bi-Langmuir Adsorption Research Articles

Theoretical Investigation of the Nonlinear General Rate Model with the Bi-Langmuir Adsorption Isotherm Using Core-Shell Adsorbents.

Core-shell particles enable the separation of intricate mixtures in a highly efficient and rapid manner. The porous shell particles increased the separation efficiency with expedited flow rates due to an abatement in the pore volume accessible for longitudinal diffusion and a decrease in diffusion path length. This study focuses on the numerical approximation of a nonlinear isothermal general rate model applied to stationary bed columns that are replete with inert core adsorbents featuring double adsorption sites. The transport of solute in heterogeneous porous media can be modeled by a nonlinear convection acquiescent partial differential equation system together with a specific nonlinear algebraic relation: the bi-Langmuir adsorption isotherm. Therefore, it is important to develop accurate and reliable numerical techniques that can perform accurate numerical simulations of these models. We extended and implemented a second-order, semidiscrete, high-resolution finite volume method to simulate the governing equations of the model. Single solute flow and multi component mixture flows are assessed through a series of numerical experiments to theoretically illustrate the repercussions of intraparticle diffusion, film mass resistance, axial dispersion, and the size of the inert core radius upon simulated elution curves. Standard performance criteria are assessed to determine the optimal core radius fraction range for optimizing the separation performance.

Simulation of Fixed-Bed Chromatographic Processes Considering the Nonlinear Adsorption Isotherms.

This paper presents the numerical approximation of a nonlinear equilibrium-dispersive (ED) model of multicomponent mixtures for simulating single-column chromatographic processes. Using Danckwerts boundary conditions (DBCs), the ED is studied for both generalized and standard bi-Langmuir adsorption isotherms. Advection-diffusion partial differential equations are used to represent fixed-bed chromatographic processes. As the diffusion term is significantly weaker than the advection term, sophisticated numerical techniques must be applied for solving such model equations. In this study, the model equations are numerically solved by using the Runge-Kutta discontinuous Galerkin (RKDG) finite element method. The technique is designed to handle sudden changes (sharp discontinuities) in solutions and to produce highly accurate results. The method is tested with several case studies considering different parameters, and its results are compared with the high-resolution finite volume scheme. One-, two-, and three-component liquid chromatography elutions on fixed beds are among the case studies being considered. The dynamic model and its accompanying numerical case studies provide the initial step toward continuous monitoring, troubleshooting, and effectively controlling the chromatographic processes.

Theoretical Analysis of a Nonequilibrium Transport Model of Two-Dimensional Nonisothermal Reactive Chromatography Accounting for Bi-Langmuir Isotherm.

The current study investigates a nonequilibrium and nonlinear two-dimensional lumped kinetic transport model of nonisothermal reactive liquid chromatography, considering the Bi-Langmuir adsorption isotherm, heterogeneous reaction rates, radial and axial concentration variations, and the adsorption and reaction enthalpies. The mathematical models of packed bed chromatographic processes are expressed by a highly nonlinear system of coupled partial differential algebraic equations connecting the phenomena of convection, diffusion, and reaction, for mass and energy balance, the differential algebraic equations for mass balance in the solid phase, and the algebraical expressions for the adsorption isotherms and for the reaction rates. The nonlinearity of the reaction term and the adsorption isotherm preclude the derivation of an analytical solution for the model equations. For this reason, a semidiscrete, high-resolution, finite-volume technique is extended and employed in this study to obtain the numerical solution. Several consistency checks are performed to evaluate the model predictions and analyze the precision of the proposed numerical scheme. A number of heterogeneously catalyzed stoichiometric reactions are numerically simulated to examine reactor performance under the influence of temperature and Bi-Langmuir adsorption dynamics, the level of coupling between mass and energy fronts, and to study the effects of various critical parameters. The numerical results obtained are beneficial for optimal predictive control and process optimization during production and the development of methods for systematic design and fault detection of nonisothermal liquid chromatographic reactors, and hence constitute the first step to provide deeper insight into the overall evaluation of integrated reaction and separation processes.

Simulations of liquid chromatography using two-dimensional non-equilibrium lumped kinetic model with bi-Langmuir isotherm

A two-dimensional non-equilibrium and non-linear lumped kinetic model of liquid chromatography is formulated and numerically approximated to simulate the separation of multi-component mixtures in a packed fixed bed cylindrical column operating under isothermal conditions. The model equations incorporate the bi-Langmuir adsorption thermo-dynamics as well as the radial and axial variations of concentration. By introducing distinct regions of injection at the column inlet, radial concentration gradients are generated to intensify the effect of mass transfer rate in the radial-direction, inside the column. The mathematical model is developed by a system of non-linear convection-diffusion partial differential equations for mass balance in the mobile phase, coupled with differential equation for mass balance in the stationary phase and algebraic equations for adsorption isotherm. In this study, a high-resolution, semi-discrete, finite-volume technique is formulated and applied to gain the numerical solution of the governing non-linear-model equations. A few numerical case studies are performed to investigate the effects of the various critical parameters on the process performance. The developed numerical algorithm provide an efficacious mechanism for investigating the retention behavior, systematic monitoring and efficient operation of non-equilibrium, liquid chromatographic processes.

A dual-carrier adsorbate-modulated surface conductance model better captures the thermal dependence of conductance in TiO2 and MoO3 powders than an inter-grain hopping model

Non-Arrhenius thermal dependence of surface conductance has previously been observed in the transition-metal oxides TiO2 and MoO3. Through the application of thermochemical modeling, kinetic modeling, and analysis of equivalent resistance networks, it is shown that a dual-charge-carrier model in which the adsorbate surface coverage is modulated by bi-Langmuir adsorption is better able to capture the thermal dependence of surface conductance in these materials than a model based on the hypothesis that conductance is governed by bottlenecks to charge hopping between grains. Adsorption energies predicted by the dual-charge-carrier model are in agreement with estimates of the same from published first-principles calculations. Particle-size dependence of the conductance likely arises from the increasing importance of surface processes to charge transport with decreasing particle size, not from an increase in the number of inter-particle contacts.

The importance of ion-pairing in peptide purification by reversed-phase liquid chromatography

The adsorption mechanism for three peptides was studied under overloaded conditions through adsorption isotherm measurements in the presence of an ion-pairing reagent, trifluoroacetic acid (TFA), on an end-capped C18-bonded stationary phase. The overall aim of the study was to obtain a better understanding of how the acetonitrile and the TFA fractions in the eluent affected the overloaded elution profiles and the selectivity between peptides using mechanistic modelling and multivariate design of experiments. When studying the effect of TFA, direct evidence for ion pair formation between a peptide and TFA in acetonitrile-water solutions was provided by fluorine-proton nuclear Overhauser NMR enhancement experiments and the adsorption of TFA on the stationary phase was measured by frontal analysis. The adsorption isotherms for each peptide were then determined by the inverse method at eight TFA concentrations ranging from 2.6mM to 37.3mM (0.02–0.29vol-%) in isocratic elution. The equilibrium between the peptide ion and the peptide-TFA complex was modelled by coupling the mass-balance to reaction kinetics and determining separate adsorption isotherms for the two species. We found that a Langmuir isotherm described the elution profile of peptide-TFA complex well while the peptide ion was described by a bi-Langmuir adsorption isotherm since it exhibited strong secondary interactions. The elution profiles had an unfavorable shape at low TFA concentrations consisting of a spike in their front and a long tailing rear due to the secondary interactions for the peptide ion having very low saturation capacity. The acetonitrile dependence on the adsorption isotherms was studied by determination of adsorption isotherms directly from elution profiles obtained in gradient elution which enabled a broad acetonitrile interval to be studied. Here, it was found that the column saturation capacity was quickly reached at very low acetonitrile fractions and that there were significant variations in adsorption with the molecular weight. Finally, practical implications for method development are discussed based on an experimental design where gradient slope and TFA concentrations are used as factors.

Determination of Competitive Adsorption Isotherm of the Etodolac Enantiomers Using Inverse Method

The competitive adsorption isotherm of etodolac enantiomers on a cellulose carbamates-based chiral stationary phase (Chiralcel OD) at 25°C was determined in this study by the inverse method (IM). An equilibrium dispersive (ED) model combined with bi-Langmuir adsorption model was used in predicting the elution profiles. The adsorption isotherm model with 5 parameters was determined by fitting the two overloaded band profiles. The non-dominated sorting genetic algorithm (NSGA-II) and Levenberg-Marquardt algorithm (LMA) were crucial tools and utilities in this process. Suitable model parameters have been obtained and the experimental results were in good agreement with the model predictions.

Lipase purification by affinity precipitation with a thermo-responsive polymer immobilized Cibacron Blue F3GA ligand

A thermo-responsive polymer (PNNB) was synthesized with lower critical solution temperature 27.5°C and over 95% recovery. The adsorption of porcine pancreatic lipase on Cibacron Blue F3GA-conjugated PNNB (PNNB-CB) closely followed the bi-Langmuir adsorption isotherm. The maximum adsorption capacity was found at pH 5.0, with a ligand density of 18.4 μmol/g polymers. The optimized eluent was a 0.01 M phosphate buffer solution at pH 8.0 containing 20% ethylene glycol. Six adsorptiondesorption recycles indicated excellent reusability of the affinity adsorbent. PNNB-CB was applied to separate porcine pancreatic lipase from its crude material giving a lipase activity recovery of 81.6% with a 16-fold purification factor. Lipase could be purified to single-band purity, according to gel electrophoresis. The purification strategy is therefore feasible and efficient for purifying proteins of interest.

Industrial products and wastes as adsorbents for sulphate and chloride removal from synthetic alkaline solution and mine process water

Abstract Two limestones and two solid wastes were tested as adsorbents for chloride and sulphate ion removal from synthetic and real alkaline process mining water. The composition and surface structure of the adsorbents were analysed by ED-XRF, XRD, SEM and MIR spectroscopy and the nitrogen adsorption method. The optimal adsorption time and amount of adsorbent were determined by batch analysis with an anion concentration of 20 mg/L. In synthetic solution adsorbents removed 99% of SO42− and 96% of Cl− and in real process water the removal rate was 85% and 74% for SO42− and Cl−, respectively. It was found that equilibrium could successfully be fitted to the Langmuir, Toth and BiLangmuir adsorption isotherms.

Using surrogate models for efficient optimization of simulated moving bed chromatography

A new approach of using computationally cheap surrogate models for efficient optimization of simulated moving bed (SMB) chromatography is presented. Two different types of surrogate models are developed to replace the detailed but expensive full-order SMB model for optimization purposes. The first type of surrogate is built through a coarse spatial discretization of the first-principles process model. The second one falls into the category of reduced-order modeling. The proper orthogonal decomposition (POD) method is employed to derive cost-efficient reduced-order models (ROMs) for the SMB process. The trust-region optimization framework is proposed to implement an efficient and reliable management of both types of surrogates. The framework restricts the amount of optimization performed with one surrogate and provides an adaptive model update mechanism during the course of optimization. The convergence to an optimum of the original optimization problem can be guaranteed with the help of this model management method. The potential of the new surrogate-based solution algorithm is evaluated by examining a separation problem characterized by nonlinear bi-Langmuir adsorption isotherms. By addressing the feed throughput maximization problem, the performance of each surrogate is compared to that of the standard full-order model based approach in terms of solution accuracy, CPU time and number of iterations. The quantitative results prove that the proposed scheme not only converges to the optimum obtained with the full-order system, but also provides significant computational advantages.

Analytical Solution of the Ideal Model of Chromatography for a Bi-Langmuir Adsorption Isotherm

The (closed-form) analytical solution of the ideal model of chromatography was derived in the case of a bi-Langmuir adsorption isotherm model. This explicit solution provides the sample concentration as a function of the elution time as the unique real and positive root of a quartic polynomial equation. Using this analytical solution, we could calculate the parameters of the bi-Langmuir adsorption model for phenol on a column packed with Poroshell 120 C18 core-shell particles, eluted with a mixture of methanol and water, and operated under high inlet pressure using the retention time method. The method permitted a rapid, economical determination of the best adsorption isotherm parameters for phenol. It required less than 32 mg of sample, 50 mL of eluent, and less than 4 h to complete the measurement of 20 adsorption data points. The relative precisions of the isotherm parameters were 5% for the equilibrium constant and 9% for the saturation capacity of the strong adsorption sites and 24% for the equilibrium constant and 5% for the saturation capacity of the weak adsorption sites. Compared with determinations made with the standard HPLC technology and frontal analysis experiments, the working time, eluent volume consumed, and mass of compound used were reduced by factors of 4, 20, and 400, respectively.

Fast estimation of adsorption isotherm parameters in gradient elution preparative liquid chromatography. I: The single component case

The inverse method is a numeric method for fast estimation of adsorption isotherm parameters directly from overloaded elution profiles. However, it has previously only been used for isocratic experiments. Here we will extend the inverse method so it can be used for gradient elution too. This extended inverse method will make it possible to study the adsorption of substances whose retention factor vary strongly with the mobile-phase composition, like peptides and proteins, where the classic methods will fail. Our extended inverse method was verified using both simulations and real experiments. For simulated overloaded elution profiles we were able to determine almost exact Langmuir adsorption isotherm parameters with the new approach. From real experimental data, bi-Langmuir adsorption parameters were estimated using both the perturbation peak method and the extended inverse method. The shape of the acquired adsorption isotherms did match over the considered concentration range; however, the adsorption isotherm parameters found with the two methods were not the same. This is probably due to the fact that adsorption isotherm estimated with the inverse method is only a good approximation up to the highest eluted concentration in the used chromatograms. But this is not a serious drawback from a process point of view where the main objective is to make accurate predictions of elution profiles. The bi-Langmuir adsorption isotherm obtained with both methods could accurately predict the shape of overloaded elution profiles.

Adsorption Equilibria of Succinic Acid and Lactic Acid on Amberchrom CG300C Resin

One of the prerequisites to the development of a simulated moving bed (SMB) or a temperature-gradient SMB process for separation of succinic acid and lactic acid is to obtain their adsorption equilibrium data on a properly selected adsorbent. It was first found that an Amberchrom CG300C resin could function well as a qualified adsorbent for the separation processes of interest. On the basis of the selected adsorbent, the single-component adsorption equilibria of succinic acid and lactic acid were measured using a staircase frontal analysis method over the temperature range of (30 to 50) °C and the liquid-phase concentrations up to 10 g·L−1. The resultant adsorption data were correlated with the Langmuir and the bi-Langmuir adsorption models. For these two models, the effect of temperature on the Langmuir and the bi-Langmuir equilibrium constants was examined, which revealed that the adsorption of each acid onto Amberchrom CG300C was exothermic. Such a temperature effect was expressed mathematically, which...

Comparison between heterogeneous multi-Langmuir and homogeneous electrostatically modified Langmuir models in accounting for the adsorption of small organic ions in reversed-phase liquid chromatography

Adsorption isotherm data were measured by frontal analysis (FA) for sodium nicotinate (anionic species, pH W S 9.14) and atenololium chloride (cationic species, pH W S 2.60) on a column packed with hybrid porous particles (BEH-C 18), eluted with an aqueous solution of methanol at two different ionic strengths. These data were well accounted for by both a heterogeneous bi-Langmuir adsorption isotherm model and a homogeneous electrostatically modified Langmuir isotherm. In the case of the former model, two different types of adsorption sites are available for the ions. The saturation capacity and the binding constant of the stronger type of adsorption sites are nearly independent of the ionic strength of the eluent. These sites could be consistent with residual, accessible silanol groups, the surface concentration of which was estimated at 0.08 μmol/m 2. In contrast, the equilibrium constant of the weaker type of adsorption sites markedly increases with increasing elution strength of the eluent, a result consistent with a salting-out process. These weak adsorption sites are likely located at the interface between the C 18-bonded layer and the bulk eluent. In the case of the latter isotherm model, there is only one type of adsorption sites, its equilibrium constant increases with decreasing eluent ionic strength, consistent with classical electrostatics, but its saturation capacity strongly decreases when the ionic strength drops. This last result suggests that the homogeneous electrostatic adsorption model is physically inconsistent.

Validation of the Tracer-Pulse Method for Multicomponent Liquid Chromatography, A Classical Paradox Revisited

The tracer-pulse method was extended and validated for the determination of multicomponent adsorption isotherms in liquid chromatography. Competitive adsorption isotherms can be determined for any number of solutes, up to the column resolution limit. The basic principle is to equilibrate the column with an eluent containing a mixture of the solutes and then measure the migration velocity of each of them through the column. It is easy to calculate the stationary phase concentrations from these velocities, given the eluent composition. As in frontal analysis, real competitive isotherm data are measured using this method, unlike other methods, which only produce parametric estimates. The method was used to measure the binary isotherms of beta-blockers on a Kromasil C8 column. The data were fitted to competitive bi-Langmuir adsorption isotherm functions and was found to agree well with the results of frontal analysis and the perturbation method. Computer simulations based on the isotherm parameters were performed and displayed very good agreement with the experimental chromatograms. An intriguing and seemingly paradoxical property is visualized and discussed: the fact that the injected molecules are not found in the detected peaks.

Identification and predictive control of a simulated moving bed process: Purity control

A model predictive control strategy for a simulated moving bed (SMB) chromatographic process is proposed. For this, the average purities over one switching period of target components in extract and raffinate ports are selected as output variables, while the flow rates in Sections 2 and 3 of the SMB unit are chosen as the input variables. With this arrangement a linear input–output prediction model is identified through subspace identification and used for dynamic control. The realization of this concept is discussed and the implementation on a virtual eight column SMB unit is assessed, in the case of the separation of enantiomers behaving according to the binary bi-Langmuir adsorption isotherm. The identified prediction model is proven to be in good agreement with the first principles model used to simulate the actual SMB process. For typical control objectives encountered in real operation, i.e., disturbance rejection or set-point tracking, it is shown that the proposed controller demonstrates satisfactory control performances in minimizing off-spec products.

Adsorption Equilibria of Benzodiazepines on a Hybrid Polymeric Chiral Stationary Phase

The chromatographic behavior of a series of racemic benzodiazepines was evaluated under linear and nonlinear conditions on a new hybrid polymeric (DACH-ACR) chiral stationary phase (CSP). Differently substituted benzodiazepines were employed as probes to make hypotheses concerning possible molecular interaction mechanisms originating between target compounds and active sites on the CSP. Hydrogen bonds were found to be pivotal for chromatographic retention and chiral selectivity. The competitive effect from a mobile-phase (MP) modifier able to interact with the CSP through H-bonds was investigated. The performance of the polymeric DACH-ACR CSP for preparative purposes was also evaluated. The competitive adsorption isotherms of two benzodiazepines, lorazepam and temazepam, were measured at different MP compositions through the so-called inverse method. The adsorption data were fitted with a competitive bi-Langmuir adsorption isotherm. Enantiomeric separations under nonlinear conditions were modeled by using the equilibrium dispersive (ED) model of chromatography. Theoretical overloaded band profiles (obtained by solving the system of partial differential equations described by the ED model) matched, in a significantly accurate way, the profiles experimentally measured.

Measurement and simulation of tailing zones of a cationic dye in analytical-scale reversed phase chromatography

A quantitative physical description of tailing is reported here for analytical-scale reversed phase chromatography with Type B silica. Simulations of experimental chromatograms for a cationic dye, 1,1′-didodecyl-3,3,3′3′-tetramethylindocarbocyanine perchlorate (DiI) were performed as a function of DiI concentration and flow rate, revealing nonlinear tailing due to a bi-Langmuir adsorption isotherm. The strong site comprises less than 0.1% of the residual silanols, the desorption rate constant of DiI from this type of site is (85±8 ms) −1, and the free energy of the silanophilic interaction is 16 kJ/mol, indicating hydrogen bonding or another strong electrostatic interaction.

Thermodynamic Study of an Unusual Chiral Separation. Propranolol Enantiomers on an Immobilized Cellulase

The thermodynamics of interaction of (R)- and (S)-propranolol between an acetic acid buffer (pH = 4.7 and 5.5) and the protein cellobiohydrolase I immobilized on silica gel was studied between 5 and 45 °C. The equilibrium data were fitted to a biLangmuir adsorption isotherm with excellent agreement. One of the two Langmuir contributions is the same for both enantiomers and accounts for the nonspecific interactions between these compounds and most sites on the surfaces (type-I, nonselective sites). It has a large saturation capacity. The second contribution accounts for the chiral selective interactions (type-II sites). It has a lower monolayer capacity than the first. The interaction enthalpy and entropy on type-I sites are −1.1 kcal/mol and +0.1 cal/(mol K), respectively. For type-II sites, they are −1.9 kcal/mol and −2.6 cal/(mol K), respectively, for (R)-propranolol and +1.6 kcal/mol and + 11.6 cal/(mol K), respectively, for (S)-propranolol at pH = 5.5. This explains why at this pH the retention time o...