Minimum plate number

Everybody has heard or used that term. For example chromatography column manufacturers assure a certain specification e.g. the minimum plate number or separation efficiency for defined analytes. In our context that means make sure that the instra-ment and our method works reliably within certain limits. To be certain that they really do, you should check this e.g. with a reference material (in liquid... 

Calculation of the minimum plate number by the Fenske equation for ideal mixtures and =00... 

Nomogram for the determination of minimum plate numbers for ideal mixtures and v = cxj (Melpolder and Headington)... 

A method for the exact calculation of the minimum plate number in a multi-component distillation is reported by Chien [175b]. An approximate method was developed, by Serov et al. [175a]. 

Fig. 2.3.2-9 Balance lines and staircase construction, a) Minimum reflux ratio, infinite plate number, b) Finite reflux ratio, resp. finite plate number, c) Total reflux, minimum plate number.

For an overview approximation and dimensioning, the relationships of Fenske and Underwood can be used to determine the minimum plate number N j and the minimum reflux ratio (Equations 2.3.2-26 and 2.3.2-27) ... 

By definitioii the Fenske equation for the minimum plate number only applies for plate columns with a plate efficiency of unity. The use of this equation for packed columns leads to considerable errors, especially at high relative volatilities. The minimum plate number of packed columns shoul be calculated with Equation 2.3.2-28 ... 

Economic designs result for plate numbers that are about 1.3 times the minimum plate number or 1.2-1.3 times the minimum thermal power. With regard to controllability and the minimum trickle density, the reflux ratio should not be less than about 0.3-0.5. 

As a secondary consideration, the chromatographer may also need to know the minimum value of the separation ratio (a) for a solute pair that can be resolved by a particular column. The minimum value of (a) has also been suggested [8] as an alternative parameter that can be used to compare the performance of different columns. There is, however, a disadvantage to this type of criteria, due to the fact that the value of (a) becomes less as the resolving power of the column becomes greater. Nevertheless, a knowledge of the minimum value of (cxa/b) can be important in practice, and it is of interest to determine how the minimum value of (aA/B) is related to the effective plate number. 

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 this mode, the solid is no longer moving. The shifting of the inlet and outlet lines only simulates solid flow, and the solid flowrate downward is directly linked to the shift period. Proper selection of flowrates is required to stabilize the different fronts of species A and B in the proper zones. The adequate choice of the flowrates requires a minimum knowledge of the physico-chemical properties of the system. The influence of adsorption isotherms and plate numbers is simulated by the software. 

The object of a chromatographic separation is to achieve satisfactory resolution of solutes in the minimum time. Resolution is influenced by the capacity factor of the solutes and the selectivity and plate number of the column. 

Plot a graph of //versus Ti and calculate the optimum gas velocity, the corresponding minimum plate height and the maximum plate number. 

Both Eqs. (43) and (44) show that the minimum pressure is proportional to the plate number and inversely proportional to the square of the particle diameter. 

Fig. II. Miniinuin analysi time as a function of the maximum available pressure and (be panicle size. Solid lines represent constant plate numbers (I) 1000 (2) 3000 (3) 20,000 (4) 100,000 (5) 300,000 (6) 1,000,000 dotted lines represent constant particle size stated in micrometers at each line. The columns are operated at minimum plate height of h 2, and the other conditions are as follows v 3,i - 3,ij 0.4cP, < - 1 x 10", - 1 x 10" ...

Therefore we shall optimize the experimental conditions by looking for the minimum pressure at constant analysis time and efficiency for a given solute pair. It has been shown that this goal is accomplished when the column is operated at the optimum flowrate at which the plate height is minimum (19). The particle size and column length then depend on the plate number and the required analysis time. 

It is also of interest to the chromatographer to know the minimum (a) value of a pair of solutes that can be separated on a particular column. In fact, this has been suggested, (11), as a basis for comparing the resolving power of different columns. The disadvantage of this type of criteria is that the value of (a) becomes smaller the higher the resolving capacity of the column. Nevertheless, the minimum value of (a) is important in practice and it is of interest to see if it can be related to the effective plate number of the column. 

This measure was based upon the ratio of the minimum necessary number of plates, A min (averaged over the reboiler composition) in a column to the actual number of plates in the given column, Nj. Christensen and Jorgensen assumed that the mixture has a constant relative volatility a and the column operates at total reflux using constant distillate composition (x o) strategy (section 3.3.2) and evaluated Nmin using the Fenske equation ... 

Luo and Andrade have reexamined [66] the potential of CEC by comparing the effect of the conclusions of the Rice-Whitehead theory [35] of doublelayer overlap on the determination of minimum dp with those which result from more recent treatments of the velocity profile in electroosmotic flow. They concluded that, for ionic strength <10 mM, the particle size can again be less than 1 pm, and that plate numbers up to 1 x 106 should be theoretically possible. An obstacle to the realization of such efficiencies in CEC is, however, the consequence of the recognition [6] by Giddings that there is no satisfactory mathemat-... 

Generally, there is little difference between the relationships described by Eqs. (1.10) and (1.11). In both cases in agreement with experiments, the plots show a minimum H corresponding to an optimum velocity of the mobile phase for which the maximum efficiency and highest plate number is found for a given column (Fig. 1..3B). 

The calculated plate number and pressure drop for the column may also be roughly compared with Figures 2.29 and 2.30. Something must be wrong if five- or tenfold deviations are observed (the column must be tested not far from its van Deemter minimum). 

In the case of the detection limit we have to distinguish between the minimum detectable concentration and the minimum detectable mass. The minimum detectable concentration of a solute in the sample solution depends only on the detector properties and on the optical properties of the solute, i.e. its absorbance, if the maximum tolerable sample volume with respect to the retention volume of this solute is injected. The minimum detectable concentration is independent if the column dimensions, plate number or capacity factor. 

For a given column at optimum flow conditions the maximum efficiency and theoretical plate number can be calculated, as well as the minimum H. 

In SFC this increase is less dramatic, because the diffusion coefficient is 2 to 3 orders of magnitude larger than in HPLC. As a consequence the minimum H becomes almost independant of the flow rate over a large r2uige of linear velocity. For 3 ym columns a linear flow velocity between 0.4 and 1.2 cm/s or 2.8 to 8.5 ml in for a column of 4.6 mm inner diameter may be achieved with a plate number around 120,000 per meter. 

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