Effective Plate Number Research Articles

Use of kinetic plots for the optimization of the separation time in ultra‐high‐pressure LC

The kinetic-plot approach, in which experimental t(0) and N-values are extrapolated to the performance at maximum system pressure by increasing the column length, was validated by coupling 250×3 mm columns packed with 3 μm particles. The extra-column volume introduced by coupling columns could be neglected with respect to the peak volumes. Plate numbers of up to 132,000 were experimentally achieved by coupling four columns. The maximum deviation between the experimental and predicted plate numbers was 7% for two coupled columns, and decreasing to 0.1% for four coupled columns. Kinetic plots were used to find the conditions to separate a critical pair, with a preset value for the effective plate number, in the shortest possible time. For high-efficiency separations yielding 100,000 effective plates, the optimum critical-pair retention factor was around 4.5. Kinetic plots are presented to find the optimal column length to obtain the fastest possible 100,000 effective-plate separation, taking into account the effect of mobile-phase viscosity on column pressure, and consequently the optimum column length.

Use of the kinetic plot method to analyze commercial high-temperature liquid chromatography systems: I: Intrinsic performance comparison

The present study aimed at mapping the separation speed potential of a critical pair on commercial high-temperature HPLC (HT-HPLC) supports at elevated temperatures. For this purpose, band broadening and pressure drop measurements were conducted on three different commercial HT-HPLC columns operated at various elevated temperatures but by keeping the same retention factor. The plate height data were subsequently transformed into a plot showing the minimal required analysis time needed to yield a given required effective plate number. For the considered RPLC alkylbenzene separations, it was found that the maximal gain in separation speed of the critical pair that can be obtained by varying the operating temperature from T=30 to 120°C can be expected to be of the order of a factor of 3–4, if using an individually optimized column length for each considered temperature and if no secondary adsorption effects occur at the lower temperature. This gain factor, remaining more or less constant over the most relevant range of plate numbers, largely paralleled the reduction of the mobile phase viscosity accompanying the temperature increase.

Selection of comparison criteria and experimental conditions to evaluate the kinetic performance of monolithic and packed-bed columns

The present study concerns the problem of finding appropriate experimental conditions and comparison criteria to assess the kinetic performance of LC supports with different sizes or morphologies. A general procedure, based on evaluating each support for its own optimal mobile-phase composition, is proposed. The practical elaboration of the procedure is illustrated using the specific case of a capillary LC separation of a series of polycyclic aromatic test compounds employing silica-monolith capillary columns and capillary columns packed with 6-μm porous particles. To compare the systems for their ability to yield the fastest critical-pair separation, plate-height measurements are transformed into an effective plate number kinetic plot, i.e., a plot of the extrapolated retention time divided by the square of the extrapolated effective plate number ( t R / N eff 2 ) versus N eff. This type of data representation provides a direct and universal basis to compare the kinetic performance of different LC supports and it corrects for differences in retention strength arising from different phase ratios.

Chromatographic properties of the ion-exclusion column IonPac ICE-AS6 and application in environmental analysis. Part I: Chromatographic properties.

The chromatographic performance of the Dionex IonPac ICE-AS6 ion exclusion column is investigated. Therefore, capacity factors, efficiency, peak symmetry, resolution, and selectivity are determined for various mono- and polyfunctional aliphatic carboxylic acids under selected chromatographic conditions. Except for the stronger acids (pKa1 < 3.75), the highest chromatographic efficiency is achieved at a column temperature of 40 or 50 degrees C, and peak shape is found to be optimal at approximately 60 degrees C. The separation of the stronger acids is favored by an eluent pH below 3.0 and column temperatures below 40 degrees C. The maximal effective plate numbers range between 126 (tartronic acid) and 6380 (4-oxovaleric acid). Hydroxy-substituted acids are less retained and less influenced by temperature changes than the unsubstituted compounds. It is estimated that size exclusion effects take part in the separation of aldonic acids. The addition of 1% isopropanol to the acidic eluent increases the chromatographic efficiency generally, whereas higher concentrations reduce the retention of several acids drastically.

Influence of Linear Velocity, Column Length, and Pressure Drop in SFC. II. Plate Numbers, Effective Plate Numbers, and Resolutions

The plate number, the effective plate number, the effective plate height, and the resolution are determined as a function of the average linear velocity, the column length, and the pressure drop over a packed column in supercritical fluid chromatography (SFC). The chromatographic system consists of an 80:20 (v/v) mixture of C02 and methanol as the mobile phase, unbonded silica gel in a packed column as the stationary phase, and a mixture of four polycyclic aromatic hydrocarbons as the analytes. Nearly identical columns are used either singly or connected in series to produce longer columns. The column exit pressures are controlled by a self-adjusting valve and kept constant at 200, 250, or 300 bar, and the temperature is kept at 125°C. It is found that the plate number and the effective plate number increase almost proportionally with the column length, and the effective plate height remains about the same regardless of column length. The resolution of neighboring peaks increases with column length but not as strongly as the plate number, as would be expected. A flat maximum of resolution is found with changing average linear velocity; the height of the maxima is strongly dependent on pressure. Because greater column length is beneficial to plate number and resolution, no net detrimental effect of pressure drop on these chromatographic parameters appears to be present.

Efficiency in supercritical fluid chromatography as a function of linear velocity, pressure/density, temperature and diffusion coefficient employing n-pentane as the eluent

The effect of the physical factors linear velocity, pressure/density, and temperature on the efficiency expressed in terms of effective plate number, N eff, or height equivalent to a theoretical plate, H eff, were studied for supercritical fluid chromatography using n-pentane as the mobile phase modified with a small amount of methanol (0.5%, v/v), unbonded silica gel as the stationary phase, and a mixture of polycyclic aromatic hydrocarbons as the analytes on a packed analytical column (4.6 mm I.D.). The results are presented as three-dimensional graphs which, on plotting N eff of chrysene, N eff(C), versus column average pressure, p , and temperature, T, at different constant linear velocities, u , show movement of the maxima of N eff to higher temperatures when u increases. Moreover, the maxima are highest at medium u , i.e., at u opt. An analogous behaviour is found when N eff(C) is plotted versus the average density in the column, ρ . On replacing N eff(C) with the capacity factor of chrysene, k'(C), and again plotting versus p and T, the k′(C) values do not change greatly with increasing u . If the customary Van Deemter plots of H eff(C) versus u are combined with p or ρ as a third axis, keeping T = constant, the dependence of u opt on p or ρ becomes obvious. As expected, p and ρ should be kept as low as possible in order to obtain low H eff(C). Employing T as the third dimension for the Van Deemter plots and keeping p = constant, it is seen that only specific ranges of T yield the low H eff(C). The graphs are explained in terms of the interdiffusion coefficient, D 1,2. Three-dimensional graphs for the dependence of D 1,2 or Of the viscosity,on pressure and temperature are shown. The three-dimensional plots of N eff(C) and H eff(C) can be rationalized with respect to their dependence on the average linear velocity, pressure/density and temperature.

Comparison of Different Compositions of Mixed Pentane/1,4-Dioxane Mobile Phases in SFC

Abstract The effective plate number has been chosen for a comparison between different mixed mobile phases composed of pentane and 1,4-dioxane. A column packed with unmodified silica gel and pyrene as the analyte was used. The dependence of the effective plate number on pressure and composition for a constant temperature, or a constant reduced temperature, both at constant mass flow, are shown in three dimensional network plots. The same dependence is shown at constant temperature and constant linear velocity. For a detailed discussion, the dependence of the effective plate number on pressure, composition, capacity ratio, and other chromatographic parameters is given in two dimensional graphs. The main result for the present chromatographic system is that a Financial support by the Arbeitsgemeinschaft Industrieller Forschungsvereinigungen (AIF) is gratefully acknowledged.

An Improved Extractor for Dual-Flow Extraction

An improved apparatus for dual-flow countercurrent extraction was constructed. Further, a simple method to evaluate the extractor was developed, by which the effective plate number could be calculated by a couple of measurements of fractional recoveries. To find the optimum operation condition, an apparatus with a shorter column (10 cm in length) was prepared, the efficiency of which was evaluated as being about one plate per cm of the column length by the method. It was also shown that the distribution constant of a compound could be calculated from the fractional recoveries measured by dual-flow countercurrent extraction. The distribution constants, thus obtained, agreed with values determined independently by liquid-liquid chromatography, which settled theoretical correlations between chromatography and extraction.

Isocratic networks in supercritical fluid chromatography II: Selectivities and effective plate numbers

AbstractThe dependence of the selectivity α and the effective plate number, N, on temperature and pressure is shown in three‐dimensional diagrams. The specific system studied was pentane as the mobile phase, unmodified silica as the stationary phase, and a set of four polycyclic hydrocarbons as the test mixture. Temperature and pressure ranges were from 25 to 300°C and from 30 to 75 bar, respectively. The plots for α and N are found to resemble those for capacity ratio, k′, and resolution, R, studied earlier with the same system [1]. A distinct maximum is observed for N in the supercritical region, as found earlier for k′ and R. This applies also to α for the homologous substrate pair naphthalene/anthracene, while the resemblance for α is less pronounced for the pair anthracene/pyrene.

Three-dimensional network plots in supercritical fluid chromatography with n-pentane 1,4-dioxane

Using n-pentane-1,4-dioxane as a binary eluent system in supercritical fluid chromatography (SFC) and silica as the stationary phase, three-dimensional network plots of capacity ratios, k′, selectivities, α, effective plate numbers, N, resolutions, R, of four polycyclic aromatic hydrocarbons versus column temperature eluent composition at constant column pressure were obtained. Although the effects of the physical parameters temperature, composition pressure on the chromatographic properties k′, α, N or R of the binary eluent are found to be complex in detail, general information can be derived from the three-dimensional plots. The individual shapes of all three-dimensional surfaces are similar inasmuch as they are characterized by elevations located above the boiling temperature, T b, when the pressure is subcritical, or above the critical temperature, T c, at supercritical pressures of the eluent mixtures. Differences exist between k′, α, N and R with respect to the individual shapes and details of the elevations. Whereas above T b or T c the selectivities, α, for instance, remain high relatively independent of composition, the other chromatographic parameters change considerably with composition. An increase in pressure always reduces the overall height of the elevations.

On-line testing of gas chromatographic columns with a programmable computing integrator

A program is described which calculates the number of effective plates and the coating efficiency over the entire range of a test chromatogram. The peak widths at half height are derived by assuming a Gaussian peak shape. The interpolated peak width at k=4 is used for computing a standardized number of effective plates. Plate height, column permeability, overall performance and a novel parameter called sampling efficiency are calculated from 5 other figures — i. e. carrier gas code, pressure drop, column length, column temperature and particle size.

On the use of the separation number as a criterion for the evaluation of gas chromatography capillary columns in isothermal conditions

Although widely used to compare the performances of capillary columns the separation number is a poor index of the quality of a column. It is shown that it is a rubber ruler whose length is a function of temperature: the separation number of a column is a function not only of the effective plate number, which itself varies largely with the retention as measured by the capacity factor k′, but also of the relative retention of then-alkanes used for the measurement. This relative retention is strongly dependent upon the temperature for a given stationary phase. Unless the temperature at which the separation number is measured be normalized as well as the k′ range in which the second alkane of the pair used is eluted, the separation numbers are meaningless for the appreciation of the performance of a column or comparison of different columns. Using alkanes eluted in the same k′ range to measure the separation number of a column we obtained a value almost twice as large at 80°C as at 180°C. In spite of their imperfections the plate number and the coating efficiency are easier to use and less misleading.

Critical and statistically based evaluation, testing, comparison and optimization of capillary chromatography systems, the “ABT-concept” in capillary GC

Capillary chromatography is important owing to its separating power, but much of this power is theoretical only because in current practice the separation efficiency theoretically possible, expressed in peaks separated per time unit or per “chromatographic unit” (i.e. k-units) is not yet even partially realized. A dramatic improvement would be possible, if we could learn to master the most important and basic parameter “bo”, the starting peak width, which is a time value. “bo”, the “slope a” (of peak width which increases with time) and the dead time “tm” are the three basic chromatographic parameters, independent of the substances being chromatographed. They build a complete “practically oriented theory”. Application of this theory ensures full optimization of the separation capillary, improvement of the instrument and technique used and the data handling. The theoretical background, experimental results, and the statistically based data handling for testing a capillary and independently, for testing an instrument, are given. Everything discussed here is based on the critical evaluation of the chromatogram and the use of small programmed pocket computers. It is shown that the theoretical or the effective plate number or the plate height data basically and principally cannot describe the separation efficiency in capillary chromatography because of incomplete correlation. Therefore three basic quantities, independent of the substances used and independent of each other are necessary to develop and describe critical quality data for testing and optimization of capillary chromatography. An improved plate height concept is useful but it is better to develop a best possible capillary and describe its true quality. This “real plate height” unit which is free from instrumental influences when measured experimentally, is defined and introduced in capillary chromatography. Dramatic improvements should be possible depending on how we can reach the theoretical limit of bo.

Whisker-walled open-tubular glass columns in gas chromatography : II. Chromatographic performance

A variety of parameters relating to column efficiency (including the plate height, effective plate height, number of effective plates per unit time, phase ratio, sample capacity, performance index and percentage utilization of the theoretical efficiency) have been determined experimentally for whisker-walled open-tubular glass columns, and compared with values pertaining to other types of open-tubular columns.

Liquid chromatography with a dynamic temperature gradient

The theoretical principles of chromatography using a dynamic temperature gradient are described in terms of aspects of liquid-solid systems. Along the chromatographic column, an oven moves in the direction of flow of the mobile phase and thus creates a temperature gradient on the column, the temperature of which decreases in the direction of flow of the mobile phase. Each component of the mixture under analysis has a characteristic temperature in the gradient at which it is eluted from the column. The use of the dynamic temperature gradient has some advantages similar to those for the technique using a concentration gradient of the mobile phase (reduction in the time of analysis, linearization of the sorption isotherms, etc.). However, some additional advantages were found that can be used particularly in high-efficiency liquid chromatography. The composition of the mobile phase does not change and therefore the response of the detector can be used for the quantitative evaluation of the chromatogram. The column has the same adsorption properties after the analysis as before the application of the dynamic temperature gradient. An increase in the number of effective plates per second and in the peak capacity of the column were found, simultaneous with a decrease in the capacity ratio. The method can also be used for the enrichment of samples containing trace amounts of admixtures.

The effect of surface treatments of glass capillaries on column performance

The effects of etching and/or silylation of glass capillaries on column efficiency were studied. Coated with apolar OV-101, only columns subjected to the combined treatment showed an increase of about 50% in the number of effective plates. Surface hydroxylation, prior to silylation, gave a small additional improvement for this stationary phase.