Theoretical plates per unit time

Most analyses are run at carrier gas velocities that are 1.5 to 2 times as great as the optimum velocity at the minimum of the van Deemter curve. The higher velocity is chosen to give the maximum efficiency (most theoretical plates) per unit time. A small decrease in resolution is tolerated in return for faster analyses. 

Similarly, the number of theoretical plates per unit time can be calculated ... 

In pressure-driven operation, considerable band broadening was observed at high linear velocity, although the separation impedance was much lower than that of a particle-packed column owing to the much lower flow resistance. The separation impedance (E = AP to / r N2 = (AP / N) (to / N) (l/r )) expresses the total column performance in terms of the reciprocal number of theoretical plates per unit time and pressure drop. Because the contributions of the B- and C-terms are expected to be similar for a pressure-driven mode and an electro-driven mode, the difference in performance can be attributed to the greater contribution of the A-terms in Eqn. 5.2 in the pressure-driven mode. The contribution of the A-term is known to be less in CEC than in HPLC [6],... 

When the partition ratio is large, the plate height at the minimum is 1.9r and the velocity 2. DJr. The important conclusion to be reached here is that, the smaller the diameter of the capillary, the smaller the optimum plate height and the higher the optimum flow velocity. This situation means more theoretical plates per unit length and the possibility of shorter analysis time for a given level of separation. 

A typical HPLC separation using a 15-cm column of 15,000 theoretical plates produces peak capacity (Giddings, 1991) of about 80-100 under isocratic conditions and up to 150 under gradient conditions in 1 h(Eq. 7.3, n peak capacity, A number of theoretical plates of a column, and fR and t retention time of the last and the first peak of the chromatogram, respectively). An increase in the number of separated peaks per unit time can be achieved by increased separation speed made possible by monolithic silica columns (Deng et al., 2002 Volmer et al., 2002). This has also been shown for peptides and proteins (Minakuchi et al., 1998 Leinweber et al., 2003). 

The HETP curve clearly shows, that for a packed column, the particle size has a profound effect on the minimum value of the HETP of a column and thus the maximum efficiency attainable. It would also appear that the highest efficiency column would be obtained from columns packed with the smallest particles. This will in due course be shown to be a fallacy, but what is true, is that the smaller the particle diameter the smaller will be the minimum HETP and thus, the larger the number of plates per unit length obtainable from the column. At this time it will suffice to point out that the total number of theoretical plates that can be obtained will depend on the length of the column which, in turn, must take into account the available inlet pressure... 

This is known as the plate time and has units of seconds. It is equivalent to the amount of time it takes to generate one theoretical plate. Its inverse would be plates per second, N/to. Plates per second may also be expressed more generally as N/t for elution times other than the void time [2,3]. These terms more effectively describe the criteria of resolution per unit time that are desired to be maximized (actually, N/t is proportional to resolution squared per time) unfortunately, they are not widely used in the literature, and for the sake of continuity will not be used in this discussion. The following sections will look at what influences plate height and velocity and how best to minimize H/u. 

When compared to the batchwise preparative chromatography, Simulated moving bed (SMB) units exhibit a number of advantages. These advantages are primarily because of the continuous nature of the operation and the efficient use of the stationary and mobile phases, which allows a decrease in desorbent requirement and an improvement of the productivity per unit time and per unit mass of stationary phase. In addition, high performances can be achieved even at rather low values of selectivity and with a relatively small number of theoretical plates. Due to these positive features, SMB is particularly attractive in the case of enantiomer separations, since it is difTicult to separate enantiomers by conventional techniques. More recent applications related to chiral technology were reported [1-3]. 

After the column has come to equilibrium, the reflux ratio is adjusted. As was mentioned previously, it is usually advisable to maintain the reflux ratio equal to the number of theoretical plates the column possesses at total reflux. The ratio is usually measured either by noting the number of drops returned to the column by the head and the number withdrawn per unit time, or by the lengths of the off and on periods if a magnetically operated valve is used. 

The column consists of theoretical plates, that is, equilibrium exists at each plate. The vapor (D in moles per unit time) and liquid (F in moles per unit time) streams in the rectification and stripping sections are constant (prerequisite the molar enthalpies of evaporation of A and B are almost equal and adiabatic conditions are present). 

The quantity c nj(Nj is the concentration of analyte emerging from the last theoretical plate into the detector, so Equation [3.11] corresponds to the desired theoretical expression for Rd(V) for cases in which the chromatographic detector has a concentration dependent response (Section 4.4.8 and Appendix 4.1) UV-visible absorption detectors are an important example since their response is described by the Beer-Lambert Law, but elecirospray ion sources for mass spectrometers can also behave in this fashion in some circumstances (Section 5.3.6b). Electron ionization ion sources provide a response that is mass flux dependent (Section 4.4.8) however, for a fixed mobile phase flow rate U (volume per unit time), the conversion from c ni(N) to the mass flow rate is trivial and this distinction is not important in the discussion of the present Section although the practical imphcations are discussed in Section 5.3.6b. 

The same units must be used to measure t and W. These parameters are illustrated in Figure 3.1. Column efficiencies may be described in terms of theoretical plates per metre, or as the column length (plate height) equivalent to a single theoretical plate. Ideally, retention volumes rather than times should be used, but the two are obviously related in a given column. 

The Kremser equation correlates three factors (1) the fraction of a given gas component that is absorbed, (2) the number of theoretical plates in the column, N, and (3) the absorption factor, A. A is defined as L/KV, where L and V are the liquid and gas flow rates in moles per unit time, and K is the equilibrium constant for the given component, y/x. The symbols y and X have their usual meaning of mole fraction of the given component in the gas and in the liquid, respectively, at equilibrium. 

One particular advantage of using SFC is that it can generate a higher theoretical plate count per unit time than HPLC. This means that multiple chromatographic runs using small injections for each run could be used to separate complex mixtures in a small space of time. 

The smaller the particle size, the faster the rate of generating theoretical plate (HETP) per unit of time. Figure 14.8 shows a plot of HETP versus linear carrier velocity u for small particles. It indicates that the smaller the particle size, the lower the HETP. It is also important to note that small particles provide nearly the same HETP over a wider range of flow rate.14... 

From this equation it can be seen that the efficiency per unit length is inversely proportional to the capillary diameter. Decreasing the diameter of the capillary will decrease the height equivalent to a theoretical plate. The efficiency per unit length increases. Therefore, smaller-diameter capillaries can be used at shorter lengths, which ultimately decreases the separation time. 

The major reason why a reduction of the particle size or column diameter is expected to lead to an increase of separation speed (resolution power per time unit) can be found in its effect to decrease r. Separation speed is often expressed in the analytical literature in terms of the number of theoretical plates N per time unit f (for a definition of N in terms of experimental parameters see Sect. 3.1.1). For zone dispersion due to lateral non-equilibrium, the ratio N/t will be in general inversely proportional to r [20] ... 

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