Chromatography Handbook Of Hplc - Katz Eksteen Schocnmakers Miller wiley Sons -111

Mechanisms and Importance of Zone-Spreading 101\n\nvelocity, rather than plate height alone, that determines the analysis time. If we define the separation speed as SS = nal/ta, we have:\n\nSS = nal/ta = (LH/[In(1 + k)]) = 1/[H/(u_m)(X) + k] = 1/[\\sqrt{(A/(u_m)) + B/(u_m)^2 (C_m + C_j)(1 + k)]\n= 1/[(C_m + C_j)(1 + k)]\n\nfor sufficiently high velocities. This shows that for Golay- and van Deemter-type equations, the separation speed is constant and independent of the mobile-phase velocity.\n\nAt the optimum conditions at minimum plate height, the separation speed would have been:\nSS_min = 1/[(H_min/u_m)(X) + k)]\n= 1/[A/(C_m + C_j)B^(1/2) + 2(C_m + C_j)(1 + k)]\n= 1/[(2(C_m + C_j)(1 + k)]\n\nfor the usual case of small (or nonexistent, as in the capillaries) A values. This separation speed, under optimum conditions, is seen to be a factor of 2 smaller than the separation speed at velocities well above the optimum velocity. As a consequence, the fastest operation of a column does not correspond to working at or near the optimum conditions, the latter being of interest only for maximum performance irrespective of analysis time. We should, however, realize that working at elevated velocities will not necessarily lead to lower resolutions, notwithstanding the increase in plate height, because the use of longer columns or columns with smaller IDs, would yield a gain in theoretical plates, compensating for the loss in plate height. Obviously, we should make a distinction between maximizing the resolution (especially for complex samples, resolution or peak capacity is often inadequate) and optimizing the retention time if resolution is adequate.\n\nIn the first case, it is clear that the plate number should be maximized by decreasing the plate height to its minimum value; for example, by using longer columns (mile long capillaries have indeed been designed to yield some 10^6 theoretical plates). Here, we should realize that the optimal mobile-phase velocity determines the maximum plate number and the (minimum) time required to obtain a specific separation. A strong means to improve resolution is to increase the selectivity, as shown in Eq. (18); for example, by changing the stationary phase or by changing operating conditions, such as the temperature. This and the process of optimization of resolution and time, will be discussed further in Sec. IV, but here we mention that redesigning the column to greater lengths or smaller diameters, combined with higher velocities implies that higher pressures are needed to transport the mobile phase through the system. Hence, it is obvious that pressure limitations will ultimately determine the maximum separation speed.\n\nIn the early days of capillary chromatography, the late 1950s, this aspect of pressure sometimes led to hilarious discussions at conferences. For example, a quote from the 1960 Edinburgh Symposium on Gas Chromatography reads [29, p. 198]:\n\nJ.H. Knox: The point is that if you double your pressure drop across the column you could use it more efficiently by reconfiguring the column.\nC.P. Quinn: Yes, I agree again, you can carry on in this way trying first one and then the other and so on, and infinitum. However, as far as our own practical experience is concerned, we have always found that the pressure drop across the column is not the thing which limits us, but in fact it is the size of the capillary, or the size of the output particles, which is in the end the limiting factor. So when Dr. Knox gets to the end of his capillary columns and has got them so small that he cannot breathe down them, we shall double our pressure and do it twice as fast. I am afraid that is all I can\nsay.\n