Theoretical plates, number

Three separate factors affect resolution (1) a column selectivity factor that varies with a, (2) a capacity factor that varies with k (taken usually as fej). and (3) an efficiency factor that depends on the theoretical plate number. 

In-column solvents Column size (mm) Theoretical plate number Exclusion limit Poiystyrene PEG Particle size (/urn) Pore size (A) Flow Rate (ml/min) Maximum pressure (kgf/cm ) Maximum temperature (°C)... 

Column type Column size (mm) Theoretical plate number Range Flow rate (ml/min) Max Analytical column... 

FIGURE 14.1 Determination of the theoretical plate number N by the half-height method. 

A particular column can be used for different types of LC by changing the eluent components. For example, a column packed with RP-18 bonded silica gel can be used for SEC with THF, NPLC with n-hexane, and RPLC with aqueous acetonitrile. When separation cannot be achieved by improving the theoretical plate number of a column, it may be achieved by selection of an appropriate stationary phase material and/or eluent. 

The chiral recognition ability of the insoluble (+)-l was estimated by HPLC using a column packed with small particles of l.25 However, this column showed a poor efficiency because of a low theoretical plate number. This defect was overcome by coating soluble poly(TrMA) with a DP of 50 on macroporous silica gel.26 The 1-coated silica gel had higher resistance against compression and longer lifetime than the CSP of insoluble 1. Moreover, the two 1-based CSPs show quite different chiral recognition for several race-mates, which may be attributed to the different orientation of 1 in bulk and on the surface of the silica gel.27... 

Theoretical plate number is a measure of the efficiency of the separation process. 

The height equivalent to a theoretical plate (HETP) is the length of the column divided by the theoretical plate number. 

The theoretical plate number (AO is inversely related to the amount of zone broadening occurring in a column. The greater the value for N, the more efficient is the column but differences of less than 25% are not very significant. 

This equation indicates that the particle size, dp, is the main contributor to the H value. The smaller the particles, the higher the theoretical plate number. The optimum condition is obtained by the relationship between the theoretical plate height and the flow velocity. 

The theoretical plate number N of peak B can be calculated from the chromatogram given in Figure 1.3 by the following equation ... 

Commercial instruments have a reasonable balance between the recommended column size and the volume of the column and connecting tubing (XY). However, the theoretical plate number of a single column may give different values on different instruments, and even on replacement of the components and parts of a single instrument. Such discrepancies can be understood in terms of differences in the mechanics of the instruments and the design of their parts. 

The recycle elution method can be applied to mixtures of very similar compounds that cannot be fully separated by a single pass through the column. This method makes more effective use of a column. The effluent from the column is repeatedly re-passed through the same column. The number of cycles multiplies the total theoretical plate number of the column if the system is... 

If the correctly sized flow cell and connecting tubing are not used, the high efficiency of a column or high theoretical plate number columns cannot be effectively used. The detector cell volume contributes hold-up volume. The larger is the cell volume, the greater the peak broadening. The cell volume... 

The connecting tubing should be as short and narrow as possible. The volume of a 20 cm x 0.5 mm i.d. tube is 39.3 p. That of a 20 cm x 0.25 mm i.d. tube is 9.8 /A, and that of a 20 cm x 0.125 mm i.d. tube is 2.5 [A. Some detectors are equipped with a heat exchanger that consists of a metal block containing a capillary tube. The volume of this tube also affects the theoretical plate number. If highly sensitive operation is not required, the heat exchanger can be removed or bypassed. 

The narrower the particle size distribution, the higher in theory is the potential theoretical plate number. A rough sieving is achieved by a water flow, air flow, or a vibration method. A common sieving method is Hamiltonian water flow (Figure 3.4). The particle distribution can be controlled within + 1 jum by this method. A slurry of stationary phase material is allowed to float in the cylinder, and a solvent flows from the bottom to the top. The smaller and lighter particles float to the top of the cylinder and the larger and heavier particles sink to the bottom. The required particles are collected at the top of the cylinder. The selection of suspension solvent and control of the temperature are important. 

The performance of columns is determined by using a simple procedure for both new and used columns. The test method and the results are usually printed on a sheet provided by the column manufacturer. Each manufacturer uses the most suitable method for their column to obtain the best theoretical plate number. The column evaluation provides important information for all users of liquid chromatography. 

Effective theoretical plate number (Aeff), 4, 100 Eluent, 89 Enthalpy, 117, 128 Entropy, 128... 

Taking = 2and/ = 1.5, the required theoretical plate numbers fora = 1.05and 1.25 are 35,721 and 2,025, respectively. Therefore, a column with high selectivity can produce sufficient resolution, even with low theoretical plate numbers (short length). 

---