Experimental investigation of the difference in B-term dominated band broadening between fully porous and porous-shell particles for liquid chromatography using the Effective Medium Theory

On the modelling of the effective longitudinal diffusion in bi-continuous chromatographic beds

We report on the possibility to extend to bi-continuous packings the two models for the effective longitudinal diffusion Deff, or B-term band broadening, recently proposed for discontinuous chromatographic beds. In bi-continuous packings, like monolithic columns, solutes experience a connected end-to-end pathway in both the mobile and stationary zones, as opposed to discontinuous packings, wherein the stationary adsorptive zone is distributed over a set of isolated elements. Since it is unclear whether a densely packed bed of spherical particles should be treated as a continuous or a bi-continuous medium, this extension is also crucial to fully understand the behaviour of packed particle beds. The proposed models for the effective longitudinal diffusion Deff originate from the adoption of the Two Zone Moment Analysis (TZMA) method by which Deff can be expressed as a linear combination of two essential quantities γm and γs, referred to as effective zone-diffusion factors. In the present work we propose two analytical models for γm and γs that now cover both the discontinuous and the bi-continuous case. To validate the theory, several bi-continuous packings are investigated, including the tetrahedral skeleton model (TSM), six different Triple Periodic Minimal Surface (TPMS) monoliths and randomly packed beds of spheres. For all of these, the models provide highly accurate results for Deff over a wide range of porosities and zone retention factors k″. The comparison with literature experimental data for both monolithic silica columns and columns packed with fully porous and porous-shell particles is also presented.

Column-Only Band Broadening in a Porous Shell Radially Elongated Pillar Array Column

In the quest for better performing separation media for liquid chromatography, micropillar array columns have received great interest over the past years. While previous research was mainly focused around micropillar array columns (μPACs) filled with cylindrical pillars, this contribution discusses μPACs with rectangular pillars, which, for the first time, have been anodized and hence carry a mesoporous shell. We report on a series of on-chip measurements of the band broadening and flow permeability in a μPAC with very wide radially elongated pillars (3·75 μm) and with an interpillar distance (2 μm) between that of the first (2.5 μm) and second generation (1.25 μm) of cylindrical μPACs. Because of the extreme flow path tortuosity, this type of μPAC can produce very large plate numbers over a short distance. Despite the relatively large interpillar distance, we obtain Hmin = 0.26 μm for a nearly unretained component (phase retention factor, k' ≈ 0.24) and Hmin = 0.79 μm for a retained component with k' ≈ 3. The kinetic performance in terms of separation impedance (Ei = 19) is considerably improved compared to cylindrical pillar μPACs (Ei in range 40-50) and is in excellent agreement with the theoretical value for an open tubular channel with a rectangular cross-section (Ei = 18). This shows that rectangular μPACs can be represented as a parallel bundle of interconnected open-tubular channels.

Recent developments in the high-throughput separation of biologically active chiral compounds via high performance liquid chromatography

Bioactive compounds, including active pharmaceutical ingredients (APIs), are often chiral molecules where stereoisomers have different biological and therapeutic activity. Nevertheless, the preparation of these molecules can lead to racemic or scalemic mixtures (it is not trivial to produce just the optically pure compound). The evaluation of the enantiomeric purity of bioactive compounds, and therefore quality, is indeed of fundamental importance for regulatory scopes. Chiral high performance liquid chromatography (HPLC) is the gold standard technique to separate and to purify enantiomers. This comes from the wide availability of commercial chiral stationary phases (CSPs) and operational modes, which makes the technique extremely versatile. In recent years, the most relevant trend in the field of chiral analytical HPLC has been the development of CSPs suitable for fast or even ultrafast separations, thus favoring the high throughput screening of biologically active chiral compounds. This process has somehow lagged behind compared to achiral HPLC, due to a series of practical and fundamental issues. The experience has shown how in chiral chromatography even very basic concepts, such as the supposed kinetic superiority of core-shell (pellicular) particles over fully porous ones to improve the chromatographic efficiency, cannot be taken for granted. In this review, the most relevant fundamental and practical features that must be taken into consideration to design successful high-throughput, fast enantioseparations will be discussed. Afterwards, the main classes of CSPs and the most relevant, recent (last five-year) high-throughput applications in the field of the separation of chiral bioactive compounds (for pharmaceutical, forensic, food, and omics applications) will be considered.

Comprehensive analysis of the effective and intra-particle diffusion of weakly retained compounds in silica hydrophilic interaction liquid chromatography columns

A detailed analysis of intra-particle volumes and layer thicknesses and their effect on the diffusion of solutes in hydrophilic interaction liquid chromatography (HILIC) was made. Pycnometric measurements and the retention volume of deuterated mobile phase constituents (water and acetonitrile) were used to estimate the void volume inside the column, including not only the volume of the mobile phase but also part of the enriched water solvent acting as the stationary phase in HILIC. The mobile phase (hold-up) volume accessible to non-retained components was estimated using a homologous series approach. The joint analysis of the different approaches indicated the formation of enriched water layers on the hydrophobic silica mesopore walls with a thickness varying significantly with mobile phase composition. The maximal thickness of the enriched water layers, which corresponded to the minimum void volume accessible to unretained solutes, marked a transition in the retention behavior of the studied analytes. Discrepancies between deuterated solvent measurements and pycnometry were explained by the existence of an irreplaceable water layer adsorbed on the silica surface. Regarding the diffusion behavior in HILIC, peak parking experiments were used to interpret the influence of the acetonitrile content on the effective diffusion coefficient Deff. A systematic decrease in Deff and molecular diffusion Dm was observed with decreasing acetonitrile concentration, primarily attributed to variations in mobile phase viscosity. Notably, Deff/Dm remained nearly unaffected by variations in mobile phase composition. Finally, the effective medium theory was used to make a comprehensive analysis of Dpart/Dm to study the contribution to band broadening when the solute resides in the mesopores. The obtained data unveiled a curvature with a minimum corresponding to conditions of maximum water-layer thickness and retention. For the weakly retained compounds (k' < 0.5) the Dpart/Dm-values were found to be relatively high (order of 0.35-0.5), which directly reflects the high γsDs/Dm-values that were observed (order 0.35-7).

Detailed analysis of the effective and intra-particle diffusion coefficient of proteins at elevated pressure in columns packed with wide-pore core-shell particles

To determine the efficiency that can be obtained in a packed-bed liquid-chromatography column for a particular analyte, a correct determination of the molecular and effective diffusion coefficients (Dm and Deff) of the analyte is required. The latter is usually obtained via peak parking experiments wherein the flow is stopped. As a result, the column pressure rapidly dissipates and the measurement is essentially conducted at ambient pressure. This is problematic for analytes whose retention depends on pressure, such as proteins and potentially other large (dipolar) molecules. In that case, a conventional peak parking experiment is expected to lead to large errors in Deff. To obtain a better estimate ofDeff, the present study reports on the use of a set-up enabling peak parking measurements under pressurized conditions. This approach allowed us to report, for the first time, Deff for proteins at elevated pressure under retained conditions. First, Deff was determined at a (average) pressure of about 105 bar for a set of proteins with varying size, namely: bradykinin, insulin, lysozyme, β-lactoglobulin, and carbonic anhydrase in a column packed with 400 Å core-shell particles. The obtained data were then compared to those of several small analytes: acetophenone, propiophenone, benzophenone, valerophenone, and hexanophenone. A clear trend between Deff and analyte size was observed. The set-up was then used to determine Deff of bradykinin and lysozyme at variable (average) pressures ranging from 28 bar to 430 bar. These experiments showed a decrease in intra-particle and surface diffusion with pressure, which was larger for lysozyme than bradykinin. The data show that pressurized peak parking experiments are vital to correctly determine Deff when the analyte retention varies significantly with pressure.

Dimethyl carbonate as a green alternative to acetonitrile in reversed-phase liquid chromatography. Part I: Separation of small molecules

Nowadays, environmental problems are drawing the attention of governments and international organisations, which are therefore encouraging the transition to green industrial processes and approaches. In this context, chemists can help indicate a suitable direction. Beside the efforts focused on greening synthetic approaches, currently also analytical techniques and separations are under observation, especially those employing large volumes of organic solvents, such as reversed-phase liquid chromatography (RPLC). Acetonitrile has always been considered the best performing organic modifier for RPLC applications, due to its chemical features (complete miscibility in water, UV transparency, low viscosity etc); nevertheless, it suffers of severe shortcomings, and most importantly, it does not fully comply with Environmental, Health and Safety (EHS) requirements. For these reasons, alternative greener solvents are being investigated, especially easily available alcohols. In this work, chromatographic performance of the most common solvents used in reversed-phase chromatography, i.e., acetonitrile, ethanol and isopropanol, have been compared to a scarcely used solvent, dimethyl carbonate (DMC). The analytes of interest were two small molecules, caffeine and paracetamol, whose kinetics and retention behaviour obtained with the four solvents have been compared, and all contributions to band broadening have been assessed. Results about kinetic performance are very promising, indicating that a small amount (7 % v/v) of DMC is able to produce the same efficiency as a 2.5-times larger ACN volume (18 % v/v), and larger efficiency than alcohols. This paper reports, for the first time, fundamental studies concerning the mass transfer phenomena when DMC is used as an organic solvent in RPLC, and, together with the companion paper, represents the results of a research whose final aim was to discover whether DMC is suitable for chromatographic applications both in linear and preparative conditions.

Measurement of the molecular diffusion coefficient and the effective longitudinal diffusion under supercritical fluid chromatography conditions in packed bed columns

The improvement of supercritical fluid chromatography (SFC) instrumentation enhanced its reliability and utility over the past decade. The further development of high speed and high resolution separations is however obstructed by the lack of accurate models for axial dispersion in SFC. This work is a first step to tackle this by developing more reliable methods to measure molecular (D_mol) and longitudinal diffusion (D_eff) in SFC, as these affect all aspects of separation efficiency. In the present contribution, we report on an improved method, to enable more flexible, reliable and accurate measurements of D_mol in SFC using commercial instrumentation. A two-column variant of the stopped-flow experiment is proposed as an adapted set-up for measuring the effective longitudinal diffusion coefficient D_eff in SFC-conditions. Using the set-ups for a number of test-compounds, it has been found that D_eff, and the coefficients describing its constituent sub-processes (cf. particle diffusion D_part and surface diffusion γ_sD_s), all vary in a linearly proportional way with the bulk diffusion coefficient D_mol within a high degree of accuracy. It has also been found that D_eff decreases much more sharply with increasing retention factor compared to LC. By applying the effective medium theory, it was found that the relative surface diffusion coefficient γ_sD_s/D_mol decreases strongly with retention factor for the investigated solutes and column, in contrary to what is typically observed in reversed phase liquid chromatography. Results indicate that this might be related to a change in retention behavior of the analytes. Obviously, more analytes and conditions need to be explored to complete this picture and the extend range of applicability of these observations.

Detailed numerical analysis of the effect of radial column heterogeneities on peak parking experiments with slowly diffusing analytes

The origin of the peak skewness that can be observed when applying the deconvolution method to isolate the diffusion process from the flow processes for peak parking experiments conducted under conditions of slow radial equilibration and strong trans-column velocity gradients was investigated. Numerical simulations were carried out for a variety of trans-column velocity profiles and a broad range of experimental conditions and system parameters were investigated. Results show that, under the aforementioned conditions, the traditionally employed variance subtraction method displays a consistent error which follows the dynamics of the diffusive relaxation during both the peak parking and the flow steps. It is also found that, under the same conditions, the peak deconvolution method is bound to produce deconvoluted "parking-only" peaks that are strongly asymmetric, despite the perfectly symmetric nature of the pure diffusion process marking this parking step. It is shown that this asymmetry is acquired during the flow step following the parking stop. During this step, parked and non-parked peaks are deformed in different ways, despite being subjected to the same trans-column velocity profile. This different deformation cannot be filtered away with the deconvolution or the variance subtraction method, hence introducing an error. Solutions to alleviate the peak skewness and the variance error consist of parking the peak close to the inlet or the outlet or exiting the parked peak through the column inlet (flow reversal method). Under the considered conditions, these approaches could reduce the error on the measured effective diffusion coefficient up to 87%. Carrying out the variance subtraction or the deconvolution process with a peak that has also been parked for a substantially long parking time instead of using a "no-parking" peak as is customary done, is another option to counter the effect.

Measurement and modelling of the intra-particle diffusion and b-term in reversed-phase liquid chromatography

In an ongoing effort to better understand the underlying mechanisms of band broadening in particle-packed reversed-phase liquid chromatography columns, new models for intra-particle diffusion, representing an adsorption- and partition-type retention behavior, are proposed. These models assume the mesoporous zone inside the particles is subdivided in four distinct regions: a fraction f₁ filled with bulk mobile phase, a fraction f₂ enriched in pure organic modifier extending outside the stationary phase layer, a fraction f₃ comprising the liquid surrounding the alkyl chains and a fraction f₄ consisting of the stationary phase alkyl chains. Intra-particle diffusion is calculated as a residence time weighted average of the diffusion in these different regions. Experimental procedures and models are proposed to determine the volumes of these four regions and applied to three reversed-phase liquid chromatography columns with different pore sizes (80 Å versus 300 Å) and different stationary phase types (C₁₈ versus C₈). The newly proposed models are then applied to predict the intra-particle diffusion of butyrophenone across a wide range of retention factors (1 ≤ k" ≤ 40) in each of these columns. These predictions are compared to experimental data that are extracted from the effective diffusion coefficients of butyrophenone obtained via peak parking experiments. It is demonstrated that both adsorption- and partition-type models for intra-particle diffusion model the actual behavior of the test compound well, and require the determination of only one (partition) or two (adsorption) fitting factors: the obstruction to free movement the analytes experience from the alkyl chains in the retained state (partition and adsorption) and in the unretained state (adsorption). Finally, it is demonstrated that the major contributor to the intra-particle diffusion of retained compounds (k" > 2) is the diffusion these analytes undergo when retained in the organic-modifier enriched zone surrounding the alkyl chains (partition model) or when adsorbed onto the alkyl chains (adsorption model), confirming that surface diffusion plays an important role in the mass transfer of retained compounds in reversed-phase liquid chromatography columns.

An explicit expression for the retention factor and velocity dependency of the mobile zone mass transfer band broadening in packed spheres beds used in liquid chromatography

The present study proposes a ready-to-use analytical expression to calculate the mobile zone mass transfer contribution (h_Cm) in packed bed columns. For this purpose, first high-accuracy computations of the band broadening in a perfectly ordered sphere array (fcc-arrangement, external porosity ε=0.40) were made using computational fluid dynamics (CFD), covering a broad range of zone retention factors (2≤k''≤18) and reduced velocities (0≤ν_i≤48). Subsequently, these data were used to determine the value of the geometrical constants in a number of possible analytical expressions for the h_Cm-contribution. This fitting exercise showed the traditional literature approach, using the Wilson-Geankoplis correlation to calculate the dimensionless Sherwood (Sh) number for the mass transfer, leads to fitting errors on the h_Cm-term as large as 150%. Instead, a new correlation for Sh is established. In addition, we also explored the difference in fitting accuracy between h_Cm-expressions based on either a plug-flow or a laminar flow profile assumption. Surprisingly, no significant difference in fitting accuracy between both assumptions was observed. Finally, a best-fit analytical expression is proposed that can represent the CFD-computed band broadening data with an average absolute fitting error of Δh=0.005, corresponding to a relative error of 2.5% on the h_Cm-term and of only 0.3% on the total plate height in a perfectly ordered sphere packing. Defining the presently investigated fcc-ordered sphere array with external porosity=40% as the reference geometry for a perfect sphere packing, the established expression can be used as a new yardstick expression against which the degree of eddy-dispersion can be measured.

The checkerboard model for the eddy-dispersion in laminar flows through porous media. Part I: Theory and velocity field properties

The additivity assumption underlying Giddings' coupling model for the eddy-dispersion in laminar flows through heterogeneous media is critically analyzed and a potential solution for its non-additivity in the high velocity limit is presented. Whereas the unit cell in Giddings' model only consists of a single velocity bias step, the unit dispersion cell of the newly proposed model comprises two consecutive velocity bias steps. Consequently, the unit cell of this new model allows to account for the occurrence of an internal velocity bias rectification at high reduced velocities and is therefore additive in both the low and high velocity limit. First, a mathematical expression for the velocity- and diffusion-dependency of the model's dispersion characteristics has been established. Subsequently, the physical behavior of the model is discussed. It is shown the relation between the eddy-dispersion plate height h and the reduced velocity ν can be expected to display a local maximum in systems where the transversal dispersion purely occurs by molecular diffusion, as is the case in perfectly ordered flow-through media. In disordered media, where the transversal dispersion also contains a significant advective component, the model predicts a velocity-dependency that is qualitatively similar to that described by Giddings' coupling model but, all other conditions being equal, converges to a significantly smaller horizontal asymptote at high reduced velocity. The latter might shed new light on earlier eddy-dispersion studies pursuing a quantitative agreement between experimental data and the Giddings model.

Alternative method to study the radial dispersion in liquid chromatography columns. Part II: Experimental

The present contribution reports on the practical implementation and validation of a new experimental method to determine the radial dispersion (D_rad) in packed bed liquid chromatography columns, as well as on the results obtained with it. A first important validation was that the measured D_rad-values were independent of the applied relative central flow rate (varied from 25% to 57%). The obtained D_rad-values did not vary significantly when changing the concentration of the injected tracer to check potential mass overloading effects (25, 50 or 75 ppm of tracer for the acetophenone measurements; 12.5 and 25 ppm of tracer for the toluene measurements). And yet another important validation step was the observation that the D_rad-values clearly converged to the value of D_eff for velocities going to zero, as physically and theoretically expected. Plotting the obtained results as a plot of D_rad/D_mol versus the reduced velocity ν, a quasi-linear relationship is obtained. The slope of the curve (β = 0.38 and β = 0.46 for toluene and acetophenone, respectively) is significantly larger than the value that is most frequently cited in engineering literature. However, the obtained β-values and D_rad/D_mol-values still fall within the broad range of β- and D_rad/D_mol-values cited in literature.

Detailed efficiency analysis of columns with a different packing quality and confirmation via total pore blocking

We report on a systematic study involving columns with a clearly different efficiency (4 distinct quality groups) obtained by packing the columns that were C₁₈ bonded and endcapped with a different carbon loading. Using B-term analysis (via peak parking) and theoretical models to estimate the magnitude of the C_m- and C_s-term contributions, it could be concluded that the difference in efficiency among the groups was entirely due to a difference in eddy dispersion. As such, the columns provided an ideal testing ground to verify how well the total pore blocking (TPB)-method can be used to probe differences in packing heterogeneity. In agreement with earlier literature observations, it turns out the TPB-method is much more sensitive to packing heterogeneities than the eddy dispersion (H_eddy)-contribution measured under open-pore conditions via B- and C- term subtraction. Typically, differences in H_eddy on the order of 0.1-0.5μm translate into a difference on the order of 0.5-2μm in the TPB mode. This confirms the TPB as a powerful technique to make very sensitive measurements of the homogeneity of packed beds.

Retention and effective diffusion of model metabolites on porous graphitic carbon

The study of metabolites in biological samples is of high interest for a wide range of biological and pharmaceutical applications. Reversed phase liquid chromatography is a common technique used for the separation of metabolites, but it provides little retention for polar metabolites. An alternative to C18 bonded phases, porous graphitic carbon has the ability to provide significant retention for both non-polar and polar analytes. The goal of this work is to study the retention and effective diffusion properties of porous graphitic carbon, to see if it is suitable for the wide injection bands and long run times associated with long, packed capillary-scale separations. The retention of a set of standard metabolites was studied for both stationary phases over a wide range of mobile phase conditions. This data showed that porous graphitic carbon benefits from significantly increased retention (often >100 fold) under initial gradient conditions for these metabolites, suggesting much improved ability to focus a wide injection band at the column inlet. The effective diffusion properties of these columns were studied using peak-parking experiments with the standard metabolites under a wide range of retention conditions. Under the high retention conditions, which can be associated with retention after injection loading for gradient separations, Deff/Dm∼0.1 for both the C18-bonded and porous graphitic carbon columns. As C18 bonded particles are widely, and successfully utilized for long gradient separations without issue of increasing peak width from longitudinal diffusion, this suggests that porous graphitic carbon should be amenable for long runtime gradient separations as well.

Superficially porous particles with 1000Å pores for large biomolecule high performance liquid chromatography and polymer size exclusion chromatography

To facilitate mass transport and column efficiency, solutes must have free access to particle pores to facilitate interactions with the stationary phase. To ensure this feature, particles should be used for HPLC separations which have pores sufficiently large to accommodate the solute without restricted diffusion. This paper describes the design and properties of superficially porous (also called Fused-Core^®, core shell or porous shell) particles with very large (1000Å) pores specifically developed for separating very large biomolecules and polymers. Separations of DNA fragments, monoclonal antibodies, large proteins and large polystyrene standards are used to illustrate the utility of these particles for efficient, high-resolution applications.

Size exclusion chromatography with superficially porous particles

A comparison is made using size-exclusion chromatography (SEC) of synthetic polymers between fully porous particles (FPPs) and superficially porous particles (SPPs) with similar particle diameters, pore sizes and equal flow rates. Polystyrene molecular weight standards with a mobile phase of tetrahydrofuran are utilized for all measurements conducted with standard HPLC equipment. Although it is traditionally thought that larger pore volume is thermodynamically advantageous in SEC for better separations, SPPs have kinetic advantages and these will be shown to compensate for the loss in pore volume compared to FPPs. The comparison metrics include the elution range (smaller with SPPs), the plate count (larger for SPPs), the rate production of theoretical plates (larger for SPPs) and the specific resolution (larger with FPPs). Advantages to using SPPs for SEC are discussed such that similar separations can be conducted faster using SPPs. SEC using SPPs offers similar peak capacities to that using FPPs but with faster operation. This also suggests that SEC conducted in the second dimension of a two-dimensional liquid chromatograph may benefit with reduced run time and with equivalently reduced peak width making SPPs advantageous for sampling the first dimension by the second dimension separator. Additional advantages are discussed for biomolecules along with a discussion of optimization criteria for size-based separations.

Very High Efficiency Porous Silica Layer Open-Tubular Capillary Columns Produced via in-Column Sol-Gel Processing

It is demonstrated that 5 μm i.d. capillaries can be coated with mesoporous silica layers up to 550 nm thickness. All the columns produced using in-column sol-gel synthesis with tetramethoxysilane provide plate height curves that closely follow the Golay-Aris theory. In 60 cm long columns, efficiencies as high as N = 150 000 and N = 120 000 were obtained, respectively, for a 300 and 550 nm thick porous layer. An excellent retention and plate height reproducibility was obtained when the recipes were subsequently applied to produce very long (1.9 and 2.5 m) capillaries. These columns produced efficiencies up to N = 600 000 plates for a retained and around N = 1 000 000 plates for an unretained component. Given the good reproducibility on the long capillaries, and considering that mesoporous silica is still the preferred support for LC, it is believed the present study could spur a renewed interest in open-tubular LC.

Kinetic performance comparison of fully and superficially porous particles with sizes ranging between 2.7 μm and 5 μm: Intrinsic evaluation and application to a pharmaceutical test compound

The reintroduction of superficially porous particles has resulted in a leap forward for the separation performance in liquid chromatography. The underlying reasons for the higher efficiency of columns packed with these particles are discussed. The performance of the newly introduced 5 μm superficially porous particles is evaluated and compared to 2.7 μm superficially porous and 3.5 and 5 μm fully porous columns using typical test compounds (alkylphenones) and a relevant pharmaceutical compound (impurity of amoxicillin). The 5 μm superficially porous particles provide a superior kinetic performance compared to both the 3.5 and 5 μm fully porous particles over the entire relevant range of separation conditions. The performance of the superficially porous particles, however, appears to depend strongly on retention and analyte properties, emphasizing the importance of comparing different columns under realistic conditions (high enough k) and using the compound of interest.