Theoretical plate height minimum

Theoretical performance in gas chromatography. As the inside radius of an open tubular gas chromatography column is decreased, the maximum possible column efficiency increases and sample capacity decreases. For a thin stationary phase that equilibrates rapidly with analyte, the minimum theoretical plate height is given by... 

Chromatographic efficiency Efficiency of peak A and B, respectively Height equivalent to a theoretical plate (HETP) Minimum HETP Effective HETP... 

Of course, the objective is to resolve the solutes, not merely separate them, and Figure 4.10 tells us nothing about the degree of peak resolution that can be expected. The resolution will depend on the carrier-gas flow and the colunm physical parameters because the peak widths and thus the theoretical plate height influence the observed resolution. In order to characterize peak resolution across a range of column temperatures, we must either perform a series of experiments and measure resolution directly, consbuct an empirical mathematical model by fitting curves to a smaller dataset, or find a model that encompasses the additional variables and requires a minimum amount of experimental data. 

The theoretical plate height curve has a minimum that corresponds to the optimal flow rate. The minimal theoretical plate height is influenced by the average particle size of the stationary phase. The smaller the average particle size the smaller the H and the better the resolution is [35,36]. Current technologies can provide columns... 

Coating efficiency. A metric for evaluating column quality. The minimum theoretical plate height divided by the observed plate height ... 

Minimum theoretical plate height at the optimum linear velocity, ignoring stationary-phase contributions to band broadening. 

Now, the column length (L) can be defined as the product of the minimum plate height and the number of theoretical plates required to complete the separation as specified by the Purnell equation. 

In summary, the efficiency TV of a TLC plate is variable. The height equivalent to a theoretical plate has a minimum value, as in HPLC. However, it is not possible, unlike in HPLC, to vary the flow rate of the mobile phase in order to increase separation efficiency. 

The van Deemter plots in Figure 25-3 show that small particles reduce plate height and that plate height is not very sensitive to increased flow rate when the particles are small. At the optimum flow rate (the minimum in Figure 25-3). the number of theoretical plates in a column of length L (cm) is approximately3... 

NOTE Theoretical performance of 33- un-diarneter X 25-cm-long capillary for minimum plate height for solute with capacity factor k — 2 and diffusion coefficient = 6.7 X W ° m-/s in water-acetonitrile eluent. 

If the liquid holdup is too low, fractionation efficiency will be bad. We say that the height equivalent to a theoretical plate (HETP) will be high. If the liquid holdup is too high, fractionation efficiency will also be poor. We again say that the HETP will be high. This idea is expressed in Fig. 7.6. When the holdup rises above the point that corresponds to the minimum HETP, we can say that the packing is beginning to flood. The minimum HETP point on Fig. 7.6 corresponds to the point of incipient flood, discussed in Chap. 1. 

Beyond these two parameters, the minimum resolution that must be achieved will require a certain number of theoretical plates, which can be expressed in terms of the column length and plate height, H, as... 

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 very detailed study of the combined effects of axial dispersion and mass-transfer resistance under a constant pattern behavior has been conducted by Rhee and Amundson [10]. They used the shock-layer theory. The shock layer is defined as a zone of a breakthrough curve where a specific concentration change occurs (i.e., a concentration change from 10% to 90%). The study of the shock-layer thickness is a new approach to the study of column performance in nonlinear chromatography. The optimum velocity for minimum shock-layer thickness (SLT) can be quite different from the optimum velocity for the height equivalent to a theoretical plate (HETP) [9]. 

Martin et al. published a paper on the theoretical limits of HPLC which is well worth reading.They used relatively simple mathematics to calculate pressure-optimized columns for which the length L, particle size and flow rate u of the mobile phase were selected such that a minimum pressure Ap is required to solve a separation problem. It has been shown that these optimized colunms are operated at their van Deemter curve minima. Some astonishing facts have emerged from the study, provided that the chromatography is performed on well packed columns (reduced plate height h = 2-3 see Section 8.5). 

Golay ( 1 ) introduced a simplified formula for the minimum height equivalent to a theoretical plate for 11 coated capillaries, given in "Equation 4" ( )... 

Coating efficiency CE, used as a measure of column quality for GC columns by comparing the theoretical minimum plate height (maximum column efficiency), Hmin, with the plate height achieved in practice, //calc-... 

H, HETP H is the height equivalent to a theoretical plate also called the equilibrium step height. It is a measure of column efficiency, H is approximately 0.5 mm in a GC capillary column and 0.01 mm in HPLC. H = L/N where L is column length, N is number of theoretical plates in a column. /fcALC is the practical plate height of a column, Z/ min is the theoretical minimum plate height at optimmn linear velocity and maximum column efficiency, and may be calculated in terms of the retention or capacity factor of a column see A eir, van Deemter equation, capacity factor and coating efficiency. 

If the dimensions of stationary phase coating thickness and diffusion distance to the film from the gas phase have been optimized, for further improvement of GC resolution, it becomes necessary to increase the length of the column. This is seen from the simple relation of Eq. (11.7), which indicates that for an optimal minimized value of H (the height equivalent to a theoretical plate) the number of plates, N, is proportional to the length of the column. From Eqs. (11.8) and (11.9) we note that the resolution is proportional to the square root of N. For columns packed with particles of optimal size, and operated at the optimal linear flow rate at the minimum of the Van Deempter curve (Fig. 11.3), the typical maximum pressure of 100 psi achievable from a regulated gas cylinder requires that most packed columns be less than 4-7 m long. More typically they are only 1 -2 m in length. These considerations hmit the resolution achievable in packed column GC. 

Now, the minimum value of (H) (the variance per unit length of the column or the height of the theoretical plate) has been shown to be given by the approximation ... 

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