Moment equations for chromatography using superficially porous spherical particles

New moment equations were developed for chromatography using superficially porous (shell-type) spherical particles, which have recently attracted much attention as one of separation media for fast separation with high efficiency. At first, the moment equations of the first absolute and second central moments in the real time domain were derived from the analytical solution in the Laplace domain of a set of basic equations of the general rate model of chromatography, which represent the mass balance, mass-transfer rate, and reaction kinetics in the column packed with shell-type particles. Then, the moment equations were used for analyzing the experimental data of chromatography of kallidin in a Halo column, which were published in a previous paper written by other researchers. It was tried to predict the chromatographic behavior of shell-type particles having different shell thicknesses. The new moment equations are useful for a detailed analysis of the chromatographic behavior of shell-type spherical particles. It is also concluded that they can be used for the preliminarily optimization of their structural characteristics.     

Evaluation of chromatographic performance of various packing materials having different structural characteristics as stationary phase for fast high performance liquid chromatography by new moment equations

Chromatographic performance of various separation media having different structural characteristics as the stationary phase for fast HPLC was quantitatively evaluated by using the new moment equations recently developed with considering the shape and porous structure of the packing materials. Four types of separation media, i.e., full-porous, partially porous (pellicular or shell) type, and non-porous spherical particles and full-porous cylindrical fiber, were chosen as examples. The moment equations were used for predicting the chromatographic behaviors of benzene under hypothetical RPLC conditions. The overall performance of the four types of packing materials as the separation media for fast HPLC was compared with each other from the viewpoint of the peak capacity, which depends on both the retention equilibrium and the mass transfer kinetics. It seems that the full-porous cylindrical fiber and the pellicular type spherical particle are more preferable than the others, i.e., the full-porous and non-porous spherical particles. Now we can use the new moment equations for the quantitative prediction of the chromatographic behaviors of the various packing materials on the basis of a related experimental information and for the evaluation of their performance from various chromatographic points of view. The new moment equations are effective not only for the detailed analyses of chromatographic behaviors but also for the preliminarily evaluation of new types of separation media for fast HPLC.     

Modified Equilibrium-Dispersive Model for the interpretation of the efficiency of columns packed with core-shell particle

A modified Equilibrium Dispersive (ED) Model is proposed for the modeling of chromatographic processes in columns packed with shell-particle adsorbents and operated under very high pressures. This new model was validated on the basis of experimental results obtained with 2.1 mm × 150 mm columns packed with superficially porous 1.7 μm Kinetex-C(18) particles and with classical columns packed with 1.7 μm BEH-C(18) fully porous particles. The influence of the heat friction on the performance of these columns was analyzed by comparing the experimental and calculated peak profiles. Moreover a theoretical analysis of the influence the solid-core conductivity on the column efficiency was discussed.     

On the optimization of the solid core radius of superficially porous particles for finite adsorption rate

Packed chromatographic columns with the superficially porous particles (porous shell particles) guarantee higher efficiency. The theoretical equation of the Height Equivalent to a Theoretical Plate (HETP), for columns packed with spherical superficially porous particles, was used for the analysis of the column efficiency for finite rate of adsorption-desorption process. The HETP equation was calculated by the application of the moment analysis to elution peaks evaluated with the General Rate (GR) model. The optimal solid core radius for maximum column efficiency was estimated for a wide spectrum of internal and external mass transfer resistances, adsorption kinetic rate and axial dispersion. The separation power of the shell adsorbent for two component mixture, in analytical and preparative chromatography, was discussed. The conditions of the equivalence between the solutions of the General Rate model with slow adsorption kinetic and the Lumped Kinetic Model (LKM) or the Equilibrium Dispersive (ED) model were formulated.     

Practical comparison of LC columns packed with different superficially porous particles for the separation of small molecules and medium size natural products

Commercial C(18) columns packed with superficially porous particles of different sizes and shell thicknesses (Ascentis Express, Kinetex, and Poroshell 120) or sub-2-μm totally porous particles (Acquity BEH) were systematically compared using a small molecule mixture and a complex natural product mixture as text probes. Significant efficiency loss was observed on 2.1-mm id columns even with a low dispersion ultra-high pressure liquid chromatography system. The Kinetex 4.6-mm id column packed with 2.6-μm particles exhibited the best overall efficiency for small molecule separations and the Poroshell 120 column showed better performance for mid-size natural product analytes. The Kinetex 2.1-mm id column packed with 1.7-μm particles did not deliver the expected performance and the possible reasons besides extra column effect have been proved to be frictional heating effect and poor column packing quality. Different column retentivities and selectivities have been observed on the four C(18) columns of different brands for the natural product separation. Column batch-to-batch variability that has been previously observed on the Ascentis Express column was also observed on the Kinetex and Poroshell 120 column.     

Separation of natural product using columns packed with Fused‐Core particles

Three HPLC columns packed with 3 μm, sub‐2 μm, and 2.7 μm Fused‐Core (superficially porous) particles were compared in separation performance using two natural product mixtures containing 15 structurally related components. The Ascentis Express^TM C18 column packed with Fused‐Core particles showed an 18% increase in column efficiency (theoretical plates), a 76% increase in plate number per meter, a 65% enhancement in separation speed and a 19% increase in back pressure compared to the Atlantis T3^TM C18 column packed with 3 μm particles. Column lot‐to‐lot variability for critical pairs in the natural product mixture was observed with both columns, with the Atlantis T3 column exhibiting a higher degree of variability. The Ascentis Express column was also compared with the Acquity^TM BEH column packed with sub‐2 μm particles. Although the peak efficiencies obtained by the Ascentis Express column were only about 74% of those obtained by the Acquity BEH column, the 50% lower back pressure and comparable separation speed allowed high‐efficiency and high‐speed separation to be performed using conventional HPLC instrumentation.     

A study of the effects of column porosity on gradient separations of proteins

The type of the stationary phase for reversed-phase liquid chromatography significantly affects the sample elution. Hydrodynamic properties, efficiency and gradient elution of proteins were investigated on five commercial C18 columns with wide-pore totally porous particles, with superficially porous layer particles, non-porous particles and a silica-based monolithic bed. The efficiency in the terms of reduced plate height is higher for low-molecular ethylbenzene than for proteins, but depends on the character of the pores in the individual columns tested. The superficially porous Poroshell and the non-porous Micra columns provide the best efficiency for proteins at high mobile phase flow rates, probably because of similar pore architecture in the stationary phase. The Zorbax column with similar pore architecture as the Poroshell active layer, i.e. narrow pore distribution of wider pores shows better efficiency than the packed column with narrow pores and broad pore distribution. The monolithic column shows lower efficiency for proteins at high flow rates, but it performs better than the broad-pore distribution totally porous particulate columns. Different pore architecture affects also the retention and selectivity for proteins on the individual columns. The retention times on all columns can be predicted using the model for reversed-phase gradient elution developed originally for low-molecular compounds. Consideration of the limited pore volume accessible to the biopolymers has negligible effect on the prediction of retention on the columns packed with non-porous or superficially porous particles, but improves the accuracy of the predicted data for the totally porous columns with broad pore distribution.     

Physical properties and structure of fine core–shell particles used as packing materials for chromatography: Relationships between particle characteristics and column performance

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 4.6 mm 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.     

Rapid determination of parabens in seafood sauces by high‐performance liquid chromatography: A practical comparison of core–shell particles and sub‐2 μm fully porous particles

In this work, the chromatographic performance of superficially porous particles (Halo core–shell C₁₈ column, 50 mm × 2.1 mm, 2.7 μm) was compared with that of sub‐2 μm fully porous particles (Acquity BEH C₁₈, 50 mm × 2.1 mm, 1.7 μm). Four parabens, methylparaben, ethylparaben, propylparaben, and butylparaben, were used as representative compounds for calculating the plate heights in a wide flow rate range and analyzed on the basis of the Van Deemter and Knox equations. Theoretical Poppe plots were constructed for each column to compare their kinetic performance. Both phases gave similar minimum plate heights when using nonreduced coordinates. Meanwhile, the flat C‐term of the core–shell column provided the possibilities for applying high flow rates without significant loss in efficiency. The low backpressure of core–shell particles allowed this kind of column, especially compatible with conventional high‐performance liquid chromatography systems. Based on these factors, a simple high‐performance liquid chromatography method was established and validated for the determination of parabens in various seafood sauces using the Halo core–shell C₁₈ column for separation.     

Influence of the degree of coverage of C18-bonded stationary phases on the mass transfer mechanism and its kinetics

The influence of the degree of coverage of a silica surface with bonded C18 alkyl chains on the mass transfer mechanism in RPLC was investigated. Five packing materials were used, prepared with the same batch of silica particles (5 microm diameter, 90 A average pore size): one column was packed with the silica derivatized by trimethylchlorosilane (TMS) (C1, 3.92 micromol/m2), and the other four with the silica first derivatized with octadecyl-dimethyl-chlorosilane (C18, 0.42, 1.01, 2.03, and 3.15 micromol/m2), and then endcapped with TMS. A solution of methanol and water (25/75, v/v) was used as the mobile phase. The experimental HETP curves were acquired for each column by measuring the first moment and the second central moment of phenol and correcting them for the influence of the temperature increase due to the heat generated by the friction of the stream against the bed. The different kinetic parameters of the mass transfer in these packed chromatographic columns were identified (longitudinal diffusion, eddy diffusion, film mass transfer, and transparticle mass transfer) and quantified by fitting the experimental data to a new general HETP equation recently derived [F. Gritti, G. Guiochon, Anal. Chem., in press (AC-060203R).]. The agreement was excellent and allowed the comparison of the kinetic parameters among the six columns used. The highest column efficiency measured at conventional or fast flow rates (>0.5 ml/min) is obtained for the most retentive column, which has a surface coverage of 2.03 micromol/m2. The smallest HETP measured is as low as 10 microm, only twice the average particle diameter dp, due to the large contribution of surface diffusion (90%) to the particle effective diffusivity. However, no significant difference was observed between the efficiencies of the columns packed with C1 and C18 derivatized silica.     

Capillary electrochromatography with monolithic silica column: I. Preparation of silica monoliths having surface-bound octadecyl moieties and their chromatographic characterization and applications to the separation of neutral and charged species

Monolithic silica columns with surface-bound octadecyl (C18) moieties have been prepared by a sol-gel process in 100 microm ID fused-silica capillaries for reversed-phase capillary electrochromatography of neutral and charged species. The reaction conditions for the preparation of the C18-silica monoliths were optimized for maximum surface coverage with octadecyl moieties in order to maximize retention and selectivity toward neutral and charged solutes with a sufficiently strong electroosmotic flow (> 2 mm/s) to yield rapid analysis time. Furthermore, the effect of the pore-tailoring process on the silica monoliths was performed over a wide range of treatment time with 0.010 M ammonium hydroxide solution in order to determine the optimum time and conditions that yield mesopores of narrow pore size distribution that result in high separation efficiency. Under optimum column fabrication conditions and optimum mobile phase composition and flow velocity, the average separation efficiency reached 160 000 plates/m, a value comparable to that obtained on columns packed with 3 microm C18-silica particles with the advantages of high permeability and virtually no bubble formation. The optimized monolithic C18-silica columns were evaluated for their retention properties toward neutral and charged analytes over a wide range of mobile phase compositions. A series of dimensionless retention parameters were evaluated and correlated to solute polarity and electromigration property. A dimensionless mobility modulus was introduced to describe charged solute migration and interaction behavior with the monolithic C18-silica in a counterflow regime during capillary electrochromatography (CEC )separations. The mobility moduli correlated well with the solute hydrophobic character and its charge-to-mass ratio.     

High-speed analyses using rapid resolution liquid chromatography on 1.8-microm porous particles

The potential of high-speed analyses by rapid resolution liquid chromatography (RRLC) and RRLC/MS on 1.8-microm porous particles packed into short columns operated at high flow-rate was investigated and compared with the performance of 5-microm porous particles packed into conventional columns. Using similar chemistries, the ease of conversion from conventional HPLC to an RRLC method was demonstrated. In order to display the practicality of RRLC separations, the analysis of pesticides in crops and catechins in Japanese green tea was selected. Using the Japanese Food Hygiene Law method, which employs a conventional 5-microm RP column (250 mm x 4.6 mm) for quantification of pesticides in crops, the analysis time was 25 min under isocratic conditions. Using the RRLC method on the short (50 mm x 4.6 mm) column packed with 1.8-microm porous particles, the same separation could be performed in 0.8 min with the RRLC/MS method without a loss in resolution. At the highest flow rate, compared to the conventional method, the time could be reduced by a factor of 31. In gradient elution, the fastest separation of catechins in Japanese green tea was achieved by RRLC on 50-mm x 4.6-mm id or 50-mm x 2.1-mm id RRLC columns packed with 1.8-microm particles. The analysis time at 5 mL/min was less than 1 min. Compared to the conventional HPLC method on a 150-mm column packed with 5-microm particles, time was reduced by a factor of 15. The effect of other experimental parameters such as the column temperature, acquisition rate of the detector and the influence of cell volume on chromatographic performance was also investigated. After the optimization, the analysis precision under the fastest RRLC conditions was examined. RSDs of retention time and peak area were 0.2% and 0.47%, respectively.     

Interference of the electrospray voltage on chromatographic separations using porous graphitic carbon columns

The electrospray ionization (ESI) voltage is shown to interfere with liquid chromatographic separations performed with packed porous graphitic carbon (PGC) capillary columns. This interference is ascribed to the presence of an electric field over the conductive column in the absence of an earth point between the column and the ESI emitter. The current evolved alters the chromatographic behavior of the catecholamine metabolite 3-O-methyl-DOPA significantly, as both peak splitting and a dramatic decrease in the retention time were observed. Furthermore, the response from the mass spectrometer was decreased by 33% at the same time. A related compound, tyrosine, exhibited decreased retention times but no peak splitting, whereas no shifts in the retention times (or peak splitting) were seen for the less retained dopamine and noradrenaline. When the current through the PGC column was eliminated by the use of an earth point between the column and the ESI emitter, the chromatographic behavior of the column was found to return slowly to normal after hours of equilibration with 60 : 40 (v/v) methanol-ammonium formate buffer of pH 2.9. The behavior of the PGC column with and without the earth point was found to be highly reproducible during a period of 1 month. We propose that the effect of the ESI voltage on the chromatographic behavior of the PGC column is due to associated redox reactions affecting both the PGC particles and the analytes. It is concluded that (for analytical reasons), care should be taken to ensure that no current is flowing through the chromatographic system when interfacing PGC columns, and conducting parts in general, to ESI mass spectrometry.     

Determination of flavanones in Citrus juices by means of one- and two-dimensional liquid chromatography

1-D and 2-D comprehensive (LC×LC) liquid chromatography methods have been developed and compared for the separation and quantification of flavanones in various Citrus juices. 1-D analyses were carried out on a superficially porous C18 column, whereas the 2-D LC approach was composed of a polyethylene glycol silica narrow-bore column packed with totally porous particles in the first dimension (D1) and a superficially porous C18 column in the second dimension (D2). Low-selectivity correlations were ensured by the complementary separation mechanisms offered by the D1 and D2 columns. Quantification was carried out both manually and by means of a software capable of detecting and quantifying each peak from the 2-D plot. Limit of detection (LOD) values as low as 0.023 μg/mL were obtained for hesperidin used as reference material for 1-D LC analyses, whereas values as high as 0.432 μg/mL were obtained by comprehensive LC. This discrepancy can be traced back to the minor sensitivity experienced in comprehensive LC due to both sample dilution in D1 and the high flow rates employed in D2. On the other hand, the separation capabilities of the LC×LC approach allowed to reduce the interferences coming from the matrix and to achieve the separation of some critical pairs, e.g. hesperidin/naringin difficult to accomplish in 1-D LC.     

Comparison of the mass transfer in totally porous and superficially porous stationary phases in liquid chromatography

The characterization of mass-transfer processes in a chromatographic column during a separation process is essential, since the influence of the mass-transfer kinetics on the shape of the chromatographic band profiles and on the efficiency of the separation is crucial. Several sources of mass transfer in a chromatographic bed have been identified and studied: the axial dispersion in the stream of mobile phase, the external mass-transfer resistance, intraparticle diffusion, and the kinetics of adsorption–desorption. We measured and compared the characteristics and performance of a new brand of shell particles and those of a conventional brand of totally porous silica particles. The shell stationary phase was made of 2.7-μm superficially porous particles (a 1.7-μm solid core is covered with a 0.5-μm-thick shell of porous silica). The other material consisted of totally porous particles of conventional 3.5-μm commercial silica. We measured the first and second central moments of the peaks of human insulin over a wide range of mobile phase velocities (from 0.02 to 1.3 mL/min) at 20°C. The plate height equations were constructed and the axial dispersion, external mass transfer, as well as the intraparticle diffusion coefficients were calculated for the two stationary phases.     

Experimental evidence of the influence of the surface chemistry of the packing material on the column pressure drop in reverse-phase liquid chromatography

The permeabilities of six columns packed with different packing materials (neat silica, C(1) endcapped silica at 3.92 micro mol/m(2), C(18) bonded and endcapped silica with 0.42, 1.01, 2.03, and 3.15 micro mol/m(2) of C(18) bonded chains) were measured. All these materials derive from the same batch of spherical particles, 5 micro m in diameter. The columns have the same tube inner diameter (phi=0.460+/-0.003 cm) and length (L=15.000+/-0.003 cm). The experimental conditions were the same, flow-rate (F(v)=1.000+/-0.003 mL/min) and temperature (295 K). Nevertheless, it was found that the column permeability decreases significantly, by about 25%, from the neat silica column to the one packed with the highest density of C(18)-bonded silica (3.15 micro mol/m(2)). The results measured on two duplicate columns were very reproducible. Accurate (+/-0.5 %) measurements of the hold-volumes with concentrated and dilute solutions of NO(3)(-) showed that the columns had all nearly the same external porosity. The result cannot be explained by the error made on the volume of the column tube either as it was measured accurately for all the columns. The residual explanation is that the interstitial velocity distribution between the packed particles depends on the chemical nature of the external surface of these particles.     

Investigation of mass transfer properties and kinetic performance of high‐efficiency columns packed with C18 sub‐2 μm fully and superficially porous particles

Three columns packed with 2.0 μm superficially porous particles, 1.7 μm fully porous particles, and monodisperse 1.9 μm fully porous particles with narrow particle size distribution have been deeply characterized from a kinetic point of view. The 1.9 μm column showed excellent kinetic performance, comparable to that of the superficially porous one. These two columns also exhibit flatter c‐branches of the van Deemter curve compared to the 1.7 μm fully porous particles column, resulting in smaller loss of efficiency when they are operated at higher flow rates than the optimal ones. The independent evaluation of each contribution to band broadening has revealed that the difference in kinetic performance comes from the very small eddy dispersion contribution on the 1.9 μm column, surprisingly even lower than that of the superficially porous one. This finding suggests a very good packing of the monodisperse 1.9 μm column. On the other hand, the potential of 1.7 μm fully porous particles is completely broken down by the strong frictional heating effect already arising at relatively low flow rates.     

A practical approach to maximizing peak capacity by using long columns packed with pellicular stationary phases for proteomic research

Maximization of peak capacity is a very important step in developing one-dimensional separations of complex samples. In recent work, it was shown that the use of small particles in combination with the new technique of ultrahigh pressure liquid chromatography (UHPLC) was able to generate very high peak capacities. Here we show the ability of conventional HPLC instrumentation to give comparable peak capacities to those obtained in UHPLC for the important case of complex mixtures of peptides but at much lower pressures by using a 60 cm long set of columns packed with 5 microm pellicular (superficially porous) particles. We first show, in complete agreement with the well known results of the theory of isocratic separations that, when time is not limiting, the best peak capacities in gradient elution chromatography are obtained by using large particles and the longest column that can be operated at the pump's pressure limit. Two different types of 5 microm particles (superficially porous and totally porous) were compared for their efficiency in gradient chromatography of peptides. We find that the pellicular material gave about 50% higher peak capacity compared to the analogous porous material. A 60 cm column set packed with pellicular particles was made by connecting short columns in series; a peak capacity of about 460 was obtained in 4 h at room temperature. Increasing the column temperature to 70 degrees C reduced the analysis time to 2 h and further increased the peak capacity to more than 500. The number of peaks observed in the separation of bovine serum albumin tryptic peptides was greatly increased and the separation quality was significantly improved.     

Characterization and kinetic performance of 2.1 × 100 mm production columns packed with new 1.6 μm superficially porous particles

The overall kinetic performance of three production columns (2.1 mm × 100 mm format) packed with 1.6 μm superficially porous CORTECS‐C₁₈+ particles was assessed on a low‐dispersive I‐class ACQUITY instrument. The values of their minimum intrinsic reduced plate heights (h_min = 1.42, 1.57, and 1.75) were measured at room temperature (295 K) for a small molecule (naphthalene) with an acetonitrile/water eluent mixture (75:25, v/v). These narrow‐bore columns provide an average intrinsic efficiency of 395 000 plates per meter. The gradient separation of 14 small molecules shows that these columns have a peak capacity about 25% larger than similar ones packed with fully porous BEH‐C₁₈ particles (1.7 μm) or shorter (50 mm) columns packed with smaller core–shell particles (1.3 μm) operated under very high pressure (>1000 bar) for steep gradient elution (analysis time 80 s). In contrast, because their permeabilities are lower than those of columns packed with larger core–shell particles, their peak capacities are 25% smaller than those of narrow‐bore columns packed with standard 2.7 μm core–shell particles.     

Separation of 2-naphthol atropisomers on cyclofructan-based chiral stationary phases

A set of fifteen 2-naphthol-derived atropisomers were evaluated on three different cyclofructan-based chiral stationary phases (CSP). The cyclofructan CSPs were a dimethylphenyl-derivatized cyclofructan 7 (CF7-DMP), a isopropyl (CF6-P) and a R-naphthylethyl cyclofructan 6 (CF6-RN) derivative, all bonded to 5-µm spherical fully porous silica particles packed into three 25?cm?×?4.6?mm columns (commercially available as Larihc columns). The 15 atropisomers were analyzed in the normal-phase mode with heptane/alcohol mobile phases. The CF7-DMP column was the most effective partially or fully separating 14 of the 15 compounds (93%). All 15 compounds could be separated by at least one cyclofructan column. Five compounds could be partially or fully separated by all three CSPs. The effect of ethanol, 2-propanol and butanol as 5 and 10% v/v polar modifiers in heptane was studied. A prototype 15?cm?×?4.6?mm column packed with superficially porous 2.7?µm CF6-P bonded particles was tested with the same set of compounds and a standard HPLC system. The increased efficiency and solvent saving were significant.