Resolution between bands

Case 3. The injection plateau and the plateau of the pure first component have been eroded, there is a mixed zone. The resolution between bands is incomplete. This is the case of a narrow injection pulse (Figure 8.3, Eqs. in Table 8.3). 

Resolution. The degree of separation or resolution, Rs, of two adjacent peaks is defined as the distance between band peaks (or centers) divided by the average bandwidth using 14), as shown in Fig. 11.3. 

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

When only a few solutes are separated, they may occupy only a small portion of the total column volume at any given instant. In such cases, the productivity is improved by cyclic feed injections, timed so that the most strongly retained component from an injection elutes just before the least strongly retained component from the following injection (see Fig. 16-57). For a mixture of two components with k > 1, when the same resolution is maintained between bands of the same injections and bands of successive injections, the cycle time tc and the plate number requirement are ... 

The plate number in equation (4.56) corresponds to the value when the effective value of the capacity factor (equal to k when the band is at the column midpoint) is equal to the capacity factor in isocratic elution for the same column. The effective value of the capacity factor, k, is simply 1/1.15b. In most cases k, will be large and equation (4.57) is simplified by equating l/k, to zero. The resolution between two adjacent bands in a gradient program, again analogous to isocratic elution, is e q>ressed by equation (4.58)... 

FIGURE 4.5 Clustering in ID separations, (a) Resolution between adjacent SCs defines the critical distance Axo. (b) interdistances between adjacent SCs (fourth through seventh SC) are considered. I > Ax0, II < Ax0, and III > Ax0. Thus fifth and sixth SC are merged in the same band (doublet) that is completely separated from the previous and subsequent bands. 

The resolution between two solute components achieved by a column depends on the opposed effects of (a) the increasing separation of band centres and (b) the increasing band width as bands migrate along the column. The resolution Rs is defined by ... 

Resolution, on the other hand, is a more technical term. It refers to the distance between adjacent bands relative to their bandwidths and acknowledges the fact that proteins are distributed in Gaussian profiles with overlapping distributions. The numerical expression for resolution is obtained by dividing the distance between the centers of adjacent bands by some measure of their average bandwidths. It expresses the distance between band centers in units of bandwidth and gives a measure of the overlap between two adjacent bands. For preparative applications, when maximal purity is desired, two proteins to be isolated should be separated by at least a bandwidth. In many applications it is sufficient to be able to simply discern that two bands are distinct. In this case bands can be less than a bandwidth apart. 

In practice the resolution will always be specified, because our goal is to separate a given mixture, and this requires a given minimum degree of resolution between each band. Thus, the value of the required number of theoretical plates is given by the choice of the chromatographic system. 

For the small, rapidly diffusing K+ ion, we expect 100 000 plates. For the slowly diffusing protein serum albumin (FM 65 000), we expect more than 3 million plates. High plate count means that bands are very narrow and resolution between adjacent bands is excellent. 

Thus a transition between two given electronic states shows many bands, each such band corresponding to a different pair of initial and final vibrational states under high resolution, each band shows many closely spaced lines, each such line corresponding to a different pair of initial and final rotational states. (The electronic spectra of molecules are called band spectra, whereas the electronic spectra of atoms are called line spectra.) Consider the selection rules for electronic transitions. The electric di-... 

Resolution is a term used to describe the degree of separation between neighboring solute bands or peaks. It is affected by the selectivity (a), efficiency (N) and capacity (k ) of the column. The resolution equation [Eq. (1.3)] describes the relationship between those factors and indicates how they can be manipulated in order to improve the resolution between two peaks. 

It seems probable that the phenomenon of resolution of bands at low temperatures may be characteristic of compounds having certain cyclic systems. If this is the case a spectroscopic study of solutions of compounds at liquid air temperatures may serve as a ready means of recognizing the presence of such characteristic cyclic systems as are present in the porphyrins. In particular we hope that a differentiation between the porphyrins and the closely related chlorophyll derivatives may be possible. A very large number of these compounds have been prepared in this laboratory in a high state of purity and their spectra at low temperatures will be examined in the near future. 

Colin et al. [SSS] have described a different method to construct a diagram that allows the prediction of optimum conditions. Their approach is based on the calculation of so-called critical bands. If the retention surface of a solute j is known, then a forbidden zone may be defined below the capacity factor kj. If the preceding solute i has a capacity factor kp which falls in this critical band, then the resolution between i and j is insufficient. Eqn.(1.20) relates the resolution to the capacity factors of the individual solutes ... 

Now that the fundamental parameters of LC have been defined and calculated, the focus of the experiment can be directed to the primary objective resolution. Resolution is the measure of how well two compounds are separated by the LC column. The quantitative measurement of resolution between the two bands of color takes into account the separation of the band centers as well as the width of each colored band according to the equation... 

The numerator in the resolution equation is the distance between bands, which is related to the selectivity, and the denominator is the average band width, which is proportional to the efficiency of the column. For experiments A-C resolution can be calculated from the already measured values and compared for both column types. 

A detailed analysis of the UV-VIS spectrum of (spinach) plasto-cyanin in the Cu(II) state has been reported (56). A Gaussian resolution of bands at 427, 468, 535, 599, 717, 781, and 926 nm is indicated in Fig. 7. Detailed assignments have been made from low-temperature optical absorption and magnetic circular dichroic (MCD) and CD spectra in conjunction with self-consistent field Xa-scattered wave calculations. The intense blue band at 600 nm is due to the S(Cys) pvr transition, which is intense because of the very good overlap between ground- and excited-state wave functions. Other transitions which are observed implicate, for example, the Met (427 nm) and His (468 nm) residues. These bonds are much less intense. The low energy of the d 2 orbital indicates a reasonable interaction between the Cu and S(Met), even at 2.9 A. It is concluded that the S(Cys)—Cu(II) bond makes a dominant contribution to the electronic structure of the active site, which is strongly influenced by the orientation of this residue by the... 

The magnitude of is a function of the solute chemical and physical properties, the stationary and mobiles phases, and the column temperature. Also, solute retention is increased by increasing the amount of the stationary phase relative to that of the mobile phase. A large k is indicative of a slowly moving solute band, which improves the resolution between it and those of other solutes but also results in its broadening. In practice, optimum values of k are between 2 and 6, although values between 1 and 10 can be used. 

We need to indicate here what happens when total resolution of the two bands takes place. Total resolution between the two bands takes place first at point K, where the concentration of the first component becomes 0 at the time of passage of the front shock of the second component, and tR 2 = [14]. The concentration... 

We can also assume that the cycle time is equal to the time between the moment when the concentration of the first component exceeds a certain threshold, i.e., 1 X 10 M, or 1 X 10 mg/mL, and imtil the concentration of the second component becomes smaller than the same threshold [3-7]. This definition gives smaller values of the cycle time i.e., the corresponding production rate is larger), which depend on the resolution between the two bands, i.e., on most... 

Knox and Pyper [17] made the first systematic study of the optimization of the experimental conditions in preparative liquid chromatography based on the use of a simple chromatographic model. They considered touching band separation (i.e., in the ideal model, tR 2 — 1e (Figure 8.6), or approximately a imit resolution between the two bands) with the following assumptions ... 

There is no competition between the two components. Accordingly, the elution band profiles of the two components are the same, whether a given amoimt of each component is injected pure or as a mixture. They recognized that this assumption is inexact when the resolution between the bands is moderate (i.e., lower than 2). Due to the large influences of the displacement and the tag along effects on the band profiles, this assumption is unrealistic for bands having a resolution of the order of 1. 

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