Partition theoretical plate

In their original theoretical model of chromatography, Martin and Synge treated the chromatographic column as though it consists of discrete sections at which partitioning of the solute between the stationary and mobile phases occurs. They called each section a theoretical plate and defined column efficiency in terms of the number of theoretical plates, N, or the height of a theoretical plate, H where... 

Using the retention data and the chromatogram shown in Fig. 14.8, tabulate the following for each peak retention time ( r), adjusted retention time (t K), retention factor (k), partition coefficient (Kc) and number of theoretical plates (N). The column phase ratio was 250 and the gas hold up time ( m) was 0.995 min. 

Packed columns are still used extensively, especially in routine analysis. They are essential when sample components have high partition coefficients and/or high concentrations. Capillary columns provide a high number of theoretical plates, hence a very high resolution, but they cannot be used in all applications because there are not many types of chemically bonded capillary columns. Combined use of packed columns of different polarities often provides better separation than with a capillary column. It sometimes happens that a capillary column is used as a supplement in the packed-column gas chromatography. It is best, therefore, to house the capillary and packed columns in the same column oven and use them selectively. In the screening of some types of samples, the packed column is used routinely and the capillary column is used when more detailed information is required. 

These successive equilibria are the basis for the static model for which the column length L is partitioned into N theoretical plates numbered from 1 to N, all with the same height. For each of these plates, the concentration of analyte in the mobile phase is in equilibrium with the main concentration of analyte in the stationary phase. The height equivalent to a theoretical plate (HETP or II) is thus given by equation (1.5) ... 

The concept of plate theory was originally proposed for the performance of distillation columns (12). However, Martin and Synge (13) first applied the plate theory to partition chromatography. The theory assumes that the column is divided into a number of zones called theoretical plates. One determines the zone thickness or height equivalent to a theoretical plate (HETP) by assuming that there is perfect equilibrium between the gas and liquid phases within each plate. The resulting behavior of the plate column is calculated on the assumption that the distribution coefficient remains unaffected by the presence of other... 

The number of theoretical plates also depend on the partition ratio k of the test compound and its solubility in the liquid phase. Substances that have higher k values have lower plate numbers. Greater plate numbers indicate greater resolution or better separation of the component mixture. 

Equation 1 is a fundamental resolution equation Q,2) which contains the measured terms a, k and n. Theoretical Plates (n) are a measure of a column s overall efficiency, the partition ration (k) is a measure of the amount of time a solute... 

Martin and Synge (3) introduced the important concept of theoretical plates into chromatography. Their concept was derived from partition theory and random statistics, and was related to similar ideas developed for extraction and fractional distillation. They supposed that the column could be divided into a number of sections called theoretical plates, and that solutes (dissolved compounds) could be expected to achieve equilibrium between the two phases (mobile and stationary) that exist within each plate. The chromatographic process, like an extraction process, can be visualized to occur when mobile phase (solvent) is transferred to the next plate, where a new equilibrium is established. Theoretical plate numbers of 1000 or more are common for HPLC columns, which means that 1000 separate equilibria must be established to obtain the same degree of separation by solvent... 

Extraction chromatography (reversed phase partition chromatography) has been used in analytical and biochemistry to effect chemical separations. It is a method which combines the simplicity of ion exchange and the selectivity of solvent extraction. Ion exchange theory may be used to calculate the number of theoretical plates in the column and the enrichment coefficient. Extraction chromatography as a separation method has been recently reviewed by Cerrai (J) and Katykhin (7). 

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. 

FIGURE 24-9 Number of theoretical plates required to attain a resolution of 1.0 as a function of partition ratio for values of relative retention ranging from 1.005 to 1.1 [Equation (24-35)]. (From Tang and Harris. )... 

Q.26.14 (a) Define partition coefficient ratio, theoretical plate, and retention time, b) Choose a protein property (size, or charge, etc.) and describe the liquid-solid chromatographic technique you would use to separate it. Draw the device, labeling the essential parts needed for separation. 

The DCCC process is based on the partitioning of solutes between a steady stream of droplets of mobile phase and a column of surrounding stationary phase. Each drop represents more or less one theoretical plate. The system consists basically of 200 to 600 vertical columns of narrow bore glass (20 to 60 cm by 1.5 to 2 mm id) interconnected in series by Teflon tubes. A flow rate of 10 mL/hr (much slower than RLCC, producing more theoretical plates) is used for the mobile phase. The sample and the mobile phase are introduced at the bottom of the first tube (ascending mode when mobile phase is lighter than the stationary phase). At the end of the first capillary tube, the droplet is transferred to the next tube via the Teflon connection and new droplets are generated. 

Gas-liquid chromatography can be regarded as being the repeated distribution of components between a mobile gas and a stationary liquid, with each effective distribution being a theoretieal plate. The separation achieved with any column will, therefore, depend on the separation per theoretical plate and on the total number of plates. The separation per plate (separation factor, a) will be determined primarily by the nature of the liquid phase and of the components to be separated. For two components, A and B, the separation factor is the ratio of their partition coefficients, k /k kA > ks), for the gas and liquid phases. In practice, the partition coefficients are directly proportional to retention volumes, defined in Fig. 1, so that the separation factor is given by equation 1. 

Solutes locally introduced at the inlet of the coil are subjected to a partition process between the flowing mobile phase and the retained stationary phase in each partition unit and finally eluted out with the mobile phase according to the order determined by their relative partition coefficients. If the partition process in each partition unit is highly efficient, this model is expected to yield a partition efficiency close to five theoretical plates. 

The number of these theoretical transverse slices of column is known as the theoretical plate number (N) and reflects the number of times a solute partitions between the two phases. is a measure of the efficiency of the column and will determine how broad the chromatogram peaks will be. A column with a high number of theoretical plates will be efficient and will produce narrow peaks. 

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