Solution bands

Partition Ratio. The partition ratio is the additional time a solute band takes to elute, as compared with an unretained solute (for which k = 0), divided by the elution time of an unretained band ... 

Column Efficiency. Under ideal conditions the profile of a solute band resembles that given by a Gaussian distribution curve (Fig. 11.1). The efficiency of a chromatographic system is expressed by the effective plate number defined from the chromatogram of a single band. 

Progress of a column chromatographic separation showing the separation of two solute bands. 

A UV/Vis absorbance detector can also be used if the solute ions absorb ultraviolet or visible radiation. Alternatively, solutions that do not absorb in the UV/Vis range can be detected indirectly if the mobile phase contains a UV/Vis-absorbing species. In this case, when a solute band passes through the detector, a decrease in absorbance is measured at the detector. 

Using the partial chromatogram shown here, determine the resolution between the two solute bands. 

Now, the velocity of a solute band along the column (Z) is obtained by dividing the column length (L) by the retention time, (tr)j consequently. 

Recalling that a separation is achieved by moving the solute bands apart in the column and, at the same time, constraining their dispersion so that they are eluted discretely, it follows that the resolution of a pair of solutes is not successfully accomplished by merely selective retention. In addition, the column must be carefully designed to minimize solute band dispersion. Selective retention will be determined by the interactive nature of the two phases, but band dispersion is determined by the physical properties of the column and the manner in which it is constructed. It is, therefore, necessary to identify those properties that influence peak width and how they are related to other properties of the chromatographic system. This aspect of chromatography theory will be discussed in detail in Part 2 of this book. At this time, the theoretical development will be limited to obtaining a measure of the peak width, so that eventually the width can then be related both theoretically and experimentally to the pertinent column parameters. 

Equation (10) also allows the peak width (2o) and the variance (o ) to be measured as a simple function of the retention volume of the solute but, unfortunately, does not help to identify those factors that cause the solute band to spread, nor how to control it. This problem has already been discussed and is the basic limitation of the plate theory. In fact, it was this limitation that originally invoked the development of the... 

When w >3 Vn, the solute band will have virtually passed through the plate and... 

Equation (3) allows the calculation of the distance traveled axially by a solute band before the radial standard deviation of the sample is numerically equal to the column radius. Consider a sample injected precisely at the center of a 4 mm diameter LC column. Now, radial equilibrium will be achieved when (o), the radial standard deviation of the band, is numerically equal to the radius, i.e., o = 0.2 cm. 

The dispersion of a solute band in a packed column was originally treated comprehensively by Van Deemter et al. [4] who postulated that there were four first-order effect, spreading processes that were responsible for peak dispersion. These the authors designated as multi-path dispersion, longitudinal diffusion, resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Van Deemter derived an expression for the variance contribution of each dispersion process to the overall variance per unit length of the column. Consequently, as the individual dispersion processes can be assumed to be random and non-interacting, the total variance per unit length of the column was obtained from a sum of the individual variance contributions. 

Driven by the concentration gradient, solutes naturally diffuse when contained in a fluid. Thus, a discrete solute band will diffuse in a gas or liquid and, because the diffusion process is random in nature, will produce a concentration curve that is Gaussian in form. This diffusion effect occurs in the mobile phase of both packed GC and LC columns. The diffusion process is depicted in Figure 6. 

Table 2. Variance of Solute Bands Resulting from Two Internal Loop Valves...

Katz and Scott [1] measured the diffusivity of 69 different solutes having molecular weights ranging from 78 to 446. The technique they employed was to measure the dispersion of a given solute band during passage through an open tube. 

The chromatographic column has a dichotomy of purpose. During a separation, two processes ensue in the column, continuously, progressively and virtually independent of one another. Firstly, the individual solutes are moved apart as a result of the differing distribution coefficients of each component with respect to the stationary phase in the manner previously described. Secondly, having moved the individual components apart, the column is designed to constrain the natural dispersion of each solute band (i.e. the band... 

Thus, the column moves the solutes bands apart and simultaneously contains their dispersion. 

It is now necessary to attend to the second important function of the column. It has already been stated that, in order to achieve the separation of two substances during their passage through a chromatographic column, the two solute bands must be moved apart and, at the same time, must be kept sufficiently narrow so that they are eluted discretely. It follows, that the extent to which a column can constrain the peaks from spreading will give a measure of its quality. It is, therefore, desirable to be able to measure the peak width and obtain from it, some value that can describe the column performance. Because the peak will be close to Gaussian in form, the peak width at the points of inflexion of the curve (which corresponds to twice the standard deviation of the curve) will be determined. At the points of inflexion... 

The dispersion described in figure 2 shows that the longer the solute band remains in the column, the greater will be the extent of longitudinal diffusion. Since the length of time the solute remains in the column is inversely proportional to the mobile phase velocity, so will the dispersion be inversely proportional to the mobile phase velocity. Van Deemter et al derived the following expression for the... 

The dimensions of the exit tube from the detector are not critical for analytical separations but they can be for preparative chromatography if fractions are to be collected for subsequent tests or examination. The dispersion that occurs in the detector exit tube is more difficult to measure. Another sample valve can be connected to the detector exit and the mobile phase passed backwards through the detecting system. The same experiment is performed, the same measurements made and the same calculations carried out. The dispersion that occurs in the exit tube is normally considerably greater than that between the column and the detector. However, providing the dispersion is known, the preparative separation can be adjusted to accommodate the exit tube dispersion and allow an accurate collection of each solute band. 

The boundaries, m and n, define two lines in the (v, Vj) plane the line x, = m%2 and the line Xj = m2- The intersection of these two lines with the line defined by the mixture spectra gives two points A and B which are the estimates of the pure spectra. The intervals (A-A ) and (B-BO define the solution bands between which the pure spectra are situated. 

The solution bands can be somewhat narrowed by taking into consideration a second constraint namely that the resulting concentrations by solving eq. (34.3) should be non-negative. By combining eqs. (34.3) and (34.4), it follows that each measured spectrum i can be represented as ... 

In Section 34.2 we explained that factor analysis consists of a rotation of the principal components of the data matrix under certain constraints. When the objects in the data matrix are ordered, i.e. the compounds are present in certain row-windows, then the rotation matrix can be calculated in a straightforward way. For non-ordered spectra with three or less components, solution bands for the pure factors are obtained by curve resolution, which starts with looking for the purest spectra (i.e. rows) in the data matrix. In this section we discuss the VARDIA [27,28] technique which yields clusters of pure variables (columns), for a certain pure factor. 

The contribution to the plate height from molecular diffusion in the mobile phase arises from the natural tendency of the solute band to diffuse away from the zone center as it moves through the column [59,60,63,64]. Its value is proportional to the diffusion coefficient and the. time the sample spends in the column. Its contribution to the total plate height is given by... 

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