Optimum open tubular column

The efficiency obtained from an open tubular column can be increased by reducing the column radius, which, in turn will allow the column length to be decreased and, thus, a shorter analysis time can be realized. However, the smaller diameter column will require more pressure to achieve the optimum velocity and thus the reduction of column diameter can only be continued until the maximum available inlet pressure is needed to achieve the optimum mobile phase velocity. 

Equation (13) is the first important equation for open tubular column design. It is seen that the optimum radius, with which the column will operate at the optimum velocity for the given inlet pressure, increases rapidly as an inverse function of the separation ratio (cc-1) and inversely as the square root of the inlet pressure. Again it must be remembered that, when calculating (ropt)5 the dimensions of the applied pressure (P) must be appropriate for the dimensions in which the viscosity (r)) is measured. 

In a packed column the HETP depends on the particle diameter and is not related to the column radius. As a result, an expression for the optimum particle diameter is independently derived, and then the column radius determined from the extracolumn dispersion. This is not true for the open tubular column, as the HETP is determined by the column radius. It follows that a converse procedure must be employed. Firstly the optimum column radius is determined and then the maximum extra-column dispersion that the column can tolerate calculated. Thus, with open tubular columns, the chromatographic system, in particular the detector dispersion and the maximum sample volume, is dictated by the column design which, in turn, is governed by the nature of the separation. 

In the previous two chapters, equations were developed to provide the optimum column dimensions and operating conditions to achieve a particular separation in the minimum time for both packed columns and open tubular columns. In practice, the vast majority of LC separations are carried out on packed columns, whereas in GC, the greater part of all analyses are performed with open tubular columns. As a consequence, in this chapter the equations for packed LC columns will first be examined and the factors that have the major impact of each optimized parameter discussed. Subsequently open tubular GC columns will be considered in a similar manner. 

C is an apparatus constant. Usually C, a, and KH are temperature dependent, but a and Kh more so than C. Also In (a) behaves analogously to VPIE and normally increases as temperature falls according to 1/T or 1 /T2 (Chapter 5), while KH typically increases exponentially as temperature falls. These two criteria conflict so far as the best choice of temperature is concerned, and for good separations it is necessary to determine the optimum compromise. With a and KH set by the selection of operating system and temperature, resolution is proportional to Vg/Vc. For maximum resolution the vapor volume is increased by electing open tubular columns, i.e. wetted wall columns with minimal liquid loading, and therefore minimal capacity. 

It is seen that the optimum column radius for an open tubular column varies widely with inlet pressure arid the difficulty of the separation. Considering a separation of some difficulty, for example ( a = 1.02), it is seen that at an inlet pressure of lOOOp.s.f, the optimum column diameter would be about 4 micron whereas, at an inlet pressure of only 1 psi, it would be about 43 micron. The former would be quite difficult to coat with stationary phase and would demand detectors and injection systems of almost impossibly low dispersion A column of 43 micron in diameter, on the other hand, would be piactical from the point of view of both ease of coating and an acceptable system extra column dispersion. However, the lengths of such columns arid the resulting analysis times remains to be determined and may preclude their- use. 

The properties of open tubular columns shown in figures (I) to (6) indicate that the areas where such columns would have practical use is very restricted. At pressures in excess of 10 ps.i., and whatever the nature of the separation, whether simple or difficult, the optimum column diameters are so small that they would be exceedingly difficult to fabricate or coat with stationary phase. The maximum sample volumes and extra column dispersion that couid be tolerated would also be well below that physically possible at this time. At relatively low pressures, that Is at pressures less than 10 p.s.l. the diameter of the optimum column is large enough to fabricate and coat with stationary phase providing the separations required are difficult i.c. the separation ratio of the critical pair must be less than 1.03. However, even under these conditions the sample volume will be extremely small, the extra column dispersion restricted to an almost impossibly low limit and the analysis time would be very long Nevertheless, open tubular columns used for very difficult separations... 

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