Plate, theory theoretical number

The proposed model can be readily related to the plate theory. The number of theoretical plates can be deduced from the moment expressions and when Pe and the K are large then Equation 33 follows from Equation 23. 

Equation (18) displays the relationship between the column efficiency defined in theoretical plates and the column efficiency given in effective plates. It is clear that the number of effective plates in a column is not aii arbitrary measure of the column performance, but is directly related to the column efficiency as derived from the plate theory. Equation (18) clearly demonstrates that, as the capacity ratio (k ) becomes large, (n) and (Ne) will converge to the same value. 

Vacancy chromatography has some quite unique properties and a number of potentially useful applications. Vacancy chromatography can be theoretically investigated using the equations derived from the plate theory for the elution of... 

So far the plate theory has been used to examine first-order effects in chromatography. However, it can also be used in a number of other interesting ways to investigate second-order effects in both the chromatographic system itself and in ancillary apparatus such as the detector. The plate theory will now be used to examine the temperature effects that result from solute distribution between two phases. This theoretical treatment not only provides information on the thermal effects that occur in a column per se, but also gives further examples of the use of the plate theory to examine dynamic distribution systems and the different ways that it can be employed. 

Having defined that the resolution required to separate the critical pair in a specific sample is 4a it is now possible to calculate the number of theoretical plates that are necessary to provide adequate quantitative accuracy. This can be easily carried out using the information provided by the Plate Theory in the chapter 2. Restating figure 10 from chapter 2 as figure 8, it is seen that the retention volume difference between the peaks (Av) is... 

HETP = height equivalent to a theoretical plate. It is derived from the plate theory of distillation which is a confusing concept having no basis in fact in the context of modem chromatographic separations. Nevertheless the terms plate number and plate height are still very widely used. 

For the simulation of SMB-separations efficient software packages,based on the Triangle-Theory, are commercially available. The number of columns, the column dimensions, the theoretical number of plates in the columns, the feed concentration, the bi-Langmuir adsorption isotherm parameters and the number of cycles need to be defined by the user. Then the separation is simulated and values for the flow rate ratios, the flow rates, the switching time and the quality of the separation, purity and yield, are calculated. Based on these values an actual separation can be performed. However, some optimization/further development is usually necessary, since the simulations are based on an ideal model and the derived parameters and results therefore can only be taken as indications for the test runs. 

Primarily the Plate Theory provides the equation for the elution curve of a solute. Such an equation describes the concentration of a solute leaving a column, in terms of the volume of mobile phase that has passed through it. It is from this equation, that the various characteristics of a chromatographic system can be determined using the data that is provided by the chromatogram. The Plate Theory, for example, will provide an equation for the retention volume of a solute, show how the column efficiency can be calculated, determine the maximum volume of charge that can be placed on the column and permit the calculation of the number of theoretical plates required to effect a given separation. 

The Plate Theory, in whatever form, assumes that the solute is, at all times, in equilibrium with both the mobile and stationary phase. Due to the continuous exchange of solute between the mobile and stationary phases as it progresses down the column, equilibrium between the phases is, in fact, never actually achieved. As a consequence, to develop the Plate Theory, the column is considered to be divided into a number of cells or plates. Each cell is allotted a finite length, and thus, the solute spends a finite time in each cell. The size of the cell is such that the solute is considered to have sufficient time to achieve equilibrium with the two phases. Thus, the smaller the plate, the more efficient the solute exchange between the two phases tn the column and consequently the more plates there are In a given column. This is why the number of Theoretical Plates in a column is termed... 

In the development of the plate theory and the derivation of the equation for the elution curve of a solute, it was assumed that the initial charge was located In the first plate of the column. In practice, this is difficult to achieve, and any charge will, in fact, occupy a finite column volume and consequently a specific number of the first theoretical plates of the column. Consider the situation depicted in figure 1 where the initial charge is distributed over (r) theoretical plates. 

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 efficiency of a column is a number that describes peak broadening as a function of retention, and it is described in terms of the number of theoretical plates, N. Two major theories have been developed to describe column efficiency, both of which are used in modern chromatography. The plate theory, proposed by Martin and Synge,31 provides a simple and convenient way to measure column performance and efficiency, whereas the rate theory developed by van Deemter et al.32 provides a means to measure the contributions to band broadening and thereby optimize the efficiency. 

Thus the number of equilibrium stages is directly proportional to column length, if the linear flow rate remains unchanged. The role of contact time, which is obscured in the plate theory, now becomes evident. Wherever mass-transfer is independent of flow rate, a diminution of the flow velocity through a bed of constant length will increase the effective number of theoretical plates in inverse proportion. The number of plates in any one column may vary for the different components, just as Nr may, although usually the variation is not great. 

As mentioned earher, the plate theory has played a role in the development of chromatography. The concept of "plate" was originally proposed as a measmement of the performance of distillation processes. It is based upon the assumption that the column is divided into a number of zones called theoretical plates, that are treated as if there exists a perfect equilibrium between the gas and the Hquid phases within each plate. This assumption imphes that the distribution coefficient remains the same fi-om one plate to another plate, and is not affected by other sample components, and that the distribution isotherm is hnear. However, experimental evidences show that this is not true. Plate theory disregards that chromatography is a dynamic process of mass transfer, and it reveals httle about the factors affecting the values of the theoretical plate number. In principle, once a sample has been introduced, it enters the GC column as a narrow-width "band" or "zone" of its composite molecules. On the column, the band is further broadened by interaction of components with the stationary phase which retains some components more than others. Increasing... 

These successive equilibria provide the basis of plate theory according to which a column of length L is sliced horizontally into N fictitious, small plate-like discs of same height H and numbered from 1 to n. For each of them, the concentration of the solute in the mobile phase is in equilibrium with the concentration of this solute in the stationary phase. At each new equilibrium, the solute has progressed through the column by a distance of one disc (or plate), hence the name theoretical plate theory. 

Reminding the plate theory model this approach also leads to the value of the height equivalent to one theoretical plate H and to the number N, of theoretical... 

For a sufficiently large number of theoretical plates, the closed-form plate theory result (6.6-1) for the chromatographic curve can be approximated by the Gaussian distribution... 

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