Length minimum packed column

Assuming the minimum variance per unit length of a packed column is (2dp), then... 

The HETP curve clearly shows, that for a packed column, the particle size has a profound effect on the minimum value of the HETP of a column and thus the maximum efficiency attainable. It would also appear that the highest efficiency column would be obtained from columns packed with the smallest particles. This will in due course be shown to be a fallacy, but what is true, is that the smaller the particle diameter the smaller will be the minimum HETP and thus, the larger the number of plates per unit length obtainable from the column. At this time it will suffice to point out that the total number of theoretical plates that can be obtained will depend on the length of the column which, in turn, must take into account the available inlet pressure... 

To calculate the minimum diameter for a column of length (1) packed with particles of diameter (dp) which has not been optimized for a particular... 

Martin et al. published a paper on the theoretical limits of HPLC which is well worth reading.They used relatively simple mathematics to calculate pressure-optimized columns for which the length L, particle size and flow rate u of the mobile phase were selected such that a minimum pressure Ap is required to solve a separation problem. It has been shown that these optimized colunms are operated at their van Deemter curve minima. Some astonishing facts have emerged from the study, provided that the chromatography is performed on well packed columns (reduced plate height h = 2-3 see Section 8.5). 

The column is perhaps the most important feature of a GC system. It contains the stationary phase and thus effects the separation of components in a mixture. The column may be made of glass or metal and typically 2-6 mm i.d. and 1-3 m in length when packed with stationary phase material or 0.2-0.7mm i.d. and lO-lOOm long if in the form of a capillary column. Columns are formed into a coil of between 4 and Sin (10-20cm) in diameter and specially designed end fittings are used to connect the columns to the injector and detector with minimum dead volumes. A packed column contains solid particles of uniform size coated with stationary phase in GLC or uses uncoated particles as the stationary phase in GSC (Figure 5.4). 

If the dimensions of stationary phase coating thickness and diffusion distance to the film from the gas phase have been optimized, for further improvement of GC resolution, it becomes necessary to increase the length of the column. This is seen from the simple relation of Eq. (11.7), which indicates that for an optimal minimized value of H (the height equivalent to a theoretical plate) the number of plates, N, is proportional to the length of the column. From Eqs. (11.8) and (11.9) we note that the resolution is proportional to the square root of N. For columns packed with particles of optimal size, and operated at the optimal linear flow rate at the minimum of the Van Deempter curve (Fig. 11.3), the typical maximum pressure of 100 psi achievable from a regulated gas cylinder requires that most packed columns be less than 4-7 m long. More typically they are only 1 -2 m in length. These considerations hmit the resolution achievable in packed column GC. 

To minimize the effect of sample volume on dispersion, and ensure that there was minimum dispersion from the valve and valve connections, a 0.2 jxl Valeo internal loop valve was employed to place the sample on the column. In addition, the sample valve was used with an intra-column injection system [2] that ensured the sample was placed in the center of the column about 5 mm below the packing surface. TMs device also determined that, even if the packing settled, there would be no void above the point of injection and the effective length of the column was not changed. All connecting tubes were 0.007 in. I.D. and their lengths were kept to a minimum (Le., <5 cm). The detector employed was the Perkin Elmer LC-85B fitted with a cell 1.4 pi volume and was used in conjunction with an electronic amplifier that had an effective time constant of 24 millisec. The columns employed had internal diameters of 8-9 mm to ensure the peak volumes were very large compared to any dispersion introduced by extra-column dispersion. As a result, the extra-column dispersion was maintained at a level of less than 2% of the peak volume for all measurements and, in most instances, was maintained at a level of less than 1%. 

Columns may be constructed of 3.2-mm (Vi-in.), 6.4-mm ( /4-in.), or capillary tubing and usually need to be a minimum of 6 m (20 ft) in length. They usually have 20 to 40 g of liquid substrate to 100 g of solid support. If packed columns are used, the liquid may be plac on the solid support by any suitable method, provided the column has the desired resolution and sensitivity. 

Equation (24) allows the minimum column radius to be calculated from its length, the particle diameter of its packing and the extra column dispersion of the chromatographic system. Unfortunately, the extra column dispersion is rarely known and very few manufacturers even provide data on the overall dispersion of the detector. When values are given for the detector dispersion, it is often for the sensing cell alone and does not include internal connecting tubes and, as a consequence, can be very misleading. 

Employing the conditions defined in the three data bases and the appropriate equations derived from the Plate and Rate Theories the physical properties of the column and column packing can be determined and the correct operating conditions identified. The precise column length and particle diameter that will achieve the necessary resolution and provide the analysis in the minimum time can be calculated. It should again be emphasized that, the specifications will be such, that for the specific separation carried out, on the phase system selected and the equipment available, the minimum analysis time will be absolute No other column is possible that will allow the analysis to be carried out in less time. 

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