Volume plate

The function (vm + Kvs) is termed the plate volume and so the flow through the column will be measured in plate volumes instead of milliliters. The plate volume is defined as that volume of mobile phase that can contain all the solute in the plate at the equilibrium concentration of the solute in the mobile phase. The meaning of plate volume must be understood, as it is an important concept and is extensively used in different aspects of chromatography theory. 

It is seen that the peak maximum is reached after (n) plate volumes of mobile phase have passed through the column. Thus, the retention volume in ml of mobile phase will be obtained by multiplying by the plate volume, (vm + Kvg). 

Equation (3) merely sums the two peaks to produce a single envelope. Providing retention times can be measured precisely, the data can be used to determine the composition of a mixture of two substances that, although having finite retention differences, are eluted as a single peak. This can be achieved, providing the standard deviation of the measured retention time is small compared with the difference in retention times of the two solutes. Now, there is a direct relationship between retention volume measured in plate volumes and the equivalent times, which is depicted in Figure 6. 

Figure 6. Relationship between Plate Volumes and Time...

Thus, the points of inflexion occur after n - Vn and n + Vn plate volumes of mobile phase has passed through the column. It follows, the volume of mobile phase that has passed through the column between the inflexion points will be... 

Consequently, the peak width at the points of inflexion of the elution curve will be 2- /n plate volumes. Converting this to milliliters of mobile phase by multiplying by the plate volume... 

The sum expressed by equation (21) lends itself to a digital calculation and can be employed in an appropriate computer program to calculate actual peak profiles. In doing so, however, as (v) is measured in plate volumes and sample volumes are usually given in milliliters, they must be converted to plate volumes to be used with equation (21). To demonstrate the effect of a finite charge and the use of equation (21), the peak profiles resulting from a sample dispersed over the twenty-one consecutive plates of a column are shown in Figure 16. 

Now, if (p) plate volumes of pure mobile phase are injected onto a column that has been equilibrated with mobile phase containing a concentration (Xq) of a solute, then... 

After the addition of each plate volume of charge, a new concentration of solute exists in plate (1), and its contents will be eluted through the column in the normal manner. 

Consider a total of (p) plate volumes of pure mobile phase are injected onto the column followed by a further (v) plate volumes of equilibrated mobile phase. After the injection of (r) plate volumes of pure mobile phase, the new concentration of solute in plate 1 will be eluted by a further (p-r) plate volumes of sample followed by (v) plate volumes of equilibrated mobile phase. Therefore, the concentration of solute leaving the (n)th plate due to the (r)th volume of pure mobile phase will be... 

The sum expressed by equation (25) also lends itself to a digital solution and can be employed in an appropriate computer program to calculate actual peak profiles for different volumes of pure mobile phase that have been injected onto an equilibrated column. The values of (Xg) were calculated for a column having 500 theoretical plates and for sample volumes of 20, 50, 100 and 200 plate volumes, respectively. The curves relating solute concentration (Xe) to plate volumes of mobile phase passed through the column are shown in Figure 17. 

The theoretical treatment given above assumes that the presence of a relatively low concentration of solute in the mobile phase does not influence the retentive characteristics of the stationary phase. That is, the presence of a small concentration of solute does not influence either the nature or the magnitude of the solute/phase interactions that determine the extent of retention. The concentration of solute in the eluted peak does not fall to zero until the sample volume is in excess of 100 plate volumes and, at this sample volume, the peak width has become about five times the standard deviation of the normally loaded peak. 

Equation (25) can be extended to provide a general equation for a column equilibrated with (q) solutes at concentrations Xi, X2, X3,...Xq. For any particular solute (S), if its normal retention volume is Vr(S) on a column containing (n) plates, then from the plate theory, the plate volume of the column for the solute (S), i.e., (vs) is given by... 

As the plate concept is to be employed the volume flow will be measured in plate volumes, i.e.,... 

Note the italic form, (V), is used to distinguish the volumes involved in the cell from volume, (V), which will refer to the mobile phase, and the plate volume, (v). 

Now, TsK +Vm is the effective cell volume of the detector in much the same way that (ca) is the column plate volume. ... 

Flow of Mobile Phase Retention Time in Plate Volumes... 

The technique of column overloading is only feasible if more than adequate resolution is possible between the solute of interest and its nearest neighbor. Many samples require a column to be constructed that will only just separate the solutes of interest and under these circumstances the loading capacity must be increased without overloading the column. It has been shown in earlier chapters that the maximum sample (mass or volume) that can be placed on a column is proportional to the plate volume of the column and the square root of its efficiency. Thus, the maximum sample mass (M) will be given by... 

The function (vm + Kvs) has been given the name plate volume and thus, for the present, the flow of mobile phase through the column will be measured in plate volumes instead of milliliters. 

Zebrafish Brachydanio/Danio rerio) embryos can be produced in large numbers and carry sufficient nutrients within the egg sack to allow development within micro plate volumes [52, 53]. Mutation frequency has been estimated indirectly using transgenic fish [54[ and UDS, comet, MNT and alkaline filter elution methods have been used effectively [55]. At present, there has been insufficient study of the model to understand predictivity of mammalian genotoxicity, and none of the methods has been demonstrated at throughputs sufficient for hit and lead screening. 

Let the mobile phase flow be arrested, and a volume of sample be placed on the column such that it occupies (r) theoretical plates. Now on starting the column flow, the contents of each plate win develop an elution curve, the points on each curve being one plate volume away from the complimentary points on the adjacent curve. The first peak will result from the elution of... 

Since the measurement of efficiency is Important for evaluating the quality of a column, it is necessary to know the position of the points of inflection in order to measure the peak width. The inflection points are ill defined on the chromatogram and it is necessary to know at what fraction of the peak height they occur. This fraction will be the same as the ratio of the value of the solute concentration after (n - Vn) plate volumes of mobile phase has passed through the column, to the solute concentration after (n) plate volumes of mobile phase has passed through the column. 

It is seen from equation (1) that under the conditions considered, where the charge is place on the first plate, (Xn) can never equal zero and pure mobile phase will never elute from the column. However, the sample is rarely injected solely on the first plate. As it occupies a finite volume of mobile phase when it is injected onto the column, it will also occupy a finite number of theoretical plates. If (p) plate volumes of pure mobile phase are injected onto a column that has been equilibriated with mobile phase containing a concentration (X0) of a solute, then, on the application of a charge of pure mobile phase,... 

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