Bandwidth column efficiency

Bandwidth. Column efficiency may also be expressed in terms of a bandwidth. The bandwidth is defined as the volume of mobile phase containing 95% of an eluted compound, or, equivalently, four standard deviations of a statistical distribution of the same shape as the chromatographic peak ... 

Equation 1 shows that bandwidth is merely a means of expressing column efficiency, N, as a function of elution volume,... 

Effect of Injection Volume. Table II shows the effect of injection volume on peak broadening and measured column efficiency. The bandwidths listed in Table II are due to injection volume alone, and were measured using an injector connected directly into the flowcell of a low-bandwidth detector. The plate reductions were then calculated for a 24,000 plate column, such as that represented by the bottom line of Table I, assuming 5 and 10 ml, respectively, for exclusion and total permeation volumes. Efficiencies of 23,000 plates at exclusion and 25,000 plates at permeation were actually measured for the column indicated in Table II. The effect of large injection volumes is thus to lose 25 to 50% of the potential column efficiency. 

The bandwidth values in the table are those calculated for the total system the instrument plus the column. The values for number of plates are for the number of plates realized in the total system. It can be seen that the optimized system does not greatly impact column efficiency, the total loss in plates being only about ten percent at total exclusion for a 24,000 plate column. This is consistent with an instrumental bandwidth equal to a third of the bandwidth of the column. The conventional system, with a bandwidth equal to or greater than that of the column, exhibited a severe loss in realized efficiency, particularly at or near exclusion. 

Table III. Effect of instrumental bandwidth on column efficiency...

The data of Table III represent calculated bandwidths and efficiencies. Actual realized efficiencies were measured for the four chromatograms of Figure 4. For the 10-ym gel column, the conventional system produced an effective efficiency of 11,000 plates, compared with an effective efficiency of 16,000 plates for the optimized systems. These values are in excellent agreement with the calculated values shown on the top line of Table III. Similar measurements on chromatograms obtained from the 5-vim gel columns yielded values of 16,000 and 20,000 plates, respectively, for the conventional and optimized systems. This also represents good agreement with calculated effective efficiencies at total exclusion for a 24,000 plate column. 

Polymer gel GPC columns packed with 10-pm gels can exhibit efficiencies of 12,000 to 16,000 plates depending on the pore size. Single columns of this type produce bandwidths from 160 to 180 pi. As columns are coupled in series, bandwidth increases as the square root of the number of columns, as may be seen from Equation 1. Plate number doubles, but so does the exclusion volume. The 5-pm gel columns typically achieve 20,000 to 24,000 plates, and are represented by the bottom two rows of the table. The implications of the bandwidth values in Table I will be discussed below. 

Tatle II. Effect of injection volume on bandwidth ind realized efficiency of a Perkin-Elmer/PL Gel 5- m 100 Angstrom column eluted with THE at 1.0 ml/min... 

Inherent Total Column System Efficiency Bandwidth, yl Effective Plates Total System Bandwidth, yl Effective Plates... 

The 5-vim gel GPC columns are seen to produce tremendous e.fficiencies, but these efficiencies are only realized when the chromatographic system is optimized with respect to bandwidth. This also holds true to a lesser degree for a well-packed lO-ym gel column. 

The efficiency of separation in all types of column chromatography depends on the extent to which the sample bandwidth broadens during development of the chromatogram. Three factors determine this broadening (1) axial diffusion of solutes within the mobile phase, which is... 

When the sample is introduced into the column, usually in the form of a zone of vapor, it takes the form of a narrow band. During transit through the column, various factors influence the width of this band, which is continuously increased due to various dispersion processes. These include diffusion of the solute, resistance to mass transfer between and within phases, and the influence of flow irregularities and pertur-bations.f A simple concept, the theoretical plate, carried over from distillation processes, has been used to compare columns and account for the degree of dispersion that influences bandwidth. A chromatographic column may be considered to consist of numerous theoretical plates where the distribution of sample components between the stationary and mobile phase occurs. Hence, a measure of the efficiency of a GC column may be obtained by calculating the number of theoretical plates, N, in the column from ... 

The apparent plate munber can be calculated from the experimental profiles [27]. However, this number depends on the fractional height at which the bandwidth is measured. The value of Nth is calculated from the profiles predicted, under the same experimental conditions, by the ideal model. Finally, Nion is derived from the band profiles recorded in linear chromatography, e.g., with a very small sample size, using the relationships valid for Gaussian profiles. From Eqs. 7.24 and 7.26, we can derive the band width at half height, Wi/2, and the retention time of the band profile, ty, obtained with an infinitely efficient column. In the case of a Langmuir isotherm, we obtain [31]... 

A too-often-overlooked consideration in extra-column contributions is the diameter of the connecting tubing. Dolan (25) has thoroughly discussed the effect of tubing on the operation and maintenance of an efficient chromatographic system. Tables 1 and 2 show the volume of the tubing, in milliliters per centimeters and the maximum length allowable for a 5% increase in bandwidth for several typical dimensions. 

If the sum of these various contributions to band broadening produces a band of width w,-, when the column is disconnected from the separation system, an additional term must be added to Eq. (5-2) L/16(R/iv,). Extracolumn effects are most important in high efficiency separations where sample retention volumes are small, e.g., in narrow diameter columns. The initial sample bandwidth (a) can be controlled by minimizing... 

Cryogenic traps are convenient accumulation and injection devices for fast gas chromatography and interfaces for coupled-column gas chromatography, where a heartcut sample is collected and focused from the first column, and reinjected into the second column. The main requirement for a cryogenic trap used in these applications is efficient accumulation over time with rapid injection of the collected analytes as a narrow pulse in both time and space. Commercially available systems using a capacitance discharge for heating provide injection bandwidths of 5-20 ms. 

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