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than 150 cm particularly if it had a diameter in excess of 20 cm. It should be pointed out that the limits that have been placed on the physical properties of the preparative column are somewhat arbitrary and can be modified to suit the user.
in figure 2 the limits of length are included in the diagram and it is seen that, for the particular sample considered, an optimum column can not be used for the separation of mixtures where the separation ratio of the critical pair exceeds 1.3. Furthermore, at a separation ratio of 1.3, extremely low inlet pressures must be employed to ensure the use of a column 5cm or more in length. Thus, for simple mixtures, columns with excess efficiencies may have to be used which, as will be seen later, can be overloaded and the excess resolution traded in for increased sample load.
in a similar manner, by employing equation (4), the separation time can be calculated for a series of mixtures where the separation ratio of the critical pair ranged from 1.01 to 1.50, and, again, at inlet pressures of
1,10,100,1,000 and 10,000 p.s.i. The results obtained are shown in figure 3
Graph of Log. Analysis Time against Separation Ratio
¦ 10 p.s.i.
¦ 100 p.s.i. î 1000 p.s.i
¦ 10,000 p.s.i. MINIMUM MAXIMUM
1.0 1.1 1.2 1.3 1.4 1.5 1.6
It is seen from figure 3 that under optimum conditions,the range of analysis times is exceedingly wide, extending from many days to a few milliseconds.
In a similar way to particle diameter and column length, there are also some practical limits that must be imposed on the analysis time. It must be again emphasized that these limits are arbitrary in nature, and may be changed by the user if so desired. A minimum analysis time of one minute is recommended to allow time for sample manipulation and fraction collection and at the other extreme a maximum analysis time of one hour is considered acceptable. It is seen that a practical window exists between a separation ratio of 1.01 and 1.3. Furthermore, at a separation ratio of 1.3, extremely low inlet pressures must be employed to ensure the analysis time is not less than 60 seconds. Thus, the limitation of analysis time to a minimum of 60 seconds, means that for very simple mixtures, columns with excess efficiencies must be used. As has already been suggested, such columns can be overloaded and the excess analysis time also traded in for increased sample load.
The Column Radius
The radius of an analytical column is determined, among other factors, by the extra column dispersion of the chromatographic system. For preparative columns, however, the radius is determined by the sample load that is required to be placed on the column to obtain the necessary throughput.
Now the maximum charge that can be placed on the column (Vj) has been shown to be, (Chapter 5 page 54),
Now from the Plate Theory,
Vr= V,;(1+k') ........................................................................... (6)
where (V0) is the dead volume of the column.
Furthermore, V0 = enr2 i0Ft ......................................................................... (7)
where (e) is the fractional cross-section of the column occupied by the mobile phase and usually equivalent to 0.65,
(r) is the column radius, and (l0pt) is the optimum column length.
Substituting for (n) from equation (1), for (Vr) from equation (6) and for (V0) In equation (5),
1.1(1 + k‘)enr2lopt
4(l + k')
Substituting for (10pt) from equation (3) and simplifying,
3(1 + k)
(l+6k+l Ik'2) V' ÷
It is seen from equation (9) that the maximum sample volume depends on the square of the radius and inversely on the square root of the column inlet pressure. Now, although (r) and (P) are not mathematically interdependent, there is a practical dependence of (r) on (P). The column must, physically, be able to withstand the the pressure (P) and thus, the column walls must be sufficiently thick to accommodate the pressure for any given radius (r). The aspect of column strength, and weight will be discussed further in due course. Now, if the mass of the selected solute that is required per separation is (M) and is placed on the column in the maximum permissible sample volume (VO,
Then, M= wVi/100 ------------------ (10)
where («) Is concentration of solute In the sample solvent %w/v
In practice the value of (u) will vary between about 2 and 5 ( i.e sample concentrations will lie between 2%w/v and 5%w/v) before mass overload becomes a significant factor in band dispersion. A numerical value for (to) of 5 will be taken in subsequent calculations. The correct value of («), for the particular solute concerned, can be experimentally determined on an analytical column carrying the same phase system If so required.
Rearranging equation (10),
Vj = IOOM/W
Substituting for (Vi) from equation (11) in equation (9) and solving for (r),