Columns minimum length

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... 

The van Deemter plots in Figure 25-3 show that small particles reduce plate height and that plate height is not very sensitive to increased flow rate when the particles are small. At the optimum flow rate (the minimum in Figure 25-3). the number of theoretical plates in a column of length L (cm) is approximately3... 

Table 2 Calculated number of plates per meter for a range of commonly available capillary column dimensions, and the minimum length required to produce 100000 theoretical plates...

It is seen that only a connecting tube 0.005 in. I.D.could be employed with the high speed column and a tube of 0.002 in. I.D. would have to be used with the small bore column. In practice tubes having an I.D. of less than 0.007 in. are not practical due to their liability to blockage. It follows that either the minimum length of connecting tube must be used or the column connected directly to the detector cell, or alternatively, a different form of connecting tubes must be employed. 

From the experimental HRTEM images discussed in the previous sections, some conclusions may he drawn regarding the possible atomic arrangement of the r-plane sapphire with respect to the a-plane GaN. Figure 11.25a and b shows possible interfacial arrangements in the [0001 ]caN and [llOOJcaN directions for which the Al-N and Ga-O bonds have been adjusted in such a way that they have minimum lengths. The low mismatch in [llOOjcaN direction leads to an almost complete match between the O atoms of the sapphire and the Ga atoms of the nitride film. Contrary to this, the larger lattice mismatch in [0001 ]caN direction results in a rather poor match between the A1 and O columns of the sapphire with respect to the N and Ga columns of the film. This poor match results in shear forces parallel to the c planes, which are likely to increase the probability of BSE formation in the presence of stress fields, for example, those associated with the introduction of MFDs upon relaxation. 

To increase the number of theoretical plates without increasing the length of the column, it is necessary to decrease one or more of the terms in equation 12.27 or equation 12.28. The easiest way to accomplish this is by adjusting the velocity of the mobile phase. At a low mobile-phase velocity, column efficiency is limited by longitudinal diffusion, whereas at higher velocities efficiency is limited by the two mass transfer terms. As shown in Figure 12.15 (which is interpreted in terms of equation 12.28), the optimum mobile-phase velocity corresponds to a minimum in a plot of H as a function of u. 

ADM = Minimum downcomer area, fT ATM = Minimum column cross-sectional area, fr CAF = Vapor capacity factor CAFo = Flood capacity factor at zero liquid load CFS = Vapor rate, actual ftVsec DT = Tower diameter, ft DTA = Approximate tower diameter, ft FF == Flood factor or design percent of flood, fractional FPL = Tray flow path length, in. 

It is seen that by a simple curve fitting process, the individual contributions to the total variance per unit length can be easily extracted. It is also seen that there is minimum value for the HETP at a particular velocity. Thus, the maximum number of theoretical plates obtainable from a given column (the maximum efficiency) can only be obtained by operating at the optimum mobile phase velocity. 

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

It should be pointed out that equations (14) and (15) do not give an expression for the minimum column lengths, as the optimum particle diameter has yet to be identified. 

Thus as (y) will always be greater than unity, the resistance to mass transfer term in the mobile phase will be, at a minimum, about forty times greater than that in the stationary phase. Consequently, the contribution from the resistance to mass transfer in the stationary phase to the overall variance per unit length of the column, relative to that in the mobile phase, can be ignored. It is now possible to obtain a new expression for the optimum particle diameter (dp(opt)) by eliminating the resistance to mass transfer function for the liquid phase from equation (14). 

Thus, the minimum column length (L) will be given by... 

Lmin) is the minimum column length, and (e) is the fraction of the column occupied by the mobile phase. 

Now, the column length (L) can be defined as the product of the minimum plate height and the number of theoretical plates required to complete the separation as specified by the Purnell equation. 

The minimum column length increases as the value of (a) is reduced and, at the... 

The minimum column length was calculated for a series of separation ratios using equation (19) and the results obtained are shown in Figure 14. 

Figure 14. Graph of the Log of the Minimum Column Length against the Separation Ratio of the Critical Pair...

It is seen that the minimum column length ranges from 100 meters to 2 or 3 mm. It should be pointed out at this time that the theory may not predict data accurately when the column lengths become less than a few centimeters. It is now of interest to calculate the corresponding analysis times. 

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