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

Adsorbents and columns in analytical high-performance liquid chromatography: a perspective with regard to development and understanding

A brief historical survey is presented on the evaluation of silica adsorbents in analytical HPLC. The theory of analytical HPLC is mostly still being based on the height equivalent to a theoretical plate concept and the van Deemter equation that was derived from gas phase adsorption involving a linear adsorption isotherm and fast mass transfer kinetics. One can obviously wonder whether the use of the van Deemter equation is relevant and valid for the evaluation of the performance of HPLC systems, where most often the liquid solutes involve charged molecules in electrolytes and in very many cases the adsorbates are macromolecules having diffusion coefficients of small magnitude. Instead of the van Deemter equation, a multi-scale modelling approach that involves microscopic and macroscopic dynamic non-linear mass-transfer-rate models should be employed. Furthermore, advanced experimental methods for the characterisation of porous media and the distribution of the density of immobilised active sites (e.g., ligands) on surfaces as well as microscopic pore-network modelling and molecular dynamics modelling and simulation methods could be used for the design of novel adsorbents whose porous structures and immobilised active sites would provide effective mass transport and adsorption rates for realising efficient separations as well as high dynamic capacities when larger throughputs are required.

Understanding and design of existing and future chromatographic support formats

The present contribution reviews the use of alternative support formats as a means to surpass the chromatographic performance of the packed bed of spheres. First, a number of idealized structures are considered to obtain a general insight in how the performance of a chromatographic support depends on its shape and size, using the isocratic peak-capacity generation speed as the main performance indicator. Using this criterion, it is found that the packing density or, equivalently, the external porosity, is the most important of all geometrical shape factors. Depending on whether the sample consists of weakly or strongly retained components, the optimal external porosity can be expected to vary between 60% and a value near 100%. The optimal exploitation of a high external porosity, however, also requires overall shrinkage of the domain size, towards and into the sub-micron range. With the current fabrication technologies, this requirement seems difficult to achieve. In the presence of a lower limit on the characteristic support size, each range of desired plate numbers or peak capacities has its own optimal external porosity, ranging from a very low value (high packing density) for high speed, small peak capacity applications, to very high external porosities (low packing density) for applications requiring a very large peak capacity. Subsequently, the obtained theoretical insights are used to review and discuss the past and current research on alternative support formats. Finally, a number of emerging micro- and nano-fabrication technologies are introduced and their potential for the future production of supports with improved shape and homogeneity is discussed.

Theory and practical understanding of the migration behavior of proteins and peptides in CE and related techniques

CEC is defined as an analytical method, where the analytes are separated on a chromatographic column in the presence of an applied voltage. The separation of charged analytes in CEC is complex, since chromatographic interaction, electroosmosis and electrophoresis contribute to the experimentally observed behavior. The putative contribution of effects such as surface electrodiffusion has been suggested. A sound theoretical treatment incorporating all effects is currently not available. The question of whether the different effects contribute in an independent or an interdependent manner is still under discussion. In this contribution, the state-of-the-art in the theoretical description of the individual contributions as well as models for the retention behavior and in particular possible dimensionless 'retention factors' is discussed, together with the experimental database for the separation of charged analytes, in particular proteins and peptides, by CEC and related techniques.

The effect of the pore structure and zeta potential of porous polymer monoliths on separation performance in ion-exchange mode

Most often, in bioseparations involving charged macromolecules, the chromatographic systems have low Reynolds and high Peclet numbers. For such systems, an expression is developed and presented in this work for evaluating the throughput in polymeric monoliths where ion-exchange adsorption occurs, as a function of (i) the pressure drop along the length of the monolith, (ii) the functional form and width of the throughpore-size distribution of the monolith, and (iii) the magnitude of the zeta potential on the surface of the throughpores of the monolith. Gaussian and log-normal throughpore-size distributions whose mean throughpore-size and standard deviation values are based on experimentally measured throughpore-size distribution data by mercury porosimetry employed on polymeric monoliths are used in this work, and their effect on the throughput relative to that obtained from a polymeric monolith having a uniform throughpore-size distribution is studied for different values of the ratio of the standard deviation to the mean throughpore-size. The results indicate that relatively modest increases in the throughput, when compared with the throughput that could be achieved in a polymeric monolith having a uniform throughpore-size distribution, could be obtained in polymeric monoliths having disperse throughpore-size distributions, and the magnitude of the increase becomes larger when the disperse distribution is skewed to larger throughpore sizes. Furthermore, the results of this work indicate that, under certain conditions, relatively modest increases in the throughput of a charged analyte could also be achieved by altering the value of the zeta potential on the surface of the throughpores of the monolith. Due to the difficulties inherent in controlling the functional form and width of the throughpore-size distribution during the synthesis of polymeric monoliths, it would appear to be more practical to increase the value of the throughput of a charged analyte by altering the value of the zeta potential through prudent selection of the ion-exchange surface functional groups and fine-tuned with the pH of the mobile phase. Thus, for ion-exchange chromatography systems, the zeta potential could be considered an important parameter for column designers and operators to manipulate, since its alteration could increase the through-put of a charged analyte in polymeric monoliths or in columns packed with charged particles.

Pore structural characterization of monolithic silica columns by inverse size-exclusion chromatography

In this work, a parallel pore model (PPM) and a pore network model (PNM) are developed to provide a state-of-art method for the calculation of several characteristic pore structural parameters from inverse size-exclusion chromatography (ISEC) experiments. The proposed PPM and PNM could be applicable to both monoliths and columns packed with porous particles. The PPM and PNM proposed in this work are able to predict the existence of the second inflection point in the experimental exclusion curve that has been observed for monolithic materials by accounting for volume partitioning of the polymer standards in the macropores of the column. The appearance and prominence of the second inflection point in the exclusion curve is determined to depend strongly on the void fraction of the macropores (flow-through pores), (b) the nominal diameter of the macropores, and (c) the radius of gyration of the largest polymer standard employed in the determination of the experimental ISEC exclusion curve. The conditions that dictate the appearance and prominence of the second inflection point in the exclusion curve are presented. The proposed models are applied to experimentally measured ISEC exclusion curves of six silica monoliths having different macropore and mesopore diameters. The PPM and PNM proposed in this work are able to determine the void fractions of the macropores and silica skeleton, the pore connectivity of the mesopores, as well as the pore number distribution (PND) and pore volume distribution (PVD) of the mesopores. The results indicate that the mesoporous structure of all materials studied is well connected as evidenced by the similarities between the PVDs calculated with the PPM and the PNM, and by the high pore connectivity values obtained from the PNM. Due to the fact that the proposed models can predict the existence of the second inflection point in the exclusion curves, the proposed models could be more applicable than other models for ISEC characterization of chromatographic columns with small diameter macropores (interstitial pores) and/or large macropore (interstitial pore) void fractions. It should be noted that the PNM can always be applied without the use of the PPM, since the PPM is an idealization that considers an infinitely connected porous medium and for materials having a low (<6) pore connectivity the PPM would force the PVD to a lower average diameter and larger distribution width as opposed to properly accounting for the network effects present in the real porous medium.

Oscillatory transverse electric field enhances mass transfer and protein capacity in ion-exchange electrochromatography

Ion-exchange electrochromatography with an oscillatory electric field perpendicular to mobile-phase flow driven by pressure (pIEEC) was developed with a column design of rectangle cross-section. The effect of electric field strength on the dynamic binding capacity (DBC) was examined by frontal analysis of bovine serum albumin (BSA) adsorption to the packed beds of DEAE Sepharose FF in Tris-glycine buffer (pH 8.2). It was shown that the DBC at 10% breakthrough (Q(10)) in the pIEEC increased linearly with increasing the electric field strength. For example, with a packed-bed height of 15mm and electric potential gradient of 38V/cm, Q(10) increased four times over that in normal ion-exchange chromatography. So, the transverse electric field has created significant electro-kinetic mass transports (electroosmosis and electrophoresis) that intensified exterior liquid-film and intraparticle mass transfers, leading to the increased protein binding capacity. Due to the increased capacity in the pIEEC, partial resolution of BSA and IgG under an overload condition was realized without any process optimization. The results have revealed that an electric potential gradient of 20V/cm was enough to greatly enhance the DBC in the pIEEC, and when necessary, high electric field strength can be realized with a low applied voltage because the side distance of the column is usually an order of magnitude smaller than its height. The use of low voltage to carry out electrochromatography is a significant advantage of the pIEEC over conventional electrochromatography with axial electric field.

Construction by Molecular Dynamics Modeling and Simulations of the Porous Structures Formed by Dextran Polymer Chains Attached on the Surface of the Pores of a Base Matrix: Characterization of Porous Structures

Significant increases in the separation of bioactive molecules by using ion-exchange chromatography are realized by utilizing porous adsorbent particles in which the affinity group/ligand is linked to the base matrix of the porous particle via a polymeric extender. To study and understand the behavior of such systems, the M3B model is modified and used in molecular dynamics (MD) simulation studies to construct porous dextran layers on the surface of a base matrix, where the dextran polymer chains and the surface are covered by water. Two different porous polymer layers having 25 and 40 monomers per main polymer chain of dextran, respectively, are constructed, and their three-dimensional (3D) porous structures are characterized with respect to porosity, pore size distribution, and number of conducting pathways along the direction of net transport. It is found that the more desirable practical implications with respect to structural properties exhibited by the porous polymer layer having 40 monomers per main polymer chain, are mainly due to the higher flexibility of the polymer chains of this system, especially in the upper region of the porous structure. The characterization and analysis of the porous structures have suggested a useful definition for the physical meaning and implications of the pore connectivity of a real porous medium that is significantly different than the artificial physical meaning associated with the pore connectivity parameter employed in pore network models and whose physical limitations are discussed; furthermore, the methodology developed for the characterization of the three-dimensional structures of real porous media could be used to analyze the experimental data obtained from high-resolution noninvasive three-dimensional methods like high-resolution optical microscopy. The MD modeling and simulations methodology presented here could be used, considering that the type and size of affinity group/ligand as well as the size of the biomolecule to be adsorbed onto the affinity group/ligand are known, to construct different porous dextran layers by varying the length of the polymeric chain of dextran, the number of attachment points to the base matrix, the degree of side branching, and the number of main polymeric chains immobilized per unit surface area of base matrix. After the characterization of the porous structures of the different porous dextran layers is performed, then only a few promising structures would be selected for studying the immobilization of adsorption sites on the pore surfaces and the subsequent adsorption of the bioactive molecules onto the immobilized affinity groups/ligands.

Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography

In this work, expressions are constructed and solved that describe the velocity field of electroosmotic flow (EOF) in open tube capillary electrochromatography (CEC) systems when the possibility of having unequal tangential velocities at the liquid-solid interface is considered and a slip condition is employed as a boundary condition for the velocity of the EOF at the capillary wall. The coupled equations of hydrodynamics (momentum balance equation) and electrostatics (Poisson equation) are solved numerically in order to obtain the distribution of the velocity field as well as the value of the volumetric flow rate in the open tube. Also, expressions for the velocity field and the volumetric flow rate of the EOF are presented that are valid for certain electrolytic systems and for certain parameter values for which analytical solutions to the momentum balance and Poisson equations could be obtained. The results presented in this work indicate that having slip in the velocity of the EOF at the wall of the capillary could (i) substantially increase the electroosmotic velocity in the plug-flow region of the radial domain of the open capillary tube and (ii) increase the portion of the radial domain of the open capillary tube where the velocity of the EOF has a plug-flow profile, which in turn could increase the average velocity and volumetric flow rate of the EOF in the open capillary tube. Furthermore, the modeling approach and the results presented in this work indicate a method for experimentally evaluating the possibility of having slip in the velocity of the EOF at the capillary wall.