Chromatography resolution equation

As with any separation technique, the desired goal is to maximize peak resolution at the fastest speed. Higher resolution in 2DLC is easier to achieve than when using onedimensional chromatography because selectivity differences between the two different columns can give a resolution enhancement. This is easily seen through the simplified resolution equation, discussed in Chapter 2,... 

Equation 23-30 also tells us that resolution increases as the separation factor y increases. The separation factor is the relative velocity of the two components through the column. The way to change relative velocity is to change the stationary phase in gas chromatography or either the stationary or the mobile phase in liquid chromatography. Important equations from chromatography are summarized in Table 23-2. 

As in chromatography, resolution between closely spaced peaks A and B in an electio-pherogram is related to plate count, N, and separation factor, y, by Equation 23-30 resolution = (VA/4)(y — 1). The separation factor (y = anet /unetB) is the quotient of migration times tB/tA. Increasing y increases separation of peaks, and increasing N decreases their width. 

B. Karger, A critical examination of resolution equations for gas-liquid chromatography, in A Zlatkis (ed.). Advances in Gas Chromatography Preston Technical Abstracts, Evanston IL, 1967, pp. 1-9. 

Snyder s thorough model [1-5] of gradient elution provides an extremely convenient means to achieve the objectives outlined above. The model uses the general resolution equation for isocratic chromatography in terms adapted to gradient elution. This equation defines resolution between two closely resolved analytes in gradient RP-HPLC as a function of mean column efficiency N, mean selectivity a, and the effective retention factor Aavc experienced by the compounds during the elution process j 1-3,5). 

The different parameters that allow such separation are to be found in the resolution equation, which is the basic equation of liquid chromatography ... 

The general resolution equation for two neutral analytes with similar retention factors in micellar electrokinetic chromatography, is similar to the relationship for chromatography (section 1.6) with an additional term that arises from the limited migration time window [11,12,166,177,178]. 

Mazzeo JR, Swartz ME, Grover ER (1995) A resolution equation for electrokinetic chromatography based on electrophoretic mobilities. Anal Chem 67 2966-2973... 

Another approach to improving resolution is to use thin films of stationary phase. Capillary columns used in gas chromatography and the bonded phases commonly used in HPLC provide a significant decrease in plate height due to the reduction of the Hs term in equation 12.27. 

The alternative expression for resolution given in equation (7) demonstrates that the plate resolution, as in other forms of chromatography, depends on the number of theoretical plates, the selectivity and the capacity ratio of the solute for the particular plate concerned. In practice, however, the expression given in equation (7) appears to be the more practically useful for TLC. separations. 

This equation is based on experience with liquid chromatography of low molecular weight samples displaying single peaks. Its application for the GPC of polymers, however, contains a disadvantage, as it mixes two inseparable properties the retention difference for the separation and the peak width for the contrary effect of band broadening. Such a procedure is acceptable if both effects are accessible for an experimental examination. For the GPC experiment, we do not possess polymer standards, consisting of molecules that are truly monodisperse. Therefore, we cannot determine the real peak width necessary for a reliable and reproducible peak resolution R,. This equation then is not qualified for a sufficient characterization of a GPC column. 

FIGURE 2.4 Determining resolution based on a peak-valley measurement for two-dimensional chromatography. The / and g values are measured and used to calculate P =f/g giving the resolution through Equation 2.9. Reprinted with permission from Murphy et al. (1998) by courtesy of the American Chemical Society. 

In chromatography techniques, selectivity can be proved by the existence of good separation between the analyte and the other components (such as the matrix, impurities, degradation product(s), and metabolites). A consequence of this requirement is that the resolution of the analyte from the other components should be more than 1.5-2.0. In order to detect the possibility of coelution of other substance(s), the purity of the analyte peak should also be determined. For instance, the UV-Vis spectrum of the analyte peak/spot can be used to determine 4the purity of the analyte peak/spot, in this case the correlation coefficient V (this term is used by the software of DAD System Manager Hitachi, and CATS from Camag). With the same meaning and mathematical equation, other terms are used, such as Match... 

The above relationship is derived from Equations 6.36 and 6.45 and is similar to the equation correlating resolution to the separation conditions in liquid chromatography [210], except for the addition of the last term on the right-hand side, which accounts for the migration of the pseudosta-tionary phase within the capillary column. 

In order to estimate resolution among peaks eluted from a chromatography column, those factors that affect N must first be elucidated. By definition, a low value of Hs will result in a large number of theoretical plates for a given column length. As discussed in Chapter 11, Equation 11.20 obtained by the rate model shows the effects of axial mixing of the mobile phase fluid and mass transfer of solutes on Hs. 

In the optimisation process, resolution and elution time are the two most important dependent variables. The goal is to conduct a separation of the components of interest in the minimum time without neglecting the time it will take for the instrument to come back to its initial state and be ready for the next analysis. Chromatography corresponds to a slow type of analysis. If the resolution is excellent, optimisation can still be conducted in order to save time in the analysis. This can be done using a shorter column, knowing that resolution varies with the square root of the length of the column (cf. N in equation (1.26)). 

Capillary electrophoresis provides unprecedented resolution. When we conduct chromatography in a packed column, peaks are broadened by three mechanisms in the van Deemter equation (23-33) multiple flow paths, longitudinal diffusion, and finite rate of mass transfer. An open tubular column eliminates multiple paths and thereby reduces plate height and improves resolution. Capillary electrophoresis reduces plate height further by knocking out the mass transfer term that comes from the finite time needed for solute to equilibrate... 

Equation 26-14 says that, for a constant ratio LJL. plate count is independent of capillary length. In contrast with chromatography, longer capillaries in electrophoresis do not give higher resolution. 

In all forms of chromatography, a measure of column efficiency is resolution, R. Resolution indicates how well solutes are separated it is defined by Equation 3.5, where tR and are the retention times of two solutes and w and w are the base peak widths of the same two solutes. 

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