Kinetic investigation of the relationship between the efficiency of columns and their diameter

Many brands of packing materials made of fine particles are now available in both conventional (4.6 mm i.d.) and narrow-bore (2.1 mm i.d.) columns. It is a general observation that the efficiency of the former tends to be markedly higher than that of the latter. This report provides a detailed illustration of the characteristics of this enigma. The corrected reduced plate heights of three brands of columns packed with shell particles in 4.6 and 2.1 mm I.D. columns were measured. The brands were the 1.7 and 2.6 μm Kinetex-C(18) (Phenomenex, Torrance, CA, USA), the 2.7 μm Poroshell120-C(18) (Agilent Technologies, New Castle, DE, USA), and the 2.7 μm Halo-C(18) (Advanced Material Technologies, Wilmington, DE, USA). The extra-column contributions were minimized by optimizing the configuration of the instrument (injection volume <1.0 μL, 115 μm needle seat capillary, 80 μm connecting tubes, no heat exchanger, 0.8 μL detection cell). The correct peak variances were derived from the numerical integration of the first and second order moments of the experimental band profiles. These experimental results confirm that the kinetic performance of narrow-bore columns is inferior to that of conventional columns for all three brands of shell particles. We demonstrate that this difference is accounted for by a contribution to the column HETP of the long-range eddy diffusion term that is larger in the 2.1 than in the 4.6 mm I.D. columns. While the associated relative velocity biases are of comparable magnitude in both types of columns, the characteristic radial diffusion lengths are of the order of 100 and 40 μm in the wall regions of narrow-bore and conventional columns, respectively.     

The impact of extra-column band broadening on the chromatographic efficiency of 5 cm long narrow-bore very efficient columns

Small columns packed with core-shell and sub-2 μm totally porous particles and monolith columns are very popular to conduct fast and efficient chromatographic separations. In order to carry out fast separations, short (2-5 cm) and narrow-bore (2-2.1 mm) columns are used to decrease the analyte retention volume. Beside the column efficiency, another significant issue is the extra-column band-spreading. The extra-column dispersion of a given LC system can dramatically decrease the performance of a small very efficient column. The aim of this study was to compare the extra-column peak variance contribution of several commercially available LC systems. The efficiency loss of three different type 5 cm long narrow bore, very efficient columns (monolith, sub-2 μm fully porous and sub-2 μm core-shell packing) as a function of extra-column peak variance, and as a function of flow rate and also kinetic plots (analysis time versus apparent column efficiency) are presented.     

Influence of the errors made in the measurement of the extra-column volume on the accuracies of estimates of the column efficiency and the mass transfer kinetics parameters

The influences of the errors made in the measurement of the extra-column volume of an instrument on the accuracies of the estimates made of the column efficiency and of the parameters of the mass transfer kinetics were investigated from an experimental point of view. A standard HP1090 apparatus (extra-column volume, approximately 50 micro L) was used to measure the efficiency of a Sunfire-C(18) RPLC column (column hold-up volume, approximately 1.50 mL). The first and second moments of the peaks of phenol (a retained compound) and of thiourea (a practically non-retained compound) were measured at six different temperatures between 22 and 78 degrees C, for flow rates between 0.10 and 4.70 mL/min (i.e., for linear velocities between 0.025 and 1.179 cm/s). Each series of measurements was successively made with the instrument being fitted with and without the column. The experimental HETP data must be corrected for the solute dispersion in the connected tubes in order properly to assess the true column efficiency. Even with a modern, high performance instrument, the dispersion of a non-retained compound is essentially due to the band broadening phenomena that take place in the extra-column volumes, the sum of all these extra-column band broadening contributions accounting for more than 80% of the total band broadening measured. The contribution of the sampling device is particularly deleterious since, for a 2 mu L injection, the maximum solute concentration in the peak that enters into the column is nearly ten-fold lower than that of the sample. Nevertheless, the impact of the extra-column volumes on the estimates of the kinetic parameters (e.g., molecular diffusion coefficient D(m) and effective particle diffusivity D(e)) remains negligible. Obviously, the relative error made on the column efficiency of a retained compound depends much on its retention factor. It decreases from 8 to 1% when the retention factor increases from 5 to 17.     

An estimation of the column efficiency made by analyzing tailing peak profiles

It has been shown previously that most columns are not radially homogeneous but exhibit radial distributions of the mobile phase flow velocity and the local efficiency. Both distributions are best approximated by fourth-order polynomial, with the velocity in the column center being maximum for most packed columns and minimum for monolithic columns. These distributions may be an important source of tailing of elution peaks. The numerical calculation of elution peaks shows how peak tailing is related to the characteristics of these two distributions. An approach is proposed that permits estimations of the true efficiency and of the degree of column radial heterogeneity by inversing this calculation and using the tailing profiles of the elution peaks that are experimentally measured. This method was applied in two concrete cases of tailing peak profiles that had been previously reported and were analyzed by applying this new inverse approach. The results obtained prove its validity and demonstrate that this numerical method is effective for deriving the true column efficiency from experimental tailing profiles.     

Evaluation of 1.0 mm i.d. column performances on ultra high pressure liquid chromatography instrumentation

The present study focuses on the evaluation of 1.0 mm i.d. (internal diameter) columns on a commercial Ultra-High Pressure system. These systems have been developed specifically to operate columns with small volumes, typically 2.1 mm i.d., by reducing extra-column volume dispersion. The use of columns with smaller i.d. results in a reduced solvent consumption and required sample volume. The evaluation of the columns was carried out with samples containing neutral and pharmaceutical compounds. In isocratic mode, the extra-column volume produced additional band broadening leading to poor performances compared to equivalent 2.1 mm i.d. columns. By increasing the length of the column, the influence of the extra-column bandspreading could be reduced and 75,000 plates were obtained when four columns were coupled. In gradient mode, the effect of the extra-column contribution on efficiency was limited and about 80% of the performance of the 2.1 mm i.d. columns was obtained. Optimum conditions in gradient mode were further investigated by changing flow rate, gradient time and column length. A different approach of the calculation of peak capacity was also considered for the comparison of the influence of these different parameters.     

Measurement of the eddy diffusion term in chromatographic columns. I. Application to the first generation of 4.6mm I.D. monolithic columns

The corrected heights equivalent to a theoretical plate (HETP) of three 4.6mm I.D. monolithic Onyx-C(18) columns (Onyx, Phenomenex, Torrance, CA) of different lengths (2.5, 5, and 10 cm) are reported for retained (toluene, naphthalene) and non-retained (uracil, caffeine) small molecules. The moments of the peak profiles were measured according to the accurate numerical integration method. Correction for the extra-column contributions was systematically applied. The peak parking method was used in order to measure the bulk diffusion coefficients of the sample molecules, their longitudinal diffusion terms, and the eddy diffusion term of the three monolithic columns. The experimental results demonstrate that the maximum efficiency was 60,000 plates/m for retained compounds. The column length has a large impact on the plate height of non-retained species. These observations were unambiguously explained by a large trans-column eddy diffusion term in the van Deemter HETP equation. This large trans-rod eddy diffusion term is due to the combination of a large trans-rod velocity bias (?3%), a small radial dispersion coefficient in silica monolithic columns, and a poorly designed distribution and collection of the sample streamlets at the inlet and outlet of the monolithic rod. Improving the performance of large I.D. monolithic columns will require (1) a detailed knowledge of the actual flow distribution across and along these monolithic rod and (2) the design of appropriate inlet and outlet distributors designed to minimize the nefarious impact of the radial flow heterogeneity on band broadening.     

Mass transfer mechanism in liquid chromatography columns packed with shell particles: Would there be an optimum shell structure?

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.     

Peak tailing and column radial heterogeneity in linear chromatography

The correlation between the radial heterogeneity of a column and the tailing of the elution profiles of chromatographic peaks was studied using a numerical method. A parabolic distribution of the linear flow velocity of the mobile phase and of the column efficiency in the radial direction were assumed. Moment analysis showed that peak tailing takes place under such experimental conditions and that it increases with increasing range of radial variations of the flow velocity and the column efficiency. It was also found that the higher the column efficiency, the larger the effect of a given degree of radial heterogeneity on the extent of peak tailing. Peak tailing behavior of columns having different efficiencies could be correlated with each other by an equation. Some characteristic features of tailing peaks were analyzed in connection with the column radial heterogeneity.     

Comparison of monolithic silica and polymethacrylate capillary columns for LC

Organic polymer monolithic capillary columns were prepared in fused-silica capillaries by radical co-polymerization of ethylene dimethacrylate and butyl methacrylate monomers with azobisisobutyronitrile as initiator of the polymerization reaction in the presence of various amounts of porogenic solvent mixtures and different concentration ratios of monomers and 1-propanol, 1,4-butanediol, and water. The chromatographic properties of the organic polymer monolithic columns were compared with those of commercial silica-based particulate and monolithic capillary and analytical HPLC columns. The tests included the determination of H-u curves, column permeabilities, pore distribution by inversed-SEC measurements, methylene and polar selectivities, and polar interactions with naphthalenesulphonic acid test samples. Organic polymer monolithic capillary columns show similar retention behaviour to chemically bonded alkyl silica columns for compounds with different polarities characterized by interaction indices, Ix, but have lower methylene selectivities and do not show polar interactions with sulphonic acids. The commercial capillary and analytical silica gel-based monolithic columns showed similar selectivities and provided symmetrical peaks, indicating no significant surface heterogeneities. To allow accurate characterization of the properties of capillary monolithic columns, the experimental data should be corrected for extra-column contributions. With 0.3 mm ID capillary columns, corrections for extra-column volume contributions are sufficient, but to obtain true information on the efficiency of 0.1 mm ID capillary columns, the experimental bandwidths should be corrected for extra-column contributions to peak broadening.     

Effect of extra-column volume on practical chromatographic parameters of sub-2-μm particle-packed columns in ultra-high pressure liquid chromatography

Effects of extra-column volume on apparent separation parameters were studied in ultra-high pressure liquid chromatography with columns and inlet connection tubings of various internal diameters (id) using 50-mm long columns packed with 1.8-μm particles under isocratic conditions. The results showed that apparent retention factors were on average 5, 11, 18, and 41% lower than those corrected with extra-column volumes for 4.6-, 3.0-, 2.1-, and 1.0-mm id columns, respectively, when the extra-column volume (11.3 μL) was kept constant. Also, apparent pressures were 31, 16, 12, and 10% higher than those corrected with pressures from extra-column volumes for 4.6-, 3.0-, 2.1-, and 1.0-mm id columns at the respective optimum flow rate for a typical ultra-high pressure liquid chromatography system. The loss in apparent efficiency increased dramatically from 4.6- to 3.0- to 2.1- to 1.0-mm id columns, less significantly as retention factors increased. The column efficiency was significantly improved as the inlet tubing id was decreased for a given column. The results suggest that maximum ratio of extra-column volume to column void volume should be approximately 1:10 for column porosity more than 0.6 and a retention factor more than 5, where 80% or higher of theoretically predicted efficiency could be achieved.     

Effects of extra-column band spreading,liquid chromatography system operating pressure,and column temperature on the performance of sub-2-μm porous particles

The effects of extra-column band spreading, LC system operating pressure, and separation temperature were investigated for sub-2-μm particle columns using both a conventional HPLC system as well as a UPLC^® system. The contributions of both volume- and time-based extra-column effects were analyzed in detail. In addition, the performance difference between columns containing 2.5 and 1.7-μm particles (same stationary phase) was studied. The performance of these columns was compared using a conventional HPLC system and a low dead volume UPLC system capable of routine operation up to 1000 bar. The system contribution to band spreading and the pressure limitations of the conventional HPLC system were found to be the main difficulties that prevented acceptable performance of the sub-2-μm particle columns. Finally, an increase in operating temperature needs to be accompanied by an increase in flow rate to prevent a loss of separation performance. Thus, at a fixed column length, an increase in temperature is not a substitute for the need for very high operating pressures.     

Reproducibility of low and high concentration data in reversed-phase liquid chromatography. II. Overloaded band profiles on Chromolith-C18

Single-component adsorption isotherm data were acquired by frontal analysis (FA) for six low molecular weight compounds (phenol, aniline, caffeine, o-toluidine, p-toluidine and propylbenzoate) on one Chromolith-C18 column (#30, Merck, Darmstadt, Germany), using different methanol:water solutions (composition between 60/40 and 15/85 v/v, depending on the solute) as the mobile phase. These data were modeled for best agreement between the experimental data points and the adsorption isotherm model. The adsorption-energy distributions were also derived and used for the selection of the best isotherm model. Widely different models were obtained for these six compounds, four being convex upward (i.e., Langmuirian) and two having at least one inflection point. Overloaded band profiles corresponding to two different sample sizes (a low and a high loading factor) were recorded on six monolithic columns (#30-35) belonging to the same manufactured lot. These experimental band profiles were compared to the profiles calculated from the isotherm measured by FA on the first column, using the equilibrium-dispersive (ED) model of chromatography. For four of the six columns (#30, #32, #33, and #35), the reproducibility was better than 5 and 2.5% for the low and the high concentration profiles, respectively. On the other two columns (#31 and #34), the bands showed significant and systematic retention time shifts for all six compounds (with nearly identical band shapes), the relative adsorption being between 6 and 15% stronger on column #31 or between 2 and 7% lower on column #34. These differences seem to be correlated with the differences in the total porosities of these columns, which differ by 3% from columns #31 to #34, the higher porosity column giving the stronger adsorption.     

Approaches to characterise chromatographic column performance based on global parameters accounting for peak broadening and skewness

Peak broadening and skewness are fundamental parameters in chromatography, since they affect the resolution capability of a chromatographic column. A common practice to characterise chromatographic columns is to estimate the efficiency and asymmetry factor for the peaks of one or more solutes eluted at selected experimental conditions. This has the drawback that the extra-column contributions to the peak variance and skewness make the peak shape parameters depend on the retention time. We propose and discuss here the use of several approaches that allow the estimation of global parameters (non-dependent on the retention time) to describe the column performance. The global parameters arise from different linear relationships that can be established between the peak variance, standard deviation, or half-widths with the retention time. Some of them describe exclusively the column contribution to the peak broadening, whereas others consider the extra-column effects also. The estimation of peak skewness was also possible for the approaches based on the half-widths. The proposed approaches were applied to the characterisation of different columns (Spherisorb, Zorbax SB, Zorbax Eclipse, Kromasil, Chromolith, X-Terra and Inertsil), using the chromatographic data obtained for several diuretics and basic drugs (β-blockers).     

Repeatability and reproducibility of high concentration data in reversed-phase liquid chromatography. I. Overloaded band profiles on Kromasil-C18

Single-component adsorption-isotherm data were acquired by frontal analysis (FA) for six low-molecular-mass compounds (phenol, aniline, caffeine, theophylline, ethylbenzene and propranolol) on one Kromasil-C18 column, using water-methanol solutions (between 70:30 and 20:80, v/v) as the mobile phase. Propranolol data were also acquired using an acetate buffer (0.2 M) instead of water. The data were modeled for best agreement between calculated and experimental overloaded band profiles. The adsorption energy distribution was also derived and used for the selection of the best isotherm model. Widely different isotherm models were found to model best the data obtained for these compounds, convex upward (i.e. Langmuirian), convex downward (i.e. anti-Langmuirian), and S-shaped isotherms. Using the same sample size for all columns (loading factor, Lf approximately 10%), overloaded band profiles were recorded on four different columns packed with the same batch of Kromasil-C18 and five other columns packed with different batches of Kromasil-C18. These experimental band profiles were compared to the profile calculated from the isotherm measured by FA on the first column. The repeatability as well as the column-to-column and the batch-to-batch reproducibilities of the band profiles are better than 4%.     

The Effects of the Column Length on the Efficiency of Capillary Zwitterionic Organic Polymer Monolithic Columns in HILIC Chromatography

Organic polymer monolithic columns of different lengths have been prepared in 320 µm i.d. fused silica capillary by in situ radical polymerization of N,N-dimethyl-N-methacryloxyethyl-N-(3-sulfopropyl) ammonium betaine as a zwitterionic functional monomer and bisphenol A glycerolate dimethacrylate as a crosslinking monomer in the presence of porogenic solvents. The zwitterionic monolithic columns are intended for separations of polar compounds in hydrophilic interaction chromatography (HILIC). The effects of the capillary column length, from 115 to 175 mm, on separation efficiency, were investigated under HILIC conditions, using 95:5 acetonitrile in water as the mobile phase. The extra-column contributions to band broadening significantly decrease the efficiency (apparent height equivalent to a theoretical plate), especially for weakly retained samples, and increase with diminishing column length. The experimental height equivalents of theoretical plate, HETP, were corrected for the extra-column contributions, which were determined for a series of columns by extrapolation to zero column length. On a 175 mm long column, the column efficiency, HETP = 16.5 μm, measured at the optimum linear flow velocity of 0.5 mm s⁻¹, improved to HETP = 5 µm, after correction for extra-column contributions. For more strongly retained small polar compounds, interactions with zwitterionic groups and (or) water adsorbed inside the pores decrease the column efficiency at higher flow rates.

     

How to utilize the true performance of monolithic silica columns

Ways of utilizing the true separation efficiency of monolithic silica (MS) columns were studied. The true performance of MS columns, both regular-sized (rod-type clad with PEEK resin, 4.6 mm ID, 10 cm) and capillary sized (in 100 or 200 microm ID fused silica capillary, 25-140 cm) was evaluated by calculating the contribution of extra-column effects. HETP values of 7-9 microm were observed for solutes having retention factors (kvalues) of up to 4 for rod columns and up to 15 for a capillary column. The high permeability of MS columns allowed the use of long columns, with several connected together in the case of rod columns. Narrow-bore connectors gave good results. Peak variance caused by a column connector ranges from 50 to 70% of that caused by one rod-type column for up to three connectors or four columns in 80% methanol, but the addition of a 4th or 5th connector to add a 5th and 6th column, respectively, caused a much greater increase in peak variance, especially for long-retained solutes, which is greater than the variance caused by one rod column. Rod columns seem to show slightly lower efficiency at a pressure higher than 10 MPa or so. The use of acetonitrile-water as a mobile phase better preserved the ability of individual rod columns to generate up to 100,000 theoretical plates with 14 columns connected. Methods for eliminating extra-column effects in micro-HPLC were also studied. Split injection and on-column detection resulted in optimum performance. A long MS capillary measuring 140 cm produced 160,000 theoretical plates. The column efficiency of a capillary column was not affected by the pressure, showing advantages over the rod columns that exhibited peak broadening caused by connectors and pressure.     

Achieving high peak capacity production for gas chromatography and comprehensive two-dimensional gas chromatography by minimizing off-column peak broadening

By taking into consideration band broadening theory and using those results to select experimental conditions, and also by reducing the injection pulse width, peak capacity production (i.e., peak capacity per separation time) is substantially improved for one dimensional (1D-GC) and comprehensive two dimensional (GC×GC) gas chromatography. A theoretical framework for determining the optimal linear gas velocity (the linear gas velocity producing the minimum H), from experimental parameters provides an in-depth understanding of the potential for GC separations in the absence of extra-column band broadening. The extra-column band broadening is referred to herein as off-column band broadening since it is additional band broadening not due to the on-column separation processes. The theory provides the basis to experimentally evaluate and improve temperature programmed 1D-GC separations, but in order to do so with a commercial 1D-GC instrument platform, off-column band broadening from injection and detection needed to be significantly reduced. Specifically for injection, a resistively heated transfer line is coupled to a high-speed diaphragm valve to provide a suitable injection pulse width (referred to herein as modified injection). Additionally, flame ionization detection (FID) was modified to provide a data collection rate of 5kHz. The use of long, relatively narrow open tubular capillary columns and a 40°C/min programming rate were explored for 1D-GC, specifically a 40m, 180μm i.d. capillary column operated at or above the optimal average linear gas velocity. Injection using standard auto-injection with a 1:400 split resulted in an average peak width of ～1.5s, hence a peak capacity production of 40peaks/min. In contrast, use of modified injection produced ～500ms peak widths for 1D-GC, i.e., a peak capacity production of 120peaks/min (a 3-fold improvement over standard auto-injection). Implementation of modified injection resulted in retention time, peak width, peak height, and peak area average RSD%'s of 0.006, 0.8, 3.4, and 4.0%, respectively. Modified injection onto the first column of a GC×GC coupled with another high-speed valve injection onto the second column produced an instrument with high peak capacity production (500-800peaks/min), ～5-fold to 8-fold higher than typically reported for GC×GC.     

Kinetic performance optimisation for liquid chromatography: principles and practice

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.     

High-speed gas chromatography: the importance of instrumentation optimization and the elimination of extra-column band broadening

This review provides a summary of chromatographic theory as it applies to high-speed gas chromatography. A novel method for determining the optimal linear flow velocity, u (opt), from specific experimental parameters, is discussed. An in-depth theoretical understanding of u (opt) and its relation to experimental parameters is presented, in the absence of extra-column band broadening, as a means of method evaluation and optimization. Recent developments in high-speed GC are discussed, in the context of the theory presented within this review, to ascertain the influence of extra-column band broadening. The theory presented herein can be used as a means of evaluating the various areas of GC instrumentation (injection, separation, detection, etc.) that need further development to further minimize the effects of extra-column band broadening. The theoretical framework provided in this review, can be, and is, readily used to evaluate high-speed GC results presented in the literature, and thus, the general practitioner may more readily select a specific capillary length and/or internal diameter for a given application. For example, it is theoretically shown, and prior work cited, that demonstrates a peak width of approximately 1 ms is readily achievable in GC, when extra-column band broadening is eliminated.