On the optimization of the shell thickness of superficially porous particles

An alternative general model for the effective longitudinal diffusion in chromatographic beds filled with ordered porous particles

The two-zone moment-analysis method for the determination of the dispersion tensor in hierarchical retentive porous media has been adopted to compute and model the effective longitudinal diffusion Deff, or equivalently the B-term band broadening, in chromatographic beds filled with ordered porous particles. On the one hand, this approach offers accurate numerical results for Deff while keeping computational expenses low. On the other hand, it also gives direct insight for the analytical modelling, readily revealings the two main essential quantities (resp. referred to as the mobile-zone and stationary-zone effective diffusion factors γm and γs) that contribute to Deff. Modelling these two main parameters provided us with two new analytical models for Deff: a general one, valid for diluted and concentrated packings and accurate in the whole range of relevant intra-particle diffusion coefficient Dpz, and an approximate one, reliable for diluted packings and accurate also for concentrated packings with low to intermediate values of Dpz. The large advantage of both models is that they do not need any fitting parameter because all the required information is incorporated into the experimentally accessible geometric obstruction factor in the mobile phase originating from the tortuosity of the through-pore space (limiting case of fully solid particles without any retention). These models hence serve as an alternative to the Effective Medium Theory (EMT) models used so far in the literature. To validate the theory, five ordered geometries have been investigated. The accuracy of the general model proposed has been quantified and found to be comparable with that of the 3rd order approximate Torquato model for four geometries, even for macro-porosities close to the close-packing limit. The case of a 2-d triangular array of ellipsoidal particles with different elongations is also investigated to show the general validity and applicability of the models.

Nonadditivity and Nonlinearity of Mobile and Stationary Zone Mass Transfer Resistances in Chromatography

Using a two-zone moment analysis (TZMA) method based on Brenner's generalized dispersion theory for two-dimensional (2D) and three-dimensional (3D) periodic media, we investigated the mechanisms for dispersion in particulate media for liquid chromatography. This was done using a set of plate height data covering an unprecedented wide range of retention factors, diffusion coefficients, and velocities, all computed with unequaled accuracy. Applying Giddings' additivity test, based on alternatingly making the diffusion coefficient in the mobile and stationary zones infinitely large, the dispersion data clearly indicate a lack of additivity. Although this lack could be directly understood by identifying the existence of multiple parallel mass transfer paths, the additivity assumption interestingly overestimates the true C term band broadening (typically by more than 10%, depending on conditions and dimensionality of the system). However, Giddings originally asserted the occurrence of parallel paths would always lead to an underestimation of the dispersion. The origin of the lack of additivity is analyzed in detail and qualitatively explained. Finally, we also established a generic framework for the modeling of the effect of the reduced velocity and the retention coefficient on the C term in ordered chromatographic media. This led to the introduction of a new expression for the mobile zone mass transfer term, which, unlike the currently used literature expression, contains the complete k″ dependency.

Computational Fluid Dynamics Study of the Dispersion Caused by Capillary Misconnection in Nano-Flow Liquid Chromatography

It is well known that high-speed/high-efficiency separations in nano-flow liquid chromatography (LC) are very sensitive to the quality of the connections between the column and the rest of the instrument. In the present study, two types of connection errors (capillary misalignment and the occurrence of an inter-capillary gap) have been investigated using computational fluid dynamics. Interestingly, it has been found that large degrees of capillary misalignment (assuming an otherwise perfect contact between the capillary end-faces) can be afforded without introducing any significant dispersion over the entire range of investigated relative misalignment errors (0 ≤ ε/dcap ≤ 75%), even at the largest flow rates considered in nano-LC. On the other hand, when an inter-capillary gap is present, the dispersion very rapidly increases with the radial width Dc of this gap (extra variance ∼Dcn with n even reaching values above 4). The dependency on the gap length Lc is however much smaller. Results show that, when Dc ≤ 30 μm and Lc ≤ 200 μm, dispersion losses can be limited to the order of 1 nL2 at a flow of 1.5 μL/min, which is generally very small compared to the dispersion in the capillaries (20 μm i.d.) themselves. This result also reconfirms that zero-dead volume connectors with a sufficiently narrow bore can in theory be used without compromising peak dispersion in nano-LC, at least when the capillaries can be matched perfectly to the connector in- and outlet faces. The results are also indicative of the extra dispersion occurring inside microfluidic chips or in the connections between a microfluidic chip and the outer world.

Moment analysis for predicting effective transport properties in hierarchical retentive porous media

We report on a new homogenization approach to solve, with drastically improved speed and accuracy, the general advection-diffusion equation in hierarchical porous media with localized diffusion and adsorption/desorption processes, thus opening the way to a much deeper understanding of the band broadening process in chromatographic systems. The proposed robust and efficient moment-based approach allows us to compute the exact local and integral concentration moments and hence provides exact solutions for the effective velocity and dispersion coefficients of migrating solute particles. Innovative to the proposed method is also that it not only produces the exact effective transport parameters of the long-time asymptotic solution, but also their entire transient. The analysis of the transient behaviour can be used, for example, to properly identify the time and length scales needed to achieve the macro-transport conditions. If the hierarchical porous media can be represented as the periodic repetition of a unit lattice cell, the method only requires the solution of the time-dependent advection-diffusion equations for the zeroth order and first-order exact local moments, exclusively on the unit cell. This implies an enormous reduction of the computational efforts and a significant improvement of the accuracy of the results when compared to the direct numerical simulation (DNS) approaches which require flow domains that are long enough to achieve steady-state conditions, and hence often cover tens to hundreds of unit cells. The reliability of the proposed method is verified by comparing its predictions with DNS results, in one, two and three dimensions, in both transient and asymptotic conditions. The influence of top and bottom no-slip walls on the separation performance of chromatographic columns with micromachined porous and nonporous pillars is discussed in detail.

Fundamental investigation of the dispersion caused by a change in diameter in nano liquid chromatography capillary tubing

We report on a Computational Fluid Dynamics (CFD) study of the extra dispersion caused by the change in diameter when coupling two pieces of capillary tubing with different diameter. In this first investigation into the problem, the focus is on the typical flow rates (0.25≤F≤2μL/min) and diameters (d≤40μm) used in nano-LC, considering both the case of either a doubling or halving of the diameter. The CFD simulations allow to study the problem from a fundamental point of view, i.e., under otherwise perfect conditions (perfect alignment, zero dead-volume). Flow rates, capillary diameters, diffusion coefficients and liquid viscosities have been varied over a range relevant for nano-LC (Reynolds-numbers Re ≤ 1), with also an excursion made towards high-temperature nano-LC conditions (Re ≥ 10 and more). The extra dispersion caused by the change in diameter has been quantified via a volumetric variance σ²_conn, defined in such a way that the overall dispersion across the entire capillary system can be easily reconstructed from the known analytical solutions in the individual segments. When the two capillaries are longer than their diffusion entry length, covering most of the practical cases, σ²_conn converges to a limiting value σ²_conn,∞ which varies to a close approximation with the square of flow rate. Under the investigated nano-LC conditions, the σ²_conn,∞-values are surprisingly small (e.g., on the order of 0.01 to 0.15 nL² in a 20 to 40μm connection) compared to the dispersion occurring in the remainder of the capillaries.

Kinetic performance comparison of superficially porous, fully porous and monolithic reversed-phase columns by gradient kinetic plots for the separation of protein biopharmaceuticals

To find the best performing column for the analysis of protein-based biopharmaceuticals is a significant challenge as meanwhile numerous modern columns with distinct stationary phase morphologies are available for reversed-phase liquid chromatography. Especially when besides morphology also several other column factors are different, it is hard to decide about the best performing column a priori. To cope with this problem, in the present work 13 different reversed-phase columns dedicated for protein separations were systematically tested by the gradient kinetic plot method. A comprehensive comparison of columns with different morphologies (monolithic, fully porous and superficially porous particle columns), particle sizes and pore diameters as well as column length was performed. Specific consideration was also given to various monolithic columns which recently shifted a bit out of the prime focus in the scientific literature. The test proteins ranged from small proteins starting from 12 kDa, to medium sized proteins (antibody subunits obtained after IdeS-digestion and disulphide reduction) and an intact antibody. The small proteins cytochrome c, lysozyme and β-lactoglobulin could be analysed with similar performance by the best columns of all three column morphologies while for the antibody fragments specific fully porous and superficially porous particle columns were superior. A 450 Å 3,5 µm superficially porous particle column showed the best performance for the intact antibody while a 1.7 µm fully porous particle column with 300 Å showed equivalent performance to the best superficially porous column with thin shell and 400 Å pore size for proteins between 12 and 25 kDa. While the majority of the columns had C4 bonding chemistry, the silica monolith with C18 bonding and 300 Å mesopore size approximated the best performing particle columns and outperformed a C4 300 Å wide-pore monolith. The current work can support the preferred choice for the most suitable reversed-phase column for protein separations.

Fundamental to achieving fast separations with high efficiency: A review of chromatography with superficially porous particles

Types of particles have been fundamental to LC separation technology for many years. Originally, LC columns were packed with large-diameter (>100 μm) calcium carbonate, silica gel, or alumina particles that prohibited fast mobile-phase speeds because of the slow diffusion of sample molecules inside deep pores. During the birth of HPLC in the 1960s, superficially porous particles (SPP, ≥30 μm) were developed as the first high-speed stationary-phase support structures commercialized, which permitted faster mobile-phase flowrates due to the fast movement of sample molecules in/out of the thin shells. These initial SPPs were displaced by smaller totally porous particles (TPP) in the mid-1970s. But SPP history repeated when UHPLC emerged in the 2000s. Stationary-phase support structures made from sub-3-μm SPPs were introduced to chromatographers in 2006. The initial purpose of this modern SPP was to enable chromatographers to achieve fast separations with high efficiency using conventional HPLCs. Later, the introduction of sub-2-μm SPPs with UHPLC instruments pushed the separation speed and efficiency to a very fast zone. This review aims at providing readers a comprehensive and up-to-date view on the advantages of SPP materials over TPPs historically and theoretically from the material science angle.

Through-pore polymerization in polar high-performance liquid chromatography columns allowing scanning electron microscopy based imaging of the packing order

To allow an enhanced understanding of the order in packed HPLC columns, in this work a methodology for immobilizing native polar silica particles is developed based on the polymerization of a methyl methacrylate (MMA) and ethylene glycol dimethacrylate (EGDMA) as a cross-linker in the interstitial pores of HPLC columns. Subsequent mechanical cutting then allows scanning electron microscopy (SEM) based imagery of cross-sections of the packed bed. In this way, the packing efficiency of home-made and commercial HPLC columns with 4.6 mm inner diameter and 150 mm length comprising the same packing material of 5 µm silica particles are compared. The methodology is developed for native silica used in e.g. hydrophilic interaction liquid chromatography (HILIC) and in normal phase LC. In order to confirm the feasibility of the developed methodology, the conventional methods for the evaluation of column, efficiency and porosity, are also employed. The obtained porosity information is compared and showed the same trend with the external porosity measurements obtained via inverse size exclusion approach, illustrating its potential application to study the micro-heterogeneity of packed HPLC columns and to guide the optimization of the packing process of HPLC columns.

Charge variant analysis of protein-based biopharmaceuticals using two-dimensional liquid chromatography hyphenated to mass spectrometry

The profile of charge variants represents an important critical quality attribute of protein-based biopharmaceuticals, in particular of monoclonal antibodies, and must therefore becontrolled. In this work, 2D-LC methods for charge variant analysis were developed using a strong cation-exchange chromatography (SCX) as first dimension (¹D) separation. Non-porous SCX (3 µm) particle columns and different mobile phases were evaluated using a test mixture of some standard proteins of different size and pI (comprising myoglobin, bovine serum albumin, cytochrome c, lysozyme and β-lactoglobulin) and two monoclonal IgG1 antibodies (NIST mAb and Secukinumab). The most promising ¹D eluent for SCX was a salt-mediated pH-gradient system using a ternary mobile phase system with 2-(N-morpholino)ethanesulfonic acid, 1,3-diamino-2-propanol and sodium chloride. For the second dimension (²D), a desalting reversed-phase liquid chromatography (RP-LC) was chosen to enable the hyphenation of the charge variant separation with mass spectrometric (MS) detection. While for intact mAbs the ²D just served for desalting without additional selectivity, the ²D contributed some orthogonal selectivity for the mAb fragment separation. Various core-shell and monolithic columns were tested and variables such as gradient time and flow rate systematically optimized. Unexpectedly, a C4 400 Å column (3.4 µm diameter with 0.2 µm porous shell) provided higher peak capacities compared to the same 1000 Å column (2.7 µm diameter with 0.5 µm porous shell). A thinner shell appeared to be more advantageous than wider pores under high flow regime. An ultra-fast RP-LC method with a run time of one minute was developed using trifluoroacetic acid which was later replaced by formic acid as additive for better MS compatibility. The successful hyphenation of the two orthogonal separation modes, SCX and RP-LC, could be demonstrated in the multiple heart-cutting and the full comprehensive mode. MS analysis using a high-resolution quadrupole time-of-flight instrument enabled to identify different glycoforms and some major charge variants of the antibody at the intact protein level as well as on the subunit level (Fc/2, Lc, Fd') in a middle-up approach by 2D-LC-ESI-MS analysis.

Theoretical Analysis of Efficiency of Multi-Layer Core-Shell Stationary Phases in the High Performance Liquid Chromatography of Large Biomolecules

Modern analytical applications of liquid chromatography require columns with higher and higher efficiencies. In this work, the general rate model (GRM) of chromatography is used for the analysis of the efficiency of core-shell phases having two porous layers with different structures and/or surface chemistries. The solution of the GRM in the Laplace domain allows for the calculation of moments of elution curves (retention time and peak width), which are used for the analysis of the efficiency of bi-layer particles with and without a non-porous core. The results demonstrate that bi-layer structures can offer higher separation power than that of the two layers alone if the inner layer has smaller surface coverage (retentivity) and the pore size and pore diffusion of the outer layer is either equal to or higher than that of the inner layer. Even in the case of core-shell phases, there is an increase in resolution by applying the bi-layer structure; however, we can always find a mono-layer core-shell particle structure with a larger core size that provides better resolution. At the optimal core size, the resolution cannot be further improved by applying a bi-layer structure. However, in case of the most widely produced general-purpose core-shell particles, where the core is ∼70% of the particle diameter, a 15–20% gain of resolution can be obtained by using well-designed and optimized bi-layer core-shell phases.

Recent advances in capillary ultrahigh pressure liquid chromatography

In the twenty years since its initial demonstration, capillary ultrahigh pressure liquid chromatography (UHPLC) has proven to be one of most powerful separation techniques for the analysis of complex mixtures. This review focuses on the most recent advances made since 2010 towards increasing the performance of such separations. Improvements in capillary column preparation techniques that have led to columns with unprecedented performance are described. New stationary phases and phase supports that have been reported over the past decade are detailed, with a focus on their use in capillary formats. A discussion on the instrument developments that have been required to ensure that extra-column effects do not diminish the intrinsic efficiency of these columns during analysis is also included. Finally, the impact of these capillary UHPLC topics on the field of proteomics and ways in which capillary UHPLC may continue to be applied to the separation of complex samples are addressed.

Influence of particle size and shell thickness of core-shell packing materials on optimum experimental conditions in preparative chromatography

The applicability of core-shell phases in preparative separations was studied by a modeling approach. The preparative separations were optimized for two compounds having bi-Langmuir isotherms. The differential mass balance equation of chromatography was solved by the Rouchon algorithm. The results show that as the size of the core increases, larger particles can be used in separations, resulting in higher applicable flow rates, shorter cycle times. Due to the decreasing volume of porous layer, the loadability of the column dropped significantly. As a result, the productivity and economy of the separation decreases. It is shown that if it is possible to optimize the size of stationary phase particles for the given separation task, the use of core-shell phases are not beneficial. The use of core-shell phases proved to be advantageous when the goal is to build preparative column for general purposes (e.g. for purification of different products) in small scale separations.

Some practical comparisons of the efficiency and overloading behaviour of sub-2 μm porous and sub-3 μm shell particles in reversed-phase liquid chromatography

At their optimum flow, sub-3 μm superficially porous or "shell" particles demonstrate similar efficiency to sub-2 μm totally porous particles. The performance of 0.21 cm i.d shell columns is however inferior to those of 0.46 cm i.d., presumably due to packing difficulties. At high flow, shell columns can give flatter Knox curves due to lower operating pressure (half or less of that of the totally porous particles) producing less frictional heating, which combined with the increased thermal conductivity of their non-porous core, gives more efficient heat dissipation. However, the effects of frictional heating for sub-2 μm columns are considerably exaggerated when using pure ACN as mobile phase, as it has a thermal conductivity 3 times less than that of pure water, leading to poorer heat dissipation. Overloading is already problematic for ionised solutes, a group which contains many pharmaceuticals and compounds of clinical relevance, on conventional columns (5 μm porous particles). However, it becomes a more serious issue for both new column types, partially as a result of their very high efficiency, which concentrates the sample as a very narrow band. The sample capacity of one type of shell particle was estimated to be 60% of that of the small totally porous particles, in line with the fraction of the particle volume that is porous. Due to overloading, it is barely possible to achieve perfect peak symmetry for ionised acids or bases with either of these new column types, even by injecting the lowest amounts of sample detectable by UV. While ammonium formate and potassium phosphate buffers gave similar results in overloading studies, use of formic acid as sole mobile phase additive is not recommended for these solutes, as its ionic strength is too low, leading to a catastrophic deterioration in efficiency when sample concentrations of even a few mg/L are injected.

Fast liquid chromatography combined with mass spectrometry for the analysis of metabolites and proteins in human body fluids

In the last decade various analytical strategies have been established to enhance separation speed and efficiency in high performance liquid chromatography applications. Chromatographic supports based on monolithic material, small porous particles, and porous layer beads have been developed and commercialized to improve throughput and separation efficiency. This paper provides an overview of current developments in fast chromatography combined with mass spectrometry for the analysis of metabolites and proteins in clinical applications. Advances and limitations of fast chromatography for the combination with mass spectrometry are discussed. Practical aspects of, recent developments in, and the present status of high-throughput analysis of human body fluids for therapeutic drug monitoring, toxicology, clinical metabolomics, and proteomics are presented.