Influence of column radial heterogeneity on peak fronting in linear chromatography.

Using numerical calculations of elution peak profiles, an explanation of the fronting behavior of elution peaks in linear chromatography was found in certain radial distributions of the mobile phase flow velocity and local bed efficiency. Fronting peaks are observed only if the flow velocity is higher in the wall region than in the center part of the column and the local efficiency is lower near the wall than in the center. By contrast, tailing or symmetrical peaks are observed if only the flow velocity or the local efficiency are radially heterogeneous. The degree of peak fronting increases with increasing amplitude of the radial distributions. The influence of the radial heterogeneity of the flow velocity on the degree of peak fronting is more severe for high than for low efficiency columns. An equation is suggested to correlate peak fronting behavior for columns of different efficiencies and a procedure proposed for the estimation of the radial distributions of the flow velocity and the local efficiency by analyzing some characteristics of asymmetric peaks.     

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.     

Accurate measurements of peak variances: importance of this accuracy in the determination of the true corrected plate heights of chromatographic columns

The true efficiency of a column is derived from the differences between the variances of the peak profiles of the same compound recorded in the presence and the absence of the chromatographic column. These variances are usually derived using one of three methods: (1) the retention time of the peak apex and its half-height width; (2) the moments of the best fit between the experimental data and a hybrid response function, e.g., an exponentially convoluted Gaussian; or (3) the exact moments of the experimental band profiles. Comparisons of the results of these methods show that the first method is always inaccurate because all the band profiles recorded are strongly tailing. The peak fit method is accurate only for 4.6mm I.D. columns operated with instruments having low extra-column volume but fails for short narrow-bore columns due to the severe tailing of peaks passing through the complex channels of the extra-column volumes and to the inaccuracies in the fit of experimental data to the selected function. Although far better, the moment method may be inaccurate when the zero dead volume union used to measure the extra-column peak variances has a higher permeability than the column, causing the upstream part of the instrument to operate under comparatively low pressures.     

Structural radial heterogeneity of a silica-based wide-bore monolithic column

The radial distribution of the main characteristics (elution time and standard deviation) of the elution profiles of a flat injected band recorded at the exit of a monolithic column were determined. These distributions provide the radial distributions of the average mobile phase velocity, the elution time and the maximum height of the peak of an analyte, the column efficiency and the analyte concentration. The band profiles were measured at the exit of a 10-mm i.d., 100-mm long silica-based monolithic column. An on-column local electrochemical amperometric detector allowed the recording of the elution profiles at different spatial positions throughout the column cross-section. The local spatial distribution of the mobile phase velocity does not follow a piston-flow behavior but exhibits radial heterogeneity. The local efficiency near the wall is lower than that near the column center. The radial distribution of the maximum concentration of the peaks varies throughout the column exit section, partially due to the radial variations of the column efficiency. These results might explain the rather large value of the A term of the Van Deemter or the Knox equations reported previously for monolithic columns.     

Modeling of thermal processes in very high pressure liquid chromatography for column immersed in a water bath: Application of the selected models

Currently, chromatographic analyses are carried out by operating columns packed with sub-2 μm particles under very high pressure gradients, up to 1200 bar for 5 cm long columns. This provides the high flow rates that are necessary for the achievement of high column efficiencies and short analysis times. However, operating columns at high flow rates under such high pressure gradients generate a large amount of heat due to the viscous friction of the mobile phase stream that percolates through a low permeability bed. The evacuation of this heat causes the formation of significant or even large axial and radial gradients of all the physico-chemical parameters characterizing the packing material and the mobile phase, eventually resulting in a loss of column efficiency. We previously developed and successfully applied a model combining the heat and the mass balances of a chromatographic column operated under very high pressure gradients (VHPLC). The use of this model requires accurate estimates of the dispersion coefficients at each applied mobile phase velocity. This work reports on a modification of the mass balance model such that only one measurement is now necessary to accurately predict elution peak profiles in a wide range of mobile phase velocities. The conditions under which the simple equilibrium-dispersive (ED) and transport-dispersive (TD) models are applicable in VHPLC are also discussed. This work proves that the new combination of the heat transfer and the ED model discussed in this work enables the calculation of accurate profiles for peaks eluted under extreme conditions, like when the column is thermostated in a water bath.     

Numerical modeling of the elution peak profiles of retained solutes in supercritical fluid chromatography

In supercritical fluid chromatography (SFC), the significant expansion of the mobile phase along the column causes the formation of axial and radial gradients of temperature. Due to these gradients, the mobile phase density, its viscosity, its velocity, its diffusion coefficients, etc. are not constant throughout the column. This results in a nonuniform flow velocity distribution, itself causing a loss of column efficiency in certain cases, even at low flow rates, as they do in HPLC. At high flow rates, an important deformation of the elution profiles of the sample components may occur. The model previously used to account satisfactorily for the retention of an unsorbed solute in SFC is applied to the modeling of the elution peak profiles of retained compounds. The numerical solution of the combined heat and mass balance equations provides the temperature and the pressure profiles inside the column and values of the retention time and the band profiles of retained compounds that are in excellent agreement with independent experimental data for large value of mobile phase reduced density. At low reduced densities, the band profiles can strongly depend on the column axial distribution of porosity.     

Numerical modeling of elution peak profiles in supercritical fluid chromatography. Part I—Elution of an unretained tracer

When chromatography is carried out with high-density carbon dioxide as the main component of the mobile phase (a method generally known as “supercritical fluid chromatography” or SFC), the required pressure gradient along the column is moderate. However, this mobile phase is highly compressible and, under certain experimental conditions, its density may decrease significantly along the column. Such an expansion absorbs heat, cooling the column, which absorbs heat from the outside. The resulting heat transfer causes the formation of axial and radial gradients of temperature that may become large under certain conditions. Due to these gradients, the mobile phase velocity and most physico-chemical parameters of the system (viscosity, diffusion coefficients, etc.) are no longer constant throughout the column, resulting in a loss of column efficiency, even at low flow rates. At high flow rates and in serious cases, systematic variations of the retention factors and the separation factors with increasing flow rates and important deformations of the elution profiles of all sample components may occur. The model previously used to account satisfactorily for the effects of the viscous friction heating of the mobile phase in HPLC is adapted here to account for the expansion cooling of the mobile phase in SFC and is applied to the modeling of the elution peak profiles of an unretained compound in SFC. The numerical solution of the combined heat and mass balance equations provides temperature and pressure profiles inside the column, and values of the retention time and efficiency for elution of this unretained compound that are in excellent agreement with independent experimental data.     

Modeling of thermal processes in high pressure liquid chromatography: II. Thermal heterogeneity at very high pressures

Advanced instruments for liquid chromatography enables the operation of columns packed with sub-2 μm particles at the very high inlet pressures, up to 1000 bar, that are necessary to achieve the high column efficiency and the short analysis times that can be provided by the use of these columns. However, operating rather short columns at high mobile phase velocities, under high pressure gradients causes the production of a large amount of heat due to the viscous friction of the eluent percolating through the column bed. The evacuation of this heat causes the formation of significant axial and radial temperature gradients. Due to these thermal gradients, the retention factors of analytes and the mobile phase velocity are no longer constant throughout the column. The consequence of this heat production is a loss of column efficiency. We previously developed a model combining the heat and mass balance of the column, the equations of flow through porous media, and a linear isotherm model of the analyte. This model was solved and validated for conventional columns operated under moderate pressures. We report here on the results obtained when this model is applied to columns packed with very fine particles, operated under very high pressures. These results prove that our model accounts well for all the experimental results. The same column that elutes symmetrical, nearly Gaussian peaks at low flow rates, under relatively low pressure drops, provides strongly deformed, unsymmetrical peaks when operated at high flow rates, under high pressures, and under different thermal environments. The loss in column efficiency is particularly important when the column wall is kept at constant temperature, by immersing the column in a water bath.     

Influence of the column radial heterogeneity on the determination of single-component isotherms by the elution by characteristic point method

The influence of the column radial heterogeneity on the determination of equilibrium isotherm data by the elution by characteristic point (ECP) method is studied using nondimensional numerical calculations and taking into account typical radial distributions of the mobile phase flow velocity and the column efficiency across a column. Overloaded elution peaks were calculated with the equilibrium-dispersive model as a function of four dimensionless parameters, the number of theoretical plates at the center of the column, the Langmuir equilibrium constant, the retention and the loading factors. The influence of the mass transfer resistances and the radial heterogeneity of the column on the ECP data was analyzed by comparing the true isotherm and the one estimated from the diffuse profile of overloaded peaks. The results provide information on the accuracy of the ECP method. The error made increases with increasing degree of radial heterogeneity. This error can be corrected by using the results of the nondimensional numerical calculations, allowing a further extension of the applicability of the ECP method.     

Column radial homogeneity in high-performance liquid chromatography

The radial distribution of analyte molecules within an elution band in HPLC was determined by local, on-column, fluorescence detection at the column outlet. Several optical fiber assemblies were implanted in the exit frit at different points over the column cross-section and the fluorescence of a laser-dye analyte was measured. The individual elements of a diode array were used as independent detectors. The distribution of the mobile phase velocity across the column was measured for a number of standard size analytical HPLC columns of different efficiencies, operated at different mobile phase linear velocities. The dependence of the column efficiency on these profiles is discussed.     

Correction method for quantitative area determination of overlapping chromatographic peaks based on the exponentially modified Gaussian (EMG) model

A simple method is presented for peak area correction of overlapping peaks. This correction is necessary for the normal approach of dealing with overlapping peaks by a vertical line at the valley point. The relative area errors caused by this vertical line are calculated as the correction factors in three dimensions of peak separation, peak ratio, and peak tailing skew. The calculation is based on the exponentially modified Gaussian asymmetric peak model.     

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).     

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.     

Modeling of thermal processes in high pressure liquid chromatography: I. Low pressure onset of thermal heterogeneity

Heat due to viscous friction is generated in chromatographic columns. When these columns are operated at high flow rates, under a high inlet pressure, this heat causes the formation of significant axial and radial temperature gradients. Consequently, these columns become heterogeneous and several physico-chemical parameters, including the retention factors and the parameters of the mass transfer kinetics of analytes are no longer constant along and across the columns. A robust modeling of the distributions of the physico-chemical parameters allows the analysis of the impact of the heat generated on column performance. We developed a new model of the coupled heat and mass transfers in chromatographic columns, calculated the axial and radial temperature distributions in a column, and derived the distributions of the viscosity and the density of the mobile phase, hence of the axial and radial mobile phase velocities. The coupling of the mass and the heat balances in chromatographic columns was used to model the migration of a compound band under linear conditions. This process yielded the elution band profiles of analytes, hence the column efficiency under two different sets of experimental conditions: (1) the column is operated under natural convection conditions; (2) the column is dipped in a stream of thermostated fluid. The calculated results show that the column efficiency is remarkably lower in the second than in the first case. The inconvenience of maintaining constant the temperature of the column wall (case 2) is that retention factors and mobile phase velocities vary much more significantly across the column than if the column is kept under natural convection conditions (case 1).     

Implications of column peak capacity on the separation of complex peptide mixtures in single- and two-dimensional high-performance liquid chromatography

Column peak capacity was utilized as a measure of column efficiency for gradient elution conditions. Peak capacity was evaluated experimentally for reversed-phase (RP) and cation-exchange high-performance liquid chromatography (HPLC) columns, and compared to the values predicted from RP-HPLC gradient theory. The model was found to be useful for the prediction of peak capacity and productivity in single- and two-dimensional (2D) chromatography. Both theoretical prediction and experimental data suggest that the number of peaks separated in HPLC reaches an upper limit, despite using highly efficient columns or very shallow gradients. The practical peak capacity value is about several hundred for state-of-the-art RP-HPLC columns. Doubling the column length (efficiency) improves the peak capacity by only 40%, and proportionally increases both the separation time and the backpressure. Similarly, extremely shallow gradients have a positive effect on the peak capacity, but analysis becomes unacceptably long. The model predicts that a 2D-HPLC peak capacity of 15,000 can be achieved in 8 h using multiple fraction collection in the first dimension followed by fast RP-HPLC gradients employing short, but efficient columns in the second dimension.     

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.     

Chromatographic characterization of molecularly imprinted polymers

Recent efforts in the investigation of chromatographic characterization of molecularly imprinted polymers (MIPs) have focused mainly on the nature of heterogeneous binding sites. More data on the thermodynamics than on the kinetic features of MIP columns have been published. The present article addresses the sources of peak broadening and tailing, which are the main drawbacks often associated with imprinted polymers in chromatography for practical applications. With use of the theory of nonlinear chromatography, the peak properties of a MIP column, including the retention and peak broadening and tailing, can be well interpreted. Efforts to improve chromatographic efficiency using MIPs prepared by approaches different from the conventional method, including covalent imprinting and the format of uniformly sized spherical microbeads, are reviewed and discussed. This review leads to the conclusion that nonlinear chromatography theory is useful for characterizing chromatographic features of MIP columns, since a MIP is essentially an affinity-based chromatographic stationary phase. We expect more theoretical and experimental studies on the kinetic aspects of MIP columns, especially the factors influencing the apparent rate constant, as well as the analysis of the influences of mobile-phase composition on the chromatographic performance. In addition to revealing the affinity interaction by molecular recognition, slow nonspecific interactions which may be inherited from the imperfect imprinting and may be involved in the rebinding of the template to MIPs also need to be characterized. Figure The peak broadening and tailing associated often with molecularly imprinted polymers (MIPs) in column chromatography for practical applications can be well characterized by the theory of nonlinear chromatography.     

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.     

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