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Typical Chromatographic Operating Conditions
Separation Ratio (a) (Critical Pair) 1.05 Capacity Ratio (first eluted peak of the Critical Pair) 2.5
Viscosity of the mobile phase (t)) 0.023 Poises
Diffusivity of Solute (Dm) 3.5X I O'5 cm2/sec
D'Arcy's Constant (<p) 35
Inlet Pressure (P) 3000 p.s.1
Packing Factor (ß.) 0.5
Packing Factor (v) 0.6
Capacity Ratio of the last eluted peak (k'2) 5.0
Graphs of optimum particle diameter against separation ratio were calculated using equation (18), for a range of (a) values between 1.01 to
1.10 and inlet pressures of 2000, 4000, and 6000 p.s.i.. The results obtained are shown in figure (1). The calculations were carried out employing the basic chromatographic data given in table (I)
Graph of Optimum Particle Diameter against Separation Ratio
O 2000 p.s.i. ¦ 4000 p.s.i. ë 6000 p.s.i.
It is seen from figure (1) that the optimum particle diameter ranges from about 2 micron for very simple separations (a=l,12) carried out at an inlet pressure of 6000 p.s.i. to about 40 micron for difficult separations (a= 1 01 ) carried out at an inlet pressure of only 2000 p s.i Furthermore, the curves shown in figure (1) appear to be in conflict with popular opinion, in that, the more difficult separations are best achieved with particles of relatively large diameter, whereas, simple separations require particles of small diameter for optimum performance This apparent paradox will be discussed more fully later in the chapter. Equation (18) also discloses some interesting properties of the optimized column.
Firstly it is seen that that the optimum particlc diameter is inversely proportional to (a-l),
,e up<opt) « ^a_||
Consequently as shown in figure (I) the optimum particle diameter will rapidly increase as (a) becomes smaller; i e as the separation becomes more difficult.
Referring back to equation (18), it is seen that the optimum particle diameter is inversely proportional to the square root of the inlet pressure.
Thus, the larger the available inlet pressure the smaller the optimum particle diameter can be. Nevertheless, as a result of the square root function, the sensitivity of the optimum particle diameter to the magnitude of the inlet pressure is much less than it is to the separation ratio of the critical pair. This is confirmed by the curves shown in figure (1) where it is seen that, providing the inlet pressure is above 2000 p.s.i., the effect of pressure on the optimum particle diameter is not nearly as significant as might be expected.
However, it has been mentioned before, and must be bourne in mind, that it is not the pressure capability of the solvent pump that normally determines the maximum pressure that can be employed, but the maximum pressure the whole chromatographic system can tolerate. Although valves have been designed to operate at 10,000 p.s.i., or even higher, their useful lifetime at that pressure is often relatively short, usually as a result of sample contamination scoring the valve seats. For long-term continuous operation the maximum inlet pressure a valve can tolerate is often only about 3000 p si..
It is seen from figure (I) that, over the range of separation ratios chosen, the magnitude of the optimum particle diameter extends from about 1 öëï to about 30 |im and simple separations are best achieved using particles of small diameter, whereas, difficult separations require the use of particles of large diameter. As stated above, these conclusions appear to be in conflict with traditional ideas on the effect of particle size on column performance. Popular assumptions are that, for fast separations, velocities above the optimum should be employed and for high resolution and high efficiencies, particle diameters should be made as small as possible. These misconceptions have arisen, partly as a result of disregarding the fact that there is a limit to the pressure available from the pump or that can be employed with a particular apparatus, and partly from attempting to achieve
fast separations from a column of fixed length. As a consequence of limited inlet pressure the particle diameter can not be reduced beyond the limit that provides sufficient permeability to allow the optimum velocity to be realized. If higher efficiencies are required, the column must be made longer, and to achieve this, the column permeability must be increased by making the particle diameter larger. Mobile phase velocities higher or lower than the optimum would increase the HETP and thus the required efficiency would not be obtained.
However, if for some reason the length of the column can not be changed, and the column has excess efficiency to that required, the analysis time can be reduced by increasing the mobile phase velocity above the optimum, and consequently discarding the excess efficiency Nevertheless, it must be emphasized that, under these circumstances, although the analysis time will be reduced, it will not be the minimum. The analysis time would be reduced further, if the particle diameter was reduced to the optimum, the optimum column length reduced and the column operated at the optimum velocity. Unfortunately, for very simple separations the optimum particle diameter may be smaller than that commercially available, or below that which can be packed successfully with known packing techniques. Under such circumstances, non-optimized columns with excess efficiency, operated at high velocities, may be the only way to reduce the analysis time to an accepted level. Such a set of limiting conditions, however, is rarely met in practice.