep voltammogram is derived for any degree of reversibility of the electrochemical reaction for the following methods: surface voltammetry when both the oxidized and the reduced forms are strongly adsorbed, and a Langmuir isotherm is obeyed, thin layer voltammetry, and linear potential sweep coulometry. The results are expressed in one mathematical form valid for the three cases. The transfer coefficient and the rate constant of the electrochemical reaction can be deduced from an experimental study of the variations of the peak potentials as a function of the sweep rate.     

A.C. Polarography and faradaic impedance of strongly adsorbed electroactive species: Part III. Theoretical complex plane analysis for a surface redox reaction

The complex plane analysis of a cell impedance in the case of a surface redox system (strong adsorption of both O and R) is treated theoretically. The adsorption rate does not control the kinetics of the system. These systems present the general property that the equation of the curves obtained does not depend on the isotherm when the angular frequency is varied. When the concentration or the potential is varied, on the contrary, the curves differ according to the isotherm; either a Langmuir or a Frumkin isotherm is considered. The use of certain representations for the characterization of adsorption is discussed.     

Computational evaluation of mass filter acceptance and transmittance influenced by developing fields: An application of the plane method to investigate prefilter efficacy for rectangular wave operated mass filters

The acceptance of quadrupole mass filters is improved when the alternating current (AC) and direct current (DC) fields are developed separately. Physically, this is achieved when a short RF only quadrupole (prefilter) is situated directly ahead of the mass filter. The acceptance gained by a system operating with a prefilter can be observed as an increase in sensitivity over conventional operation. Frequency dynamic duty cycle based rectangular waveform driven (rectangular wave) mass filters, a recent development, currently do not operate with prefilters. Little is known about the influence of duty cycle changes on the acceptance of rectangular wave mass filters. The sensitivity gain seen by conventional systems operating with prefilters indicates that the sensitivity of duty cycle based rectangular wave systems should increase comparably. The objective of this work was to determine prefilter efficacy for nonspecific rectangular wave mass filter systems. In this work, the plane method of acceptance was used to model the change to the acceptance and transmittance of sine and rectangular waveform driven mass filters under different modes of field development. Both systems indicated a fourfold increase in sensitivity when the mass filtering DC or duty cycle was delayed.     

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.     

On the validity of Langmuir adsorption on supported nanoparticles

The general form for adsorption on nanoparticles is presented. Conditions for the validity of Langmuir adsorption isotherm for supported nanoparticles are discussed.     

Retention of ionizable compounds in high-performance liquid chromatography. 14. Acid-base pK values in acetonitrile-water mobile phases

Using competitive frontal analysis, the binary adsorption isotherms of the enantiomers of 1-phenyl-l-propanol were measured on a microbore column packed with a chiral stationary phase based on cellulose tribenzoate. These measurements were carried out using only the racemic mixture. The experimental data were fitted to four different isotherm models: Langmuir, BiLangmuir, Langmuir-Freundlich and Tóth. The BiLangmuir and the Langmuir-Freundlich models accounted best for the competitive adsorption data. An excellent agreement between the experimental and the calculated overloaded band profiles for various samples of racemic mixture was obtained when the equilibrium dispersive model of chromatography was used together with the BiLangmuir competitive isotherm. The isotherm parameters measured under competitive conditions were used to calculate the overloaded band profiles of large samples of the pure S- and R-enantiomers, too. A satisfactory agreement between the experimental and calculated band profiles was observed when using in the computation the corresponding single component BiLangmuir isotherm derived from the binary isotherm previously determined. Thus oniy data derived from the racemic mixture are required for computer optimization of the preparative chromatography separation of the enantiomers.     

A predictive approach to correlating protein adsorption isotherms on ion-exchange media

The equilibrium adsorption of three small basic proteins was measured on cation exchangers under various solution conditions and was used as the basis for developing a predictive approach for correlating adsorption behavior. A mechanistically based isotherm model is used to model the equilibrium adsorption so as to facilitate isotherm prediction using minimal experimental data. The model explicitly considers the contributions of protein-surface and protein-protein interactions, and decoupling them allows each to be correlated with different experimental measurements. Specifically, protein-surface interactions are related to chromatographic data in the form of the isocratic retention factor (k'), while protein-protein interactions are analyzed on the basis of high-coverage isotherm data on an arbitrary stationary phase. Analysis of experimental data within this framework reveals a high level of consistency. The model is also used to facilitate prediction of adsorption isotherms on other ion-exchange media using isotherms on one adsorbent.     

Sorption of zirconium ions by soils

Sorption of zirconium ions by gray forest soils of the Central Black Earth Belt has been investigated. The sorption form of the isotherm of microcomponent distribution for a heterogeneous system is presented.     

General theory of indirect detection in chromatography

Indirect detection is used in liquid chromatography to detect sample components that more or less lack detectable properties. A detectable component, the probe, is added to the mobile phase and the sample containing the components is injected. Every solute, even those not normally detectable, will give rise to detectable peaks due to the presence of the probe. The theory currently used to describe this situation is different for different adsorption isotherm models and also restrictions have to be imposed on the adsorption isotherm parameters. We present a general theory that describes both the retention times and areas of the detected peaks without making any a priori adsorption isotherm assumptions. Our general theory is compared with the current theory and validated by computer simulations. An alternative quantification method is suggested based on the measurement of the relative areas of the sample components without the requirement of having standard curves of known solutions of the sample components. Using this approach, the new theory is able to predict the solute concentrations in cases when the current theory did not, i.e., when the saturation capacities of the sample components and the probe differed from each other. In addition, a new application is proposed: the estimation of adsorption isotherm parameters.     

Modeling of adsorption on nongraphitized carbon surface: GCMC simulation studies and comparison with experimental data

We model nongraphitized carbon black surfaces and investigate adsorption of argon on these surfaces by using the grand canonical Monte Carlo simulation. In this model, the nongraphitized surface is modeled as a stack of graphene layers with some carbon atoms of the top graphene layer being randomly removed. The percentage of the surface carbon atoms being removed and the effective size of the defect (created by the removal) are the key parameters to characterize the nongraphitized surface. The patterns of adsorption isotherm and isosteric heat are particularly studied, as a function of these surface parameters as well as pressure and temperature. It is shown that the adsorption isotherm shows a steplike behavior on a perfect graphite surface and becomes smoother on nongraphitized surfaces. Regarding the isosteric heat versus loading, we observe for the case of graphitized thermal carbon black the increase of heat in the submonolayer coverage and then a sharp decline in the heat when the second layer is starting to form, beyond which it increases slightly. On the other hand, the isosteric heat versus loading for a highly nongraphitized surface shows a general decline with respect to loading, which is due to the energetic heterogeneity of the surface. It is only when the fluid-fluid interaction is greater than the surface energetic factor that we see a minimum-maximum in the isosteric heat versus loading. These simulation results of isosteric heat agree well with the experimental results of graphitization of Spheron 6 (Polley, M. H.; Schaeffer, W. D.; Smith, W. R. J. Phys. Chem. 1953, 57, 469; Beebe, R. A.; Young, D. M. J. Phys. Chem. 1954, 58, 93). Adsorption isotherms and isosteric heat in pores whose walls have defects are also studied from the simulation, and the pattern of isotherm and isosteric heat could be used to identify the fingerprint of the surface.