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.

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title: Fast liquid chromatography: an investigation of operating parameters and the separation of nucleotides on pellicular ion exchangers.
abstract: Operating parameters and separation of nucleotides on pellicular ion exchangers investigated by liquid chromatographic system

title: 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.
abstract: 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.

title: Evaluation of the properties of a superficially porous silica stationary phase in hydrophilic interaction chromatography.
abstract: The sample capacity, column efficiency (and its variation with flow) of a superficially porous unbonded silica phase (Halo) was investigated using hydrophilic interaction chromatography (HILIC), particularly for separation of basic compounds. Sample capacity compared with totally porous silica phases was somewhat reduced, broadly in line with the decreased surface area, but still favourable compared with reversed-phase separations of these solutes. Efficiencies in excess of 100,000 plates were obtained at room temperature in reasonable analysis times by using a 45 cm coupled column, while generating back pressures compatible with conventional HPLC. Shorter columns offered the possibility of fast analysis of bases, and the unfavourable mass transfer properties reported by others at high flow rate for similar reversed-phase columns, were not apparent. While excellent peak shapes were obtained for many bases on silica HILIC phases, problems may still occur for some solutes.

title: Performance characteristics of new superficially porous particles.
abstract: Superficially porous particles (also called Fused-Core, core shell or porous shell particles) show distinct advantages over comparable totally porous particles for separating small molecules. Columns of Fused-Core particles exhibit very high efficiency because of superior eddy dispersion properties (smaller van Deemter A term). The efficiency for columns of 2.7 μm Fused-Core particles actually rivals that for sub-2 μm totally porous particles with only about one-half the back pressure. These Fused-Core particles show special advantages with larger molecules for fast separations at high mobile phase velocities because of superior mass transfer (kinetic) properties (smaller van Deemter C term). This report describes the effect of different particle size and porous shell thicknesses on chromatographic performance for Fused-Core particles. Particle characteristics can significantly affect factors of separation importance. For example, the reduced plate height of packed columns is affected by particle diameter. Interestingly, larger Fused-Core particles show smaller reduced plate heights than smaller Fused-Core particles. Also, porous shell thickness has a strong effect on solute retention as well as separation efficiency, and particle surface area has a direct influence on sample loading characteristics. Fused-Core particles with a wide range of physical characteristics have been developed that allows the preparation of stable, efficient packed columns.

title: Evaluation of columns packed with shell particles with compounds of pharmaceutical interest.
abstract: The commercial C18 columns packed with sub-3 μm shell particles were tested and compared to a reference UHPLC column, in terms of kinetic performance as well as selectivity, retention capability, peak shape and loading capacity. For this purpose, a set of pharmaceutically relevant molecules was selected, including acidic, neutral and basic drugs. Regarding kinetic performance, h(opt) values for the shell particles were found between 1.7 and 2, while the UHPLC column provided a value of approximately 2.5. However, this impressive performance should be considered with caution, particularly for the construction of kinetic plots since h(opt) values were sometimes related to the column dimensions, depending on the provider (h(opt) comprised between 1.8 and 2.6 for longer columns of 150 mm packed with shell particles). Despite the non-porous inner core of the shell particles representing between 25 and 36% of the particle, we demonstrated that the decrease in retention was on the maximum equal to 15% for Ascentis column while Acquity and Poroshell were strictly equivalent in terms of retention. Concerning loading capacity, it remains comparable to that of fully porous sub-2 μm particles and always more pronounced with 0.1% formic acid vs. phosphate buffer. The loading capacity of the different columns was found to be better correlated to the pore volume or surface coverage than the shell thickness. Experimentally, the most pronounced overloading was observed with the Poroshell. Finally, the selectivity and peak shape were evaluated using a mixture of basic and acidic drugs. It appears that results were very similar between sub-3 μm shell particles and fully porous sub-2-μm particles for our mixture of compounds, showing the ability to transfer existing methods to shell particles, with only limited adjustments. This study confirms the potential of columns packed with shell particles and demonstrates the interest of such column technology with pharmaceutical compounds.

title: A comparison of overload behaviour for some sub 2 μm totally porous and sub 3 μm shell particle columns with ionised solutes.
abstract: The overloading performance of some 2.7 μm shell and sub 2 μm totally porous columns, including one pair manufactured from similar materials with similar bonding chemistries, was compared using strongly acidic and basic probe compounds. In general, the capacity of shell particles was not greatly reduced, despite containing a smaller porous volume. Nevertheless, at low pH, both types of column were overloaded by only small concentrations of ionised solute. Considerable improvement could be gained by increasing the buffer concentration, although sensitivity in mass spectrometric detection may be compromised. The capacity of columns of different internal diameter may not be directly compared merely by scaling the injection volumes, as it is possible that the sample is not homogeneously distributed across the column radius, especially in larger diameter columns, where the sample may travel preferentially through a central core of the packing. A totally porous charged surface hybrid phase gave much improved loading properties of the basic probe in low ionic strength mobile phases such as formic acid, often used in mass spectrometry. However, its relative advantage over conventional phases was reduced as the mobile phase ionic strength was increased. Furthermore, acidic compounds may give tailing on this phase. At pH 7, all columns tested showed evidence of interaction with ionised silanols; peak shapes improved as the buffer concentration was increased. Column efficiency first increased and then decreased as solute concentration was increased at constant buffer concentration, which can be attributed to the decreasing proportion of solute molecules retained by the ion exchange process.

title: Evaluation of recent very efficient wide-pore stationary phases for the reversed-phase separation of proteins.
abstract: In the present contribution, columns packed with fully porous widepore 1.7μm particles (Acquity BEH300) and widepore core-shell 3.6μm particles (Aeris WP) were evaluated for the separation of model and therapeutic proteins of varying sizes, hydrophobicity and isoelectric points. Two types of bonding were compared, namely C4 and C18 in a systematic way. The kinetic performance of these stationary phases was evaluated in a previous paper hence this new work focuses on their retention behaviour, loading capacity and selectivity. Using the Tanaka tests, model proteins, and other confirmatory experiments, it is highly probable that with proteins, strong interaction mechanisms were predominant on the Aeris WP while the hydrophobic interaction was the driving force of the retention on the Acquity BEH300 material. This explained why, despite the lower pore volume of the Aeris WP material, the apparent retention factors of proteins possessing both hydrophobic and charged amino acids residues were very close on the four investigated columns. In terms of peak widths, values for proteins were similar for all the tested stationary phases, despite the probable strong ion exchange mechanisms of Aeris WP column. This could be explained by the excellent mass transfer characteristics afforded by the thin porous layer (∼0.2μm) at the surface of the particle which probably compensates for the slow secondary ionic interaction kinetics. The loading capacity was also evaluated on all the four widepore columns, using model proteins. On average, approximately 2-4 times higher amount of proteins can be injected on the fully porous BEH300 compared to the core-shell Aeris WP columns when avoiding 10% change in peak width or in tailing. However, this result could be strongly influenced by the nature and shape of the protein, its hydrophobicity, folding, size and number of charges. Finally, all of these columns were employed for the highly efficient separation of a therapeutic protein (interferon-α-2A) and some closely related proteins and showed excellent performance and selectivity. This result confirms that RPLC gained interest in the biopharmaceutical field as it provides significantly better peak widths than size-exclusion or ion-exchange and inherent compatibility with MS.

title: Fast liquid chromatography: the domination of core-shell and very fine particles.
abstract: Columns packed with sub-2 μm totally porous and sub-3 μm core-shell particles are very widespread nowadays to conduct fast and efficient separations. In order to carry out really fast separations, short (5 cm long) columns are very popular today. The goal of this paper is to review the recent possibilities in fast or "ultra-fast" HPLC by applying short and narrow bore columns packed with modern core-shell and very fine fully porous particles. Efficiency data obtained with these recently commercialized columns from the past few years are collected, discussed and compared in terms of potential separation time and efficiency. The reasons of the success of these columns are presented. This paper also shows that theoretically expected efficiency is sometimes compromised in practical work especially in the case of narrow bore columns. The extra-column dispersion of a given LC system can also dramatically decrease the performance of small columns. It is not possible to utilize the real efficiency of these small columns in spite of their really high intrinsic separation power.

title: Relationship between the particle size distribution of commercial fully porous and superficially porous high-performance liquid chromatography column packings and their chromatographic performance.
abstract: The separation efficiency and kinetics of several commercial HPLC particle types (both fully porous and superficially porous) have been investigated using a pharmaceutical weakly basic N-containing compound as a test molecule. A strong trend between the particle size distribution (PSD) of the particles and the typically employed "goodness of packing"-parameters was observed. The relative standard deviation of the PSD of the tested particles ranged between 0.05 and 0.2, and in this range, a near linear relationship between the A-term constant, the h(min)-value and the minimal separation impedance was found. The experimental findings hence confirm the recent observations regarding the relationship between the narrow PSD of the recently commercialized porous-shell particles and their superior efficiency and kinetic performance. The outcome also suggests that the performance of the current generation of fully porous particle columns could be significantly improved if the PSD of these particles could be reduced.

title: Characteristics of superficially-porous silica particles for fast HPLC: some performance comparisons with sub-2-microm particles.
abstract: Columns of 2.7-microm fused-core (superficially porous) Type B silica particles allow very fast separations of small molecules at pressures available in most high-performance liquid chromatography instruments. These highly-purified particles with 1.7-microm solid silica cores and 0.5-microm-thick shells of 9 nm pores exhibit efficiencies that rival those of totally porous sub-2-microm particles but at one-half to one-third of the column back pressure. This presentation describes other operating features of fused-core particle columns, including sample loading characteristics and packed bed stability. The superior mass transfer (kinetic) properties of the fused-core particles result in much-improved separation efficiency at higher mobile phase velocities, especially for > 600 molecular weight solutes.

title: Instrumental considerations for the effective operation of short, highly efficient fused-core columns. Investigation of performance at high flow rates and elevated temperatures.
abstract: Fused core or superficially porous columns offer the advantages of higher efficiency compared with totally porous columns of the same particle size, but similar operating pressures. However, their performance may be adversely affected by extra-column effects that become more significant as the column efficiency increases, and as the diameter of the column is reduced. In this study, we show that 10cmx0.46cm fused-core columns can be used on modified conventional instruments ("microbore systems") without serious loss in performance, and this approach is at present likely to yield superior results compared with use of 0.21cm columns (of identical efficiency) on current UHPLC instruments that have minimised extra-column volume. Furthermore, the true efficiency of commercial narrow-bore fused-core columns appears to be reduced compared with those of conventional bore, which may be due to packing difficulties for the former type. The fused-core columns in general gave excellent performance, showing no evidence of an upturn in the Knox plots at high flow velocities and elevated temperatures. Careful control of experimental conditions is necessary to ensure accurate data for these plots.

title: Comparison of performance of high-performance liquid chromatography columns packed with superficially and fully porous 2.5 μm particles using kinetic plots.
abstract: A recently introduced 2.5 μm fully porous support (Kromasil Eternity) is compared with three different brands of superficially porous material (Kinetex, Halo and Poroshell 120) by means of the kinetic plot method using pharmaceutical compounds from GlaxoSmithKline as probe molecules. The kinetic plot method immediately shows the range of plate numbers wherein a support performs better than another. Results from experiments carried out at pH 4.5 and 8.0 are presented in order to assess the pH stability of the tested phases. Moreover, since all supports are able to withstand pressures higher than 400 bar, they have been evaluated both on HPLC and UHPLC instrumentation. True average particle sizes were determined by SEM images taken from loose stationary phases. Kinetex outperforms the other columns in HPLC conditions for practically relevant efficiencies, but shows poor packing quality in the 100×2.1-mm format. Kromasil is advantageous for simple and fast separations on short columns both in HPLC and in UHPLC conditions. Halo achieves the highest efficiencies of all columns at the lowest pressure cost and shows a noticeable lower axial diffusion. Poroshell 120 has the best packing quality reproducibility across the tested formats. All columns preserve their performance at high pH.

title: Physical properties and structure of fine core-shell particles used as packing materials for chromatography Relationships between particle characteristics and column performance.
abstract: The recent development of new brands of packing materials made of fine porous-shell particles, e.g., Halo and Kinetex, has brought great improvements in potential column efficiency, demanding considerable progress in the design of chromatographic instruments. Columns packed with Halo and Kinetex particles provide minimum values of their reduced plate heights of nearly 1.5 and 1.2, respectively. These packing materials have physical properties that set them apart from conventional porous particles. The kinetic performance of 4.6mm I.D. columns packed with these two new materials is analyzed based on the results of a series of nine independent and complementary experiments: low-temperature nitrogen adsorption (LTNA), scanning electron microscopy (SEM), inverse size-exclusion chromatography (ISEC), Coulter counter particle size distributions, pycnometry, height equivalent to a theoretical plate (HETP), peak parking method (PP), total pore blocking method (TPB), and local electrochemical detection across the column exit section (LED). The results of this work establish links between the physical properties of these superficially porous particles and the excellent kinetic performance of columns packed with them. It clarifies the fundamental origin of the difference in the chromatographic performances of the Halo and the Kinetex columns.

title: Mass transfer mechanism in liquid chromatography columns packed with shell particles: would there be an optimum shell structure?
abstract: The mass transfer mechanisms in columns packed with old (55 μm Zipax and 5 μm Poroshell) and recently commercialized shell particles (2.7 μm Halo-C(18) and Kinetex-C(18)) were investigated from a physico-chemical point of view. Combining a model of diffusion in heterogeneous packed beds (effective medium theory) with values of the heights equivalent to a theoretical plate (HETPs derived from the first and second central moments of the elution profiles) and of the peak variances provided by the peak parking method, we demonstrate that columns packed with current shell particles perform better than those packed with fully porous particles in resolving low molecular weight compounds because the eddy diffusion term of the van Deemter equation of the former is markedly smaller. The calculation of eddy diffusion in column beds suggests that the smaller A terms are due to smaller trans-column velocity bias in columns packed with shell particles. We also show that the mass transfer of large molecules (e.g., proteins) is faster when the internal volume accessible to the analyte increases. Therefore, it is suggested that shell particles made of concentric layers with average pore sizes increasing with increasing diameter would provide columns with higher efficiency.

title: Shell particles, trials, tribulations and triumphs.
abstract: The concept of pellicular particles was imagined by Horváth and Lipsky fifty years ago. They were initially intended for the analysis of macromolecules. Later, shell particles were prepared. The rational behind this concept was to improve column efficiency by shortening the pathways that analyte molecules must travel and, so doing, to improve their mass transfer kinetics. Several brands of superficially porous particles were developed and became popular in the 1970s. However, the major improvements in the manufacturing of high-quality, fully porous particles, that took place in the same time, particularly by making them finer and more homogeneous, hampered the success of shell particles, which eventually disappeared. Recently, the pressing needs to improve analytical throughputs forced particle manufacturers to find a better compromise between the demands for higher column efficiency that require short diffusion paths of analyte molecules in columns and the need for columns that can be operated with the conventional instruments for liquid chromatography, which operate with moderate column back-pressures. This lead to the apparition of a new generation of columns packed with shell particles, which bring chromatographic columns to a level of efficiency undreamed of a few years ago. This evolution is reviewed, the reason that motivated it, and the consequences of their success are discussed.

title: Mass transfer kinetics, band broadening and column efficiency.
abstract: Important progress was recently made in our understanding of the physico-chemical aspects of mass transfer kinetics in chromatographic columns, in methods used for accurate determination of the different contributions to the height equivalent to a theoretical plate (HETP), and in the application of these advances to the elucidation of mass transfer mechanisms in columns packed with recent chromatographic supports (sub-2 μm fully porous particles, sub-3 μm core-shell particles, and monoliths). The independent contributions to the HETP are longitudinal diffusion, eddy dispersion, liquid-solid mass transfer (including trans-particle or trans-skeleton mass transfer and external film mass transfer), and the contributions caused by the thermal heterogeneity of the column. The origin and importance of these contributions are investigated in depth. This work underlines the areas in which improvements are needed, an understanding of the contribution of the external film mass transfer term, a better design of HPLC instruments providing a decrease of the extra-column band broadening contributions to the apparent HETP, the development of better packing procedures giving more radially homogeneous column beds, and new packing materials having a higher thermal conductivity to eliminate the nefarious impact of heat effects in very high pressure liquid chromatography (vHPLC) and supercritical fluid chromatography (SFC).

title: Critical comparison of performances of superficially porous particles and sub-2 microm particles under optimized ultra-high pressure conditions.
abstract: The performance of 2.7 microm superficially porous particles at 600 bar and sub-2 microm fully porous particles at 1000 bar were compared by the Poppe plot method. Theoretical Poppe plots were first constructed for each stationary phase to compare their kinetic performance at different analysis times. The theory was then verified by experiments under the optimized conditions identified from the Poppe plot calculation. We found that the 2.7 microm superficially porous particles at 600 bar can provide similar performance compared to the sub-2 microm fully porous particles at ultra-high pressure (1000 bar) when analysis times are very short (e.g. sub-minute). As analysis time increases, the superficially porous particles start to outperform the sub-2 microm particles and can give much higher efficiencies (e.g. > 2 times higher plate count) at very long analysis times (>3h). The comparison was extended to gradient elution of a mixture of pharmaceutical interest by constructing gradient peak capacity Poppe plots and similar behavior was observed.

title: Kinetic plot based comparison of the efficiency and peak capacity of high-performance liquid chromatography columns: theoretical background and selected examples.
abstract: The present contribution reviews the foundations of the kinetic-plot method for the direct comparison of the kinetic performance of different chromatographic support and operating modes. The method directly uses experimental data collected for a specific sample and operating condition of one's interest, and is applicable both under isocratic- and gradient-elution conditions. Experimental proof is provided for the strong relation between the kinetic performance of a given support under isocratic and gradient conditions: a material offering superior kinetic performances under isocratic conditions will remain superior under gradient conditions and vice versa provided the comparison occurs under unbiased conditions. In addition, a review is made of the recent literature using the kinetic-plot method to compare and assess the kinetic performance of high performance HPLC columns and their operation mode.

title: Maximizing the peak capacity using coupled columns packed with 2.6 μm core-shell particles operated at 1200 bar.
abstract: We report on the peak capacity that can be produced by operating a state-of-the-art core-shell particle type (d(p)=2.6 μm) at its kinetic optimum at ultra-high pressures of 600 and 1200 bar. The column-length optimization needed to arrive at this kinetic optimum was realized using column coupling. Whereas the traditional operating mode (using a single 15 cm column operated at its optimum flow rate of 0.4 mL/min) offered a peak capacity of 162 in 10.8 min, a fully optimized train of 60 cm (4×15 cm) columns offered a peak capacity of 325 in 61 min when operated at 1200 bar. Even though the particles have a reputed low flow resistance and a relatively large size (>2 μm), it was found that the increase in performance that can be generated when switching from a fully optimized 600 bar operation to a fully optimized 1200 bar operation is significant (roughly 50% reduction of the analysis time for the same peak capacity and approximately a 20% increase in peak capacity if compared for the same analysis time). This has been quantified in a generic way using the kinetic plot method and is illustrated by showing the chromatograms corresponding to some of the data points of the kinetic plot curve.

title: Equivalence of the different Cm- and Cs-term expressions used in liquid chromatography and a geometrical model uniting them.
abstract: It is shown that all C m and C s expressions ever established in the literature are intrinsically fully identical and can be derived from a simple parallel plug flow model. Analytically solving this model yields C m- and C s-term expressions that exactly correspond to the expressions obtained via either the method of moments (general rate model) or via Giddings' nonequilibrium theory. This holds for open-tubular as well as packed and monolithic columns. From this equivalence, a set of convenient "translation" expressions could be established, enabling a swift transition between the different C m- and C s-term expressions that currently coexist in literature. The link with the parallel plug flow model provides a good physical insight into the assumptions underlying the general rate model (e.g., a plug flow in the flow-through pores) and in the physical meaning of the different parameters involved in it. The parallel plug flow model also allows us to illustrate the difference between the zone and the phase retention factor and between the intraparticle diffusion coefficient and the effective diffusion coefficient used in the general rate model. These differences are subtle, but as they can have a large impact, they constitute important potential sources of confusion currently obscuring the modeling of HPLC columns.

title: Errors involved in the existing B-term expressions for the longitudinal diffusion in fully porous chromatographic media Part II: experimental data in packed columns and surface diffusion measurements.
abstract: Peak parking experiments have been performed on three RP-HPLC different columns, using two different components and a variable mobile phase composition. The aim of the study was to investigate whether the B-term diffusion expressions currently used in the literature (which are all Knox-type models) should be replaced by the effective diffusion expressions that have been developed in the frame of the effective medium theory (EMT). Although the EMT-expressions are not fully accurate either (the mathematics of the complex interactions between different diffusion zones that are in close contact are too demanding to catch them in an exact analytical expression), they at least are physically sound and do not violate Maxwell's basic law of diffusion. Further they also provide a much better approximation of the numerically calculated effective diffusivity in the theoretical test situation considered in part I. The present study shows that the values of the surface or stationary phase diffusion coefficient that are derived from peak parking models can depend heavily on the employed B-term model. The EMT-based B-term expressions lead to values of the surface diffusion coefficient that vary much less strongly with the phase retention factor than if one of the Knox-type models is used to analyze the data. This implies that, since all peak parking experiments that have been performed in the past have all been interpreted with a Knox-type model, the conclusions that have been drawn from these studies should all be moderated or at least revisited.

title: Comparison between the efficiencies of columns packed with fully and partially porous C18-bonded silica materials.
abstract: The chromatographic performance of a new brand of shell particles is compared to that of a conventional brand of totally porous silica particles having a similar size. The new material (Halo, Advanced Materials Technology, Wilmington, DE) is made of 2.7 microm particles that consist in a 1.7 microm solid core covered with a 0.5 microm thick shell of porous silica. The other material consists of the porous particles of a conventional 3 microm commercial silica-B material. These two columns have the same dimensions, 150 mm x 4.6mm. The reduced plate heights of two low molecular weight compounds, naphthalene and anthracene, two peptides (lys-bradykinin and bradykinin), and four proteins, insulin, lysozyme, beta-lactoglobulin, and bovine serum albumin were measured in a wide flow rate range and analyzed on the basis of the Van Deemter equation and of modern models for its terms. The Halo column provides a smaller axial diffusion coefficient B and a smaller eddy dispersion term A than the other column, a result consistent with its lower internal porosity (in(p)=0.19 versus 0.42) and with the narrower size distribution of its particles (sigma=5% versus 13%). The two columns have similar C terms for the two low molecular weight compounds and for the two peptides. However, the C term of the proteins that are not excluded is markedly lower on the column packed with the Halo particles than on the other column. A recent theoretical analysis of the mass transfer kinetics in shell particles predicts a C term for moderately retained proteins (3<k'<5) that is about 35% lower for shell than for fully porous particles while the experimental data show a value nearly 45% lower, an excellent agreement considering that the internal tortuosity of the particles might be different, affecting the ratio of the effective diffusivities (D(eff)) of the proteins in the two materials. Surprisingly, the Kozeny-Carman constant of the Halo packed column is 50% larger than that of the other column, in spite of which the permeability of the Halo column is slightly larger, due to its larger external porosity.

title: 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.
abstract: The difference in B-term diffusion between fully porous and porous-shell particles is investigated using the physically sound diffusion equations originating from the Effective Medium Theory (EMT). Experimental data of the B-term diffusion obtained via peak parking measurements on six different commercial particle types have been analyzed (3 porous and 3 non porous). All particles were investigated using the same experimental design and test analytes, over a very broad range of retention factor values. First, the B-term reducing effect of the solid core (inducing an additional obstruction compared to fully porous particles) has been quantified using the Hashin-Shtrikman expression, showing that the presence of a solid core can account for a reduction of about 11% when the core diameter makes up 63% of the total particle diameter (Halo and Poroshell-particles) and a reduction of 16% when the core diameter makes up 73% (Kinetex). Remaining differences can be attributed to differences in the microscopic structure of the meso-porous material (meso-pore diameter, internal porosity or relative void volume). The much lower B-term diffusion of Halo and Kinetex particles compared to the fully porous Acquity particles (some 20-40% difference, of which about 10-15% can be attributed to the presence of the solid core) can hence largely be attributed to the much smaller internal porosity and the smaller pore size of the meso-porous material making up the shell of these particles.

title: Effective medium theory expressions for the effective diffusion in chromatographic beds filled with porous, non-porous and porous-shell particles and cylinders. Part II: Numerical verification and quantitative effect of solid core on expected B-term band broadening.
abstract: The results of a numerical simulation study of the diffusion and retention in fully porous spheres and cylinders are compared with some of the high order accuracy analytical solutions for the effective diffusion coefficient that have been derived from the effective medium theory (EMT) theory in part I of the present study. A variety of different ordered (spheres and cylinders) and disordered (cylinders) packings arrangements has been considered. The agreement between simulations and theory was always excellent, lying within the (very tight) accuracy limits of the simulations over the full range of retention factor and diffusion constant values that is practically relevant for most LC applications. Subsequently filling up the spheres and cylinders with a central solid core, while keeping the same packing geometry and the same mobile phase (same thermodynamic retention equilibrium), it was found that the core induces an additional obstruction which reduces the effective intra-particle diffusion coefficient exactly with a factor γ(part)=2/(2+ρ³) for spherical particles and γ(part)=1/(1+ρ²) for cylinders (ρ is the ratio of the core to the particle diameter, ρ=d(core)/d(part)). These expressions hold independently of the packing geometry, the value of the diffusion coefficients and the equilibrium constant or the size of the core. The expressions also imply that, if considering equal mobile phase conditions, the presence of the solid core will never reduce the particle contribution to the B-term band broadening with more than 33% (50% in case of cylindrical pillars).

title: Geometry-independent plate height representation methods for the direct comparison of the kinetic performance of LC supports with a different size or morphology.
abstract: The advantages of representing experimental plate height data as a plot of Kv/u0(2) or H2/Kv versus Kv/(Hu0) instead of as H versus u0 are discussed (Kv=column permeability). Multiplying the values on both axes by the ratio of a reference pressure drop and mobile-phase viscosity, the obtained plots directly yield the kinetic performance limits of the tested support structure, without any need for further numerical optimization. Directly showing the range of plate numbers or analysis times wherein the tested support geometry can yield faster separations or produce more plates than another support type, such kinetic plots are ideally suited to compare the performance of differently shaped or sized LC supports. The approach hence obviates the need for a common reference length, which is a clear problem if it is attempted to compare differently shaped supports on the basis of their flow resistance phi and reduced plate height h. It is also shown how an MS Excel template file, only requiring the user to paste the column permeability Kv and a series of experimental (u0, H) data, can be used to automatically establish a series of so-called kinetic performance (KP) numbers, which can be used to completely describe the performance characteristics of the considered support. The advantages of the proposed data representation methods are demonstrated by applying them to several recent literature plate height data sets, showing that the obtained kinetic plots directly visualize the range of plate numbers where new approaches such as ultra-high-pressure HPLC or the use of open-porous silica monoliths can be expected to provide a substantial gain and where not. The data analysis also showed that the most generally relevant KP numbers are N(opt) (the plate number for which the support achieves its best analysis time/pressure cost ratio), t(opt) (the time needed to obtain N(opt) plates), and t(1K) (the time needed to generate 1000 or 1 kilo of theoretical plates). These KP numbers are much more informative than the H(min), u(0,opt), and Kv data traditionally employed to quantify the performance of LC supports.

title: Method to predict and compare the influence of the particle size on the isocratic peak capacity of high-performance liquid chromatography columns.
abstract: A kinetic plot based method has been used to experimentally predict the optimal particle size yielding the maximal isocratic peak capacity in a given analysis time. Applying the method to columns of three different manufacturers and characterizing them by separating a 4-component paraben mixture at 30 degrees C, it was consistently found that the classical 3 and 3.5 microm particles provide the highest peak capacity for typical isocratic separation run times between 30 and 60 min when operating the columns at a conventional pressure of 400 bar. Even at 1000 bar, the sub-2 microm particles only have a distinct advantage for runs lasting 30 min or less, while for runs lasting 45 min or longer the 3 and 3.5 microm again are to be preferred. This finding points at the advantage for high-resolution separations that could be obtained by producing 3 and 3.5 microm particle columns that can be operated at elevated pressures.

title: The kinetic plot method applied to gradient chromatography: theoretical framework and experimental validation.
abstract: The kinetic plot method, originally developed for isocratic separations, was extended to the practically much more relevant case of gradient elution separations. A set of explicit as well as implicit data transformation expressions has been established. These expressions can readily be implemented in any calculation spread-sheet program, and allow to directly turn any experimental data set representing the relation between the separation efficiency and the flow rate measured on a single column into the kinetic performance limit curve of the tested separation medium. Since the kinetic performance limit curve is based on an extrapolation to columns with a different length, it should be realized that the curve is only valid under the assumption that the gradient time and the delay time (if any) are adapted such that the analytes are subjected to the same relative mobile phase history when the column length is changed. Both experimental and numerical data are presented to corroborate the fact that the kinetic performance limit curves that are obtained using the proposed expressions are indeed independent of the column length the experimental data were collected in. Deviations might arise if excessive viscous heating occurs in columns with a pronounced non-adiabatic thermal behaviour.

title: Kinetic performance optimisation for liquid chromatography: principles and practice.
abstract: This HPLC tutorial focuses on the preparation and use of kinetic plots to characterise the performance in isocratic and gradient LC. This graphical approach allows the selection of columns (i.e. optimum particle size and column length) and LC conditions (operating pressure and temperature) to generate a specific number of plates or peak capacity in the shortest possible analysis time. Instrument aspects including the influence of extra-column effects (maximum allowable system volume) and thermal operating conditions (oven type) on performance are discussed. In addition, the performance characteristics of porous-shell particle-packed columns and monolithic stationary phases are presented and the potential of future column designs is discussed.

title: Automatic column coupling system to operate chromatographic supports closer to their kinetic performance limit and to enhance method development.
abstract: A new hardware solution is proposed that allows one to automatically change the length of a chromatographic bed. The setup is based on the serial coupling of chromatographic columns using two rotor-stator valves (with N positions, N + 1 ports). Despite the use of a prototype setup requiring rather long connection tubing, only 9% loss in efficiency is observed for compounds with a retention factor above 4 compared to the efficiency expected on the basis of the individual column results. It has been demonstrated for a number of isocratic and gradient separations that the system allows one to realize considerable analysis time savings by adapting the total column length to the specific sample requirements and/or to the stage of method development wherein one is working. During method development, a separation on a short column length can first be used to rapidly gain insight into the composition of the sample, leaving fewer runs to be done on a column of maximal length (offering efficiencies that are inaccessible with individual column systems). The ease with which information can be obtained on columns of different lengths can furthermore be exploited for screening purposes to detect coeluting components in a stage wherein they still appear completely unresolved (i.e., have a resolution well below R(s) = 0.5).

title: A variable column length strategy to expedite method development.
abstract: A variable length method development (or VL-MD)strategy, exploiting the potential of an automatic column coupling system, is proposed and has been applied to a number of different pharmaceutical and environmental samples with a varying degree of complexity. The proposed strategy consistently produced separation methods that had at least an equally good critical pair resolution and an equally short run time to those of methods produced using commercially available MD assistance software. In some cases, the VL-MD strategy allowed the MD time to be drastically shortened from >30 h to an overnight run of only 12 h. The developed strategy has the potential to become fully automated provided that reliable chromatogram read-out software becomes available. The advantage of combining different stationary phase types to improve the available selectivity and the integration into the general VL-MD strategy was also demonstrated.

title: Evaluation of LC Methods for the Separation of Amoxicillin and Its Related Substances
abstract: Five isocratic liquid chromatography (LC) methods have been examined for the separation of amoxicillin and its related substances on C18 or C8 columns. The United States Pharmacopeia (USP) assay method gave better selectivity. Similar selectivity was obtained not only on C18 columns but also on C8 and poly(styrene-divinylbenzene) columns. The good selectivity was confirmed by a second laboratory. A resolution test using cefadroxil was developed for the method performance. Based on the USP method, a gradient LC method was developed for the analysis of related substances in amoxicillin. This method has been proposed for the assay and purity control in the amoxicillin monographs of the European Pharmacopoeia and will be further examined in a collaborative study.

title: Kinetic plot equations for evaluating the real performance of the combined use of high temperature and ultra-high pressure in liquid chromatography. Application to commercial instruments and 2.1 and 1 mm I.D. columns.
abstract: The use of ultra-high pressure liquid chromatography (UHPLC) with pressures up to 1000 bar and columns packed with sub-2-microm particles combined with high-temperature mobile phase conditions (up to 90 degrees C) is assessed according to the current available instrumentation via constrained kinetic plot equations. It is shown that the gain in separation speed, theoretically expected from high-temperature UHPLC (HT-UHPLC), is significantly reduced when taking into account the existing instrumental constraints (extra-column band broadening, flow-rate and column length limitations). This study also shows that significant improvements could be expected on the current commercial instruments by increasing the flow-rate limit and/or using packing columns with particle size in the range 2.5-3.5 microm instead of the current sub-2 microm. These particles should obviously withstand very high pressure.

title: Approximate transient and long time limit solutions for the band broadening induced by the thin sidewall-layer in liquid chromatography columns.
abstract: Using a combination of both analytical and numerical techniques, approximate analytical expressions have been established for the transient and long time limit band broadening, originating from the presence of a thin disturbed sidewall layer in liquid chromatography columns, including packed, monolithic as well as microfabricated columns. The established expressions can be used to compare the importance of a thin disturbed sidewall layer with that of other radial heterogeneity effects (such as transcolumn packing density variations due to the relief of packing stresses). The expressions are independent of the actual velocity profile inside the layer as long as the disturbed sidewall layer occupies less than 2.5% of the column width.

title: Effect of temperature in reversed phase liquid chromatography.
abstract: The high temperature liquid chromatography (HTLC) reveals interesting chromatographic properties but even now, it misses some theoretical aspects concerning the influence of high temperature on thermodynamic and kinetic aspects of chromatography: such a knowledge is very essential for method development. In this work, the effect of temperature on solute behavior has been studied using various stationary phases which are representative of the available thermally stable materials present on the market. The thermodynamic properties were evaluated by using different mobile phases: acetonitrile-water, methanol-water and pure water. The obtained results were discussed on the basis of both type of mobile phases and type of stationary phases. Type of mobile phase was found to play an important role on the retention of solutes. The kinetic aspect was studied at various temperatures ranging from ambient temperature to high temperature (typically from about 30 to 200 degrees C) by fitting the experimental data with the Knox equation and it was shown that the efficiency is improved significantly when the temperature is increased. In this paper, we also discussed the problem of temperature control for thermostating columns which may represent a significant source of peak broadening: by taking into account the three main parameters such as heat transfer, pressure drop and band broadening resulting from the preheating tube, suitable rules are set up for a judicious choice of the column internal diameter.

title: Kinetic plot and particle size distribution analysis to discuss the performance limits of sub-2 microm and supra-2 microm particle columns.
abstract: To contribute to the current debate about the "ideal" particle size range (sub-2 microm vs. supra-2 microm), the present study compares the kinetic performance of some commercially available sub-2 microm and 3.5 microm particles used under quasi-adiabatic conditions via the kinetic plot method. Under the adopted assumption that viscous heating effects can be neglected (which is uncertain in a pressure range above 400 bar), the obtained kinetic plots show that, provided each particle size is used in a column with properly optimized length, the gain in separation speed that sub-2 microm particle columns might have over maximally performing 2.5 microm particle columns is very small. Sub-2 microm particle columns can only yield a gain in separation speed in the range of high-speed/low-resolution-separations (total time based on k=10 below 5 or 10 min). And even in this range, the actual gain that can be expected is only marginally small (only a few %). The present study hence suggests that the development and the use of particles in the 2-3 microm range should deserve more attention than it did in the past few years. However, to be competitive, this 2-3 microm material should be packed in relatively long columns, with a packing quality matching that of the current best performing 3.5 microm particle columns. The supra-2 microm particles should also be able to withstand the same pressures as the sub-2 microm particle material one is comparing it to.

title: High performance liquid chromatography column packings with deliberately broadened particle size distribution: relation between column performance and packing structure.
abstract: The effect of the addition of 25%, 50% and 75% (weight percent, wt%) of larger particles (resp. 3 and 5 μm) to a commercial batch of 1.9 μm particles has been investigated as an academic exercise to study the effects of particle size distribution on the kinetic performance of packed bed columns in a magnified way. Comparing the performance of the different mixtures in a kinetic plot, it could be irrefutably shown that the addition of larger particles to a commercial batch of small particles cannot be expected to lead to an improved kinetic performance. Whereas the addition of 25 wt% of larger particles still only has a minor negative effect, a significantly deteriorated performance is obtained when 50 or 75 wt% of larger particles are added. In this case, separation impedance number increases up to 200% were observed. Studying the packing structure through computational packing simulations, together with the experimental determination of the external porosity, helped in understanding the obtained results. This showed that small particles tend to settle in the flow-through pores surrounding the larger particles, leading to very high packing densities (external porosities as low as 32% were observed) and also negatively influencing the column permeability as well as the band broadening (because of the broadened flow-through pore size range).

title: Method to predict and compare the influence of the particle size on the isocratic peak capacity of high-performance liquid chromatography columns.
abstract: A kinetic plot based method has been used to experimentally predict the optimal particle size yielding the maximal isocratic peak capacity in a given analysis time. Applying the method to columns of three different manufacturers and characterizing them by separating a 4-component paraben mixture at 30 degrees C, it was consistently found that the classical 3 and 3.5 microm particles provide the highest peak capacity for typical isocratic separation run times between 30 and 60 min when operating the columns at a conventional pressure of 400 bar. Even at 1000 bar, the sub-2 microm particles only have a distinct advantage for runs lasting 30 min or less, while for runs lasting 45 min or longer the 3 and 3.5 microm again are to be preferred. This finding points at the advantage for high-resolution separations that could be obtained by producing 3 and 3.5 microm particle columns that can be operated at elevated pressures.