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950 A • ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
5
separative performance, hinging on thoughtful experimental design. The equations also show the magnitude of potential gains stemming from the stretching of limiting operating pa rameters, such as pressure or voltage. Furthermore, the equations show where little progress is to be expected, thus helping close off unproductive pathways. Table II shows performance ceilings for a group of contrasting techniques. Equations are shown for both separat ing power and speed. Separating power is expressed in terms of number of theoretical plates Ν (applicable even to electrophoresis (9)), and in terms of peak capacity n, the latter more generally useful because the plate concept does not extend well to such steady-state methods as isoelec tric focusing (10). Ceilings for separation speed are ex pressed as number of plates per unit time, N/t. Table II has, of course, been simpli fied in the interest of clarity, and does not begin to explain how each equa tion is to be used or the nature of any qualifications. But it captures the es sence if not the details of each meth od's potential. The equations have been collected from the previously cited literature (5, 7-11). Even casual inspection shows that there are many similarities among the equations in any of the columns of Table II. This reflects the underlying systematics of separation, but space permits only a few points in this regard. We note that the terms θ and Θ' rep resent the extent to which any disper sive process increases zone spreading. Ideally, θ at 0* at 1. Parameter y plays the same role in the chromatographic equations, but is usually less than unity due to tortuous diffusion in packed columns. Ν is always inversely proportional to one of these parame ters, while η is always inversely pro portional to the square root of one of them. Reducing θ or Θ' is therefore a general goal for separations. Of significance, we note that every equation for separation speed N/t is inversely proportional to friction coef ficient /, or proportional to diffusivity D, which is one and the same thing ac cording to Equation 3. This illustrates the validity of our earlier general con clusion that separation time is scaled with / and separation speed inversely with / and directly with D. (No sepa ration speed equations are available for the steady-state methods where zones form by an unusual mechanism
(ID). We note also that peak capacities are almost the same in the two com plementary pairs: electrophoresis-iso electric focusing and rate zonal sedimentation-isopyenic sedimentation
